MATHEMATICAL MODELLING AND CONTROL OF A FLUID CATALYTIC.CRACKING UNIT ADEMOLA S. OLUFEMI AND PAUL E. OMORO

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1 MATHEMATICAL MODELLING AND CONTROL OF A FLUID CATALYTIC.CRACKING UNIT ADEMOLA S. OLUFEMI AND PAUL E. OMORO ABSTRACT The Matrixes Laboratory, MATLAB K> software was used to obtain a mode/that can simulate the pe1j'ormance of an industrial Fluidized Catalytic Cracking (FCC) unit in steady and dynamic state, and which will subsequently be used in studies ofcontrol and realtime optimization. In this study, a dynamic mode/for a R2R type FCC unit is presented. The model includes the rise1~ the stripper/disengager; th e regeneration system and the catalyst transport lines. Materials, energy and pressure balances are pe1jonned for each of these sections. Model simulation resit!ts for steady and dynamic states are presented and compared qualitatively with those from previous FCC models. Keywords: FCC, Dynamic-simulation, Mathematical-modelling, Process-control Mathematical Modelling and Control of a Fluid Catalytic Cracking Unit Nomenclature A;: Pre-exponential factor of the reaction t -t j (s 1 or m 3 s 1kg- 1 ); Eii: Activation energy(j/mol); Ci:.. :Mass concentrarion of component! (kg/m 3 ); Ci : Molar concentration gj~.9ul..p5?esu!!. (mol/m 3 ); CD: Drag coefficient for a particle on an infinite medium; C P :Specific heat capacity (Jkg- 1 K 1); dci : Catalyst cluster mean diameter (m); D : Diarneter(rn); F; : 1.fass flow rate of component~ (kg/s); g: Gravity acceleration (m/s2); H.~ :Enthalpy of phase kin stream~- (J.1kg); L: Length (m); J( : Molar ma?s (kg/mol); 1~ :Order of reaction;.v 1 g :!'violar flow rate of component / in the gas phase (mol/s);? :Pressure (Pa); Q,: Gl obal rea.ction heat (J/s);.If: Rate of fom1ation of lump ~. (kgm 3s l); r; : Rate of reaction i -t j (kgm 3s 1); ~; : Rate of the reaction j (molm >s l or molkg-ls l); R:Universal gas constant (Jmol 1K- 1 ); r: Time (s); T: Temperamre (K); v: Velocity (m s);v: Volume (m ~ ) ; W: Inventory (kg); Y:: Component ~ (in coke) content of catalyst(kgikg); z: Axial coordinate (m); fu.!.jcrk: Heat of cracking per kg of VGO (Ji kg)~ :Volume fraction; <P : Deactivation function; 1f: constant Pi; p : Density (kglm 3 ); o :Intrinsic CO~ / CO molar ratio; vji: ~~9.l.S..hl..9E.!,~E:LS. coefficient of componeni ~. :;.:je}fs...~p.se! to the reaction j; 0 : Cross sectional area (m 2 ); C~: 'vt% of aromatic in the residual oil; g : gas; cat : catalyst; s: solid; j: lump cracked; t :lump fom1ed 95

