Modeling Conversion in a Fluid Catalytic Cracking Regenerator

7/29/2019 Modeling Conversion in a Fluid Catalytic Cracking Regenerator

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Res. J . Appl. Sci. Eng. Technol., 3(6): 533-539, 2011

534

Fig.1: Schematic diagram of an FCC unit

region the catalyst inventory is very low, it is assumedthat the dilute region has no effect on the regeneratorperformance (Ali et al., 1997). Most of the combustionreactions occur in the dense bed region and will be theregion of focus. This region is characterized by a bed ofsolid catalyst particles and the air which flows through thebed for catalyst regeneration. The dense bed is furtherdivided into two sections namely the emulsion phase andthe bubble phase. In this model however, the entire densebed is considered as a single CSTR and a single PRF forthe sake of simplicity. The assumption is also made thatthe regenerator is a constant density system. For aconstant density fluid flowing in a system of volume V at

a flow rate Q, the mean residence time (J) of fluid istheoretically defined as J =V/Q (IAEA, 2008). It isalso assumed that the coke consists of only carbon(Ali et al., 1997).

The ideal steady-state mixed flow reactor is one inwhich the contents are well stirred and uniformthroughout. Thus, the exit stream from this reactor has thesame composition as the fluid within the reactor. For thistype of reactor, mixing is complete, so that thetemperature and the composition of the reaction mixtureare uniform in all parts of the vessel and are the same asthose in the exit stream (Levenspiel, 1999)

For a given reactor, the general material balance equationis given by:

Input =output +disappearance +accumulation (1)

From Fig. 2, and at steady state, if FA0 =L0CA0 is themolar feed rate of component A to the reactor, then:

Input of A, moles/time = (2)( )F X FA A A0 0 01 =

Fig. 2: Notation of a mixed reactior

Output of A, moles/time = (3)( )F X FA A A0 1 =

Disappearance of A by reaction, moles/time:

(4)( ) ( )( )( )= =

r V

molesof Areacting

time volumeof fluidVolumeof reactorA

Introducing (2), (3) and (4) into Eq. (1), we obtain:

(5)( )F X r VA A A0 =

This on rearrangement becomes:

(6)V

F Cor

V

V

VC

F

C X

rA A

A

A

A A

A0 0 0

0

0

0= = =

where XA and rA are measured at exit stream conditions.For the special case of constant density systems, XA =1 -CA/CA0, in which case Eq. (6) can be written in terms ofconversion as:


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Fig. 3: Plug flow notation

(7)

= =

=

V C X

r

C C

rA A

A

A A

A

0 0

Equation (7) represents the performance equation for

mixed reactors.Therefore, for the second order reaction for the

combustion of coke in an ideal mixed flow reactor withequimolar feed of coke and air, the performance equationis given by:

(8)k or Ck C

k

C C

C AAA A

A

= =

+ + 0 2

1 1 4

2

0

0

where;k =rate constant in the rate equationJ =mean residence time

CA0 =inlet/initial concentration of A into reactorCA =final or concentration of A at reactor outlet

In the plug flow reactor, as shown in Fig. 3, the feedenters at one end of a cylindrical tube and the productstream leaves at the other end. The long tube and the lackof provision for stirring prevent complete mixing of thefluid in the tube. The absence of longitudinal mixing isthe special characteristic of this type of reactor. In a plugflow reactor, the composition of the fluid varies frompoint to point along a flow path (Levenspiel, 1999).Consequently, the material balance for a reactioncomponent must be made for a differential element ofvolume dV. Thus for reactant A, Eq. (1) at steady state,becomes

Input = output + disappearance by reaction +accumulation

From Fig. 3, we see for volume dV thatInput of A, moles/time =FAOutput of A, moles/time =FA+dFADisappearance of A by reaction, moles/time:Introducing these into (1), we obtain:

( )( )( )

( )

= =

r V

molesof Areacting

time volumeof fluid

Volumeof reactor

A

( ) ( )F F d r dVA A FA A= + +

Noting that:

( )[ ]dF d F X F dXA A A A A= = 0 01

On replacement we obtain:

(9)( ) =r dV F dXA A A0

This then is the equation which accounts for A in thedifferential section of reactor of volume dV. For thereactor as a whole, the expression must be integrated.Now FA0, the feed rate is constant but rA, is certainlydependent on the concentration or conversion ofmaterials. Grouping the terms accordingly, we obtain:

dV

F

dX

r

Af

A

A

A

Xv

0 00

=

Thus:

(10)

V

F C

dX

r

Afor

V

v

VC

FC

dV

r

Af

A

A

A

X

A

AA

A

X

0 40 0

0

0

0

00

= =

= = =

For second order irreversible reaction with equimolar feedfor any g:


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(11)

( ) ( )

( )

C k X X

X

X

A A A A A A

AA

A

02

2

2 1 1

11

= +

+ +

ln

For constant density systems, the expansion factor,g =0,Eq. (11) becomes:

(12)C kX

Xor X

C k

C kA

A

AA

A

A0

0

01 1

=

=

+

where XA =Conversion of A

This is the performance equation for a second orderreaction in an ideal plug flow reactor However, realequipment always deviates from these ideals. Deviation

from the two ideal flow patterns can be caused bychanneling of fluid, by recycling of fluid, or by creationof stagnant regions in the vessel. This is because elementsof fluid taking different routes through the reactor maytake different lengths of time to pass through the vessel.

The time an atom spends in a reactor is called theresidence time. The distribution of these times for thestream of fluid leaving the vessel is called the exit agedistribution E, or the Residence Time Distribution (RTD)of fluid (Richardson and Peakok, 1994). Therefore, the Ecurve is the distribution needed to account for the non-ideal flow (Levenspiel, 1999).

The RTD is determined experimentally by injectingan inert chemical molecule or atom called tracer, into the

reactor at some time t =0 and then measuring the tracerconcentration C, in the effluent stream as a function oftime. The tracer usually possesses physical propertiessimilar to those of the reacting mixture, so that itsbehavior will reflect that of the material flowing throughthe reactor. The tracer must not disturb the flow pattern ofthe system. The analysis of the output concentration withtime, gives the desired information about the system andhelps to determine the residence time distribution functionE(t) (Meyers, 1992; Smith et al., 1996; Fogler, 1997).However, in this work, the tank-in-series model is used togenerate the RTD curve for the simulation.

The application of the RTD to the prediction of

reactor behavior is based on the assumption that eachfluid (assume constant density) behaves as a batch reactorand that the total reactor conversion is then the average ofthe fluid elements, that is:

The RTD function given by the tank-in-series model is asfollows:

(14)( ) ( )E t tt

t

N

N e

N N tN

t

=

1

1

1

!

where;

=mean residence time =Jtt =timeN =number of tanksIntroducing (8), (12) and (14) into (13), we obtain:

(15)

( )

Ck C

k C t

t

t

N

N e dt

A

A

A

N

NtN t

= + +

1 1 4

2

1

1

0

00

1

!

/

(16)( )

XC k

C k t

t

t

N

Ne dtA

A

A

N NtN t=

+

0

0

1

01

1

1

!

/

Equations (15) and (16) therefore, are theperformance equations for the non ideal mixed and plugflow regenerator respectively, with A equal to C, coke-on-catalyst.

Regenerator kinetics: The reactions taking place in theregenerator are coke combustion reactions. This coke isthe byproduct of the cracking reactions taking place in theriser and gets deposited on the catalyst surface in thecourse of cracking. The intrinsic carbon combustion onthe surface of the catalyst corresponds to a couple ofreactions producing CO and CO2 with second orderkinetics (Bollaset al., 2005). The oxidation of CO takesplace by two ways with different first order rate constants,one is homogeneous oxidation in the gas phase and theother is catalytic oxidation (Krishna and Parkin, 1985;Arbel et al., 1995). The overall rate expression for the COoxidation can be obtained by adding the rates ofhomogeneous and heterogeneous oxidation reactions.

