calculation of ipfbr

8/8/2019 Calculation of Ipfbr

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Pressure Drop in an

Interconnected Pressurised Fluidised Bed Reactor for

Chemical Looping Combustion

Research Report

Jens Wolf

February 2004

Energy ProcessesDepartment of Chemical Engineering and Technology

Royal Institute of TechnologyTRITA KET R189

ISSN 11043466ISRN KTH/KET/R--189--SE


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Abstract

Chemical Looping Combustion (CLC) is a new technique for CO2 capture in power

generation systems. In CLC, pure CO2 is obtained by applying a two-step combustion

with inherent CO2-separation. A subsequent CO2 separation process is not necessary.

Therefore, CLC has the potential to capture CO2 with lower penalties in efficiency.

The two-step combustion may be realised in an interconnected pressurised fluidised

bed reactor (IPFBR). This report presents a mathematical model for a rough

calculation of the pressure drop of such an IPFBR for CLC.


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Table of contents

1 BACKGROUND 5

2 THE CLC REACTOR HYPOTHETICAL DESIGN 7

3 CALCULATION OF THE PRESSURE LOSS IN THE IPFBR 9

3.1 The freeboard-entrainment model 9

3.2 Pressure drop and booster power 9

3.3 Terminal velocity 10

3.4 Height of the fluidised bed in the fuel reactor 11

3.5 Mean value of solid fraction in the freeboard 11

4 CALCULATION OF THE PRESSURE DROP IN A CYCLONE 13

5 CALCULATION OF THE PRESSURE SHELL 15

5.1 The cylinder 15

5.2 The ellipsoidal head 15

6 CONCLUSION 17

7 NOMENCLATURE 19

7.1 Greek letters 19

7.2 Indices 20

7.3 Abbreviation 20

8 REFERENCES 21


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1 BACKGROUND

Figure 1 illustrates the principles of CLC. A solid oxygen carrier circulates between

two fluidized bed reactors and transports oxygen from the combustion air to the fuel;

thus, the fuel is not mixed with air. The oxygen carrier is a metal oxide that is reduced

in a fuel reactor thereby oxidizing the fuel. The oxygen carrier is then transported into

an air reactor where it is oxidized by air and after passing a cyclone it is recycled back

into the fuel reactor. The reactions occur in two separate reactors.

The connection between the oxygen carriers and the system is the reactor. We assume

a reactor that we call the interconnected pressurised fluidised bed reactor (IPFBR)

which is described in Chapter2. Compared to a commercial gas turbine combustor the

IPFBR will cause a higher pressure drop when integrated in a power generation

process such as, for example, a natural gas fired combined cycle.

Fig. 1. Principles of the CLC

CO2H2O

N2 (+ O2)

CH4 (Fuel)N2+O2 (air)

Cyclone

Fuel reactor

Air-

reactor

Oxygen carrier

MetalOxygen

CO2H2O

N2 (+ O2)

CH4 (Fuel)N2+O2 (air)

Cyclone

Fuel reactor

Air-

reactor

Oxygen carrier

MetalOxygen


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2 THE CLC REACTOR HYPOTHETICAL DESIGN

The dimension of the air reactor is mainly determined by the size of the cyclones, the

fuel reactor, and a particle seal between the cyclones and the fuel reactor. The

cyclones may be about 16 m high and 4 m in diameter for the capacity of the 800

MWth (thermal input) of the CLC system. The input velocity is 15 m/s. For the fuelreactor, we assumed a height of 5 m and a diameter of 12 m. This height should lead

to a sufficient separation of the particles from the gas stream without any cyclones. In

ca 22 m

ca 25 m

4 5 m

ca 15 m

From compressor

To turbine

H2O/CO2

Fuel gas/ methane

ca 5 m

From compressor

To turbineH2O/CO2

Fig. 2. Example for a ca.800 MW CLC reactor system.


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order to leave enough space for the downcomer and the particle seal, we assume a

height of 25 m for the air reactor (the riser) (Figure 4). The diameter of the riser is 5

to 6 m. For this dimension assumption, a pressure vessel will be needed that has a

diameter of at least 18 m and a height of about 30 m.

