Use of orthogonal collocation on finite elements with moving boundaries for fixed bed catalytic reactor simulation

A numerical procedure for the solution of transient models for the simulation of fixed bed catalytic reactors is developed. The most general model examined includes axial dispersion in the external fluid phase, interphase mass and heat transfer resistances,intraphase mass resistance and any given kinetic scheme with complex reaction rate expressions. The solution technique is based on the method of lines, in which the space variables are discretized using the orthogonal collocation method on finite elements, with elemination of the node unknown functions, coupled with an integration method for stiff ordinary differential equations. An efficient procedure for updating during the integration the position of the finite element boundaries, in order to follow the movement of steep concentration and temperature profiles along the space variable during the reactor transient, is proposed. Application examples of the developed computer program are also given.     

Mass transfer and biochemical reaction in enzyme membrane reactor systems—II: Expanded analysis for single enzyme systems: effects of enzyme intermediates,denaturation and elution

A detailed study of the dynamics of a packed-bed reactor containing immobilized enzyme particles is presented. The analysis consists of (i) transient state behavior; (ii) models for interphase and interfacial mass transfer between fluid and solid phases and intraphase mass transfer for the solid phase; (iii) detailed reaction rate model for the Bodenstein intermediates; (iv) mass balances for substrates, Bodenstein intermediates, unoccupied enzyme active sites, and products; and (v) models for enzyme denaturation and elution. The general reactor model consists of a set of nonlinear, coupled, partial differential equations. Numerical solutions of the system equations were obtained, using the discrete-space, continuous-time method of lines and realistic parameter values. A generalized map of the range of validity of the Steady-State Hypothesis was established under conditions where multiple mass transfer gradients were present within the reactor.A detailed analysis of the computational errors was performed. It was conclusively shown that the computer simulation solutions obtained in the analyses were not disguised to any significant degree as a result of employing finite difference approximations to the spatial derivatives.It was shown that the level of “error” involved in invoking the Steady-State Hypothesis depends on the relative magnitude of the kinetic parameters and also on the level of “disturbance” at the reactor inlet (i.e. per cent change in substrate inlet concentration). The “error”, however, did appear to be strikingly insensitive to the magnitude of the resistances to mass transfer, as characterized by the Modified Sherwood Number. It was concluded that, given any complete set of kinetic parameters, a transient, heterogeneous, isothermal reactor model based on the Steady-State Hypothesis may be used for predicting time-varying concentration profiles for minor (i.e., less than 5 per cent change in substrate inlet concentration) “disturbances” at the reactor inlet. The corresponding “errors” would be at an acceptable level (i.e., less than 2 per cent in the concentration and less than 10 per cent in the time lag) under these conditions.Further, various mechanisms for enzyme denaturation and elution were incorporated in the general reactor model. Numerical solutions of the resulting system of partial differential equations were obtained, using hypothetical parameter values. Through extensive simulation research, it was shown that the loss in activity of immobilized enzyme reactors cannot be uniquely ascribed to any one particular set of mechanistic deactivation modes.     

Development and testing of an interconnected multiphase CFD-model for chemical looping combustion

An interconnected multi-phase CFD model is developed capable of describing the transient behavior of a coupled chemical looping combustion systems comprising of both air and fuel reactors. The air reactor is modeled as a high velocity riser, the fuel reactor as a bubbling fluidized bed. The models of both reactors are implemented as separate CFD simulations allowing for an exchange of solid mass through time-dependent inlet and outlet boundary conditions as well as mass, momentum, heat and species sinks. The developed framework is applied to a chemical looping combustion system based on Mn₃O₄ as carrier material in combination with CH₄ as fuel gas. Starting from a base case, different system configurations are investigated. The results indicate clearly that interconnected multi-phase CFD models are well suited for the design process of coupled chemical looping systems.     

