# Modelling and simulation of an industrial RFCCU-riser reactor for catalytic cracking of vacuum residue

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## Abstract

A one-dimensional adiabatic mathematical model was developed for the riser reactor of an industrial residue fluid catalytic cracking unit (RFCCU). A seven-lump kinetic model was presented for the catalytic cracking of vacuum residue, taking cognisance of diffusion resistance, which is a departure from the general norm in the literature. Also, heat transfer resistance between the fluid and solid phases was incorporated into the energy balances for instantaneous and one-dimensional vaporization of feedstock. The developed model was a set of twelve coupled, highly non-linear and stiff ordinary differential equations, ODEs, which was numerically solved with an implicit MATLAB built-in solver, ode23t, designed deliberately for handling stiff differential equations to circumvent the problem of instability associated with explicit methods. An excellent agreement was achieved between the industrial RFCCU plant data and the simulated results of this study, with average absolute deviation being < ± 5% for instantaneous vaporization of feedstock in all cases investigated. Moreover, the simulated results revealed that half of the reactor was relatively redundant as this accounted for only 3% of the conversion. Hence, the findings of this study could be useful to the production practice for the Khartoum Refinery Company.

## Keywords

Adiabatic RFCCU-riser reactor Catalytic cracking Seven-lump Diffusion resistance ode23t## List of symbols

- AAD
Average absolute deviation

- \(A_{\text{gs}}\)
Specific surface area of the particulate based on the unit reactor volume, m

^{2}/m^{3}- \(A_{\text{R}}\)
Cross-sectional area of riser, m

^{2}- \(c_{A0}\)
Initial molar concentration of reactant

*A*, kmol A/m^{3}- \(c_{i}\)
Concentration of lump

*i*, mol/kg- \(c_{\text{p}}\)
Specific heat capacity, J/(mol K)

- COR
Catalyst-to-oil ratio, dimensionless

- \(D_{\text{c}}\)
Cluster diameter, m

- \(D_{\text{R}}\)
Riser diameter, m

- \(F_{\text{c}}\)
Mass flow rate of cluster phase, kg/s

- \(F_{i}\)
Mass flow rate of component

*i*, kg/s- \(Fr\)
Froude number \(\left( { = \,{{U_{\text{g}} } \mathord{\left/ {\vphantom {{U_{\text{g}} } {\sqrt {gD_{\text{R}} } }}} \right. \kern-0pt} {\sqrt {gD_{\text{R}} } }}} \right)\), dimensionless

- \(Fr_{\text{t}}\)
Froude number based on terminal velocity, dimensionless

*g*Acceleration due to gravity, m/s

^{2}- \(G_{\text{c}}\)
Mass flux of cluster phase (catalyst + coke), kg/(m

^{2}s)- \(G_{\text{v}}\)
Superficial mass flux of gas mixture, kg/(m

^{2}s)- \(\Delta H_{\text{vap}}\)
Gas oil enthalpy of vaporization, J/kg

- \(j_{\text{D}}\)
*j*-factor for mass transfer, dimensionless- \(j_{\text{H}}\)
*j*-factor for heat transfer, dimensionless- \(k_{n}\)
Specific reaction rate constant per unit volume, s

^{−1}- \(k_{n}^{\prime \prime }\)
Specific reaction rate constant per surface area, m/s

- KRPC
Kaduna Refining and Petrochemical Company

*L*Length of riser reactor, m

- \(M_{i}\)
Molecular weight of lump

*i*, kg/kmol- \(\bar{M}_{\text{g}}\)
Average molecular weight of oil gas in the riser reactor, kg/kmol

- \(p_{\text{R}}\)
Pressure in the riser, Pa

- \(\bar{p}_{\text{R}}\)
Dimensionless pressure in the riser

- \(R_{\text{u}}\)
Universal gas constant, J/(mol K)

- \(S_{\text{v}}\)
True weight hourly space velocity, s

^{−1}- \(S_{\text{a}}\)
Surface area of catalyst per unit mass of catalyst, m

^{2}/g cat- \(Sc\)
Schmidt’s number, dimensionless

- \(T\)
Riser temperature, K

- \(T_{\text{c}}\)
Cluster-phase temperature, K

- \(T_{\text{g}}\)
Gas-phase temperature, K

- \(T_{\text{vap}}\)
Vacuum residue vaporization temperature, K

- \(T_{\text{VR}}\)
Feed temperature, K

- \(\nu_{\text{c}}\)
Cluster-phase velocity in the riser, m/s

- \(\nu_{\text{g}}\)
Gas interstitial velocity in the riser, m/s

- \(X_{\text{VR}}\)
Conversion of VR, dimensionless

- \(y_{i}\)
Weight yield of lump i, dimensionless

*z*Axial position in the reactor, m

## Greek symbols

- \(\alpha_{i,j}\)
Chemical measurement coefficient for the reaction of lump

*i*to lump*j*, dimensionless- \(\varepsilon_{\text{c}}\)
Average voidage of the clusters, dimensionless

