Desalination, 65 (1987) 43-55 Elsevier Science Publishers B.V., Amsterdam-Printed in The Netherlands

43

PARAMETRIC STUDY ON FALLING-FILM SEAWATER DESALINATION

G. ALY’ , A. AL-HADDAD' and M. ABDEL-JAWAD' 1 Kuwait University, P.O.' Box 5969, 13060 Safat, Kuwait 2 Kuwait Institute for Scientific Research, P.O. Box 24885, 13109 Safat, Kuwait

ABSTRACT A computer program "as constructed for the calculation of the heat transfer

and fluid hydrodynamic characteristics of falling-film evaporation of natural seawater. The evaporator unit is provided with a recirculation loop. The heat transfer surface is divided into small segments where local heat transfer co- efficients are calculated using correlations for different flow regimes.

The package has been optimized with respect to convergence, accuracy and CPU time consumption. A parametric study "as conducted to investigate the effect of such process variables as feed conditions, steam temperature, circulation ratio, boiling temperature and fouling thermal resistance. The results of an extensive sensitivity analysis indicate that the evaporation process is more sensitive to changes in the thickness of the scale layer and live steam tempera- ture and less sensitive to changes in feed temperature.

INTRODUCTION

Distillation of seawater in multiple falling-film evaporators is an establish

ed technique to produce salt-free water. The heat transfer area usually

consists of a bundle of long vertical tubes, on the inside surface of which a

thin liquid film flows down under gravity in an annular type of flow. The

thermal energy source is often the exhaust steam extracted from the low-pressure

stage of a steam power plant. The vapor generated in one effect condenses on

the outside surface of the tubes in the next effect, causing seawater inside the

tubes to boil. 1n such evaporators, the temperature differences necessary to

maintain a certain heat flux from the condensing steam to the boiling seawater

can be kept small. This is particularly important to seawater desalination

plants where a large number of effects are incorporated or vapor pressure

techniques are applied. Furthermore, the boiling mechanism becomes generally

one of evaporation at the liquid-vapor interface without formation of vapor

bubbles on the heating surface.

Falling-film evaporators are characterized by high heat transfer coefficients,

short residence time of the falling liquid film, small liquid hold-up and rela-

tively small pressure drops. That is why falling-film evaporation is widely

applied not only for seawater desalination but also in all branches of the

chemical industry, as well as in the pharmaceutical, food, and pulp and paper

OOll-9X4/87/$03.50 0 1987 Elsevier Science Publishers B.V.

44

industries.

This paper describes a computer program specially designed to provide some

insight into the heat transfer and fluid dynamic characteristics of falling-

film evaporation of natural seawater. The program can be used for parametric

studies of the process variables that influence this process.

THE MATHEMATICAL MODEL

The evaporator unit considered in this study is schematically shown in Fig.1.

A fraction of the concentrated brine can be circulated if necessary. The model

does not account for the pressure drop over the heat transfer surface. Conden-

sate streams are assumed to be saturated, and only smooth heated surfaces (tubes

and plates) are considered. Finally, surface evaporation is assumed to prevail.

Fig. 2 shows the physical model of the evaporator and the coordinate system.

The temperature profiles in the bulk of heating steam, condensate film, tube

wall, liquid film and the bulk of the generated vapor are also illustrated.

The hydrodynamics of falling films can be divided into three flow regimes:

laminar flow, wavy-laminar flow and turbulent flow. There are two main mecha-

nisms of falling film evaporation depending on the heat flux. Surface evapora-

tion occurs at low heat fluxes while bubble formation, i.e., nucleate boiling,

takes place at high heat fluxes. The surface evaporation regime is dominant in

most falling-film evaporators. In this regime, the local heat transfer coeffi-

cients are virtually independent of the heat flux.

Heat Transfer Correlations

With respect to the boiling temperature at the prevailing pressure inside the

evaporator, the seawater fed to the liquid distributors above the upper edge of

the heat transfer bundle may be subcooled, saturated or superheated. For a

subcooled feed, two distinct convective heat transfer regions can be defined

within the evaporator length: a thermal developing region and a fully developed

region. In the thermal developing region, where no evaporation occurs, all heat

transferred across the tube wall is utilized to preheat the-seawater to its

boiling temperature. That is why this region is sometimes called the preheating

zone. The local heat transfer coefficient in this zone will generally be higher

than that in the fully developed region. This is analogous to the case of

single phase convective heat transfer in pipes, where the heat transfer coeffi-

cient is substantially higher near the entrance than further downstream. There

are a number of heat transfer correlations reported in the literature (refs.l-3)

to calculate the liquid-side heat transfer coefficient in the preheating zone.