CFD simulation of hydrodynamics of gas-liquid-solid fluidised bed reactor

A three dimensional transient model is developed to simulate the local hydrodynamics of a gas-liquid-solid three-phase fluidised bed reactor using the computational fluid dynamics (CFD) method. The CFD simulation predictions are compared with the experimental data of Kiared et al. [1999. Mean and turbulent particle velocity in the fully developed region of a three-phase fluidized bed. Chemical Engineering & Technology 22, 683-689] for solid phase hydrodynamics in terms of mean and turbulent velocities and with the results of Yu and Kim [1988. Bubble characteristics in the racial direction of three-phase fludised beds. A.I.Ch.E. Journal 34, 2069-2072; 2001. Bubble-wake model for radial velocity profiles of liquid and solid phases in three-phase fluidised beds. Industrial and Engineering Chemistry Research 40, 4463-4469] for the gas and liquid phase hydrodynamics in terms of phase velocities and holdup. The flow field predicted by CFD simulation shows a good agreement with the experimental data. From the validated CFD model, the computation of the solid mass balance and various energy flows in fluidised bed reactors are carried out. The influence of different interphase drag models for gas-liquid interaction on gas holdup are studied in this work.     

Coarse grained computational fluid dynamic simulation of sands and biomass fluidization with a hybrid drag

The bubbling fluidized bed reactor is widely used in fast pyrolysis of biomass. Discrete simulation of this reactor is challenging due to many sand particles and lack of accurate drag corrections accounting for the interaction of two different solid particles with different properties. In this research, the computational cost is reduced by using the coarse-grained computational fluid dynamic-discrete element method, where many sand particles are lumped into a larger numerical parcel. The Syamlal–O'Brien drag model is used for sand, while Ganser correction coupled with Gidaspow model is used for the nonspherical biomass particles. This hybrid approach shows superior behavior over other drag models using pressure drops as a benchmark. The predicted bed height and pressure fluctuating frequencies compare well with experiment. The mixing of biomass is close to perfect if the superficial velocity is larger than four times the minimum fluidization velocity.     

拟泡-乳曳力模型在大型高温费托流化床反应器中的CFD模拟研究

以带冷却盘管的大型高温费托流化床反应器为研究对象,开展三维计算流体力学模拟研究。传统双流体模型基于局部平均的假设,认为单位控制体内气固两相均匀分布,网格尺寸必须足够小才能正确揭示局部非均匀结构的所有细节。采用双流体模型模拟大型工业化流化床装置时,将导致网格数量过于庞大,远超现有计算能力。为提高计算效率的同时不损失模拟精度,提出了基于局部非均匀假设、适用于粗网格的拟泡-乳三相非均匀曳力(PBTD)模型。该模型将流化床分为乳化相气体、乳化相颗粒以及气泡三相,分别建立守恒方程,体现气泡的非均匀特性对气固曳力的影响。乳化相内气固曳力以及气泡相与乳化相内颗粒的曳力分开考虑。采用PBTD模型耦合传质和反应模型,建立基于局部非均匀假设的高温费托合成反应器三维流动-传递-反应模型,包括各相守恒控制方程、气泡尺寸模型、相间物质和动量交换模型、高温费托合成反应动力学模型以及初始和边界条件,预测反应器内的流场和组分浓度分布。研究结果表明:在粗网格条件下,非均匀曳力模型可以预测床层内相含率的分布情况,预测的床层膨胀高度与经验公式计算值接近,偏差为1.2%。反应器出口气体组分的质量分数与试验测量值相近,偏差在1.5%~16.0%。模拟结果证实,基于非均匀假设的PBTD模型适用于模拟工业规模的鼓泡流化床反应器,对其设计开发和工业运行具有指导价值。     

Coupling of CFD with PBM for a pilot-plant tubular loop polymerization reactor

A computational fluid dynamics model, coupled with population balance model (CFD–PBM), was developed to describe the liquid–solid two-phase flow in a pilot-plant tubular loop propylene polymerization reactor. The model combines the advantage of CFD to calculate the entire flow field and that of PBM to calculate the particle size distribution (PSD). Particle growth, aggregation and breakage were taken into account to describe the evolution of the PSD. The model was first validated by comparing simulation results with the classical calculated data. Furthermore, four cases studies, involving particle aggregation, particle breakage, particle growth or involving particle growth, breakage and aggregation, were designed to identify the model. The entire flow behavior and PSD in the tubular loop reactor, i.e. PSD, solid holdup and liquid phase velocity distribution, were also obtained numerically. The results showed that the model is effective in describing the entire flow behavior and in tracking the evolution of the PSD.     

