Optimal temperature policies for catalytic transport reactors under periodic operation

The influence of inlet gas concentration cycling on the optimal temperature policy of catalytic transport reactors is studied theoretically. The model considered is based on plug flow of gas and catalyst particles with negligible interand intra-particle diffusional resistances and concentration dependent deactivation kinetics. To utilise the concentration of the reactant and the activity of the deactivating catalyst fully a proper temperature sequence along the reactor is needed. Thus, a general optimal temperature policy using the continuous minimum principle is derived for the reactor under periodic operation. The model equations are solved analytically for gas concentration, activity and temperature profiles. Resonance behaviour (maximum in conversion with pulse width) is obtained using the optimal temperature policy for certain sets of parameters. The effects of activation energy groups, reaction and deactivation constant groups and inlet temperature on the optimal temperature policy under periodic operation are evaluated. In all cases an improvement in conversion with the optimal temperature policy under periodic operation over that with an isothermal policy under periodic operation is obtained. A suboptimal policy, comprising constant temperature over different reactor sections, which is useful for implementation purposes is also discussed.     

Optimal temperature profiles for tubular reactors implemented through a flow reversal strategy

Optimal steady-state reactor temperature profiles in classic jacketed tubular reactors often exhibit a (nearly) trapezoidal shape along the reactor, i.e., in a first part the temperature is raised, then a constant temperature interval follows, and (possibly) the temperature is lowered towards the outlet. The practical realisation of these optimal reactor temperature profiles is, however, complex because of the spatially varying jacket fluid temperature profile that is required for the constant reactor temperature part. Since similar trapezoidal temperature profiles are encountered in reverse flow configurations, this reactor type may be an alternative to implement the optimal profiles in practice. This article conceptually proves the feasibility of this concept and provides an optimisation procedure for its design and operation.     

Periodic operation of isothermal plug-flow reactors with input multiplicities

The performance of isothermal plug-flow tubular reactors under periodic inlet concentrations is theoretically analyzed for improvement in yield for homogeneous consecutive reactions A→ B → C which, under conventional steady-state operation, show input multiplicities in the flow rate on the yield of B. Two values of flow rate give an identical yield of B under steady-state operation. For periodic operation, a rectangular pulse is assumed for the inlet concentration. It is shown in three numerical examples that under concentration forcing the yield is significantly different for these two inlet flow rates. Under periodic operation the larger value of flow rate gives a higher yield of B.     

Periodic operation of transport reactors for catalytic reactions

Based on plug flow of gas and catalyst particles and concentration dependent deactivation kinetics, the performance of transport reactors under a periodic (rectangular pulse) inlet concentration is analysed for improvement in conversion and extent of catalyst decay. The effects of reaction and deactivation orders, reaction and deactivation constant groups, and γ (cycle split) on the performance of the reactors are evaluated theoretically. For reaction orders greater than one, periodic operation improves conversion. Resonance behaviour is observed for certain combinations of parameters. For identical operating conditions vertical upflow, downflow and horizontal flow reactors are compared. Conversion in upflow reactors is higher than that in either horizontal flow or downflow reactors. However, catalyst decay is the least in downflow reactors.     

Optimal temperature profiles in tubular reactors for several catalyst decay laws

Theoretical and experimental work on tubular reactors has shown that a high temperature reaction zone can be induced to move counter to the flow of reactants by conduction and/or radiation through the solid phase. This naturally occurring phenomenon represents a transient mode of operation that can be argued to be preferable to conventional modes of operation. In order to test this hypothesis the complete time and space dependent optimal temperature policy was generated for a tubular reactor subject to several catalyst decay laws. The solutions revealed that a critical parameter is the ratio of the activation energy for the main reaction to that for the catalyst decay reaction. For values of this ratio less than one, the optimum temperature profiles represent a low temperature reaction zone that occupies the entire active bed at all times, essentially a conventional mode of operation. However, for this ratio greater than one the profiles represent a short high temperature reaction zone that propagates with time along the length of the reactor. For a catalyst decay law independent of conversion, propagation in either axial direction was optimal, but for a decay law dependent upon conversion the optimization procedure only generated reverse propagating zones.     