- \(\varepsilon_{\text{g}}\)
Average voidage of the gas-phase, dimensionless

- \(\in_{\text{c}}\)
Volume fraction of the cluster phase (catalyst + coke), dimensionless

- \(\in_{\text{g}}\)
Volume fraction of the gas phase, dimensionless

- \(\phi_{\text{p}}\)
Catalyst porosity, dimensionless

- \(\rho_{\text{c}}\)
Density of cluster phase (catalyst + coke) in the riser, kg/m

^{3}- \(\rho_{\text{cat}}\)
Density of catalyst, kg/m

^{3}- \(\rho_{\text{p}}\)
Density of solid particles (catalyst + coke) in the riser, kg/m

^{3}- \(\sigma\)
Dimensionless riser length

- \(\varPsi\)
Slip factor, dimensionless

## Subscripts

- cat
Catalyst

- s
Solid

- stm
Dispersion steam

## Superscripts

- L
Liquid

- V
Vapor

## Introduction

The residue fluid catalytic cracking unit (RFCCU) of Khartoum Refinery Company (KRC) uses conradson carbon residue and metal-contaminated feedstocks (such as atmospheric residue or mixtures of vacuum residue and gas oils) to produce more valuable products (especially gasoline) using active zeolite catalyst in a circulating fluidized bed [1]. In the RFCCU, the oil feed and dispersion steam enter the catalytic riser reactor together with the regenerated catalyst, where cracking of vacuum residue into lighter hydrocarbons starts as it contacts the hot regenerated catalyst from the regenerator. The regenerated catalyst is made to rise by steam introduced at the base of the riser reactor between the regenerator and the feed inlet point. The vaporized feed and the catalyst pass through the riser reactor into disengager for cracked products and catalyst separation. During the cracking process, coke is deposited on the catalyst, and the spent catalyst flows down by gravity into the regenerator, where air is used to burn off the coke deposited on the catalyst in a combustion environment so that it is returned to a stable state for catalysing the cracking reaction. The hot regenerated catalyst is then re-injected into the base of the riser reactor [2]. The complexity of the typical FCCU feed makes it extremely difficult to characterize and describe the inherent kinetics at a molecular level. In this way, similar components are grouped into lumps. Therefore, lumping scheme has been used to study the reactions involved in the catalytic cracking of heavy oil. To give an insight into a comprehensive prediction of products’ distribution, there is an increasing number of lumps of the proposed models for catalytic cracking reactions [3]. In the first kinetic model of Weekman [4, 5] for catalytic cracking of heavy oil, three lumps were identified as gas oil (feedstock), gasoline, and light gas + coke as products, without incorporating diffusion characteristics of solid and gas phases. Lee et al. [6, 7] modified the three-lump model by splitting the light gas + coke lump into two different lumps of *C*_{1}–*C*_{4} gas and coke; therefore, resulting in the four-lump model for catalytic cracking of heavy oil. Corella and Frances [8] developed a five-lump model, in which the gas oil lump was divided into its heavy and light fractions. Different modified versions of five-lump model were developed by Dupain et al. [9], Kraemer et al. [10], and Ancheyta et al. [11]. Other proposed kinetic models for catalytic cracking of heavy oil include: 6-lump [1, 12, 13, 14, 15], 8-lump [16], 10-lump [17, 18], 11-lump [19], 13-lump [20], 14-lump [21], and 19-lump [22], without taking cognisance of diffusion resistance. A comprehensive review was presented by Pinheiro et al. [23] on the subject of fluid catalytic cracking process modelling, simulation, and control. Obviously, the number of lumps of the proposed kinetic models for catalytic cracking of heavy oil may be increased to obtain more detailed descriptions of the catalytic cracking reactions and product distribution [24, 25]. However, sparing kinetic investigations have been carried out with the incorporation of diffusion resistances. Taking into account mass and heat transfer resistances between the reacting fluid and solid phases helps with conceiving the lump concentration on the catalyst surface as well as temperature profiles of the fluid and solid phases. Flinger et al. [26] considered mass transfer between the fluid and solid phases in the FCCU-riser reactor model equation. Gupta and Subba Rao [27] and Nayak et al. [28] applied the relationship for Sherwood number proposed by Ranz and Marshall [29] in their model to demonstrate the effects of mass transfer. The lump concentration within the catalyst is reduced by intraparticle mass transfer. In this way, the presence of an internal concentration gradient reduces the average rate of cracking [30]. Pruski et al. [31] validated adsorption coefficients for the four-lump model of catalytic cracking of gas oil. Bidabehere and Sedran [32] set up a model to investigate the impacts of diffusion, adsorption, and reaction at high temperature inside commercial FCC catalyst pellets and analysed the significance of these phenomenon. Dupain et al. [9] discussed external and internal mass transfer relationships utilised for FCC riser.

