Scaling of catalytic cracking fluidized bed downer reactor based on CFD simulations—Part II: effect of reactor scale

The practical realization of the scaling up of gas–solid multiphase flow reactors with chemical reactions is hindered by chaotic flow behaviors and complex heat and mass transfers in the reactor. In addition, a law to scale up complex reaction mechanisms in multiphase flow systems has been rarely proposed in the existing literature. Thus, this study aims to investigate the scaling up of the catalytic cracking fluidized bed downer reactor based on the similitude method of chemical reaction performance. Three downer reactor scales with a height of 5, 15, and 30 m, were investigated. To anticipate the behavior of reactive flow, a Eulerian–Eulerian CFD model, two-fluid model, was constructed, which was combined with the kinetic theory of granular flow. A four-lump kinetic model was chosen to represent the mechanism of the catalytic cracking reaction of heavy oil from the pyrolysis of waste plastic. The CFD model accurately predicted the species composition distribution. The scaling law based on the geometric similarity, kinematic similarity, and chemical reaction similarity, was proposed. The catalytic cracking performance similarity of the downer reactor was obtained. With variances in the range of 10% and mean relative absolute error less than 5%, the axial and lateral distributions of chemical performance (heavy oil conversion, gasoline mass fraction, and gasoline selectivity) were found to be extremely similar.


Introduction
The rapid increase in the amount of plastic waste has become a critical environmental issue that needs to be urgently addressed. 1,2 Fluid catalytic cracking (FCC) is a remarkable technology for the treatment and removal of plastic wastes. 3 This method exhibits considerable potential for converting heavy oil from plastic waste and other hydrocarbons into more valuable light gas. In this method, solid particles serve as catalysts and the chemical reactions of the gas species involve a complex mechanism of consecutive or parallel competition; 4,5 furthermore, a downer reactor, in which both gas and solid travel downward, is found to be suitable for this reaction. 6 The downer reactors have a distinct characteristic that provides various benets, including a homogeneous gas-solid ow structure in the lateral direction, less gas-solid back-mixing, near plug-ow reactor performance for fast reaction processes, and higher gas-solid contact efficiency. 7-10 These advantages are especially benecial for operations that need minimal contact time between phases, i.e., FCC reactions. In addition, less backmixing in the system enhances the yield and selectivity of the desired products. 11 In the last two decades, studies on FCC in downer reactors have been conducted via experiments and simulations. However, most of the investigations were conducted using lab-scale reactors. With a large amount of plastic waste produced annually, a large downer reactor is required to eliminate the accumulation of plastic waste.
Chemical reactor upscaling is a difficult issue in the area of chemical engineering, but it is a necessary stage in the design and optimization of chemical processes. 12 To realize this task, a similitude method is applied to commercialize the characteristics of the lab-scale reactor. Numerous researchers have identied a number of parameters for scaling up uidized bed reactors. Sanderson et al. 13 investigated how the solid-to-gas density ratio of Glicksman et al. 14 's simplied scaling parameters affected the scaling up of a bubbling uidized bed reactor for hydrodynamic similarities. This index was considered because it is strongly inuenced by the minimum uidization velocity, a condition under which bubbling uidized beds were operated. The density ratio had a signicant impact on the scaling up of Geldart group A particle bubbling beds. When scaling the system of Geldart group B particles with Reynolds numbers < 12, however, there is some exibility in changing the density ratio. The full set scaling parameter given by Glicksman et al., 15 on the other hand, can ensure that gassolid and liquid-solid circulating uidized beds are hydrodynamically identical. 