Optimal operation of simulated-moving-bed reactors for nonlinear adsorption isotherms and equilibrium reactions

An explicit design procedure for simulated-moving-bed reactors (SMBRs) is presented, incorporating a nonlinear, competitive isotherm, and an equilibrium reaction involving three species, e.g., A⇔B+C. This design procedure is based on an equilibrium theory model of a true-moving-bed (TMB) reactor and it is in close analogy to the well-known design procedure for purely separative SMB-units, the so-called ‘triangle theory’ (Journal of Chromatography A, 769, 3 (1997)). It allows an easy determination of the optimal point of operation and can also evaluate the robustness of an operation point. The operating region of full conversion and complete separation for the TMBR is compared to the one of a purely separative TMB unit, to which only the products are fed. The underlying explicit relations for the new design procedure are presented and their reliability is validated by comparison with experimental data of a SMBR for the synthesis of methyl acetate.     

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.     

Optimal operation of ethylene polymerization reactors for tailored molecular weight distribution

This work presents a comprehensive steady‐state model of the high‐pressure ethylene polymerization in a tubular reactor able to calculate the complete molecular weight distribution (MWD). For this purpose, the probability generating function technique is employed. The model is included in an optimization framework, which is used to determine optimal reactor designs and operating conditions for producing a polymer with tailored MWD. Two application examples are presented. The first one involves maximization of conversion to obtain a given MWD, typical of industrial operation. Excellent agreement between the resulting MWD and the target one is achieved with a conversion about 5% higher than the ones commonly reported for this type of reactor. The second example consists in finding the design and operating conditions necessary to produce a polymer with a bimodal MWD. The optimal design for this case involves a split of the initiator, monomer, and modifier feeds between the main stream and two lateral injections. To the best of our knowledge, this is the first work dealing with the optimization of this process in which a tailored shape for the MWD is included. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007     

Analysis of deactivation disguised kinetics in transport reactors by periodic operation

Deactivation disguised kinetic schemes in an isothermal transport reactor are differentiated by means of periodic operation of the reactor. A periodic rectangular pulse is assumed for the inlet concentration. Three numerical examples are given to demonstrate that the deactivation disguised kinetic models give different conversions under periodic operation.     

使用管式过滤器和树脂塔的注意事项

从α－纤维素、安装维修、盐水质量、操作条件等方面分析管式过滤器,从树脂质量、操作条件、盐水水质、压差等方面分析树脂塔使用过程中易出现的问题,指出注意事项。     

Optimal temperature profiles for parallel-consecutive reactions with deactivating catalyst

A cocurrent tubular reactor with temperature profile control and recycle of moving deactivating catalyst has been investigated. For the temperature-dependent catalyst deactivation, the optimization problem has been formulated in which a maximum of a profit flux is achieved by the best choice of temperature profile and residence time of reactants for the set of catalytic reactions A+B→R and R+B→S with desired product R, the rates of reactions have been described separately for every reagent by the expressions containing (temperature dependent) reaction rate constants, concentrations of reagents, catalyst activity, as well as catalyst concentration in the reacting suspension and a measure of the slip between reagents and solid catalyst particles. The algorithms of maximum principle have been used for optimization. The optimal solutions show that a shape of the optimal temperature profile depends on the mutual relations between activation energies of reactions and catalyst deactivation. It has been proved that the optimal temperature profile is a result of the compromise between the overall production rate of desired reagent R (production rate in the first reaction minus disappearance rate in the second one), necessity of saving of reagents residence time (reactor volume) and necessity of saving catalyst; the most important influence on the optimal temperature profile is associated with necessity of saving the catalyst. When catalyst recycle ratio increases (mean number of catalyst particles residing in reactor increases), optimal temperatures save the catalyst, as the optimal profile is shifted in direction of lower temperatures. The same is observed when catalyst slip increases (catalyst residence time in reactor increases). Despite of variation in the catalyst concentration the optimal profile is practically the same because the decay rate is affected only by instantaneous activity of catalyst. When reactor unit volume price decreases, catalyst residence time increases, whereas optimal temperature profile is shifted to lower temperatures. When economic value of unit activity of outlet catalyst increases (catalyst with a residual activity still has an economic value), catalyst saving should be more and more intense. As far as possible, the optimal profile is shifted in direction of lower temperatures, whereas the optimal residence time is still the same. Then the optimal profile is isothermal at the level of minimum allowable temperature, whereas the catalyst is saved as its residence time in reactor decreases.     

