The FCC riser cracks gas oil into useful fuels such as gasoline, diesel and some lighter products such as ethylene and pro- pylene, which are major building blocks for the polyethylene and polypropylene production. The production objective of the riser is usually the maximization of gasoline and diesel, but it can also be to maximize propylene. The optimization and parameter estimation of a six-lumped catalytic cracking reaction of gas oil in FCC is carried out to maximize the yield of propylene using an optimisation framework developed in gPROMS software 5.0 by optimizing mass flow rates and tempera - tures of catalyst and gas oil. The optimal values of 290.8 kg/s mass flow rate of catalyst and 53.4 kg/s mass flow rate of gas oil were obtained as propylene yield is maximized to give 8.95 wt%. When compared with the base case simulation value of 4.59 wt% propylene yield, the maximized propylene yield is increased by 95%. Keywords FCC riser · Maximization · Propylene · Optimization · Parameter estimation List of symbols K Ther mal conductivity of hydrocarbons A Surface area (m ) L Length (m) A Effective interface heat transfer area per unit M Molecular weight ptc w 2 3 volume (m /m ) P Pressure (kPa) C Mole concentration (kg mol/m ) Q Rate of heat generation or heat removal by reac- react C Gas heat capacity (kJ/kg K) tion (kJ/s) R Ideal gas constant (8.3143 kPa m /kg mol K or C Solid heat capacity (kJ/kg K) kJ/kg mol K) D Diameter (m) RAN Aromatics-to-naphthenes ratio in liquid d Catalyst average diameter (m) feedstock E Activation energy (kJ/kg mol) S Average sphericity of catalyst particles F Mass flow rate (kg/s) S T otal mass interchange rate between the emul- H Specific enthalpy (kJ/kg) sion and bubble phases (1/s) ΔH Heat of reaction (kJ/kg) T Temperature (K) ΔH Heat of vaporization of liquid feedstock in the vlg u Superficial velocity (m/s) feed vaporization section (kJ/kg) V Volume (m ) h Enthalpy of reaction (kJ/kg) Y W eight fraction of Conradson carbon residue in cc h Inter face heat transfer coefficient between the a feedstock catalyst and gas phases y Weight fraction h Interface heat transfer coefficient (kJ/m s K) Z Gas compressibility factor or Z factor k F requency factor in the Arrhenius expression i0 (1/s) Greek symbols K Rate coefficient of the four-lump cracking reac - Ω Cross-sectional area tion (1/s) ρ Density (kg/m ) Catalyst deactivation function ε Voidage * Iqbal M. Mujtaba α Catalyst deactivation coefficient I.M.Mujtaba@bradford.ac.uk Exponent for representing α μ Viscosity Chemical Engineering Division, School of Engineering, University of Bradford, Bradford BD7 1DP, UK Vol.:(0123456789) 1 3 80 Applied Petrochemical Research (2018) 8:79–95 Subscripts in demand for propylene in the world has maintained focus cc Coke on catalyst on the refineries toward FCC technologies for the maximi- cL1 Cyclone 1 zation of propylene production to achieve economic profit ck Coke . In addition, the FCC operates below 550 °C and does c4 Butylene not require extreme ‘cold’ for the separation of propylene c3 Propylene from liquefied petroleum gas (LPG) [5 ]. Therefore, the cost ds Disperse steam of producing propylene from the FCC is much lower than FS Feed vaporization section that from steam pyrolysis . The FCC unit is thus ideally g Acceleration (m/s ) suited for the manufacture of ethylene and propylene from gl Gasoline the light products. Currently, there is an increasing interest g Gas in maximizing propylene yield of FCC units [7, 8]. The FCC go Gas oil unit has the ability to produce high yields when suitable dg Dry gas operating conditions are selected. However, due to changes MABP Molal average boiling temperature (K) in quality, nature of the crude oil feedstock, changes in the MeABP Mean average boiling temperature (K) environment and the desire to achieve maximum profitabil- pc Pseudo-critical ity, it results in many different operating conditions in the pr Pseudo-reduced FCC riser unit [5, 9]. RS Riser According to Almeida and Secchi  and John et al. , RT Disengager-stripping section the riser can produce large profits when it runs at maximum capacity with maximum feed rate and power applied to the equipment. Optimization of the design and operation is cru- Introduction cial to facilitate the constantly changing quality and nature of blends of feedstocks while meeting the maximum capac- The fluid catalytic cracking (FCC) is one of the most impor - ity requirements. Some factors such as the large amount of tant refining processes within an oil refinery [1 ]. It is a key feed processed, valuable gasoline yield, gas lump yield, the technology that converts heavy distillates, such as bottoms various processes occurring in the riser and its economic of vacuum and atmospheric distillation units, into desirable operation affects the overall economic performance of the products such as gasoline, diesel and middle distillates, using refinery; thus it is vital to improve the performance of the zeolite-cracking catalyst . These cracking reactions take riser through process optimization strategies [9, 11]. place in the riser column . The FCC is a type of secondary The production of propylene is mostly achieved using unit operation and one of the most important processes in a catalytic reactions with special selectivity for propylene [7, petroleum refinery. The FCC unit is mostly used to increase 8, 12, 13]. A number of lumps for catalytic cracking were gasoline and diesel yield to meet high demand of fuel which reported in the literature but most of them lumped the gase- is due to increase in transportation. However, it is not just ous products in a single lump, thereby making it difficult to to increase gasoline and diesel but middle distillates such as optimize or maximize a particular gas, for instance propyl- the gas lump as well, which comprises light olefins such as ene. Usman et al.  conducted experiment using three ethylene and propylene; major sources of the raw materials different crudes (Super Light, Extra Light and Arab Light) for the polyethylene and polypropylene industries. These catalytically cracked to produce light olefins, where they light olefins are the most important raw materials for many presented propane and propylene as different lumps. They chemicals such as acrylonitrile, propylene oxide, and other used different catalysts: base-equilibrated catalyst and oth- chemicals that are consumed as substitutes for non-plastic ers; (Z30 and Z1500) which are the base-equilibrated cata- materials . lyst + MFI Zeolite at varying Si/Al ratio. The results shows In recent times, there has been an increase in the demand that the total weight fraction of the two lumps; propylene and for propylene, a petrochemical industry feedstock  and propane has propylene about 80–89% for all the crude oils it is chiefly sourced from light olefins in the naphtha steam and catalysts used . This percentage is high, therefore, a pyrolysis process. Naphtha steam pyrolysis process is a high combined lump of propylene and propane can be treated as a energy consumption process because it is carried out at single lump of propylene and the kinetic model of Ancheyta about 800 °C and separation of olefins is done at a tempera- and Rogelio  is suitable for this work. Hence, in this ture as low as − 100 °C . This makes the naphtha steam study, the FCC riser is simulated based on a six-lumped pyrolysis process a more capital intensive one. However, kinetic model  consisting of vacuum gas oil, gasoline, propylene and ethylene are sourced cheaply from the FCC