Characteristics of vacuum residue feedstock [37]

Property | Value | Test method |
---|---|---|

Boiling range | > 500 °C | |

Specific gravity @70 °C | 0.993 g/cm | ASTM D-1298 |

Condrason carbon residue | 19 wt% | ASTM D-1289 |

Sulphur content | 5 wt% | IP 63 |

Asphaltene content (+ resin) | 6 wt% | IP 143 |

Aromatic content | 89 wt% | ASTM D2007 adopted from Rossini and Mair [38] |

Saturate content | 11 wt% | ASTM D2007 adopted from Rossini and Mair [38] |

Metals | ||

Nickel | 138 ppm | |

Vanadium | 1643 ppm |

The modelling of a riser reactor is very complicated owing to the many complex reactions occurring in it, coupled with mass and heat transfer resistances, and catalyst deactivation kinetics. Therefore, a complete model of the riser reactor should include all the important physical phenomena and detailed reaction kinetics. In this study, a one-dimensional adiabatic mathematical model of the riser-type of KRC–RFCCU was developed containing the following components: kinetic model of the catalytic cracking of vacuum residue, catalyst deactivation model, comprehensive hydrodynamic model of the riser reactor, material, force, and energy balances. The simulated results from the model were validated by comparison with industrial RFCCU-riser reactor vacuum residue conversion and yield data. Moreover, the effects of catalyst-to-oil ratio, COR, on catalyst residence time at different input temperatures of catalyst, as well as the effect of different inlet temperatures of catalyst-on-catalyst residence time at different CORs were investigated with a view to providing succinct information on catalyst management and minimizing losses.

## Development of mathematical models for riser reactor an industrial residue fluid catalytic cracking unit

### Kinetics of catalytic cracking of vacuum residue in the riser reactor of RFCCU

In Fig. 2, it was assumed that chemical reactions are the rate-determining steps, and that catalytic cracking of vacuum residue and other reactions are irreversible first-order. All reactions take place in the gas phase. Moreover, mass transfer resistance between the reacting fluid and the catalyst are incorporated in the kinetic model, as against previous works in the literature. The specific reaction rate constant, \(k_{\text{r}} ( = k_{i,j} )\), of the reaction from lump *i* to lump *j* as depicted in Fig. 2 was modified by multiplying each of them by the effectiveness factor, \(\eta\), and the parallel additive of rate constants and mass transfer coefficient, \(k_{\text{g}}\) was used to determine the overall rate constant for the reaction of lump *i* to lump *j*, as given in Eqs. (9) or (10). Equally, heat transfer resistance between the reacting fluid and the solid (catalyst and coke) was considered in the energy balance for the riser reactor, as expressed in Eqs. (63), (64), and (69).

*n*th-order reaction in a spherical pellet is given by Smith [30]:

*A*based on the interfacial surface area, \(r_{Ai}\), of a fluid reacting on active centres at the surface of a solid for a first-order, irreversible reaction is:

*A*at the interface has to be compensated for by transport from the bulk fluid, the flux, \(N_{A}\), of which is given by:

*i*, with the incorporation of mass transfer resistance and effectiveness factor, was obtained as [30]:

### Catalyst deactivation model

### Continuity equation of component in riser reactor of RFCCU

- 1.
Adiabatic and one-dimensional transported ideal plug flow for gas phase and cluster phase (catalyst + coke) but with different velocities, no axial back-mixing and no radial dispersion.

- 2.
Diffusion resistances are significant, and no adsorption within the catalyst particle.

- 3.
There is no heat loss from the riser, and the temperature of the reaction mixture (hydrocarbon vapors and solid particles) falls only because of the endothermicity of the cracking reactions [40].

- 4.
The pressure drop along the riser length is due to the hydrostatic head of catalyst, solid acceleration, solid and gas friction in the riser [41].

- 5.
A variable gaseous superficial velocity with axial position along the riser length is assumed.

- 6.
The catalyst particles are assumed to move as clusters to account for the observed high-slip velocities.

- 7.
The coke exists as solid and its deposition on the catalyst particles does not affect the fluid flow.

- 8.
In each section of riser, the cluster (catalyst + coke) and gas have different temperatures to account for the heat transfer between the fluid and the solid phases.

*i*, \(( - r_{i}^{\prime } )\), for a first-order reaction is given by Meng et al. [42]:

*i*from lump

*j*, \(r_{ji}\), is directly proportional to the molar concentration of lump

*j*\((\rho c_{j} )\), the stoichiometric coefficient, \(\alpha_{ji}\), for the reaction of lump

*j*to lump

*i*\(\left( { = \,{{M_{j} } \mathord{\left/ {\vphantom {{M_{j} } {M_{i} }}} \right. \kern-0pt} {M_{i} }}} \right)\), and the mass density of solid particle to gas volume fraction \(\left( {{{\rho_{\text{c}} } \mathord{\left/ {\vphantom {{\rho_{\text{c}} } { \in_{\text{g}} }}} \right. \kern-0pt} { \in_{\text{g}} }}} \right)\). The rate of formation of lump

*i*, \((r_{i}^{\prime } )_{\text{f}}\), is the sum of all \(r_{ji}\), and is given by Meng et al. [42]:

*i*, \(r_{i}^{\prime }\), without mass transfer is given by Meng et al. [42]:

*i*involved in the reaction network was obtained, which was used in Eq. (19) to yield the steady-state model of component in riser reactor of RFCCU, thus:

*i*generating lump

*j*, expressed using Arrhenius equation, thus:

### Hydrodynamic model of the riser reactor of RFCCU

*i*th component is calculated by the following correlation [51]:

*T*is temperature in K.

