Effect of feed atomization on FCC performance: simulation of entire unit

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Effect of feed atomization on FCC performance:

simulation of entire unit

Ajay Gupta

¹

, D. Subba Rao*

Department of Chemical Engineering, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110016, India Received 11 June 2002; received in revised form 1 July 2003

Abstract

Entire 4uid catalytic cracking (FCC) unit, comprising of a riser and a regenerator, is simulated by integrating FCC riser model presented in our earlier work (Chem. Eng. Sci. 56 (2001) 4489) with an FCC regenerator model. The effect of feed atomization (quantified by average drop size generated by the feed nozzle) on the performance of the unit is evaluated.

Keywords: Fluid catalytic cracking; Atomization; Riser; Regenerator; Selectivity; Simulation

1. Introduction

Fluid catalytic cracking (FCC) unit is a major system in a petroleum re8nery. It converts vacuum gas oil (VGO) to useful products like LPG, gasoline and cycle oils by catalytic cracking. Schematic of an FCC unit is shown in Fig. 1.

The unit primarily comprises of two reactors, a riser and a regenerator. VGO is dispersed into the riser bottom in the form of drops through a feed nozzle system. The VGO drops contact hot regenerated catalyst particles entering from the regenerator and get vaporized. The vapor entrains the catalyst particles and liquid drops while getting cracked on the catalyst surface along the riser height. In the process the catalyst progressively gets deactivated due to deposition of coke (formed during cracking reactions) on its surface. The deactivated catalyst leaving the riser top is transferred to the regenerator where its activity is restored by burning the coke.

Performance of the riser and regenerator are closely linked.

Combustion of the coke on catalyst particles, produced in the riser by cracking reactions, in the regenerator generates the heat needed in the riser for VGO feed vaporization and endothermic heat of cracking reactions. The intricate heat

and coke balance between the riser and the regenerator is maintained by adjusting the catalyst circulation rate between the two. Models of riser and regenerator need to be integrated to simulate the performance of entire FCC unit.

1.1. Models on riser performance

FCC riser is a complex system to model because of in- tricately interrelated hydrodynamics, heat transfer, mass transfer and catalytic cracking kinetics. The parameters in4uencing these aspects also change all along the riser height:

• The feed is injected into the riser along with hot catalyst particles from the regenerator. The feed vaporizes and entrains catalyst as well as liquid drops along the riser height.

• Gas velocity increases due to vaporization of liquid feed.

• Gas velocity also increases due to molar expansion resulting from cracking of VGO to lower molecular weight products.

• Gas velocity in4uences the axial (and radial) pro8le of catalyst volume fraction.

• There is considerable slip between gas and catalyst particles.

• Hydrocarbon vapor gets cracked at the surface of catalyst particles to produce lighter hydrocarbons as well as coke.

Reactant and product hydrocarbons diffuse to and away

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Cracked Products

Flue Gas

FEED NOZZLE

M,,,T1Nl

FEED + STEAM Fig. 1. Schematic diagram of FCC unit.

from catalyst surface while coke deposits on the catalyst surface to progressively deactivate the catalyst.

• Catalyst temperature falls due to heat transfer for raising sensible heat of feed, its vaporization and endothermic heat of cracking reactions.

Several FCC riser models with varying degree of sim- pli8cations and assumptions are available in the literature.

Most of the reported FCC riser models assume

• Instantaneous vaporization of feed and thermal equilibrium between catalyst and hydrocarbons.

• Plug 4ow for gas and catalyst.

• Slip factor, ratio between gas velocity and catalyst velocity, equal to 1.

• Reactor as either isothermal or adiabatic.

• Lumped kinetics.

• Catalyst activity varying either with time-on-stream or coke concentration on catalyst with non-selective deactivation.

• Vapor velocity to be either constant along the riser height or increase due to molar expansion based on ideal gas law.

• Hydrocarbon concentration on catalyst surface to be same as that in the gas i.e. no resistance to mass transfer between hydrocarbon vapor and catalyst surface.

Corella and Frances (1991) considered the riser to consist of 3-4 well-mixed compartments and used a 8ve lump kinetic model. Variation of important variables such as slip factor, molar expansion factor, temperature dependent kinetics and catalyst deactivation factor from compartment to compartment were considered while they were assumed to be constant within each compartment. Fligner, Schipper, Sapre, and Krambeck (1994) proposed a cluster model approach to explain experimentally observed high slip factors.