Figure 2 shows the assumed design of the IPFBR with the fuel reactor of the bubble

bed type and the air reactor being essentially a pneumatic transport reactor. The

oxygen carrier particles are separated from the hot gases by a cyclone system similar

to that in a pressurised fluidised bed combustion (PFBC) system.


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3 CALCULATION OF THE PRESSURE LOSS IN THE IPFBR

3.1 The freeboard-entrainment model

The distribution of the fraction of solids over the freeboard is calculated using a

freeboard-entrainment model described by Kunii and Levenspiel2. According to this

model, the reactor may be divided into four fluidisation regions:

At the bottom is a relatively short entry zone. Because the contribution of this zone

to the total mass of solids in the reactor is of minor importance, the entry zone has

been neglected in the following calculations.

Following the entry zone, there is a portion of the vessel of almost constant solid

fraction. These lower portions may be called the dense region. The solid fraction

sd in this region was assumed to be 0.11. This figure was obtained by

extrapolating experimental results presented by Kunii and Levenspiel2. The section

of the vessel between the surface of the dense phase and the exit of the reactor is

called the freeboard, and its height is called the freeboard height (Hf).

Above the dense region is an upper entrained region where the solid fraction

decreases progressively to about s = 0.01-0.02. When increasing the freeboard

height, eventually, a solid fraction of 0.01 is reached. This may be called the

transport disengaging height (TDH). When the freeboard height exceeds the TDH,

the entrainment rate does not change significantly.

At the TDH, the fast fluidised bed may turn into a saturated pneumatic transport

with a particle fraction ofsp = 0.01.

If the freeboard is higher than the TDH, the maximum flowrate of solids between the

air reactor and the fuel reactor (also called carryover) is limited by the saturated

pneumatic transport flow.

3.2 Pressure drop and booster power

The pressure drops of the fuel reactor and air rector are calculated using Equations 1

and 2:

fD,fB,f PPP += (1)

CaD,aB,a PPPP ++= (2)

where PB,f is the pressure drop in the fluidised bed and PD,f the pressure drop

caused by the gas distribution. PC is the pressure drop over the cyclone. The pressure

drop over the fluidised bed PB is calculated using Equation (3), which is derived

form the hydrodynamics described by Carberry and Varma1

and Kunii and

Levenspiel2.


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A

gM2.1PB

= (3)

According toEquation (3), the pressure drop is the total fluidised mass (M) per area

(A) of the reactor multiplied by the gravitation constant. Because of the large diameter

of the reactors, the pressure loss caused by friction with the wall is neglected.

The fluidised mass in the fuel reactor Mf is calculated as the product of the carryover

( sm& ) and the residence time (f) of the particles in the fuel reactor(Equation 4).

fsf mM = & (4)

The fluidised mass in the air reactor Ma is calculated using Equation (5),

( ) sasFfsdda AHHM += (5)

where Hd is the height of the dense region, sd its solid fraction and Hf is the height of

the freeboard. sF is the mean value of the solid fraction over the freeboard. The

detailed calculation of sF is shown in Section 3.5.

The pressure drop across the gas distributors is calculated fromEquation (6)2

BD P0.4P = (6)

For the cyclones, an overall pressure drop (PC) has been calculated according to a

model described by Sinnott3(Chapter 4). In this study four pairs of cyclones are used

(Figure 4).

The gas turbine compressor or an additional booster fan has to overcome the pressure

loss in the fluidised beds. This booster power FW& was calculated by the flow equation

for a reversible adiabatic process and the isentropic efficiency of the fan (Equation 7).

( ) ( )12pfan

12

fan

F TTcmhhmW =

= &&& (7)

By assuming a perfect gas, T2 is calculated for the reversible adiabatic process where

n is equal to the isentropic coefficient (Equation 8).

+=

n

n1

1

112

PP

PTT (8)

For the power loss in the air reactor, T1 is the temperature of the air after compression.

For the fuel reactor T1 was 180C, because the natural gas was preheated to 180C.

The heat capacity (cp) was assumed to be constant.

3.3 Terminal velocity

The terminal velocity exists when the velocity drag force equals the gravitational

force. At this state, each particle is individually supported and they no longer rest

upon one another(Equation 8).


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g

s

D

p

T 1C3

dg4u

= (9)

The drag coefficient, CD, was calculated as a function of the Reynolds number for

particles at terminal velocity (ReT).

b

T

1D

Re

aC = (10)

= gpTT

duRe (11)

The constants a and b were approximated as Howard5(Table 1).