C ’s (propane and propene), C ’s (butane and butene), dry 3 4 unit due to the abundance and cheapness of the FCC feed-gas (H, C –C ) and coke. Vacuum gas oil is the feed whilst 2 1 2 stock compared with Naphtha [4, 5], and the recent growth gasoline, butylene, propylene and dry gas are products with 1 3 Applied Petrochemical Research (2018) 8:79–95 81 coke deposited on the catalyst. The yield of the propylene of a FCC process consists of two major units; the riser and is further enhanced by optimizing the operating conditions regenerator. of the riser. This study is focused on the riser unit of the FCC since it The FCC riser is a complex unit that involves strong is where the products are made. It is modelled as plug flow multi-variable interactions, complex hydrodynamics and and the vaporization of gas oil was considered to be instan- operating restrictions, which poses as a major difficulty in taneous in the vaporization section. The hot regenerated the simulation of the process. However, minimal changes catalyst from the regenerator meets the feed at the vaporiza- due to simulation and optimization can result in higher yield, tion section and vaporizes the feed with the aid of disper- thus increasing economic benefits. In the FCC unit, the yield sion steam to move upward into the riser where the gas oil of propylene is influenced by the reaction temperature, cat- gets cracked on the catalyst and produces desirable products alyst-to-oil ratio (C/O), residence time, nature of feed and . The riser in this work is of industrial size; 30 m high the catalyst system [16–18], and when any of the foregoing and 1.0 m diameter, whose simulation and further optimiza- variables is optimized, the yield of propylene can consider- tion is carried out using the mathematical models obtained ably increase. from the literature [2, 19, 20] as presented in Table 1. The Hence, gPROMS software 5.0 will be utilized for the choice of the mathematical model is based on the fact that simulation and optimization of the riser to obtain results it captures the actual hydrodynamic model of an industrial showing the effects of changing variables such as tempera- FCC unit and has been used extensively in the literature. The ture and mass flow rates [9 ] on the yield of propylene. To riser is simulated using a six-lump kinetic model as shown carry out this optimization, a single objective function was in Fig. 2, and the kinetic data for the various constants in developed and implemented in gPROMS software that uses Fig. 2 are estimated using parameter estimation technique. a successive reduced quadratic programming (SRQPD) opti- The simulation involves many other parameters such as the mization technique. This technique is a Sequential Quadratic feed conditions, catalyst properties and riser dimensions Programming-based solver imbedded in the gPROMS soft- which were obtained from the literature and presented in ware. Hence, the aim of this work is to maximize the yield Appendix Tables 8 and 9. The steady state model is derived of propylene by varying different sets of riser operational from mass, energy and momentum balance equations for conditions. the catalyst and gaseous phases of the riser, while assuming that there is no loss of heat from the riser to the surrounding . In addition, it is assumed that the cracking reactions Riser model only take place on catalyst surface. Equations (1)–(6) represent the overall rates of reaction The FCC unit (Fig. 1) houses the cylindrical vessel called for gas oil; R , gasoline; R , gas; R , butylene; R , pro- go gl C4 C3 riser, which is the main reactor, where the cracking reac- pene; R , dry gas, and R , coke; for the six-lump kinetic dg ck tion takes place in the presence of a catalyst. The catalyst, a reactions. Each overall rate of reaction is a function of over- mixture of crystalline alumina silicates (zeolites) is a sand- all rate constants, den fi ed by the Arrhenius equation given in like material which is fluidized into a fluid via contact with Eqs. (7)–(18). The rate of heat removal by reaction Q is react liquid fed into the FCC unit [2, 9]. A typical configuration given by Eq. (19), while Eqs. (20)–(25) and Eqs. (26)–(27) result from the material and energy balance of the catalyst and gas phases, respectively. The equations describing the Product hydrodynamics of the riser are Eqs. (28)–(53) [2, 19]. Equa- tions (28) and (29) describe the catalyst and gas velocity profiles across the riser [2 ]. Equations (30) and (31) describe Fractionator the gas volume fraction, ɛ , and catalyst volume fraction, ɛ ; g c Flue gas they provide a hydrodynamic constrain such that the sum- mation of the volume fractions is unity. The riser pressure is described by Eq. (37), which is obtained from the simple RiserRegenerator ideal gas relationship with Z as compressibility factor  described in Eq. (47). gPROMS is a robust software used for solving the set of differential algebraic equations describing the riser. It is an equation-oriented software and all solvers have been Feed designed specifically for large-scale systems such as the FCC unit with no restrictions regarding the size of the dif- Fig. 1 A schematic diagram of the FCC unit ferential–algebraic equations other than those imposed by 1 3 82 Applied Petrochemical Research (2018) 8:79–95 Table 1 Equations and descriptions Description of variable Equations Eq. no. Kinetic model equations for the six-lumped model Gas oil R reaction rate (1) R = −(K + K + K + K + K )y � go go 1 2 3 4 5 c go Gasoline R reaction rate R =(K y − K y − K y − K y − K y )� (2) gl gl 1 6 gl 7 gl 8 gl 9 gl c go Butylene R reaction rate R =(K y + K y − K y − K y )� (3) C4 C4 2 go 6 gl 10 C4 11 C4 c Propylene R reaction rate (4) R =(K y + K y + K y − K y )� C3 C3 3 7 gl 10 C4 12 C3 c go Light gas R reaction rate (5) R =(K y + K y + K y + K y )� dg dg 4 8 gl 11 C4 12 C3 c go Coke R reaction rate (6) R =(K y + K y )� Ck ck 5 9 gl c go −E Gas oil to gasoline overall rate constant 1 (7) K = k exp 1 10 RT −E Gas oil to butylene overall rate constant (8) K = k exp 2 20 RT −E Gas oil to propylene overall rate constant 3 (9) K = k exp 3 30 RT Gas oil to dry gas overall rate constant −E (10) K = k exp 4 40 RT −E Gas oil to coke overall rate constant (11) K = k exp 5 50 RT −E Gasoline to butylene overall rate constant 6 (12) K = k exp 6 60 RT −E Gasoline to propylene overall rate constant (13) K = k exp 7 70 RT −E Gasoline to dry gas overall rate constant 8 (14) K = K exp 8 80 RT Gasoline to coke overall rate constants −E (15) K = k exp 9 90 RT −E Butylene to propylene overall rate constant (16) K = k exp 10 100 RT −E Butylene to dry gas overall rate constant 11 (17) K = k exp 11 110 RT −E Propylene to dry gas overall rate constant (18) K = k exp 12 120 RT 2 2 2 Q is the rate of heat generation or heat removal by reaction (19) Q = −(ΔH K y +ΔH K y + ΔH K y react react 1 1 2 2 3 3 go go go 2 2 +ΔH K y +ΔH K y +ΔH K y + ΔH K y 4 4 5 5 6 6 gl 7 7 gl go go +ΔH K y +ΔH K y + ΔH K y 8 8 gl 9 9 gl 10 10 C4 +ΔH K y +ΔH K y )� 11 11 C4 12 12 C4 c Riser equations from material balance Gas oil fractional yield y (20) go c c = R go dx F Gasoline fractional yield gl (21) c c = R gl dx F Butylene fractional yield C4 (22) c c = R C4 dx F Propylene fractional yield C3 c c (23) = R C3 dx F Dry gas fractional yield (24) dg c c = R dg dx F Coke fractional yield ck c c (25) = R ck dx F Riser equations from energy balance h A dT p p Temperature of catalyst along the riser height c (26) = (T − T ) g c dx F C c pc 1 3 Applied Petrochemical Research (2018) 