2 Mathematical Modelling And Control Of A Fluid Catalytic Cracking Unit 1. INTRODUCTION Modern refinery has many processes. Fluid Catalytic Cracking (FCC) unit is one of the most important units in a refinery, and is sometimes referred to as the heart or workhorse of the refinery, having passed through spectacular development(elamurugan & Dinesh, 2010; Yousuo, 2015).There are several types of fluid catalytic cracking unit (FCCU) in operation, using various designs. Each type has more than a few parts and is equipped with numerous internals such as cyclone separators and baffles. The fluid catalytic cracking unit (FCCU) has become the test bench of many advanced control methods(elamurugan & Dinesh, 2010). Today, both academia and industry are expressing great interest in the development of new control algorithms and in their efficient industrial FCC implementation. Analysis and control of FCC process have been known as challenging problems due to the following process characteristics, (i) very complicated and little known hydrodynamics, (ii) complex kinetics of both cracking and coke burning reactions, (iii) strong interaction between the reactor and regenerator, (Rajkumar, Vineet, & Srivastava, 2005)many operating constraints. FCCU s steady state behavior is highly nonlinear, leading to multiple steady states, input multiplicities etc. In the earlier years before the development of zeolite catalysts, the major control problem has been one of stabilization, of just keeping the unit running. Later with zeolite catalysts, the emphasis is shifted to increasing production rates in the face of unit constraints and to handle heavier feeds. The requirements for reformulated gasoline have added the need to control the product composition. This is a more complex problem since the number of process variables that one would like to control substantially exceeds the number of manipulating variables that are available for the task. Several studies have been made on the modelling, simulation, kinetics, multiplicity of steady states, chaotic behavior, on-line optimization and control of FCC units. However, there are still large areas to be examined due to the complexity and to the economic importance of this process. In this study, a dynamic model is presented for aregenerator to regenerator (R2R) unit comprising a riser, a stripper, a disengager, two standpipes and a regeneration system composed of two regenerators linked by a lift. The R2R process was first developed by Total and is now licensed by Axens/IFP and Stone & Webster. This technology is used to process feedstocks with high residual content. The first regenerator (Regenerator 1) acts as a mild pre-combustion zone to achieve 40 to 70% of the coke combustion. The partially regenerated catalyst with less than 0.5 wt% coke is then airlifted to the elevated second regenerator (Regenerator 2) where complete regeneration is achieved with slight air excess and under a low steam partial pressure in order to minimize catalyst deactivation (Gauthier, Bayle, & Leroy, 2000). 2. Mathematical Model 2.1 The riser kinetic model For kinetic modeling, the complexity of charge stocks is infeasible to characterize and describe, so attempts have been made to lump large numbers of chemical compounds into a kinetic species to describe the complex reactions(wei & Kuo, 1969; Xu, Su, Mu, & Chu, 2006). Sophisticated models, normally with more than 10 lumps, have basically two advantages; a 96

3 Nigerian Journal Of Oil And Gas Technology single group of estimated kinetic constants can be used for various feedstocks and all the most important FCC products can be predicted separately. The disadvantages of these models are that a large number of kinetic constants must be estimated and as each lump represents a differential equation in the mathematical model, the complexity of the numerical solution may increase exponentially (Souzaa, Vargasa, Von Meiena, & Martignonib, 2003). Figure 1: The 7-lump reaction scheme for the FCCU The riser hydrodynamics are modelledas a plug-flow reactor accounting for coke formation and leading to catalyst deactivation, while the cracking kinetics is described by a 7-lump model of(ahmed, Maulud, Ramasamy, & Mahadzir, 2010; Xu et al., 2006), with a deactivation function depending on the catalyst cokecontent. Figure 2. R2R Fluid Catalytic Cracking Process(Ahmed et al., 2010) 97