Conceptual design and CFD simulation of a novel metal-based monolith reactor with enhanced mass transfer

This paper introduces a novel structured metallic catalyst that improves mass transfer performance of a monolith reactor for highly exothermic gas–solid reactions. The monolith channels are designed to have metallic substrates that consist of two layers with one of the layers being the metallic support and another layer being a foam metal annular that is tightly deposited onto the support surface by some means. Parametrical studies based on a 2D monolith reactor model showed that the present design yields an enhanced mass transfer between the bulk fluid and the catalyst layer due to a decrease in external film resistance, and an enhanced mass transfer within the solid phase mainly due to the viscous flow effect within the porous catalyst layer.     

A finite element solution of coupled heat and mass transfer with chemical reaction

A finite element method is presented for solving the coupled non-linear parabolic differential equations describing transient transport of heat and mass in chemically reacting systems. The method appears to be a useful approximation for a wide variety of problems. Typical numerical results are reported for non isothermal catalytic solid—fluid reactions. Applications to other fields such as absorption accompanied by reaction and non-catalytic solid—fluid reaction models are also formulated.     

CFD simulation of gas and solids mixing in FCC strippers

The gas and solid mixing in fluid catalytic cracking strippers with and without internals were investigated using computational fluid dynamics simulations. The Eulerian–Eulerian two‐fluid model coupled with the modified Gidaspow drag model was used to simulate the gas‐solid flow behavior. The grid independency study and the comparison of 2D and 3D simulations were carried out first. The residence time distribution model and axial dispersion model were utilized to obtain the parameters indicating the back‐mixing degree, such as mean residence time, dimensionless variance and Peclet number of gas and solids. Moreover, the influence of bubble size and gas/solid flow distribution on the mass transfer between the bubble and emulsion phase were also analyzed. The results show that the baffles in the V‐baffle stripper can efficiently enhance the gas and solids mixing, reduce the back‐mixing degree of gas and solids, strengthen the mass transfer between the bubble and emulsion phase, and hence improve the stripping efficiency. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Models for the Numerical Simulation of Bubble Columns: A Review

This work reviews the state‐of‐the‐art models for the simulation of bubble columns and focuses on methods coupled with computational fluid dynamics (CFD) where the potential and deficits of the models are evaluated. Particular attention is paid to different approaches in multiphase fluid dynamics including the population balance to determine bubble size distributions and the modeling of turbulence where the authors refer to numerous published examples. Additional models for reactive systems are presented as well as a special chapter regarding the extension of the models for the simulation of bubble columns with a present solid particle phase, i.e., slurry bubble columns.     

Liquid‐Phase Alkylation of Benzene with Propylene Catalysed by HY Zeolites

Benzene alkylation with propylene over a Ca modified HY zeolite to obtain cumene has been studied. Time on stream behavior of the catalyst was quite steady without any sign of deactivation and the results were reproducible. The external mass transfer does not influence the cumene reaction. The pore diffusion has a substantial influence on the cumene reaction only in the final region of the reactor, where the olefin concentration is very low. A simple power law kinetic model fits the experimental data significantly better than other models. A general time and space dependent model was developed to analyze the performance of a two‐phase downflow fixed bed reactor used for alkylation of benzene with zeolite catalyst. The model could be instructive in exploratory simulations evaluating the conditions for benzene alkylation in liquid phase.     

