heat and mass transfer for the diffusion driven
TRANSCRIPT
HEAT AND MASS TRANSFER FOR THE DIFFUSION DRIVEN DESALINATION
PROCESS
By
YI LI
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2006
Copyright 2006
by
YI LI
This dissertation is dedicated with love and gratitude to my family. Without their love, support and faith in me, this accomplishment would not have been possible.
iv
ACKNOWLEDGMENTS
My appreciation and respect go to my advisor, Professor James Klausner, for
introducing me to the field of multiphase flow and for giving me the opportunity to study
heat and mass transfer dynamics for my Ph.D. dissertation. His continuous support and
patience helped me to achieve this work. I would like to express my special thanks to
Professor Renwei Mei for his help and encouragement in my study of turbulence and
numerical analysis. I sincerely thank my committee members for their comments and
help.
I would like to thank all my colleagues, in particular Jessica Knight and Jun Liao. I
also extend my thanks to the individuals in the department who have helped me in one
way or another during my graduate studies.
I would like to acknowledge the support of the U.S. Department of Energy under
Award No. DE-FG26-02NT41537 for this research. I also thank the University of Florida
for the financial assistance through the UF Alumni Fellowship I was awarded for the
academic years 2003-2006.
Finally, I would like to thank my family for their continuous support and
encouragement through the years of my studies. To them, I dedicate this dissertation.
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TABLE OF CONTENTS page
ACKNOWLEDGMENTS .............................................................................................. iv
LIST OF TABLES .......................................................................................................viii
LIST OF FIGURES........................................................................................................ ix
NOMENCLATURE.....................................................................................................xiii
ABSTRACT.................................................................................................................xvi
CHAPTER
1 INTRODUCTION AND LITERATURE REVIEW..................................................1
Description of Thermal Desalting and Membrane Separation ...................................2 Description of HDH and MEH Process.....................................................................4 Description of DDD Process.....................................................................................6 Comparison of the DDD Process with HDH and MEH.............................................8 Comparison of the DDD Process with MSF and RO ...............................................10 Potential Applications for the DDD Process ...........................................................12 Properties of Saline Water ......................................................................................17 Objectives of the Study...........................................................................................21 Scope of Work........................................................................................................21
2 THERMODYNAMIC ANALYSIS OF THE DDD PROCESS...............................23
Mathematic Model .................................................................................................23 Computation Results and Analysis..........................................................................26
3 EXPERIMENTAL STUDY....................................................................................35
Experimental System Description...........................................................................35 Experimental Facility and Instrumentation..............................................................38
4 HEAT AND MASS TRANSFER FOR THE DIFFUSION TOWER.......................48
Heat and Mass Transfer Model for the Diffusion Tower .........................................48 Model Comparison with Experiments for the Diffusion Tower ...............................57 Pressure Drop through the Packing Material ...........................................................60
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Optimization of the Packing Material .....................................................................61
5 HEAT AND MASS TRANSFER FOR THE DIRECT CONTACT CONDENSER 73
Mathematical Model of the Packed Bed Direct Contact Condenser.........................75 Model Comparison with Experiments for the Packed Bed Direct Contact
Condenser..........................................................................................................82 Wetting Phenomena within Packed Bed..................................................................87 Experimental Results of the Droplet Direct Contact Condenser ..............................90 Condenser Effectiveness.........................................................................................95
6 DDD PROCESS OPTIMIZATION DESIGN AND ECONOMIC ANALYSIS.......98
Mathematical Model...............................................................................................99 Computation Results and Analysis........................................................................ 101 Economic Analysis............................................................................................... 111
7 CONCLUSIONS.................................................................................................. 119
APPENDIX
A ONDA’S CORRELATION ..................................................................................122
B EXPERIMENTAL DATA OF THE DIFFUSION TOWER.................................. 123
C EXPERIMENTAL DATA OF THE AIR SIDE PRESSURE DROP THROUGH THE PACKING MATERIAL .............................................................................. 125
D EXPERIMENTAL DATA OF THE COUNTERCURRENT FLOW DIRECT CONTACT CONDENSER STAGE WITH PACKED BED ................................. 126
E EXPERIMENTAL DATA OF THE CO-CURRENT FLOW DIRECT CONTACT CONDENSER STAGE WITH PACKED BED .................................................... 128
F EXPERIMENTAL DATA OF THE DROPLET DIRECT CONTACT CONDENSERS WITH CO-CURRENT AND COUNTERCURRENT FLOW..... 129
G EXPERIMENTAL DATA OF THE DROPLET DIRECT CONTACT CONDENSER STAGE WITH COUNTERCURRENT FLOW............................. 132
H UNCERTAINTY ANALYSIS OF THE FLUID PROPERTIES ........................... 133
Theory of Uncertainty .......................................................................................... 133 Uncertainty of the Calculated Fluid Properties...................................................... 134 Uncertainty of the Mass and Heat Transfer Coefficients ....................................... 141 Results and Analysis............................................................................................. 144
LIST OF REFERENCES............................................................................................. 151
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BIOGRAPHICAL SKETCH ....................................................................................... 155
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LIST OF TABLES
Table page 1-1 Pumping and heating energy consumption of some desalination processes .............4
1-2 Comparison of electricity consumption for DDD, MSF, and RO desalination technologies .........................................................................................................10
1-3 Comparison of advantages and disadvantages of DDD, RO, and MSF desalination technologies......................................................................................11
4-1 Packing material configurations ...........................................................................63
6-1 Summary of direct costs ..................................................................................... 114
6-2 Details of cost calculations ................................................................................. 114
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LIST OF FIGURES
Figure page 1-1 Schematic diagram of mechanical vapor compression process ...............................2
1-2 Schematic diagram of thermal vapor compression combined multi-effect destillation process .................................................................................................3
1-3 Schematic diagram for diffusion driven desalination process..................................7
1-4 Depth to saline ground water in the United States [18] .........................................13
1-5 Flow diagram of DDD process driven by solar energy..........................................14
1-6 Flow diagram of DDD process driven by geothermal energy................................15
2-1 Flow diagram for diffusion driven desalination process.......................................23
2-2 Rate of entropy generation for different exit brine temperature, Th=27°C .............27
2-3 Variation of exit brine temperature with exit air temperature, Th=27°C ................28
2-4 Fresh water production efficiency, Th=27° C........................................................28
2-5 Rate of entropy generation for different exit brine temperature: a) Th=50° C, b) Th=80° C..............................................................................................................29
2-6 Variation of exit brine temperature with exit air temperature: a) Th=50° C, b) Th=80° C..............................................................................................................30
2-7 Fresh water production efficiency: a) Th=50° C, b) Th=80° C ..............................32
2-8 Rate of energy consumption: a) Th=50° C, b) Th=80° C........................................33
2-9 Minimum rate of energy consumption for different Th..........................................34
3-1 Pictorial view of the laboratory scale DDD experiment ........................................36
3-2 Schematic diagram of laboratory scale DDD facility ............................................37
3-3 Schematic diagram of experimental diffusion tower .............................................39
x
3-4 Schematic diagram of experimental direct contact condenser ...............................40
3-5 Pictorial view of spray nozzle...............................................................................41
3-6 Pictorial view of packing matrix...........................................................................42
3-7 Schematic diagram of the instrumentation system for the DDD experiment..........42
3-8 Example program of SoftWIRE............................................................................44
3-9 “Main” panel of the DDD data acquisition program .............................................45
3-10 “Schematic view” panels of the DDD data acquisition program............................46
3-11 “Histogram view” panels of the DDD data acquisition program ..........................46
4-1 Diagram of diffusion tower ..................................................................................49
4-2 Differential control volume for liquid/vapor heat and mass transfer within diffusion tower.....................................................................................................50
4-3 Comparison of predicted exit conditions with the data of Huang [33]: a) L = 2.0 kg/m2-s, b) L = 4.1 kg/m2-s ..................................................................................56
4-4 Comparison of predicted exit conditions with the experimental data for different liquid mass fluxes: a) L= 1.75 kg/m2-s, b) L= 1.3 kg/m2-s, c) L= 0.9 kg/m2-s .......58
4-5 Air specific pressure drop variation with air mass flux for different water mass fluxes ...................................................................................................................60
4-6 Energy consumption rate for fresh water production: Berl Saddle – a) 0.5”, b) 0.75”, c) 1.0”, d) 1.5”; Raschig Ring – e) 0.5”, h) 1.0”, g) 1.5”, h) 2.0” ................64
4-7 Maximum possible exit humidity for feed water mass flux ...................................67
4-8 Gas mass transfer coefficient for air mass flux......................................................68
4-9 Gas pressure drop for air mass flux.......................................................................69
4-10 Required tower height for feed water mass flux...................................................70
4-11 Energy consumption rate for feed water mass flux................................................71
4-12 Energy consumption rate for fresh water mass flow rate (cross section diameter of the packed bed is 15 m)....................................................................................71
5-1 Differential control volume for liquid/gas heat and mass transfer within a) countercurrent flow, b) co-current flow condensers ..............................................77
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5-2 Flow diagram for the countercurrent flow computation ........................................82
5-3 Comparison of predicted exit temperatures and humidity with the experimental data for countercurrent flow: a) Ta,in=36.9° C, b) Ta,in=40.8° C, c) Ta,in=42.8 °C...83
5-4 Comparison of predicted exit temperatures and humidity with the experimental data for co-current flow: a) Ta,in=35.5° C, b) Ta,in=39.6° C, c) Ta,in=42.9° C .........85
5-5 Droplet residence positions on the packing material: a) on the top, b) in the corner, c) beneath the packing ..............................................................................87
5-6 Observation of the liquid blockages within the packed bed: a) side view, b) Top view .....................................................................................................................89
5-7 Total temperature drop of the air/vapor mixture with varying water to air mass flow ratios and different air inlet temperatures (without packing) .........................91
5-8 Total fresh water production rate with varying water to air mass flow ratios and different air inlet temperatures (without packing) .................................................91
5-9 Temperature drop of the air/vapor mixture with varying water to air mass flow ratios in the a) co-current, b) countercurrent stage (without packing) ....................92
5-10 Fresh water production rate with varying water to air mass flow ratios and different air inlet temperatures in the a) co-current, b) countercurrent stage (without packing) .................................................................................................93
5-11 Comparison of the packed bed condenser effectiveness between co-current and countercurrent flow ..............................................................................................96
5-12 Comparison of the countercurrent flow condensation effectiveness between droplet condenser and packed bed condenser........................................................97
6-1 Required diffusion tower height with variations in air to feed water mass flow ratio ................................................................................................................... 101
6-2 Maximum exit humidity ratio variation with air to feed water mass flow ratio.... 102
6-3 Exit air temperature variation with air to feed water mass flow ratio................... 103
6-4 Water side pressure drop variation with air to feed water mass flow ratio ........... 103
6-5 Air/vapor side pressure drop variation with air to feed water mass flow ratio ..... 104
6-6 Temperature and humidity ratio profiles through the condenser.......................... 105
6-7 Condenser temperature and humidity ratio variation with fresh water to air mass flow ratio ........................................................................................................... 106
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6-8 Required direct contact condenser height with variations in air mass flux.......... 106
6-9 Condenser fresh water exit temperature variation with air mass flux................... 107
6-10 Variation of the fresh water production efficiency with air mass flux ................. 108
6-11 Variation of the energy consumption with air to feed water mass flow ratio in diffusion tower................................................................................................... 108
6-12 Variation of the energy consumption with air mass flux in condenser................. 109
6-13 Variation of the total energy consumption rate with air mass flux....................... 110
6-14 Net fresh water profit variation with electricity retail price for different fresh water retail price ................................................................................................ 115
6-15 Percent increase in profit with electricity profit for different fresh water profit ... 116
6-16 Water price in different countries for year 2001 & 2002..................................... 117
H-1 Variation of the relative uncertainties of the calculated water properties with water temperature............................................................................................... 145
H-2 Variation of the relative uncertainties of the calculated vapor properties with air temperature ........................................................................................................ 145
H-3 Variation of the relative uncertainties of the calculated air properties with air temperature ........................................................................................................ 146
H-4 Variation of the relative uncertainties of the calculated air/vapor mixture properties with air temperature ...........................................................................146
H-5 Variation of the relative uncertainties of the wetted area and mass transfer coefficients with temperature by using Onda’s correlation.................................. 148
H-6 Variation of the relative uncertainties of the heat transfer coefficients with temperature ........................................................................................................ 149
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NOMENCLATURE
A control surface area (m2)
a specific area of packing material (m2/m3)
ai amortization factor (yr–1)
Cp specific heat (kJ/kg)
D molecular diffusion coefficient (m2/s)
DC direct capital cost ($)
d diameter (m)
dp diameter of the packing material (m)
f plant availability
G air mass flux (kg/m2-s)
g gravitational acceleration (m/s2)
H diffusion tower height (m)
h enthalpy (kJ/kg)
hfg latent heat of vaporization (kJ/kg)
i interest rate
k mass transfer coefficient (m/s)
L water mass flux (kg/m2-s)
l channel half width (m)
Mv vapor molecular weight (kg/kmol)
m mass flow rate (kg/s)
xiv
n plant life (yr)
P pressure (Pa or kPa)
Pw electrical power consumption for pumps (W, kW or MW)
Q retail price ($)
R universal gas constant (kJ/kmol-K)
s entropy generation rate in the diffusion tower (kW/K)
T temperature (°C or °K)
U heat transfer coefficient (W/m2-K)
v air/vapor velocity (m/s)
V control volume (m3)
VG air/vapor volumetric flow rate (m3/s)
β economic increase rate
γ specific cost of operating labor ($/m3)
ε condensation effectiveness
µ dynamic viscosity (kg/m-s)
ρ density (kg/m3)
σL surface tension of liquid (N/m)
σC critical surface tension of the packing material (N/m)
ω humidity ratio
Ф relative humidity
Π profit ($)
Subscripts
a air
xv
c centerline
elec electricity
evap the portion of liquid evaporated
f fresh water
fixed fixed cost
G air/vapor mixture
GA gas side parameter based on the specific area of packing
h high
i interface
in inlet parameter
L liquid phase
LA liquid side parameter based on the specific area of packing
Labor labor cost
low low
LW liquid side parameter based on the specific wet area of packing
out exit parameter
sat saturate state
unit, p unit amount in terms of production
v vapor phase
sink sink temperature
x local value of variable in transverse direction (all the temperatures
are bulk temperatures unless denoted by subscript x)
z fluid flow direction
xvi
Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
HEAT AND MASS TRANSFER FOR THE DIFFUSION DRIVEN DESALINATION PROCESS
By
Yi Li
May 2006
Chair: James F. Klausner Major Department: Mechanical and Aerospace Engineering
This research concerns a diffusion driven desalination (DDD) process in
which warm water is evaporated into a low humidity air stream, and the vapor is
condensed out to produce distilled water. Although the process has a low fresh water to
feed water conversion efficiency, it has been demonstrated that this process can
potentially produce inexpensive distilled water when driven by low-grade energy such as
waste heat. A dynamic analysis of heat and mass transfer demonstrates that the DDD
process can yield a fresh water production of 1.14 million gal/day by utilizing waste heat
from a 100 MW steam generating power plant based on a condensing steam pressure of
only 10.159 kPa in the main condenser. The optimal operating condition for the DDD
process with a high temperature of 50° C and sink temperature of 25° C has an air mass
flux of 1.5 kg/m2-s, air to feed water mass flow ratio of 1 in the diffusion tower, and a
fresh water to air mass flow ratio of 2 in the direct contact condenser. Operating at these
conditions yields a fresh water production efficiency (mf/mL) of 0.035 and electric energy
xvii
consumption rate of 0.0022 kW-hr/kgfw. This dissertation describes the research progress
made in the development and analysis of the DDD process. Throughout the past three
years, the main focus of the desalination process has been on the heat and mass transport
phenomena in the diffusion tower and direct contact condenser within the packed bed.
Detailed analyses required to size and analyze these heat and mass transfer devices have
been developed. A laboratory scale experimental DDD facility has been fabricated.
Temperature and humidity data have been collected over a range of flow and thermal
conditions for the diffusion tower and direct contact condenser. The analyses agree quite
well with the current data. The condensation effectiveness of the direct contact condenser
with and without packed bed has been compared. It has been experimentally observed
that the fresh water production rate is significantly enhanced when packing is added to
the condenser. It has also been observed that the condensation effectiveness increases
considerably when air and water flow configuration is countercurrent. Recently, it has
been recognized that the heat and mass transfer within the packed bed can be
significantly diminished with water blockages. High-speed cinematography has been
used to observe the liquid formation on the packing material. The cause of this
phenomenon is addressed. Further experimental and analytical analyses are required to
evaluate its influence on the heat and mass transfer coefficients for liquid and air flow
within the packed bed.
1
CHAPTER 1 INTRODUCTION AND LITERATURE REVIEW
Water is not only indispensable to life, industrial development, economic growth,
preservation of natural resources and social well-being, but sufficient drinking water
resources are necessary for the development of humanity. Adequate water supply has
historically been the foundation for the growth of civilizations. Between 1900 and 1995,
drinking water demand has grown twice as fast as the world population. By 2025, this
demand is expected to grow another 40% [1]. In fifty years, it is expected that without
further technological developments, forty countries will lack adequate drinking water. In
many parts of the world the discrepancy between freshwater needs and available supply
has already limited further development, and has even jeopardized survival. Growing
pollution in many regions is causing water shortages where such problems were
inconceivable just a few decades ago. Due to economic and social development, the
growth of water demand never ceases. It is estimated that fresh water shortages affect the
lives of hundreds of millions of people on a daily basis worldwide. Fresh water shortages
limit food production and lead to destitution and poverty. When fresh water resources dry
up, the affected populations have no choice but disappearance or exodus.
One obvious solution to alleviate the fresh water shortages is seawater desalination.
Desalination technologies are currently used throughout the world and have been under
development for the past century.
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Description of Thermal Desalting and Membrane Separation
The most common ways to desalt seawater involve some form of boiling or
evaporation. In a simple still, seawater can be boiled releasing steam which, when
condensed, forms pure water. Many stills can be connected together making the process
more efficient. To achieve this, each still, or effect, must be at different pressure. This is
because in a vacuum, water can boil or flash at much lower temperatures. Multiple Effect
Distillation (MED) and Multi-Stage Flash desalination (MSF) makes use of this
phenomenon.
Other thermal processes include a variation of the simple still such as vapor
compression (VC). The vapor compression (VC) distillation process is generally used for
small and medium scale seawater desalting units. The heat for evaporating the water
comes from the compression of vapor rather than the direct exchange of heat from steam
produced in a boiler. The two primary methods used to create a vacuum and compress the
vapor are mechanical compression and steam jet. Fig. 1-1 shows a schematic diagram of
the mechanical vapor compression desalination process.
Figure 1-1 Schematic diagram of mechanical vapor compression process [2]
3
The mechanical compressor creates a vacuum in the liquid vessel and then
compresses the evaporated vapor from the vessel. The compressed vapor condenses
inside a tube bundle and gives up heat to the liquid side in the vessel. Seawater is sprayed
on the outside of the heated tube bundle where it evaporates completing the cycle. With a
steam jet type VC unit, also called a thermocompressor, a venturi orifice on the steam jet
eductor produces a vacuum and extracts evaporated water vapor from the main vessel.
The extracted water vapor is compressed by the steam jet within the diverging portion of
the eductor. This mixture is condensed in the tube bundle to provide the thermal energy
(heat of condensation) to evaporate the seawater sprayed over the outside of the tube
bundle. A simplified schematic diagram of the thermal vapor compression combined
multi-effect desalination process is shown in Fig. 1-2.
Figure 1-2 Schematic diagram of thermal vapor compression combined multi-effect destillation process [2]
Semi-permeable and ion specific membranes can also be used to desalt seawater.
Membrane processes are based on separation rather than distillation. Reverse osmosis
membranes basically let water pass through them but reject the passage of salt ions. In
reality a small percentage, approximately 1%, of sea salts pass through the membranes, or
4
leak around the seals. For potable water this leakage is acceptable, but for industrial
purposes it may require further treatment. The operational pressure of reverse osmosis
systems is a function of the salinity of the feed water. The salinity results in a colligative
property known as osmotic pressure. The osmotic pressure of brackish water is much
lower than that of seawater. Typical 500 ppm potable water has an osmotic pressure of
0.2 MPa while normal seawater is close to 2.5 MPa.
Another type of membrane separation process is Electro-Dialysis Reversal (EDR).
It makes use of ion specific membranes, which are arrayed between anodes and cathodes
to drive salt ions in controlled migrations to the electrodes. While not as widespread as
RO, it is still commonly used.
RO is by far the most widely used separation process and has tremendous energy
advantages over other thermal processes when 1% salt passage can be tolerated, and good
quality seawater is available. Table 1-1 shows the pumping and heating energy
consumption of some commonly used desalination processes [3].
Table 1-1 Pumping and heating energy consumption of some desalination processes Energy Consumption (kW-hr/kgfw)
Technology Unit Capacity (×106 kg/day) Electrical/Mechanical Thermal
MSF 60 0.004 - 0.006 0.008-0.018 MEB 60 0.002 - 0.0025 0.0025-0.01
MED-VC 24 0.007 - 0.009 NA RO 24 0.005 - 0.007 NA
Description of HDH and MEH Process
A desalination technology that has drawn interest over the past two decades is
referred to as Humidification Dehumidification (HDH). This process operates on the
principle of mass diffusion and utilizes dry air to evaporate saline water, thus
humidifying the air. Fresh water is produced by condensing out the water vapor, which
5
results in dehumidification of the air. A significant advantage of this type of technology
is that it provides a means for low pressure, low temperature desalination and can operate
off of waste heat, which is potentially very cost competitive. Bourouni et al. [4], Al-
Hallaj et al. [5], and Assouad and Lavan [6] respectively reported on the operation of
HDH units in Tunisia, Jordan, and Egypt. Muller-Holst et al. [7] fabricated an
experimental Multi-Effect Humidification (MEH) facility driven by solar energy and
considered its performance over a wide range of operating conditions. The fresh water
production varied on a seasonal basis since the process is driven by solar energy. The
average fresh water production was about 52 gal/day with a maximum of 90 gal/day in
May and a minimum of 14 gal/day in January. A computer simulation of the operational
performance of the process was developed, and the predicted behavior agreed well with
the actual behavior. An excellent comprehensive review of the HDH process is provided
by Al-Hallaj and Selman [8]. It was concluded that although the HDH process operates
off of low-grade energy, it is not currently cost competitive with reverse osmosis (RO)
and mult-istage flash evaporation (MSF). There are three primary reasons for the higher
costs associated with the HDH process:
1. The HDH process is typically applied to low production rates and economies of scale cannot be realized in construction.
2. Typically natural draft is relied upon, which results in low heat and mass transfer coefficients and a larger surface area humidifier.
3. Film condensation over tubes is typically used, which is extremely inefficient when non-condensable gases are present. Thus a much larger condenser area is required for a given production rate, and the condenser accounts for the majority of the capital cost.
Therefore, an economically feasible diffusion driven distillation process must
overcome these shortcomings. Klausner et al. [9] have reported on a diffusion driven
6
desalination (DDD) process that overcomes these shortcomings, resulting in an
economically viable desalination process applied on a large scale (>1 million gal/day).
Another type of desalination technology that makes use of water evaporating into
an air stream is the Carrier-Gas Process (CGP) reported by Larson et al. [10]. This
process has been further refined by Beckman [11, 12]. The CGP is designed to operate
with a feed water temperature range of 55 – 88° C. Beckman demonstrates (based on 88°
C feed water) that the CGP can produce fresh water with an operating cost of 3.35
$/103gal using natural gas for heating and 1.52 $/103gal when waste heat is used as the
thermal source. The capital cost is apparently low, approximately $1397 for a 1000
gal/day facility.
Description of DDD Process
A simplified schematic diagram of the DDD process and system, designed to be
operated off of waste heat discharged from thermoelectric power plants, is shown in Fig.
1-3. The process includes three main fluid circulation systems denoted as feed water,
air/vapor, and freshwater. In the feed water system, a low pressure condensing steam
from an adjacent power plant heats the feed water in the main feed water heater (a). The
main feed water heater is typically a main condenser when used in conjunction with
thermoelectric power plants. Because the required feed water exit temperature from the
heater can be relatively low for the DDD process, the required heat input can be provided
by a variety of sources such as low pressure condensing steam in a power plant, exhaust
from a combustion engine, waste heat from an oil refinery, low grade geothermal energy,
or other waste heat sources. The heated feed water then is sprayed into the top of the
diffusion tower (b). A portion of feed water will evaporate and diffuse rapidly into the
7
air. Evaporation in the tower is driven by a concentration gradient at the liquid/vapor
interface and bulk air, as dictated by Fick’s law. Via gravity, the water falls downward
through a packed bed in the tower that is composed of very high surface area packing
material. A thin film of feed water will form over the packing material and contact the
upward flowing air through the diffusion tower. The diffusion tower should be designed
so that the air/vapor mixture leaving it should be fully saturated. The purpose of heating
the water prior to entering the diffusion tower is that the rate of evaporation and the exit
humidity ratio increase with increasing temperature, thus yielding greater water vapor
production. The water, not evaporated in the diffusion tower will be collected at the
bottom and discharged or re-circulated.