8:79–95 83 Table 1 (continued) Description of variable Equations Eq. no. dT Temperature of gas phase along the riser height g (27) = [h A (T − T )+ Q ] p p c g c c react dx F C g pg Riser hydrodynamic equations C (v −v ) dv d 2f v g Catalyst velocity f g c (28) c c rc c =− G + − − dx F dx F D v c c c dv C (v −v ) 2f v dP g Gas velocity g RS f c g rg g (29) =− + − − dx F dx F D v g g g Gas volume fraction, E = 1 − (30) g g c Catalyst volume fraction, (31) c = c c Riser cross-sectional area (32) Catalyst deactivation � = exp(− C ) (33) c c ck −E Catalyst deactivation coefficient c (34) c∗ = exp (R ) c c0 AN RT F y g ck Coke on catalyst (35) C = C + ck ckCL1 Gas phase density (36) g g RT Riser pressure (37) P = RS g wg Catalyst-to-oil ratio (C/O) (38) C∕O ratio = Riser pseudo-reduced temperature (39) T = pr pc RS Riser pseudo-reduced pressure (40) P = pr pc (−8.76 +5.43) Stress modulus of the catalyst  g (41) G = 10 F F C Catalyst temperature in the vaporization section lg ds pds (42) T = T − C (T − T )+ (T − T )+ ΔH cFS cCL1 p lg gFS lg gFS ds v lg F C F cCL1 pc lg lg Gas phase temperature in the vaporization section (43) T = − C gFS lg A −log(P y ) lg FS goFS Pressure at vaporization P = P +ΔP (44) FS RT RS lg Weight fraction of feed (gas oil) in the vaporization section (45) y = goFS F +F lg ds F +F lg ds Velocity of gas phase in the vaporization section (46) v = gFS (1− ) gFS cCL1 FS cCL1 Velocity of entrained catalyst in the vaporization section (47) v = cFS c cCL1 FS P M FS wgFS Gas oil density in the vaporization section (48) gFS RT Z gFS gFS (0) Catalyst phase velocity (49) v = v cFS cRS (0) Gas phase velocity (50) v = v gFS gRS Catalyst mass flow rate F = F (51) cRS cCL1 Gas phase mass flow rate F = F + F (52) gRS lg ds −M Heat of vaporization of gas oil 3 wm (53) ΔH = 0.3843T + 1.0878 × 10 exp − 98.153 vlg MABP A A A 5 2 9 11 Z factor of Heidaryan et al.  A +A ln(P )+ +A (ln P ) + + ln(P ) (54) 1 3 pr 7 pr 2 pr T T pr T pr pr Z = ln A A A 4 8 10 1+A ln(P )+ +A (ln P ) + + ln(P ) 2 pr 6 pr 2 pr T T pr T pr pr F Y (0) lg cc Weight fraction of Coke at inlet (55) y = ck F gRS (0) Gas phase velocity (56) T = T c cFS (0) Catalyst mass flow rate (57) T = T gFS 1 3 84 Applied Petrochemical Research (2018) 8:79–95 the eight-lumped model  which include ethylene as a lump and a separate propylene lumped with butylene. Where propylene is required as a separate lump, this eight- lumped model may not be useful. Some kinetic models for the propylene production are based on catalytic cracking, such as the four-lumped model which includes propylene as a component of a gas lump ; the ten-lumped model with propylene as a distinct lump  and six-lumped model with distinct propylene lump . To maximize the yield of propylene in a lumped kinetic model, propylene has to be a separate lump. The gas lump in Hussain et al.  is a mixture of propylene, butylene and some dry gas; hence, it is unsuitable for use to maximize propylene because maxi- mizing gas lump would mean maximizing other gases along. Fig. 2 Six-lump model [2, 15] The ten-lumped model of Du et al.  and six-lumped model of Ancheyta and Rogelio  are most suitable for available machine memory . gPROMS is a process mod- their ability to have propylene as unique lumps. However, the elling software for simulation, optimisation and control (both yields of lumps were obtained at a particular constant tem- steady state and dynamic) of highly complex processes such perature; 580 °C  and 500 °C , instead of progressive as the FCC unit riser. Due to its robustness, more research temperature profile of the catalyst and vapour phases as it is work on the FCC unit is being carried out using gPROMS obtainable in the industrial FCC riser. Specific rate constants in recent time [9, 20, 24, 25]. These are the first attempts on for the various cracking reactions and catalyst deactivation the FCC unit and gPROMS displayed great capability and in a typical industrial riser also vary along the length of the reliability. The riser model construction is described in the riser. In this work, the catalyst deactivation is represented by model section and the parameters are specified in the process Eq. (33) which as a function of varying temperature of the section of the gPROMS software 5.0.0. gas phase of the riser. Since temperature varies in the riser and has effect on some important kinetic variables such as rate constants and catalyst deactivation, it therefore means Riser kinetics and parameter estimation that heat required at every point in the riser varies. This heat requirement is estimated by heat of reaction of all cracking The kinetic studies on the production of propylene have been reactions as shown in Eq. (19). carried out and they are mostly based on catalytic pyroly- The riser mathematical model used in this work requires sis. However, catalytic pyrolysis includes catalytic reactions kinetic data that involves activation energy, frequency factor and thermal reactions , and the cracking extent of cata- and heat of reaction, and all vary along the riser. Hence, in lytic pyrolysis is more comprehensive than that of catalytic this work, heats of reactions, frequency factors and activa- cracking . In addition, catalytic cracking is favoured over tion energies for varying rate constants are estimated using thermal cracking for maximum propylene production espe- parameter estimation. Where the kinetic parameters to be cially in high severity FCC unit . Moreover, just like estimated are numerous and especially with limited labo- the catalytic cracking reactions require the understanding ratory data available, it poses a lot of challenges [31, 32]. of the kinetics of the reaction involved for reactor design, For the parameter estimation and simulation of the riser, the the design of the catalytic pyrolysis reactor would require six-lumped model  is chosen over the ten-lumped model the understanding of both the thermal and catalytic reac- because it predicts propylene as a single lump and has less tions involved to design a catalytic pyrolysis reactor. This is parameters to be estimated which reduces the complexity true because kinetic study is an essential mean for thorough of the model. understanding of reactions and catalysis for any catalysed chemical reaction which helps in the correct design of chem- ical reactors and determines the progress of the chemical Parameter estimation reaction . In this study, mathematical and kinetic mod- els used are based on the kinetic-lumping approach which Parameter estimation is carried out for a certain model by catalytic cracking as a form of reaction was employed [2, optimizing nearly all or some parameters by means of exper- 9, 19]. imental data. The optimized estimated parameters are those One of the kinetic-lumped models for the production best matches between the experimental data and predicted of propylene based on catalytic pyrolysis of heavy oils is data by the model . There are several techniques used for 1 3 Applied Petrochemical Research (2018) 8:79–95 85 parameter estimation in chemical and biochemical engineer- Table 2 presents the experimental data obtained from the ing for systems of dynamic and steady state models [31–36]. literature . A technique for parameter estimation is carried out through There are two approaches here: first, simulation for con- online optimization where the estimates are taken from mini- verging all the equality constraints and satisfying the ine- mization of the sum of squared errors of the optimization quality constraints; second, carrying out