They assumed riser to consist of two phases—a dispersed cluster phase containing all the catalyst and a continuous phase containing only gas. Reactions take place in cluster phase with consumption of reactants and generation of products. The resulting concentration gradients between gas phase and cluster phase provide the driving force for mass transfer between the two phases. Theologos and Markatos (1993) and Gao, Xu, Lin and Yang (1999) proposed three dimensional CFD models for FCC riser based on Eulerian approach. All these models assumed instantaneous vaporization of feed at riser bottom and hence neglected the effect of rate of feed vaporization on FCC riser performance. The performance of FCC unit (quanti8ed in terms of conversion and product selectivity) is affected significantly by the rate of vaporization of feed in the entry zone of the riser. The feed in liquid phase cannot react to crack. Slow vaporiza-

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tion of feed leads to very high catalyst to vaporized feed ratio coupled with high temperature and catalytic activity in the riser entry zone. These factors can lead to undesir- able secondary cracking reactions. Faster vaporization rates can be realized by effective feed atomization into fine drops.

A feed nozzle system which could atomize the liquid feed into very minute drops is therefore of prime importance for achieving higher conversion and better product yield distribution. Several re8neries across the world have replaced older FCC feed injection systems with newer designs and observed improvement in conversions and yield patterns.

Theologos, Nikou, Lygeros, and Markatos (1996, 1997) extended the CFD model of FCC riser proposed by Theologos and Markatos (1993) to include feed vaporization. The model could predict effect of geometrical place- ment of feed nozzles on the riser performance. In their later work Theologos, Lygeros, and Markatos (1999) accounted for the effect of feed atomization (quantified by average initial drop size produced by the feed nozzle) on overall reactor performance. Gao, Xu, Lin, and Yang (2001) extended the two phase gas-solid CFD model proposed by Gao et al.

(1999) to include vaporization of liquid feed in the form of spray in the entry zone of the FCC riser. Recently Gupta and Subbarao (2001) developed a three phase model for FCC riser taking into account effect of feed atomization on conversion and yield patterns achievable in a riser reactor.

The model could predict pro8les of overall conversion, product yields, temperature, axial solid holdup, catalyst activity besides several other parameters. The model results compared well with the industrial observations.

1.2. Models on regenerator performance

Most of the earlier regenerator models were based on the two phase bubbling bed models (Davidson & Harrison, 1963; Kunii & Levenspiel, 1969). These models assumed that most of the gas 4ows as bubbles through the dense phase, with dense phase in well mixed state and bubble phase in plug flow. To account for the effect of distributor design on the performance of regenerator, Behie and Kehoe (1973) and Errazu, de Lasa, and Sarti (1979) developed a Grid Model by considering the regenerator bed to consist of grid region and bubbling bed region axially. de Lasa, Errazu, Barreiro, and Solioz (1981) analyzed industrial FCC regenerators using five different models. They concluded that A CSTR model predicted results within 2% of Grid model predictions. The pure bubble model predictions were found to be at large deviation from Grid model. It was also concluded that one need not consider freeboard in combination with grid models.

All the models discussed above did not consider post combustion reaction of CO to CO2 and modeled the CO2/CO ratio as a function of temperature only. Krishna and Parkin (1985) modeled the regenerator dense bed assuming the catalyst to be well mixed and gas to 4ow through it in plug

4ow. Both homogeneous as well as catalytic post combustion reaction of CO with O2 to form CO2 were considered in the dense phase. Arbel, Huang, Rinard, Shinnar, and Sapre (1995) also modeled the dense bed region on lines of Krishna and Parkin's model however they assumed gas 4ow as three compartments (each well mixed with in itself) in series instead of plug 4ow. Sapre, Leib, and Anderson (1990) proposed a CFD model for the FCC regenerator to study the effect of catalyst entry and exit geometries.

1.3. Simulation of entire FCC unit

There are many attempts to simulate entire FCC unit (Arbel et al., 1995; Kumar, Chadha, Gupta, & Sharma, 1995;

Ali, Rohani, & Corriou, 1997; Malay, Milne, & Rohani, 1999; Arandes, Azkoiti, Bilbao, & de Lasa, 2000; Han &

Chung, 2001 a,b). These simulations were based on the assumption of instantaneous vaporization of feed at riser entry. In the present work, entire FCC unit is simulated by integrating the riser model of Gupta and Subbarao (2001) (which considered vaporization of feed drops in the riser) with a regenerator model to study the effect of feed atomization on FCC unit performance.