Table 1 Constants a and b for calculation of the drag coefficient.

Range of ReP Region a1 b0 < ReP < 0.4 Stokes law 24 1

0.4 < ReP < 500 Intermediate law 10 0.5

500 < ReP Newtons law 0.43 0

3.4 Height of the fluidised bed in the fuel reactor

The height of the fluidised bed in the fuel reactor was calculated usingEquation 12.

sf

fBfA

MH

= )1( (12)

The overall voidage fof the bubble bed (fuel reactor) was assumed to be 0.62. This is

in the range presented by Kunii and Levenspiel2

and Basu and Fraser4.

3.5 Mean value of solid fraction in the freeboard

The coefficient a inEquation 13 is estimated fromEquation 14.

F2 za

spsd

spsFe

=

(13)

constantua 02 = (for constant dp) (14)

The constant is estimated to five based on experimental results presented by Kunii

and Levenspiel2. However, the constant has to be determined experimentally for the

particles of oxygen carrier and the relatively large diameter of the air reactor for a fast

fluidisation.

The mean solid fraction over the freeboard is calculated withEquation 15.

( )F2F HaF

spsd

sp

H

0FsF

F

sF e1Ha

dz

H

1

+== (15)


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4 CALCULATION OF THE PRESSURE DROP IN A CYCLONE

According to Sinnott3, Stairmand developed two standard designs for gas-solid

cyclones: a high efficiency cyclone and a high throughput design. The high

throughput design, Figure 3, is suitable for high gas rates which we have in the

IPFBR.

The pressure drop in the cyclone will be due the entry and exit losses, and friction

kinetic energy losses in the cyclone. The empirical equation given by Stairman can be

used to estimate the pressure drop (PC):

+

+= 22

e

t22

1f

C 2u1r

2r21u

203

P (17)

Here the inlet duct velocity is u1 and the exit duct velocity is u2. rt is the radius of the

circle to which the center line of the inlet is tangential and re is the radius of exit pipe.

The factor can be taken fromFigure 4, where the parameter is proportional the

ratio of As, which is the surface area of the cyclone exposed to the spinning fluid, and

A1 , which is the area of the inlet duct:

1

sC

A

Af =

The friction factor (fC) is 0.005 for gases. For design purpose As can be taken as equal

to the surface area of a cylinder with the same diameter as the cyclone and length

equal to the total height of the cyclinder (barrel pus cone).

Fig. 3. Standard cyclone dimension of a high rate cyclone (Picture from Sinnott)


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Fig. 4. Cyclone pressure drop factor (Sinnott)


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5 CALCULATION OF THE PRESSURE SHELL

The dimensions of the pressure shell can be calculated according to the Swedish

standards for pressure vessels (Tryckkrlskommissionen6). In order to simplify the

calculation no holes and welding seams are considered.

5.1 The cylinder

The minimum thickness of the wall (Smin) for the cylinder was calculated with

Equation (18).

zS

20

PDS

f

desmin

= (18)

D is the inner diameter of the shell and P is the design pressure (overpressure). The

security factor was taken as Sf = 1.5. Z is a strength factor, which depends on holes

and welding seams in the shell. Here, we neglect the impact of holes and welding

seams and set the strength factor to one.

des is the design stress for the steal and can be found, for example, in the Swedish

standards for pressure vessels (Tryckkrlskommissionen7). These calculations are only

valid for Smin/D 0.05.

5.2 The ellipsoidal head

The minimum wall thickness of the head can be calculated according to Equation

(19).

zS

20

yPDS

f

des

y

min

= (19)

Here Dy is the outer diameter of the ellipsoidal head and y is a form factor, depending

on the shape of the head. If the form for the head is determined byEquations (20) to

(22), the form factor is y = 1.3.

h = height of the ellipsoidal head yD25.0 = [mm] (20)

R = crown radius yD8.0 = [mm] (21)

r = knuckle radius yD154.0 = [mm] (22)

For the ellipsoidal head, the security factor is Sf= 1.1 mm


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6 CONCLUSION

The presented mathematical model for calculating the pressure drop of an

interconnected pressurised fluidised bed reactor (IPFBR) for chemical looping

combustion (CLC) gives an idea about the pressure loss in such a reactor depending

on its dimensions. However, the size of the cyclone system is very important for theoverall size of the reactor. For this reason a more detailed model for the cyclone

system is required.