the optimization problem by matching the experimental and calculated results where the objective function is within some given range of constraints [37, 38]. This method has acceptance in the parameter estimation of chemical pro- exp cal 2 Obj(SSE)= (y − y ) , (58) cesses  and it is the method used in this work. It uses M=1 the Successive Quadratic Programming (SQP)  on the optimization framework of gPROMS software  and it is where y is the mass fraction of lumps and i is the various proved to be very capable . lumps in the riser. gPROMS parameter estimation requires the use of experi- The parameter estimation problem statement can be writ- mental data for validation and for the design of experiments ten as on the gPROMS platform. In this work, the experimental results were obtained from the literature  for each of the Given The fixed riser reactor configuration, feed quality and characteristics, cata- six-lumped models are used as experimental data to generate lyst properties and process operational the predicted results. Ancheyta and Rogelio  presented conditions 15 sets of fractional yields for the six lumps obtained at fif- Optimize The kinetic parameters; activation teen different weight hourly space velocities (WHSV) from energies E, heat of reactions ΔH and −1 6 to 48 h and at 773 K. These sets of fractional yields for frequency factors k at given process conditions the six lumps were read with a software called Webplot- So as to minimize The sum of squared errors (SSE) digitizer 3.8 and are presented in Table 2. On the gPROMS Subject to Equality and inequality constraints parameter estimation framework, the fifteen sets of results are used with each set for a single experiment that repre- exp Mathematically, sents experimental values y . Along with the complete riser mathematical model (hydrodynamic, kinetic, mass and min SSE, cal energy conservation equations), the calculated values y are , , i i0 i i obtained and the sum of squared errors (SSE) are minimized. s. t. Table 2 Six-lumps yield used as experimental data −1 WHSV (h )Propylene (C ’s) Butylene (C ’s) (wt%) Gas oil (wt%) Gasoline (wt%) Dry gas (wt%) Coke (wt%) 3 4 (wt%) 6 5.38 9.49 23.63 55.19 1.81 4.55 7 5.03 9.15 24.88 55.11 1.63 4.34 10 4.80 8.80 26.16 54.58 1.44 4.20 11 4.94 8.80 26.59 53.96 1.51 4.20 13 4.87 8.66 27.76 53.91 1.40 4.18 15 4.77 8.50 28.54 53.34 1.37 4.09 16 4.75 8.36 28.85 53.12 1.33 4.08 20 4.63 8.27 30.17 52.96 1.28 4.04 24 4.56 8.08 31.02 52.19 1.23 4.01 28 4.45 8.08 31.80 51.62 1.16 3.92 32 4.40 7.82 31.95 51.58 1.09 3.82 36 4.35 7.68 32.02 51.19 1.09 3.87 40 4.28 7.75 32.25 51.26 1.06 3.89 44 4.26 7.52 32.64 50.85 0.99 3.91 48 4.23 7.50 32.55 50.85 0.99 3.93 Average 4.65 8.30 29.39 52.78 1.29 4.07 Range 4.23–5.39 7.50–9.49 23.63–32.55 50.85–55.19 0.99–1.81 3.82–4.55 1 3 86 Applied Petrochemical Research (2018) 8:79–95 described by a procedure, or set of procedures to find the f (x, z (x), z(x), u(x), v)= 0 (model equations, equality constraints), best optimal solution for a particular problem. Common (59) examples include maximizing the yield from a chemical l u reaction [9, 33] or minimizing the amount of energy con- ≤ ≤ (inequality constraints), (60) sumed in a particular process . l u ≤ ≤ (inequality constraints), (61) An optimisation study of a FCC unit was carried out using genetic algorithm by . It was a multi-variable- l u ≤ ≤ (inequality constraints), (62) multi-objective optimization technique in which a three- where f (x, z (x), z(x), u(x), v)= 0 is the model equation, x is objective function optimisation was carried out. It included the height of the riser and the independent variable, u(x) is the maximization of the gasoline yield, minimisation of the decision variable; ξ is the upper and lower limits of the the air flow rate and minimisation of CO in the flue gas. frequency factors k ; η is the upper and lower limits of the This technique works by the principle of a population being oi activation energies E ; θ is the upper and lower limits of the generated within the upper and lower limits of the decision heat of reactions ΔH . z(x) is the differential and algebraic variables. Thereafter, an individual is selected from the equations while z′(x) is their derivative and v is the constant population depending on their “fitness”. This individual is parameters. then copied to formulate a new generation until a global Upper and lower limits are set for the decision variables maximum or minimum is found. Results obtained showed which of course they are the parameters requiring to be esti- good stability but computational times were found to be very mated. They are set based on the assumption that the kinetic long. A dynamic real-time optimisation study of a FCC unit values will be within the range found in the literature for was carried out . They developed a NLP problem and four-, five- and six-lumped models. Moreover, six-lumped was solved using a simultaneous strategy where a continuous model was derived based on the sequential strategy . problem was converted into an NLP. The solution included They assumed that the major reactant and products of the the use of DAE system being converted into a system of cracking reactions have similar rate constants, hence derived algebraic equations. Results obtained matched plant data the four-lumped model from the three-lumped model and very closely. A real-time optimisation strategy for an FCC hence the six-lumped model from the five-lumped model unit controller was presented , where a linear model in a sequential strategy. Therefore, it is expected in this predictive controller was optimized so that it would be able work that the upper and lower limits for the activation to handle disturbances in the commissioning or load distur- energy, heat of reaction and frequency factors should be bance phases. The objective function in their work was to within the existing range. The values from the literature maximize the production of LPG. Results had shown that are: activation energy (31,923–57,278.96 kJ/kg mol) [43, the dynamic response of the controller was smooth and 44] and (31,820–66,570 kJ/kg mol) , heat of reaction fast in the real controller and there were major issues with −1 (195–745 kJ/kg) and frequency factor (0.000629–1457.5 s ) the controller response. John et al.  undertook a study . The upper and lower limits are opened further wide to maximize the gasoline output in a FCC unit using SQP on the gPROMS parameter estimation framework to allow on gPROMS. The objective function was the maximization the software make the best estimates. Hence, the upper and of the yield of gasoline and the variables being optimized lower limits for the following variables are activation energy were mass flow rates of catalyst and gas oil and temperatures (0 and 100,000 kJ/kg mol), heat of reaction (0 and1000 kJ/ of catalyst and gas phases. Their results showed a feasible −1 kg), and frequency factors (0 and 2000 s ). Another reason solution, whereby yield of gasoline had increased by 4.51%. for opening the limits of the decision variables is to allow for Another SQP algorithm was used to maximize propylene the adjustment of data obtained from the laboratory model yield in a secondary reaction and 16.68 vol% was achieved to get modified since they are being used on a mathematical . model that represents an industrial unit . With respect to the FCC process, it is obvious that the optimisation of the process can yield significant gains in different areas such as maximizing the yield of the product. FCC riser optimization