2. Modeling approach and assumptions

2.1. Riser

The riser model presented in our earlier work (Gupta &

Subbarao, 2001) is used. The riser is conceptually considered to consist of a number of equal sized compartments along the axis as shown in Fig. 2. In the entry zone each compartment consists of three phases—solid phase (catalyst particles), gas phase (atomizing/dispersion steam, vaporized feed, products) and liquid phase (drops). The catalyst particles and liquid drops are accelerated upwards due to drag exerted by the gas phase. The gas velocity also increases continuously along the riser height because of feed vaporization as well as decrease in vapor density due to formation of lower molecular weight products on cracking of VGO. Catalyst particles are assumed to move as clusters to account for the observed high slip velocities. The size of the cluster is assumed to be 6 mm (Fligner et al., 1994). The vapor density is calculated by using ideal gas law. A simple hydrodynamic model is proposed for the axial solid holdup and liquid drop holdup considering the local force balance.

The liquid fraction of feed, which is 1 at the riser en- trance, decreases progressively along the riser height due to vaporization. It is assumed that the liquid drops do not break or coalesce along the riser height and their size changes because of vaporization only. The liquid phase disappears as the feed is completely vaporized leaving only gas phase and solid phase in subsequent compartments.

In the heat transfer model, the riser is assumed to be adiabatic. The heat in the catalyst particles provides for heating

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4570

GAS

f, =

1

SOLIDS

LIQUID

T T

GAS

t

•1st;

Km-

T

SOLIDS

i-l

dd 0 >

^ l . T ^ Mst,Tgill,p

gin W , T si n ) P p

Fig. 2. Conceptual riser model.

of liquid, its vaporization, heating of vapor and endothermic heat of reaction. The heat transfer and vaporization of feed droplets in the riser is modeled on the lines of Buchanan (1994). The heat transfer is assumed to be predominantly convective. For heat transfer between 4uidized bed and liquid drops heat transfer coeNcients are corrected for enhance- ment due to presence of solids as well as reduction due to vapors emanating from the surface of a droplet.

The vaporized VGO diffuses to solid phase and gets cracked at the catalyst surface. While gaseous products diffuse back to gas phase, the coke produced gets deposited on the catalyst surface. A four lump model for kinetics of cracking reactions is used. The four lumps considered are feed, gasoline, gases and coke. The primary cracking of gas-oil is assumed to follow second order kinetics whereas secondary cracking of gasoline is assumed to follow 8rst order kinetics. The catalyst deactivation model is based on coke deposited on the catalyst. The kinetic model used in the present model can be easily substi- tuted by a more complex kinetic model with more number of lumps (corresponding to industrial FCC products) in future work.

Model equations are formulated for each phase in ith compartment for each jth lump in terms of material and energy balances considering hydrodynamics, heat transfer, mass transfer and reaction kinetics while accounting for gas phase properties and catalyst activity. Computations are performed for each compartment starting from the 8rst (bottommost) to generate values of variables shown for ith compartment in Fig. 2. The inlet conditions at the riser bottom are known. Within a compartment, each phase is assumed to be well mixed. In general outlet conditions for (i — 1 )th compartment serve as inlet conditions for ith com- partment. The solution procedure within a compartment is iterative. Size of each compartment is considered to be equal to size of cluster. The 4ow of computations is shown in Fig. 3. Salient FCC riser model equations are summarized in Appendix A.

2.2. Regenerator

Spent catalyst from the riser outlet, after steam stripping, enters the regenerator and is 4uidized by air entering through a distributor. Most of the modern regenerators operate in turbulent 4uidization regime with a dense region at the bottom containing most of the catalyst inventory and a dilute region on top.

The oxygen in air reacts with coke on catalyst to form carbon monoxide and carbon dioxide. Carbon monoxide fur- ther reacts with oxygen to form carbon dioxide. Catalytic as well as homogeneous oxidation of carbon monoxide is considered. Most of these combustion reactions take place in the bottom dense region of the regenerator. The dense region of the regenerator is modeled on the lines of Arbel et al. (1995). In the dilute region, the catalyst inventory and oxygen concentration is very low and it is assumed that coke combustion is essentially complete in the dense region.