### Force balance

### Energy balance for the riser reactor of RFCCU

- 1.
Instantaneous vaporization, where the feedstock vaporizes as soon as the catalyst gets in contact with it at the riser inlet. The fluid is thus considered as an ideal gas and the enthalpy balances for the fluid and solid phases are given by Eqs. (62) and (63), respectively.

- 2.One-dimensional vaporization of the feedstock, where a distillation curve is employed for the fraction of gas oil vaporized, \(X_{\text{vap}} ,\) [17]:which is valid from 319.5 to 689.8 K. The gas oil liquid and gas phases take place together for a certain period in the riser reactor. Therefore, the enthalpy, \(h_{\text{f}}\), of the mixture is computed by:$$X_{\text{vap}} = 0.0027T - 0.1254,$$(65)$$h_{\text{f}} = h_{\text{V}} X_{\text{vap}} + \left( {1 - X_{\text{vap}} } \right)h_{\text{L}} .$$(66)

## Computational procedure

The computer program for the numerical solution of the resulting differential equations was written in MATLAB R2017a environment. The program employed semi-implicit Runge–Kutta method with step-size adjustment strategy for the numerical solution of the developed differential equations with a view to predicting the yield of each lump, temperature and pressure profiles and other process parameters in the riser of an industrial RFCCU during the catalytic cracking of vacuum residue. This numerical method is efficient, accurate, and stiffly stable so any unenvisaged problem of instability associated with explicit methods is removed.

*β*and

*γ*, used were 162.15 and 0.76, respectively [14, 15, 17]. The adsorption constant of aromatics, resins, and asphaltenes, \(K_{A}\), was 0.128 [14, 15]. The density of the catalyst was 1700 kg/m

^{3}[1]. The kinetic and thermodynamic parameters used to simulate the RFCCU-riser reactor are presented in Table 2.

Kinetic and thermodynamic parameters used for riser reactor-type of FCCU simulation [1]

Parameters | Frequency factor, \((k_{i,j} )_{0}\) (m | Activation energy, \(E_{i,j}\) (J/mol) | Heat of reaction, \(\left( {\Delta H_{\text{rxn}} } \right)_{i}\) (J/mol) |
---|---|---|---|

| 35,520 | 50,727 | 402,130 |

| 13,750 | 50,727 | 301,360 |

| 2780 | 50,727 | 286,100 |

| 42.68 | 16,150 | 183,360 |

| 4.268 | 16,150 | 2,347,770 |

| 137.3 | 16,150 | 1,960,710 |

| 13,750 | 50,727 | − 40,970 |

| 1130 | 46,240 | − 46,960 |

| 1284 | 59,750 | 317,440 |

| 128.4 | 59750 | 790600 |

| 3101 | 59,750 | 633,300 |

| 686.4 | 46,240 | 3600 |

| 81.22 | 59,750 | 212,570 |

| 8.122 | 59,750 | 493,340 |

| 564.6 | 59,750 | 400,080 |

| 43.66 | 78,490 | 111,190 |

| 21.83 | 78,490 | 255,590 |

| 241,931.9 | 77,300 | 42,420 |

| 31.78 | 59,750 | 57,240 |

| 684 | 31,500 | 2100 |

The kinetic parameters for coke formation from gasoline and LPG lumps were obtained from Xiong et al. [13, 39]. The enthalpies of reaction for both reactions were obtained from Dasila et al. [39].

*n*-octahexacontane, C

_{68}H

_{138}, was used as a surrogate for VR.

*n*-Heptacosane, C

_{27}H

_{56}, and

*n*-hexadecane, C

_{16}H

_{34}, were used as surrogates for VGO and LFO, respectively [18]. Gasoline consists of several hydrocarbons, as revealed in the mass spectrometric analysis of 1 mol of gasoline. For use in the energy balance equation, the specific heat capacities’ constants of the components in gasoline lump were obtained from Sinnott and Towler [57] and ASPEN PLUS/HYSYS 9.0, and are presented in Tables 3 and 4.

Constants in the specific heat capacities of components in gasoline [57]

Source: Ground water Management Review, Spring, 1990 p. 167 (excluding those hydrocarbons whose weight fractions in the gasoline were zero)

S/no. | Component | Mol. wt (kg/kmol) | mass fraction | \(a\) | \(b\) | \(c \times 10^{4}\) | \(d \times 10^{8}\) |
---|---|---|---|---|---|---|---|