Main Feed Water Heater (a)
Main Feed Pump
Seawater Reservoir
Fresh WaterPump
Water Cooler (d)
Cooler Pump
DiffusionTower (b)
Direct ContactCondenser (c)
Exhaust
Fresh WaterProduction
Fresh WaterStorage Tank
Low Pressure Steam
Seawater
Air/Vapor
Fresh Water
Forced DraftBlower
Power Plant
Figure 1-3 Schematic diagram for diffusion driven desalination process
8
In the air/vapor system, low humidity cold air is pumped into the bottom of the
diffusion tower, and flows upward to be heated and humidified by the feed water. As
mentioned before, the air/vapor mixture leaving the diffusion tower is saturated and
drawn into the direct contact condenser (c), where it is cooled and dehumidified by the
fresh water in the condenser. The air could be directed back to the diffusion tower and
used repeatedly. The condenser is another important component of the DDD process
because film condensation heat transfer is tremendously degraded in the presence of non-
condensable gas. In order to overcome this problem Bharathan et al. [13] describe the use
of direct-contact heat exchangers. The direct contact condenser approach is best suited
for the DDD process.
In the fresh water system, the cold fresh water will gain heat and mass due to air
side vapor condensation in the condenser. After discharging from the direct contact
condenser, it will be cooled in a conventional shell-and-tube heat exchanger (d) by the
incoming feed water. Here, the intake feed water flow is preheated by the heat removed
from the fresh water, which helps to reduce the amount of energy needed in the main feed
water heater. Finally, a portion of the cooled fresh water will be directed back to the
direct contact condenser to condense the water vapor from the air/vapor mixture
discharging from the diffusion tower. The remaining fresh water is production.
Comparison of the DDD Process with HDH and MEH
The DDD process has following advantages compared with HDH and MEH:
1. The DDD process utilizes thermal stratification in the seawater to provide improved performance. In fact, the DDD process can produce fresh water without any heating by utilizing the seawater thermal stratification.
2. The thermal energy required for the DDD process may be entirely driven by waste heat, therefore eliminating the need for additional heating sources. This helps keep the DDD plant compact, which translates to reduced cost. The DDD process
9
recommends using whatever heat source is best suited for the region requiring fresh water production. The DDD process is very well suited to be integrated with steam power plants, and use the waste heat coming from these plants. Renewable resources such as solar heating, wind power and geothermal energy may be used as well.
3. In the DDD process the evaporation occurs in a forced draft packed bed diffusion tower as opposed to a natural draft humidifier. The diffusion tower is packed with low pressure drop, high surface area packing material, which provides significantly greater surface area. This is very important because the rate of water evaporation is largely influenced by the liquid/vapor contact area available. In addition, the forced draft provides for high heat and mass transfer coefficients. Thus, a diffusion tower is capable of high production rates in a very compact unit. Since the unit is compact, the capital cost will be minimized. The price paid in using forced draft is the pumping power required to pump the fluids through the system, but the projected cost is low, thus providing potential for an economically competitive desalination technology.
4. The DDD process uses a direct contact condenser to extract fresh water from the air/vapor mixture. This type of condenser is significantly more efficient than a conventional tube condenser, as is used with the HDH process. Thus, the condenser will be considerably more compact for a given design production rate. This also adds to cost reduction.
5. The diffusion tower and direct contact condenser can accommodate very large flow rates, and thus economies of scale can be taken advantage of to produce large production rates.
6. No exotic components are required to manufacture a DDD plant. All of the components required to fabricate a DDD plant are manufactured in bulk and are readily available from different suppliers. This facet of production also translates to reduced cost.
The advantages of the DDD process compared with HDH and MEH are obvious.
However, since the fraction of feed water converted to fresh water using the DDD
process is largely dependent on the difference in high and low temperatures in the
system, when driving the process using waste heat, this temperature difference will be
moderate. Thus the fraction of feed water converted to fresh water will be low. A large
amount of water and air must be pumped through the facility to accomplish a sizable
fresh water production rate. This disadvantage is an inherent characteristic of the DDD
10
process. However, as long as the production cost of fresh water using the DDD process is
cost competitive, it is a tolerable characteristic.
Comparison of the DDD process with MSF and RO
Table 1-2 below compares the energy consumption of the DDD process with
reverse osmosis (RO) and multi-stage flash (MSF). It is readily observed that the thermal
energy consumption for DDD is very high. This is to be expected because the DDD
process is driven by low thermodynamic availability energy. However, because the waste
heat can be considered a free resource, the total energy required to drive the DDD process
is quite competitive. Fresh water production using the DDD process has potential to be
very inexpensive and comparative when driven by waste heat that would have otherwise
been discarded. Therefore, to determine whether or not the technology is cost
competitive, greater attention should be paid to the electric energy consumption.
Table 1-2 Comparison of electricity consumption for DDD, MSF, and RO desalination technologies
Energy Consumption (kW-hr/kgfw) Technology
Electrical/Mechanical Thermal Total DDD 0.002-0.0053 0.75 (free) 0.002 – 0.0053 MSF 0.004 - 0.006 0.008-0.018 0.012 – 0.024 RO 0.005 - 0.007 NA 0.005 – 0.007
A comparison of the advantages and disadvantages of the DDD, RO, and MSF
processes is shown in Table 1-3. The DDD process is essentially a thermal distillation
process that operates using waste heat. It therefore has all of the same operational
advantages as MSF. In contrast to MSF, the DDD process has very low energy
consumption and thus a low operating cost. The main disadvantage of the DDD process
is that the conversion efficiency is low, typically 5-10%. Despite the low conversion
efficiency, the energy consumption is still low since pumping occurs at low pressure.
11
Table 1-3 Comparison of advantages and disadvantages of DDD, RO, and MSF desalination technologies.
Process Advantage Disadvantage
DDD
− Low energy consumption and low cost of water production
− Waste heat utilized − Low salinity concentration
discharge, minimal environmental impact
− Low maintenance cost
− Lower conversion efficiency
RO
− Feed water doesn’t require heating
− Lower energy requirements − Removal of unwanted
contaminants such as particles and bacteria
− High maintenance cost − Performance degrades with time − High salinity concentration
discharge, environmental impact − High cost of filer replacement
MSF
− Large production rates and economies of scale
− Continuous operation without shutting down
− Large energy consumption − High cost of water production
However, the low conversion efficiency provides an environmental advantage for
the DDD process over RO and MSF. That is the salinity discharge concentration in the
brine is comparatively very low. This environmental advantage is a very important issue
within North America, Europe, and Japan. For example, the city of Tampa, Florida
recently constructed a 25 million gal/day RO desalination facility. But since its first days
of construction there has been growing criticism from environmental groups because of
the high salinity discharge concentration into Tampa Bay [14]. Although nearly 5 billion
gallons of drinking water has been produced since March 2003, the plant has run
sporadically, producing far short of its intended output, because the pretreatment process
of the plant isn’t rigorous enough to filter out the suspended particles from the intake
seawater from Tampa Bay. Without significant modification, the plant is too expensive to
12
operate. Three of the companies involved in the project have filed for bankruptcy. The
plant was taken off-line in June 2005 for repair, and it is scheduled to resume operations
in the fall 2006 [15].
Potential Applications for the DDD Process
The attractive feature of the DDD process is that it can operate at low temperatures
so that it requires an energy input with low thermodynamic availability. This is important
because the process can be driven by waste heat that would otherwise not be suitable for
doing useful work or driving some other distillation process (such as flash distillation). A
very interesting application for the DDD process is to operate in conjunction with an
existing process that produces large amounts of waste heat and is located in the vicinity
of an ocean or sea. One such potential benefactor of the DDD process is the electric
utility industry. Conventional steam driven power plants dump a considerable amount of
energy to the environment via cooling water that is used to condense low pressure steam
within the main condenser. Typically this cooling water is either discharged back to its
original source or it is sent to a cooling tower, where the thermal energy is discharged to
the atmosphere. Instead of dumping the thermal energy to the environment, the DDD
process provides a means for putting the discarded thermal energy to work to produce
fresh water. Of course this application is limited to power producing facilities sited along
the coastline. However, this should not be a significant limitation. Bullard and Klausner
[16] studied the geographical distribution of fossil fired power plants built in the United
States from 1970 to 1984. In their study they found that the two most significant
attributes for siting a new fossil fired plant in a given geographical region are 1)
proximity to a large body of water and 2) proximity to a large population base. The
demographic make-up of the United States as well as other industrialized nations is such
13
that major population centers reside along the coastline. Thus, the DDD process appears
to be well suited for the power generation infrastructure in the United States.
Another potential application for the DDD process is for fresh water production in
the range of 1000-10000 gal/day. It is envisioned that the potential customers that can
benefit from this application include single users such as small business entities,
agricultural entities and small or middle size residency communities whose locations are
such that they have access to saline ground water, seawater or a geothermal reservoir.
The extent of saline ground water resources in the United States are substantial, although
little is known about the hydrogeology about most aquifers that contain saline ground
water, since most efforts have focused on characterizing fresh water aquifers [17]. Fig. 1-
4 below shows the depth of many saline ground water resources known in the U.S. This
map illustrates the fact that there is a substantial population that can benefit from the
successful development of the DDD process.
Depth to saline ground water (feet)
Less than 500
500 - 1000
More than 1000
Inadequate information
Figure 1-4 Depth to saline ground water in the United States [18]
14
The fresh water conversion efficiency, defined as the ratio of the fresh water output
to the feed water input, is low for the DDD process. Therefore, the process is best suited
for applications using low-grade heat. One such resource is solar heating, which is
abundantly available in the Southeast and Western United States. Figure 1-5 shows a
simple flow diagram for the DDD process coupled with solar collectors. In this process
the feed water will be drawn from saline ground water or seawater, and then heated by a
solar thermal heating system. The electrical power required to drive the pumps and
blowers can be driven by either a solar electric panel or a wind turbine. In order to make
efficient use of the thermal energy, the feed water is preheated in the chiller using the
discharge heat from the direct contact condenser.
Diffusion
Tower (b)
Fresh Water Chiller
(d)
Sea Water
Direct Contact
Condenser (c)
Solar Heating System (a)
Fresh Water Out
Warm Fresh Water
Cool Fresh Water
Wet Air
Dry Air
Feed Water
(1)
(2)
(3)
(4)
(7) (5)
(6)
Warm Drain
Feed Water
Sea Water Preheater (e)
Cool Drain
Figure 1-5 Flow diagram of DDD process driven by solar energy
Many investigations [19] show that solar heating is a mature technology and is
already being widely used in the United States. In 1897 30% of the homes in Pasadena,
just east of Los Angeles, were equipped with solar water heaters. As mechanical
improvements were made, solar systems entered use in Arizona, Florida and many other
sunny regions of the United States. By 1920, tens of thousands of solar water heaters had
been sold. Today there are more than half a million solar water heaters in California
15
alone. They are used for heating water inside homes and businesses as well as for heating
swimming pools. It is interesting to note that the communities that have a high rate of
solar heater installations also have access to seawater or saline ground water and suffer
from fresh water shortages.
Another interesting facet of renewable energy resources is that wind energy is
abundantly available along the coastline of the United States. Therefore, it will be of
interest to explore the combination of solar energy collectors providing the thermal
source and wind energy turbines providing the electrical source for the DDD process.
Some special geographic regions, such as islands, have access to seawater or saline
ground water, have substantial solar resources available, have sufficient wind power, and
have middle sized residency communities that can benefit from the solar/wind combined
DDD system.
Diffusion
Tower (b)
Air
Cooling Tower
(d)
Geothermal Water
Reservoir
Direct Contact
Condenser (c)
Pre-treatment Equipment (a)
Fresh Water Out
Warm Fresh Water
Cool Fresh Water
Wet Air
Dry Air
Hot Feed Water
(1)
(2)
(3)
(4)
(7) (5)
(6)
Cold Drain Heat Exchanger (e) Warm Drain
Figure 1-6 Flow diagram of DDD process driven by geothermal energy
Because the DDD process can operate off of low-grade thermal energy, one
interesting potential application is the demineralization of geothermal water in shallower
reservoirs or the demineralization of the discharge water from geothermal power plants.
16
Geothermal resources are most abundant in the Western United States. The west coast
boundary between the North American and Pacific plates is "sliding" along the San
Andreas fault (many earthquakes but few volcanoes) from the Gulf of California up to
northern California and sub-ducting from the Cascade volcanoes north through the
Aleutians. There are also volcanic hot spots under Yellowstone and Hawaii and intra-
plate extensions with hot springs in the Great Basin. The history data of EIA [20] show
that California generates the most geothermal electricity with about 824 MW at the
Geysers (much less than its capacity, but still the world's largest developed field and one
of the most successful renewable energy projects in history), 490 MW in the Imperial
Valley, 260 MW at Coso, and 59 MW at smaller plants. There are also power plants in
Nevada (196 MW), Utah (31 MW), and Hawaii (25 MW). Due to environmental
advantages and low capital and operating costs, direct use of geothermal energy has
skyrocketed to 3858 GW-hr/yr, including 300,000 geothermal heat pumps. In the
Western United States, hundreds of buildings are heated individually and through district
heating projects (Klamath Falls, Oregon; Boise, Idaho; San Bernardino, California; and
soon Mammoth Lakes and Bridgeport, California). Large greenhouse and aquaculture
facilities in Arizona, Idaho, New Mexico and Utah use low-temperature geothermal
water, and onions and garlic are dried geothermally in Nevada. However, geothermal
water is usually highly mineralized containing many components such as silica, chloride,
sulphate, bicarbonate, boron, sodium, potassium, lithium, calcium, rubidium, caesium,
magnesium, ammonia, and hydrogen sulfide. The customers typically only use the high
temperature geothermal water to produce electricity, after which the temperature of the
water is lower than 60° C and is directly ejected. If these geothermal consumers want to
17
sufficiently use the low temperature geothermal water, they could couple it with the DDD
process to produce fresh water as a by-product. It could potentially increase their
economic profits. A simple schematic of a geothermal DDD process is shown in Fig. 1-6.
The diffusion driven desalination process is very versatile, in that it can be driven
by many different energy resources. Here we have identified solar, wind, and geothermal
energy resources that should be explored in conjunction with diffusion driven
desalination.
Properties of Saline Water
There are two important factors that affect the physical properties of saline water:
salt concentration rate and relative proportions of the components in the salt. These
properties directly cause the scale formation, corrosion and bacteria contamination
problems in desalination facilities. The dominant chemical and physical characteristics of
seawater are as follows [21],
1. Abundant dissolved oxygen is the most important environmental factor for corrosion of steels, copper alloys, and stainless steels. The oxygen content of seawater varies between 0-12 ppm depending on the temperature, salinity, and biological activity. The solubility of oxygen decreases with increasing water temperature or seawater concentration rate.
2. Seawater contains about 19,000 ppm chloride. The high chloride ion concentration will help seawater to penetrate the protective films of the facility and enhance corrosion reactions.
3. Seawater has excellent electrolytic conductivity.
4. Seawater contains a certain amount of heavy metal ions such as Cu, Zn, Cd and Pb.
5. Abundant calcareous scale formers (cathodic inhibitors), such as calcium, strontium and magnesium ions, result in deposition of tight and adherent films of lime salts (CaCO3, SrCO3, MgCO3, and Mg(OH)2).
Normally, there are 4 type of scale that can form in the desalination plants,
18
1. Alkaline scale occurs when the heating of seawater causes the decomposition of bicarbonate content.
2. Calcium carbonate scale may be deposited even at low temperature.
3. Calcium sulfate scale occurs when the concentration temperature path is not within its solubility. The deposition of calcium sulfate takes place because of its inverted solubility.
4. Magnesium hydroxide scale forms at higher temperature and/or when seawater has been concentrated to a considerable level.
In applying stability data for calcium sulfate, magnesium hydroxide, and calcium
carbonate to seawater, Spiegler [22] made the following conclusions about preventing
scaling problems,
1. Discharge the brine when it reaches high concentration level. When seawater is concentrated to 2/3 of its volume, crystallization will occur if seeds, such as calcium sulfate scale, can be provided in the system.
2. Add acid to increase the solubility of calcium carbonate. The solubility of calcium carbonate can be greatly increased even with weak acids such as carbonic.
3. Precipitation of magnesium hydroxide liberates acid that inhibits the precipitation of calcium carbonate.
4. Maintain a lower operation temperature of the system because the scale will mainly consists of calcium carbonate when the water temperature is less than 60°C.
To reduce the corrosion due to seawater, the following methods are usually used,
1. To prevent the corrosion on the surface of the evaporator and eliminate the carbonate scale problem, deaeration is used to remove the dissolved gases in the seawater.
2. Control the pH level of seawater to minimize corrosion, but it must be lower than the magnesium hydroxide scaling point. A pH level between 7 - 7.7 is desirable.
3. Select proper materials for the desalination plants such as stainless steel, copper alloys, aluminum alloys, titanium, and plastics.
Since the DDD process is a low temperature and low fresh water conversion
process, bacterial contamination is considered as the most important problem for the
system. Methods for disinfecting water include microfiltration, chlorination, iodine,
19
ozone, and ultraviolet light. Many of these methods are also effective at removing other
contaminants from water.
Extremely fine ceramic filters can be used to remove bacteria from water. Their
pore size is normally 1 micron or less. To prevent clogging they can be brushed clean and
reused many times. Silver compounds are used to prevent bacteria growing through the
filter medium. Although microfiltration is the simplest and cheapest disinfection method,
it is only feasible for low flow rate units because of it high flow resistance.
Iodine can also be used to disinfect water. Tablet form or solution form can be
introduced manually to small batches of water, or automatically mixed with pumped
water. The effective contact time is fifteen minutes under most circumstances. Because it
costs around twenty times more than chlorine, it is used primarily for emergencies and
other special circumstances.
Ozone, an activated form of oxygen, is a powerful oxidizer. It is usually created
with electricity and mixed with water. It kills microorganisms and breaks down organic
chemicals. Carbon filtration generally follows ozonation. However its energy
consumption and cost are very high.
Ultraviolet light is another method of killing microorganisms in water. Water is
circulated in a thin layer past an ultraviolet bulb encased in a quartz sleeve. The light
energy kills microorganisms very quickly. Clear water is needed for effective treatment
because the particles in the water can shade the bacteria from the light. Also the water
flow has to be fully stopped when the light output is ineffective or during regular
maintenance. Ultraviolet bulbs generally need replacing at least once a year.
20
Carbon, generally in the form of granular activated carbon, can be used to remove
organic chemicals, including pesticides and chlorinated products as well as many tastes,
odors and colors from water. It attracts and holds the molecules of the organic chemicals.
Carbon filters are available as cartridge filters for in-line use. However, for greatest
effectiveness the water needs to flow slowly through the carbon. A replacement is
required when the carbon reaches its adsorption limit because it may begin releasing
contaminant chemicals back into the water.
The most popular water disinfection method used in this country is chlorination.
This is because the chlorine is very effective in killing microorganisms if high enough
concentration and sufficient time are provided. Simple chlorination uses only 1 ppm (one
gallon per 50,000 gallons of water) concentration, and a contact time of at least 30
minutes is needed. Chlorine is generally added at the pump to ensure adequate contact
time to the water system. When 30 minutes of contact time is not possible, super
chlorination can be used. The contact time can be reduced to around 5 minutes if the
concentration is about 5 ppm (one gallon chlorine bleach per 10,000 gallons water). At
this level, other methods may be needed to remove the strong taste of water. Chlorination
may be done manually or with automatic feed on-site systems. Shock chlorination at 50-
200 ppm (1-4 gallons chlorine bleach per 1,000 gallons water) concentration is only used
for emergent treatment or the start of a new system. The entire system including pipes
should be washed and allowed to sit overnight filled with this high concentration
solution. One advantage of chlorination is that residual chlorine in the water can prevent
recontamination. It will continue to kill microorganisms at low concentrations for a long
time. However, there are problems with chlorination. Reactions with iron, sulfur,
21
ammonia, slime, organic materials, and other chemicals can reduce the effective level of
chlorine. In addition, some of the chemicals formed when chlorine reacts with organic
chemicals are toxic or carcinogenic.
Objectives of the Study
There are four primary objectives for the research, and provided these objectives
are successfully met, this work will provide a basis for the design and fabrication of a
diffusion driven desalination facility of any size. These objectives are
1. Develop a thermodynamic model for the DDD process to evaluate the potential for fresh water production for a variety of operating conditions.
2. Fabricate a laboratory scale DDD diffusion tower, experimentally measure the thermal and mass transport properties, the evaporation rate and the associated energy consumption required to heat the feed water and pump water and air through the facility. Measurements will be made over a wide range of operating conditions in order to find an optimum condition where fresh water production is maximized with low energy consumption.
3. Fabricate a laboratory scale DDD direct contact condenser, experimentally measure the thermal and mass transport properties, the condensation rate and the associated energy consumption required to condense the vapor and pump water and air through the facility. Measurements will be made over a wide range of operating conditions in order to find an optimum condition where fresh water production is maximized with low energy consumption.
4. Develop a computational modeling tool that reliably simulates the heat and mass transfer processes within a DDD facility. The development of a dynamic modeling tool for the diffusion tower and direct contact condenser is required. The successful completion of this objective will allow the fresh water production rate of a specified DDD configuration to be predicted as well as provide design recommendations for specific applications.
Scope of Work
In order to meet the research objectives outlined, the following major tasks have
been undertaken:
1. Develop and implement a computational model for the countercurrent flow diffusion tower and the co-current and countercurrent flow direct contact condenser with a packed bed.
22
2. Conduct experiments in the diffusion tower and direct contact condenser to validate or calibrate the computational model.
3. Conduct DDD experiments to compare the condensation effectiveness of different condenser configurations.
4. Conduct a parametric investigation using the DDD computational model to investigate operating conditions that yield the minimum energy consumption and maximum fresh water production.
5. Conduct an economic analysis to assess the marketability of the DDD process.
It is the ultimate goal of the research to assess the energy requirements and
equipment specifications associated with fresh water production using the DDD process.
Such an analysis will provide guidance as to the economic viability of the DDD process,
and will provide guidance for the future design of large scale plants. In order to
accomplish this task, detailed and reliable modeling of the heat and mass transport
phenomena in the diffusion tower and direct contact condenser is required. Such
modeling will provide detailed information on the size of the required DDD facility
components, energy requirements, flow rates and pumping requirements. In what follows,
the thermodynamic model of the diffusion tower, the lab-scale DDD experimental
facility, the dynamic models for the diffusion tower and packed bed direct contact
condensers, the parametric study and economic analysis of a DDD facility including one
diffusion tower and one countercurrent flow direct contact condenser with packed bed
will be presented.
23
CHAPTER 2 THERMODYNAMIC ANALYSIS OF THE DDD PROCESS
In order to explore the performance and parametric bounds of the Diffusion Driven
Desalination process, a thermodynamic cycle analysis has been performed. A simplified
schematic diagram of the DDD process used for this analysis is shown in Figure 2-1.
(i) Regenerative Heater
(a) Main Feed Pump
(b) Main Feed Water Heater
(c) Diffusion Tower
(g) Direct Contact Condenser
(e) Brine Pump
(d) Forced Draft Blower
Salt Water
Heat Input ••••Waste Heat
(f) Forced Draft Blower
(h) Water Chiller
Saturated Air Dry Air
Chiller Pump
(1)
(2)
(4)
(3)
(7) (5)
(6)
(4)
Fresh Water Out
ControlValve
Figure 2-1 Flow diagram for diffusion driven desalination process
Mathematic Model
In performing the thermodynamic analysis the following assumptions have been
made,
1. The process operates at steady state conditions,
2. There are no energy losses to the environment from the heat and mass transfer equipment,
24
3. Air and water vapor may be treated as perfect gas,
4. Changes in kinetic and potential energy are relatively small,
5. The pumping power is neglected in the energy balance (estimating the required pumping power would require significant details regarding the construction of the diffusion tower, direct contact condenser and other heat transfer equipment; these are beyond the scope of the current analysis).
In the analysis, the temperature of the feed water drawn into the main feed pump is
fixed at 27° C. It is assumed that a large supply of cool water will be available at a sink
temperature, Tsink, of 15° C. The condensate in the direct contact condenser will be
chilled and a portion of it re-circulated. To avoid providing specifics on the heat transfer
equipment, it is assumed that the heat transfer effectiveness in the water chiller and direct
contact condenser is unity, in which case Tsink=T5=T7=15° C. The temperature of the feed
water leaving the main feed water heater is the highest temperature in the DDD system,
Th=T1, and is a primary controlling variable for the process. Different performance curves
will be shown for a variable Th.
The air/vapor mixture leaving the diffusion tower is assumed to be fully saturated
(relative humidity of unity), and due to heat transfer limitations, its maximum
temperature will be taken to be that of the feed water entering the diffusion tower
(T4≤T1).
The main purpose of this analysis is to explore the performance bounds of the
DDD process. However, specification of the system operating variables is not arbitrary.
Namely there are two constraints that must be satisfied,
1. The brine temperature leaving the diffusion tower must not be lower than the air inlet temperature (T2>15° C), so that the air can always absorb heat from the feed water during the humidification process through the diffusion tower, and
2. The net entropy generation in the diffusion tower must be positive.
25
These constraints govern the parametric bounds for the diffusion tower operation.