4 Mathematical Modelling And Control Of A Fluid Catalytic Cracking Unit The j-lumps considered are: Residue (RGS); Vacuum Gas Oil (VGO) +Decanted Oil(> 360 C); Light Cycle Oil (LCO) ( C); Gasoline (GLN) (C5-220 C);Liquefied Petroleum Gas (LPG) (C3 and C4); Fuel Gas (FG) (H2, Cl, C2 and H2S) andcoke. Besides the second order VGO cracking reactions, all reactions are first order. Gas molar expansion as well as slip velocity between gas and solids are accounted for inthe riser model. The stripper/disengager section is modelled as a CSTR without anycracking reactions occurring. Both regenerators are also modelled as CSTR reactors. In this model, coke, dry gas and LPG were lumped separately and the combustion kinetics considered in this modelwere previously studied at IFP (Vale, 2002) Coke is considered to be composed of <;:arbon and hydrogen, although in practicesulfur and nitrogen are also present in small quantities. The combustion of carbon can be given by the follo'.y'ing overall reaction: / 1/J.. a + / 2 ( a \, ( 1 c -,- l. o, ~ l-_._ jco, -r 1 - _._ ]co a -,- 1 a. l \ a. l / The probability of the cracking reaction from gasoline to coke and gases to coke can be neglected since constants for these reactions are many orders of magnimde smaller than that of others, which simplifies the kinetic parameters detennination. The lift is!l!qq~!l~,q as a plug-flow reactor where combustion reactions continue. Since the residence time in the lift is much smaller than in the regenerators, it is considered to be in pseudo steady state. Spent and regenerated catalyst standpipes are also!1!9_<k1k9: as being in pseudo steady state at incipient fluidization with the solids and aeration gases moving in plug flow along the standpipes. Pressure balances in all the sections are made considering that the gases have ideal gas behavior. The riser is considered to be in pseudo steady state and the reaction rate of the pseudo-species j, is assumed to be a function of the molar concentration of species j (paa), the mass density of catalyst relative to the gas volume (P;{) and reaction constant ( k~ ), as in equation 2., pa. r. =-k p - 1 J j c 8 The reaction constant k~, decayed with time as : k 1 f( C""' )<D(tc) f(n) The heayy in en aromatic adsorption function f ( ca:d is described by: (2) (1) (3)! ( c ) = 1. <r!; ( l +K;, C z~; ) (4) Catalyst deactivation accounted for by a hyperbolic function cd(tc) as: <1>(1,) = ( I +~~: J The nitrogen poisoning function /( N) is defined as : f(n)- l (6) l+k 0 N \Vith regard to high catalyst to oil ratio, the nitrogen poisoning deactivation can be neglected because of its insignificance. The average molecular weight of all lumps, 1Vf,.,... changing along the distance of the riser is given as: (5) 98

5 Nigerian Journal Of Oil And Gas Technology M 1_ 1 w-, L,.Qj Mass, force, energy and pressure balances.in the Riser (RS); ap; o.. L... L "... ( Eg J. "' - = "s e r. r, = r.. - r.. r.. = <DA.. exp -- C ~ oz j....i..._ "- c! Jl q q II RT! O;=)F 8(0 _,. o e ) a"' e o'""! ca: _ O P.;:; cr ca c _ 0 ""c _ c c - -- <::::> - <=>----- (9) c.z az 8z,., (}z av e,l'i cz C. c. az!_ =! vg(l-ej cc, (7) (8) (6) P (,. -v )" -d ~. :rd;, :rd;! - 0 (10) g -;: c. '' c. _..p c. o-p --g- CD 2 4. g 6 0 : =: 6 ~r 0 6J{ r 0?.S = --?.s e c r:rk DO (I 1) cz LF 1 Cp 1 ap l az = - pao:g P av = 8 cp car + egpg (12) Regenerator Model The FCC control unit should maintain a suitable reactor temperature distribution, so to achieve better product characteristics. The regenerator temperature profile should also be bound so as to prevent abnormal combustion and excessive temperatures. At the same time, energy and material balances must be maintained between the two parts ofthe unit. The reactor pressure can be maintained by manipulating the fractionator overhead gas compressor speed or the overhead gas recycle rate. The flue gas rate can be manipulated to maintain the regenerator pressure. The hot flue gas in the regenerator is also separated from catalyst in a cyclone and used for recovery of the-rmal and combustion energies. Mass, force, energy and pressure balances in the Regenerator (Souzaa et al., 2003);. 8 C; RG. l/.... "j = rg -,. g ~...:... ~ ~ E vg -.,. ~v... 3 v::..a "r l\t.tn 1\ to:a:,ou: x c t,?.o ~ ::..d.ogl ( 1 ; _,; )+ 8 cf. cc.x L(r 1 ;t) ( L ) o.. j j / fvc,rg c l ~. RG F,, ;, v Fc,ou: v v ""' ( ~ ~ ). c H (14) _-- = --.I t,tl t ---.I t,.~g+ oui c P c L..., l j V;t, ' I= or Jv[ w,! O l 1\f..,.,! Af ><,! cl F. -F _..!3Q_ = " ~ m c,out ot n }>S e, p, (15) cfvg,rg ;;:--- = ~,!n - ""'(. ) F,,o-.a + L.. ~,!n~,! n - ""'( ) L..., Fc, o-.jt~, RG (16) V l 1 1 o(w,cp,tro +Hi~CPgTRo) =F. H +Qo -Fg+cuurH our (17) g~ c. o t in,. r PRO,_..,,... = ~. RO + P c c cl RG g (18) 99