1 | Propane | 44.097 | 0.0001 | − 4.224 | 0.30626 | − 1.586 | 3.2146 |

2 | Isobutane | 72.151 | 0.0122 | − 9.525 | 0.5066 | − 2.729 | 3.7234 |

3 |
| 58.124 | 0.0629 | 9.487 | 0.3313 | − 1.108 | − 0.2822 |

4 |
| 56.108 | 0.0007 | 18.417 | 0.25636 | 0.70138 | 0.8989 |

5 | 3-Methyl-1-butene | 70.135 | 0.0006 | 21.742 | 0.38895 | − 2.007 | 4.0105 |

6 | Isopentane | 86.178 | 0.1049 | − 16.634 | 0.62928 | − 3.481 | 6.8496 |

7 |
| 72.151 | 0.0586 | − 3.626 | 0.48734 | − 2.58 | 5.3047 |

8 | 2-Methyl-2-butene | 70.135 | 0.0044 | 11.803 | 0.3509 | − 1.117 | − 0.5807 |

9 | 3,3-Dimethyl-1-butene | 84.162 | 0.0049 | − 12.556 | 0.54847 | − 2.915 | 5.2084 |

10 | 2,3-Dimethylbutane | 86.178 | 0.073 | − 14.608 | 0.61504 | − 3.376 | 6.8203 |

11 | 2-Methylpentane | 86.178 | 0.0273 | − 10.567 | 0.61839 | − 3.573 | 8.0847 |

12 |
| 86.178 | 0.0283 | − 4.413 | 0.58197 | − 3.119 | 6.4937 |

13 | Methylcyclopentane | 84.162 | 0.0083 | − 50.108 | 0.63807 | − 3.642 | 8.0135 |

14 | 2,2-Dimethylpentane | 100.205 | 0.0076 | − 50.099 | 0.89556 | − 6.36 | 17.358 |

15 |
| 100.205 | 0.0063 | − 5.146 | 0.67617 | − 3.651 | 7.6677 |

16 | Benzene | 78.114 | 0.0076 | − 33.917 | 0.47436 | − 3.0174 | 7.1301 |

17 | 2,3-Dimethylpentane | 100.205 | 0.039 | − 7.046 | 0.70476 | − 3.734 | 7.8335 |

18 | 2,2,4-Trimethylpentane | 114.232 | 0.0121 | − 7.461 | 0.77791 | − 4.287 | 9.1733 |

19 | 2,2-Dimethylhexane | 114.232 | 0.0055 | − 9.215 | 0.78586 | − 4.4 | 9.6966 |

20 | Toluene | 92.141 | 0.055 | − 24.355 | 0.51246 | − 2.765 | 4.9111 |

21 | 2,3,4-Trimethylpentane | 114.232 | 0.0121 | − 9.215 | 0.78586 | − 4.4 | 9.6966 |

22 | 2-Methylheptane | 114.232 | 0.0155 | − 89.744 | 1.2422 | 11.76 | 46.18 |

23 |
| 114.232 | 0.0013 | − 6.096 | 0.77121 | − 4.195 | 8.8551 |

24 |
| 106.168 | 0.0957 | − 25.091 | 0.60416 | − 3.374 | 6.8203 |

25 |
| 120.195 | 0.0841 | − 31.288 | 0.7486 | − 4.601 | 10.81 |

26 | 1,3,5-Trimethylbenzene | 120.195 | 0.0411 | − 19.59 | 0.6724 | − 3.692 | 7.6995 |

27 | 1,2,4-Trimethylbenzene | 120.195 | 0.0213 | − 4.668 | 0.62383 | − 3.263 | 6.3765 |

28 | 1-Methyl-2-ethylbenzene | 134.222 | 0.0307 | − 16.446 | 0.69961 | − 4.12 | 9.3282 |

29 | 1,2,4,5-Tetramethylbenzene | 134.222 | 0.0133 | 15.265 | 0.65188 | − 2.879 | 3.2569 |

30 |
| 170.34 | 0.023 | − 9.328 | 1.1489 | − 6.347 | 13.59 |

31 | Naphthalene | 128.174 | 0.0045 | − 68.802 | 0.84992 | − 6.506 | 19.808 |

32 | 1-Methylnaphthalene | 142.201 | 0.0023 | − 64.82 | 0.93868 | − 6.942 | 20.155 |

Constants in specific heat capacities of other components in gasoline, VR (*n*-octahexacontane) and VGO (*n*-heptacosane) obtained from ASPEN PLUS/HYSYS 9.0

S/no. | Component | Mol. wt (kg/kmol) | mass fraction | | | | | | | |
---|---|---|---|---|---|---|---|---|---|---|