While the first constraint is initially obvious, the second constraint is simply a
restatement of the second law of thermodynamics for the present adiabatic system
(diffusion tower). The control volume formulation of the second law of thermodynamics
for an open system is expressed as,
dAA
Q
TAdvsVsd
tDt
Ds
AAV
&rr
∫∫∫ ≥⋅⋅+⋅∂∂= 1ρρ , (2.1)
where V denotes the control volume, A is the control surface, and s is the entropy per unit
mass. Assuming steady state processing of fresh water, the adiabatic diffusion tower
assumption leads to,
0≥⋅⋅== ∫ AdvsDt
Dss
A
rr& ρ , (2.2)
and
3331144422 vvaaLLvvaaLL smsmsmsmsmsms −−−++=& . (2.3)
where m denotes the mass flow rate and the subscripts L, a, and v respectively refer to the
liquid, air, and vapor phases. The numerical subscripts denote that the property is
evaluated at the state corresponding to the position in the process as shown schematically
in Figure 2-1. Conservation of mass dictates that,
)( 3412 ωω −−=
a
L
a
L
m
m
m
m. (2.4)
The entropy generation rate in the diffusion tower per rate of air flow, which must
be positive, is obtained from rearranging Eqn. (2.3) and combining with Eqn. (2.4) as,
11
33443
4
3
4234
1 lnln)( La
Lvv
a
aaL
a
L
a
sm
mss
P
PR
T
TCps
m
m
m
s −−+
−
+
−−= ωωωω&
, (2.5)
26
where ω is the humidity ratio, Cp is the specific heat, R is the engineering gas constant,
and Pa is the partial pressure of air.
The control volume formulation of energy conservation applied to the adiabatic
diffusion tower leads to,
04442233311 =−−−++ vvaaLLvvaaLL hmhmhmhmhmhm . (2.6)
where h denotes the enthalpy. The enthalpy of the brine exiting the diffusion tower is
obtained from Eqs. (2.6) & (2.4) as,
)(
)(
)(
341
44333411
22
ωω
ωω
−−
−+−−=
a
L
vvaLa
L
L
m
m
hhTTCphm
m
Th , (2.7)
and the brine temperature (T2) is evaluated from the enthalpy. The air to feed water mass
flow ratio through the diffusion tower, ma/mL1, is another controlling variable in the
analysis. For all computations the feed water mass flow rate is fixed at 100 kg/s while the
air mass flow rate will be varied.
The humidity ratio entering the diffusion tower, ω3, is determined by recognizing
that it is the same as the humidity ratio exiting the condenser, where T7 is 15° C.
Computation Results and Analysis
The first case considered is where there is no heating in the main feed water heater.
The desalination process is entirely driven by the difference in temperature of the feed
water drawn at shallow depths and the cooling water drawn at more substantial depth. In
this case, Th=27°C, Tsink=15° C. Figure 2-2 shows the rate of entropy generation within
the diffusion tower and the brine temperature exiting the diffusion tower for a locus of
possible operating conditions. Here it is observed that the second law of thermodynamics
27
is always satisfied for the entire parametric range considered, but there is a maximum
entropy generation point for each air to feed water mass flow ratio.
Exit Brine Temperature T2 (C)
16 18 20 22 24 26
Rat
e of
Ent
ropy
Gen
erat
ion
(kW
/K)
0.0
0.1
0.2
0.3
0.4
0.5
0.250.50.7511.251.51.7522.252.5
Th = 27 C
η=ma/mL1
increase η
Figure 2-2 Rate of entropy generation for different exit brine temperature, Th=27°C
Figure 2-3 shows the brine temperature (T2) exiting the diffusion tower as a
function of the exit air temperature from the diffusion tower (T4) for the same locus of
operating conditions as in Figure 2-2. It clearly shows that the exit brine temperature
decreases as the exit air temperature increases, and the rate of brine temperature decrease
increases with increasing the air to feed water mass flow ratio. Since it is assumed that
the exit air is saturated, it is advantageous to have a high air temperature leaving the
diffusion tower so that the humidity ratio and fresh water production rate are as high as
possible. For this case the exit air temperature is constrained by the inlet feed water
temperature (T1) when the air to feed water mass flow ratio is lower than unity. When the
air to feed water mass flow ratio exceeds unity, the exit air temperature is limited by the
fact that the brine exit temperature must be higher than the air inlet temperature.
28
Exit Air Temperature T4 (C)
20 22 24 26
Exi
t Brin
e T
empe
ratu
re T
2 (C
)
15
17
19
21
23
25
27
0.250.50.7511.251.51.7522.252.5
Th = 27 C
η=ma/mL1
increase η
Figure 2-3 Variation of exit brine temperature with exit air temperature, Th=27°C
Exit Air Temperature T4 (C)
20 22 24 26
Fre
sh W
ater
to F
eed
wat
er R
atio
(m
f /m
L1)
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.250.50.7511.251.51.7522.252.5
increase η
Th = 27 C
η=ma/mL1
Figure 2-4 Fresh water production efficiency, Th=27° C
Figure 2-4 shows the fresh water to feed water mass flow ratio as a function of the
exit air temperature for different air to feed water mass flow ratios. Clearly, the
production rate increases with increasing exit air temperature under the same air to feed
water mass flow ratio, meanwhile the production rate grows with increasing air to feed
water mass flow ratios under the same exit air temperature. However, both of these
29
parameters are constrained because the exit air temperature must not exceed Th. For the
case of no heating of the feed water (Th=27°C, Tlow=15° C), the maximum fresh water
production efficiency (mf /mL1) is approximately 0.014.
20 25 30 35 40 45 500.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.250.50.7511.251.51.7522.252.5
increase η
(a)Th = 50 C
η=ma/mL1
Exit Brine Temperature T2 (C)
Rat
e of
Ent
ropy
Gen
erat
ion
(kW
/K)
20 30 40 50 60 70 800
2
4
6
8
10
12
0.250.50.7511.251.51.7522.252.5
increase η
(b)Th = 80 C
η=ma/mL1
Exit Brine Temperature T2 (C)
Ra
te o
f Ent
ropy
Gen
erat
ion
(kW
/K)
Figure 2-5 Rate of entropy generation for different exit brine temperature: a) Th=50° C,
b) Th=80° C
The next cases considered are where the diffusion tower inlet water temperatures
are 50° C and 80° C. Figures 2-5 a-b show the rate of entropy generation in the diffusion
tower for Th=50° C and 80° C, respectively. Again the second law of thermodynamics is
30
satisfied for the entire parametric range considered. The entropy generation tends to be
lower for lower air to feed water flow ratios under the same exit brine temperature and
has the maximum value with a certain exit brine temperature under the same air to feed
water mass flow ratio. At higher air to feed water flow ratios, the constraint is that the
brine temperature must be higher than the air inlet temperature.
20 25 30 35 40 45 50
20
30
40
50
0.250.50.7511.251.51.7522.252.5
(a)Th = 50 C
η=ma/mL1
increase η
Exit Air Temperature T4 (C)
Exi
t Brin
e T
empe
ratu
re T
2 (C
)
20 30 40 50 60 70 80
20
30
40
50
60
70
80
0.250.50.7511.251.51.7522.252.5
increase η
(b)Th = 80 C
η=ma/mL1
Exit Air Temperature T4 (C)
Exi
t Brin
e T
empe
ratu
re T
2 (C
)
Figure 2-6 Variation of exit brine temperature with exit air temperature: a) Th=50° C, b)
Th=80° C
31
Figure 2-6 a-b shows the range of possible exit brine temperatures and exit air
temperatures for different air to feed water flow ratios when the diffusion tower inlet
water temperature is 50° C and 80° C, respectively. The maximum fresh water production
will occur with as high an exit air temperature as possible. For the energy balance on the
diffusion tower, the exit brine temperature decreases with increasing exit air temperature
and the rate of brine temperature decrease increases with increasing air to feed water
mass flow ratio. In contrast to the case with no heating, the exit air temperature is
primarily constrained by the fact that the brine cannot be cooler than the inlet air,
especially at higher air to feed water flow ratios. At very low air to feed water flow ratios,
the exit air temperature is constrained by the inlet water temperature when Th is 50° C,
meanwhile it is constrained by the fact that entropy generation must be positive when Th
is 80° C.
For respective diffusion tower inlet water temperatures of 50° C and 80° C, Figures
2-7 a-b show the ratio of fresh water production efficiency as a function of the exit air
temperature for different air to feed water flow ratios. It is observed that the fresh water
production efficiency increases with increasing exit air temperature and increasing air to
feed water flow ratio. The maximum fresh water production efficiency for Th=50° C is
approximately 0.045 when air to feed water flow ratio is 1, while that for Th=80° C is
approximately 0.1 when air to feed water flow ratio is 0.75. Therefore, one advantage of
increasing the diffusion tower inlet water temperature is that the fresh water production
efficiency increases.
32
Exit Air Temperature T4 (C)
20 25 30 35 40 45 50
Fre
sh W
ater
to F
eed
Wat
er R
atio
(m
f/mL1
)
0.00
0.01
0.02
0.03
0.04
0.05
0.250.50.7511.251.51.7522.252.5
(a)Th = 50 C
η=ma/mL1
increase η
Exit Air Temperature T4 (C)
20 30 40 50 60 70 80
Fre
sh W
ater
to F
eed
Wat
er R
atio
(m
f/mL1
)
0.00
0.02
0.04
0.06
0.08
0.10
0.250.50.7511.251.51.7522.252.5
(b)Th = 80 C
η=ma/mL1
increase η
Figure 2-7 Fresh water production efficiency: a) Th=50° C, b) Th=80° C
For respective diffusion tower inlet water temperatures of 50° C and 80° C, Figures
2-8 a-b show the thermal energy consumed per unit of fresh water production as a
function of exit air temperature for different air to feed water flow ratios over the entire
parameter space considered. Although, details of the low energy consumption regime are
difficult to discern, it is interesting to observe that increasing both the exit air temperature
and the air to feed water mass flow ratio results in a reduced rate of energy consumption.
33
20 25 30 35 40 45 500
5
10
15
20
25
30
0.250.50.7511.251.51.7522.252.5
increase η
(a)Th = 50 C
η=ma/mL1
Exit Air Temperature T4 (C)
Rat
e of
Ene
rgy
Con
sum
ptio
n (k
W-h
r/kg
fw)
20 30 40 50 60 70 80
Rat
e of
Ene
rgy
Con
sum
ptio
n (k
W-h
r/kg
fw)
0
10
20
30
40
50
60
0.250.50.7511.251.51.7522.252.5
(b)Th = 80 C
η=ma/mL1
increase η
Exit Air Temperature T4 (C) Figure 2-8 Rate of energy consumption: a) Th=50° C, b) Th=80° C
In order to explore the lower energy consumption regime Figure 2-9 has been
prepared for diffusion tower inlet water temperatures of 50° C, 60° C, 70° C, and 80° C.
It shows the lowest energy consumed per unit of fresh water production as a function of
different air to feed water flow ratios for different Th. Obviously there exists a minimum
at a certain air to feed water mass flow ratio for every Th. For Th=50°C the minimum rate
of energy consumption is about 0.56 kW-h/kgfw when the air to water mass flow ratio is
34
1, while that for Th=80° C is approximately 0.65 kWh/kgfw when the air to water mass
flow ratio is 0.5. The results also indicate that the minimum rate of energy consumption
will occur with lower air to feed water mass flow ratio when Th is higher.
Air to Feed Water Mass Flow Ratio η
0.5 1.0 1.5 2.0 2.5
0.6
0.8
1.0
1.2
1.4
50607080
Rat
e of
Ene
rgy
Con
sum
ptio
n (k
W-h
r/kg
fw)
Th (C)
increase Th
Figure 2-9 Minimum rate of energy consumption for different Th
In this analysis the energy consumption due to pumping is neglected, however, it is
another important aspect of the energy consumption required for the system. It is
especially important when the driving energy of the system is considered to be the waste
heat where the electricity consumption of the pumps and blowers will be considered the
only energy cost of the fresh water production. Therefore, a dynamic simulation model
must be developed to deduce the required pumping power for the DDD process.
35
CHAPTER 3 EXPERIMENTAL STUDY
A laboratory scale DDD facility will be used to (a) measure the thermal and mass
transport properties within the diffusion tower and direct contact condenser, (b) measure
the fresh water production rate for different inlet thermal and flow conditions, and (c)
measure the associated energy consumption required to heat the feed water and pump
water and air through the facility. These data will be used to validate the numerical model
that will simulate the DDD process. Measurements will be made over a wide range of
operating conditions in order to find an optimum condition where fresh water production
is maximized with low energy consumption.
Experimental System Description
Fig. 3-1 shows a pictorial view of the laboratory scale DDD system. Fig. 3-2 shows
a schematic diagram of the experimental facility. The main feed water, which simulates
the seawater, is drawn from one municipal water line. The feed water initially passes
through a vane type flowmeter and then enters a preheater that is capable of raising the
feed water temperature to 50° C. The feed water then flows through the main heater,
which can raise its temperature to saturated conditions. The feed water temperature is
controlled with a PID feedback temperature controller where the water temperature is
measured at the outlet of the main heater. The feed water is then sent to the top of the
diffusion tower, where it is sprayed over the top of the packing material and gravitates
downward. The portion of water that is not evaporated is collected at the bottom of the
diffusion tower in a sump and discharged through a drain. The temperature of the
36
discharge water is measured with a thermocouple. Strain gauge type pressure transducers
are mounted at the bottom and top of the diffusion tower to measure the static pressure. A
magnetic reluctance differential pressure transducer is used to measure the pressure drop
across the length of the packing material.
Air Heating Section
Diffusion Tower
Co-current Stage
Countercurrent Stage
Figure 3-1 Pictorial view of the laboratory scale DDD experiment
Dry air is drawn into a centrifugal blower equipped with a 1.11 kW motor. The
discharge air from the blower flows through a 10.2 cm inner diameter PVC duct in which
a thermal air flowmeter is inserted. The air flow rate is controlled by varying the speed of
the blower. A three-phase autotransformer is used to control the voltage to the motor and
therefore regulate the speed. Downstream of the air flowmeter the inlet temperature and
relative humidity of the air are measured with a thermocouple and a resistance type
humidity gauge. The air is forced through the packing material in the diffusion tower and
discharges through an aluminum duct at the top of the diffusion tower. At the top of the
tower, the temperature and humidity of the discharge air are measured in the same
manner as at the inlet.
37
Figure 3-2 Schematic diagram of laboratory scale DDD facility
The condenser is designed to with two stages in a twin tower structure. The main
feed water, which simulates the cold fresh water, is drawn from another municipal water
line. The feed fresh water is separated into two waterlines and passes through two
different turbine flowmeters. After the fresh water temperature is measured by a
thermocouple at the inlet of the condenser tower, it is sprayed from the top of each tower.
The air drawn by the centrifugal blower flows out of the top of the diffusion tower
with an elevated temperature and absolute humidity. It then flows into the first stage of
the direct contact condenser, which is also called the co-current flow stage. Here, the cold
fresh water and hot saturated air will have heat and mass exchange as they both flow to
38
the bottom of this tower. The twin towers are connected by two PVC elbows where the
temperature and relative humidity of air are measured by a thermocouple and a resistance
type humidity gauge. The air is then drawn into the bottom of the second stage of the
condenser. Because the fresh water is sprayed from the top and the wet air comes from
the bottom, this stage of the condenser is denoted as the countercurrent flow stage. The
air will continue being cooled down and dehumidified by the cold fresh water until it is
discharged at the top of the second stage. At the outlet, the temperature and humidity of
the discharge air are measured in the same manner as at the inlet.
The water sprayed on top of the condenser gravitates toward the bottom. The
portion of the water condensate from the vapor is collected together with the initial inlet
cold fresh water at the bottom of the twin towers and discharged through a drain. The
temperature of the discharge water is measured with a thermocouple.
There is one optional component of the condenser, the packing materials. Whether
or not it is required depends on the condensation effectiveness yielded by the direct
contact condenser.
Experimental Facility and Instrumentation
A CAD design for the diffusion tower is shown in Fig. 3-3. The diffusion tower
consists of three main components: a top chamber containing the air plenum and spray
distributor, the main body containing the packing material, and the bottom chamber
containing the air distributor and water drain. The top and bottom chambers are
constructed from 25.4 cm (10” nominal) ID PVC pipe and the main body is constructed
from 24.1 cm ID acrylic tubing with wall thickness of 0.64 cm. The three sections are
connected via PVC bolted flanges. The transparent main body accommodates up to 1 m
of packing material along the length.
39
Figure 3-3 Schematic diagram of experimental diffusion tower
A CAD design of the direct contact condenser is shown in Fig. 3-4. The condenser
includes two towers. Each tower consists of two main components: a top chamber
containing the air plenum, spray distributor and packing material, and a bottom chamber
containing the packing material and water drain. The top chamber is constructed from
25.4 cm (10” nominal) ID acrylic tubing and the bottom chamber is constructed from
25.1 cm ID PVC pipe. The two sections are connected via PVC bolted flanges. The
transparent body accommodates up to 50 cm of packing material along the length. The
40
two towers are connected by two 25.4 cm (10” nominal) ID PVC elbows which provide
sufficient space for both holding drain water and providing an air flow channel.
Figure 3-4 Schematic diagram of experimental direct contact condenser
The water distributors for the entire experimental system consist of 3 full cone
standard spray nozzles manufactured by Allspray. Each nozzle maintains a uniform cone
angle of 60°. The nozzle is designed to allow a water capacity of about 14.7 lpm, and it is
placed more than 30 cm away from the packing material in the diffusion tower and
41
condenser to ensure that the spray covers the entire desired area. The spray nozzle
pictured in Fig. 3-5 is a one-piece construction machined from brass bar stock.
Figure 3-5 Pictorial view of spray nozzle
The pre-heater used for the present experiment is a 240 V point source water
heater. It possesses a self-contained temperature controller and can deliver water outlet
temperatures ranging from 30 to 50° C.
The main heater consists of two 3 kW electric coil heaters wrapped around a copper
pipe through which the feed water flows. The power to the heaters is controlled with two
PID feedback temperature controllers with a 240 V output. The feedback temperature to
the controllers is supplied with a type-J thermocouple inserted in the feed water flow at
the discharge of the heater.
The packing material used in the experiments is HD Q-PAC manufactured by
Lantec and is shown pictorially in Fig. 3-6. The HD Q-PAC, constructed from
polyethylene, was specially cut using a hotwire so that it fits tightly into the main body of
the diffusion tower and condenser. The specific area of the packing is 267 m2/m3 and its
effective diameter for modeling purposes is 17 mm.
42
Figure 3-6 Pictorial view of packing matrix
Figure 3-7 Schematic diagram of the instrumentation system for the DDD experiment
43
The instrumentation system layout is shown in Fig. 3-7. The vane-type water mass
flowmeter, constructed by Erdco Corporation, has a range of 1.5-15.14 lpm. It has been
calibrated using the catch and weigh method. The flowmeter has a 4-20 mA output that is
proportional to the flow rate and has an uncertainty of ±2.21×10-2 kg/m2-s for the water
inlet mass flux.
The turbine water flowmeters, constructed by Proteus Industries Inc., have a range
of 1.5-12 gpm. They are also calibrated using the catch and weigh method. These
flowmeters have a 0-20 mA or 0-5 V output that is proportional to the flow rate, and the
measurement uncertainty is ±3.45×10-2 kg/m2-s for the water inlet mass flux.
The air flow rate is measured with a model 620S smart insertion thermal air
flowmeter. The flowmeter has a response time of 200 ms with changes in air mass flow
rate. The air flowmeter has a microprocessor-based transmitter that provides a 0-10 V
output signal. The air flowmeter electronics are mounted in a NEMA 4X housing. The
meter range is 0-1125 SCFM of air. The measurement uncertainty is ±5.92×10-3 kg/m2-s
for the air inlet mass flux at 101.3 kPa, 20° C, and 0% relative humidity.
The relative humidity is measured with 4 duct-mounted HMD70Y resistance-type
humidity and temperature transmitters manufactured by Vaisala Corp. The humidity and
temperature transmitters have a 0-10 V output signal and have been factory calibrated.
The measurement uncertainty is ±1.185×10-3 for the absolute humidity.
All temperature measurements used in the thermal analysis are measured with type-
E thermocouples with an estimated uncertainty of ±0.2° C..
The pressures at the inlet and exit of the diffusion tower are measured with two
Validyne P2 static pressure transducers. All of the wetted parts are constructed with
44
stainless steel. The transducers have an operating range of 0-0.34 atm (0-5 psi) and have
a 0-5 V proportional output. The transducers have an accuracy of 0.25% of full scale.
They are shock resistant and operate in environments ranging in temperature from –20°
to 80° C.
The pressure drop across the test section is measured with a DP15 magnetic
reluctance differential pressure transducer. The pressure transducer signal is conditioned
with a Validyne carrier demodulator. The carrier demodulator produces a 0-10 VDC
output signal that is proportional to the differential pressure. The measurement
uncertainty is ± 0.25% of full scale.
Figure 3-8 Example program of SoftWIRE
A digital data acquisition facility has been developed for measuring the output of
the instrumentation on the experimental facility. The data acquisition system consists of a
16-bit analog to digital converter and a multiplexer card with programmable gain
manufactured by Computer Boards calibrated for type E thermocouples and 0-10V input
45
ranges. A software package, SoftWIRE, which operates in conjunction with Microsoft
Visual Basic, allows a user defined graphical interface to be specified specifically for the
experiment. SoftWIRE also allows the data to be immediately sent to an Excel
spreadsheet. An example program layout using SoftWIRE is shown in Fig. 3-8.
The experimental data acquisition system is designed using the Virtual
Instrumentation module. The control and observation panels are shown in Figs. 3-9 – 3-
11. On the “Main” panel, shown in Fig. 3-9, there is a switch button to begin or stop the
data acquisition program. Once the program begins, the experimental data will be
recorded in a database file. The file’s name, destination and recording frequency can be
defined on this panel. Also, all of the experimental measurements are displayed here in
real time.
Figure 3-9 “Main” panel of the DDD data acquisition program
46
This program also supplies the schematic view panels for the diffusion tower and
direct contact condenser, shown in Fig. 3-10. It shows the position and values of all the
measurements from the experimental facility so that the operator can easily control the
fresh water production.
Figure 3-10 “Schematic view” panels of the DDD data acquisition program
Because the current research investigation focuses on steady-state operation it is
important to know when the physical processes have reached steady-state. The
“Histogram View” panels, shown in Fig. 3-11, are used to display the measurement
variations with time. The x-axis is the time coordinate and y-axis displays the
measurement value. The measurement range shown on the y-axis can be changed
manually at any time during the experiment to accurately observe the parametric trend.
Figure 3-11 “Histogram view” panels of the DDD data acquisition program
47
Experimental measurements were taken at steady state conditions. Data were
automatically recorded with a frequency of 1 Hz.
48
CHAPTER 4 HEAT AND MASS TRANSFER FOR THE DIFFUSION TOWER
The diffusion tower is one of the most important heat and mass transfer devices in
the DDD process. An appropriately designed DDD fresh water production plant requires
a detailed heat and mass transfer analysis of the diffusion tower and direct contact
condenser. This chapter will focus on the evaporative heat and mass transfer analyses
required to design and analyze the diffusion tower.
The evaporation of feed water in the diffusion tower, shown in Fig. 4-1, is achieved
by spraying heated feed water on top of a packed bed and blowing the dry air
countercurrently through the bed. The falling liquid will form a thin film over the packing
material while in contact with the low humidity turbulent air stream. Heat and mass
transfer principles govern the evaporation of the water and the humidification of the air
stream. When the system is operating at design conditions, the exit air stream humidity
ratio should be as high as possible. The ideal state of the exit air/vapor stream from the
diffusion tower is saturated.
Heat and Mass Transfer Model for the Diffusion Tower
The most widely used model to estimate the heat and mass transfer associated with
air/water evaporating systems is that due to Merkel [23], which is used to analyze cooling
towers. However Merkel’s analysis contains two restrictive assumptions,
1. On the water side, the mass loss by evaporation of water is negligible and
2. The Lewis number ( vv DLe α= , which is a measure of the ratio between
characteristic lengths for thermal and mass diffusion) is unity.
49
Heated feed water inlet
Air/vapor plenum
High surface area packing
Dry air inlet
Suction line to brine pump
Figure 4-1 Diagram of diffusion tower
Merkel’s analysis is known to under-predict the required cooling tower volume and
is not useful for the current analysis since the purpose of the diffusion tower is to
maximize the evaporation of water for desalination. Baker and Shryock [24] have
presented a detailed analysis of Merkel’s original work and have elucidated the error
contributed from each specific assumption in Merkel’s model. Sutherland [25] developed
an analysis that includes water loss by evaporation but ignores the interfacial temperature
between the liquid and air. Osterle [26] assumed that air is saturated throughout the
whole process, Lewis number is unity, and air in contact with the liquid film is saturated
50
at the water temperature. El-Dessouky et al. [27] have presented improved analyses for
counter flow cooling towers, yet they assumed the available interfacial area for heat
transfer is the same as that for mass transfer, which is only true when the packing is
thoroughly wetted and is rare. An empirical enthalpy equation is used for the air/vapor
mixture and is only valid for temperatures between 10-50° C. The present model does not
require any of the assumptions used in prior works. The current model includes the
evaporation of water, the interfacial heat resistance between water and air, and the
different interfacial areas for heat transfer and mass transfer.
