ADVANCED CHEMICAL REACTION ENGINEERING

CBE9450 Project

A Dispersion Model for Fluid Catalytic Cracking Downer

Reactor with a Six Lump Kinetic Model

Written and Illustrated by:

Dawood Al-Mosuli

MEng in CBE at Western University

Instructor: PROFESSOR HUGO DE LASA

April 24 ,2013

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A Dispersion Model for Fluid Catalytic Cracking Downer

With a Six Lump Kinetic Model

Abstract

The fluid catalytic cracking FCC is a process and apparatus where riser is used for cracking of oil

feed stocks in the presence of catalyst and regenerator is used to regenerate the spent catalyst.

This process is modified by the development of the downflow riser (downer). In downer reactor

where the solids and gas move downward co-currently the flow behavior is near plug flow

reactor, it is possible to obtain uniform distribution of the catalyst with the feed and to reduce

the contact time between them. In addition the amount of coke produced in the process is

reduced. In this work, a dispersion model for downer reactor is proposed. The model will

combine the six lump kinetic models, the hydrodynamic model of the downer and the

dispersion mixing model to predict the fluid catalytic cracking performance. The results should

be compared with that of a dispersion model for the riser reactor. This will give a prediction of

the effect of back mixing on both types of FCC reactors, and if the assumption of plug flow

reactor is an oversimplification for any of these reactors.

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CONTENTS

ABSTRACT 2

CONTENTS 3

NOMENCLATURES 4

1- INTRODUCTION AND LITRATURE SURVEY. 6

1-1– DEVELOPMENT OF DOWNER FREACTOR. 6

1-2- MATHEMATICAL MODELING RELATED TO DOWNRS. 8

1-3-AIM AND SCOPE OF WORK. 9

2- MODELING RELATED TO DOWNERS 9

2-1- DISPERSION MODEL AND ASSUMPTIONS RELATEDTO

OUR MODEL. 9

2-2- THE KINETIC MODEL 12

2-3- CONCENTRATION, TEMPERATURE, PRESSURE AND

REACTION TIME PROFILES IN THE REACTOR. 13

3

2-4- HYDRODYNAMIC MODEL 15

2-5-MIXING TEMPERATURE 16

3- SEQUENCE OF CALCULATION STEPS 17

4- CONCLUSIONS AND SUDGUSTIONS FOR FURTHER

WORK. 18

REFERENCES 19

NOMENCLATURES

A Reactor cross section area (m2)

Ar Archimedes number (-)

Cp Heat capacity (kJ/kg.K)

D Reactor diameter (m)

d Particle diameter (m)

Ej Activation energy (kJ/kmole)

Fr Fround number

H Heat enthalpy (kJ/s)

Hj Heat enthalpy of jth reaction (kJ/kg)

Kj Kinetic reaction rate constant of jth reaction

Kuop UOP characterization factor

4

L Reactor Height (m)

MW Molecular weight (kg/kg mole)

m Mass rate (kg/s)

P Reactor pressure (Pascal)

R Universal ideal gas constant (atm ∙ m3/kmole ∙ K)

Re Reynold number

SG Feed specific gravity

T Temperature (K)

u Velocity (m/s)

X Conversion (wt %)

yi Weight fraction of ith lump

z Axial position of riser height (m)

Greek letters

ε Voidage

ϕ Catalyst deactivation function

ρ Density (kg/m3)

ψ Slip factor

μ Viscosity (Pa.s)

factor of VGO to gasoline reaction

Subscripts

cok Coke

cat Catalyst

ds Dispersion or Atomizing steam

5

f Feed

fg Flue gas

fl Feed in the liquid phase

fv Feed in the vapor phase

g Gas phase

in Flowing in

j 1,2,3,4 and 5 for the reactions VGO to GLN, VGO to C4s, C5s,etc

o Superficial

out Flowing out

p Particle

rcat Regenerated catalyst

rcoke Coke on the regenerated catalyst

s Steam

scat Spent catalyst

scok Coke on the spent catalyst

t Terminal velocity

1-Introduction and literature survey

1-1– Development of downer reactors

This search deals with improved process used to convert heavy oil fractions to more valuable

light products like gasoline light and heavy cycle gasoils ,etc with reducing the amount of coke

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produced in the process. In order to understand the important of this development, It is

important to notice that for up flow riser (see e.g., U.S. pat. No. 3565790,U.S. pat. NO.

3607126, U.S. pat.NO. 3492221), the petroleum feed should be in contact with the catalyst for

a relatively long time to obtain an efficient conversion for the feed. This long contact time is

necessitated by the upflowing configuration of the riser which includes acceleration of the

catalyst from stationary case to feed velocity against the gravity force. This caused a lot of

problems with the riser like catalyst backmixing and non-uniform catalyst distribution through

the feed. Due to this relatively long contact time with the catalyst and inefficient contact

between the catalyst and petroleum feed, there will be an increase in natural tendency of

heavy petroleum cuts to form large amounts of coke at the expense of gasoline production.

