Theoretical study of the application of porous membrane reactor to oxidative dehydrogenation of n-butane

This paper is the theoretical study of the oxidative dehydrogenation of n-butane in porous membrane reactors. Performance of the membrane reactors was compared with that of conventional fixed-bed reactors. The porous membrane was employed to add oxygen to the reaction side in a controlled manner so that the reaction could take place evenly.Mathematical models for the fixed-bed reactor and the membrane reactor were developed considering non-isothermal condition and both radial heat and mass dispersion. From this study, it was found that the hot spot problem was pronounced particularly near the entrance of the conventional fixed-bed reactor. In addition, the assumption of plug flow condition did not adequately represent the reaction system. The effect of radial dispersion must be taken into account in the modelling.The use of the porous membrane to control the distribution of oxygen feed to the reaction side could significantly reduce the hot spot temperature. The results also showed that there were optimum feed ratios of air/n-butane for both the fixed-bed reactors and the membrane reactors. The membrane reactor outperformed the fixed-bed reactor at high values of the ratio. In addition, there was an optimum membrane reactor size. When the reactor size was smaller than the optimum value, the increased reactor size increased the reaction and heat generation and, consequently, the conversion and the selectivity to C₄ increased. However, when the reactor size was larger than the optimum value, oxygen could not reach the reactant near the stainless steel wall. It was consumed to react with the product, C₄. As a result, the yield dropped. Finally, it was found that the increase of wall temperature increased the yield and that the feed air temperature could help control the temperature profile of the reaction bed along the reactor length.     

Optimal design of n membrane reactors in series using michaelis-menten kinetics

Exact analytical expressions are derived for the optimal design (minimum overall reaction volume) of N perfectly mixed membrane reactors in series carrying out an enzyme catalysed reaction with Michaelis-Menten kinetics. These equations enable the direct calculation of the smallest total reactor volume (holding time) needed for a given overall conversion degree, as well as the individual reactor volume and conversion degrees. Results are compared with the ones obtained with a series of N CSTRs and with a plug flow reactor. The theoretical superiority of membrane reactors versus CSTRs is demonstrated.     

Dynamic operation of butadiene dimerization reactor undergoing catalyst deactivation

Operation of fixed-bed catalytic reactors undergoing catalyst deactivation has been investigated as an optimal control problem to yield optimal temperature policies. An efficient numerical scheme using a control vector iteration method based on gradients in functional space is developed. The procedure is applied to develop optimal temperature profiles for a butadiene dimerization process. The temperature-time trajectories and dynamic activity profiles are strongly influenced by kinetics. A sensitivity analysis is done to study the effect of flow rates, conversion level and parameters that influence kinetic and deactivation processes. These results have been validated with experimentation on a lab scale reactor and a 9.14 m pilot-plant reactor.     

A comparative study of combination of Fischer–Tropsch synthesis reactors with hydrogen-permselective membrane in GTL technology

This work proposes a one dimensional heterogeneous model to analyze the performance of combination of Fischer–Tropsch synthesis (FTS) reactors in which a fixed-bed reactor is combined with a membrane assisted fluidized-bed reactor. This model is used to compare the performance of the proposed system with a fixed-bed singlestage reactor. In the new concept, the synthesis gas is converted to FT products in two catalytic reactors. The first reactor is water-cooled fixed-bed type while the second reactor is gas-cooled and fluidized-bed. Due to the decrease of H₂/CO to values far from optimum reactants ratio, the membrane concept is suggested to control hydrogen addition. Moreover, a fluidized-bed system has been proposed to solve some observed drawbacks of industrial fixed-bed reactors such as high pressure drop, heat transfer problem and internal mass transfer limitations. This novel concept which has been named fluidized-bed membrane dual-type reactor is used for production of gasoline from synthesis gas. The reactor model is tested against the pilot plant data of the Research Institute of Petroleum Industry. Results show an enhancement in the gasoline yield, a main decrease in CO₂ formation and a favorable temperature profile along the proposed concept.     

