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Dispersion models for the simulation of an industrial Fluid Catalytic Cracking Riser Reactor have been developed. The models were developed based on the principle of conservation of mass and energy on the reacting species due to bulk flow and axial dispersion.
The four-lump kinetic scheme was used to describe the cracking reactions occurring in the reactor.
The model equation
s
were a set of parabolic Ordinary Differential Equations which were reduced to first order differential equations by appropriate substitutions and integrated
numerically using 4^{th} order Runge Kutta algorithm using Visual Basic 6.0. Results obtained showed a maximum percentage deviation ranging from 0.31
%
to 5.7% between model predictions and industrial plant data indicating reasonable agreement. Simulation of model at various operating parameters gave optimum gasoline yield of 45.6% of the most significant variable of temperature (658
K), superficial velocity
(0.1
m/s), catalyst to gas oil ratio (7.0) and diffusion coefficient of 0.23
m^{2}/s.

The Fluid Catalytic Cracking Unit (FCCU) is a very important unit in the refinery. This unit is often referred to as the “cash cow” of all refining operations, since it cracks heavy residual stocks recovered from other refinery operations into more valuable hydrocarbons. Fluid catalytic cracking employs an extremely hot circulating fluidized bed catalyst to crack the high molecular weight hydrocarbons into low molecular weight hydrocarbons [

Circulating fluidized beds are especially useful in processes involving high gas and solids flux, and in catalytic reactions requiring quick catalyst regeneration [

In the F.C.C.U., the atomized feed (vacuum gas oil) is sprayed into the reactor, where it comes in contacts with extremely hot fluidized bed of catalyst that supplies the heat required for the cracking reaction. The cracking process is endothermic and takes place in few seconds. The hot catalyst vaporizes the feed and catalyzes the cracking reactions that breakdown the high molecular weight oil into higher components, including; gasoline, liquefied petroleum gas (LPG), fuel gas and coke. The hydrocarbon mixture flows to the main fractionator via cyclones for separation into: fuel gas, LPG, gasoline, high cycle oil and main-column bottom (decanted oil). The spent catalyst is disengaged from the cracked hydrocarbon vapours and reactivated in a regenerator by burning the coke deposited on its active surface. This regeneration reaction is exothermic. Fernandes et al. [

riser Reactor in which reactions and axial dispersion occurs. In developing model equations to investigate the catalytic cracking of vacuum gas oil in the reactor has led to a measure of axial dispersion characterized by a dimensionless group as

D u L . Where F_{Ao} & F_{Af} are the initial and final flow rate, C_{Ao} & C_{Af} are the initial

and final concentration, L is the length, u is the velocity and the application of fundamental quantities viz.: mass and energy to obtain the state equations with respect to the differential element of volume as shown in

The following simplifying assumptions were made in the derivation of the mathematical model:

1) Axial dispersion is taken into consideration and catalyst particles have a uniform size in the given differential element. Both gas oil and gasoline have identical activity decay function, f [

2) Constant superficial velocity, u is assumed [

3) C_{1}-C_{4} gases do not produce coke, and the coke content in the feed is negligible [

4) The mass and energy balance in the riser reactor are considered at quasi-steady state [

5) The cracking reactions are almost complete in the riser [

Under these assumptions, the component mass balance for the mass concentrations due to bulk flow and axial dispersion and rate of depletion of the reacting species operating at steady state in the riser (plug-flow) reactor can be obtained as:

u d ρ A d l − D d 2 ρ A d l 2 + ( − r A ) ρ g R ε = 0 (1)

A dimensionless catalyst bed height and residence time are defined as: z = l L R , and τ = L R u = V R v o , Equation (1) becomes;

d ρ A d z − D u L R d 2 ρ A d z 2 + ( − r A ) ρ g R ε τ = 0 (2)

where, u is the velocity of gas oil, D is the diffusion coefficient, ρ g R is the total density of feed and products, ρ A is the density of gas oil, ( − r A ) is the rate of reaction.

But the density of reactant, A is

ρ A = y A ρ g R (3)

where y A = mass fraction of gas oil.