The VDI correlations (ref. 3) were adopted in this work.

In the fully developed region , convective heat transfer leads to evaporation

at the liquid-vapor interface as mentioned earlier. Chun and Seban (ref. 4)

45

-I II

N

N

S 0

v ,” 1

46

developed the following model for heat transfer to evaporating liquid films on

smooth vertical tubes:

For laminar flow:

Nu = 1.1 Re-lj3

For wavy-laminar flow:

Nu = 0.825 Re-2'g

(1)

(2)

For turbulent flow:

Nu = 3.e* lo-3 Reom4 Pro.65 (3)

The first equation is the well-known Nusselt equation for film condensation

(ref. 5). The second equation, which is based on the work of Zazuli (ref. 6),

assumes that the effective film thickness is reduced by the action of capillary

waves and ripples. The net effect is an increase in heat transfer in comparison

with eqn. (1). The third equation is based on the experimental work of Chun and

&ban (ref. 4) in the interval of Pr = 1.77 - 5.7 and Re = 9000 - 22000.

The intersection of eqns. (1) and (2) yields a pseudo-transition Reynolds

IlUmber:

(Re)lam - w.lam = 2.43 Ka l/11

(4)

where

Ka = Kapitza number = po3/gn4 (5)

The intersection of eqns. (2) and (3) gives the second pseudo-transition

Reynolds number:

(Re)rlam-tub = 5800 Px-~.'~ (6)

Eqns. (5) and (6) should not be regarded as an actual indication of the transi-

tion from one flow regime to another, but only as the point of transition from

one correlation to the other in order to facilitate the numerical simulations.

There are other heat transfer correlations for the turbulent flow regime

(refs. 7-10). However, the Chun-Seban model was adopted in this work.

THE COMPUTER PROGRAM

The total length of the heat transfer areas is divided into a number of seg-

ments N. Within each segment, the physical properties of the liquid and the

flow regime are assumed to be constant. It is obvious that the greater the

number of segments N, the more accurate the simulation results. Fig. 3 shows

the first three segments,' the first of which is used as an updating segment.

The input data fed to the package include the feed conditions, saturation

temperature of live steam, pressure of the separator, circulation ratio, geo-

metric data of the heat transfer surface, thickness of deposits and thermal

conductivities of the metal and deposits. Following the initiation phase in

which input data are checked and initial values are assigned to some process

variables, the program compares the feed temperature with the boiling tempera-

ture corresponding to the separator pressure. If the feed is subcooled, it will

be preheated to its boiling temperature in a number of segments. If the feed

is superheated, it will be flashed down to the boiling temperature. The evapo-

ration calculations begin in the subsequent segments unless the feed enters the

evaporator already at its saturation temperature. The WI correlations are

used in the preheating zone. The Chun-Seban correlations are used in the

evaporation zone to calculate the liquid-side heat transfer coefficient. They

are also used throughout the whole surface area to calculate the condensate-

side heat transfer coefficient.

Fig. 3 Segmentation of the heat transfer area.

48

The calculations are iterative within each segment and over the evaporator

itself. The different iteration loops contain three parameters that check for

convergence with respect to concentration, E w, temperature, ct, and amount of

heat transferred, 'q'

An exact solution was created by setting all convergence

parameters equal to 10-5 and the number of segments equal to 50. A series of

runs were then executed to determine the optimum values of these four parameters

that yield a reasonable level of accuracy in an acceptable computer time. The

results of these runs gave the following values:

E = 10-3 = 10-z x ct

E = 5*10-z N = is q

The same procedure was repeated to optimize a number of relaxation variables.

The final results of these runs gave the following allowable errors for process

variables:

flow rate f 0.001 kg/s

concentration + 0.001 wt. fraction

temperature + 0.01 oc

heat flux/transfer coefficient f 0.5 W/m2.k

The package includes a comprehensive data base for calculating the physical

properties of the liquid such as dynamic viscosity, density, thermal conducti-

vity, boiling point elevation, specific heat capacity, and surface tension.

These properties are calculated as functions of concentration and temperature

for a number of liquids such as natural seawater, black liquor, sugar solutions

and skim milk. The thermodynamic properties of steam are also included in the

data base.