Furthermore, optimisation of FCC riser can be undertaken to minimize the operating cost as well as the capital cost During optimisation, one tries to minimize or maximize a if observed from a design standpoint. It can also be used global characteristic of a process such as cost and time by to minimize certain outputs such as carbon dioxide emis- exploiting the degrees of freedom under a set of constraints sions to meet legislations . Due to the complex nature of . Therefore, it can be said that effective optimisation the FCC process, very few simulation optimisation studies is needed to achieve the best process possible, in terms of have been carried out and optimisation of FCC units have obtaining more of a desired product. Optimisation can be been primarily through experimental means. However, the 1 3 Applied Petrochemical Research (2018) 8:79–95 87 optimisation of the process through mathematical models min max T ≤ T ≤ T is now gaining grounds in research. As computers become (68) g g more powerful, it is now becoming possible to undertake min max rigorous models of the FCC unit through first principle mod- T ≤ T ≤ T , (69) c c elling and empirical correlations. The benefit of using these numerical optimisation models is that the costs involved are min Equality constraints: y ≤ y . gl (70) gl very small compared to utilising lab scale experiments as well as the speed of computation once a model is built. The entire DAE model equations can be written in a com- There are three main issues called the constraint triangle pact form as for maximizing propylene production; the effects of exist- f (x, z ̇ (x), z(x), u(x), v) = 0 , wher e x is the independent ing FCC technology, operation variables and catalysts on variable which in this case is the height of riser, z(x) is the product quality and quantity . Since the alteration of set of all state variables, z ̇ (x) is the derivatives of z(x) with the FCC unit configuration and catalyst development is not respect to the height of the riser, u(x) is the vector of control the focus of this work, even though they are very impor- variables (mass flow rates of feed and catalyst) and v is a tant in FCC unit optimization, only the operation variables vector of invariant parameters, such as design variables are manipulated to maximize the yield of propylene lump (riser diameter and height). In addition, y is the objective C3 (C ’s). Higher propylene production comes at the expense function which is the yield of propylene, the desired product of gasoline. For traditional refiners, maximizing gasoline to be maximized in the riser. T is the catalyst phase tem- yield is more important than the propylene yield, while for perature, T is the gas phase temperature, FF is the mass g g those interested in petrochemical applications, the target is flow rate of gas oil, FF is the mass flow rate of catalyst, x is operating at maximum propylene yield . max the height of the riser, x is the maximum riser height min (30 m) and y is the yield of gasoline. y is the minimum gl gl Optimization problem statement value of gasoline to be maintained while propylene is maxi- min max mized. T and T are the minimum and maximum c c Optimisation of the yield of propylene. bounds of the catalyst phase temperature The optimization problem can be described as min max (700 ≤ T ≤ 1000 K) and T and T are the minimum g g and maximum bounds of the gas phase temperature Given The fixed volume of the riser min max (520 ≤ T ≤ 800 K). FF and FF are the minimum and Optimize The mass flow rate of catalyst, g c c mass flow rate of gas oil and maximum bounds of the mass flow rate of catalyst kg min max temperatures of gas and catalyst ( 20 ≤ FF ≤ 500 ) and FF and FF are the minimum g g phases and maximum bounds of the mass flow rate of gas oil So as to maximize The yield of propylene lump kg max (C ’s) y (10 ≤ FF ≤ 100 ). x is the fixed height of the riser; 3 C3 Subject to Constraints on the mass flow 30 m, and y is the minimum allowable limit for gasoline gl rates of catalyst and gas oil, 0.40 < Y . gl temperatures of gas and catalyst The boundaries for the mass flow rates of gas oil and phases, and exit concentration of catalyst are chosen such that it reflects the typical industrial gasoline FCC unit limits for C/O ratios of 4:1–10:1 by weight , Sadeghbeigi , . C/O ratios for propylene production The optimisation problem can be written mathematically in high severity units and riser-downer are higher  than as the C/O ratios used in conventional FCC units, which vary Objective function: Max y . between 1 and 6 [16, 29, 50] and 3–25. Hence, the bounda- C3 (63) T ,FF ,y j j gl ries for the mass flow rates are open wide enough to accom- Subject to modate low and high C/O ratios (1–25) on the optimization framework. Process model: f (x, z ̇ (x), z(x), u(x), v)= 0, (64) max Boundary: x = x , (65) min max Inequality constraints: FF ≤ FF ≤ FF g (66) g g min max FF ≤ FF ≤ FF (67) c c 1 3 88 Applied Petrochemical Research (2018) 8:79–95 Table 3 New kinetic parameters estimated Case studies Rate constant Frequency factors Activation Heat of −1 Case 1: Optimizing catalyst mass flow rate FF between 20 (s ) energy (kJ/ reaction (kJ/ kg mol) kg) and 500 kg/s; gas oil temperature, T (520–800 K); catalyst temperature, T (700–1000 K), while gas oil mass flow rate, k1 1233.51 45,005.4 284.151 FF , is kept constant at 58.02 kg/s. k2 841.36 66,364.1 22.452 Case 2: Optimizing gas oil mass flow rate FF between 20 k3 1333.60 62,582.7 103.432 and 500 kg/s; gas oil temperature, T (520–800 K); catalyst k4 6.019 66,568.4 25.596 temperature, T (700–1000 K), while the catalyst mass flow k5 0.493 66,054.1 194.867 rate, FF , is kept constant at 134.94 kg/s. k6 26.056 35,760.4 675.894 Case 3: Optimizing catalyst mass flow rate FF between k7 63.008 66,426.2 645.963 20 and 500 kg/s; gas oil temperature, T (520–800 K); cata- −6 k8 8.19 × 10 62,591.5 250.896 lyst temperature, T (700–1000 K); and gas oil mass flow rate k9 12.048 36,983.7 565.387 FF between 20 and 500 kg/s. k10 1367.37 60,938.7 496.002 Since FCC’s major goal is the production of gasoline, a k11 1359.88 57,575.9 899.319 minimum of 40 wt% of gasoline is imposed as a constraint −6 k12 8.19 × 10 45,880.0 682.498 on all the optimization cases, else most of the gasoline will deplete due to secondary cracking. The choice of 40 wt% is based on the average gasoline yield presented in the litera- ture; 44.13–45.65 wt% , 44 wt% [21, 52] and 40 wt% ygo ygl yC4 yC3 ydg yck . 0.9 0.8 0.7 Results and discussion 0.6 0.5 0.4 Model validation and parameter estimation results 0.3 0.2 The reason for presenting the simulation results is to deter- 0.1 mine the capability of gPROMS in handling complex non- linear DAEs of the riser using the kinetic model of Ancheyta 05 10 15 20 25 30 Riser Height (m) and Rogelio , and to compare the simulated results obtained with those predicted results of the same kinetic Fig. 3 Lumps of gas oil cracking model obtained experimentally by Ancheyta and Rogelio . Even though the experimental results were obtained at 773 K, the simulated riser temperature was progressive come to 971.4 K at the entrance of the riser. Cracking reac- along the length of the riser. tions begin immediately at the riser entrance and the profiles The mass flow rates for gas oil and catalyst used in this of these cracking reactions are presented in Fig. 3, while the simulation are 51.8 kg/s and 190.9 kg/s, respectively, while temperature profiles are presented in Fig. 4. the C/O ratio is 3.685. These mass flow rates predicted the The feed in this study is a 97.00 wt% gas oil and the yields of the six lumps in the range presented by Ancheyta remaining 3.00 wt% is steam. Figure 3 shows that the frac- and Rogelio  while the parameter estimation was car- tion of gas oil at the exit of the riser is 26.12 wt% which ried out. The estimated kinetic parameters are presented in is 26.93% of gas oil unconverted. It also shows that about Table 3. 