Packing material
Liquid
Gas/Vapor
z
z+dz
ma+mv
mL
dmv evap
dq
Figure 4-2 Differential control volume for liquid/vapor heat and mass transfer within diffusion tower
The current formulation is based on a two-fluid film model for a packed bed in
which conservation equations for mass and energy are applied to a differential control
volume shown in Figure 4-2. In this Figure, there is a clear interface between liquid film
and gas side. And because the gas is blown from bottom to top of the packed bed, the z-
axis denotes the axial direction through the packed bed. The conservation of mass applied
to the liquid phase of the control volume in Fig. 4-2 results in,
51
)()( ,, evapVzL mdz
dm
dz
d = . (4.1)
where m is the mass flow rate, the subscript L, v, and evap denotes the liquid, vapor, and
the portion of liquid evaporated respectively. Likewise, the conservation of mass applied
to the gas (air/vapor mixture) side is expressed as,
)()( ,, evapvzv mdz
dm
dz
d = . (4.2)
For an air/vapor mixture the humidity ratio, ω, is related to the relative humidity,
Φ, through,
)(
)(622.0
asat
asat
a
v
TPP
TP
m
m
Φ−Φ
==ω , (4.3)
where P is the total system pressure and Psat(Ta) is the water saturation pressure
corresponding to the air temperature Ta. It is assumed the total system pressure is
constant. It is noted that the pressure drop is on the order of 100 Pa, which is a fraction of
a percent of the absolute pressure. Using the definition of the mass transfer coefficient
applied to the differential control volume and considering the interfacial area for mass
transfer may differ from that of heat transfer, then,
ATTakmdz
davLsatvwGevapv )]()([)( ,,, ∞−= ρρ . (4.4)
Applying the perfect gas law [28] to the vapor, the gradient of the evaporation rate
is expressed as,
AT
TP
T
TP
R
Makm
dz
d
a
asat
i
isatvwGevapv )
)()(()( ,
Φ−= , (4.5)
where Gk is the mass transfer coefficient on gas side, a is the specific area of packing,
which is defined as the total surface area of the packing per unit volume of space
52
occupied, wa is the wetted specific area, vM is the vapor molecular weight, R is the
universal gas constant, Ti is the liquid/vapor interfacial temperature and A is the cross
sectional area of the diffusion tower. Combining Eqs. (4.2), (4.3) & (4.5) the gradient of
the humidity ratio in the diffusion tower is expressed as,
)622.0
)((
ai
isatvwG
T
P
T
TP
R
M
G
ak
dz
d
ωωω
+−= , (4.6)
where G = Ama is the air mass flux. Equation (4.6) is a first order ordinary differential
equation with dependent variable, ω, and when solved yields the variation of humidity
ratio along the height of the diffusion tower.
In order to evaluate the liquid/vapor interfacial temperature, it is recognized that the
energy convected from the liquid is the same as that convected to the gas,
)()( aiGiLL TTUTTU −=− , (4.7)
where UL and UG are the respective liquid and gas heat transfer coefficients, and the
interfacial temperature is evaluated from,
L
G
aL
GL
i
UU
TUUT
T+
+=
1. (4.8)
In general the liquid side heat transfer coefficient is much greater than that on the
gas side, thus the interfacial temperature is only slightly less than that of the liquid. The
conservation of energy applied to the liquid phase of the control volume yields,
ATTUahdz
mdhm
dz
daLFg
evapvLL )(
)()( , −+= , (4.9)
53
where U is the overall heat transfer coefficient, h is the enthalpy, and hFg is the latent
heat. Noting that LLL dTCpdh = , dz
dhm
dz
dmhhm
dz
d LL
LLLL +=)( and combining with
Eqs. (4.9) & (4.1) results in an expression for the gradient of water temperature in the
diffusion tower,
LCp
TTUa
Cp
hh
dz
d
L
G
dz
dT
L
aL
L
LFgL )()( −+
−= ω
, (4.10)
where L= AmL is the water mass flux. Equation (4.10) is also a first order ordinary
differential equation with TL being the dependent variable and when solved yields the
water temperature distribution through the diffusion tower.
The conservation of energy applied to the air/vapor mixture of the control volume
yields,
ATTUahdz
mdhmhm
dz
daLFg
evapvvvaa )(
)()( , −−=++− . (4.11)
Noting that the specific heat of the air/vapor mixture is evaluated as,
vva
va
va
aG Cp
mm
mCp
mm
mCp
++
+= , (4.12)
and the latent heat of vaporization is evaluated as,
)()()( aLavaFg ThThTh −= , (4.13)
combining with Eqs. (4.11) & (4.2) yields the gradient of air temperature in the diffusion
tower,
)1(
)()(
1
1
ωω
ω +−
++
−=GCp
TTUa
Cp
Th
dz
d
dz
dT
G
aL
G
aLa . (4.14)
54
Equation (4.14) is also a first order ordinary differential equation with Ta being the
dependent variable and when solved yields the air/vapor mixture temperature distribution
along the height of the diffusion tower. Equations (4.6), (4.10), and (4.14) comprise a set
of coupled ordinary differential equations that are used to solve for the humidity ratio,
water temperature, and air/vapor mixture temperature distributions along the height of the
diffusion tower. However, since a one-dimensional formulation is used, these equations
require closure relationships. Specifically, the overall heat transfer coefficient and the gas
side mass transfer coefficient are required. A significant difficulty that has been
encountered in this analysis is that correlations for the water and air/vapor heat transfer
coefficients for film flow though a packed bed, available in the open literature (McAdams
et al. [29] and Huang and Fair [30]), are presented in dimensional form. Such correlations
are not useful for the present analysis since a structured matrix type packing material is
utilized, and the assumption employed to evaluate those heat transfer coefficients are
questionable. In order to overcome this difficulty the mass transfer coefficients are
evaluated for the liquid and gas flow using a widely tested correlation and a heat and
mass transfer analogy is used to evaluate the heat transfer coefficients. This overcomes
the difficulty that gas and liquid heat transfer coefficients cannot be directly measured
because the interfacial film temperature is not known.
The mass transfer coefficients associated with film flow in packed beds have been
widely investigated. The most widely used and perhaps most reliable correlation is that
proposed by Onda et al. [31]. Onda’s correlation, shown in Appendix A, is used to
calculate the mass transfer coefficients in the diffusion tower, kG and kL. However, it was
55
found that Onda’s correlation under-predicted the wetted specific area of the packing
material. Therefore, a correction was made as follows,
−−= − 5/105.02/1
4/3
Re2.2exp1 LLLAL
cw WeFraa
σσ
, (4.15)
see Appendix A for details.
As mentioned previously, the heat and mass transfer analogy [32] is used to
compute the heat transfer coefficients for the liquid side and the gas side. Therefore the
heat transfer coefficients are computed as follows,
Heat transfer coefficient on the liquid side
2/12/1Pr L
L
L
L
Sc
ShNu = , (4.16)
2/1)(L
LPLLLL D
KCkU ρ= , (4.17)
Heat transfer coefficient on the gas side
3/13/1Pr G
G
G
G
Sc
ShNu= , (4.18)
3/23/1 )()(G
GPGGGG D
KCkU ρ= , (4.19)
Overall heat transfer coefficient
111 )( −−− += GL UUU , (4.20)
where K denotes thermal conductivity and D denotes the molecular diffusion coefficient.
In order to test the proposed heat and mass transfer model, consideration is first
given to the cooling data of Huang [33]. Using the analysis presented above, the exit
56
water temperature, exit air temperature and exit humidity ratio are computed using the
following procedure:
1. Specify the water mass flux, air mass flux, water inlet temperature, air inlet temperature and inlet humidity ratio;
2. Guess the exit water temperature;
3. Compute the temperature and humidity distributions through the packed bed using Eqs. (4.6), (4.10), and (4.14) until z reaches the packed bed height used in the experiment;
4. Check whether the predicted inlet water temperature agrees with the specified inlet water temperature, and stop the computation if agreement is found, otherwise repeat the procedure from step 2.
A comparison between the measured exit water temperature, exit air temperature
and exit humidity ratio reported by Huang [33] with those computed using the current
model are shown in Figs. 4-3 a-b for 2.54 cm pall ring packing. As seen in the figures the
comparison is generally good. The exit air temperature and exit water temperature are
slightly over-predicted. The exit humidity ratio prediction is excellent.
Air Mass Flux G (kg/m2-s)
0.6 0.8 1.0 1.2
Tem
per
atu
re T
(C
)
0
10
20
30
40
50
Hu
mid
ity
0.00
0.05
0.10
0.15
0.20
0.25
L = 2.0 kg/m2-sPredicted Measured
(a)
Ta,outTL,outωωωωout
Ta,outTL,outωωωωout
Figure 4-3 Comparison of predicted exit conditions with the data of Huang [33]: a) L = 2.0 kg/m2-s, b) L = 4.1 kg/m2-s
57
Air Mass Flux G (kg/m2-s)
0.6 0.8 1.0 1.2 1.4 1.6
Tem
per
atu
re T
(C
)
0
10
20
30
40
50
Hum
idit
y
0.00
0.05
0.10
0.15
0.20
0.25
L = 4.1 kg/m2-sPredicted Measured
(b)
Ta,outTL,outωωωωout
Ta,outTL,outωωωωout
Figure 4-3 Continued
Model Comparison with Experiments for the Diffusion Tower
Heat and mass transfer experiments were carried out in the diffusion tower with a
packed bed height of 20 cm. The liquid mass flux was fixed at 1.75, 1.3 and 0.9 kg/m2-s
and the air mass flux was varied from about 0.6-2.2 kg/m2-s. The inlet air temperature
was about 23° C while the inlet water temperature was 60° C. The experiments were
repeated to verify the repeatability of the results. The measured exit humidity, exit air
temperature, and exit water temperature are compared with those predicted with the
model for all three different liquid mass fluxes in Figs. 4-4 a-c. It is observed that the
repeatability of the experiments is excellent. The exit water temperature, exit air
temperature and exit humidity ratio all decrease with increasing air mass flux for a certain
water mass flux. The comparison between the predicted and measured exit water
temperature and exit humidity ratio agreed very well, and the exit air temperature is
58
slightly over predicted. Detailed experimental data associated with Figs. 4-4 a-c are
tabulated in Appendix B.
Air Mass Flux G (kg/m2-s)
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Tem
per
atu
re T
(C
)
0
10
20
30
40
50
Hu
mid
ity
0.00
0.05
0.10
0.15
0.20
0.25
L=1.75 kg/m2-sPredicted Measured Set 1 Set 2
Ta,outTL,outωωωωout
(a)
Ta,outTL,outωωωωout
Air Mass Flux G (kg/m2-s)
0.6 0.8 1.0 1.2 1.4 1.6
Tem
per
atu
re T
(C
)
0
10
20
30
40
50
Hu
mid
ity
0.00
0.05
0.10
0.15
0.20
0.25
L=1.3 kg/m2-sPredicted Measured Set 1 Set 2
Ta,outTL,outωωωωout
(b)
Ta,outTL,outωωωωout
Figure 4-4 Comparison of predicted exit conditions with the experimental data for different liquid mass fluxes: a) L= 1.75 kg/m2-s, b) L= 1.3 kg/m2-s, c) L= 0.9 kg/m2-s
59
Air Mass Flux G (kg/m2-s)
0.7 0.8 0.9 1.0 1.1 1.2 1.3
Tem
per
atu
re T
(C
)
0
10
20
30
40
50
Hu
mid
ity
0.00
0.05
0.10
0.15
0.20
0.25
L=0.9 kg/m2-sPredicted Measured Set 1 Set 2
Ta,outTL,outωωωωout
(c)
Ta,outTL,outωωωωout
Figure 4-4 Continued
In general, the analytical model proves to be quite satisfactory in predicting the
evaporative heat and mass transfer of counter flow packed beds. The excellent agreement
of the model with the measured exit water temperature and exit humidity ratio is most
important for desalination and water-cooling applications. A rigorous set of conservation
equations have been developed for a two-fluid model and mass transfer closure has been
achieved using a widely tested empirical correlation, while heat transfer closure has been
achieved by recognizing the analogous behavior between heat and mass transfer. The
model does not require questionable assumptions that have plagued prior analyses. It is
believed that the current model will be very useful to both designers of diffusion towers
for desalination applications as well as designers of cooling towers for heat transfer
applications.
60
Pressure Drop through the Packing Material
The pressure drop through the packing material on the air side influences the
energy consumption prediction of the DDD process. Therefore experiments considering
the air pressure drop with water loading is another important objective in the research.
This experiment is executed without heating the water. The comparison of the predicted
pressure drop and the experimental data are shown below in Fig. 4-5 for different water
mass flux loadings. Detailed experimental data associated with Figs. 4-5 are tabulated in
Appendix C.
Air mass flux (kg/m2-s)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Spe
cific
air
pres
sure
dro
p (P
a/m
)
0
20
40
60
80
100
Data Model
0.8
1.7
2.0
Water mass flux (kg/m2-s)
Figure 4-5 Air specific pressure drop variation with air mass flux for different water mass fluxes
The pressure drop is predicted using the empirical correlation specified by the
manufacturer of the packing material. Figure 4-5 clearly shows that the pressure drop
correlation is accurate for HD Q-Pac packing material. An interesting feature of the data
is that the air specific pressure drop increases with increasing water mass flow rate under
the same air mass flow rate.
61
The air side dimensional pressure drop correlation specified by the manufacturer of
the HD Q-Pac packing material is,
)10176.1654.01054.3( 4244252GGLLGG vvvv
z
P ρρ ×++×=∆ − , (4.21)
where z is the height of the packing material (m), P∆ is the pressure drop through the
packing (Pa), Gρ is the gas density (kg/m3), Gv is the superficial gas velocity through the
packing (m/s), and Lv is the superficial liquid velocity through the packing (m/s).
Optimization of the Packing Material
Optimization of the Diffusion Driven Desalination system includes two major
objectives,
1. For a specified packing material, find the optimal operating conditions to maximize the fresh water production rate with low energy consumption rate.
2. For a specified operating condition, find the optimal packing material to maximize the fresh water production rate with low energy consumption rate.
The mathematic model developed in this chapter can be used for the diffusion
tower analysis and design, as well as optimization of the packing material used for the
diffusion tower. Energy consumption due to pumping power required for the pumps and
blowers is considered in the analysis. Since the thermal energy is assumed to be waste
heat and free, it is not considered. The flow resistance for packing material is an
important feature for the packing selection. It is also well understood that large contact
surface area between water and air can enhance the heat and mass transfer within packed
beds. However, the packing materials with large surface area usually have high flow
resistance because of the narrow flow passages between the packing units. The optimal
packing material will balance these two competitive factors for a specified operating
62
condition to yield the best performance from the diffusion tower. Two different types of
optimal packing materials have been found in this analysis,
1. The packing material that can minimize the tower height for specified operating conditions. This kind of packing material will directly reduce the facility construction cost.
2. The packing material that can minimize the energy consumption rate of fresh water production for specified operating conditions. This kind of packing material has a long-term cost advantage.
The energy consumption rate on the water side is calculated as,
LL
LL PLA
gzmPw ∆==ρ
, (4.22)
where Pw (W) denotes the electrical power consumption, and the water side pressure
drop is assumed to be equivalent to the gravitational head loss which is given by,
gzP LL ρ=∆ . (4.23)
The energy consumption rate on the gas side is calculated as,
GG
GG
inaGGG P
GAP
mPVPw ∆=∆
+=∆=
ρρω )1(
, (4.24)
where GV is the gas volume flow rate.
The total energy consumption is calculated as,
GL PwPwPw += , (4.25)
The energy consumption rate per unit of fresh water production is defined as,
ff m
PwPw = , (4.26)
where fm is the ideal fresh water production rate from the diffusion tower and is defined
as,
)( inoutaf mm ωω −= . (4.27)
63
Combining above equations with the dynamic computational model of the diffusion
tower, the performance characteristics of a specified packing material can be explored,
such as the exit water/air temperature, exit humidity, air to feed water mass flow ratio,
packed bed height, fresh water production rate, pressure drop and energy consumption
rate. The comparison of these parameters for different packing materials will reveal the
optimal packing material for the diffusion tower. As an example, eight different types of
packing material are investigated. They can be categorized into 2 geometric shapes and 8
nominal sizes. Detailed information is listed in Table 4-1.
The frictional pressure drop of air through the packed bed depends on the size and
geometry of the packing material, and is calculated using Leva’s correlation [34] as,
G
La
G Ga
z
PL
ρρ
28
1 )10)(10(2
−=∆
. (4.28)
In this equation, a1 and a2 are the pressure drop constants for tower packing and are given
by Treybal [35].
Table 4-1 Packing material configurations
Packing Nominal size
(inch) Specific area (m2/m3)
Specific packing diameter (m)
0.5 470 0.01 0.75 280 0.017 1.0 250 0.019
Berl Saddle
1.5 144 0.033 0.5 394 0.012 1.0 190 0.024 1.5 118 0.039
Raschig Ring
2.0 94 0.05 The procedure used to identify the optimum packing material is as follows:
1. Specify water inlet temperature, TL,in, water mass flux, L, air to water mass flow ratio, ma/mL, air inlet temperature, Ta,in and inlet humidity ωin. Find the thermodynamic states of the air and water entering the diffusion tower and their states discharging from the diffusion tower for each packing material using Eqs. (4.6), (4.10) & (4.14),
64
2. Compute the required packed bed height in the diffusion tower for the specified operating conditions for each packing material,
3. Compute the water and gas side pressure drop through the packing material for each packing material using Eqs. (4.23) & (4.28),
4. Compute the energy consumption rate for each packing material using Eqs. (4.22), (4.24), (4.25) & (4.26),
5. Determine the optimal operating conditions for each packing material. Under these conditions, the energy consumption rate is minimized for this packing material.
6. Find the best packing material by comparing the optimum operating conditions for each packing.
For all the computations, the water inlet temperature TL,in, air inlet temperature Ta,in
and inlet humidity ωin, diameter of the diffusion tower d are fixed at 50° C, 15° C, 0.0107
and 15 m respectively. The water inlet mass flux L will vary from 0.5 kg/m2-s to 5 kg/m2-
s, meanwhile the air to water mass flow ratio (ma/mL) will vary from 0.3 to 1.5 for each
fixed water inlet mass flux.
For each type of packing material, Figures 4-6 a-h show the energy consumption
rates for different air to water mass flow ratios with varying fresh water production level.
Fresh water mass flow rate (kg/s)
10 20 30 40
Ene
rgy
cons
umpt
ion
rate
(kW
-hr/
kgfw
)
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.30.40.50.751.01.251.5
Berl Saddle 0.5"TL,in=50 CTa,in=15 C
ωin=0.0107
ma/mL
Figure 4-6 Energy consumption rate for fresh water production: Berl Saddle – a) 0.5”, b) 0.75”, c) 1.0”, d) 1.5”; Raschig Ring – e) 0.5”, h) 1.0”, g) 1.5”, h) 2.0”
65
Fresh water mass flow rate (kg/s)
10 20 30 40
Ene
rgy
cons
umpt
ion
rate
(kW
-hr/
kgfw
)
0.00
0.02
0.04
0.06
0.08
0.10
0.30.40.50.751.01.251.5
Berl Saddle 0.75"TL,in=50 CTa,in=15 C
ωin=0.0107
ma/mL
Fresh water mass flow rate (kg/s)
10 20 30 40
Ene
rgy
cons
umpt
ion
rate
(kW
-hr/
kgfw
)
0.00
0.02
0.04
0.06
0.08
0.30.40.50.751.01.251.5
Berl Saddle 1"TL,in=50 CTa,in=15 C
ωin=0.0107
ma/mL
Fresh water mass flow rate (kg/s)
10 20 30 40
Ene
rgy
cons
umpt
ion
rate
(kW
-hr/
kgfw
)
0.00
0.02
0.04
0.06
0.08
0.30.40.50.751.01.251.5
Berl Saddle 1.5"TL,in=50 CTa,in=15 C
ωin=0.0107
ma/mL
Figure 4-6 Continued
66
Fresh water mass flow rate (kg/s)
10 20 30 40
Ene
rgy
cons
umpt
ion
rate
(kW
-hr/
kgfw
)
0.0
0.2
0.4
0.6
0.30.40.50.751.01.251.5
Raschig Ring 0.5"TL,in=50 CTa,in=15 C
ωin=0.0107
ma/mL
Fresh water mass flow rate (kg/s)
10 20 30 40
Ene
rgy
cons
umpt
ion
rate
(kW
-hr/
kgfw
)
0.00
0.05
0.10
0.15
0.20
0.25
0.30.40.50.751.01.251.5
Raschig Ring 1"TL,in=50 CTa,in=15 C
ωin=0.0107
ma/mL
Fresh water mass flow rate (kg/s)
10 20 30 40
Ene
rgy
cons
umpt
ion
rate
(kW
-hr/
kgfw
)
0.00
0.05
0.10
0.15
0.20
0.30.40.50.751.01.251.5
Raschig Ring 1.5"TL,in=50 CTa,in=15 C
ωin=0.0107
ma/mL
Figure 4-6 Continued
67
Fresh water mass flow rate (kg/s)
10 20 30 40
Ene
rgy
cons
umpt
ion
rate
(kW
-hr/
kgfw
)
0.00
0.05
0.10
0.15
0.20
0.30.40.50.751.01.251.5
Raschig Ring 2"TL,in=50 CTa,in=15 C
ωin=0.0107
ma/mL
Figure 4-6 Continued Fig. 4-6 a-h clearly show that for each packing material, the energy consumption
rate is minimized for the same fresh water production rate when the air to water mass
flow ratio is 0.75. The air to water mass flow ratio of 0.75 will be maintained when
investigating the influence of other variables on the diffusion tower performance.
Feed water mass flux (kg/m2-s)
1 2 3 4 5
Max
imum
pos
sibl
e ex
it hu
mid
ity
0.00
0.02
0.04
0.06
0.08
0.10
Berl Saddle Raschig RingTL,in=50 CTa,in=15 C
ωin=0.0107ma/mL=0.75
0.5"1.0"1.5"2.0"
0.5"0.75"1.0"1.5"
Figure 4-7 Maximum possible exit humidity for feed water mass flux
68
Figure 4-7 shows the maximum possible exit humidity ratio for different packing
materials and varying water inlet mass flux with air to water mass flow ratio of 0.75. The
variation of the maximum possible exit humidity isn’t dependent on the water mass flux
or the packing material because the height of the packed bed will change to insure the
exit air is always saturated.
Figure 4-8 shows the gas side mass transfer coefficient for different packing
materials and varying air mass flux. For the same packing material, the gas mass transfer
coefficient increases with increasing the air mass flux. It also shows that the gas mass
transfer coefficient increases with increasing the specific area of the packing material.
Increasing the air mass flux will increase the shear on the air water interface, and
increasing the specific surface area of packing will increase the maximum possible
contact area between water and air. This may explain why large air mass flux and large
specific surface area can enhance the mass transfer rate.
Air mass flux (kg/m2-s)
0.5 1.0 1.5 2.0 2.5 3.0 3.5
Ave
rage
air
mas
s tr
ansf
er c
oeffi
cien
t (m
/s)
0.00
0.05
0.10
0.15
0.20
Berl Saddle Raschig RingTL,in=50 CTa,in=15 C
ωin=0.0107ma/mL=0.75
Increasing specific surface area of packing
0.5"0.75"1.0"1.5"
0.5"1.0"1.5"2.0"
Figure 4-8 Gas mass transfer coefficient for air mass flux
69
Figure 4-9 shows the air side pressure drop through the packed bed for different
packing materials and varying air mass flux. The air side pressure drop increases
substantially with increasing the air mass flux for some packing materials. It also shows
that the air pressure drop increases with the specific surface area of the packing materials
with the same geometric shape.
Air mass flux (kg/m2-s)
0.5 1.0 1.5 2.0 2.5 3.0 3.5
Air
side
pre
ssur
e dr
op (
Pa)
0
10000
20000
30000
40000
50000
60000
Berl Saddle Raschig RingTL,in=50 CTa,in=15 C
ωin=0.0107ma/mL=0.75
0.5"0.75"1.0"1.5"
0.5"1.0"1.5"2.0"
Figure 4-9 Gas pressure drop for air mass flux
Figure 4-10 shows the required packed bed height for different packing materials
with varying water inlet mass flux. The tower height is computed such that the maximum
possible humidity ratio leaves the diffusion tower. For each type of the packing material,
the required diffusion tower height increases with increasing the water inlet mass flux,
and the rate of increase decreases after the water inlet mass flux exceed about 1.5 kg/m2-
s. It also shows that under the same water mass flux, the required diffusion tower height
decreases almost proportionally with increasing the specific surface area of the packing
material. Considering Fig. 4-10 in conjunction with Fig. 4-7, it is obvious that Berl
70
Saddle 0.5” can minimize the tower height without decreasing fresh water production
rate, which implies that Berl Saddle 0.5” is the first type of optimal packing material of
the different packing materials considered.