The following combustion reactions are consideredto be taking place in the regenerator where the summationis over all fluid elements in the reactor exit stream whichcan be written analytically as:

Meanconcentration

of reac tinreactor

outlet

concentrationof reac t

remainingin fluidelement

of agebetweentandt dt

fractionof exitstreamthat

consistsof fluidelementsof age

betweentandt dt

tan

tan

=

+

+


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Table 1: Industrial data for the regenerator reported by Ali et al. (1997)

Regenerator diameter (m) 5.8Regenerator height (m) 11Catalyst flow rate (kg/s) 144Coke on spent catalyst (kg coke/kg catalyst) 0.0081

Regenerator temperature (K) 960Regenerator volume (m3) 290.66Density of coke (kg/m3) 2267Density of CO (g) (kg/m3) 4.355

( ) ( ) ( )C C t E t dt or X X EdtA A A A element= =

0 0

.

in conversion terms (13)

C(s) + O2 (g) CO(g) k1 (17)C(s) +O2 (g) CO2(g) k2 (18)

Combining Eq. (1) and (2) gives:

2C (s) +3/2 O2(g) CO +CO2 k1 +k2 =Kc (19)2CO(g) + O2(g) 2 CO2 (g) kca+kh =Kco (20)

The initial ratio of CO/CO2 at the catalyst surfacegiven by Weisz (1966) is:

(21)COCO k k c esurface

c

E RT

21 2 0

= = =

/

wherek1 =Coke combustion rate constant to form CO

[1/(atm s)]k2 =Coke combustion rate constant to form CO2

[1/(atm s)]$c =CO/CO2 ratio at the catalyst surface in the

regenerator$c0 =Pre-exponent constant in$cexpressionE$ =Energy of activationR =Gas constant [kJ/(kmol K)]

T =Temperature (K)

IfKcis the overall coke combustion rate, then:

Kc =k1 +k2

Table 3: Calculated parameters

Coke-on-catalyst (kg/h), (m3/h) 4197.6, 1.8516Mean residence time, J, (h) 156.98Initial coke concentration, CAO, (kmol/m

3) 1.203Coke combustion rate constant, kc (1/atm.h) 1098

CO Combustion rate constant, kco((1/atm.h) 150.12

where k1 =($ckc/ $c+1), k2 =kc/ $c +1Kc =kcoe

-Ec /RT Kca=kcao e-Ecao /RT Kh =Kho e

-Eho /RT

Regenerator simulation: The regenerator is simulatedusing the plant data given in Table 1 reported byAli et al. (1997). The values of other parameters used inthe simulation are listed in Table 2. Table 3 also presentsparameters which were calculated with data from Table 1and 2 and also used for the simulation.

Using Eqs. (15) and (16), an Excel Spreadsheet wasdeveloped which gives the overall coke-on-catalystconversion. The regenerator was modeled as a mixedreactor and as a plug flow reactor assuming variousregenerators operating conditions, such as number oftanks, dead volume and flow rate.

In a mixed flow regenerator, the influence of thepresence of dead volume (Vd) on the overall conversionwas investigated keeping the volumetric flow rate of cokeconstant. The dead volumes assumed to exist in theregenerator are 40.66, 90.66 and 140.66 m3 and theircorresponding calculated mean residence times are 135.02h, 108. 01 h and 81.01 h. The effect of flow rate onconversion was also investigated. Coke-on-catalyst flowrates of 1.5, 0.5, and 0.1 m3/h and their correspondingmean residence times of 193.77, 581.32 and 2906.6 h

were used for the simulation. The results of the simulationare shown in Fig. 4-8.

RESULTS AND DISCUSSION

For the regenerator modeled as a mixed flow reactor,the maximum overall coke-on-catalyst conversion of88.85% was obtained for n =1, which represents perfectmixing condition of continuously stirred tank as shown bythe E-curves (Fig. 5) generated by the simulation. Thisconversion is the same as what was obtained when theperformance equation of a continuously mixed reactor(without the RTD function) was used. As the number

Table 2: Parameters used for the simulation of regenerator

MW coke, Molecular weight of coke (kg/kmol) 12.0 (Arbel et al., 1995)$co, Pre-exponent constant in$c expression 9.5310-4 (Arbel et al., 1995)kco, Pre-exponent constant in kc, [1/(atm s] 1.06910

8 (Arbel et al., 1995)Kcao, Pre-exponent constant in kca[kmol CO/(kg catalyst atm

2 s)] 116.68 (Arbel et al., 1995)Ec, Activation energy for coke combustion [E/R,

oK] 18889 (Arbel et al., 1995)Eh, Activation energy for homogeneous CO combustion [E/R,

oK] 35556 (Arbel et al., 1995)Eca, Activation energy for catalytic CO combustion [E/R, K] 13889 (Arbel et al., 1995)Kho, Pre-exponent constant in k3h[kmol CO,(m