73.07% of gas oil was consumed and about 70% of the frac- When gas oil meets the catalyst, it begins to crack to tion is consumed in the first 20 m of the riser. In the litera- form gasoline, butylene, propylene, dry gas and coke. In ture result , the fraction of gas oil at the exit of the riser this study, the cracking reaction takes place at gas oil inlet was presented as a range because it was obtained at varied temperature of 523.0 K at the vaporization section rising WHSV, and it is between 23.50 and 32.50 wt% which cor- to 719.9 K at the first 6 m height of the riser and levelling responds to 67.5–76.5% of gas oil consumed. The value of out for the remaining height of the riser with 706.2 K as the 26.93 wt% of unconverted gas oil obtained in this simulation exit temperature. The inlet temperature of catalyst from the at C/O ratio of 3.685 falls within the range of results from cyclone is 1010 K which mixes with regenerated catalyst Ancheyta and Rogelio . in the vaporization section to have the catalyst temperature 1 3 wt% Applied Petrochemical Research (2018) 8:79–95 89 endothermic heat which is determined in this simulation with the aid of the heat of reaction estimated is represented Catalyst Temperature Gas Phase Temperature 900 by the profile of the gas phase temperature and shown along with the profile of the catalyst phase temperature in Fig. 4. 800 The temperature of the catalyst phase is about 971.4 K at the entrance of the riser but decreases for the first 5 m and then essentially levels out. The temperature profile of the gas phase at the entrance of the riser is about 523.0 K but rises to a maximum in the first 5 m of the riser and levels out to the exit of the riser. Both profiles start with a difference of about 448.5 K at the entrance of the riser and came so close to the 05 10 15 20 25 30 same value with temperature difference of about 4.4 °C at Height (m) the exit of the riser. This temperature difference is required to accomplish Fig. 4 Temperature profile across the riser the endothermic reaction. The temperature of the cracking reactions in Ancheyta and Rogelio  experimental work Likewise, gasoline started yielding as soon as cracking is 773 K. This temperature was reached at the riser entrance starts at the entrance of the riser. It rises from 0 to 51.36 wt% where both catalyst and oil mixed vigorously. However, at the exit of the riser. This accounts for 52.95% of the total the temperature of cracking in a typical riser varies at the product of the riser with about 80% of the gasoline formed entrance to the exit because the reaction is progressive at in the first 20 m of the riser. The value of 51.36 wt% of varied temperatures along the riser as seen in Fig. 4. The gasoline yield in this simulation is within the range of temperature profiles obtained in this work are similar to 50.85–55.19 wt% presented by Ancheyta and Rogelio . those obtained in many literatures [19, 21, 55]. The butylene lump (C ’s) rises from 0 to 9.39 wt% at the Table 4 shows the comparison of the results obtained exit of the riser. This accounts for 9.68% of the total prod- in this simulation at C/O ratio 3.685, already presented in uct of the riser and it is within the range of 7.50–9.49 wt% Figs. 3 and 4, with the results presented by Ancheyta and presented by Ancheyta and Rogelio . Rogelio  experimental work. All the results are within Similarly, the propylene lump (C ’s), which is of more the corresponding range for each lump which validates the interest in this work, also builds up as cracking commences results obtained. With an increment of 50 kg/s of catalyst at the riser entrance from 0 to 4.59 wt% at the exit of the mass flow rate, the C /O ratio was varied and the results are riser, accounting for 4.73 wt% of total riser products. The also presented for C/O ratios of 4.651, 5.616 and 6.581 in propylene yield of 4.80 wt% is also within the range of Table 4. 4.23–5.38 wt% presented by Ancheyta and Rogelio  and The unconverted gas oil yields at the varied C/O ratios are others in the literature . outside and lower than the range of the results by Ancheyta The dry gas lump also rises from 0 to 1.55 wt% at the and Rogelio . This is expected because increasing the exit of the riser. This is 1.60 wt% of the total product of C/O ratio increases gas oil conversion as a result of increase the riser and it is within the range of 0.99–1.81 wt% pre- in cracking temperature. The absolute difference between sented by Ancheyta and Rogelio . The remainder being the simulated results (C/O = 3.685) and the varied C/O coke deposited on the catalyst which also rises from 0 to ratios (C/O = 4.651, 5.616 and 6.581) shows decrease for 0.0399 wt% and it represents 4.11 wt% of the total product of both gas oil and gasoline. All other lumps increase due to the riser. It is also found within the range of 3.82–4.55 wt% increase in the C/O ratio and eventual rise in cracking tem- presented by Ancheyta and Rogelio . perature which increases the conversion of the cracking reac- In general, the yields of the six lumps are within the range tion. Gasoline undergoes secondary cracking to add to the presented by Ancheyta and Rogelio . This shows that butylene, propylene and dry gas lumps with additional coke the estimated kinetic parameters are true representation of deposit on the catalyst. This trend shows that increasing the the cracking reactions. The values also show that the experi- C/O ratio may favour the yield of the light products such mental data of Ancheyta and Rogelio  can actually be as butylene, propylene and dry gas. However, the absolute used for the parameter estimation and the estimated kinetic difference for propylene (5.46 wt%) at C /O ratio of 6.581 is parameters are useful for simulation of industrial riser. The more than that of butylene (4.31 wt%), which suggest that it profiles of the reactant and products are qualitatively consist- would be necessary to operate the riser at C/O ratio of 6.581 ent with those found in the literature [9, 19]. to have more propylene in the light components. To get the As cracking takes place, the endothermic reaction best operating condition for propylene yield, optimization gives up heat from the catalyst to the gaseous phase. The of the unit is necessary. 