A CFD‐PBM‐PMLM integrated model for the gas–solid flow fields in fluidized bed polymerization reactors

Although the use of computational fluid dynamics (CFD) model coupled with population balance (CFD‐PBM) is becoming a common approach for simulating gas–solid flows in polydisperse fluidized bed polymerization reactors, a number of issues still remain. One major issue is the absence of modeling the growth of a single polymeric particle. In this work a polymeric multilayer model (PMLM) was applied to describe the growth of a single particle under the intraparticle transfer limitations. The PMLM was solved together with a PBM (i.e. PBM‐PMLM) to predict the dynamic evolution of particle size distribution (PSD). In addition, a CFD model based on the Eulerian‐Eulerian two‐fluid model, coupled with PBM‐PMLM (CFD‐PBM‐PMLM), has been implemented to describe the gas–solid flow field in fluidized bed polymerization reactors. The CFD‐PBM‐PMLM model has been validated by comparing simulation results with some classical experimental data. Five cases including fluid dynamics coupled purely continuous PSD, pure particle growth, pure particle aggregation, pure particle breakage, and flow dynamics coupled with all the above factors were carried out to examine the model. The results showed that the CFD‐PBM‐PMLM model describes well the behavior of the gas–solid flow fields in polydisperse fluidized bed polymerization reactors. The results also showed that the intraparticle mass transfer limitation is an important factor in affecting the reactor flow fields. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1717–1732, 2012     

Experimental and Numerical Study of Gas-Liquid Flow in a Sectionalized External-Loop Airlift Reactor

The external loop airlift reactor(EL-ALR) is widely used for gas-liquid reactions. It's advantage of good heat and mass transfer rates compared to conventional bubble column reactors. In the case of fermentation application where a medium is highly viscous and coalescing in nature, internal in riser helps in the improvement of the interfacial area as well as in the reduction of liquid-phase back mixing. The computational fluid dynamic(CFD) as a tool is used to design and scale-up of sectionalized external loop airlift reactor. The present work deals with computational fluid dynamics(CFD) techniques and experimental measurement of a gas hold-up, liquid circulation velocity, liquid axial velocity, Sauter mean bubble diameter over a broad range of superficial gas velocity 0.0024≤U_G≤0.0168 m·s~(-1). The correlation has been made for bubble size distribution with specific power consumption for different plate configurations. The effects of an internal on different mass transfer models have been completed to assess their suitability.The predicted local mass transfer coefficient has been found higher in the sectionalized external loop airlift reactor than the conventional EL-ALR.     

Steady state multiplicity behavior of an isothermal axial dispersion fixed-bed reactor with nonuniformly active catalyst

An isothermal, heterogeneous fixed-bed reactor packed with nonuniformly active catalyst pellets where a biomolecular Langmuir-Hinshelwood reaction occurs, is studied using an axial dispersion model. A catalyst activity distribution given by a Dirac delta function, where the active catalyst is deposited at a specific location within the pellet, is considered. This includes the common case of externally coated pellets with external mass transfer resistance. The steady state multiplicity behavior of this reactor, and its limiting cases: CSTR, PFR and pseudohomogeneous axial dispersion, are examined in detail. The nonlinearity of the reaction kinetics provides two sources of multiplicity, through the heterogeneous nature of the reactor and the presence of axial dispersion in the fluid phase. Their roles in determining reactor multiplicity behavior are fully explored. It is shown that this system can admit at most nine steady state solutions. The limiting behavior of the heterogeneous axial dispersion model as Pe → 0 or ∞ is not represented fully by the CSTR or PFR models because of ignition phenomenon. Finally, the effects of mixing on reactor conversion are discussed.     