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7 NOMENCLATURE

A = area [m2]

A1 = area of the inlet duct (Eq. 17) [m2]

As = surface area of cyclone exposed to the spinning fluid (Eq. 17) [m2]

CD = drag coefficient [-]

cp = heat capacity [kJ/kg,K]

D = inner diameter of the shell (Eq. 18) [mm]

Dy = outer diameter of the ellipsoidal head (Eq. 19) [mm]

dp = particle diameter [mm]

fC = friction factor, taken as 0.005 for gases (Eq. 17) [-]

g = gravitation constant [m/s2]

HBf = height of the fluidised bed in the fuel reactor [m]

Hd = height of the dense region [m]

HF = height of the freeboard [m]

Hf = height of the fuel reactor [m]

hi = specific enthalpy [kJ/kg]

M = mass of fluidised bed [kg]

m& = mass flowrate [kg/s]

n = isentropic coefficient (Eq.8) [-]

P = pressure [bar]

P = design pressure (overpressure) (Eq. 18 + 19) [bar]

PC = cyclone pressure drop (Eq. 17) [mbar]

ReT = Reynolds number for particles at uT [-]

rt = radius of circle to which the center line of the inlet is tangential [m]

re = radius of exit pipe (Eq. 17) [m]

Sf = security factor (Eq. 18 + 19) [-]

T = temperature [C]

uT = terminal velocity [m/s]

u1 = inlet duct velocity (Eq. 17) [m/s]

u2 = exit duct velocity (Eq. 17) [m/s]

FW& = fan power [MW]

z = variable of height [m]

z = strength factor (Eq. 18 + 19) [-]

7.1 Greek letters

= voidage = (Vg-Vs)/Vg [-]

s = solid fraction = 1- [-]


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s = mean solid fraction [-]

sd = solid fraction in the dense region [-]

sp = solid fraction at saturated pneumatic conditions [-]

fan = isentropic efficiency of the fan [-]

= dynamic viscosity [N,s/m2

]f = gas density (Eq. 17) [kg/m

3]

g = fluid density [kg/m3]

s = particle density [kg/m3]

= factor fromFigure 4 (Eq. 17) [-]

= Parameter inFigure 4 (Eq. 17) [-]

= residence time/ reaction time [s]

des = design stress (Eq. 18 + 19) [N/mm2]

7.2 Indices

a = air reactor

B = fluidised bed

C = cyclone

d = dense region

D = distributor

F = freeboard

f = fuel reactor

g = gas

s = solid

7.3 Abbreviation

CLC = chemical-looping combustion

PFBC = pressurized fluidised bed combustion

IPFBR = two interconnected pressurised fluidised bed reactors

TDH = transport disengaging height

TIT = turbine inlet temperature (temperature of the gas when it

enters the first expander step


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8 REFERENCES

1. Carberry, J. and Varma, A., Chemical Reaction and Reactor Engineering,

Dekker, New York, USA 1986, ISBN: 0-8247-7543-0.

2. Kuni, D. and Levenspiel, O., Fluidization Engineering, 2nd Edition,Butterworth-Heinemann, USA 1991, ISBN 0-409-90233-0.

3. Sinnott, R.K, Coulson and Richardsons, Chemical Engineering, Vol. 6,

Butterworth-Heinemann, Great Britain 1996, ISBN 0-7506-2558-9

4. Basu, P. and Fraser, S. A., Circulating Fluidized Bed Boilers Design and

Operations, Butterworth-Heinemann, USA 1991, ISBN 0-7506-9226-X.

5. Howard, J.R., Fluidized Bed Technology - Principles and Application, Adam

Hilger, Bristol, UK, 1989

6. Tryckkrlskommissionen, Tryckkrlsnormer Normer fr

hllfastighetsberkning av tryckkrl, fifth edition, Lagerblads Tryckeri AB,Stockholm, Sweden 1987, ISBN 91-85254-00-2.

7. Tryckkrlskommissionen, Tryckkrlsnormer Kapitel 4 - Material, Lagerblads,

Karlshamn, Sweden 1987, ISBN 91-85254-00-2.

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