1 3 Temperature (K) 90 Applied Petrochemical Research (2018) 8:79–95 Table 4 Comparing simulated riser output with that of Ancheyta and Rogelio  Lump (wt%) Output range  Riser output (wt%) C/O = 3.685 C/O = 4.651 Difference C/O = 5.616 Difference C/O = 6.581 Difference Gas oil (wt%) 23.63–32.55 26.11 19.50 − 6.61 15.58 − 10.53 13.06 − 13.05 Gasoline (wt%) 50.85–55.19 51.36 49.69 − 1.67 46.40 − 4.96 42.86 − 8.5 Butylene (C ’s) (wt%) 7.50–9.49 9.39 12.06 2.67 13.37 3.98 13.70 4.31 Propylene (C ’s) (wt%) 4.23–5.39 4.59 6.37 1.78 8.22 3.63 10.05 5.46 Dry gas (wt%) 0.99–1.81 1.55 3.36 1.81 5.58 4.03 7.92 6.37 Coke (wt%) 3.82–4.55 4.00 6.04 2.04 7.86 3.86 9.41 5.41 Cat. temp. (K) 710.6 734.0 23.4 753.2 42.6 769.6 59.0 Gas phase temp. (K) 706.3 729.1 22.8 748.0 41.7 764.1 57.8 The optimized catalyst mass flow rate is 282.0 kg/s; it is a Optimization results 47.72% increase on the 190.9 kg/s base case simulation. This increase produced results consistent with the riser hydro- Table 5 presents the riser exit values of this simulation along dynamics where increase in mass flow rate of catalyst can with those riser exit concentrations from the optimization result in an increase in the reaction temperature and con- cases. sequent yield of intermediate products [9, 19, 56]. There The results for both optimization cases 1, 2 and 3, and is 3.81 and 3.89% increase in the temperatures of the gas base case simulation (this simulation, Figs. 3, 4) are pre- phase and catalyst, respectively, which in turn causes the sented in Table 5, showing the riser exit values of the six increase in the yield of a difference of 5.26 wt% of dry gas lumps; gas oil as feed, while gasoline, butylene, propylene, from 1.55 wt% at C/O ratio of 3.69–6.81 wt% at C/O ratio dry gas and coke as products, and temperatures of the cata- of 5.44. Similarly, the yield of butylene has a difference of lyst and gas phases. It compares the base case simulation 5.10 wt% from 9.39 wt% at C/O ratio of 3.69–14.49 wt% at results with the optimized cases 1, 2 and 3. C/O ratio of 5.44. Due to increase in C/O and temperature In the optimisation case 1, as propylene is maximized, of reaction, more gas oil cracks, a further 12.02 wt% was the decision variable (catalyst mass flow rate) was set to be achieved from 26.11 wt% at C/O ratio of 3.69–14.09 wt% optimized between 20 and 500 kg/s, while gas oil tempera- at C/O ratio of 5.44. This is also a reason for more yield ture, T , was between 520–800 K and catalyst temperature, of propylene and other intermediate products; butylene and T , between 700 and 1000 K. The gas oil mass flow rate dry gas. Gasoline also cracks in a secondary reaction and was fixed at 51.8 kg/s. The maximized value of propylene depletes from 51.36 wt% at C/O ratio of 3.69–43.68 wt% is 8.93 wt% at C/O ratio of 5.44 (gas oil mass flow rate is at C/O ratio of 5.44 giving rise to a loss of 7.68 wt%, this 51.8 kg/s and catalyst mass flow rate is 282.0 kg/s). The secondary reaction was also observed in the literature . absolute difference between the maximized value and this In optimization case 1, at C/O ratio of 5.44, 9.00 wt% of simulation is 4.34 wt%, an increase from 4.59 to 8.93 wt%. coke was deposited on the catalyst, against 4.00 wt% at C/O Table 5 Propylene optimization results for cases 1, 2 and 3 and simulation results Lump Riser optimization output (wt%) Current simulation Case 1 Difference Case 2 Difference Case 3 Difference C/O = 3.69 C/O = 5.44 1.75 C/O = 5.48 1.79 C/O = 5.45 1.76 Gas oil (wt%) 26.11 14.09 − 12.02 14.06 − 12.05 14.07 − 12.04 Gasoline (wt%) 51.36 43.68 − 7.68 43.64 − 7.72 43.65 − 7.71 Butylene (C ’s) (wt%) 9.39 14.49 5.10 14.50 5.11 14.50 5.11 Propylene (C ’s) (wt%) 4.59 8.93 4.34 8.93 4.34 8.95 4.36 Dry gas (wt%) 1.55 6.81 5.26 6.85 5.30 6.83 5.28 Coke (wt%) 4.00 9.00 5.00 9.00 5.00 9.01 5.01 Cat. temp. (K) 710.6 737.7 27.1 738.5 27.9 737.7 27.1 Gas phase temp. (K) 706.3 733.8 27.5 734.2 27.9 733.8 27.5 1 3 Applied Petrochemical Research (2018) 8:79–95 91 ratio of 3.69 leading to an addition of 5.00 wt% of coke on set between 520 and 800 K and catalyst temperature, T , catalyst. It is also a consequence of increased C/O ratio and between 700 and 1000 K. reaction temperature. This increase in coke on catalyst may The optimized gas oil and catalyst mass flow rates are lead to high deactivation of the catalyst, which is not desir- 53.4 and 290.8 kg/s, respectively, showing a 3.09% increase able, however, regeneration of the catalyst can be achieved on the 51.8 kg/s base case condition for gas oil mass flow and any eventual consequence is compensated by the much rate and 52.33% increase on the 190.9 kg/s base case condi- increase in the yield of propylene achieved. tion for catalyst mass flow rate. These optimized flow rates Optimization cases 2 and 3 present similar outcomes correspond to a C/O of 5.45, an increased C/O of 1.74 on as optimization case 1 because their optimum C/O ratios the base case simulation bringing about a 94.99% increase are quite similar; 5.44, 5.48 and 5.45 for cases 1, 2 and 3, in propylene yield from 4.59 to 8.95 wt%. There is a slight respectively, with an absolute average difference of 0.016. increase of 0.05 wt% of propylene in case 3 over cases 1 and This very slight difference is responsible for the slight aver - 2, which represents a 0.44% increase. This increase makes age variation of 0.01 wt% in the riser outputs for the six optimization case 3 most preferable because any small lumps. improvement to the yield of products in FCC unit amounts The optimisation case 2 has its decision variable changed to great profitability. In general, the maximized value of from the mass flow rate of catalyst in case 1 to mass flow propylene is 8.95 wt% achieved at C/O ratio of 5.45, even rate of gas oil. The gas oil mass flow rate was set to be opti - though, an average of 7.70 wt% of gasoline is lost due to sec- mized between 20 and 500 kg/s, while gas oil temperature, ondary reaction with much coke deposited on the catalyst. T , between 520 and 800 K and catalyst temperature, T , It is observed that the improved yield of propylene is g c between 700 and 1000 K. The catalyst mass flow rate was accompanied with increase in some undesirable products fixed at 190.9 kg/s. The optimized gas oil mass flow rate is such as dry gas and butylene as well as its isomer. It also 34.86 kg/s, which is a 32.7% decrease on the 51.8 kg/s of increased catalyst deactivation. However, FCC units can be the base case simulation and corresponds to C/O of 5.48, an modified or operated in a mode shift to produce propylene increase of C/O ratio of 0.04 compared with the C/O ratio with less of the aforementioned consequences. This could of optimization case 1. This result, as in case 1, is consistent be achieved by the harmonious combination of the catalyst, with the riser hydrodynamics where increase in C/O results temperature, C/O ratio, time, coke make, and hydrocarbon in increase in the reaction temperature and yield of interme- partial pressure . diate products [7, 56]. There is 3.90 and 3.95% increase in An industrial size conventional FCC riser is simulated in the temperatures of the gas phase and catalyst, respectively. this work to maximize the yield of propylene as a separate The increase in temperature in cases 1 and 2 is very similar lump. The common view is where experimental works were because only C/O ratio difference of 0.04 between cases 1 carried out at specific temperature in fixed bed reactors, and and 2 exists, which even though the optimized conditions propylene mostly considered as part of a general lump of in case 2 increased the maximum value of propylene by olefins. Instead of using catalyst additives to improve the 94.55% the same as case 1 compared with the simulation yield, only the operational conditions of the riser were used value of 4.59 wt%; there is no difference between the values in this work. However, it is recommended that the use of of maximized propylene (8.93 wt%) between cases 1 and both improved catalyst and optimum operating conditions 2. Similarly, the yield of butylene and dry gas increased, will greatly increase the yield of propylene. respectively, by 5.11 and 5.26 wt% due to an increase in C/O ratio of 1.79 (C/O of 3.69–5.48). The amount of coke deposited in case 2 is as in case 1, which is 9.00 wt%. Since Conclusions maximizing propylene is the main aim of this work, and cases 1 and 2 could achieve the