Gasoline | ||||||||||

33 | 2,4,4-TMH | 128.3 | 0.0087 | 114.32 | 577.753 | 1438.11 | 353.216 | 611.651 | 200 | 1500 |

34 | 3,3,4-TMH | 128.3 | 0.0281 | 96.2348 | 593.269 | 1412.62 | 380.094 | 590.171 | 200 | 1500 |

35 | 2,2,4-TMH | 142.3 | 0.0105 | 120.042 | 571.456 | 1469 | 342.509 | 633.091 | 200 | 1500 |

36 | MPB | 120.2 | 0.0351 | 79.104 | 449.751 | − 552.6 | − 233.25 | 626.259 | 200 | 1000 |

37 | 1,2,3,4-TMB | 148.2 | 0.0129 | 144.254 | 403.88 | 1596.4 | 264.536 | 743.01 | 298 | 1000 |

VR | 954 | 1 | 1180.74 | 2859.27 | − 827.36 | 3261.38 | − 24141.2 | 200 | 1000 | |

VGO | 380 | 1 | 366.648 | 765.026 | 564.637 | 903.806 | − 1530.6 | 200 | 1000 |

Since ASPEN PLUS/HYSYS 9.0 is a very good software to characterize feedstock and/or product by pseudo-components from an assay, it was used to populate the VR and VGO properties, as presented in Table 4 while those of LFO were obtained from Sinnott and Towler [57]. These give specific heat capacities as functions of temperature to be used in the energy balance equation. However, representing a property of a lump with a surrogate single component may have significant deviations on the simulated results when compared with plant data. In this study, this was not the case as revealed that there was excellent agreement between simulated results and the plant data.

Constants in specific heat capacities of LFO and components in LPG and dry gas

Component | Mol. wt (kg/kmol) | Mass fraction | \(a\) | \(b\) | \(c \times 10^{4}\) | \(d \times 10^{8}\) |
---|---|---|---|---|---|---|

LFO ( | 226.448 | 1.0 | − 13.017 | 1.5290 | − 8.537 | 18.497 |

LPG | ||||||

Propane | 44.097 | 0.55 | − 4.224 | 0.30626 | − 1.586 | 3.2146 |

| 58.124 | 0.45 | 9.487 | 0.3313 | − 1.108 | − 0.2822 |

Dry gas | ||||||

Hydrogen | 2.016 | 0.33 | 27.143 | 92.748 × 10 | − 0.1381 | 0.78451 |

Methane | 16.043 | 0.34 | 19.251 | 52.126 × 10 | 0.11974 | − 1.132 |

Ethane | 30.070 | 0.33 | − 5.409 | 0.17811 | − 0.60938 | 0.087127 |

*n*-heptacosane) obtained from ASPEN PLUS/HYSYS 9.0 are in the form:

*f*and

*g*are the upper and lower temperature limits.

The specific heat capacity of catalyst does not change with temperature during reaction such that \(c_{{{\text{p,}}\,{\text{cat}}}} = 1.087\) kJ/(kg K) [59].

*T*is in K and the viscosities are expressed in Ns/m

^{2}.

Other parameters used in computation

Parameter | Value | Source |
---|---|---|

Catalyst type | Zeolite | [1] |

Particle diameter, | 77 μm | [1] |

Reaction pressure, | 361.3 kPa | [1] |

Catalyst-to-oil ratio, COR | 6.88 | [1] |

Pre-lift steam | 2.46 kg/s | [1] |

Feed flow rate, | 219.17 t/h | [1] |

Recycle oil (wt% of feed) | 15 | [1] |

Feed inlet temperature, | 613 K | KRPC plant data |

Steam inlet temperature, | 543 K | KRPC plant data |

Catalyst inlet temperature, | 927 K | KRPC plant data |

Steam heat capacity, | 2000 J/(kg K) | [60] |

Sphericity(or specularity), φ | 0.5 | [1] |

Porosity | 0.4 | [61] |

Particle pore diameter, | 2 nm | KRPC plant data |

Tortuosity, τ | 7 | [62] |

Constriction factor, σ | 0.8 | [61] |

Delta coke | 1.1515 kg/s | [37] |

Catalyst thermal conductivity, | 1.02 W/(m K) | |

Basic nitrogen poisoning absorption coefficient, \(K_{N}\) | 2.835 | [13] |

Basic nitrogen content in gas oil, \(w_{N}\) | 689 μg/g | [13] |

Due to the dearth of some data from the Khartoum Refinery Corporation, data were obtained from a similar refinery in Nigeria, Kaduna Refining and Petrochemical Company, Plc., Kaduna, as indicated in Table 6 for computational purposes. Also, the basic nitrogen parameters, \(K_{N}\) and \(w_{N}\) in Table 6 were obtained from Xiong et al. [13], where the feedstock parameters were for the residual fluid catalytic cracking of China National Petroleum Corporation Refinery. Also, as stated earlier, owing to the inability to obtain a complete data for the Khartoum Refinery Company, these parameters were used in computation in this study as the current model is also for a residual fluid catalytic cracking unit and it was assumed that the nitrogen content should be similar.

### Estimation of liquid and vapor phase heat capacities of feed, and its enthalpy of vaporization

The enthalpy of vaporization of the feed was obtained from ASPEN PLUS/HYSYS 9.0 as the enthalpy of vaporization of the pseudo-component for vacuum residue, n-octahexacontane, i.e., \(\Delta H_{\text{vap}}\) = 9.21253045 × 10^{7} J/kmol, with its boiling point specified at \(T_{\text{vap}}\) = 930.16 K.

