Journal of King Saud University – Engineering Sciences (2015) 27, 130–136
King Saud University
Journal of King Saud University – Engineering Sciences www.ksu.edu.sa www.sciencedirect.com
ORIGINAL ARTICLE
Prediction of gasoline yield in a fluid catalytic cracking (FCC) riser using k-epsilon turbulence and 4-lump kinetic models: A computational fluid dynamics (CFD) approach Muhammad Ahsan
*
School of Chemical & Materials Engineering, National University of Sciences & Technology, Islamabad 44000, Pakistan Received 9 May 2013; accepted 4 September 2013 Available online 14 September 2013
KEYWORDS FCC riser; Computational fluid dynamics (CFD); Cracking reaction kinetics; Hydrodynamics; 4-Lump kinetic model; k-Epsilon turbulence model
Abstract Fluid catalytic cracking (FCC) is an essential process for the conversion of gas oil to gasoline. This study is an effort to model the phenomenon numerically using commercial computational fluid dynamics (CFD) software, heavy density catalyst and 4-lump kinetic model. Geometry, boundary conditions and dimensions of industrial riser for catalytic cracking unit are conferred for 2D simulation using commercial CFD code FLUENT 6.3. Continuity, momentum, energy and species transport equations, applicable to two phase solid and gas flow, are used to simulate the physical phenomenon as efficient as possible. This study implements and predicts the use of the granular Eulerian multiphase model with species transport. Time accurate transient problem is solved with the prediction of mass fraction profiles of gas oil, gasoline, light gas and coke. The output curves demonstrate the breaking of heavy hydrocarbon in the presence of catalyst. An approach proposed in this study shows good agreement with the experimental and numerical data available in the literature. ª 2013 Production and hosting by Elsevier B.V. on behalf of King Saud University.
1. Introduction Fluid catalytic cracking (FCC) is considered to be one of the most important petroleum refining processes. The fluid cata* Tel.: +92 3336057937. E-mail address:
[email protected] Peer review under responsibility of King Saud University.
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lytic cracking involves the conversion of heavy oil feedstock into gasoline and other valuable products (Wang et al., 2012). The FCC reaction riser presents a complex scenario as it contains a multiphase flow and not less than a double figure of intermediate products such as liquid petroleum gas (LPG), coke and others. Optimization of the FCC riser is generally experimental as a result of complex relations among the enormous number of dependent and independent variables. Study of optimum operating variables for different modes of operation by experimentally changing the process conditions on a commercial FCC unit is neither realistic nor suitable. Therefore, there has been numerous simulation studies focused on
1018-3639 ª 2013 Production and hosting by Elsevier B.V. on behalf of King Saud University. http://dx.doi.org/10.1016/j.jksues.2013.09.001
Prediction of gasoline yield in a fluid catalytic cracking (FCC) riser using k-epsilon turbulence
131
Nomenclature CD Cl ds es g go Hi khs ki P Ps qi Res Ts Ui y1
Drag coefficient Turbulence constant Diameter of solid particles, m Particle collision coefficient Gravitational acceleration, m s2 Radial distribution function The specific enthalpy of ith phase, J kg1 Diffusion coefficient, kg m1 s1 Turbulent kinetic energy, J kg1 Static pressure, Nm1 Solid Pressure, Nm1 The heat flux, Wm2 Relative Reynolds number Solid stress tensor, Pa Velocity of ith phase, m s1 Gasoil mass fraction
FCC (Ancheyta-Jua´rez and Murillo-Herna´ndez, 2000; Theologos and Markatos, 2004; Lopes et al., 2011). However, most of these simulations suppose the idealized mixing conditions within the riser reactors. In FCC risers, multi-nozzle gas oil feed injectors are used for quick feed vaporization, these injectors also mix the catalyst and oil uniformly. The finite mixing length at the bottom of the riser has a major effect on the operation of FCC (Novia et al., 2007). The hydrodynamics of FCC riser reactor has been studied with different modeling approaches. The accurate analysis of the flow field has not yet been achieved, and most times, it is still limited to a two-dimensional flow model. The most popular approach in modeling of FCC riser reactor is the 1-D plug flow model with slip between the phases (Snoeck et al., 1997). On the other hand, this model is not able to explain the complex hydrodynamics in FCC riser reactors. In current years, among large amount of research, increasing attention has been paid to the method using better computer ability to develop mathematical models to