same value of 8.93 wt%, In this work, optimization of the FCC riser has been carried any of the operating conditions of cases 1 or 2 can be used out using a detailed riser process model of a six-lumped for optimal operation of the riser to produce optimum value kinetic model to maximize the conversion of gas oil to pro- of propylene, however, case 2 is preferable because of the pylene, which is a major building block for the polypro- difference of C/O ratio of 0.05. pylene production. Parameter estimation was also done to The optimisation case 3 used two decision variables, estimate the kinetic variables useful in the model used in unlike cases 1 and 2. These were gas oil and catalyst mass this simulation. It is a steady state optimization carried out flow rates. The gas oil mass flow rate was set to be opti- on a FCC riser and the following were found: mized between 20 and 500 kg/s as in case 1, and the cata- lyst mass flow rate was also set to be optimized between 20 In the case 1 optimization, the maximum value of propyl- and 500 kg/s as in case 2. The gas oil temperature, T , was ene obtained is 8.93 wt% at optimal value of 282.0 kg/s catalyst mass flow rate. Compared with the base case 1 3 92 Applied Petrochemical Research (2018) 8:79–95 simulation value of 4.59 wt% propylene yield, the maxi- The distillation coefficient used in this simulation is based mized value shows an increase by 95%. on the 10, 50 and 90 vol% as used in Ancheyta and Rogelio Likewise, in the case 2 optimization, the maximum . value of propylene obtained is the same 8.93 wt% at Heat capacity of gas, C , is pg optimal value of 34.86 kg/s gas oil mass flow rate. When C = + T + T , it is compared with the base case simulation value of (71) pg 1 2 g 3 4.59 wt% propylene yield, the maximized value shows where , , β and β , the catalyst decay constants, given as 1 2 3 4 an increase by 95%, as in case 1. When the two optimal values of 290.8 kg/s mass flow 1.04025 rate of catalyst and 53.4 kg/s mass flow rate of gas oil =−1.492343 + 0.124432K + 1.23519 − , 1 f 4 were obtained in case 3, the maximized propylene yield g (72) is 8.95 wt%, slightly higher than cases 1 and 2. When it is compared with the base case simulation value of −4 = (−7.53624 × 10 ) 4.59 wt% propylene yield, the maximized value shows 5.0694 2.9247 −(1.5524 − 0.05543K )K + 6.0283 − , an increase by 95%. f f 4 New kinetic parameters (frequency factor, activation (73) energies and heat of reactions) were estimated for and −6 used with a six-lumped kinetic model with a separate =(1.356523 × 10 )(1.6946 + 0.0884 ), (74) 3 4 propylene lump. The yields of the six lumps fall within the range of yields presented in the literature. 12.8 10 𝛽 = − 1 1 − S − 0.885 S − 0.7 10 4 g g The optimization in all three cases (cases 1, 2 and 3) was Kf Kf for 10 < Kf < 12.8. achieved at C/O ratios of 5.44, 5.48 and 5.45, respec- (75) tively. C/O ratio 5.45 gave the higher maximum value Else = 0 for all other cases of propylene, hence the riser is required to operate at a Kf is the Watson characterization factor written as minimum C/O ratio of 5.44 if optimal operation of the riser is required to maximize propylene yield. 1.8T MeABP (76) Kf = , Acknowledgements Gratitude to Petroleum Technology Development Fund, Nigeria, who financially sponsored the lead author’s PhD study. where M is the molecular weight of the gas and can be wg calculated using Open Access This article is distributed under the terms of the Crea- tive Commons Attribution 4.0 International License (http://creat iveco −4 M = 42.965 exp 2.097 × 10 T − 7.787S mmons.or g/licenses/b y/4.0/), which permits unrestricted use, distribu- wg MeABP g tion, and reproduction in any medium, provided you give appropriate (77) −3 1.26007 4.98308 +2.085 × 10 T S (T S ), MeABP g credit to the original author(s) and the source, provide a link to the MeABP g Creative Commons license, and indicate if changes were made. T = T − 0.5556 exp[−0.9440 − 0.0087 MeABP VABP 0.6667 0.3333 × 1.8T − 491.67 + 2.9972(Sl) , VABP Appendix (78) where T is the volume average boiling temperature and VABP Table 6 and Eqs. (71)–(92) are correlations of physical and (Sl) is the slope given as transport parameters adopted from the literature [2, 19]. Sl = 0.0125(T − T ), ( ) (79) 90ASTM 10ASTM T = 0.333(T + T + T ). (80) VABP 10ASTM 50ASTM 90ASTM The ASTM D86 distillation temperatures are calculated Table 6 Distillation coefficients Volume % a b using distilled 10 0.5277 1.0900 10 (81) T = a T , 10ASTM 10TBP 30 0.7429 1.0425 50 0.8920 1.0176 70 0.8705 1.0226 50 b (82) T = a T , 50ASTM 50TBP 90 0.9490 1.0110 1 3 Applied Petrochemical Research (2018) 8:79–95 93 − Table 8 Specifications of constant parameters and differential vari- T = a T , ables at x = 0 90ASTM 90TBP (83) Variable Value where a and b are the distillation coefficients (Table 6) and i i T is the TBP distillation temperature. iTBP Riser height, L (m) 30 Interface heat transfer coefficient between the catalyst and D riser diameter (m) 1.0 gas phases, h , p T (0) (temperature of gas oil, K) 523 T (0) (temperature of gas catalyst, K) 971 K (v − v ) g g c g g FF (catalyst mass flow rate, kg/s) 190.9 h = 0.03 . p (84) g FF (gas oil mass flow rate, kg/s) 51.8 y (0) mass fraction of gasoline 0.0 gl y (0) mass fraction of dry gas 0.0 dg Thermal conductivity of hydrocarbons y (0) mass fraction of butylene 0.0 C4 −6 K = 1 × 10 (1.9469 − 0.374M + 1.4815 y (0) mass fraction of propylene 0.0 C3 g wm (85) y (0) mass fraction of coke 0.0 −3 2 ck × 10 M + 0.1028T ), wm M molecular weight coke (kg/k mol) 14.4 wck where M is the mean molecular weight of the combined WM M molecular weights of hydrogen (kg/k mol) 2 wH catalyst and gas M molecular weights of methane (kg/k mol) 16 wC M molecular weights of ethane (kg/k mol) 30 wC 1 2 M = WM M molecular weights of propane (kg/k mol) 44 y y y wC y y y 3 go gl dg (86) C4 C3 ck + + + + + M molecular weights of butane (kg/k mol) 58 M M M M M M wC wgo wgl wC4 wC3 wdg ck g, acceleration due to gravity (m/s ) 9.8 R, ideal gas constant (kPa m3/kg mol K) 8.3143 M = M wgo wg (87) M = 0.0146M + 0.4161M + 0.5693M . dg wH wC wC (88) 2 1 2 6 −3 The viscosity of the gas (Table 7) P = 4.6352 × 10 exp −8.505 × 10 T pc MeABP −3 −4.8014S + 5.749 × 10 T S g MeABP g (92) M P WM pc −0.4844 4.0846 −8 × T S . (89) MeAB g = 3.515 × 10 , g pr pc Table 9 Catalyst and feed properties Variable Value 0.6921 = 0.435 exp 1.3316 − T P T + 0.0155, (90) pr pr pr pr Han and Chung  d (average particle diameter, m) 0.00007 −4 T = 17.1419 exp −9.3145 × 10 T pc MeABP C (Coke on catalyst, wt%) 0.001 ckCL1 −4 α (pre-exponential factor of α ) 0.000011 −0.5444S + 6.4791 × 10 T S c0 c g MeABP g (91) α (catalyst deactivation coefficient) 0.1177 −0.4844 4.0846 c* × T S , MeAB g C (heat capacity of catalyst, kJ/kg K) 1.15 pc S (average sphericity of catalyst particles) 0.72 Table 7 Tuned coefficients for Coefficient Tuned coefficient E catalyst activation energy (kJ/kg mol) 49,000 0.2 ≤ P ≤ 3  pr A1 2.827793 Ancheyta and Rogelio  ρ (density of catalyst, kg/m ) 890 A2 − 0.4688191 A3 −1.262288 API 24 S (specific gravity) 0.91 A4 −1.536524 A5 −4.535045 T TBP distilled 10 volume%, K 619 10TBP T TBP distilled 50 volume%, K 706 A6 0.06895104 50TBP A7 0.1903869 T TBP distilled 90 volume%, K 790 90TBP Paraffinics (wt%) 61.0 A8 0.6200089 A9 1.838479 Naphthenics (wt%) 19.3 Aromatics (wt%) 19.6 A10 0.4052367 A11 1.073574 R (aromatics/naphthenes in liquid feedstock) 1.02 AN 1 3 94 Applied Petrochemical Research (2018) 8:79–95 19. 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