A special algorithm

the different loops of

RESULTS AND DISCUSSION

(ref. 11) is used to accelerate the convergence within

the package.

The program was tested for both smooth tubes and smooth plates. Both surface

configurations have the same behavior as far as heat transfer and fluid dynamics

are concerned. Because of lack of space, only the results for evaporation of

seawater on vertical smooth tubes are presented here.

To study the influence of process variables on the overall heat transfer

coefficient (U value), numerous sensitivity analysis runs were executed and

analyzed. The process variables studied and the numerical intervals investiga-

ted are illustrated in Table 1. The geometrical data of the evaporator tube

bundle were fixed during the simulation. The number of tubes was 71 with dia-

meters between 34 and 29 mm, length of 3.0 m and thermal conductivity of 238

W/I&, which represents an average value for the most common scale materials

49

encountered in seawater desalination.

TABLE 1

Sensitivity Analysis Data

Variable Numerical Interval

Unit Default Min. Max. step

Feed rate 0.9 0.4 1.0 0.05 kg/s Feed temperature 100 75 110 5 OC Feed concentration 4.2 3.5 10.5 1.0 Wt.% Steam temperature 115 106 120 2.0 OC Separator pressure 1.013 0.5 1.5 0.1 bar

Circulation ratio 0. 0. 0.7 0.1 -

Deposits thickness 0. 0. 0.8 0.05 mm

The influence of each variable on the behavior of the evaporation process

is discussed below.

Feed Flow Rate

The feed flow rate F was changed from 0.4 to 1.0 kg/s. Within this interval,

the flow regime on the liquid and condensate side of the tubes turned out to be

wavy-laminar. When F increases the evaporation decreases, since the hold-up

time of the liquid film decreases while the temperature difference across the

tube wall is practically constant. Rewriting eqn. (2) for the wavy-laminar

flow regime in the form:

= 0 825( X3gp2/w2,1/3 (4r/P)-2'g CL . (7)

it becomes clear that the local heat transfer coefficients on both sides of the

tubes (~1~ and CLC) would decrease when the liquid load, r, increases. It must

be emphasized that changes in liquid viscosity would greatly affect the values

according to eqn. (7). This influence is denounced in the case of seawater

since changes in the viscosity are very small due to moderate changes in the

concentration. The net result on the U value is shown in Fig. 4.

Feed Temperature

The feed temperature was changed from 75 to llO°C to cover both subcooling

and superheating cases. The liquid-side heat transfer coefficient increases

very little (l-2%) within this interval, due to small changes in Reynolds

number. The liquid film will remain within the wavy-laminar flow regime. The

condensate-side heat transfer coefficient shows the same behavior. Consequently,

the U value will increase by less than 2% within the investigated interval as

shown in Fig. 5.

8

Y

Ni .

3 -I

aJ I3

a == 4000

2

0.4 0.6 0.8 1.0

Feed flow rate, kg Is

x

NE 3 aJ- 3

a > I

3

30101 ! I I I I I

75 85 1

95 105

Feed temperature, “C

Fig. 4 U value as a function of feed flow rate. Fig. 5 u value as a function of feed temperature.

51

Feed Concentration

The feed concentration X was changed from 3.5 to 10.5 wt.%, which covers the

wide concentration range usually encountered in a multiple-effect evaporation

unit. Within this interval, both liquid and condensate films will remain'with-

in the wavy-laminar flow regime. The average liquid load p will remain relati-

vely constant as feed concentration increases, and therefore will not affect aL.

On the other hand, the average liquid concentration and hence the viscosity will

increase. The influence of brine viscosity on (IL will therefore dominate and

will decrease by 2.6% (from 5528 W/m2K at X = 3.5 wt.% to 5387 W/m'k at X = 10.5

wt.%).

Since aL

decreases with an increase in feed concentration, the condensate

flow rate will decrease as a result of a decreasing heat flux q. Since the

condensate flow regime is also wavy-laminar, then uC will increase by 6.5% as

X increases (from 8059 W/m2K at X = 3.5 wt.% to 8578 W/m2k at X = 10.5 wt.%).

The net result is a slight increase in the U value, as shown in Fig. 6.