Computation of the near-optimal temperature and initiator policies for a batch polymerization reactor

Optimal control theory is applied to a batch polymerization reactor for PMMA to calculate the near-optimal temperature and initiator policies that are required to produce a polymer with a desired final conversion, and desired number average and weight average molecular weights. The two-point boundary value problem that results from the application of the Pontryagin minimum principle to the mathematical model of the reactor is solved by the discretization control method. According to this, the total reaction time is divided into N equal subintervals. It is assumed that the control variables remain constant in each interval and the Hamiltonian is minimized by a first-order gradient technique. It is shown that the introduction of the “target set” concept, which is well suited to industrial practice, simplifies the numerical solution of the TPBV problem. Results of the simulations demonstrate the potential gains possible from the application of the optimal control theory to the batch polymerization of PMMA.     

Optimal temperature policies by distributed control for reactors with lhhw catalyst deactivation

An approximate procedure for solving the problem of temperature optimal control distributed in both space and time coordinates is presented. It is applied to chemical reactors suffering from catalyst decay whose model is described by a complex second order partial differential equation deduced from LHHW kinetics. The proposed algorithm uses a finite-difference approximation method to solve the state equation, and the control vector parametrization technique to obtain the optimal control. Numerical examples are computed and the results obtained show that distributed control reaches significantly higher production than lumped control.     

Applying Reaction Kinetics to Pseudohomogeneous Methanation Modeling in Fixed-Bed Reactors

Reactor simulations can reduce the effort when designing fixed-bed reactors for methanation processes. Several microkinetic models were developed under a variety of operating conditions. However, most production-scale fixed-bed methanation processes exceed the temperature range in which these kinetic models were obtained. In addition, heat and mass transport limitations strongly influence the reaction kinetics. In this work, microkinetic rate equations for CO and CO₂ methanation were analyzed with respect to their suitability for high-temperature, pseudohomogeneous reactor modeling. The best-suited kinetic model was fitted to the operating conditions and validated by means of CFD simulations. It is shown that the simulations match the experimental data for various operating conditions.     

Influence of the turbulence model in CFD modeling of wall-to-fluid heat transfer in packed beds

Computational fluid dynamics as a simulation tool allows obtaining a more detailed view of the fluid flow and heat transfer mechanisms in fixed-bed reactors, through the resolution of 3D Reynolds averaged transport equations, together with a turbulence model when needed. In this way, this tool permits obtaining of mean and fluctuating flow and temperature values in any point of the bed. An important problem when modeling a turbulent flow fixed-bed reactor is to decide which turbulence model is the most accurate for this situation. To gain insight into this subject, this study presents a comparison between the performance in flow and heat transfer estimation of five different RANS turbulence models in a fixed bed composed of 44 homogeneous stacked spheres in a maximum space-occupying arrangement in a cylindrical container by solving the 3D Navier-Stokes and energy equations by means of a commercial finite volume code, Fluent 6.0^®. Air is chosen as flowing fluid. Numerical pressure drop, velocity and thermal fields within the bed are obtained. In order to judge the capabilities of these turbulence models, heat transfer parameters (Nu_w, k_r/k_f) are estimated from numerical data and together with the pressure drop are compared to commonly used correlations for parameter estimations in fixed-bed reactors.     

Simulation and optimal control of catalytic reactors governed by partial differential equations with boundary control

This paper examines a theory of optimal control of chemical reactors governed by a system of partial differential equations linked by a second non-linear member and where the control variable is only present in the boundary conditions. An integral transformation procedure of the mathematical model associated with the use of Pontryagin's Principle permits a solution in terms of a classical differential problem.     