investigate the multiphase reaction and transport in FCC riser reactors. Theologos and Markatos (2004) constructed a three-dimensional model of the two-phase flow, heat transfer and reaction in a riser reactor. Although it ignored the turbulence of gas and solids, and used a simple 4lump kinetic model, the model predicted the flow field, heat distribution and concentrations of all species throughout the reactor, which testified the importance of such a method. It is a challenge for the researchers to describe the kinetic mechanism of cracking of hydrocarbons in the area of mathematical modeling of fluid catalytic cracking. The existence of thousands of unidentified components in the feed to the riser and the parallel/series reactions of these components creates difficulty in kinetics modeling. The information of main chemical reactions arising during catalytic cracking was shared by Guisnet and Ribeiro, 2011. The catalytic cracking of hydrocarbons is very complex due to many reactions and chemical species involved. Therefore, the reaction kinetics has been investigated by lumping a numbers of chemical compounds. Several catalytic cracking reaction kinetic models for the FCC process have been proposed by different researchers. Weekman and Nace (1970) developed a simple kinetic scheme, based on the theory of Wei and Prater,
y2 y3 a b qi ei ei si cs hs lb li ls,dil lt
Gasoline mass fraction Light gas plus coke mass fraction Turbulent kinetic energy dissipation rate, m2 s3 Solid gas exchange coefficient, kg m3 s1 Density of ith phase, kg m3 Volume fraction of ith phase Turbulent dissipation rate, m2 s3 Shear stress tensor of ith phase, Nm2 Collisional dissipation of energy, kg m1 s3 Granular temperature, m2 s1 Solid bulk viscosity, kg m1 s1 Viscosity of ith phase, kg m1 s1 Solid phase dilute viscosity, kg m1 s1 Turbulent viscosity kg m1 s1
1963 for the kinetic modeling of cracking reactions occurring in the riser reactor. This work can be considered as pioneer in developing the simple kinetic mechanism for FCC modeling purposes. Authors divided the charge stock and products into three components, namely, the original feedstock, the gasoline (boiling range C5-410 0F), and the remaining C4’s (dry gas and coke), and hence simplified the reaction scheme. The model predicted the conversion of gas oil (the feedstock) and gasoline yield in isothermal condition in fixed, moving, and fluid bed reactors. The kinetic parameters of the model were evaluated using the experimental data. Since the gas oil and gasoline cracking rates have different activation energies, an optimum reactor temperature was also determined for the system. This scheme was further extended to several other kinetic schemes. Among them the four lump models, five lump models, six lump models, ten lump models, eleven lump models, twelve lump models, thirteen lump models, and nineteen lump models are widely used (Gupta et al., 2007). For simplification and less computational constraints, this present work used the 4-lump kinetic model of cracking reactions, which considers the heavy gas oil, gasoline and the remaining component as the lumps. Generally, the overall heat balance around the reactorregenerator system in an FCC unit includes: (1) the enthalpy of combustion of coke-on-catalyst; (2) the endothermic heat of cracking reactions; (3) the heat of vaporization of gas-oil at the entrance of the riser; and (4) other enthalpies such as the heat of feed air, product stream, and exit flue gas from the regenerator (Novia et al., 2007). However, the calculation of the endothermic heat of cracking reactions in FCC riser reactors still presents a significant challenge. Elnashaie and Elshishini (1993) assumed the constant heat of cracking reaction in the riser height. However, the heat of reaction varies from the bottom to the top of the riser. For a typical commercial FCC unit, the heat of cracking varies between 200 and 700 kJ/kg and the temperature drop of about 30–40 C. In the present study, a heavy density catalyst has been used to develop a two dimensional hydrodynamics and reaction kinetics model of FCC riser reactor. Heavy density catalyst provides catalytic activity sites, as compared to zeolite there are larger pores that provide entry for larger molecules. This
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M. Ahsan
makes the cracking of larger molecules of higher boiling point possible. Alumina increases the conversion of light gases to gasoline significantly. The CFD code FLUENT 6.3 is used to simulate FCC riser reactors. The model studies the twophase flow of catalyst and vapor. It described the temperature profiles, mass fraction profiles and the yield of gasoline product in the FCC riser reactor.