The heat generated due to combustion of coke and oxidation of CO is used to raise sensible heat of catalyst and gas.

Heat losses from the regenerator to the surroundings are considered.

The conceptual model of regenerator dense bed is shown in Fig. 4. The regenerator dense region is considered to consist of two phases—gas phase (N2, O2, CO, CO2 and H2O) and cluster phase (catalyst particles). The gas phase keeps clusters in a 4uidized state. The bed voidage is estimated using King's (1989) correlation. It is assumed that molar 4ow rate of gas does not change due to combustion reactions. This assumption is justi8ed due to presence of large quantity of inert N2.

The cluster phase is assumed to be well mixed. The gas phase is conceptualized as 8ve equal sized well-mixed compartments in series, which approximate to plug 4ow. The gas phase and the cluster phase are assumed to be in thermal equilibrium. It is also assumed that there is no resistance to mass transfer of gaseous components between gas phase and cluster phase.

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Perform material balance to compute

From hydrodynamic model compute

8cj)8gj and 5^

Compute

Perform enthalpy balance to recompute

fi,,TgiandTsi

ij); = fyf F.Err

Fig. 3. Computation 4ow diagram of FCC riser model.

The inlet conditions for the 8rst gas phase compartment are known. For subsequent gas phase compartments the inlet conditions are same as the outlet conditions of compartment below. The values of coke on regenerated catalyst (CRC) and regenerator temperature (Trg) are uni- form everywhere in the regenerator and an initial guess is provided. The material balance equations are solved for each gas phase compartment considering regeneration kinetics and hydrodynamics. Overall material balance closure and energy balance equations are solved to calculate new values of CRC and Trg. The solution procedure is iterative. The 4ow of computations is shown in Fig. 5.

Salient FCC regenerator model equations are summarized in Appendix B.

3. Simulation of entire FCC unit

The riser' and the regenerator of FCC unit are highly coupled. The interaction between the two and the connect- ing variables are shown in Fig. 6. The catalyst enters the riser from the regenerator at temperature Trg (regenerator dense bed temperature), coke concentration CRC (coke on regenerated catalyst) and at a circulation rate of W. CRC de- termines the initial activity of the catalyst entering the riser.

Along the riser height, the catalyst temperature decreases while coke on catalyst increases. The deactivated/spent cat- alyst leaves the riser outlet, at temperature T^rx^o and coke on spent catalyst CSC, and enters the regenerator at a circula- tion rate W. At a given steady state the entire heat generated

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4572

GAS ^SOLIDS

W, Tm,C[ l p

Flue Gas

Cracked products W, 1 CSC

y, j= O,,CO,CO2,H2O

FA, Y O ^ O . H J T ^

1-B

1 e

Fig. 4. Conceptual regenerator model.

Input

Guess T_ and C__

Regenerator

TIg, CRC

i

I

Riser

Air

FA,Tain W,Ttg,CRC

Independent variables to riser model:

Independent variables to regenerator model:

Variable adjusted to achieve heat and coke balance : Dependent variables :

Q,d, F A . - W

Feed Q.<W

(o,CSC,Tra,CRC

Fig. 5. Computation 4ow diagram for regenerator model.

Fig. 6. Riser regenerator connectivity.

in the regenerator shall be consumed in the riser. Similarly the entire coke generated in the riser shall be consumed in the regenerator. These two conditions are achieved by adjusting catalyst circulation rate W. Other associated vari- ables Trg, CRC, Trxo and CSC settle to steady state values accordingly.

The feed rate Q, feed inlet temperature T\^m and drop size ddo are independent inputs to the riser model whereas air 4ow rate FA and air inlet temperature T^m are independent inputs to the regenerator model.

For simulating entire FCC a steady state base case (assuming 50 urn drop) with exact heat balance and coke balance between riser and regenerator was established.

Thereafter parametric study on effect of feed atomization (quanti8ed by average drop size produced by the feed nozzle) on performance of entire FCC unit was carried out.

The objective was to evaluate product yields, regenera- tor temperature T^rg, Catalyst circulation rate W and CSC on varying the drop size dd while maintaining a constant coke yield at riser outlet and constant CRC (at base case levels).