Heterogeneous catalytic reactor design with optimum temperature profile I: application of catalyst dilution and side-stream distribution

A generic method for the design of reactors with optimal temperature profiles has been developed. This paper focuses on the use of side-streams and inert pellets to control the temperature profiles in addition to external cooling. These two aspects of reactor design have so far been developed separately and mainly applied to laboratory-scale reaction systems. In this work, a reactor design procedure is developed that considers the combination of these two aspects simultaneously. Nitrobenzene hydrogenation and ethylene oxidation in non-isothermal and non-adiabatic reactors are used as case studies. The results show that higher reactor performance, characterised by conversion, yield or selectivity, can be achieved with optimal temperature profiles manipulated by side-streams and inert pellets. Temperature can be effectively controlled to be below a certain maximum point that causes hot spots, or thermal run-away behaviour. Various reactor designs such as Packed-Bed Membrane Reactor (PBMR), Multi-Bed Multi-Tubular Reactor (MBMTR) with side-stream injection are considered and compared with typical fixed-bed reactors. Pseudo-homogeneous (1D) and heterogeneous (1D) reactor models are used for the modelling of the reactor with SQP (Successive Quadratic Programming) and stochastic methods applied for the optimisation.     

Modeling steady-state heterogeneous gas–solid reactors using feedforward neural networks

A new method for solving gas–solid heterogeneous reactors is proposed. Mass balance inside the pellet (numerical integration of a differential equations system) is replaced by an analytical function, which functionality corresponds to an adequate trained three-layer feedforward neural network. The global reaction rate evaluated by using this function includes the complex phenomena of simultaneous diffusion and chemical reaction into the solid. The methodology was successfully applied to the steam reforming of methane. Both methods are compared. Results of the reactor simulation are very similar in both cases but the one that used neural networks is about 20 times faster. The method proposed could also be applied to any type of two-phase heterogeneous reactors.     

Evaluation and improvement of dynamic optimality in electrochemical reactors

A systematic approach for the dynamic optimization problem statement to improve the dynamic optimality in electrochemical reactors is presented in this paper. The formulation takes an account of the diffusion phenomenon in the electrode/electrolyte interface. To demonstrate the present methodology, the optimal time-varying electrode potential for a coupled chemical-electrochemical reaction scheme, that maximizes the production of the desired product in a batch electrochemical reactor with/without recirculation are determined. The dynamic optimization problem statement, based upon this approach, is a nonlinear differential algebraic system, and its solution provides information about the optimal policy. Optimal control policy at different conditions is evaluated using the best-known Pontryagin's maximum principle. The two-point boundary value problem resulting from the application of the maximum principle is then solved using the control vector iteration technique. These optimal time-varying profiles of electrode potential are then compared to the best uniform operation through the relative improvements of the performance index. The application of the proposed approach to two electrochemical systems, described by ordinary differential equations, shows that the existing electrochemical process control strategy could be improved considerably when the proposed method is incorporated.     

The use of preconditioned conjugate gradient and Newton-like methods for a two-dimensional,nonlinear, steady-state,diffusion/reaction problem

A combination of the Newton-like S-method of Bank and Rose[1] and the conjugate gradient method for nonsymmetric matrices described by Axelsson[7] with appropriate pre-conditioning is used in the numerical solution of a system of nonlinear elliptic partial differential equations. The S-method is used to linearize the equations and provides quadratic convergence. The preconditioned conjugate gradient algorithm is used to solve the system of N² linear equations in far fewer than N² iterations without destroying the sparsity of the matrix. The methods can be applied to a large class of problems. A two-dimensional, nonlinear, steady-state diffusion/reaction problem is solved to illustrate the use of the methods. The problem describes diffusion and reaction in a catalyst slab applicable to a two-phase, cross-flow reactor. Results for extreme problems are presented to demonstrate the usefulness and efficiency of the methods.     