Modeling of transient heterogeneous two-dimensional catalytic packed bed reactor

A two-dimensional transient catalytic packed bed model, incorporating all transport parameters and resistances, along with boundary conditions based on a catalytic single pellet has been developed. Thermal conduction through the solid phase is included in the model. The overall steady state reactor performances of packed bed reactor using a model proposed in this study are compared with those from different models which are often used for a packed bed reactor. The model presented is very useful in the presence of internal temperature and concentration gradients in the catalyst pellets. The dynamic behavior in feed temperature change is examined during ethane hydrogenolysis. A transient thermal runaway is observed by feed temperature decrease. The sensitivities of the computation to each physical parameter and the effects of some simplifying assumptions in the model are also analyzed. The magnitude and position of hot spot in catalytic packed bed reactor are relatively sensitive to thermal parameters and characteristic parameters of a catalyst pellet.     

CFD analysis of hydrodynamic, heat transfer and reaction of three phase riser reactor

Catalytic cracking reaction and vaporization of gas oil droplets have significant effects on the gas solid mixture hydrodynamic and heat transfer phenomena in a fluid catalytic cracking (FCC) riser reactor. A three-dimensional computational fluid dynamic (CFD) model of the reactor has been developed considering three phase hydrodynamics, cracking reactions, heat and mass transfer as well as evaporation of the feed droplets into a gas solid flow. A hybrid Eulerian-Lagrangian method was applied to numerically simulate the vaporization of gas oil droplets and catalytic reactions in the gas-solid fluidized bed. The distributions of volume fraction of each phase, gas and catalyst velocities, gas and particle temperatures as well as gas oil vapor species were computed assuming six lump kinetic reactions in the gas phase. The developed model is capable of predicting coke formation and its effect on catalyst activity reduction. In this research, the catalyst deactivation coefficient was modeled as a function of catalyst particle residence time, in order to investigate the effects of catalyst deactivation on gas oil and gasoline concentrations along the reactor length. The simulation results showed that droplet vaporization and catalytic cracking reactions drastically impact riser hydrodynamics and heat transfer.     

TWO-DIMENSIONAL TRANSIENT NUMERICAL SIMULATION OF SOLIDS AND GAS FLOW IN THE RISER SECTION OF A CIRCULATING FLUIDIZED BED

A computational fluid dynamics software (CFX) was modified for gas/particle flow systems and used to predict the flow parameters in the riser section of a circulating fluidized bed (CFB). Fluid Catalytic Cracking (FCC) particles and air were used as the solids and gas phases, respectively. Two-dimensional, transient, isothermal flows were simulated for the continuous phase (air) and the dispersed phase (solid particles). Conservation equations of mass and momentum for each phase were solved using the finite volume numerical technique. Two-dimensional gas and particle flow profiles were obtained for the velocity, volume fraction, and pressure drop for each phase. Calculations showed that the inlet and exit conditions play a significant role in the overall mixing of the gas and particulate phases and in the establishment of the flow regime. The flow behavior was analyzed based on the different frequency of oscillations in the riser. Comparison of the calculated solids mass flux, solids density and pressure drop with the measured pilot-scale PSRI data (reported in this paper) showed a good agreement.     

Two-dimensional transient numerical simulation of solids and gas flow in the riser section of a circulating fluidized bed

A computational fluid dynamics software (CFX) was modified for gas/particle flow systems and used to predict the flow parameters in the riser section of a circulating fluidized bed (CFB). Fluid Catalytic Cracking (FCC) particles and air were used as the solids and gas phases, respectively. Two-dimensional, transient, isothermal flows were simulated for the continuous phase (air) and the dispersed phase (solid particles). Conservation equations of mass and momentum for each phase were solved using the finite volume numerical technique. Two-dimensional gas and particle flow profiles were obtained for the velocity, volume fraction, and pressure drop for each phase. Calculations showed that the inlet and exit conditions play a significant role in the overall mixing of the gas and particulate phases and in the establishment of the flow regime. The flow behavior was analyzed based on the different frequency of oscillations in the riser. Comparison of the calculated solids mass flux, solids density and pressure drop with the measured pilot-scale PSRI data (reported in this paper) showed a good agreement.