Feed water mass flux (kg/m2-s)
1 2 3 4 5
Pac
ked
bed
heig
ht (
m)
0
1
2
3
4
5
6
Berl Saddle Raschig RingTL,in=50 CTa,in=15 C
ωin=0.0107ma/mL=0.75
Increasing specific surface area of packing
0.5"0.75"1.0"1.5"
0.5"1.0"1.5"2.0"
Figure 4-10 Required tower height for feed water mass flux
Figure 4-11 shows the energy consumption rate for each packing material with
varying water mass flux. The energy consumption rate increases with increasing the
water mass flux for the same packing material. It also shows that under the same water
inlet mass flux, the energy consumption rate increases with increasing air side pressure
drop. Although the air side pressure drop is far less than the water side pressure drop
through the packed bed, the volumetric flow rate of air is much higher than that of the
water. This may explain why the air side pressure drop has large influence on the total
energy consumption rate in the diffusion tower.
71
Feed water mass flux (kg/m2-s)
1 2 3 4 5
Ene
rgy
cons
umpt
ion
rate
(kW
-hr/
kgfw
)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
Berl Saddle Raschig RingTL,in=50 CTa,in=15 C
ωin=0.0107ma/mL=0.75
Increasing air side pressure drop
0.5"0.75"1.0"1.5"
0.5"1.0"1.5"2.0"
Figure 4-11 Energy consumption rate for feed water mass flux
Fresh water mass flow rate (kg/s)
5 10 15 20 25 30 35
En
ergy
con
sum
ptio
n ra
te (
kW-h
r/kg
fw)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Berl Saddle Raschig RingTL,in=50 CTa,in=15 C
ωin=0.0107ma/mL=0.75
Increasing air side pressure drop
0.5"1.0"1.5"2.0"
0.5"0.75"1.0"1.5"
Figure 4-12 Energy consumption rate for fresh water mass flow rate (cross section diameter of the packed bed is 15 m)
72
Figure 4-12 shows the energy consumption rate for each packing material with
varying fresh water production level. It clearly shows that under the same fresh water
production level, the total energy consumption rate is always minimized for Berl Saddle
1.5” since it has the lowest air side pressure drop shown in Fig. 4-9, which means Berl
Saddle 1.5” is the second type of optimal packing material for the diffusion tower in the
current analysis.
Finally, it can be concluded that for a specified operating condition and fresh water
production rate, using the packing materials with large specific surface area can help
reduce the tower height, and using the packing materials with low air side flow resistance
can help reduce the total energy consumption rate. However, it is noticed that the current
model cannot reveal the influence of the packing material geometric shape on the
diffusion tower performance since no parameter in the current model explicitly describes
the packing material shape.
73
CHAPTER 5 HEAT AND MASS TRANSFER FOR THE DIRECT CONTACT CONDENSER
In order for the DDD process to be cost effective, an efficient and low cost method
is required to condense water vapor out of the air stream. With a large fraction of the
air/vapor mixture being non-condensable, direct contact condensation is considerably
more effective than film condensation. Another important heat and mass transfer device
in the DDD process is the direct contact condenser. This chapter describes the
performance of droplet direct contact condenser and packed bed condenser for both co-
current and countercurrent flow.
While a significant amount of literature is available on droplet direct contact
condensation, considerably less information is available for packed bed direct contact
condensation. In analyzing direct contact condensation through packed beds, Jacobs et al.
[36] and Kunesh [37] used a volumetric heat transfer coefficient for the rate of convective
heat transport and penetration theory [38] to relate the heat and mass transfer coefficient.
The volumetric approach does not account for local variations in heat and mass transfer.
Penetration theory assumes the liquid behind the interface is stagnant, infinitely deep, and
the liquid phase resistance is controlling. As suggested by Jacobs et al. [36] these may or
may not be reasonable assumptions, depending on the liquid film condensate resistance.
Bharathan and Althof [39] and Bontozoglou and Karabelas [40] improved the analysis of
packed bed direct contact condensation by considering conservation of mass and energy
applied to a differential control volume. Local heat and mass transfer coefficients were
74
used. Both analyses relied on penetration theory to relate heat and mass transfer
coefficients.
The motivation for this work is to explore the heat and mass transfer process within
a direct contact condenser and develop a robust and reliable predictive model from
conservation principles that is useful for design and analysis. A fresh approach is used
that does not rely on penetration theory. One of the difficulties encountered is that the
interfacial temperature between the liquid and vapor cannot be directly measured, and
thus the liquid and vapor heat transfer coefficients cannot be directly measured.
Following the methodology used by Klausner et al. [41] for the evaporative heat and
mass transfer analysis, the extensively tested Onda [31] correlation was used to evaluate
the mass transfer coefficients on the liquid and gas side. A heat and mass transfer analogy
was applied to evaluate the liquid and gas heat transfer coefficients. Excellent results
were obtained, and a similar approach will be pursued here.
A laboratory scale direct contact condenser has been fabricated. The condenser is
constructed as a twin tower structure with two stages, co-current and countercurrent. The
performance of each stage has been evaluated over a range of flow and thermal
conditions. As expected, the countercurrent stage is significantly more effective than the
co-current stage. In addition, direct contact condensation within a packed bed is more
effective than droplet direct contact condensation. It is also found that the manner in
which the packing is wetted can significantly influence the heat and mass transfer
performance. Visual observations of the wetted packing have been made and a
discussion relating the wetting characteristics to the different empirical constants
suggested by Onda [31] is provided.
75
Mathematical Model of the Packed Bed Direct Contact Condenser
To explore the variation of temperature and humidity within the countercurrent
flow stage of the direct contact condenser, a physical model is developed for direct
contact condensation by considering that cold water is sprayed on top of a packed bed
while hot saturated air is blown through the bed from the bottom. The falling water is
captured on the packing surface and forms a thin film in contact with the saturated
turbulent air stream. Energy transport during the condensation process is accomplished
by a combination of convective heat transfer due to the temperature difference between
water and air and the latent heat transport due to vapor condensation. Mass and energy
conservation principles govern the condensation of the vapor and the dehumidification of
the air stream. Noting that the relative humidity of the air is practically unity during the
condensation process, the ideal state of the exit air/vapor temperature from the condenser
is close to the water inlet temperature.
A general approach for modeling the flow of water/air through a packed bed is to
consider flow through an array of round channels with both transverse and longitudinal
variations of temperature, pressure and humidity. This method was applied by Bemer
and Kalis [42] in predicting the pressure drop and liquid hold-up of random packed beds
consisting of ceramic Raschig rings and metal Pall rings. It was also used by Bravo et. al
[43, 44] for structured packing. Because the air flow through the packing is highly
turbulent, a 1/7th law variation of air temperature in the transverse direction can be
assumed [28] as,
7/1
,
, 1
−=−−
l
x
TT
TT
caL
xaL. (5.1)
76
where Ta,c is the centerline air temperature, TL is the bulk liquid temperature, l is the half
width of the hypothetical flow channel, and x is the transverse axis. Although the 1/7th
law profile may not be exact, it has proven to be robust in other channel and film flow
applications. The centerline air temperature is in terms of the respective bulk air and
liquid temperatures as,
( )LaLca TTTT −+= 224.1, . (5.2)
Eqn. (5.1) is used to evaluate the transverse distribution of air temperature. The local
absolute humidity ωx, based on local transverse air temperature Ta,x, is related to the
relative humidity Φ as,
)(
)(622.0
,
,
xasat
xasat
a
Vx TPP
TP
m
m
Φ−Φ
==ω , (5.3)
where P (kPa) is the total system pressure, and Psat (kPa) is the water saturation pressure
corresponding to the local air temperature Ta,x.
The area-averaged humidity ωm at any cross section is expressed as,
∫=l
xm xdxl 0
2
2 ωω , (5.4)
and the bulk humidity ω at any cross section is calculated from Eqn. (5.3) based on the
air bulk temperature Ta, which is a cross-sectional area-averaged value.
A careful examination of the area-averaged humidity and the bulk humidity
calculated at the same cross section shows that: for a given total system pressure P=101.3
kPa, the air bulk temperature Ta ≤ 75º C, and the bulk temperature difference between the
air and water |Ta-TL| ≤ 20º C, the relative difference of the area-averaged humidity and
the bulk humidity m
m
ωωω −
≤ 1.8%. It implies that replacing the area-averaged humidity
77
ωm with the bulk humidity ω to account for the transverse variation of air temperature
will only cause minimal error in predicting the heat and mass transfer within the packed
bed. Therefore, the air temperature non-uniformity in the transverse direction is
considered by using the bulk humidity in the current formulation. This observation
allows a one-dimensional treatment of the conservation equations to be used along the z-
direction with confidence.
The current formulation is based on a two-fluid film model in which one-
dimensional conservation equations for mass and energy are applied to a differential
control volume shown in Fig. 5-1a. In this figure, the air/vapor mixture is blown from
bottom to top (z-coordinate). Such an approach has been successfully used by Klausner
et al. [41] to model film evaporation in the diffusion tower.
Liquid Air/Vapor
G
ma+mv
L
mL
dz
z
z+dz dmv,cond
dq
(a) Countercurrent flow
Liquid Gas/Vapor
G
ma+mv
L
mL
z
z+dz
dmv,cond
dq
(b) Co-current flow
Figure 5-1 Differential control volume for liquid/gas heat and mass transfer within a)
countercurrent flow, b) co-current flow condensers
78
The conservation of mass applied to the liquid and vapor phases of the control
volume in Fig. 1a results in,
)()()( ,,, condvzLzv mdz
dm
dz
dm
dz
d −== , (5.5)
where m is the mass flow rate, the subscripts L, v, and cond denote the liquid, vapor, and
condensate respectively.
The conservation of energy applied to the liquid phase of the control volume yields,
ATTUahdz
mdhm
dz
daLFg
condvLL )(
)()( , −+−= , (5.6)
where U is the overall heat transfer coefficient and h is the enthalpy. Noting that
LLpL dTCdh = and combining with Eqs. (5.5) & (5.6) results in an expression for the
gradient of water temperature in the condenser,
LCp
TTUa
Cp
hh
dz
d
L
G
dz
dT
L
aL
L
LFgL )()( −+
−= ω
, (5.7)
where L is the water mass flux. Eqn. (7) is a first order ordinary differential equation
with TL being the dependent variable and when solved yields the water temperature
distribution through the condenser.
The conservation of energy applied to the air/vapor mixture of the control volume
yields,
ATTUaThdz
mdhmhm
dz
daLaFg
condvvvaa )()(
)()( , −−=−+− . (5.8)
Noting that the specific heat of the air/vapor mixture is evaluated as,
vpva
vPa
va
a
Gp Cmm
mC
mm
mC
++
+= , (5.9)
79
and combining with Eqs. (5.5) & (5.8) yields the gradient of air temperature in the
condenser,
)1(
)()(
1
1
ωω
ω +−
++
−=GCp
TTUa
Cp
Th
dz
d
dz
dT
G
aL
G
aLa . (5.10)
Equation (5.10) is another first order ordinary differential equation with Ta being
the dependent variable and when solved yields the air/vapor mixture temperature
distribution along z direction. Thus Eqs. (5.7) & (5.10) are solved simultaneously to
evaluate the temperature and humidity fields along the height of the condenser. Since a
one-dimensional formulation is used, these equations require closure relationships.
Specifically, the humidity gradient and the overall heat transfer coefficient are required.
The bulk humidity, ω, based on air temperature Ta, is related to the relative
humidity Φ and calculated from Eqn. (5.3). An empirical representation of the saturation
curve is,
( )32exp)( dTcTbTaTPsat +−= , (5.11)
where empirical constants are a=0.611379, b=0.0723669, c=2.78793×10-4,
d=6.76138×10-7, and T (° C) is the temperature.
Noting that the relative humidity of air remains approximately 100% during the
condensation process, the absolute humidity ω is only a function of air temperature Ta
when the total system pressure P remains constant. Differentiating Eqn. (5.3) with
respect to Ta and combining with Eqn. (5.11), the gradient of humidity can be expressed
as,
)32()(
2aam
asat
a dTcTbTPP
P
dz
dT
dz
d +−−
= ωω. (5.12)
80
Eqn. (5.12) is used to compute the humidity distribution through the condenser. Eqs.
(5.3) & (5.12) are used in the one-dimensional condensation model (Eqs. (5.7) & (5.10))
for closure.
Following the methodology of Klausner et al. [41], the mass transfer coefficients are
evaluated using a widely tested correlation and the heat transfer coefficients are evaluated
using a heat and mass transfer analogy for the liquid and gas. This approach overcomes
the difficulty that gas and liquid heat transfer coefficients cannot be directly measured
because the interfacial film temperature is not known. The mass transfer coefficients
associated with film flow in packed beds have been widely investigated. The most widely
used and perhaps most reliable correlation is that proposed by Onda et al. [31] as listed in
the Appendix.A. As mentioned previously, the heat and mass transfer analogy [32] is
used to compute the heat transfer coefficients for the liquid and gas. Therefore the heat
transfer coefficients are computed as described in Chapter 4. The overall heat transfer
coefficient is also used in the one-dimensional condensation model (Eqs. (5.7) & (5.10))
for closure.
A similar mass and energy balance analysis has been done for the co-current flow
condenser stage. The one-dimensional conservation equations are applied to a
differential control volume shown in Fig. 1b. The equations for evaluating the humidity
gradient and air temperature gradient are the same as that for countercurrent flow. The
gradient of water temperature in the co-current flow condenser stage is,
LC
TTUa
C
hh
dz
d
L
G
dz
dT
Lp
aL
Lp
LFgL )()( −−−
−= ω, (5.20)
81
Thus Eqs. (5.10) & (5.20) are used to evaluate the temperature fields in the co-current
flow condenser stage. The humidity gradient, Onda’s correlation and the heat and mass
transfer analogy are used for closure.
The condensation rate in the condenser is calculated as,
)( outinacond mm ωω −= . (5.21)
The condenser effectiveness is defined as the ratio of the condensation rate in the
condenser to the maximum possible condensation rate.
)( sinkina
cond
m
m
ωωε
−= , (5.22)
Here, ksinω is the minimum possible humidity exiting the condenser, which is evaluated
with Eqn. (5.3) assuming the air exits the condenser at the water inlet temperature. The
condenser effectiveness is very useful in comparing the performance of the co-current
and countercurrent flow condenser stages.
For the countercurrent condensation analysis, the exit water temperature, exit air
temperature, and exit humidity are computed using the following procedure: 1) specify
the inlet water temperature, TL,in, air temperature, Ta,in, and bulk humidity ωin; 2) guess
the exit water temperature TL,out; 3) compute the temperatures and humidity at the next
step change in height, starting from the bottom of the packed bed, using Eqs. (5.7), (5.10)
& (5.12) until the computed packed bed height matches the experimental height; 4) check
whether the computed inlet water temperature agrees with the specified inlet water
temperature, and stop the computation if agreement is found, otherwise repeat the
procedure from step 2. A detailed flow diagram of the computation procedure is
illustrated in Fig. 5-2.
82
The computation is much simpler for the co-current flow condensation analysis.
The exit water temperature, exit air temperature, and exit humidity are computed using
the following procedure: 1) specify the inlet water temperature, TL,in, air temperature,
Ta,in, and bulk humidity ωin; 2) compute the temperatures and bulk humidity, Ta, TL, & ω,
at the next step change in z-direction, starting from the top of the packed bed, using Eqs.
(5.10), (5.12) & (5.20) until the computed height matches the experimental height.
Output TL,,out, Ta,out,,
ωout
Stop Start
Calculate U by analogy method
from Eqs. (5.16), (5.18) &
(5.19)
Calculate kG , kL using Onda’s
correlation from Eqs. (5.13) &
(5.14)
Calculate ω, Ta ,TL at next z
using Eqs. (5.7), (5.10) &
(5.12); use 4th order Runge -
Kutta method
If z < H
Guess TL,out at z=0
Update TL, Ta, & ω
for the current z location
Yes
No
Input TL,in at z = H,
input Ta,in, and ωin
at z = 0
If TL ? TL,in
No
Yes
Figure 5-2 Flow diagram for the countercurrent flow computation
Model Comparison with Experiments for the Packed Bed Direct Contact Condenser
The effective packing diameter dp for the structured polyethylene packing is 17
mm. In Onda’s original work [31] he suggested that the coefficient in Eqn. (5.14) should
83
be C=5.23 for dp>15 mm and C=2.0 for dp≤15 mm. However, careful scrutiny of the data
shows that the change in the coefficient is smooth, and the abrupt change represented by
a bimodal coefficient is only an approximation. The 17 mm effective packing diameter
used in this work is very close to the threshold suggested by Onda. Good comparison
between the measured data and the model is achieved for co-current and countercurrent
flow by following Onda’s approximation for C=2.0. Onda did not attempt to explain the
physical mechanism for reduced mass transfer rate with smaller packing diameter. We
believe that the reduced gas mass transfer coefficient in condensers is due to increased
liquid hold-up, which causes liquid bridging and reduced area for mass transfer. The
wetting of the packing will be discussed in detail following presentation of the heat and
mass transfer data.
Water to air mass flow ratio (mL/ma)
0.8 1.0 1.2 1.4 1.6 1.8 2.0
Exi
t te
mp
erat
ure
(C)
20
25
30
35
40
45
Exi
t hum
idity
0.000
0.005
0.010
0.015
0.020
0.025
0.030
Data ModelTL,out
Ta,out
ωout
G = 0.6 kg/m2-s
TL,in = 19.8 C
Ta,in = 36.9 C
(a)
Figure 5-3 Comparison of predicted exit temperatures and humidity with the experimental data for countercurrent flow: a) Ta,in=36.9° C, b) Ta,in=40.8° C, c) Ta,in=42.8 °C
84
Water to air mass flow ratio (mL/ma)
0.8 1.0 1.2 1.4 1.6 1.8 2.0
Exi
t tem
pera
ture
(C
)
25
30
35
40
45
50
Exi
t hum
idity
0.00
0.01
0.02
0.03
Data ModelTL,out
Ta,out
ωout
G = 0.6 kg/m2-s
TL,in = 19.5 C
Ta,in = 40.8 C
(b)
Water to air mass flow ratio (mL/ma)
0.8 1.0 1.2 1.4 1.6 1.8 2.0
Exi
t tem
pera
ture
(C
)
20
30
40
50
60
Exi
t hum
idity
0.00
0.01
0.02
0.03
0.04
TL,out
Ta,out
ωout
G = 0.6 kg/m2-s
TL,in = 20.0 C
Ta,in = 42.8 C
Data Model(c)
Figure 5-3 Continued
Heat and mass transfer experiments were carried out in the countercurrent flow
stage. The air mass flux G was fixed at 0.6 kg/m2-s with the water to air mass flow ratio
mL/ma varying from 0 to 2.5. The saturated air inlet temperature Ta,in was fixed at 36.9,
40.7, and 43.0° C respectively. The inlet water temperature was about 20° C. The
measured exit humidity ωout, exit air temperature Ta,out, and exit water temperature TL,out
85
are compared with those predicted with the model for all three different saturated air inlet
temperatures in Figs. 5-3 a-c.
It is observed that the exit water temperature, exit air temperature and exit humidity
all decrease with increasing water mass flux for a specified air mass flux. The
comparison between the predicted and measured exit water temperature, exit air
temperature and exit humidity agrees very well. Detailed experimental data associated
with Figs. 5-3 a-c are shown in Appendix D.
Heat and mass transfer experiments were also carried out in the co-current stage.
The saturated air inlet temperature was fixed at 35.5, 39.6, and 43° C for each experiment
set. The air mass flux was fixed at 0.6 kg/m2-s, and the water to air mass flow ratio was
varied from 0 to 2.5. The inlet water temperature was about 22° C. Figs. 5-4 a-c show
the measured exit humidity, exit air temperature, and exit water temperature compared
with those predicted with the model for all three different saturated air inlet temperatures.
Water to air mass flow ratio (mL/ma)
1.0 1.2 1.4 1.6 1.8 2.0 2.2
Exi
t tem
pera
ture
(C
)
26
28
30
32
34
Exi
t hum
idity
0.00
0.01
0.02
0.03
TL,out
Ta,out
ωout
G = 0.6 kg/m2-s
TL,in = 21.7 C
Ta,in = 35.5 C
Data Model(a)
Figure 5-4 Comparison of predicted exit temperatures and humidity with the
experimental data for co-current flow: a) Ta,in=35.5° C, b) Ta,in=39.6° C, c) Ta,in=42.9° C
86
Water to air mass flow ratio (mL/ma)
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Exi
t tem
pera
ture
(C
)
26
28
30
32
34
36
38
40
Exi
t hum
idity
0.00
0.01
0.02
0.03
0.04
TL,out
Ta,out
ωout
G = 0.6 kg/m2-s
TL,in = 22.4 C
Ta,in = 39.6 C
Data Model(b)
Water to air mass flow ratio (mL/ma)
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Exi
t tem
pera
ture
(C
)
25
30
35
40
45
50
Exi
t hum
idity
0.01
0.02
0.03
0.04
0.05
TL,out
Ta,out
ωout
G = 0.6 kg/m2-s
TL,in = 22.3 C
Ta,in = 42.9 C
Data Model(c)
Figure 5-4 Continued
It is observed that the exit water temperature, exit air temperature and exit humidity
all decrease with increasing water to air mass flow ratio. The predicted exit temperatures
and exit humidity agree well with the experimental measurements. The exit water
temperature has the largest deviation, although the error is acceptable for design and
87
analysis applications. Detailed experimental data associated with Figs. 5-4 a-c are
tabulated in Appendix E.
Wetting Phenomena within Packed Bed
In order to explore the influence of the packing surface wetting on the condensation
heat and mass transfer rate, a high speed digital camera was used to study the water film
formation and shape on the packing. A static liquid film formation has been observed
when there is no water or air flow through the packed bed and only one droplet of water
is on the packing surface. It is found that the water droplet could have 3 possible
residence locations as shown in Figs. 5-5 a-c. It is also found that the contact angle of
water with the polypropylene packing is approximately 90°, which is in agreement with
Sellin et al [45].
(a)
Figure 5-5 Droplet residence positions on the packing material: a) on the top, b) in the
corner, c) beneath the packing
88
(b) (c)
Figure 5-5 Continued
Observations of the dynamic water film formation on the packing surface have
been made with water and air flowing countercurrently through the packed bed. Frames
of the side view and top view are shown in Figs. 5-6 a-b respectively. These images
show that some hemispherical water drops block the flow channels within the packed
bed. It is observed that the water bridges are always present even at high air to water
mass flow ratio. The local heat and mass transfer rate decreases with increasing the water
blockages since the active interfacial area between water and air is decreased. Also the
air velocity in the vicinity of the blockages is largely reduced.
It is well understood that the heat and mass transfer rate within the packed bed is
directly related to the contact surface area between the air and water. In order to achieve
a high rate of heat and mass transfer, it is important to provide good surface wetting and
liquid contact with air. The wettability of the packing surface with liquid depends on the
contact angle between the liquid film and the packing surface. Water on polyethylene is
poorly wetting. It is apparent that packing material with small packing diameter and poor
wettability has a higher probability to form liquid bridges and block the air flow. Also,
89
the condensation process will enhance liquid hold-up and increase the probability of
blocking flow passages. This may explain why the local air side heat and mass transfer
coefficients are lower for the condensation process than for the evaporation process.
Despite its poor wetting characteristics, the polyethylene packing is used for the DDD
process because it has a very low cost and is inexpensive to replace.
(a)
(b)
Figure 5-6 Observation of the liquid blockages within the packed bed: a) side view, b)
Top view
The wide span of experimental data shown in Onda’s original work [31] reveal that
there exist more factors important to packed bed heat and mass transfer than are
accounted for in the correlation. For example, the water blockage problem on the
90
packing is similar to a local flooding situation, and it could happen at any operating
condition depending on the contact angle, packing surface conditions/geometry and
heat/mass transfer rate. Predictive models for water blockage are not currently available.
Further understanding of liquid flow blockage within packed beds is required to improve
existing heat and mass transfer correlations.
Experimental Results of the Droplet Direct Contact Condenser
The steady state heat and mass transfer experiments were carried out in the droplet
direct contact condenser. The hot saturated air mass flux was fixed at 0.875 kg/m2-s and
its inlet temperature was varied from 37° C to 42° C. The inlet cold fresh water
temperature was about 25° C. For a fixed air inlet temperature, a full range of cold water
flow rates varying from zero to maximum was explored where steady state conditions
were maintained for several distinct flow rates. Thus data of the condenser’s performance
for several different steady states is obtained. The data are shown in the figures to follow.
Fig. 5-7 shows the total temperature drop of the air/vapor mixture as it passes
through both the co-current and countercurrent condenser stages. The air temperature
drop increases with water to air mass flow ratio for a specified air inlet temperature. And
it also increases with increasing air inlet temperature when the water to air mass flow
ratio is fixed. With no water flow, there is a finite temperature drop of the air/vapor
mixture, which implies there is a degree of cooling due to heat loss to the environment
from the condenser walls. Indeed, for a practical condenser design the heat loss is good
since it enhances condensation. The U-shape design of the condenser not only reduces the
construction area, but also increases the wall area of the condenser that increases the heat
loss of the air. This is demonstrated clearly in the experiments. However, the figure also
91
shows that for a certain air inlet temperature there exists a threshold water to air mass
flow ratio that yields a maximum temperature drop. Once this threshold is exceeded, the
air temperature drop hardly changes with increasing water to air mass flow ratio.