16,17 Banerjee and Agarwal 18 proposed the new scaling laws for dynamic similarity in chemical looping combustion spouted uidized beds. These scaling laws based on terminal velocity improve the similarity compared with those proposed by Glickman et al. 14 and Link et al. 19 Leckner and Werther, 20 studied the scaling up of a circulating uidized bed boiler. The scaling criteria were dened by Damköhler in terms of the ratio of transport to reaction times, dened as the Granular temperature conservation equation The species conservation equation Damköhler number. 21 The number based on the vertical ows is reasonably to scale the combustion behavior in risers. However, the horizontal Damköhler number cannot scale the combustion behavior, except in some special cases. In 2020, the scaling up of a catalytic cracking uidized bed downer reactor was examined by Khongprom et al. 22 The Damköhler number was modied for such a complex reaction mechanism. Chemical performance similarity was taken into account in terms of reactant conversion and mass fraction and selectivity of desired product (gasoline). The proposed scaling parameter exhibited adequate chemical performance similarity both in axial and lateral distributions. However, this scaling parameter was limited to an identical reactor. Therefore, the scaling up for different reactor sizes and complex reaction mechanisms is a necessary and challenging task for commercial application. Computational uid dynamics (CFD) is the effective tool to simulate gas-solid ow systems in recent years. 23,24 CFD offers a qualitative and quantitative prediction of the performance of uid ows via mathematical modeling, numerical methods, and soware tools. 25 Using existing experimental data from the literature, [26][27][28][29] the accuracy of the CFD model prediction of ow behavior in multiphase ow reactors has been statistically conrmed. The progress of CFD simulation of uidized bed reactors was reviewed by Alobaid et al. 30 The CFD simulation approaches for gas-solid ow systems are broadly classied into Eulerian-Lagrangian (E-L) and Eulerian-Eulerian (E-E) approaches. The E-L method treats the particle phase as a discrete phase and tracks particle contact and collision. [31][32][33] The detail behavior at the particle level can be obtained. The E-E approach treated both gas and solid phases as interpenetrating continua according to kinetic theory of granular ows (KTGF). These two approaches are the effective methods that currently used to predict gas-solid multiphase ow behaviors coupled with chemical reaction, heat and mass transfer. [34][35][36][37][38][39][40] However, the latter is widely used due to its simplicity and relatively low computational cost. In addition, several researchers applied the CFD approach to simulate FCC in uidized bed reactors. Liu et al. 41 simulated gas-particle ow with an FCC reaction in a downer reactor. The ndings showed that the gas velocity has a direct impact on the axial distribution of the solid velocity and fraction, which has a signicant impact on the chemical reaction. Shuyan et al. 42 applied CFD to simulate the cracking reaction of a particle cluster in an FCC riser reactor. The mass uxes of gas and gasoline increase with the temperature and molar concentration of gas oil, but decrease due to the formation of coke, according to the simulation results. Zhang et al. 43 used CFD simulations to examine ow behavior and cracking processes in xed bed reactors. The results show that the predicted product distribution matches the actual data reasonably well, and that the performance of the modied xed-bed reactor is comparable to that of an ideal plug ow reactor. Ahsan 44 used the CFD approach to predict the gasoline in the FCC in a riser reactor. This approach exhibited a high level of consistency between experimental and numerical data from the literature. Owing to the exibility of the CFD setup, this method is suitable for reactor scale-up studies. Thus, Table 3 The operating conditions and corresponding modified dimensionless group Solid phase stress Collisional dissipation of solid uctuating energy Radial distribution function 18 Solid phase shear viscosity Solid phase bulk viscosity Exchange of the uctuating energy between gas and solid B s ¼ À3b gs $Q s 21 numerous researches have applied CFD simulations to study the scaling up of circulating uidized bed reactors. 16,17,22 In this study, CFD models are used to explore the hydrodynamics and chemical performance of catalytic cracking of heavy oil from waste plastics in various downer reactors. The goal of this research is to scale up the catalytic cracking downer reactor to achieve chemical reaction performance similarity.