Steam Temperature

The steam temperature was changed from 106 to 12OOC. This would give a

temperature difference At of 6-20°C relative to the feed temperature. The

amount of heat transferred to the liquid will increase as At increases. This

would enhance evaporation and hence decreases the liquid load r. Since the

liquid film flow is in the wavy-laminar regime, then aL will increase as At

increases (from 5309 W/&K at At = 6OC to 5665 W/m'K at At = 2O'C). The

condensate film load will increase with an increase in the heat flux. Conse-

quently. uc will decrease when t increases. These two contradictory results

will keep the U value almost constant as can be seen in Fig. 7. The maximum

change in the u value is 1.5% within the interval investigated.

Pressure of the Separator

The pressure of the separator P was changed from 0.5 to 1.5 bar. This

corresponds to a saturation temperature of pure water of 81.9 to 111.4'C. The

temperature difference, and hence the heat flux, will decrease as the pressure

in the separator increases. The evaporation will decrease and the liquid load

will therefore increase. This would result in a decrease in a as P increases. L

In fact dL decreased from 5816 W/m*K at P = 0.5 bar to 5562 W/m2K at P = 1.5

bar.

The average condensate flow rate will decline as P increases. This would

result in an increase in CL C

from 7044 W/&K at P = 0.5 bar to 9902 W/m2K at

P = 1.5 bar. The net result on the U value is shown in Fig. 8, where it first

decreases and then increases with the pressure in the separator.

3220 , , , , , ,, , , , , , , , ,

~ 3210-

i

2 a. 3200-

$

= 3190-

3180 ' 11 11 11 ' 1 '1 1 ' 11 3 4 5 6 7 8 9 IO

Feed concentration , wt *lo

Fig. 6 U value as a function of feed concentration.

3175

3150

1c

NE 3125

3 a; 3100 3 a 'r 3075

I I I I I I

30251 I I I I I I 106 110 114 118

Saturation temp. of live steam,OC

Fig. 7 U value as a function of live steam tempera-

ture.

-J

53

54

Circulation Ratio

The circulation ratio (R=FR/F) was changed from 0.0 to 0.7. The average

liquid load will increase when R increases, and this will obviously have the

same effect as with the feed flow rate. The U value will therefore decrease a!

R increases, as shown in Fig. 9.

Fouling Resistance

A fouling layer was simulated with a thickness range of 0.0 - 0.8 mm. This

is to be compared with the tube wall thickness of 2.5 mm. The U value will

drastically deteriorate as illustrated in Fig. 10.

In conclusion the sensitivity analysis runs revealed that the falling-film

evaporator simulated was more sensitive to changes in the thickness of a scale

layer and in live steam temperature, and less sensitive to changes in feed

temperature.

x

NE 2700 3 a~- 23M 3

2

' 19oc 1

1500 I I I I I I I __ 0.2 0.4 0.6

Thickness of deposits, mm 0.8

Fig. 10 U value as a function of thickness of deposits.

55

REFERENCES

W.H. mAdams, Heat Transmission, McGraw-Hill Co., 3rd ed., 1954.

M.N. Chepurnoy, V.E. Shnayaer and A.D. Berkuta, Heat Transfer in turbulent

flow of liquid films over vertical surfaces, Heat Transfer Soviet Research,

E(l), 62, 1976. VDI-Heat Atlas, 2nd ea., VDI-Verlag, Dusseldorf, 1974'.

K.R. Chun and R.A. &ban, Heat transfer to evaporating liquid films, J. of

Heat Transfer, Trans. ASME, 93C. 391-396, 1971.

W. Nusselt, Die Oberflachenkonaensation aes Wasserdamp fes., 2. vD1 60, 541-

546, 1916.

R. Zazuli in S.S. Kutadeladze, Fundamentals of Heat Transfer, Arnold, London, 1963.

A.E. Dukler, Fluid mechanics and heat transfer in vertical falling-film

systems, Chem. Eng. Prog. Symp. Ser. 30, l-20, 1960.

H. Struve, Heat transfer in a rising liquid film, VDI-Forschungsheft 534,

1969.

V.N. Murthy and P.K. Sarma, The Canadian Journal of them. Eng., 55, 732, 1977.

1U G. Schnabel and E.U. Schlunder, VT Verfahrenstechnik, 14(Z), 79-83, 1980. 11 A. Jernqvist, ADJUST-An adaptive convergence algorithm for general trial and

error computations, Report No. 75-F-1, Dept. of Chem. Eng. I, Lund University,

Sweden, 1975.