Water to air mass flow ratio (mL/ma)
0 1 2 3 4 5 6 7
Tot
al te
mpe
ratu
re d
rop
of a
ir/va
por
mix
ture
(C
)
2
4
6
8
10
12
36.940.041.9
Ta,in (C)
Increasing Ta,in
Figure 5-7 Total temperature drop of the air/vapor mixture with varying water to air mass flow ratios and different air inlet temperatures (without packing)
Water to air mass flow ratio (mL/ma)
0 1 2 3 4 5 6 7
Tot
al fr
esh
wat
er p
rodu
ctio
n ra
te (
lpm
)
0.01
0.02
0.03
0.04
0.05
0.06
0.07
36.940.041.9
Ta,in (C)
Increasing Ta,in
Figure 5-8 Total fresh water production rate with varying water to air mass flow ratios and different air inlet temperatures (without packing)
92
Fig. 5-8 shows the total fresh water production rate by both condenser stages. It
shows that for a fixed feed water inlet temperature and air inlet mass flux, the fresh water
production rate is strongly dependent on both the water to air mass flow ratio and the air
inlet temperature. Trends show that the fresh water production decreases significantly
with a small drop in the air inlet temperature. This trend suggests that there will be little
to no fresh water production when the air inlet temperature is lower than 30° C. The peak
in temperature drop observed in Fig. 5-7 results in a peak in fresh water production as
shown in Fig. 5-8. Therefore increasing the water to air mass flow ratio past the threshold
does not result in increasing the fresh water production rate.
Water to air mass flow ratio (mL/ma)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Tem
pera
ture
dro
p of
the
air/
vapo
r m
ixtu
re (
C)
2
3
4
5
6
7
8
9
36.940.041.9
Ta,in (C)
Increasing Ta,in
(a) co-current
Figure 5-9 Temperature drop of the air/vapor mixture with varying water to air mass flow ratios in the a) co-current, b) countercurrent stage (without packing)
Figs. 5-9 a-b show the temperature drop of the air/vapor mixture through the co-
current and the countercurrent condenser stages, respectively. The air/vapor mixture’s
temperature drop shows the same trend in these figures as in Fig. 5-7. The main
difference is that the heat loss in the countercurrent condenser stage is very small because
93
the air/vapor mixture already loses a lot of energy in the co-current stage before it enters
the countercurrent condenser stage. The heat transfer driving potential is not large enough
to overcome the heat resistance of the condenser wall.
Water to air mass flow ratio (mL/ma)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Tem
pera
ture
dro
p of
the
air/
vapo
r m
ixtu
re (
C)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
36.940.041.9
Ta,in (C)
Increasing Ta,in
(b) Countercurrent
Figure 5-9 Continued
Water to air mass flow ratio (mL/ma)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Fre
sh w
ater
pro
duct
ion
rate
(lp
m)
0.01
0.02
0.03
0.04
0.05
0.06
36.940.041.9
Ta,in (C)
Increasing Ta,in
(a) Co-current
Figure 5-10 Fresh water production rate with varying water to air mass flow ratios and different air inlet temperatures in the a) co-current, b) countercurrent stage (without packing)
94
Water to air mass flow ratio (mL/ma)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Fre
sh w
ater
pro
duct
ion
rate
(lp
m)
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
36.940.041.9
Ta,in (C)
Increasing Ta,in
(b) Countercurrent
Figure 5-10 Continued
Figs. 5-10 a-b show the fresh water production rate through the co-current and the
countercurrent condenser stages, respectively. By comparing Figs. 5-10 a & b for the
same air inlet temperature, the maximum fresh water production rate in the
countercurrent condenser stage is about 25% of that in the co-current stage, which means
the countercurrent stage is very important to the total production of the system.
Detailed experimental data associated with Figs. 5-7 – 5-10 are tabulated in
Appendix F. All figures show that there exists a threshold water to air mass flow ratio
where the air temperature drop and fresh water production rate reach a maximum. When
the water to air mass flow ratio increases beyond this threshold, neither the air
temperature drop nor the fresh water production rate shows much increase. This
interesting phenomenon can be explained by considering the droplet heat transfer process
in the condenser. High-speed cinematography has been used to observe the droplet size
and velocity for different water flow rate. It is found that increasing the cold water flow
rate will result in increased droplet velocity and decreased droplet size. High droplet
95
velocity will reduce the droplet residence time in the condenser, which results in reduced
heat transfer. Meanwhile, the smaller droplet size increases the heat transfer surface area
between the water and air for a given amount of water. Therefore, as the water flow rate
is initially increased, an increase in heat transfer is initially observed because the overall
surface area for heat transfer is increased. Also the heat capacity is larger and a larger
driving potential for heat transfer can be maintained. However, after the threshold is
reached, no further increase in heat transfer is observed because the deleterious effect
from the droplet velocity becomes severe. Another result shown in the above figures is
that the threshold cold water flow rate increases with increasing condenser air inlet
temperature. For a fixed water to air mass flow ratio, hotter saturated air provides a larger
driving potential for heat transfer. This larger driving potential overcomes the negative
effects of increasing droplet velocity as described earlier.
Condenser Effectiveness
In order to compare the packed bed direct contact condensation effectiveness
between co-current and countercurrent flow, several sets of experiments have been
compiled where the air flow rate, air inlet temperature/humidity, and water inlet
temperature are almost the same for each condenser stage. The condensation
effectiveness is shown in Fig. 5-11 with varying the water to air mass flow ratio and
different saturated air inlet temperatures. Detailed experimental data associated with Fig.
5-11 are tabulated in Appendix D & E.
These data elucidate the fact that the countercurrent flow condenser stage is
evidently more effective than the co-current stage for the same water to air mass flow
ratio, air inlet temperature/humidity and water inlet temperature. The condensation
effectiveness is strongly dependent on the water to air mass flow ratio and not very
96
sensitive to the air inlet temperature/humidity. The condenser effectiveness, for both co-
current and countercurrent flow, appears to reach a threshold when the water to air mass
flow ratio exceeds 2.0. Operating with this threshold water to air mass flow ratio appears
to be an optimal operating condition. In general, the difference between the condenser
effectiveness of the co-current and countercurrent stages is approximately 15% for the
same water to air mass flow ratio.
Water to air mass flow ratio (mL/ma)
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Con
dens
atio
n ef
fect
iven
ess
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
35.539.642.836.940.743.0
Co-current
Countercurrent
Ta,in
Figure 5-11 Comparison of the packed bed condenser effectiveness between co-current and countercurrent flow
Similarly, a comparison of the countercurrent flow condensation effectiveness
between the droplet condenser and packed bed condenser has been done. Several
experiment sets of countercurrent flow droplet condensation have been taken when the
water to air mass flow ratio, air inlet temperature/humidity, and water inlet temperature
are almost the same as that for the packed bed condensation experiments. The
condensation effectiveness is shown in Fig. 5-12 with varying the water to air mass flow
97
ratio and different saturated air inlet temperatures. Detailed experimental data associated
with Fig. 5-12 are tabulated in Appendix D & G.
Water to air mass flow ratio (mL/ma)
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Con
dens
atio
n ef
fect
iven
ess
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
35.539.642.836.940.743.0
Droplet
Packed bed
Ta,in
Figure 5-12 Comparison of the countercurrent flow condensation effectiveness between droplet condenser and packed bed condenser
These data clearly show that the direct contact condensation is generally 15% more
effective when the packed bed is applied in the condenser for the same water to air mass
flow ratio, air inlet temperature/humidity and water inlet temperature.
.
98
CHAPTER 6 DDD PROCESS OPTIMIZATION DESIGN AND ECONOMIC ANALYSIS
The three main parameters that dominate direct contact heat and mass transfer
performance include the retention time, the interfacial area and the heat/mass transfer rate
of water and air in the tower. In lieu of droplet direct contact, the current investigation
focuses on packed bed direct contact evaporation and condensation due to the increased
residence time and contact surface of the air and water. The increase in capital cost of the
diffusion tower and condenser with packing is small because it is normally 10 - 20% of
the total cost depending on the type and size of the tower (Skold [46]). The maintenance
of such a tower is routine since fouled packing can be easily and inexpensively replaced.
The disadvantage of the packed bed direct contact heat and mass transfer is that increased
pumping energy is required to drive the air/vapor mixture through the tower.
In designing direct contact heat exchangers, it is prudent to use mathematical
models that reliably capture the dominant physics governing the heat and mass transfer.
Burger [47] reported that the size and capital cost of a cooling tower can be reduced by
10% by lowering the cold water temperature by 1˚ C using an appropriately designed
packed tower. In order to reduce the capital cost of the DDD process and operate at the
optimal flow and thermal conditions, it is necessary to size the diffusion tower and
condenser. Once the size is determined, its performance requires determination of the
temperature/humidity distribution, energy consumption and fresh water production rate.
Therefore mathematical models that simulate the diffusion tower described in Chapter 4
99
and the direct contact condenser with packed bed described in Chapter 5 are combined in
order to evaluate the DDD performance over a range of operating conditions.
The objective of this computational analysis is to explore the influence of the
operating parameters on the overall DDD process performance. These parameters include
the water/air/vapor temperatures, humidity ratio, water mass flux, air to feed water mass
flow ratio, and tower size. The water mass flux and the air to feed water mass flow ratio
through the tower are two primary controlling variables in the analysis. A DDD facility,
including a diffusion tower and a countercurrent flow direct contact condenser with
packed bed, is considered in this analysis.
Mathematical Model
In performing the analyses, the following assumptions have been made:
1. The process operates at steady-state conditions;
2. There are no energy losses to the environment from the heat and mass transfer apparatus.
3. Both the air and water vapor may be treated as perfect gases,
4. Changes in kinetic and potential energy are relatively small.
5. The pumping power for water is that which is necessary to overcome gravity (estimating the exact required pumping power would require significant details regarding the construction of the diffusion tower, heat transfer equipment, and the plumbing; these are beyond the scope of the current analysis).
The current formulation for the diffusion tower is based on a two-fluid film model
(Eqs. (4.6), (4.10) & (4.14)) described in Chapter 4. When solving, it yields the humidity
ratio, water temperature, and air/vapor mixture temperature distributions along the height
of the diffusion tower.
For the countercurrent flow direct contact condenser with packed bed, the current
formulation is based on the analytical model described in Chapter 5. The water
100
temperature, air temperature and the humidity distribution in the condenser are found by
solving Eqs. (5.7) (5.10) & (5.12) simultaneously.
Onda’s correlation is used to calculate the mass transfer coefficients in the diffusion
tower and condenser, kG and kL. The heat transfer coefficients for the air and water are
evaluated using the mass transfer analogy as described by Klausner et al. [41].
The fresh water production rate equals to the condensation rate in the condenser,
which is calculated from Eqn. (5.21). It is assumed that the inlet humidity to the diffusion
tower equals to the exit humidity from the condenser.
An empirical relation provided by the manufacturer of the packing material, which
has been validated with experiments and expressed as Eqn. (4.21), is used to compute the
pressure drop for air/vapor passing through the packing material.
It is noted that estimating the exact required pumping power would require
significant details regarding the construction of the diffusion tower, condenser and other
equipments. However, the majority of pumping power is consumed pumping the fluids
through the diffusion tower and the direct contact condenser. Therefore, the pumping
power for water is that which is necessary to overcome gravity in raising water to the top
of the diffusion tower and condenser and is calculated from Eqn. (4.22). The pumping
power for air/vapor through the diffusion tower and direct contact condenser is calculated
from Eqn. (4.24). The total pumping energy consumption rate for the DDD process
includes the pumping power consumed by the diffusion tower and condenser for both the
water side and air/vapor side and is calculated from Eqn. (4.25). So the energy
consumption rate per unit of fresh water production is defined as Eqn. (4.26).
101
Computation Results and Analysis
For all computations considered in the diffusion tower, the water inlet temperature
TL,in, gas inlet temperature Ta,in, inlet humidity ωin, specific area a and diameter of the
packing material dp are fixed as 50° C, 26° C, 0.023, 267 m2/m3 and 0.017m. The inlet
feed water mass flux is varied from 0.5 kg/m2-s to 3 kg/m2-s, meanwhile the air to feed
water mass flow ratio (ma/mL) is varied from 0.5 to 1.5 for every fixed inlet feed water
mass flux. All the cases analyzed in this report are below the flooding curve of the
packing material. The reason that the inlet feed water temperature is fixed at 50° C is that
this is typically the highest water temperature that can be expected to exit the main
condenser of a thermoelectric power plant.
Air to Feed Water Mass Flow Ratio
0.4 0.6 0.8 1.0 1.2 1.4
Diff
usio
n T
ower
Hei
ght (
m)
0
1
2
3
4
5
0.511.522.53
Diffusion TowermL (kg/m2-s)
Figure 6-1 Required diffusion tower height with variations in air to feed water mass flow ratio
Figure 6-1 shows the required diffusion tower height for different inlet water mass
flux and varying air to feed water mass flow ratio. The tower height is computed such
that the maximum possible humidity ratio leaves the diffusion tower. For every fixed air
to feed water mass flow ratio, the required diffusion tower height decreases with
102
increasing inlet water mass flux and decreases with increasing air to feed water mass flow
ratio. It also shows that for a fixed inlet water temperature and the maximum possible exit
humidity ratio, the required diffusion tower height is strongly influenced by both the inlet
water mass flux and the air to feed water mass flow ratio. It is particularly noteworthy
that the typically required diffusion tower height does not exceed 2 m for an air to feed
water mass flow ratio above unity. This is an important consideration in evaluating the
cost of fabricating a desalination system. Due to the small size of the diffusion tower, it is
feasible to manufacture the tower off site and deliver it to the plant site following
fabrication and thus lower the overall cost.
Air to Feed Water Mass Flow Ratio
0.4 0.6 0.8 1.0 1.2 1.4
Max
imum
Exi
t Hum
idity
Rat
io
0.04
0.05
0.06
0.07
0.08
0.09
0.511.522.53
Diffusion TowermL (kg/m2-s)
Figure 6-2 Maximum exit humidity ratio variation with air to feed water mass flow ratio
Figure 6-2 shows the maximum possible exit humidity ratio for different inlet water
mass flux and varying air to feed water mass flow ratios. For fixed inlet water and air
temperatures, the maximum possible exit humidity ratio is strongly dependent on the air
to feed water mass flow ratio and is largely independent of the inlet water mass flux.
These results indicate that increasing the air to water mass flow ratio will not necessarily
103
assist in increasing the fresh water production since the exit humidity ratio decreases with
increasing air to water mass flow ratio.
Air to Feed Water Mass Flow Ratio
0.4 0.6 0.8 1.0 1.2 1.4
Exi
t Air
Tem
pera
ture
(C
)
38
40
42
44
46
48
50
52
0.511.522.53
Diffusion TowermL (kg/m2-s)
Figure 6-3 Exit air temperature variation with air to feed water mass flow ratio
Figure 6-3 shows the exit air temperature for different inlet water mass flux and
varying air to feed water mass flow ratios. The exit air temperature is sensitive to
variations in both the inlet water mass flux and the air to feed water mass flow ratio.
Air to Feed Water Mass Flow Ratio
0.4 0.6 0.8 1.0 1.2 1.4
Wat
er P
ress
ure
Dro
p (k
Pa)
0
10
20
30
40
50
0.511.522.53
Diffusion TowermL (kg/m2-s)
Figure 6-4 Water side pressure drop variation with air to feed water mass flow ratio
104
Figure 6-4 shows the variation of the water side pressure drop across the diffusion
tower with varying air to feed water mass flow ratio. The water pressure drop decreases
with increasing inlet water mass flux and decreases rapidly with increasing air to feed
water mass flow ratio. Figures 6-4 illustrates that the water side pressure drop follows the
same trend as the diffusion tower height, which is to be expected since the water side
pressure drop is due to the gravitational head which must be overcome to pump the water
to the top of the diffusion tower.
Air to Feed Water Mass Flow Ratio
0.4 0.6 0.8 1.0 1.2 1.4
Air/
Vap
or P
ress
ure
Dro
p (k
Pa)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.511.522.53
Diffusion TowermL (kg/m2-s)
Figure 6-5 Air/vapor side pressure drop variation with air to feed water mass flow ratio
Figure 6-5 shows the variation of the air side pressure drop with the air to feed
water mass flow ratio. For high water mass flux, the air side pressure drop increases
rapidly when the air to feed water mass flow ratio exceeds 0.5. The main energy
consumption for the DDD process is due to the pressure loss through the diffusion tower
and condenser. Although the air side pressure drop is much lower than that for water, the
volumetric flow rate of air is much larger than that of water. Thus, both the air and water
pumping power contribute significantly to the total energy consumption.
105
The flow conditions used to investigate temperature and humidity variations in the
countercurrent flow packed bed direct contact condenser are the exit flow conditions
from the diffusion tower. A typical set of flow conditions are as follows, inlet air
temperature of 42.5° C, air mass flux of 2.0 kg/m2-s, and fresh water inlet temperature of
25° C. When the fresh water to air mass flow ratio is 2, the required condenser tower
height is 1.37 m, and Figure 6-6 shows the water temperature, air temperature and
humidity ratio distributions through the condenser. With a fresh water mass flux of 4.0
kg/m2-s, the exit humidity ratio is approximately 0.021, which corresponds to a fresh
water production rate of about 0.069 kg/m2-s.
Condenser Tower Height (m)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Tem
pera
ture
s (C
)
25
30
35
40
45
50
Hum
idity
Rat
io
0.00
0.01
0.02
0.03
0.04
0.05
0.06
WaterAir/VaporHumidity Ratio
Condenserma = 2.0 kg/m2-sTa,in = 42.442 C
ωin = 0.0553TL,in = 25 C
Figure 6-6 Temperature and humidity ratio profiles through the condenser
Figure 6-7 shows the condenser exit water temperature, minimum air temperature
and exit humidity ratio variation with varying fresh water to air mass flow ratio with the
same inlet air temperature and mass flux. Although not shown, all the values decrease
with increasing inlet water mass flux. However, the results in Figure 6-7 show that there
is no further decreases in exit humidity ratio when the fresh water to air mass flow ratio
106
exceeds 2. Thus the optimum fresh water to air mass flow ratio that yields the maximum
fresh water production is 2.
Fresh Water to Air Mass Flow Ratio
2 4 6 8 10
Tem
per
atur
es (
C)
0
10
20
30
40
50
60
Hum
idity
Rat
io
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0.050
WaterAir/VaporHumidity Ratio
Condenserma = 0.5 kg/m2-sTa,in = 48.611 C
ωin = 0.078TL,in = 25 C
Figure 6-7 Condenser temperature and humidity ratio variation with fresh water to air mass flow ratio
Air Mass Flux (kg/m2-s)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Con
dens
er H
eigh
t (m
)
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0.511.522.53
Diffusion TowermL (kg/m2-s)
Condensermfw/ma = 2
Figure 6-8 Required direct contact condenser height with variations in air mass flux
107
Figure 6-8 shows the required condenser height for different air mass flux with a
constant fresh water to air mass flow ratio of 2 in the condenser. The tower height is
computed such that the minimum humidity ratio leaves the condenser. For a fixed feed
water mass flux at the inlet of the diffusion tower, the required condenser height
decreases with increasing air mass flux, and it also decreases with decreasing the feed
water mass flux with the same air mass flux. Figures 6-8 indicates that the condenser
height follows the same trend as the diffusion tower exit air temperature, which is to be
expected since the required condenser height strongly depends on the air inlet humidity
ratio.
Air Mass Flux (kg/m2-s)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Exi
t Fre
sh W
ater
Tem
pera
ture
(C
)
32
34
36
38
40
42
44
46
48
0.511.522.53
Diffusion TowermL (kg/m2-s)
Condensermfw/ma = 2
Figure 6-9 Condenser fresh water exit temperature variation with air mass flux
Because the sink temperature is 25° C, the minimum condenser exit air temperature
is taken as 26° C. Figure 6-9 shows the condenser fresh water exit temperature for
different inlet feed water mass flux in the diffusion tower and varying air mass flux. The
fresh water exit temperature is sensitive to variations in both the feed water inlet mass
flux and air mass flux.
108
Air Mass Flux (kg/m2-s)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Fre
sh W
ater
Pro
duct
Effi
cien
cy (
mfw
/mL)
0.024
0.026
0.028
0.030
0.032
0.034
0.036
0.038
0.040
0.042
0.511.522.53
Diffusion TowermL (kg/m2-s)
Condensermfw/ma = 2
Figure 6-10 Variation of the fresh water production efficiency with air mass flux
Air to Feed Water Mass Flow Ratio
0.4 0.6 0.8 1.0 1.2 1.4
Ene
rgy
Con
sum
ptio
n R
ate
(kW
-hr/
kgfw
)
0.000
0.002
0.004
0.006
0.008
0.511.522.53
Diffusion TowermL (kg/m2-s)
Figure 6-11 Variation of the energy consumption with air to feed water mass flow ratio in diffusion tower
Figure 6-10 shows the fresh water production efficiency of the system with varying
air mass flux. It is clear that the fresh water production efficiency increases rapidly with
the air to feed water mass flow ratio. But the rate of increase diminishes when the air to
feed water mass flow ratio exceeds unity. It is also interesting to note that the maximum
fresh water production efficiency tends to approach a value of 0.04 when the feed water
109
mass flux is 0.5 kg/m2-s. The maximum production efficiency is largely controlled by the
ratio of the diffusion tower inlet water temperature to the sink temperature. In this case, it
is 1.12.
Perhaps the most important consideration in this analysis is the rate of energy
consumption due to pumping because the operating cost of the DDD process is largely
dependent on the cost of electricity to drive the pumps and blowers. Figure 6-11 shows
the energy consumption rate for the diffusion tower for different inlet feed water mass
flux and varying air to feed water mass flow ratios. The energy consumption increases
with increasing inlet water mass flux for a fixed air to feed water mass flow ratio. It is
particularly interesting that a minimum energy consumption occurs when the air to feed
water mass flow ratio is approximately 0.5. As the inlet water mass flux decreases, the
energy consumption becomes relatively insensitive to variations in the air to feed water
mass flow ratio.
Air Mass Flux (kg/m2-s)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ene
rgy
Con
sum
ptio
n R
ate
(kW
-hr/
kgfw
)
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.511.522.53
Diffusion TowermL (kg/m2-s)
Condensermfw/ma = 2
Figure 6-12 Variation of the energy consumption with air mass flux in condenser
110
Figure 6-12 shows the energy consumption rate for the direct contact condenser
with fixed fresh water to air mass flow ratio of 2. It shows clearly that there exists a
critical point for every feed water mass flux. When the air mass flux is higher than the
critical condition, the energy consumption rate in the condenser will increase very rapidly
with increasing air mass flux. An interesting result is that the energy consumption rate in
the condenser will remain low for all feed water inlet mass flux considered provided the
air mass flux remains below 1.5 kg/m2-s.
Air Mass Flux (kg/m2-s)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ene
rgy
Con
sum
ptio
n R
ate
(kW
-hr/
kgfw
)
0.000
0.005
0.010
0.015
0.020
0.025
0.511.522.53
Diffusion TowermL (kg/m2-s)
Condensermfw/ma = 2
Figure 6-13 Variation of the total energy consumption rate with air mass flux
Figure 6-13 shows the variation of the total energy consumption rate for the system
with air mass flux. There exists a minimum energy consumption rate for every feed water
mass flux, and it increases with increasing feed water inlet mass flux. However, when the
air mass flux is less than 1.5 kg/m2-s the total energy consumption rate for the system is
below 0.0039 kW-hr /kgfw for all feed water inlet mass flux. The minimum shown in this
Figure, 0.0004 kW-hr/kgfw, occurs when the air mass flux is 0.5 kg/m2-s, air to feed water
mass flow ratio is 1, and fresh water to air mass flow ratio is 2. At these conditions a
fresh water production rate of 0.018 kg/m2-s is realized. This minimum is about an order
111
of magnitude less energy consumption than reverse osmosis. However, operating at these
low mass fluxes requires a sizable land footprint, and is not likely to be practical for a
large production rate facility.
Finally, the optimum operating conditions of the system should satisfy competing
requirements: high fresh water production efficiency and low energy consumption rate.
Based on data presented in Fig. 6-10 and Fig. 6-13, a reasonable optimum operating
condition has an air mass flux of 1.5 kg/m2-s, air to feed water mass flow ratio of 1, and
fresh water to air mass flow ratio of 2. These conditions can yield a fresh water
production efficiency of 0.035 and energy consumption rate of 0.0022 kW-hr/kgfw.
Economic Analysis
As an example, consider a 100 MW power plant where the thermal efficiency is
40%. The total input energy is then 250 MW. If the power plant operates with 10.159 kPa
pressure in the main condenser, there would be approximately 150 MW of energy at 50°
C available from low pressure condensing steam. If retrofitted with a diffusion driven
desalination (DDD) plant, there is a potential to produce as much as 1.14 million
gallons/day of fresh water assuming the feed water temperature enters the diffusion tower
at 50° C. The energy consumption from the feed water, air, and cold fresh water pumps in
the DDD process is about 0.0022 kW-hr per kilogram of fresh water. This requires a land
footprint of approximately 0.47 acres. The total electrical power requirement is 391 kW
in total. The thermal energy consumed in the DDD process is waste heat, and is not of
concern for the economic analysis.