### Estimation of effective diffusivity and mass and heat transfer coefficients

*Pr*, [30]:

*j*-factors (\(j_{\text{D}}\) and \(j_{\text{H}}\)) are approximately equal and was estimated using the correlation given thus [58]:

## Simulation results and discussion

The API equation of viscosity of lumps was not used for VR and VGO lumps because they ran into negative values for all temperatures studied. Instead, the viscosity equation for the pseudo-components of VR and VGO were obtained from ASPEN PLUS/HYSYS 9.0, as given in Eqs. (77) and (78), respectively.

The unit factors estimated by Xu et al. [14] were adopted to adjust the kinetic parameters to improve correlation of yields with RFCUU-riser reactor plant data, as the kinetic parameters are flexible for use for different feedstocks [1]. The unit factors used were as follows: FU(1) = 1.508 to adjust all reaction constants: \(k_{1,2}\) ~ \(k_{5,7} \,\), FU(2) = 0.5239 to adjust VGO, LFO, and GA lumps’ formation reaction constants from VR (\(k_{1,2} ,k_{1,3} ,\,\) \(k_{1,4}\)) and LFO formation reaction constant from VGO (\(k_{2,3} \,\)); FU(3) = 0.2225 to adjust LPG, DG, and CK lumps’ formation reaction constants from VR: \(k_{1,5} ,k_{1,6} ,\,k_{1,7} \,\); FU(4) = 0.4015 to adjust GA formation reaction constants from VGO and LFO: \(k_{2,4}\) and \(k_{3,4} \,\), FU(5) = 1.676 to adjust LPG and DG formation reaction constants from VGO and LFO: \(k_{2,5} ,k_{2,6} ,\,k_{3,5} \,\) and \(k_{3,6} \,\); FU(6) = 2.267 to adjust CK formation reaction constants from VGO and LFO: \(k_{2,7}\) and \(k_{3,7}\), FU(7) = 0.9756 to adjust LPG, DG, and CK formation reaction constants from GA: \(k_{4,5} ,k_{4,6}\) and \(k_{4,7}\); FU(8) = 0.8245 to adjust DG and CK formation reaction constant from LPG: \(k_{5,6}\) and \(k_{5,7}\). These factors were regressed by the modified Levenberg–Marquardt algorithm with two sets of plant data from Xu et al. [14].

Comparison of predicted yield of lump after recycling CSO (15 wt% of feed) with RFCCU plant data [1]

Lumps | Plant data | Instantaneous | One-dimensional | ||
---|---|---|---|---|---|

Yield | Yield | % error | Yield | % error | |

CSO | 0.0469 | 0.0473 | − 0.85 | 0.0392 | 16.42 |

LFO | 0.2152 | 0.2203 | − 2.37 | 0.1891 | 12.13 |

GA | 0.4433 | 0.4413 | 0.34 | 0.4160 | 6.16 |

LPG | 0.1544 | 0.1494 | 3.24 | 0.1131 | 26.75 |

DG | 0.0441 | 0.044 | 0.23 | 0.037 | 16.10 |

CK | 0.0932 | 0.0935 | − 0.32 | 0.0789 | 15.34 |

The comparison of the predicted results with RFCCU-riser reactor data in terms of yields of lumps is depicted in Fig. 3 and 4. It can be seen in Fig. 3 that most of the conversion (about 90%) occurs in the first 5 m of the riser reactor. This agrees with the literature findings and it can be inferred that the rate of cracking is fastest at the entrance into the riser reactor [14, 15, 65, 66, 67, 68, 69, 70]. Also, for both instantaneous and one-dimensional vaporization of feedstock, 95% of the conversion occurs in the first-third of the reaction, while 97% of the conversion occurs in the first half of the reactor, and only 3% of the conversion occurring in the second half of the reactor, implying that the second half of the riser reactor is redundant. Excellent agreements between the predicted results and the plant data were achieved for instantaneous vaporization of feedstock with maximum % error being 3.24 as shown in Table 7, where optimal yields of the cracked products needed to meet market demands and ensuring maximum profit were achieved. The predicted results for one-dimensional vaporization of feedstock yielded poor results. Hence, instantaneous vaporization of feedstock must have occurred at the entrance of the riser reactor.

Figure 5 shows the temperature profile for solid and fluid phases along the height of the RFCUU-riser reactor. There is a rapid increase in the temperature of the gas phase for both models of instantaneous and one-dimensional vaporization of feedstock near the inlet of the riser reactor (at about 2.3 m). This agrees with theory that vaporization occurs towards the inlet of the riser reactor. The solid-phase temperature drops rapidly from 927 K to about 765.5 K for the instantaneous model near the inlet of the riser reactor, and both the solid and gas phases’ temperatures reached a constant value of 765.5 K from 2 m till the end of the riser reactor. The predicted exit temperature of 765.5 K using instantaneous vaporization of feedstock is in excellent agreement with the RFCCU-riser reactor of 755 K, with % error being ± 1.39. However, for the one-dimensional vaporization of the feedstock, the solid and gas phases attained a constant temperature of about 907.5 K near the inlet of the reactor, and afterwards, their temperature profile dropped more evenly across the height of the reactor, reaching a value of 798.15 K at the end of the reactor. This predicted exit temperature is in variance with the plant value of 755 K. For both instantaneous and one-dimensional models, thermal equilibrium of the gas and solid phases occurs in the first 2 m of the riser reactor, which is about 5% of the total riser length, and then drops very gently across the remaining height of the riser reactor for the instantaneous model and a little steep for the one-dimensional vaporization model. Using the heat balance equation for the solid (coke and catalyst), almost 74 MJ and almost 9 MJ of heat was transferred by the solid to the fluid in 1 s within 2 m riser length for instantaneous and one-dimensional vaporization of feedstock, respectively. The point of intersection of the solid and gas phases’ temperature profiles is a direct function of the gas-particulate heat transfer coefficient while the riser reactor exit temperature is a function of the cracking reactions and mass balance between the phases.