2.3. Solid pressure The solid phase pressure (Ps) consists of kinetic term and the particle collision term. It is calculated from the equation of state which is the same as the van der Walls equation of state for gases (Chapman and Cowling, 1991). Ps ¼ ð1 þ 2ð1 þ es Þes go Þes qs Hs ¼ qs es Hs þ 2go qs e2s Hs ð1 þ es Þ
2. Mathematical modeling A granular Eulerian–Eulerian multiphase model is used to simulate the hydrodynamics of the multiple phases. In Fluent 6.3 CFD code, the finite volume method is used to discretize the conservation equations. 2.1. Conservation equations
ð1Þ
with definition: eg + es = 1. The conservation of momentum of phase i (i = gas, solid, k „ i) can be written as @ ðq ei Ui Þ þ r ðqi ei Ui Ui Þ ¼ ei rP þ r si þ qi ei g @t i bðUi Uk Þ
ð2Þ
The conservation of energy for phase i yield. @ @Pi ðei qi Hi Þ þ r ðei qi Ui Hi Þ ¼ ei þ si @t @t : rUi r q þ Si
ð3Þ
2.2. Interphase exchange coefficients From the Syamlal–O’Brian model for the drag force formulation (Syamlal and O’Brien, 1989). 3 es eg qg Res jUs Ug j b ¼ CD ð4Þ 2 ds vr;s 4 The drag coefficient, CD is given by Di Felicea and Rotondia (2012). !2 4:8 CD ¼ 0:63 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð5Þ Res =mr;s Res ¼
qg ds jUs Ug j lg
ð6Þ
where mr,s is the terminal velocity correlation for the solid phase (Garside and Al-Dibouni, 1977). qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mr;s ¼ 0:5 ð0:06Res Þ2 þ 0:12Res ð2B AÞ þ A2 þ 0:5A 0:03Res where:
where Hs is the granular temperature, es is the coefficient of restitution for particle collisions. g0, the radial distribution function (Ogawa et al., 1980) is given by: " 1 #1 es 3 go ¼ 1 ð9Þ es;max The value of maximum solid packing, es, max for this simulation is 0.53.
The continuity equation of phase i (i = gas, solid): @ ðq ei Þ þ r ðqi ei Ui Þ ¼ 0 @t i
ð8Þ
ð7Þ
2.4. Solid shear stress The solid stress tensor contains bulk and shear viscosities. The solid phase bulk viscosity can be expressed as (Chepurniy, 1984): 1=2 4 Hs lb ¼ es qs go ð1 þ es Þ ð10Þ 3 p The solid phase shear viscosity is given by Gidaspow et al. (1991)). 2 1=2 2ls;dil 4 4 Hs ls ¼ 1 þ ð1 þ es Þgo es þ es qs ds ð1 þ es Þ 5 5 ð1 þ eÞgo p ð11Þ The solid phase dilute viscosity is: pffiffiffiffiffiffiffiffiffiffiffi 5 ls;dil ¼ qs es ls 2pHs 16 where pffiffiffi 2 ds ls ¼ 12 es
ð12Þ
ð13Þ
2.5. Granular temperature The granular temperature hs is calculated by solving the turbulent kinetic equation for solid phase: 3 @ ðq es Hs Þ þ r ðqs es Us Hs Þ ¼ Ts : r ðkHs rHs Þ cs 2 @t s
ð14Þ
The diffusion coefficient for granular energy, kHs is represented by: kHs ¼
2 1=2 2kHs;dil 6 Hs 1 þ ð1 þ es ÞgO es þ 2e2s qs ds gO ð1 þ es Þ 5 ð1 þ es ÞgO p ð15Þ
where:
A ¼ e4:14 g
pffiffiffiffiffiffiffiffiffiffiffi 75 q es ls 2pHs 64 s
B ¼ 0:8eg1:28 foreg 6 0:85
kHs;dil ¼
B ¼ 0:8eg2:65 foreg > 0:85
The collisional energy dissipation, cs, is given by:
ð16Þ
Prediction of gasoline yield in a fluid catalytic cracking (FCC) riser using k-epsilon turbulence " # 1=2 4 Hs 2 2 cs ¼ 3ð1 þ es Þes qs gO Hs rUs ds p
133
ð17Þ
2.6. K–E turbulence model Generally, the FCC riser reactor is under turbulent flow conditions. Therefore, it is important to use an appropriate turbulence model to describe the effect of turbulent fluctuations of velocities and scalar variables for the basic conservation equations. A k-epsilon model was used to describe the turbulent motions in both phases. In the k-epsilon model, the turbulent viscosity is defined as: ðtÞ lt;i
k2 ¼ qi ei Cl i 2i
Figure 1
Table 1 1994).
ð18Þ
The turbulence kinetic energy, k, and its rate of dissipation, e, can be calculated from the following transport equations: @ l ðq ei ki Þ þ r ðqi ei ki Ui Þ ¼ r ei t rki þ ðei Gk ei qi 2i Þ ð19Þ @t i rk @ l 2i ðei qi 2i Þ þ r ðqi ei 2i Ui Þ ¼ r ei t r2i þ ðC12 ei Gk C22 ei qi 2i Þ ð20Þ rk k @t
Four lump kinetic model.