6 Mathematical Modelling And Control Of A Fluid Catalytic Cracking Unit 2.4. Materials and Method The average molecular weight, the thermodynamic properties of the feed, the plant operating conditions and the properties of the catalyst used in this study, the specific heat of different lumps and the kinetic parameters for cracking reactions are shown in table 2 to 6 and others are found elsewhere (Jafar, Ahari, & Khaled, 2008; NNPC, 1987; Rajkumar et al., 2005). The simulations in this work used the 2-dimensional model of the MatLab 2015 software in a windows10; computer model:dell Inspiron 2025 Notebook PC, Processor: Intel (R) Core(TM)2 Duo CPU 2.00 GHz GHz, Memory (Ahmed et al.): 750GB (6GB) and System type: 64-bit operatin system. 3. Simulation Results and Discussion A. Effect of COR on temperatures, conversion and product yields The plots in Figure 2 show the influence of the steady state catalyst-to-oil ratio (COR) on some process variables. It can be seen that increasing the COR leads to an increase in riser outlet temperature, since a larger amount of catalyst enters the riser for a same quantity of hydrocarbons. The increase in COR also leads to a lower coke content of the spent catalyst. Because of the higher catalyst flowrate, the residence time of the catalyst in the regenerators is lower, leading to lower regenerator temperatures for a given heat release. These temperature evolutions with COR are in agreement with the results presented by (Yousuo, 2015). However, no maximum was found in the regenerators temperature curves, as presented in the works of (Arbel, Rinard, Shinnar, & Sapre, 1995; Han & Chung, 2001; Malay, Milne, & Rohani, 1999). Nevertheless, the regenerationsystem in all these works is different from the one presented here. The effect of COR on VGO conversion and product yields presented in this paper isalso in agreement with the results presented by (Malay et al., 1999; Yousuo, 2015). Higher temperaturespromote higher conversion rates and, at the same time, a higher COR also means morecatalyst, and hence more active centres available for reaction leading again to higherconversions and light product yields. Figure 2. Effect of COR on temperatures, conversion and product yields. 100

7 Nigerian Journal Of Oil And Gas Technology B. The effect of yield in the reactor riser versus riser axial distance Figure 3 shows the profiles of some important process variables along the axial coordinate in the riser. It can be seen that most of the cracking reactions occur in the first meters of the riser. Figure 3. Steady state profiles along the axial coordinate in the riser. This is an expected result when one considers the highesttemperatures and lowest catalyst coke content are encountered at the riser inlet. Thevelocity profiles clearly show that there is a slip factor between the two phases, whichrapidly tends to a value of 2. C. The dynamic response to a step perturbation of fresh feed flowrate, followed by a step perturbation to the previous value of the fresh feed flowrate. Figure 4 shows the dynamic response of the system to a step perturbation in the gas oil feed rate. Decreasing the fresh feed flow-rate initially results in a steep increase of the riser temperature due to a higher COR. 101