The fresh water production cost strongly depends on the process capacity, site
characteristics and design features. The system capacity defines the required sizes for
112
various process equipment, pumping units, and required heat exchanger surface area. Site
characteristics have a strong influence on the type of pretreatment and post-treatment
equipment, and consumption rate of chemicals. Process design features affect
consumption of electric power and chemicals (Wangnick et al [48] and Hisham et al
[49]). Production cost is divided into direct and indirect capital costs and annual
operating costs. Direct capital costs include the purchase cost of major equipment,
auxiliary equipment, land and construction. Indirect capital costs include labor,
maintenance, and amortization. They are usually expressed as percentages of the total
direct capital cost.
Land – The cost of land may vary considerably, from zero to a sum that depends on site
characteristics. Government-owned plants normally have zero charges. Plants constructed
under build-own-operate-transfer (BOOT) contracts with governments or municipalities
can have near zero or greatly reduced charges. The price of the land near the coast of
Florida varies significantly from 1k - 1000k $/acre.
Building construction – Construction costs vary from 100 - 1000 $/m2. This cost is site-
specific and depends on the building type. Buildings could include a control room,
laboratory, offices and workshops.
Process equipment – This category includes processing equipment, as well as
instrumentation and controls, pipes and valves, electric wiring, pumps, process cleaning
systems, and pre- and post-treatment equipment. These are some of the most expensive
items, and their cost depends on the type of process and capacity. Equipment costs may
be less than $1000 (e.g., a laboratory scale RO unit used to treat low-salinity water). On
the other hand, the equipment cost for a 100000 m3/day RO system could approach $50
113
million. MSF and MEE equipment are generally more expensive than that of RO systems
— current estimates for a plant capacity of 27000 m3/day are $40 million. Because the
increase in salinity concentration of the DDD discharge water is small, there is no need
for post-treatment. Also the feed water flow is supplied by the main pumps used in the
power plant’s cooling system. So the capital cost of the pre-treatment, post-treatment and
main feed water pumps will not be included in this analysis. The other process equipment
costs among different manufacturers range from $200k-$1700k.
Auxiliary equipment – The following are considered auxiliary equipment: open intakes or
wells, transmission piping, storage tanks, generators and transformers, pumps, pipes and
valves. The current analysis will not include these items.
As an example, consider the DDD system coupled with a 100 MW power plant.
Table 6- summarizes the variation in direct costs while Table 6-2 shows calculation
details for the unit fresh water production cost. The capital cost calculations are based on
the following assumptions:
1. interest rate i = 5%;
2. plant life n = 30 yr;
3. amortization factor ai = 1)1(
)1(
−++
n
n
i
ii = 0.0651 /yr;
4. plant availability f = 0.9;
5. chemical costs are not considered;
6. electricity is considered as operating cost;
7. the specific cost of operating labor γ is typically ranges from 0.025 to 0.05 $/m3 since DDD is a low temperature and pressure process. (γ is typically $0.1/m3 for the thermal processes and $0.05/m3 for RO).
114
Table 6-1 Summary of direct costs Name Land Building construction Major equipment
Cost ($) 470-470000 190202-1902023 200000-1700000 Total Direct Cost
DC ($) 390672-4072023
Table 6-2 Details of cost calculations
Name Formula Result Annual fixed charges
ACfixed ($) DCaiAC fixed ⋅=
25433 – 265089
Annual labor cost AClabor ($)
365⋅⋅⋅= flabor mfAC γ 35389 – 70779
Total annual cost ACtotal ($) laborfixedtotal ACACAC += 60822 – 335868
Unit product cost ACunit, p ($/m3)
1, )365( −⋅⋅⋅= ftotalpunit mfACAC 0.043 – 0.237
The computation reveals that the production cost, not including electricity costs,
ranges from 0.163 – 0.895 $/103 gal. For illustrative purposes, we take the production
cost to be 0.525 $/103gal. Here two cases are considered:
First, the DDD utility is economically independent from the power plant, which
means although the DDD process utilize the waste heat from the power plant, it needs to
pay the electricity cost in additional to basic production cost. So the fresh water profit in
this situation can be calculated as,
elecfpunitff QPwACQ −−=Π , , (6.1)
where Πf ($/103 gal) is the net fresh water profit, Qf ($/103 gal) is the retail price of fresh
water, and Qelec ($/kW-hr) is the retail price of electricity. Here ACunit,p is 0.525 $/103gal.
Figure 6-14 shows the net fresh water profit variation with the electricity retail price for
different fresh water retail price. The fresh water profit decreases with increasing
electricity cost, and increases with increasing the fresh water price. As seen in Fig. 6-14,
profit is only realized when the fresh water retail price is greater than 1 $/103gal.
115
Electricity Retail Price ($/kW-hr)
0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
Net
Fre
sh W
ater
Pro
fit (
$/10
3 gal)
0
1
2
3
4
5
6
123456
Water Retail Price($/103 gallon)
Figure 6-14 Net fresh water profit variation with electricity retail price for different fresh water retail price
Second, the DDD utility is combined with a power plant, which means this
combined system has a fresh water production capacity of 1.14 million gallons/day
besides the electricity production. But the total electrical power requirement of the DDD
process will be subtracted from the total electricity production of the power plant as the
operating cost. The daily profit of the combined system is calculated from,
elecffelecfftotal PwmEm Π−+Π=Π )(24 , (6.2)
where Πtotal ($/day) is the daily profit of the combined system, Eelec (MW) is the
electricity production capacity of the power plant before combining with the DDD
system, and Πelec ($/kWhr) is the electricity profit. The percent increase in profit of the
combined power plant is calculated as,
elecelec
elecelectotal
E
E
ΠΠ−Π
=β . (6.3)
The percent increase in profit for the power plant combined with the DDD process
for different fresh water profits is shown in Fig. 6-15. This Figure shows that the profit
116
increase decreases with increasing electricity profit. It is also important to note that the
profit increase of the combined power and DDD plant tends to be zero when the
electricity profit is higher than 0.2 $/kW-hr, which is not likely in the near future. The
profit increase grows almost proportionally with the fresh water price that can be
commanded on the open market. It clearly shows that the combined power and DDD
plants yield a profit increase when the fresh water is sold at a rate higher than 1 $/103gal.
This is strongly competitive in most regions of the world.
Electricity Profit ($/kW-hr)
0.001 0.01 0.1
Pro
fit In
crea
se (
%)
1
10
100
1000
123456
Water Profit($/103 gallon)
0.2
Figure 6-15 Percent increase in profit with electricity profit for different fresh water profit
A recent survey [50] by the NUS Consulting Group studying water rates across the
world found that rates increased from 2001 to 2002 in 12 of 14 countries surveyed. The
result is shown in Figure 6-16. The survey was based on prices as of July 1, 2002 for an
organization with an annual usage of at least 10000 cubic meters. Where there was more
than a single supplier, an unweighted average of available prices was used. The
percentage change for each country was calculated using the local currency in order to
eliminate currency exchange distortion. Water rates in the United States were among the
117
lowest in the countries surveyed and were one half to one third the rates charged in most
European countries. And it is also important to recognize that most countries investigated
show a positive increase in water price, which reflects the increased demand for fresh
water.
0 1 2 3 4 5 6 7 8
Australia
Belgium
Canada
Denmark
Finland
France
Germany
Italy
South Africa
Spain
Sweden
The Netherlands
United Kingdom
United States
Fresh Water Cost ($/1000 gallon)
2002
2001
Figure 6-16 Water price in different countries for year 2001 & 2002
Finally, an investigation of the electricity market in the United States is conclueded
to explore the economic advantage of the DDD process within different geographical
markets. The average revenue in the United States for electricity generation [51] is
$0.0693/kW-hr. The average cost to produce electricity in 2001 [52] is $0.06/kWhr for
gas and oil and $0.02/kW-hr for coal. Since electricity profits are low, the DDD process
118
provides an opportunity for electric utilities to realize additional revenues through fresh
water production.
The above considerations suggest that there exists economic benefit for the DDD
process to electric utilities. It is anticipated that this benefit will grow as the world fresh
water supply continues to diminish.
119
CHAPTER 7 CONCLUSIONS
An innovative Diffusion Driven Desalination (DDD) process has been studied
theoretically and experimentally. Although the process has a low fresh water to feed
water conversion efficiency, it has been demonstrated that this process can potentially
produce inexpensive distilled water when driven by low-grade energy such as waste heat.
A detailed parametric analysis shows that the waste heat from a 100 MW steam
generating power plant can be used to produce 1.14 million gallons of fresh water per day
using the DDD process. Since the energy used to drive the process is low thermodynamic
availability energy, the only energy cost is that used to power the pumps and blowers. An
economic simulation of the DDD system shows that the fresh water production cost of
the DDD combined power plant is very competitive compared with the costs required for
reverse osmosis or flash evaporation technologies.
A laboratory scale DDD facility, which includes the diffusion tower and direct
contact condenser has been fabricated. The whole system has been fully instrumented for
detailed heat and mass transfer measurements. Extensive measurements of the diffusion
tower and direct contact condenser were taken to validate their numerical simulation
models. It has been experimentally proved that in the current operating condition range,
the condensation effectiveness is much higher for countercurrent flow than for co-current
flow within the packed bed, and it is also higher for packed bed condenser than for
droplet condenser. The models of the diffusion tower and packed bed direct contact
condenser prove to be quite satisfactory in predicting the thermal performance of packed
120
beds evaporation and condensation. Nevertheless, due to the empiricism involved in the
correlations, they must be used with caution. High-speed cinematography is used to
explore the mechanism for the decrease in the gas side mass transfer coefficient for
packing material with a small effective packing diameter. The local heat and mass
transfer rate decreases with an increasing number of local water blockages. This is due to
a reduction in the active interfacial area between water and air, and the air velocity near
the vicinity of the blockages is reduced. It is believed that there exists a higher probability
to form liquid blockages within packing material which has a small packing diameter and
poor wettability. The analysis and observations presented in this work should be useful to
the designers of direct contact heat exchangers.
Although the current analysis shows that the Diffusion Driven Desalination process
appears to be an economically attractive distillation process, the precise values presented
in the dissertation need to be viewed with caution since losses other than pressure losses
have not been considered, and the assumed feed water temperature into the diffusion
tower may be optimistic. Nevertheless, the trends presented demonstrate the potential that
can be gained from the DDD process, and it provides useful and practical guidance for
choosing the operating conditions to achieve near optimum performance.
Furthermore, although the Diffusion Driven Desalination is a promising technology
for fresh water production using waste heat from electric power plants, current industry
practice will limit its implementation until the value of fresh water sharply increases. The
current practice of electric power plants is to pump a very large rate of cooling water
through the main condenser so that the temperature rise of the water across the condenser
is only about 6° C. The DDD requires the discharge water from the main condenser to be
121
approximately 45° C. This could be accomplished by lowering the flow rate through the
main condenser and providing more heat transfer surface area to compensate for the
reduced heat transfer rate. This would require a power plant installing a DDD facility to
also replace or modify the main condenser. This is not a likely scenario. The best
prospect for incorporating the DDD facility into an electric power plant for fresh water
production is with the fabrication of new plants where the main condenser could be sized
appropriately for the specified flow conditions.
Recently it has been recognized that the fresh water production efficiency can be
significantly enhanced with air heating. Air heating can be accomplished with air-cooled
condensers used in power plant applications. The heated air discharging the condenser
could be directly ducted to the diffusion tower. The laboratory experimental DDD facility
has been modified with an air heating section, and temperature and humidity data have
been collected over a range of flow and thermal conditions. It has been experimentally
observed that the fresh water production rate is enhanced when air is heated prior to
entering the diffusion tower. While a significant amount of literature is available on
evaporative heat and mass transfer between hot water and cold air within the packed bed
for cooling tower applications, considerably less information is available for the air
heating configuration. Therefore, more experiments need to be conducted to fully
understand the benefits of the heated air input. Further analytical analysis is required to
predict the thermal and mass transport with this configuration. In addition, a cost analysis
should be performed to analyze the additional costs of the heated air.
122
APPENDIX A ONDA’S CORRELATION
3/1
4.05.03/2 )(Re0051.0
= −
L
LpLLwL
gadSck
ρµ
,
GpGGAG aDadScCk 23/17.0 )(Re −= , (C=5.23 if dp > 15 mm; C=2 if dp ≤ 15 mm)
−−= − 5/105.02/1
4/3
# Re2.2exp1 LLLAL
cw WeFraa
σσ
LwLW a
L
µ=Re ,
GGA a
G
µ=Re ,
LLA a
L
µ=Re
LL
LL D
Scρ
µ= , GG
GG D
Scρ
µ= ,
g
aLFr
LL ρ
2
= , a
LWe
LLL σρ
2
=
# This equation has been modified from Onda’s original correlation.
123
APPENDIX B EXPERIMENTAL DATA OF THE DIFFUSION TOWER
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,out
(° C) Ta, in
(° C) ωout
ωin
0.042 0.030 60.8 32.6 42.3 22.2 0.059 0.009 0.042 0.040 60.6 30.8 39.6 22.5 0.051 0.009 0.042 0.051 60.7 27.9 37.2 22.7 0.044 0.010 0.042 0.059 60.5 26.7 35.7 22.8 0.041 0.010
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,out
(° C) Ta, in
(° C) ωout
ωin
0.042 0.031 59.1 32.8 41.5 22.2 0.057 0.009 0.042 0.039 60.2 31.3 39.1 22.4 0.049 0.009 0.042 0.051 60.2 30.5 36.3 22.7 0.042 0.010 0.042 0.061 60.1 27.4 34.8 23.0 0.038 0.010
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,out
(° C) Ta, in
(° C) ωout
ωin
0.059 0.021 60.5 37.3 50.4 22.6 0.091 0.005 0.059 0.031 59.5 33.3 46.3 22.5 0.072 0.005 0.059 0.041 60.0 31.3 43.4 22.1 0.061 0.005 0.059 0.050 60.6 29.3 42.0 22.3 0.056 0.005 0.059 0.061 60.1 28.2 39.2 22.5 0.048 0.005 0.059 0.070 59.8 28.8 37.2 22.6 0.043 0.005 0.059 0.080 60.3 26.4 36.0 22.7 0.040 0.005
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,out
(° C) Ta, in
(° C) ωout
ωin
0.059 0.021 59.8 38.8 50.0 22.7 0.090 0.005 0.059 0.032 59.9 36.7 45.7 22.9 0.069 0.005 0.059 0.041 59.6 33.7 44.2 22.6 0.067 0.005 0.059 0.050 59.7 31.3 41.8 22.7 0.058 0.005 0.059 0.061 60.0 29.3 39.3 22.9 0.047 0.005 0.059 0.071 59.8 25.9 37.5 23.2 0.045 0.005 0.059 0.080 59.5 26.1 36.4 23.4 0.040 0.005
124
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,out
(° C) Ta, in
(° C) ωout
ωin
0.080 0.029 60.7 35.3 49.5 23.1 0.087 0.010 0.080 0.039 60.7 33.7 46.1 23.0 0.071 0.010 0.080 0.049 60.5 33.6 44.3 22.7 0.063 0.010 0.080 0.060 60.5 30.7 42.6 22.9 0.058 0.010 0.080 0.069 60.8 29.4 40.5 23.1 0.051 0.010 0.080 0.078 60.3 28.2 39.2 23.2 0.047 0.010 0.080 0.089 61.3 27.9 37.6 23.5 0.043 0.010 0.080 0.101 60.9 26.6 34.9 23.8 0.037 0.010 0.080 0.109 60.3 26.4 33.1 24.1 0.034 0.010
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,out
(° C) Ta, in
(° C) ωout
ωin
0.080 0.031 60.8 36.9 48.7 23.1 0.083 0.010 0.080 0.039 60.6 34.3 46.7 23.2 0.074 0.010 0.080 0.051 60.3 33.3 43.9 22.8 0.062 0.010 0.080 0.060 60.4 29.3 41.8 22.9 0.054 0.010 0.080 0.070 60.7 29.0 40.1 23.2 0.049 0.010 0.080 0.079 60.6 27.9 38.8 23.6 0.046 0.010 0.080 0.092 60.7 27.4 36.9 23.9 0.041 0.010 0.080 0.101 60.7 26.6 34.3 24.2 0.035 0.010 0.080 0.108 60.4 25.8 33.9 24.6 0.035 0.010
125
APPENDIX C EXPERIMENTAL DATA OF THE AIR SIDE PRESSURE DROP THROUGH THE
PACKING MATERIAL
L (kg/m2-s) G (kg/m2-s) ∆P/z (Pa/m) 0 0
0.258384 2.511111 0.524775 7.8 0.810332 20.44444 1.054124 28.28889 1.346835 56.8 1.544484 75.26667
0.803389
1.941271 77.97778 0 0
0.148759 0.955556 0.405831 9.133333 0.951576 34.42222 1.543965 66.13333 1.868464 88.4
1.373636
2.047198 83.8 0 0
0.292747 7 0.512864 11.25 0.887309 25.15 1.150059 37 1.470995 69.1 1.661633 88.75
1.733611
2.03956 84.8 0 0
0.280726 2.977778 0.550711 11.13333 0.754084 17.04444 1.020072 32.71111 1.332571 65.35556 1.631835 92.06667
2.000957
1.717701 76.42222
126
APPENDIX D EXPERIMENTAL DATA OF THE COUNTERCURRENT FLOW DIRECT CONTACT
CONDENSER STAGE WITH PACKED BED
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.024 0.031 19.0 33.2 36.5 30.0 0.041 0.029 0.033 0.030 19.3 32.2 36.8 28.0 0.041 0.026 0.048 0.030 19.4 30.4 36.8 25.8 0.041 0.023 0.062 0.030 19.5 28.6 37.0 24.4 0.042 0.021
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.054 0.030 19.4 29.5 37.0 24.7 0.042 0.021 0.044 0.030 19.3 30.2 37.0 26.2 0.042 0.023 0.038 0.031 19.2 31.4 37.1 27.1 0.042 0.025 0.031 0.031 19.7 32.0 37.1 28.6 0.042 0.027
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.024 0.029 19.5 36.1 40.8 31.6 0.052 0.032 0.035 0.031 19.3 34.6 40.6 29.4 0.052 0.028 0.048 0.030 19.4 32.9 40.9 27.4 0.053 0.025 0.058 0.031 19.0 31.3 40.7 26.2 0.053 0.023
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.053 0.031 18.9 31.9 40.7 26.5 0.053 0.024 0.044 0.030 19.1 32.7 40.7 27.5 0.053 0.025 0.038 0.031 19.3 33.1 40.7 28.3 0.053 0.026 0.031 0.030 19.3 34.5 40.8 29.6 0.053 0.029 0.023 0.030 19.4 35.4 40.8 31.4 0.053 0.032
127
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.024 0.029 19.8 40.3 42.7 34.9 0.059 0.039 0.033 0.030 19.9 38.5 42.7 32.1 0.059 0.033 0.041 0.031 19.8 37.2 42.7 30.4 0.059 0.030 0.051 0.031 19.7 34.8 42.8 28.4 0.060 0.026
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.061 0.030 19.5 33.3 42.8 27.1 0.060 0.024 0.054 0.030 19.7 34.0 42.9 28.0 0.061 0.026 0.045 0.030 19.8 34.8 42.9 29.1 0.061 0.028 0.034 0.030 19.8 37.0 42.9 32.0 0.061 0.033 0.030 0.030 19.6 37.8 42.9 33.2 0.061 0.035
128
APPENDIX E EXPERIMENTAL DATA OF THE CO-CURRENT FLOW DIRECT CONTACT
CONDENSER STAGE WITH PACKED BED
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.032 0.031 22.5 29.0 35.6 31.2 0.038 0.029 0.042 0.031 21.6 27.7 35.5 29.4 0.038 0.026 0.053 0.031 21.5 26.7 35.5 28.6 0.038 0.025 0.058 0.031 21.4 25.7 35.4 28.0 0.038 0.024 0.066 0.031 21.4 25.5 35.2 27.4 0.037 0.023
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.025 0.031 23.6 34.0 39.7 35.1 0.048 0.037 0.042 0.031 22.2 31.9 39.7 32.4 0.048 0.031 0.052 0.031 22.2 30.7 39.7 31.6 0.048 0.030 0.059 0.031 22.0 30.3 39.6 30.7 0.048 0.028 0.069 0.031 22.1 28.6 39.2 29.5 0.047 0.026
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.024 0.032 23.5 38.5 42.8 38.3 0.058 0.044 0.044 0.031 22.2 34.6 43.1 34.3 0.059 0.035 0.055 0.031 22.0 33.5 42.9 33.2 0.058 0.033 0.060 0.031 22.1 32.0 43.0 32.5 0.058 0.032 0.067 0.031 22.2 31.6 42.9 31.8 0.058 0.030
129
APPENDIX F EXPERIMENTAL DATA OF THE DROPLET DIRECT CONTACT CONDENSERS
WITH CO-CURRENT AND COUNTERCURRENT FLOW
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) ωin
Diffusion tower 0.062 0.040 60.0 37.7 26.9 0.010
mL (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.005 22.9 23.2 42.4 38.5 0.056 0.045 0.070 22.3 27.8 42.3 35.9 0.056 0.039 0.081 23.6 27.9 42.2 35.2 0.056 0.037 0.098 24.2 28.1 41.6 34.3 0.054 0.035 0.110 24.2 28.1 41.4 33.8 0.053 0.034 0.123 24.3 28.1 41.7 33.5 0.054 0.034 0.119 24.4 28.1 41.9 33.5 0.055 0.034 0.109 24.7 28.2 42.1 33.8 0.055 0.034 0.092 24.9 28.0 41.6 34.4 0.054 0.035 0.075 25.0 28.0 42.1 35.6 0.055 0.038
Co-current condenser stage
0.006 25.1 27.9 42.3 38.8 0.056 0.046 0.001 22.9 23.2 38.5 38.8 0.045 0.046 0.063 22.3 27.8 36.0 34.1 0.039 0.035 0.075 23.6 27.9 35.2 32.9 0.037 0.032 0.089 24.2 28.1 34.3 31.6 0.035 0.030 0.101 24.2 28.1 33.8 30.9 0.034 0.029 0.115 24.3 28.1 33.5 30.4 0.034 0.028 0.111 24.4 28.1 33.5 30.6 0.034 0.028 0.100 24.7 28.2 33.8 31.0 0.034 0.029 0.084 24.9 28.0 34.4 31.9 0.035 0.031 0.067 25.0 28.0 35.6 33.5 0.038 0.034
Countercurrent condenser stage
0.001 25.1 27.9 38.8 39.0 0.046 0.046
130
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) ωin
Diffusion tower 0.047 0.040 60.7 39.1 26.9 0.010
mL (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.006 23.0 23.8 40.5 37.3 0.050 0.042 0.069 25.1 27.6 40.4 35.0 0.050 0.037 0.073 26.0 28.0 40.0 34.5 0.049 0.036 0.086 26.2 28.0 40.1 33.8 0.049 0.034 0.100 26.3 28.3 40.2 33.2 0.049 0.033 0.118 26.2 28.0 40.0 32.7 0.049 0.032 0.123 26.2 28.0 39.8 32.5 0.049 0.032 0.107 26.0 28.0 39.8 32.9 0.049 0.032 0.090 26.0 28.1 39.7 33.4 0.048 0.033 0.074 26.1 28.0 40.0 34.2 0.049 0.035
Co-current condenser stage
0.006 26.2 28.0 40.2 36.9 0.050 0.041 0.001 23.0 23.8 37.3 37.6 0.045 0.046 0.061 25.1 27.6 35.0 33.4 0.039 0.035 0.066 26.0 28.0 34.5 32.8 0.037 0.032 0.079 26.2 28.0 33.8 31.8 0.035 0.030 0.092 26.3 28.3 33.2 30.9 0.034 0.029 0.110 26.2 28.0 32.7 30.2 0.034 0.028 0.113 26.2 28.0 32.5 30.0 0.034 0.028 0.097 26.0 28.0 32.9 30.5 0.034 0.029 0.080 26.0 28.1 33.4 31.4 0.035 0.031 0.066 26.1 28.0 34.2 32.6 0.038 0.034
Countercurrent condenser stage
0.001 26.2 28.0 36.9 37.0 0.046 0.046
131
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) ωin
Diffusion tower 0.065 0.041 51.4 36.4 26.8 0.010
mL (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.006 21.9 23.3 37.0 34.0 0.041 0.034 0.071 24.2 27.9 36.9 32.3 0.041 0.031 0.088 24.9 27.8 36.5 31.6 0.040 0.030 0.097 25.4 27.9 36.5 31.5 0.040 0.030 0.110 25.6 28.0 36.8 31.2 0.041 0.029 0.123 25.7 28.1 37.2 31.0 0.042 0.029 0.117 25.6 28.1 37.3 31.0 0.042 0.029 0.098 25.6 28.1 37.0 31.5 0.041 0.030 0.079 25.6 28.0 37.1 32.1 0.042 0.031
Co-current condenser stage
0.006 25.5 27.4 37.2 34.5 0.042 0.036 0.001 21.9 23.3 34.0 34.2 0.034 0.035 0.062 24.2 27.9 32.3 31.3 0.031 0.029 0.079 24.9 27.8 31.6 30.2 0.030 0.027 0.088 25.4 27.9 31.5 30.0 0.030 0.027 0.100 25.6 28.0 31.2 29.5 0.029 0.026 0.116 25.7 28.1 31.0 29.2 0.029 0.026 0.108 25.6 28.1 31.0 29.3 0.029 0.026 0.089 25.6 28.1 31.5 29.9 0.030 0.027 0.071 25.6 28.0 32.1 30.8 0.031 0.029
Countercurrent condenser stage
0.001 25.5 27.4 34.5 34.7 0.036 0.036
132
APPENDIX G EXPERIMENTAL DATA OF THE DROPLET DIRECT CONTACT CONDENSER
STAGE WITH COUNTERCURRENT FLOW
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.072 0.037 24.6 29.7 36.1 29.6 0.039 0.027 0.060 0.037 24.6 30.6 36.3 30.1 0.040 0.027 0.048 0.037 24.7 30.8 36.4 31.5 0.040 0.030 0.039 0.038 24.6 31.0 36.6 32.3 0.040 0.031 0.031 0.038 24.6 31.1 36.6 33.0 0.040 0.033
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.070 0.034 25.3 30.9 39.9 31.6 0.049 0.030 0.064 0.034 25.1 31.5 40.0 32.0 0.049 0.031 0.058 0.035 25.2 31.5 40.1 32.8 0.049 0.032 0.046 0.035 24.9 31.7 40.2 34.5 0.050 0.036 0.042 0.035 25.3 32.2 40.3 35.1 0.050 0.037 0.038 0.035 25.1 32.6 40.3 35.6 0.050 0.038 0.028 0.035 25.1 33.3 40.3 36.5 0.050 0.040
mL (kg/s)
ma (kg/s)
TL, in (° C)
TL,out (° C)
Ta,in
(° C) Ta, out
(° C) ωin
ωout
0.069 0.033 24.9 33.0 42.8 32.2 0.058 0.031 0.061 0.033 24.8 34.1 42.8 33.1 0.057 0.033 0.049 0.033 24.7 34.5 42.8 34.7 0.058 0.036 0.042 0.033 25.0 34.4 42.8 36.1 0.058 0.039 0.035 0.033 24.9 34.6 42.9 37.0 0.058 0.041 0.029 0.034 24.9 35.8 42.9 37.7 0.058 0.043
133
APPENDIX H UNCERTAINTY ANALYSIS OF THE FLUID PROPERTIES
Experimental data will have errors and uncertainties. These uncertainties will be
introduced into the computational model when using the experimental data to calibrate a
numerical model. The performance of the DDD process is affected by this problem.