Kinetic data for cracking reactions (Gianetto et al.,
Cracking reaction
Pre exponential factor
Activation energy (J/kg mol)
Gas oil to gasoline Gas oil to light gases Gas oil to coke Gasoline to coke
0.4272 · 107 0.1012 · 108 0.5504 · 105 0.1337 · 103
87821.4 97552.4 87504.1 72988.7
The advantage of using the k-epsilon turbulence model is that it is computationally cheap but major weakness is overestimation of turbulence (Ahsan, 2012). 2.7. Reaction scheme The catalytic cracking of gas oil produces a wide range of products. The present work used a 4-lump kinetic scheme proposed by Gianetto et al. (1994) to describe the catalytic cracking reactions. In this scheme, the gas oil feed is converted to gasoline, light gases and coke, while a portion of the gasoline is converted to coke. The catalytic cracking reaction scheme for the 4-lump model is shown in Fig. 1. The gas oil, gasoline, light gases and coke are shown as separate lumps in Fig. 1. Kinetic data for cracking reactions are shown in Table 1. The reaction kinetics is merged into the mathematical model by solving the species equations of the components in the form of chemical reaction rates (Novia et al., 2007): dy1 dt dy2 dt dy3 dt dy4 dt
¼ K1 y21 / K3 y21 / ¼ ðK1 þ K3 Þy21 / ¼ K0 y21 /
ð21Þ
¼ K1 y21 / K2 y2 / ¼ ðK1 y21 þ K2 y2 Þ/
ð22Þ
¼ ðK3 y21 þ K2 y2 Þ/
ð23Þ
¼ K4 y21 /
ð24Þ
2.8. Boundary conditions Fig. 2 shows the geometry of the riser. GAMBIT pre-processor is used to construct the 2-D geometry. Meshing of the geometry is done by using rectangular grids. The height of the riser is 8.25 m and diameter is 0.2 m. The flow rate of the gas oil is 13 kg/s at the bottom of the riser. Other properties of gas oil and solids are mentioned in Table 2.
Figure 2
FCC riser mesh.
134
M. Ahsan
Table 2
Properties of gas oil and solids (catalyst).
Gas oil
Solids
Property
Units
Density Temperature Cp (specific heat) Thermal conductivity Viscosity Molecular weight Standard state enthalpy
3
kg m K J kg1 K1 W m1 K1 kg m1 s1 kg kg1 mol1 J kg1 mol1
Value(s) 9.4 620 2430 0.0178 7 · 106 226.2 3.3e + 08
Property
Units
Density Temperature Diameter Cp (specific heat) Thermal conductivity Molecular weight Standard state enthalpy
3
kg m K lm J kg1 K1 W m1 K1 kg kg1 mol1 J kg1 mol1
Value(s) 3890 980 60 880 35 102 1657.7
2.9. Assumptions
3. Simulation set up
Following assumptions reported by different researchers are made to simplify the model
The 2D geometry is discretized using 19,915 rectangular cells. Grid size analysis is carried out using three different mesh intervals, i.e. 1, 2 and 3 mm. All the simulation results did not show any major difference. The novel approach of making
At the riser inlet, hydrocarbon feed comes in contact with the hot catalyst coming from the regenerator and instantly vaporizes (taking away latent heat and sensible heat from the hot catalyst). The vapor thus formed moves upwards in thermal equilibrium with the catalyst (Ali et al., 1997; Gupta and Subba Rao, 2001). There is no loss of heat from the riser and the temperature of the reaction mixture (hydrocarbon vapors and catalyst) falls only because of the endothermicity of the cracking reactions (Ali et al., 1997; Dasila et al., 2012). Ideal gas law is assumed to hold while calculating gas phase velocity variation on account of molar expansion due to cracking and gas phase temperature (Dasila et al., 2012). Catalyst particles are assumed to move as clusters to account for the observed high slip velocities (Dasila et al., 2012). Heat and mass transfer resistances are assumed as negligible (Ali et al., 1997; Dasila et al., 2012). Both phases are assumed in plug flow condition hence back mixing in both phases is neglected (Dasila et al., 2012).
Figure 4
Figure 3
Phase temperature (gas oil and catalyst).
Figure 5
Temperature in a FCC riser.
Mass fraction profiles in the riser.
