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Transcript of Reactor design Project
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
1
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.
2
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
6
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).
7
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
8
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:
10
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)
11
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:
12
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:
13
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
14
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
15
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.
16
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.
17
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,
18
changing physical properties along the reactor, changing the deactivation function along
the reactor.
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