Substituting Equation (3) into Equation (2) and assuming constant total mass density gives;

( D u L R d 2 y A d z 2 ) − d y A d Z − τ ( − r A ) ε = 0 (4)

But, V R = A R L R z and v o = F g r C T O ρ g R (5)

hence;

τ = A R L R z ρ g R F g R C T O (6)

Substituting Equation (6) into Equation (4) gives;

( D u L R d 2 y A d z 2 ) − d y A d Z − A R L R Z ρ g R F g R C T O ( − r A ) ε = 0 (7)

Similarly, the basic material equations governing the yield of the cracking products gasoline (B), light gases (F) and coke (G) are expressed respectively as;

( D u L R d 2 y B d z 2 ) − d y B d Z − A R L R Z ρ g R F g R C T O ( − r B ) ε = 0 (8)

( D u L R d 2 y F d z 2 ) − d y F d Z − A R L R Z ρ g R F g R C T O ( − r F ) ε = 0 (9)

( D u L R d 2 y G d z 2 ) − d y G d Z − A R L R Z ρ g R F g R C T O ( − r G ) ε = 0 (10)

The four-lump Kinetic model as proposed by [

The overall rake constant of reaction is k 1 + k 2 + k 3 . The rate constant of over cracking is k 4 + k 5 and the rate constant of by-product and residue obtained is k 2 + k 3 from the cracking of gas oil kinetic model. The cracking of gas oil to gasoline, light gases and coke is a second-order reaction while the cracking of gasoline to light gases and coke is first-order reaction [

( − r A ) = k 1 y A 2 ϕ + k 2 y A 2 ϕ + k 3 y A 2 ϕ (11)

Hence,

( − r A ) = ( k 1 + k 2 + k 3 ) y A 2 = k o y A 2 (12)

( − r B ) = − k 1 y A 2 + k 4 y B + k 5 y B

( − r B ) = [ − k 1 y A 2 + k B y B ] (13)

where k B = k 4 + k 5

( − r F ) = − k 2 y A 2 − k 4 y B

( − r F ) = − [ k 2 y A 2 + k 4 y B ] (14)

( − r G ) = − k 3 y A 2 − k 5 y B

( − r G ) = − [ k 3 y A 2 + k 5 y B ] (15)

Substituting Equations (12)-(15) into Equations (7)-(10) gives;

GAS OIL (A)

( D u L R d 2 y A d z 2 ) − d y A d Z − A R L R Z ρ g R F g R C T O k o y A 2 ϕ ε = 0 (16)

GASOLINE (B)

( D u L R d 2 y B d z 2 ) − d y B d Z − A R L R Z ρ g R F g R C T O [ − k 1 y A 2 + k B y B ] ε = 0 (17)

C_{1}-C_{4} GASES (F)

( D u L R d 2 y F d z 2 ) − d y F d Z − A R L R Z ρ g R F g R C T O [ − ( k 2 y A 2 + k 4 y B ) ] ε = 0 (18)

COKE (G)

( D u L R d 2 y G d z 2 ) − d y G d Z − A R L R Z ρ g R F g R C T O [ − ( k 3 y A 2 + k 5 y B ) ] ε = 0 (19)

The deactivation model for a deactivation order of m equal to 1 as proposed by [

ϕ = exp ( − α τ ) (20)

The deactivation constant, α in Arrhenius temperature dependent equation is determined by:

α = α 0 exp ( − E α R T ) (21)

where T = Reaction temperature, α = Catalyst decay constant, α 0 = Pre-exponential constant for catalyst decay, E α = Activation energy for catalyst deactivation, R = Universal gas constant.

Substituting Equation (6) and Equation (21) into Equation (20) gives;

ϕ = exp [ − α 0 ( A R L R Z ρ g R F g R C T O ) exp ( − E α R T ) ] (22)

Applying the law of conservation of energy for a differential element of the reactor to the reacting species and the heterogeneous endothermic cracking reactions at steady state, the energy balance can be written mathematically as:

d T 2 d Z 2 − ( ρ g u c p + ρ s u c p s ) d T R d l − ∑ i = 1 5 ρ g R ε ( Δ H i ) ( − r i ) = 0 (23)

where ρ g , ρ s are the density of gas and catalyst respectively.