Figure 6 shows the pressure profile along the height of RFCCU-riser reactor. The pressure drop for both instantaneous and one-dimensional vaporization of feedstock is gentler towards the entrance of the riser reactor; this can be attributed to the faster reaction rate towards the entrance of the reactor resulting in rapid expansion of the gas-phase. Thus, a more relaxed drop in pressure at the entrance of the reactor is expected. The steeper drop in pressure as the reaction progresses can be attributed to lower rate of reaction and therefore less expansion, thus the pressure drops due to loss in hydrodynamic energy as the products and catalysts are transported along height of the riser reactor. Overall, there is a 26% and 33% drop in pressure in the instantaneous and one-dimensional vaporization models, respectively.

Figure 7 shows the predicted catalyst- and gas-phase residence times along the height of RFCCU-riser reactor. The catalyst spends more time at the inlet of the reactor due to its initial low-velocity, but as reaction occurs, its velocity increases. Averagely, the catalyst residence time increases fairly evenly across the height of the riser reactor. The respective total catalyst residence times for instantaneous and one-dimensional vaporization of feedstock are about 2.03 s and 1.54 s. These are within the plant reaction time of cracking of 1–5 s. The gas spends less time of about 0.65 s and 0.55 s for the respective instantaneous and one-dimensional vaporization of feedstock in the reactor, owing to the higher velocity of the gas phase.

Figure 8 shows the variation of the solid and gas phases’ velocities with height of RFCCU-riser reactor for instantaneous and one-dimensional vaporization of feedstock. For both models, the velocity of solid and vapor phases increases along the height of the riser reactor. The cluster-phase velocity is lower than that of the gas superficial velocity owing to the high momentum of the gas particles moving the solid phase. The cluster-phase velocity increases from 0.69 to 39 m/s and to 47 m/s for instantaneous and one-dimensional vaporization of feedstock, respectively. The gas superficial velocity increases from 0.41 to 3.00 m/s and to 3.06 m/s for instantaneous and one-dimensional vaporization of feedstock, respectively, while the gas interstitial velocity from 4 m/s to 58.5 m/s and from 9 to 68.5 m/s, respectively. These high values of velocities may be attributed to the pressure at which the RFCCU is operating. The inlet pressure being almost twice and the exit pressure being similar to that of commercial RFCCU. The slip factor between the solid and vapor phases was seen to drop to about 1.5; however, the slip factor at the outset of cracking is about 1.9 for both models which agrees with theoretical range from 1.2 to 4, where 2 is considered typical in a commercial FCCU [40].

Figure 9 shows the effect of *COR* on catalyst residence time at different input temperatures of catalyst, \(T_{\text{cat}}\). It was observed that for both instantaneous and one-dimensional vaporization of feedstock, the catalyst residence time reduced as COR increased for all input temperatures of catalyst as a result of higher flow rate of catalyst, thus higher velocity of catalyst.

Figure 10 shows the effect of different inlet temperatures of catalyst on catalyst residence time at different CORs. It was observed that, an increase in the inlet temperature of catalysts also reduced catalyst residence time at different catalyst oil ratios. A higher input temperature of catalyst, resulted in higher temperatures of reaction mixture, thus resulting in faster reaction rates, and ultimately in higher velocities of the gas phase and thus the catalysts. However, the COR has a greater effect on catalyst residence time than catalyst inlet temperature.

## Conclusion

A comprehensive one-dimensional adiabatic mathematical model was developed for RFCCU-riser reactor using modified version of the seven-lump kinetics of vacuum residue cracking. Also, the model incorporated material balance, energy balance, mass and heat transfer resistances, adsorption characteristics of asphaltenes, resins, and aromatics, and of basic nitrogen, and coking characteristics based on time-on-stream of catalyst. The resulting coupled ODEs were numerically integrated using MATLAB built-in function of ode23t. It was found that most of the cracking reaction occurs toward the inlet of the riser reactor, with 90% of the final conversion occurring in the first 5 m, 95% and 97% of the conversion occurring in the first half and third of the riser reactor, respectively. With the other half of the reactor accounting for only 3% of the conversion, it could be inferred that this half is relatively redundant. Comparison was made between the KRC–RFCCU data and the simulated results for both instantaneous and on-dimensional vaporization of feedstock, where an excellent agreement was achieved with AAD < ± 5% in the former for all cases investigated.

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