Model predictive control of an industrial pyrolysis gasoline hydrogenation reactor

This study focuses on the implementation of a nonlinear model predictive control (MPC) algorithm for controlling an industrial fixed-bed reactor where hydrogenations of raw pyrolysis gasoline occur. An orthogonal collocation method is employed to approximate the original reactor model consisting of a set of partial differential equations. The approximate model obtained is used in the synthesis of a MPC controller to control the temperature rising across a catalyst bed within the reactor. In the MPC algorithm, a sequential optimization approach is used to solve an open-loop optimal control problem. Feedback information is incorporated in the MPC to compensate for modeling error and unmeasured disturbances. The control studies are demonstrated in cases of set point tracking and disturbance rejection.     

A systematic generation of reactor designs: I. Isothermal conditions

A new method is proposed for systematic generation of conceptual design of reactor networks. Given feed compositions and a kinetic model, the objective is to find the optimal mixing structure and feed distribution. The method aims at finding the optimal sequence and sizes of ideal reactors and the optimal addition of extra feed streams along the reactor path. The total reaction time is calculated so as to maximize the space time yield subject to a minimum yield of the key product component. The method does not have any limitations with respect to the number of components or reactions. A new model formulation is proposed that comprises both CSTR and PFR model equations and the design problem is formulated as an optimal control problem. In this paper, only isothermal conditions are considered.     

Probleme der Modellbildung bei technischen Festbettreaktoren

Problems and potential of mathematical modelling for industrial fixed-bed reactors . Modelling and computer simulation for the purpose of design and operation of industrial fixed-bed reactors are discussed with the aid of examples. Emphasis is placed upon difficulties and problems arising from the adequate model formulation. The following aspects are discussed in some detail: (1) The influence of heat and mass transport in the catalyst pellet, especially with complex reaction. (2) The relations between radial heat transfer and radial flow profile and its influence upon the axial temperature profile in packed tubes with or without heat generation by reaction. (3) The modelling of activity-variations along the packed bed during the lifetime of a catalyst. (4) The scale-up problem of multitubular fixed-bed reactors, i.e. the problem of achieving and maintaining equal operating conditions inside and outside all the tubes of the bundle.     

Integrated thermodynamic and kinetic model of homogeneous catalytic N-oxidation processes

The homogeneous phosphotungstic acid catalyzed N-oxidation of alkylpyridines by hydrogen peroxide has important applications in pharmaceutical and fine chemical industries. Current industry practice is to employ a semibatch reactor with gradual dosing of hydrogen peroxide into an alkylpyridine/catalyst solution under isothermal conditions. However, due to lack of understanding of reaction mechanism and thermodynamic behavior, this system is subject to significant risk of flammability, fires and explosions due to hydrogen peroxide decomposition. In this study, we conducted semibatch N-oxidation process in an isothermal reaction calorimeter (RC1) over a wide range of temperature, catalyst amount and oxidizer dosing rates. Reactor pressure, reaction heat generation rate and in situ FTIR spectra of liquid phase species were recorded in real-time during experiments, and final product was quantified using HPLC and GC–MS analytical tools. We developed an integrated thermodynamic and kinetics model of homogeneous N-oxidation reaction based on experimental results and past literature findings. More specifically, Wilson excess Gibbs model was employed to estimate activity coefficients of highly nonideal liquid mixture. We found ideal gas law was satisfactory in calculating incondensable oxygen pressure. First principle reaction mechanism and kinetics parameters of (a) catalytic N-oxidation reaction; (b) catalytic hydrogen peroxide decomposition reaction; (c) noncatalytic N-oxidation reaction; (d) noncatalytic hydrogen peroxide decomposition reaction was derived based on experimental findings of this study and past literature. The proposed integrated thermodynamic model and kinetics model successfully predicted highly nonlinear reactor pressure, species concentration and reaction enthalpy generation rate profile of homogenous catalytic N-oxidation and H₂O₂ decomposition reaction. The optimal reactions conditions with maximum N-oxide product yield and minimum reactor pressure and catalyst usage was theoretically identified and further verified by experiments. The obtained model can be used for inherently safer reactor design and applied to other homogeneous tungstic acid catalytic hydrogen peroxide oxidation processes.