3 atm2 s)] 5.0641014(Arbel et al., 1995)Density of coke (kg/m3) 2267


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89.5

87.5

88.5

86.5

85.5

84.5

89

88

87

86

85

0 5 10 15 20 25

Vd=0

Vd=40m3

V=90m3V=140m3

Number of tanks (N)

Conversion

(

)

0.014

0.012

0.01

0.008

0.006

0.004

0.002

0

-0.002

E(t), n=1

E(t), n=2

E(t), n=5E(t), n=10

E(t), n=20

0 500 1000 1500 2000 2500

t(s)

E(t)

102

100

98

96

94

92

90

880 5 10 15 20 25

Q=1.5m3h

Q=0.5m3/h

Q=0.1m3h

Number of tanks (N)

Conversion(%)

1.4

1.2

1

0.8

0.6

0.4

0.2

01 2 3 4 5

Vd=0

Vd=40m3

V=90m3V=140m3

Number of tanks (N)

Conve

rsion(%)

0.6

0.5

0.4

0.3

0.2

0.1

01 2 5 10 20

Q=1.5m3/h

Q=0.5m3/h

Q=0.1m3/h

Number of tanks (N)

Conversion(

)

Fig. 4: Effect of dead volume (Vd) on coke-on-catalystconversion in mixed flow regenerator

Fig. 5: E(t) functions for different degrees of non-ideality in amixed fcc regenerator

Fig. 6: Effect of coke-on-catalsyt flow on conversion in mixedregenerator

of tanks (n) increased, conversion of coke-on-catalystdecreased as seen in Fig. 4. Increasing n implies moremixing zones indicating more non-ideality andmalfunction resulting in poor conversion. It is also evidentfrom the above figures that beyond n =2, there was nochange in the model prediction.

Simulation results also revealed that for a given n,conversion decreased with increasing dead volume. Thedead volume normally is considered a blocked zone which

Fig. 7: Effect of dead volume (Vd) on coke-on-catalystconversion in a plug flow regenerator

Fig. 8: Effect of coke-on-catalyst flow rate on coke conversionin plug flow regenerator

does not take part in the reaction. It could be caused byscaling, solidified material or other barrier or poorequipment design. The long tails of the E-curves depictsthe slow exchange of flow between the active and the

dead volume (IAEA, 2008). Thus the presence of deadvolume reduces effective volume of reactants for reaction,thereby decreasing conversion.

Conversion decreased with increasing n for coke-on-catalyst flow rates 1.5 and 0.5 m3/h. For a flow rate of 1.5m3/h, the model prediction of conversion did not changebeyond n =5. However, at a flow rate of 0.1 m3/h, it wasobserved that conversion increased with increasing n.Generally, however, conversion increased with decreasingcoke flow rate as shown by Fig. 6. A conversion of99.99% was obtained for a flow rate of 0.1 m3/h forn =10 in the mixed flow regenerator. A small flow rateimplies a large residence time. When the residence time

is large, there is a higher chance for mixing to occur in thereactor since on average reactants are spending moretime in the reactor, thus increasing the chance ofconversion, holding all other parameters constant(Ingham et al., 2000). For a plug flow regenerator,conversion was found to increase with increasing deadvolume for a given n and decrease with increasing n for agiven dead volume. Beyond n =5, conversion did notchange (Fig. 7). It was also observed that conversiondecreased with decreasing flow rate for a given n and for


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539

a given flow rate conversion decreases with increasing n(Fig. 8). Since the ideal plug flow reactor has no provisionfor mixing or dispersion, there is no easy interactionbetween the reactants and hence the generally poor

conversion in the plug flow regenerator.

CONCLUSION

The simulation of conversion of coke-on-catalyst ina mixed flow and plug flow regenerator suggests that it isless efficient as plug flow reactor. This may be due toseveral factors such as channeling or bypassing of thefluid in the reactor. If the reactor had been designed usingthe usual plug flow model, the actual performance in theplant would be far less than expected. For a higherconversion in the reactor, some modifications would berequired to remedy the non-ideal flow.

ACKNOWLEDGMENT

The authors are grateful to the IAEA (InternationalAtomic Energy Agency) for technical support.

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Modeling Conversion in a Fluid Catalytic Cracking Regenerator

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