To overcome these problems, the FCC reaction vessel is provided with a transport reactor at

the top of the reaction vessel. In this arrangement, the catalyst is forced to flow downward

from the regenerator into the reactor. This downflow eliminates the problems of catalyst

backmixing and its non-uniform distribution in through the feed. Moreover the uniform catalyst

distribution in the feed stream is gained in a relatively short time. This will enable rapid

separation of catalyst at the bottom of the reactor and low coke formation. So, the net result

of of providing a downflow riser is decreasing coke formation, increasing gasoline selectivity

and production of higher octane gasoline at same conversion. Detailed representation of

downflow riser technology is given in (U.S. pat.No. 4385985, U.S. Pat.NO.7087154, US. Pat.NO.

4411773, U.S. Pat.NO.5582712, U.S. Pat.NO.4693808, U.S. Pat.NO. 4797262).

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Because of the importance of this development in refining, then it is important to develop a

mathematical model to simulate the dynamic behavior of the downer. In addition, this model

will be an important tool to study the effect of operational parameters on the productivity and

performance of the process.

1-2- Mathematical modeling related to downers

Hydrodynamic study in downflow systems was started by Shimizu et al. (1978)[12].

More recently, (Wang et al., 1992[13]; Cao,et al.[3], 1994; Wei et al., 1994[15], 1995)

carried out a series of hydrodynamic and mixing studies in downers. They found that the

radial profile for solids is more flat than that of risers. This was an indication that

backmixing in downers is less than that in risers. Since the backmixing has a negative

effect on the yield and selectivity of FCC reactions, then it was stated that downers were

the most promising reactor for the FCC process. Plug flow model was assumed to

represent the condition of gas and solids in the reactor by Kraemer and de Lasa

(1988[8]), Gianetto et al. (1994)[6], and Bolkan-Kenny et al. (1994[2]). Studies on gas

and solid mixing in riser showed that plug flow model may oversimplify the modeling

process. Wei Fei and Ran Xing et al 1997[18] combine a four-lump kinetic network with

one dimensional dispersion mixing model for both riser and downer reactors, they

compared the results of numerical solution with experimental results from pilot scale

downer reactor.

In this paper, starting from the dispersion model of Wei Fei et al1997[18] a new

formulation is done after extending the kinetic model to six lumps. The numerical

solution of the system of equations should provide a better representation of the

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influence of the operating conditions and feed properties on the yield of downer type

reactor.

1-3- Aim of this work

1- Short literature survey of previous FCC Downer and simulation studies.

2-Formulation of mathematical model which has the ability to describe the physical behavior and

reaction kinetics of the downer reactor in the FCC unit using 6 lumps model for the kinetics

description combined with the axial dispersion model.

3-After solving this model, we can make use of this solution to optimize the operating conditions

of this unit and compere the effect of axial dispersion with six lump with the available

experimental results. This will give a good estimation about the deviation of downer reactor from

the plug flow model.

4- Solution of this model can provide a prediction of the performance and productivity of downer

reactor when there is a need to change the feed or operating condition, or if operating problems is

happened so that the cost and losses could be minimized.

2-Modeling related to downer

2-1- Dispersion model and assumptions related to our model

The axial gas dispersion of a pilot-scale downer reactor was studied by Wei et al. (1995)

[16]. They found that the axial Peclet number is 1-2 times larger than that of riser. These

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studies in both the riser and downer indicate that the dispersion model can describe the

model and that a certain extent of gas and solids mixing occurs in both the riser and

downer reactors. To make the formulation in a simple way, the assumptions are

needed:

1.The system is at a steady state condition.

2. No heat or mass transfer resistance between gas and solid phases due to high

mixing rate.

3. Axial mixing can be described by one dimensional dispersion model.

4. Due to good mixing then the cracking reactions is controlled by chemical kinetics.

5. Temperature of chemical reaction is constant.

6. The flow in the reactor is a fully developed flow.

7. Pressure changes through the riser length is due static head..

8. Immediate evaporation of feed at the riser inlet.

1-4- Mass and heat balance

The axial dispersion model is combined with the six lump kinetic model to gas-oil

catalytic cracking. The system is assumed to be close-close boundary, then the

boundary conditions of Danckwerts (1953)[] could be applied to the system.