The riser and regenerator models were simulated itera- tively to attain the above objective. The procedure for simulation is summarized in Fig. 7. On simulating the riser for a

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Change base case inputs to riser model new drop size and guess value of TIC

Adjust W till you get coke make at base case level

Input

new W, corresponding CSC and Tftl

to the regenerator simulator

Table 1

Industrial FCC riser data reported by Ali et al. (1997)

Variable Value

Adjust air until you get CRC at base case level and get T

Fig. 7. Flow sequence for simulation of entire FCC unit.

feed drop size bigger than that of base case, keeping all the other variables unchanged, higher coke yield at the riser outlet was predicted. To bring the predicted coke yield to base case level, catalyst circulation rate W was adjusted. The ad- justed W and coke on spent catalyst (CSC), calculated for base case coke yield, were given as inputs to the regenerator model. The regenerator was then simulated while adjusting air 4ow rate to obtain CRC same as the base case (assumed to be 0.1%). The new Trg and W were fed back to riser model and predicted coke yield observed. The above procedure was repeated till we got coke make in the riser at the base case level.

4. Results and discussions

Data on FCC unit reported by Ali et al. (1997), presented in Table 1, were used for simulations assuming an initial drop size of 50 urn as the base case. Properties and kinetic constants used for simulations are provided in Appendix C.

After establishing the base case, simulations for the entire unit were carried out for bigger drop sizes up to 500 urn.

Results normalized with respect to the corresponding base case values are shown in Fig. 8a. It is predicted that for a bigger drop size, catalyst circulation rate has to be decreased (Fig. 8a) to achieve base case level coke yield. Lower catalyst circulation rate amounts to lower heat withdrawal from

Riser I.D.

Catalyst 4ow rate

Regenerator dense bed temperature Riser pressure

Riser outlet temperature Riser height

Feed 4ow rate Feed inlet temperature Air to regenerator

0^:8 m 144 kg=s 960 K 2:9 atm 795 K 33 m 20 kg=s 494 K 16 kg=s

the regenerator. This increases regenerator bed temperature (Fig. 8b). The trend is in line with observations in FCC units 8tted with improved nozzle systems where drop in regenerator temperature is observed. Kako (1991) reported a drop of 15°C in the regenerator temperature on replacing the old feed injection system with a new one. In our studies, since coke yield is 8xed at the base case, CSC corresponding to lower catalyst circulation rate (for bigger drop size) increases as shown in Fig. 8c. On the riser side it is predicted that with increase in feed drop size the conversion, gasoline yield and gas yield exhibit a falling trend (Fig. 8d-f). Re- garding behavior of gas yield versus feed drop size it shall be noted that the gas lump considered in the kinetic model comprise of dry gas (C1-C2) + LPG (C3-C4). In industry generally dry gas yield decreases with improved feed atomization, while LPG increases. Combined gas yield (C1-C4) increases with improved feed atomization. The model predictions are in line with the observations in industry. Table 2 presents the improvements in FCC unit performance reported by Goelzer (1986) and Bienstock, Draemel, Shaw, and Terry (1991), on replacing old feed nozzle systems with new improved ones. The delta changes reported are at a 8xed coke make.

5. Conclusions

Entire FCC unit comprising of a riser and a regenerator has been simulated. Effect of feed atomization (quantified by initial drop size produced by the feed nozzle) on the performance of the unit at a constant coke yield, has been studied through simulations. It is observed that catalyst circulation rate has to be adjusted to lower levels for bigger drop size to achieve heat and coke balance between the riser and the regenerator. Predicted values of overall conversion, gasoline yield and gas (C1-C4) yield increase with decreasing drop size. On the regenerator side, lower regenerator tempera- tures are predicted for smaller drop sizes. The predictions are in line with the improvements reported in industry on replacing a multi-pipe feed nozzle (poor atomization) with an improved spray feed nozzle.