Prediction of gasoline yield in a fluid catalytic cracking (FCC) riser using k-epsilon turbulence Table 3
135
Comparison of model results with other models and plant data. Gasoline yield (wt%)
Light gases (wt%)
Coke (wt%)
Unconverted gas oil (wt%)
Riser temperature [K]
Comparison 1
Plant (Ali et al., 1997) This model % Deviation
44 41 6.82
20 26 30
6 5 16.67
28 26 7.14
795 755 5.03
Comparison 2
Model (Gupta et al., 2007) This model % Deviation
43 41 4.65
20 26 30
4 5 25
30 26 13.33
775 755 2.58
Comparison 3
Model (Lan et al., 2009) This model % Deviation
40 41 2.5
21 26 23.81
4 5 25
33 26 21.21
773 755 2.33
the bottom grid of the riser thicker is introduced to predict the results more efficiently. FLUENT 6.3 worked out a time of 65 h for 10 s of real time simulation at a mean time step of 0.001, number of time steps 100,000, maximum iterations per time step 40 on a dual core Microsystems with 32 bit processor and 1 GB RAM. There are no universal metrics for judging convergence. Residual definitions that are useful for one class of problem are sometimes misleading for other classes of problems. Therefore it is a good idea to judge convergence not only by examining residual levels, but also by monitoring relevant integrated quantities such as drag or heat transfer coefficient. For most problems, the default convergence criterion in FLUENT is sufficient. This criterion requires that the scaled residuals decrease to 103 for all equations except the energy and radiation equations, for which the criterion is 106. In this simulation the residuals decrease to 1012 (Fluent-Inc, 2006). 4. Results and discussion This study illustrates simulation results for computational parameters. In this paper the model predicts the temperature profile in the riser, phase temperature profile and mass fraction profile of a gasoil, gasoline, light gases and coke. Although the model is very simplified in this study, it reasonably predicts the trends of variations of gas and particle temperatures in the FCC riser as shown in Fig. 3. At the moment of initial contact between the hot regenerated catalyst and the vaporized feedstock (directly as the gas phase), the gas phase is heated sharply to a mixer temperature in the inlet region of the riser reactor, as shown in Fig. 3. As expected the temperature decreases significantly from the bottom to top of the riser. The variations of the phase temperatures are qualitatively consistent with the literature (Pareek et al., 2002; Benyahia et al., 2003; Das et al., 2003; Mahecha-Botero et al., 2009). Fig. 4 shows the temperature of a riser. We can observe that the temperature of the riser is descending as the nature of the reaction is endothermic. Due to the high temperature at bottom of the riser the gasoline yield increased, but because of coke deposition the gasoline yield decreased after attaining a maximum value. Fig. 5 predicts the mass fraction profiles of gasoline light gases and coke in FCC riser. The model shows that the conversion of gas oil mostly occurs in the first 4 m of the riser, which is alike to the profiles, reported by other researchers. The mass
fraction of gas oil is descending gradually while the yield of gasoline is increasing significantly. There are several reasons for this; riser has a high catalyst activity at the bottom. Moreover, the concentration of the gas oil decreases at the bottom due to molar expansion and reaction, thus the reaction rate of gas oil to gasoline is greatest at the bottom of riser. Gasoline yield is also increasing due to the flow pattern of a riser which is closer to plug flow (Pareek et al., 2002; Das et al., 2003; Novia et al., 2007). The simulation results are discussed and presented in this paper. Table 3 shows the comparison of plant and model data with the results predicted by this model. We can observe the good agreement between the results. 5. Conclusions A two dimensional multiphase flow reaction model for FCC riser has been developed by using commercial CFD code FLUENT 6.3 with the four lump reaction kinetics model of Gianetto et al. It is observed that, the model prediction of the gasoline yield and the riser temperature gives the lowest deviations from the plant data among the five parameters studied. The model predictions of the gasoline yield and temperature were confirmed by evaluation with plant data supplied by Ali et al., (1997). Very good agreement was found between the model predictions and the industrial data when the more realistic kinetic parameters reported by Gianetto et al. (1994) were considered. Mass fraction profiles, phase temperature profiles and riser temperature profiles are predicted by using the multiphase model. The simulation predicts that the inlet zone of the FCC riser is the most complex segment. Mostly the reaction occurs in first 1– 3 m of the FCC riser length. A good agreement is observed with the plant data reported in the literature and data predicted by other models. For each combination of feed and catalyst the rate constant parameters can be obtained from the literature. The values of rate constants for cracking reactions played an important role in the prediction of the FCC riser model. It is more appropriate to use these rate constants for the pair of specific feedstock and catalyst instead of kinetic constants obtained by regression analysis. The proposed model is applicable for all simulation processes of FCC riser. The model can be enhanced for control and optimization of FCC riser modeling. More accurate results can be predicted by implementing the model to a 3D geometry with fewer assumptions.
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