Optimal Control for Chemical Reactors with Distributed Parameters Using Genetic Algorithms

Genetic algorithms (GA) have been very seldom applied in the optimization of chemical reactors with distributed parameters, described by models containing differential equations. GA are applied here in the frame of four case studies. In all four cases, the GA are superior in comparison to other methods, such as maximum principle (up to 20.72 %), simulated annealing (up to 0.11 %), and particle swarm optimization (up to 36.74 %). Possibly, the solutions obtained by GA can be improved by a better selection of the values of the method parameters, but this was not the aim of the present work. The use of optimal control can produce an important economic improvement, especially by increasing the selectivity, which significantly enhances the use of raw materials.     

Function space methods for analysis of nonadiabatic tubular reactors with axial mixing-I. Uniqueness criteria of the steady state and computation of the steady state profiles

Use is made of abstract function spaces to investigate the uniqueness of the steady state of nonadiabatic tubular reactors with axial mixing. For the study, the system differential equations are first transformed into integral equations. The properties of the integral operators are then investigated in the space of square integrable functions in order to obtain sufficient conditions for the uniqueness of solution of the system equations. A uniqueness criterion is obtained by use of the Contraction Mapping theorem, which permits one to compute the steady state profiles of reactor temperature and concentration by means of successive iteration with the transformed integral system equations. The computation involved here is quite simple compared to the numerical solution of the system differential equations with split boundary conditions. Numerical examples are given to investigate the effects of various system parameters on the steady state profiles of reactor temperature and concentration.     

醋酸甲酯侧反应精馏过程的多变量动态控制

侧反应器与精馏塔的耦合结构与物料交换方式的灵活性,造成系统的自由度高、设计变量多,增加了该过程的稳态优化模拟和动态控制的难度。针对侧反应精馏过程(SRC)的平滑操作和自动控制问题,以醋酸甲酯工业生产过程为例,采用基于独立反应量的稳态设计方法获取最佳的反应精馏集成结构和操作参数,在此基础上设计了以产品成分调节变比值控制为主的多变量控制方案,并通过在Aspen流程模拟软件建立醋酸甲酯侧反应精馏动态流程模拟系统,验证控制方案的有效性。     

Continuous polymerization in tubular reactors with prepolymerization: Analysis using two‐dimensional phenomenological model and hybrid model with neural networks

Continuous polymerization processes have advantages when large amounts of product are required; moreover, higher quality can be obtained because of the elimination of variability between batches. Tubular reactors are economically attractive because of their simple geometry and high heat exchange area; however, they are not commonly used for commercial purposes, mainly because of the large radial profiles. This study elucidates the operation of this kind of reactors in three different ways: first a detailed two‐dimensional mathematical model was developed, in which a complete visualization of all axial and radial profiles is possible, allowing a safe analysis at different operating conditions. In a second step a system composed of a continuously stirred tank reactor in series with a tubular reactor was used. A reduction in radial profiles can be clearly observed when prepolymerization is taken into account, improving both the homogeneity and the end properties of the polymer. In a third approach neural networks (NNs) were used in parallel with a one‐dimensional model. The objective of this study was to illustrate how NNs can improve the prediction capability when it is not possible to build a reliable model because of uncertainties in parameters and incomplete knowledge of the system. The NNs generated good results, showing that the hybrid model was able to accurately simulate the reactor, even when uncertainty in kinetic and diffusional parameters was imposed to the model. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 871–882, 2004     