Reactor geometry
A circulating uidized bed reactor based on Cao and Weinstein's experiment, 45 shown in Fig. 1(a), was used for the CFD model validation and as a based case reactor. However, solely the downer section, where the catalytic cracking reaction occurred, was investigated to simplify the system. The height and ID. of the downer reactor are 5 and 0.127 m, respectively. Two larger reactors with the same height to diameter ratio (Z/D) of 39.37 were investigated for the similarity of the catalytic cracking performance, as shown in Fig. 1(b). The medium and large downer reactors were scaled up from the small-scale downer to 3 and 6 times their size, respectively.

Kinetic cracking model
The catalytic cracking of heavy oil yields thousands of different species of products. To describe the process of such a complex reaction, a lump technique was developed. The product species were grouped according to their boiling points. To describe the complex catalytic cracking of heavy oil from waste plastic, the present study employed the four-lump kinetic model proposed by Songip et al. 46 Heavy oil is converted with the second reaction order to gasoline as a desired product, and with the rst order to form light gas and coke (undesired byproducts). Additionally, gasoline can be further cracked with the rst reaction order to form light gas and coke. The details of four-lump mechanism model and kinetic data are summarized by Songip et al. 46 and in our previous study. 22 2.3 Mathematical model CFD simulations facilitate the investigation of the hydrodynamic, thermal, and mass transport in multiphase ow systems. In the  present study, the reactive ow behavior in a CFB downer was simulated using a two-uid model (TMF) combined with the kinetic theory of granular ow (KTGF). An isothermal condition was considered owing to the dilute reactant concentration used in this work. The Gidaspow drag model 47 was employed as an interphase exchange coefficient between phases because this model can be applied to a wide range of rates of solid circulation with accurately prediction of ow behaviour. 29,48 The k-e turbulent with standard wall function was adopted to account for the turbulence effect in the system. 29,31,33 Tables 1 and 2 show the governing and constitutive equations, respectively. The pressure and velocity coupling was rectied using the SIMPLE algorithm. To solve the convection terms, rst-order upwind discretization methods were employed. Convergence was assumed for each time step when all residuals fall below 10 À4 and maximum iterations were set at 100 for each time step. Ansys-FLUENT 15.0, a commercial CFD program, was used to simulate the transient reactive ow behavior. The user-dened functions of the source term for chemical reactions of each species were developed. These source terms are included in the species conservation equation. Table 3 summarizes the operating conditions employed in this research.

Model validation
The accuracy of the CFD model prediction of the chemical reaction performance was veried with the data obtained by Songip et al. 35 The distributions of the reactant and products for various time factors at a temperature of 673 K are depicted in Fig. 2. As expected, the reactant composition decreases with the increasing time factor. Inversely, the production compositions, particularly gasoline and light gas, tend to increase. Furthermore, the modeling results are consistent with the experimental data. The CFD model validations of hydrodynamics and the chemical reaction performance from the existing experimental results in the literature 45,46 was also presented in our previous  work. 22 The axial and radial distributions of solid volume fraction were compared with the experimental data. The distributions of the reactant and products for various time factors at a temperature of 573 K were used to validate of chemical reaction performance. The validation results show that the experimental and simulation results are in good agreement. As a result, the CFD model can be used to simulate the performance of the catalytic cracking downer reactor.

Scaling up of the catalytic cracking downer reactor
The similitude is a method to scaling up of various engineering applications. In uid mechanic, the similitude is achieved when the testing conditions are satised the geometric similarity, kinematic similarity, and dynamic similarity. Since the chemical reaction performance depends on the mass transfer, heat transfer, kinetic, and hydrodynamics. Thus, the additional terms involving with these phenomena must be concerned for the scaling up of chemical reactor. In 1936, Damköhler 21 proposed a law to scale up a chemical reactor consisting of Z D , The rst two terms are the dimensionless parameters to satisfy the geometric similarity. The third term represents the Reynolds number that can be account for kinematic similarity. The fourth term is the ratio of the chemical reaction time to the gas residence time,  which is an essential term for reactive system. The last two terms involve the thermal similitude due to heat of reaction. Khongprom et al. 22 modied the Damköhler scaling law for catalytic cracking reactions under isothermal conditions and identical reactor sizes. Therefore, only the dimensionless parameter, k*Z U g , was modied. The proposed scaling law for the second-order catalytic cracking reaction can be expressed as This dimensionless term can guarantee the similarity of both the axial and lateral distributions of the downer reactor. However, this scaling law was limited to an identical reactor size. To scale up for commercial production, the operating conditions and the reactor size should be increased. The last two terms of the Damköhler scaling law can be neglected in this work due to the isothermal assumption.
Thus, the additional dimensionless groups Z D , d s D , and U g d s r s m should be considered in this case study.
Hence, the set of our proposed dimensionless groups for scaling up the catalytic cracking downer reactor consists of Z D , This proposed scaling law satises the geometric similarity, kinematic similarity, and chemical kinetic similarity. The dynamic similarity was excluded in this scaling law. According to the gas and solid cocurrently ow in the gravitational direction, the uniform ow pattern in the downer reactor was obtained 49,50 resulting in less impact of dynamic similarity on the scaling up of this reactor type. Table 3 lists the conditions that were utilized to verify the scaling parameter. As chemical performance indicators, heavy oil conversion, gasoline mass fraction and selectivity were used. Fig. 3 and 4 display the effect of the scaling parameter on the lateral and axial distributions of heavy oil conversion, gasoline   Table 3. Although the conditions and the reactor size vary considerably, as the proposed scaling law keeps constant, the chemical performance indicators of all downer scales exhibit good agreement. Fig. 5 shows the comparison of the chemical performance of the lateral and axial distributions between medium-and large-scale downers with small downer. The deviation of the conversion and the gasoline mass fraction were observed to be in the range of AE10%, and the mean relative absolute error was lower than 5%, as listed in Table 4 (Set 1). This indicates that the proposed scaling parameters can be used for scaling up the catalytic cracking downer reactor for chemical performance similarity in both axial and lateral distributions.
The second set of the operating conditions was used to verify the performance of the scaling parameter, as shown in Set 2 of Table 3. As mentioned, as long as the scaling parameter keeps constant, the similarities of the chemical performance can be achieved for both lateral and axial distributions, as shown in Fig. 6 and 7. The deviation of all data was in the range of AE10%, as shown in the parity plot in Fig. 8, and the mean relative absolute error was lower than 5%, as listed in Table 4 (Set 2)