To express Equation (23) in dimensionless form, the following dimensionless

parameters are defined: d z = d l L R , d T = d T R T r e f , and τ = L R u gives;

( K T r e f 2 L R 2 ) d 2 T d Z 2 − ( ρ g c p g + ρ s c p s ) T r e f τ d T d Z − ∑ i = 1 5 ρ g R ε ( Δ H i ) ( − r i ) = 0 (24)

where T = dimensionless temperature, T r e f = reference temperature, T_{R }= axial reaction temperature, K = thermal conductivity, c p g & c p s = specific capacity of gas oil and catalyst respectively.

Substituting Equation (6) into Equation (24) gives;

( K T r e f 2 L R 2 ) d 2 T d Z 2 − ( ρ g c p g + ρ s c p s ) F g r C T O T r e f A R L R z ρ g R d T d Z − ∑ i = 1 5 ρ g R ε ( Δ H i ) ( − r i ) = 0 (25)

Multiplying through by ( L R 2 K T r e f 2 ) , Equation (25) becomes;

d 2 T d z 2 − ( ρ g c p g + ρ s c p s ) F g r C T O T r e f A R L R z ρ g R d T d Z − ( L R 2 K T r e f 2 ) ∑ i = 1 5 ρ g R ε ( Δ H i ) ( − r i ) = 0 (26)

But,

( Δ H i ) ( − r i ) = y A 2 [ k 1 ( Δ H 1 ) + k 2 ( Δ H 2 ) + k 3 ( Δ H 3 ) ] + y B [ k 4 ( Δ H 4 ) + k 5 ( Δ H 5 ) ] (27)

Substituting (27) into (26) gives;

d T 2 d z 2 − ( ρ g c p g + ρ s c p s ) F g r C T O L R A R ρ g R K T r e f − L R 2 K T r e f 2 ∑ i = 1 5 ρ g R ε ⋅ ( y A 2 [ k 1 ( Δ H 1 ) + k 2 ( Δ H 2 ) + k 3 ( Δ H 3 ) ] + y B [ k 4 ( Δ H 4 ) + k 5 ( Δ H 5 ) ] ) = 0 (28)

The properties and compositions of feed and products of the industrial Fluid Catalytic Cracking process, the dimensions of FCC reactors, are presented in

The set of parabolic Ordinary Differential Equations (ODE) from the models were not amenable to analytic solution technique. The equations were solved numerically if all the parameters are known. The second order differential equations were reduced to first order differential equations by substitutions. The boundary value was converted into an initial-value problem and solved numerically using the fourth order Runge Kutta algorithm. Visual Basic 6.0 program was used to simulate the model.

Since gas oil cracked to the various products, the mass fraction of gas oil is 1 at L R = 0 ; while the mass fraction of the products at the inlet is zero. The boundary condition at the inlet of the reactor; mathematically is

z = 0 { y A O = 1 y B O = y G O = y F O = 0 (29)

Component | API Gravity | Specific Gravity | Composition Weight % | Flow rate (kg/hr) |
---|---|---|---|---|

Gas oil feed | 21.2 | 0.927 | 100 | 244,090 |

Fuel gas | - | - | 5.4 | 13,181 |

C3 LPG | - | - | 6.3 | 15,388 |

C4 LPG | - | - | 10.7 | 26,118 |

Gasoline | 60.0 | 0.739 | 45.9 | 112,037 |

Light Cycle oil | 14.0 | 0.973 | 17.8 | 43,448 |

Bottoms | 0.5 | 1.072 | 8.8 | 21,480 |

Coke | - | - | 5.1 | 12,448 |

Parameter | Value (m) |
---|---|

Length | 22.9 |

Diameter | 2.9 |

Cyclone height | 14.24 |

Cyclone diameter | 1.5 |

Disengager height | 24.5 |

Paraffins | Naphthenes | Aromatics |
---|---|---|

35.4 | 16.1 | 48.1 |

Parameter | Units | Value |
---|---|---|

Vapour density | kg∙m^{−3} | 9.52 |

Liquid density at 2880 K | kg∙m^{−3} | 924.8 |

Specific heat of gas | kj∙kg^{−1}∙K^{−1} | 3.3 |

Specific heat of liquid | kj∙kg^{−1}∙K^{−1} | 2.67 |

Heat of vaporization | kj∙kg^{−1} | 156 |

Temperature of vapourization | K | 698 |

-gas oil to gasoline | kj | −2970 |

-gas oil to light hydrocarbon gases | kj | −9240 |

-gas oil to coke | kj | 23,820 |

-gasoline to light hydrocarbon | kj | −6030 |

-gasoline to coke gases | kj | 22,606 |

Catalyst | ||

Bulk density | kg∙m^{−3} | 975 |

Particle size | m | 95 × 10^{−6} |

Specific heat capacity | kj∙kg^{−1}∙K^{−1} | 1.12 |

Mass flow rate of catalyst from the reactor to regenerate | kg/hr | 1,729,750 |

Parameter | Plant Data | Model Prediction | Percentage Deviation |
---|---|---|---|