8 Mathematical Modelling And Control Of A Fluid Catalytic Cracking Unit Figure 4. An open loop dynamic response to a step perturbation of 5% in the fresh feed flowrate, followed by a step perturbation to the previous value of the fresh feed flowrate. This immediately leads to a steep increase inconversion. On the other hand, a lower concentration of hydrocarbons leads to apressure decrease in the stripper, which causes a steep decrease in the flow-rate of spentcatalyst and an increase in the regenerated catalyst flow-rate. The evolution to the newsteady state is achieved through a pressure balance compensation caused by a decreaseof the catalyst level in the regenerator 1 and an increase of the stripper catalyst level. Coke on catalyst decreases, due to a lower feed flow-rate. After a small initial increase, thetemperature in the regenerator 1 also decreases, since the coke content decreased as well asthe residence time of catalyst (lower catalyst holdup). The CO/CO2 ratio shows aninverse behaviour from temperature with steeper decreases and increases, which is expected since the literature shows that decreases exponentially with temperature(vale, 2002). Due to lower temperatures in the regenerators, the temperature in the risereventually decreases as well as the conversion.after the second perturbation to the previous value of the fresh feed flowrate, all variablesreturn to their initial steady state. 4. Conclusions A mechanistic dynamic model has been developed for the simulation of the steady stateand dynamic behaviour of a R2R type FCC unit. The model includes a riser reactor, astripper, a 102

9 Nigerian Journal Of Oil And Gas Technology disengager, a regeneration system and catalyst transport lines.from the simulation results presented, it can be seen that the model shows a behaviourthat is consistent with the experimental data and literature results. In future work, themodel will be used for studies of advanced control and real time optimization. REFERENCES Ahmed, A. O. M., Maulud, A. S., Ramasamy, M., & Mahadzir, S. (2010). Steady state modeling and simulation of the riser in an industrial RFCC Unit. Journal of Applied Sciences, 10(24), Arbel, A., Rinard, I. H., Shinnar, R., & Sapre, A. V. (1995). Dynamic and Control of Fluidized Catalytic Crackers. 2. Multiple Steady States and Instabilities. Industrial & Engineering Chemistry Research, 34, Elamurugan, P., & Dinesh, K. D. (2010). Modeling and Control of Fluid Catalytic Cracking Unit in Petroleum Refinery. International Journal of Computer Communication and Information System, 2(1), Gauthier, T., Bayle, J., & Leroy, P. (2000). FCC: Fluidization Phenomena and Technologies, Oil & Gas Science and Technology AReview. IFP, 55 (2), Han, I. S., & Chung, C. B. (2001). Dynamic Modeling and Simulation of a Fluidized Catalytic Cracking Process. Part II: Property Estimation and Simulation Chemical Engineering Science, 56, Jafar, S., Ahari, A. F., & Khaled, F. (2008). A Mathematical Modeling of the riser Reactor in Industrial FCC Unit. Petroleum and Coal, 50(2), Malay, P., Milne, B. J., & Rohani, S. (1999). The Modified Dynamic Model of a Riser Type Fluid Catalytic Cracking Unit,. The Canadian Journal of Chemical Engineering, 77, NNPC. (1987). Port Harcourt Refinery Company (PHRC) Project, Area 3 FCCU, Project No. 9465ANigerian National Petroleum Corporation Process, 16, Rajkumar, G., Vineet, K., & Srivastava, V. K. (2005). Modeling and simulationof fluid catalytic cracking unit Reviews in Chemical Engineering, 21(2), Souzaa, J. A., Vargasa, J. V. C., Von Meiena, O. F., & Martignonib, W. (2003). Numerical simulation of FCC risers. Engenharia Termica, 4, Vale, H. (2002). Development of a Simulator for a Complete R2R Catalytic Cracking Unit: IFP Report. Wei, J., & Kuo, J. C. W. (1969).Alump analysis in monomolecular reaction systems:analysis of the exactly lumpable system. Ind. Eng. Chem. Fundam., 8, Xu, O., Su, H., Mu, S., & Chu, J. (2006). 7-lump kinetic model fro residual oil catalytic cracking. J. Zhejiang Univ. Sci. A., 7, Yousuo, D. (2015). A Study of the Ten-Lump Kinetic Model in the Fluid Catalytic Cracking Unit Using COMSOL Multiphysics. International Journal of Applied Science and Technology, 5(5),