A highway in state space for reactors with minimum entropy production

Thousands of numerical solutions of an optimal control problem for plug flow reactors were found to give, what we call a “highway in the reactors’ state space”. The problem was to find the heat transfer strategy which minimise the entropy production in reactors with fixed chemical conversion. The control variable was always the temperature of the heating/cooling medium along the reactor. The highway represents the most energy efficient way to travel far in state space. Such highways were studied for five reactor systems, endothermic and exothermic ones. Numerical analysis showed that the reactor highway is characterised by approximately constant thermodynamic driving forces/local entropy production for reasonable process intensities. Each solution represents a compromise between the entropy production of reactions, heat transfer and frictional flow (pressure drop). The solutions enter and leave the highway at different positions depending on how far from the highway their initial and final destinations are. Knowledge about the nature of the highway, e.g. when the reactor operates in a reaction mode or a heat transfer mode, may be important for energy efficient reactor design. The theoretical formulation of the optimisation problem is valid for plug flow as well as batch reactors. We showed that important results in literature like the Spirkl-Ries quantity, the theorems of equipartition of entropy production and equipartition of forces are contained in our general formulation. The numerical results showed that the analytical results are good approximations to the optimum also in problems where they do not apply in a strictly mathematical sense.     

MPC of distillation column with side reactors for methyl acetate

This paper focuses on the dynamic control of distillation column with side reactors(SRC)for methyl acetate pro-duction.To obtain the optimum integrated structure and steady state simulation,the systematic design approach based on the concept of independent reaction amount is applied to the process of SRC for methyl acetate produc-tion.In addition to the basic control loops,multi-variable model predictive control modular with methyl acetate concentration and temperature of sensitive plate is designed.Then,based on process simulation software Aspen Plus,dynamic simulation of SRC for methyl acetate production is used to verify the effectiveness of the control scheme.     

Analysis of the lumped and distributed optimal temperature trajectories for packed bed reactors with concentration dependent catalyst deactivation

Algorithms published previously by the authors for solving the problem of spatially uniform and non-uniform temperature optimal control in tubular fixed bed reactors have been applied to three systems with series catalyst deactivation and different ratios between the activation energies of the main and deactivation reactions. The optimal temperature and conversion trajectories as well as the maximum production obtained have been compared at the same final duration of operation. Systems with slow deactivation obtain maximum production with spatially uniform control, whilst for systems with rapid deactivation the temperature trajectory distributed both in space and time improves the production obtained with lumped control.     

Kinetic model for the esterification of free fatty acids from palm oil with methanol using sulfuric acid as catalyst and sensitivity analysis in tubular reactors

Industrial biodiesel production from crude palm oil (CPO) by homogeneous transesterification requires some conditioning stages. One is deodorization, where free fatty acids (FFA) are stripped out from the CPO. The FFA from the deodorizer is esterified using a homogeneous acid catalyst to produce more biodiesel and improve process profitability. This work studied the sulfuric acid-catalyzed esterification of FFA with methanol. The factors evaluated were temperature (between 40 and 60°C) and catalyst concentration (between 0.15 and 1.5 wt% based on the mixture). The parameters of a reversible second-order kinetic model were adjusted from experimental data using a genetic algorithm. The kinetic model, which adequately represents the esterification reaction, according to the Fisher–Snedecor test, was used to perform a sensitivity analysis in isothermal, adiabatic, and non-isolated continuous tubular esterification reactors using ASPEN HYSYS V10. The results showed that the highest conversion (~96%) was predicted using an isothermal reactor. However, its installation and operational costs could also be the highest. An adiabatic reactor was preferred, which optimal conversion of 94.5% was predicted at temperature, catalyst concentration, residence time, and methanol-to-FFA molar ratio of 140°C, 0.3 wt%, 47 min, and 6.7, respectively, its predicted operational cost was 0.63 dollars per biodiesel kilogram. Therefore, the adjusted and validated model has a relevant importance in the biofuel sector, not only in Colombia, but also worldwide.     

Numerical evidence for a “highway in state space” for reactors with minimum entropy production

We report on the nature of the state of minimum entropy production. Thousands of solutions for this state in chemical reactors controlled by the temperature of the coolant medium, show that the solutions fall more or less on what we have called a “highway in state space”. The solutions were found using optimal control theory for reactors that produce a fixed amount of product. A subset of the solutions, for the oxidation of sulphur dioxide, is presented. Each solution gives the most energy-efficient way of operating a reactor for the given boundary conditions. For reasonable process intensities, the highway is characterised by approximately constant entropy production and driving forces, but not necessarily by linear flux-force relations. Knowledge about the highway has implications for energy-efficient reactor design. The results give theoretical support to engineering practices.