Parameter sensitivity
Generally, the preferred scaling law should exhibit the excellent similarity of each reactor scale without hindering practical application; thus, a small set of scaling laws was found to be suitable. Therefore, the sensitivity of the dimensionless terms was studied to eliminate the insignicant dimensionless group.    Based on the proposed scaling law, the dimensionless parameter Z D is the fundamental term to represent the geometric similarity. Additionally, the dimensionless term r s ðk 1 þ k 2 þ k 3 ÞC AO U g G s r s U g strongly affects the chemical performance of the heavy oil cracking reaction, as reported by Khongprom et al. 22 Hence, only the dimensionless terms U g d s r s m and d s D were investigated for sensitivity.
The sensitivity analysis of the dimensionless term U g d s r s m in the range of 10.1 to 242 was evaluated. The conditions in this case study are displayed in Set 3 of Table 3. Fig. 9 and 10 shows the lateral and axial distributions of the heavy oil conversion, gasoline mass fraction, and gasoline selectivity for various dimensionless terms U g d s r s m . The chemical performances of medium-and large-scale downer reactors were found to be considerably lower than those of the smallscale downer, particularly near the outlet region. The dimensionless term U g d s r s m represents the Reynolds number.
Thus, the increase in this dimensionless group enhances the turbulence of the ow, leading to high mixing in the system. For the second-order reaction, the performance of the mixed-ow reactor is lower than that of the plug ow reactor. 51 Hence, lower heavy oil conversions of medium-and large-scale downers, which are highly mixed, were obtained. Fig. 11 shows the comparison of the chemical performance of the lateral and axial distributions between medium-and large-scale downers with small downer. The deviation of the conversion and the gasoline mass fraction were observed to be higher than AE10%, and the maximum absolute relative error was 17.25%, as listed in Table 4    The dimensionless parameter d s D was proposed to achieve the geometric similarity, which was included in several scaling laws. 15,21 This dimensionless term cannot be neglected when realizing the scaling up required for the hydrodynamics similarity of gas-solid CFB and liquid-solid CFB. 16,17 Thus, the inuence of this term on the chemical reaction performance similarity was discussed in this section. The operating conditions for investigating the sensitivity of this dimensionless term on the scaling up are shown in Set 4 of Table 3. Fig. 12 and 13 present the lateral and axial proles of the chemical performance for various dimensionless terms d s D in the range of 0.00059 to 0.00010. The chemical performance of the scaled-up downer reactors slightly differed from that of the small-scale downer. Although, a deviation in the range of AE10% was observed, as shown in Fig. 14, the mean relative absolute error was higher than 5.00%, as summarized in

Conclusions
The scaling up of the catalytic cracking CFB downer reactor was studied via CFD simulations. A TMF based on Eulerian-Eulerian approach, coupled with KTGF, was adopted to predict the hydrodynamics and chemical reaction performance of reactive ow. The CFD model predicted well the species composition distribution under various time factors. The chemical performance similarity was characterized using the lateral and axial distributions of heavy oil conversion, gasoline mass fraction, and gasoline selectivity in three downers with a height of 5, 15, and 30 m. Based on our study and the parameter sensitivity, the proposed scaling law for the catalytic cracking downer reactor consists of the dimensionless groups Z D , d s D , U g d s r s m , and r s ðk 1 þ k 2 þ k 3 ÞC AO Z U g G s r s U g , which take into account the geometric similarity, kinematic similarity, and kinetic similarity. A wide range of operating condition was carried out to verify the proposed scaling law. The excellent similarity of chemical performance was obtained with a deviation in the range of AE10% and a mean relative absolute error of less than 5%.

Author contributions
Conceptualization, P. K. and S. L.; methodology and analysis, P. K., S. R. and P. B.; investigation, S. R., P. B. and W. W., writing-original dra preparation, S. R. and W. W.; writing-review and editing, P. K.; supervirion, S. L. All authors reviewed the manuscript.

Conflicts of interest
There are no conicts to declare.