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50 100 150 200 250 300 350 400 450 500 550 50 100 150 200 250 300 350 400 450 500 550 ( a ) Drop size (microns) ( b ) Drop size (microns)

1.14

1.12

1.1

S 1-08

1

8 1.06

J

1.04

1.02

1

/ /

/

50 100 150 200 250 300 350 400 450 500 550 ( c ) Drop size (microns)

50 100 150 200 250 300 350 400 450 500 550 (d) Drop size (microns)

£ 0.92 o JS

!ai 0.9 c

"5

\

\ •

\\ \\\

50 100 150 200 250 300 350 400 450 500 550 50 100 150 200 250 300 350 400 450 500 550 ( e ) Drop size (microns) (f) Drop size (microns)

Fig. 8. (a) Effect of feed atomization of catalyst circulation rate; (b) effect of feed atomization on regenerator temperature; (c) effect of feed atomization of carbon on spent catalyst; (d) effect of feed atomization on conversion; (e) effect of feed atomization on gasoline yield; (f) effect of feed atomization on gas yield.

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Table 2

Improvements in FCC unit performance on replacing old feed nozzle with new atomizing feed nozzle

Product yields/conversion

Dry gas, C1-C2 (wt%) LPG, C3-C4

Gasoline (vol%) Cycle oil (vol%) Bottoms (vol%) Coke

Overall conversion (vol%)

Delta change on Goelzer (1986) -0.90 +6^:60 vol%

+5.1 - 5 . 2 - 3 . 3 0 +8.5

replacing feed Bienstock et -0.10 + 1^:3 wt%

+4.2 -3.3 - 1

0 +4.4

nozzle al. (1991)

Notation

A

cc

c

^Ps

c

^Psi

C^T. C^pl C^P, Cd

dd

dp

Ej

fl

FA

g hl

hs

Hf Hr

Krj

M^st MWa

MWc

MWj P

qgl qsg

Q

heat transfer area between gas-liquid, m2

heat transfer area between gas-solid, m2

cross sectional area of riser, m2

coke concentration on catalyst, wt:=wt: cat coke on spent catalyst (CSC), wt:=wt: cat coke on regenerated catalyst (CRC), wt:=wt: cat speci8c heat of air, kJ=kg K

speci8c heat of gas phase, kJ=kg K

speci8c heat of component j in gas phase, kJ=kgK

speci8c heat of vaporized feed speci8c heat of liquid feed, kJ=kg K speci8c heat of solid, kJ=kg K drag coeNcient,

cluster diameter, m drop diameter, m particle diameter, m

activation energy for jth reaction, kcal/kmol liquid mass fraction of feed

4ow rate of air to regenerator, kmol/s gravitational acceleration, m=s2

gas-liquid convective heat transfer coeNcient, kW=m2 K

gas-solid convective heat transfer coeNcient, kW=m2 K

heat of formation, kJ/kmol heat of reaction, kJ/kg

heat generated in regenerator, kJ/s

mass transfer coeNcient of component j, 1/s reaction kinetic constant for jth

reaction, mr3=mcat3 s

mass 4ow rate of steam, kg/s molecular weight of air, g/mol molecular weight of coke, g/mol molecular weight of component j, g/mol pressure, atm

heat transfer from gas to liquid phase, kW heat transfer from solid to gas phase, kW mass 4owrate of hydrocarbon feed, kg/s

rj rate of production of component j: in riser, kg=s m3 cat; in regenerator, kmol=s m3

R gas constant, kcal=kmol K R! gas constant, atm m3=kmol K S slip factor

t time, s

TAin air temperature at regenerator inlet, K

Te equilibrium temperature of gas and solid after complete vaporization, K

T^g temperature of gas, K

T\^m liquid feed temperature at riser inlet, K Tl^s liquid boiling temperature, K

T^s temperature of solids (catalyst), K

T^siⁿ temperature of solids at riser inlet (=T^rg), K T^rg regenerator dense bed temperature, K Trxo temperature of catalyst at riser outlet, K u gas super8cial velocity, m/s

uc cluster velocity, m/s ud drop velocity, m/s ug gas actual velocity, m/s Vc volume of cluster, m3

Vp volume of particle, m3

W mass 4ow rate of solids, kg/s

yj mole fraction of component j (regenerator), j = O2 ;C O;C O2 ;H2O

ycj mass fraction of component j in cluster phase (riser), j = 1;2;3;4 ( V G O , gasoline, gas, coke) ygj mass fraction of component j in gas phase (riser), j = 1;2;3;4 ( V G O , gasoline, gas, coke) yldj yield o f component j , wt% o f feed

z axial height, m

Zd total dense bed height, m Az height of compartment, m Greek letters

bc cluster holdup fraction bg gas holdup fraction (l liquid holdup fraction s voidage

sc cluster phase voidage 4> catalyst activity factor

X latent heat of vaporization, kJ/kg p^c cluster density, kg=m³

pg gas phase density, kg=m3

Pgo V G O v a p o r density, kg=m3

pi liquid density, kg=m3

pp particle density, kg=m3

Hg gas phase viscosity, kg=m s Appendix A. Riser equations

A.1. Liquid phase material balance

Mass in from (i — 1 )th compartment—Mass out from ith compartment = Mass vaporized in the ith compartment:

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A.2. Gas phase material balance

For VGO Mass vaporized in ith compartment + Mass in from (i — 1 )th compartment — Mass out from ith compart- ment = Mass transfer to cluster phase:

li) + (Q(1 - //,_,) +M fli) + Mst)ygj;i = mji:

For gasoline and gas

(A.2) Mass in from (i — 1 )th compartment — Mass out from ith compartment = Mass transfer to cluster phase:

(Q(1 - f

=mji

- fli)+Mst)ygj;i

(A.3) 3. Cluster phase material balance

For VGO, gasoline and gas

Mass transferred from gas phase = Mass consumed in cluster phase:

mji = (-rjj)VPl. (A.4)

For coke

Mass out of ith compartment — Mass in from (i — 1 )th compartment = Mass produced:

(Q(1 " fli) +Mst)ycJj - (Q(1 - /,,_,) +Mst)ycj;i

=rj^;iV^pi: (A.5)

A.4. Energy balance for sensible heat transfer in the first compartment

Sensible heat lost by solids = Sensible heat gained by liquid:

WCPs(Tsm -TS1) = QCpl(Tls - Tlin);

QC^pl(T^ls - T^lin)

T — T • —

1 s = T sin WCp

(A.6) (A.7) A. 5. Energy balance in ith compartment before complete vaporization

Solid phase

Sensible heat lost by solids = Heat transferred from solid phase to gas phase + Endothermic heat of reaction:

WCpfT^ - T^Si) = q^sgi + H^ri: (A.8) Gas phase

Heat transferred from solid phase to gas phase = Change in sensible heat of gas + Heat transferred from gas to liquid phase:

sgⁱ = (Q(1 " A _ i ) +M^st)C^pgi(T^gi - T^g,_,) , ~ fli)C^phv(T^gi - T^ls) + q^gli

Liquid phase

Heat transferred from gas to liquid phase = Latent heat for vaporization:

A.6. Energy balance after complete vaporization

Sensible heat lost by catalyst and gas mixture = Endother- mic heat of reaction:

(WC^ps + (Q + M^st)C^pgi )(T^ei - T^ei_,) = H^ri:

A. 7. Heat transfer rates Solid to gas heat transfer rate qsgi =hsiapi(Tsi -Tgi).

Gas to liquid heat transfer rate q^gli = hlⁱa^li(Tgⁱ - T^ls)^:

A.8. Solid to gas heat transfer coefficient Nu = 2 + 0^:60Re¹⁼²Pr^1=3:

A. 9. Gas to liquid heat transfer coefficient Nu = [1^:0 + C^Pg(T^g-T^ls)/l]⁰¹

Buchanan (1994)^: A.10. Mass transfer rates

A.11. Mass transfer coefficients Sh = 2 + 0:60Re1=2 Sc1=

A. 12. Reaction kinetics

VGO -• Gasoline + Gas + Coke^; Gasoline —> Gas + Coke:

Reaction rate C n

W

(Pachovsky & Wojciechowski, 1971);

(A.11)

(A.12)

(A.13)

(A.14)

(A.15)

(A.16)

(A.17)

(A.18) (A.19)

(A.20)

(A.9)

where, Cj is concentration of component j, Cj^o is initial concentration of pure component j, n=1 for VGO cracking, n = 0 for gasoline cracking.