Therefore, understanding the possible errors is an important issue for the experiments and
computations. The conclusions drawn from the analytical model will depend on how well
the uncertainties are controlled in both the experiment and computation. This work
analyzes the uncertainties in predicting the fluid properties by using the current empirical
correlations. The uncertainties of the calculated values introduced by the current
experimental measurements are presented.
Theory of Uncertainty
There are two ways to record uncertainties: the absolute value of the uncertainty or
the uncertainty relative to the mean value. The absolute uncertainty has the same units as
the mean value. The relative uncertainty has no units since it is the ratio of the absolute
uncertainty to the mean value.
If a result is calculated based on a number of measured quantities, the total
uncertainty is the combination of the uncertainties of the individual components, where
each component will have a certain influence on the final result. For example, in the
DDD formulations, temperature, relative humidity, and volumetric flow rate are
measured to calculate the mass transfer coefficients using Onda’s correlation. Each
measured quantity has an associated uncertainty and will affect the computation result.
134
Assuming N is the computed quantity, it is a function of several directly measured
quantities X1, X2, X3 ··. The relation of N with Xi can be expressed as [53],
),,( 321 LXXXfN = . (H.1)
The absolute uncertainty of N, N∆ , is calculated by,
∑∑ ∆∂∂=
∂∂==∆ )()( i
ii
i
XX
fdX
X
fDfN , (H.2)
and the relative uncertainty of N, N
N∆, is calculated by,
∑∑
∆
∂∂
=
∂∂
===∆i
ii
i
XX
fdX
X
ffD
f
Df
N
N )(ln)(ln)(ln . (H.3)
Uncertainty of the Calculated Fluid Properties
The current experiment system can only measure the water temperature, air
temperature, relative humidity, gas side pressure, water volumetric flow rate and air
volumetric flow rate. Many other fluid properties such as viscosity, surface tension and
heat conductivity have to be calculated by empirical formulations based on the measured
values. The following analysis will elucidate the influence of the measurement
uncertainties on the calculated values. However, since this analysis only focuses on the
influence from the measurement uncertainties, it is assumed that all the empirical
formulations of the fluid properties will not introduce additional numerical error to the
calculated result.
Water Viscosity
Water viscosity is expressed as,
1210178811.0 NL e−×=µ , (H.4)
where 362311 10935912.010237304.010332283.0)( LLLL TTTTN −−− ×−×+×−= , (H.5)
135
The relative uncertainty of water viscosity is expressed as,
L
L
L
L
T
TF
∆=
∆1µ
µ, and 3623
11 10935912.0210237304.0)( LLL TTTNF −− ××−×+= . (H.6)
Water Density
Water density is expressed as,
12873 )10655823.010329673.010999968.0()( −−−− ×+×−×= LLLL TTTρ . (H.7)
The relative uncertainty of water density is expressed as,
L
L
L
L
T
TF
∆=∆2ρ
ρ, and )()10655823.010999968.0(1 283
2 LLL TTF ρ−− ×−×−= . (H.8)
Water Surface Tension
Water surface tension is expressed as,
263 10233607.010146149.00757742.0)( LLLL TTT −− ×−×−=σ . (H.9)
The relative uncertainty of water surface tension is expressed as,
L
L
L
L
T
TF
∆=
∆3σ
σ, and
)(
10233607.00757742.01
26
3LL
L
T
TF
σ
−×+−= . (H.10)
Water Diffusivity
Water diffusivity is expressed as,
298
15.2731016.2)( 9 +
×= − LLL
TTD . (H.11)
The relative uncertainty of water diffusivity is expressed as,
L
L
L
L
T
TF
D
D ∆=
∆4 , and
15.273
15.27314 +
−=LT
F . (H.12)
Water Specific Heat
Water specific heat is expressed as,
136
242 1088714.010316356.021662.4)( LLLL TTTCp −− ×+×−= . (H.13)
The relative uncertainty of water specific heat is expressed as,
L
L
L
L
T
TF
Cp
Cp ∆=
∆5 , and
)(
1088714.021662.41
24
5LL
L
TCp
TF
−×−−= . (H.14)
Water Heat Conductivity
Water heat conductivity is expressed as,
252 10892407.010201072.0562574.0)( LLLL TTTK −− ×−×+= . (H.15)
The relative uncertainty of water heat conductivity is expressed as,
L
L
L
L
T
TF
K
K ∆=
∆6 , and
)(
10892407.0562574.01
25
6LL
L
TK
TF
−×+−= . (H.16)
Vapor Viscosity
Vapor viscosity is expressed as,
21276 10815994.01039911.01001801.8)( aaav TTT −−− ×+×+×=µ . (H.17)
The relative uncertainty of vapor viscosity is expressed as,
a
a
v
v
T
TF
∆=
∆7µ
µ, and
)(
10815994.01001801.81
2126
7av
a
T
TF
µ
−− ×−×−= . (H.18)
Vapor Density
Vapor density is expressed as,
2108.206 NV e−=ρ , (H.19)
where 362312 10672679.010271791.010687293.0)( aaaa TTTTN −−− ×−×+×−= . (H.20)
The relative uncertainty of vapor density is expressed as,
a
a
v
v
T
TF
∆=
∆8ρ
ρ, and 3623
28 10672679.0210271791.0)( aaa TTTNF −− ××−×+= . (H.21)
137
Vapor Saturation Pressure
Vapor saturation pressure is expressed as,
3611379.0 Nsat eP = , (H.22)
where 362313 10676138.010278793.010723669.0)( aaaa TTTTN −−− ×+×−×−= . (H.23)
The relative uncertainty of vapor saturation pressure is expressed as,
a
a
sat
sat
T
TF
P
P ∆=
∆9 , and 3623
39 10676138.0210278793.0)( aaa TTTNF −− ××+×−= . (H.24)
Vapor Specific Heat
Vapor specific heat is expressed as,
253 10326009.010518644.085406.1)( aaav TTTCp −− ×+×+= . (H.25)
The relative uncertainty of vapor specific heat is expressed as,
a
a
v
v
T
TF
Cp
Cp ∆=
∆10 , and
)(
10326009.085406.11
25
10av
a
TCp
TF
−×−−= . (H.26)
Vapor Heat Conductivity
Vapor heat conductivity is expressed as,
274 10943145.010549804.00182188.0)( aaav TTTK −− ×+×+= . (H.27)
The relative uncertainty of vapor heat conductivity is expressed as,
a
a
v
v
T
TF
K
K ∆=
∆11 , and
)(
10943145.00182188.01
27
11av
a
TK
TF
−×−−= . (H.28)
Air Viscosity
Air viscosity is expressed as,
21074 10335868.010490401.010172011.0)( aaaa TTT −−− ×−×+×=µ . (H.29)
The relative uncertainty of air viscosity is expressed as,
138
a
a
a
a
T
TF
∆=
∆12µ
µ, and
)(
10335868.010172011.01
2104
12aa
a
T
TF
µ
−− ×+×−= . (H.30)
Air Density
Air density is expressed as,
242 1011752.010458748.029238.1)( aaaa TTT −− ×+×−=ρ . (H.31)
The relative uncertainty of air density is expressed as,
a
a
a
a
T
TF
∆=
∆13ρ
ρ, and
)(
1011752.029238.11
24
13aa
a
T
TF
ρ
−×−−= . (H.32)
Air Specific Heat
Air specific heat is expressed as,
264 10486923.010193781.000379.1)( aaaa TTTCp −− ×+×+= . (H.33)
The relative uncertainty of air specific heat is expressed as,
a
a
a
a
T
TF
Cp
Cp ∆=
∆14 , and
)(
10486923.000379.11
26
14aa
a
TCp
TF
−×−−= . (H.34)
Air Heat Conductivity
Air heat conductivity is expressed as,
aaa TTK 41072538.00241462.0)( −×+= . (H.35)
The relative uncertainty of Air heat conductivity is expressed as,
a
a
a
a
T
TF
K
K ∆=
∆15 , and
)(
0241462.0115
aa TKF −= . (H.36)
Gas Diffusivity
Gas diffusivity is expressed as,
139
5.1
5
298
15.273106.2)(
+×= − a
aG
TTD . (H.37)
The relative uncertainty of gas diffusivity is expressed as,
a
a
G
G
T
TF
D
D ∆=
∆16 , and
15.273
15.27315.116 +
−×=aT
F . (H.38)
Gas Mass Flow rate
The measurement output value from the air flowmeter in the experiment is a
standard air flow rate, mstd, which is an air flow rate when P=Pstd=14 psi and
Ta=Tstd=20ºC. The actual air flow rate, ma, is calculated from,
−=
std
a
sat
stdstda T
T
PP
Pmm
φ. (H.39)
The relative uncertainty of gas mass flux is expressed as,
∆+∆
−+
∆+
∆=
∆φφ
φφ
sat
sat
sat
sat
a
a
std
std
a
a
P
P
PP
P
T
T
m
m
m
m. (H.40)
Absolute Humidity
Absolute humidity is calculated from,
φφω
sat
sat
PP
P
−=
622.0. (H.41)
The relative uncertainty of the absolute humidity is expressed as,
∆+∆
−=∆
φφ
φωω
sat
sat
sat P
P
PP
P. (H.42)
Gas Viscosity
Gas viscosity is calculated from,
avG µω
µω
ωµ+
++
=1
1
1. (H.43)
140
The relative uncertainty of gas viscosity is expressed as,
a
a
a
vv
v
v
a
v
aG
G
µµ
µµωµ
µ
µµ
ωωω
ωµµ
ωµµ ∆
++
∆
++∆
++
+=
∆
1
11
1
11
1
11
1
1, (H.44)
Gas Density
Gas density is expressed as,
avG ρω
ρω
ωρ+
++
=1
1
1. (H.45)
The relative uncertainty of gas density is expressed as,
a
a
a
vv
v
v
a
v
aG
G
ρρ
ρρωρ
ρ
ρρ
ωωω
ωρρ
ωρρ ∆
++
∆
++∆
++
+=
∆
1
11
1
11
1
11
1
1. (H.46)
Gas Specific Heat
Gas specific heat is expressed as,
avG CpCpCpωω
ω+
++
=1
1
1 . (H.47)
The relative uncertainty of gas specific heat is expressed as,
a
a
a
vv
v
v
a
v
aG
G
Cp
Cp
Cp
CpCp
Cp
Cp
Cp
Cp
CpCp
Cp ∆
++
∆
++∆
++
+=
∆
ωω
ωω
ωω1
11
1
11
1
11
1
1. (H.48)
Gas Heat Conductivity
Gas heat conductivity is expressed as,
avG KKKωω
ω+
++
=1
1
1. (H.49)
The relative uncertainty of gas heat conductivity is expressed as,
141
a
a
a
vv
v
v
a
v
aG
G
K
K
K
KK
K
K
K
K
KK
K ∆
++
∆
++∆
++
+=
∆
ωω
ωω
ωω1
11
1
11
1
11
1
1. (H.50)
Uncertainty of the Mass and Heat Transfer Coefficients
In the current evaporation and condensation computational models, the mass
transfer coefficients are evaluated for the liquid and gas flow using Onda’s correlation
and a heat and mass transfer analogy is used to evaluate the heat transfer coefficients. The
temperature and humidity profiles through the packed bed can be calculated using the
energy and mass conservation equations. It is apparent that Onda’s correlation and the
heat/mass transfer analogy formulations are the core of the current analytical models.
However, the calculated fluid properties will be used in Onda’s correlation and the heat
and mass transfer analogy formulations to get the mass and heat transfer coefficients of
liquid and gas. This use of fluid properties will pass the measurement uncertainties to the
calculated heat and mass transfer coefficients and eventually affect the accuracy of the
model predictions.
Wetted Area of Packing
Onda’s correlation is shown in Appendix A, and the wetted area of packing can be
expressed as,
0aNaw = , (H.51)
where
110XeN −−= , 5/105.02/1
4/3
1 Re2.2 LLLAL
c WeFrX −
=
σσ
. (H.52)
142
Assuming the uncertainties of the gravitational acceleration and the critical surface
tension are negligible, where 0=∆=∆ cg σ , the relative uncertainty of the wetted area can
be expressed as,
∆+
∆+∆+
∆+
∆−
+∆=∆
L
L
L
L
L
L
L
LX
w
w
a
a
m
m
e
X
a
a
a
a
ρρ
µµ
σσ
25.05.075.095.011
1 . (H.53)
Recall Taylor’s series of ex as,
L+++==∑∞
21
!
2
0
xx
n
xe
nx , (H.54)
Using the first order Taylor series expansion of 1Xe and combining with Eqn. (H.53), the
relative uncertainty of the wetted area of packing can be expressed as,
L
L
L
L
L
L
L
L
w
w
m
m
a
a
a
a
ρρ
µµ
σσ ∆+∆+∆+∆+∆=
∆25.05.095.075.1 . (H.55)
Mass Transfer Coefficient on the Liquid Side
The liquid side mass transfer coefficient is calculated by,
3/1
4.05.03/2 )(Re0051.0
= −
L
Lg
adSck pLLwL ρµ
. (H.56)
The relative uncertainty of the liquid side mass transfer coefficient can be expressed as,
p
p
L
L
L
L
L
L
L
L
L
L
L
L
d
d
D
D
m
m
a
a
k
k
∆+
∆+
∆+
∆+
∆+∆+
∆=
∆
4.05.0633.0
333.1567.1833.1
σσ
ρρ
µµ
. (H.57)
Mass Transfer Coefficient on the Gas Side
The gas side mass transfer coefficient is expressed as,
GpGGAG aDadSck 23/17.0 )(Re23.5 −= . (H.58)
143
The relative uncertainty of the gas side mass transfer coefficient can be expressed as,
G
G
a
a
G
G
G
G
p
p
G
G
m
m
D
D
a
a
d
d
k
k
ρρ
µµ ∆
+∆
+∆
+∆
+∆+∆
=∆
333.07.0033.1333.17.12 . (H.59)
Finally, the uncertainties of the liquid and gas mass transfer coefficients can be calculated
by Eqs (H.57) and (H.59). They clearly show the influence of the uncertainty from each
individual fluid property to the total uncertainty of the liquid/gas mass transfer coefficient
by using Onda’s correlation. For example, Eqn. (H.57) shows that when all the fluid
properties have the same amount of relative uncertainties, the uncertainty of liquid
viscosity has the largest influence on the prediction accuracy of the liquid mass transfer
coefficient.
Heat Transfer Coefficient on the Liquid Side
Using the heat and mass transfer analogy method, the liquid side heat transfer
coefficient can be expressed as,
2/1)(L
LPLLLL D
KCkU ρ= . (H.60)
The relative uncertainty of the liquid side heat transfer coefficient can be expressed as,
L
L
L
L
L
L
L
L
L
L
L
L
K
K
D
D
Cp
Cp
k
k
U
U ∆+
∆+
∆+
∆+
∆=
∆5.05.05.05.0
ρρ
. (H.61)
Heat Transfer Coefficient on the Gas Side
The gas side heat transfer coefficient is calculated from,
3/23/1 )()(G
GPGGGG D
KCkU ρ= . (H.62)
The relative uncertainty of the gas side heat transfer coefficient can be expressed as,
G
G
G
G
G
G
G
G
G
G
G
G
Cp
Cp
D
D
K
K
k
k
U
U ∆+
∆+
∆+
∆+
∆=
∆333.0333.0667.0667.0
ρρ
. (H.63)
144
Results and Analysis
To calculate the uncertainties of the heat and mass transfer coefficients in the
current model, following assumptions are made,
1. The uncertainties of the specific area of the packing and the diameter of the packing are negligible, 0=∆=∆ pda .
2. Water temperature, TL, varies from 20-70º C.
3. Air temperature, Ta, varies from 20-70º C.
4. Relative humidity, Φ, is unity.
The experimental measurements have different uncertainties and are shown below as,
1. Absolute uncertainty of water temperature: CTL °=∆ 5.0 ;
2. Absolute uncertainty of water temperature: CTa °=∆ 5.0 ;
3. Relative uncertainty of water mass flux: %5.1=∆
L
L
m
m;
4. Relative uncertainty of water mass flux: %1=∆
std
std
m
m;
5. Relative uncertainty of relative humidity: %5.2=∆φφ
.
Figure H-1 shows that the relative uncertainty of water property predictions varies
with water temperature measurement. It clearly shows that among all the calculated water
properties, water viscosity prediction has the largest relative uncertainty of about 1%,
whereas the other properties only have a relative uncertainty of approximately 0.1%.
Noting that the water mass flow rate has a 1.5% relative uncertainty, and considering the
result of this figure together with Eqn. (H.57), it is obvious that the prediction uncertainty
of the liquid mass transfer coefficient is mainly influenced by the uncertainties of the
water mass flow rate and the water viscosity.
145
Water temperature (C)
20 30 40 50 60 70
Rel
ativ
e U
ncer
tain
ty (
%)
0.01
0.1
1
µL
DL
KL
σL
ρL
CpL
Figure H-1 Variation of the relative uncertainties of the calculated water properties with water temperature
Air temperature (C)
20 30 40 50 60 70
Rel
ativ
e U
ncer
tain
ty (
%)
0.01
0.1
1
10
Psat
ρv
µv
Cpv
Kv
Figure H-2 Variation of the relative uncertainties of the calculated vapor properties with air temperature
Figure H-2 shows the relative uncertainty of calculated vapor property influenced
by the air temperature. It shows that the vapor saturation pressure and density have very
high uncertainty of 6%, the vapor viscosity and heat conductivity have 0.5% relative
146
uncertainty, and vapor specific heat prediction has the smallest relative uncertainty of
about 0.05%.
Air temperature (C)
20 30 40 50 60 70
Rel
ativ
e U
ncer
tain
ty (
%)
0.001
0.01
0.1
1
ρa
µa
Ka
Cpa
Figure H-3 Variation of the relative uncertainties of the calculated air properties with air temperature
Air temperature (C)
20 30 40 50 60 70
Rel
ativ
e U
ncer
tain
ty (
%)
1
10
ωma
DG
KG
ρG
µG
CpG
Figure H-4 Variation of the relative uncertainties of the calculated air/vapor mixture properties with air temperature
Figure H-3 shows the relative uncertainty of the computed air property influenced
by the air temperature. It clearly shows that the relative uncertainty of the air specific heat
147
calculation is only 0.01% when Ta < 70 ºC, which means that the current air temperature
measurement has the least influence on the air specific heat calculation. The other
property calculations have a much higher relative uncertainty of 0.3% comparing to the
air specific heat.
The gas side of the DDD process is an air and vapor mixture. During the
computation, the mixture properties are used to calculate the mass and heat transfer
coefficients. Figure H-4 shows the relative uncertainty of the calculated air/vapor mixture
property influenced by air temperature. It clearly shows that there are mainly two types of
uncertainties varying with air temperature measurement. The first type, which includes
the absolute humidity, mixture mass flow rate, and viscosity, is barely varying with the
air temperature. The other type, which includes the diffusivity, heat conductivity, density,
and specific heat of the mixture, is increasing almost exponentially with the air
temperature. Obviously, the second type of variation is undesirable for a numerical
calculation because it will limit the applicable temperature range of the model.
Fig. H-5 shows that the wetted area prediction has approximately 2% uncertainty
caused by the measurement error. However, Onda [31] analyzed the relative uncertainty
of the wetted area prediction to be approximately 20% based on his collection of
experiment data including the column packed with rachig rings, berl saddles, spheres and
rods made of ceramic, glass, and polyvinylchloride. Therefore, it is clear to see that the
major uncertainty in predicting the wetted area is still from the original Onda’s
experimental data and the manner that he correlated them. The current experiment
measurement method only introduces minimal uncertainty on the prediction.
148
Water temperature (C)
20 30 40 50 60 70
20 30 40 50 60 70
Rel
ativ
e U
ncer
tain
ty (
%)
1
10
Air temperature (C)
aw
kL
kG
Figure H-5 Variation of the relative uncertainties of the wetted area and mass transfer coefficients with temperature by using Onda’s correlation
Fig. H-5 also shows that the liquid side mass transfer coefficient prediction has a
4.5% relative uncertainty caused by the measurement error. It is interesting to note that
there exists a minimum prediction uncertainty of the gas mass transfer coefficient of 5%
when the gas is about 35° C, and the uncertainty will increase quickly when the air
temperature exceeds 50º C. This result indicates that the current analytical models are
relatively more accurate and reliable when the highest air temperature is less than 50º C.
Although this indication may limit the applicable temperature range of the current model,
the air side temperature of 50º C seems to be the most practical operating temperature for
the DDD applications.
The uncertainty will also be introduced into the heat transfer coefficients using the
heat and mass transfer analogy method. Figure H-6 shows the relative uncertainty of the
heat transfer coefficient varying with the temperature measurement. It is clear to see that
the liquid side heat transfer prediction has a 4% relative uncertainty. The gas side heat
149
transfer coefficient relative uncertainty maintains at 8% when the operating air
temperature is lower than 50º C, then it increases very fast with the air temperature.
Water temperature (C)
20 30 40 50 60 70
20 30 40 50 60 70
Rel
ativ
e U
ncer
tain
ty (
%)
0
5
10
15
20
Air temperature (C)
UL
UG
Figure H-6 Variation of the relative uncertainties of the heat transfer coefficients with temperature
In conclusion, the influence of the experimental data uncertainties on the calculated
fluid properties has been explored. When the measured temperature is less than 60º C, the
current measurement method will only introduce a relative uncertainty of 2% to the
wetted area prediction, 10% to the mass transfer coefficient prediction, and 8% to the
heat transfer coefficient prediction. Onda et. al [31] announced that the relative
uncertainty to be approximately 20% to the wetted area prediction, and 30% to the mass
transfer coefficient prediction based on his experimental database. It indicates that the
major error of the current model is caused by the empiricism involved in the correlations.
Using the current experimental system to calibrate Onda’s correlation should be
acceptable and reliable. The results shown in this analysis indicates that the accuracy of
the current model can be improved by using better formulations of the air saturation
150
pressure and absolute humidity, and by using more accurate measurement methods of air
flow rate and air temperature. And the largest improvement on the accuracy of the
predictions could be achieved by the experimental calibration of Onda’s correlation based
on only one specified packing material.
151
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BIOGRAPHICAL SKETCH
Yi Li obtained a bachelor’s degree in engineering mechanics in September 2000
and a master’s degree in nuclear engineering in January 2003 at Tsinghua University in
P.R. China. He started his Ph.D. research in the Department of Mechanical and
Aerospace Engineering at the University of Florida in May 2003.