The mass balance of the small element in reactor is formulated as follows:

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In order to solve the model numerically, the riser is divided into equal sized disc like elements of

thickness (dz) as in the figure below

d2 yi/dz2=Pe/L*{dyi/dz+r(i)} (i=1,2,3,4,5,6) (a)

With Danckwerts’ (1953) boundary conditions:

At Z=0 dyi/dz-Pe/L*{yi (at z=0+) –yi (z=0-)} (b)

At Z=L dyi/dz=0 (c)

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Where the rate of reaction r(i) is obtained from the kinetic model. The volumetric

expansion due to generation of moles is taken into account by calculating the superficial

gas velocity at the exit of each control volume.

2-2- The kinetic model

The kinetic model of cracking reaction is the initial step in determining the accuracy and

complexity of the model. In this study the six lump model is used to represent the reaction

kinetics fig (3.3). Experimental data related to this model and calculated kinetic parameters

are given by (Ancheyata [21 } and Zaidoon [20 ].

Fig 3.3 representation of the six lump model

For each reaction the rate r was given as a function of weight fraction yi , deactivation ф

and kinetic constant ki. The rate constant for each of the above reactions is given as below:

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Gas oil: r1 = -(k1 + k2 +k3 + k4 +k5)*y1^2* ф ---------------------------1

Gasoline: r2= (k1y1^2 – k6y2 – k7y2 – k8y2 – k9y2)* ф -----------2

C4’s : r3 = (k2y1^2 + k6y2 –k 10 y3 – k11y3)* ф --------------------------3

C5’s: r4= (k3y1^2 + k7y2 + k10y3 – k12y4)* ф -----------------------------4

Dry gas: r5 = (k4y1^2 + k8y2 + k11y3 + k12y4)* ф -----------------------5

Coke: r6 = (k5y1^2 + k9y2)* ф --------------------------------------------------6

ф is the deactivation function, ki are the kinetic constants and yi are the weight fractions

for each of the six lumps.

The values of k is given by Arrhenius equation

ki = Ai exp(-Ei/RT) -----------------------------------------------------------------7

The kinetic parameters are taken from literatures as[ 20,22,23].

2-3- CONCENTRATION, TEMPERATURE, PRESSURE AND REACTION

TIME PROFILES IN THE REACTOR.

Following the procedure given by (rohani[29] ,faheem[24]), the concentration profile for each

lump along the reactor length could be put in the following set of ODE:

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For VGO lump: d2 y1/dz2 =(PE/L)*{-dy1/dz-C*{k1+k2+k3+k4}*y1^2 } ------------------8

For gasoline lump: d2 y2/dz2 =(PE/L)*{-dy2/dz+C*{k1*y1^2-(k6+k7+k8+k9)*y2}} -----9

For C4’s : d2 y3/dz2 =(PE/L)*{-dy3/dz+ C*{k2*y1^2+k6*y2-k10*y3-k11*y3)} ----------10

For C5’s : d2 y4/dz2 =(PE/L)*{- dy4/dz+C*{k3*y1^2+k7*y2+k10*y3-k12*y4}} -----------11

For dry gas : d2 y5/dz2 =(PE/L)*{-dy5/dz+C*{k4*y1^2+k8*y2+k11*y3+k12*y4}}------------12

For coke : d2 y6/dz2 =(PE/L)* {-dy6/dz+C*(k5*y1^2+k9*y2} } ------------------------------13

Where C =A *ԑg* ф* ρg/mg ------------------------------------------------------14

In the same way the Danckwerts’ boundary conditions (equations (b) and (c)) should be

defined for each component.

The temperature profile along the reactor could be obtained using the following equation as

in (rohani et al [29] and [24])

dT/dz= −{ (A *ԑg* ф* ρg )/(mcat*cpcat+mg*cpg)}(k1 ΔH1 +k2 ΔH2 +k3 ΔH3+k4 ΔH4+k5 ΔH5)*y1^2+(k6 ΔH6 +k7 ΔH7+k8 ΔH8+k9 ΔH9 )*y2+(k10 ΔH10+k11 ΔH11)*y3+k12 ΔH12y4 -----------------------15The catalyst residence time could be calculated using the following equation[ 24]dtc/dz=A* ψ*ρcat{mcat* ψ+[1/Mwg]*mg*(1-y6)* ρcat*(101325*RT/P)}-----16

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The vapor mass flow rate through the reactor can obtained by the following equation[ 24]

mg=mf*(y1+y2+y3+y4+y5}+Mds --------------------------------------------------------17

Where the quantitiesof dispersion steam (Mds) 1% [ 8]. The vapor phase densityis calculated by ideal gas law. Ρg=P*Mwg/(101325RT)

---------------------------------------------18

Average vapor phase molecular weight is obtained from [25]

Mwg=1/{(y1/MwVGO)+(y2/Mwgasolie)+(y3/MwC4’s)+(y4/MwC5’s)+(y5/Mwdry gas)} ----19

The pressure drop through the reactor could be obtained by [34]dp/dz=- ρcat*g*(1- ԑg)-------------------------------------------------------------------------20

The deposition of coke on the catalyst surface is represented by the catalyst activation

function using this formula given by Koratiya et al.[30]

Ф=(1+51(mxcok/mcat)}^(-2.78)

mxcoke is mass flowrate of carbonized catalyst, mcat is the mass flowrate of catalyst.