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A. 13. Kinetic constants

(A.21)

A. 14. Catalyst activity

A B+1

B + exp(Acci)

Assuming ideal gas behavior, A. 15. Gas phase density

(A.22)

P P^:(A.23)

A. 16. Gas phase specific heat

2.^1 (A.24)

A.17. Drop size

d^di = (fli⁾1⁼³d^d0:

A. 18. Momentum balance

(A.25)

Clusters

Net force on cluster=Drag force on cluster—Gravitational force:

duc 1 2

mc — = QAdjPgiug -uc) ) - mcg: (A.26) Liquid drops

Net force on liquid drop=Drag force on liquid drop- Gravitational force:

dW^ /I ON

dutd = CdAd {jPg(Ug - udy) - mdg: (A.27)

Appendix B. Regenerator equations

B.1. Gas phase material balance for ith compartment Moles in from (i — 1)th compartment—Moles out from ith compartment =Moles consumed in ith compartment:

= O2 ;CO;CO2 ;H2O:

B.2. Overall material balance closure

Number of moles of coke consumed = Number of moles of CO + CO2 produced:

W(cco-cc) MWc

B.3. Energy balance

= FA(y CO+ yCO2): (B.2)

Heat generated in regenerator=Heat of formation of (CO + CO2 + H2O):

Hreg = F^a(yCOHfCO + yCO²HfCO² + yH2OHfH²O): (B.3) Heat generated in regenerator = Gain in sensible heat of air 4owing through+Gain in sensible heat of catalyst 4owing through + Heat Loss:

Hrêg = FÂMWâ C^pa(T^rg - TÂin)

+ WCPs(TTg-TTXo)+HL. (B.4) Regenerator temperature

T = Hreg -HL+FA MWa Cpa TAin + WCps Trxo

rg F^A MW^a C^pa + WC^{ps :} B.4. Dense bed voidage

u+1 (King^; 1989)^: (B.6)

M + 2

B.5. Combustion kinetics

Intrinsic combustion of coke can be represented by

Rate of consumption of coke -rc=KcPyo2MCc=KcPyO2 PpCc

MWC

(B.7)

(B.8) (B.9) Besides intrinsic combustion of coke there is catalytic and homogeneous oxidation of CO:

The kinetic rate expression for catalytic oxidation is -r3c=K3P2ycoyOl. (B.11) The kinetic rate expression for homogeneous oxidation is

-r3k =K3hP2yCOyO2: (B.12) Kinetic constants

Ej

(B.1) Kj=KJexp\- (B.13)

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Table 3

Properties of hydrocarbon feed/products at operating conditions

Property Value

Sp. ht. of liquid VGO

Sp. ht. of gas, gasoline and vapor VGO Latent heat of feed vaporization Vaporization temperature Liquid VGO density Gas phase viscosity Gas phase conductivity Diffusivity

Heat of reaction

3:56 kJ=kg K 3:0-3:5 kJ=kg K 96 kJ=kg 700 K 650 kg=m3

1:3 x 10~5 kg=m s 3:15 x 10~5 kW=m K 1.0 x 10~5 m2=s

525 kJ=kg of VGO cracked

Table 4

Catalyst properties Property Particle density

Average particle diameter Coke on regenerated catalyst

Table 5

Molecular weights of components in riser Lump

Value 1200 kg=m3

75 urn 0:1 wt%

Molecular wt.

VGO Gasoline Gas Steam

382 120 45 18

Table 6 Kinetic constants

Kinetic constant Value (I=mcat3: s) at 756 K

Kr4

68.30 17.15 2.32 0.20 0.55

Appendix C. Numerical values of properties/parameters used for simulation

C.1. Riser

Numerical values of properties/parameters used in simulation are provided in Tables 3-8.

C.2. Regenerator

Kc = 1:069 x 1 08e x p ( — - — T 1=(atm s);

( 1 3889 \

K3C = 116.68exp( I kg mol=(kg cat atm2 s);

K3h = 2:532 x 1014exp ~3^5 5 6 T kg mol=(m3 atm2 s);

Table 7

Activation energy for cracking reactions

Cracking reaction Activation energy Ej

(kcal=kmol) VGO -> Gasoline

VGO -> Gas VGO -> Coke Gasoline —» Gas Gasoline —> Coke

16 328 21344 15 449 12612 27 621

Table 8

Deactivation constants

Deactivation parameter Value

A B

4.29 10.24

CO2=CO ratio :

The heats of formation (kJ=kg mol) of CO, CO2 and H2O at temperature T(K) are

H^fCO = -111120^:3 + 11^:54T - 0^:334 x 10~³r² 7:82 x 105

T ;

HfCO2 = -401490.7 + 48:24T - 2:0 x 10~3r2

0:334 x 105

T^;

H^fH2O = -243046.1 + 3^:26T + 3^:51 x 10~³r² 0:50 x 105

+ T :

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