Weight Fraction of Gas-oil | 0.266 | 0.2689 | −1.09 |

Weight Fraction of Gasoline | 0.459 | 0.456 | 0.65 |

Weight Fraction of Light Gases (C_{1}-C_{4}) | 0.224 | 0.2233 | 0.31 |

Weight Fraction of Coke | 0.051 | 0.0518 | −5.7 |

Riser Outlet Temperature (K) | 658 | 646.41 | 1.76 |

(Equations (16)-(19) and Equation (28)), indicating that the predicted data agree reasonably well with plant data. The results showed a deviation of −1.09% for gas-oil, 0.65% for gasoline, 0.31% for light-gases, −5.7% for coke, and 1.76% for the riser outlet temperature.

The model predicts a gas oil conversion of 73.1% and a yield of 45.6%, 22.33% and 5.18% for gasoline, light gases and coke respectively. The results showed that the mass fraction of gas-oil decreased, that is, conversion increased along the bed height. The yield of gasoline, Light gases, and coke increased but the yield of gasoline decreased from a height of16m due to its secondary cracking to form gases and coke predicated by higher temperature and catalyst deactivation as shown in

A simulation model can be used to optimize plant performance by choosing the optimal set of operating condition such as temperature, pressure, flow rate etc. in this section a sensitivity analysis was performed to determine the effects of certain process variables on the performance of the model developed.

1) Variation of Vessel Dispersion Number

The vessel dispersion number measures the level of deviation from plug flow assumption. It is the ratio of the dispersion coefficient to the product of the superficial velocity and the reactor length. The dispersion number decreased with an increase in reactor length. Hence, the reactor flow pattern tends to plug flow which is characterized with an increase in the yield of products.

As shown in

2) Variation of Catalyst to Gas-Oil Ratio (CTO)

The effect of catalyst to gasoil ratio (CTO) on the mass fraction of gasoil, gasoline, gases and coke is depicted in

heat associated with catalyst inflow, hence reactor temperature were higher and secondary cracking of gasoline occurred resulting in a sparing/gradual decrease in the yields of gasoline and corresponding gradual increase in the yields of gases and coke.

3) Variation of Mass Flow Rate of Gasoil

The result showed significant effect of the mass flow rate on the mass fraction of gas-oil decreased (conversion increased) with increase in mass flow rate of gas oil. The yield of gasoline increased progressively while the yield of dry gases decreased but had a negligible effect on coke yield.

4) Variation of Mass Fraction of Gas-Oil with yields of gasoline at various flow rates

5) Variation of Reference Temperature with mass fraction of gas-oil and yield of products

The inlet temperature of the feed affects the conversion of the feed. The feed have to attain a significant high temperature for proper atomization of the molecules, the volatility of the feed increases with an increase in the temperature. This favours the conversion of gas-oil. The effect of temperature on the conversion of gas-oil, yield of gasoline, light gases and coke are shown in

A dispersion model that incorporates four-lump kinetic scheme for the simulation

of an industrial FCC riser reactor has been presented. The inclusion of dispersion number which represents the ideal flow pattern of the heterogeneous reactions that occur in the riser superimpose the oversimplification of previous researchers that assumed negligible dispersion. The results obtained from the model matched reasonably well with plant data with minimum deviation of −1.09 and maximum deviation of 1.76. Simulation results indicate that the vessel dispersion number, catalyst to gasoil ratio, reaction temperature and flow rate of gasoil are major process variables that affect the performance of FCC riser reactor.

The author declares no conflicts of interest regarding the publication of this paper.

Dagde, K.K. (2018) Development of Dispersion Models for the Simulation of Fluid Catalytic Cracking of Vacuum Gas Oil in Riser Reactor. Advances in Chemical Engineering and Science, 8, 298-310. https://doi.org/10.4236/aces.2018.84021