2-4- Hydrodynamic model

According to the assumptions of the model, we have two phases (gas-solid ) in a fully

developed condition. The following empirical correlation put by Patience et al. is used

to obtain slip factor.

Ψ=interstitial gas velocity/average solid velocity =ug/up=uo/( ԑg*up)=1+(5.6/Fr)

+0.47*Frt^0.41 -------23

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Fr=uo/√ g∗D --------------------------------------------------------------------24

Frt=ut/√ g∗d---------------------------------------------------------------------25

The super ficial velocity uo=mg/(A* ρg) -------------------------------------26

Average particle velocity up=mcat/( ρcat*A*(1- ԑg) --------------------27

By combination of equations 23 ,26 ,27, we get the average void fraction in gas phase

ԑg

ԑg= ρcat*mg/( ρg*mcat* Ψ+ ρcat*mg) -------------------------------------28

and gas velocity can be evaluated by ug=uo/ԑg ---------------------------29

particle velocity up=ug/ Ψ -------------------------------------------------------30

residence time in gas phase t= z/ug ------------------------------------------31

particle terminal velocity can be calculated from [35 36 37]

ut =Ret*ug/( ρg*dp) ------------------------------------------------------------32

Ret = Ar/{18+(2.3348-1.7439*Sph)*Ar^0.5} -------------------------------33

Ar = ρg *( ρcat- ρg)*g*dp^3/µg^2 --------------------------------------------34

2-5- Mixing temperature

By making heat balance on three steams entering the downer (steam, catalyst and atomizing

steam), we can calculate the temperature of the mixture from equation 35 below.

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Tmix=A/B ------------------------------------------------------------------------35

A=(mrcat∗cpcat+mrcok∗cpcok )∗Trcat−(mls∗cps )∗Ts-mf*cpf*Tf

B= (mrcat + mxcat)*cpcat+(mrcok)*cpcok+mls*cps +mf *cpf

Equation 35 is the initial boundary condition for the differential equation (15)

3- SEQUENCE OF CALCULATION STEPS

1. Introduce the data required to calculate Tmix1 to axel program ( mrcat , mrcok,Trcat,

mls,Tls,cpcat,cpcok,cps) .

2. Calculate Tmix (equation 35).

3. At z=0, input initial values of ODE from 8-16 y1=1, y2=y3,y4,y5,y6,=0,T=Tmix

4. Calculate values (ϕ,k1,k2,k3,k4,k5,k6,k7,k8,k9, Mwg ,ρg ,mg, Uo , Ar, Ret, Ut, ψ, εg,

Ug , Up, X) using equations 7 and 17-32. The calculated values represent the exit

conditions of the current volume element and at the same time the inlet conditions of the

next volume element. Also initial values for the first step of the equation are given by

computing results of the plug flow model ( without dispersion). With these initial values

and the boundary conditions in the outlet of the reactor it is possible to compute the

conditions for each incremental step.

5. Increasing the amount of z by small value to move to the next volume element.

6. Calculating the new values of ODE 8-16 depending on exit values of previous volume

element (step4).

7. Steps 4- 6 should be repeated until the value of z reaches the total height of the reactor.

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8- It is possible to repeat the calculation for a number of iterations till reaching a certain

degree of accuracy

The previous calculation can be calculated using Microsoft Excel depending on Runge –

Kutta numerical method technique.

10. Now the output variables i.e. yield, conversion cracking efficiency, selectivity, delta coke

etc can be calculated.

4- Conclusions and suggestions for further work

After my short literature survey, It seems that a lot of work is still needed to develop a

mathematical representation of both downer and riser FCC reactors. Developing such a

model is much better than using the empirical correlations provided by the manufacturing

companies. Empirical correlations couldn’t be generalized to all types of downers or risers.

Non ideality of FCC reactors can have a large effect on the productivity of gasoline, for

example increasing axial Peclet no. from 0.1 to1000 will increase the yield of gasoline by

11% under the same conversion[18]. Moreover, incorporating six lumps model make the

model more accurate than the traditional 4 or 3 lumps model used in many previous works.

Providing accurate model is an important issue especially when it is necessary to change

the feed or the operating conditions or both, or it is necessary to make an optimization or

control system for the FCC process.

More work could be done by changing the assumptions done to simplify the model. For

example by introducing any one or more of the following inside the model: radial

dispersion, two dimensional flow model, heterogeneous model, no isothermal behavior,

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changing physical properties along the reactor, changing the deactivation function along

the reactor.

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