Scaling and sensitivity analysis of a reverse flow reactor

Scaling analysis is presented as a systematic procedure to analyze and understand the operation of a complex process such as the autothermal reverse flow reactor (RFR). The reactor is complex from an operational point of view due to its hybrid and periodic nature. An adequate model of the RFR involves highly nonlinear equations. Using simple mathematical operations, these model equations are non-dimensionalized, scaled to order 1 and used to determine the contributions of the controlling physical phenomena taking place in it. The scale factors lead to several analytical expressions useful for suggesting efficient operational strategies for the RFR. Based on a specified error tolerance, we also illustrate how model approximation can be carried out and justified. The sensitivity of important operational parameters that determine sustainability (i.e., maximum temperature and overall conversion) to variables such as reactor length, switching time and mass transfer rate are also analyzed for the pseudo-steady-state condition. The results obtained prove that prudent ways of operating an RFR can be determined through scaling and sensitivity analysis.     

Hybrid fuzzy model-based predictive control of temperature in a batch reactor

Processes in industry, such as batch reactors, often demonstrate a hybrid and non-linear nature. Model predictive control (MPC) is one of the approaches that can be successfully employed in such cases. However, due to the complexity of these processes, obtaining a suitable model is often a difficult task. In this paper a hybrid fuzzy modelling approach with a compact formulation is introduced. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for the hybrid fuzzy modelling purposes is presented. An efficient method for identifying the hybrid fuzzy model is also proposed.

A MPC algorithm suitable for systems with discrete inputs is treated. The benefits of the MPC algorithm employing the proposed hybrid fuzzy model are verified on a batch-reactor simulation example: a comparison between MPC employing a hybrid linear model and a hybrid fuzzy model was made. We established that the latter approach clearly outperforms the approach where a linear model is used.     

Hybrid fuzzy predictive control based on genetic algorithms for the temperature control of a batch reactor

In this paper we describe the design of hybrid fuzzy predictive control based on a genetic algorithm (GA). We also present a simulation test of the proposed algorithm and a comparison with two hybrid predictive control methods: Explicit Enumeration and Branch and Bound (BB). The experiments involved controlling the temperature of a batch reactor by using two on/off input valves and a discrete-position mixing valve. The GA-hybrid predictive control strategy proved to be a suitable method for the control of hybrid systems, giving similar performance to that of typical hybrid predictive control strategies and a significant saving with respect to the computation time.     

Control of a reverse flow reactor for VOC combustion

A flow reversal reactor for VOC combustion is controlled by the linear quadratic regulator (LQR), which uses dilution and internal electric heating as controls to confine the hot spot temperature within the two temperature limits, in order to ensure complete conversion of the VOC and to prevent overheating of the catalyst. Three phases of operation, i.e., dilution phase, heating phase and inactive phase, are identified. In dilution and heating phases, the cost functions of the LQR control are defined in quadratic forms. In the inactive phase, the controllers are inactivated. A linear model is derived by linearization of a countercurrent pseudo-homogeneous model at two nominal operating conditions in the dilution phase and the heating phase, respectively. The feed concentration and the temperature profile are estimated on-line by using a high-gain observer with three temperatures measurements and are used in the LQR feedback control. Experiments are carried out on a medium-scale reversed flow reactor to demonstrate the proposed LQR control strategy. Results show that the LQR controller is highly efficient in maintaining normal operation of the reactor.     

Enhanced model predictive control of a catalytic flow reversal reactor

The combustion of lean methane air mixtures in a catalytic flow reversal reactor (CFRR) is studied using a two dimensional heterogeneous continuum model, based on mole and energy balance equations for the solid (the inert and catalytic sections of the reactor) and the fluid phases. Following a design of experiments (DOE), many simulations were carried out to investigate the reactor performance. The results show the impact on the methane conversion and the maximum temperature in the reactor of key process parameters such as the methane inlet concentration, the superficial gas velocity, the switching time, and the mass extraction rate. A simple empirical model is deduced to predict the maximum temperature and conversion of methane in the reactor at stationary state. This model is combined with a model predictive control (MPC) strategy in the form of a terminal constraint to improve the controller performance. Results show that the control of the reactor is improved.     

LMI-based robust model predictive control for a continuous MMA polymerization reactor

A linear matrix inequality (LMI)-based robust model predictive control (MPC) is applied to a continuous stirred-tank reactor for the polymerization of methyl methacrylate (MMA). The polytopic model is constructed to predict the responses to various control input sequences by using Jacobians of uncertain nonlinear model at several operating points and the controller design is characterized as the problem of minimizing an upper bound on the ‘worst-case’ infinite horizon objective function subject to constraints on the control input and plant output. Simulation studies under different conditions are conducted to validate the feasibility of the optimization problem and evaluate the applicability of such a control scheme. Simulation results show that, despite the model uncertainty, the LMI-based robust model predictive controller performs quite satisfactorily for the property control of the continuous polymerization reactor and guarantees the robust stability.     

Optimization of a flow reversal reactor for the catalytic combustion of lean methane mixtures

This paper describes a parametric study of a catalytic flow reversal reactor used for the combustion of lean methane in air mixtures. The effects of cycle time, velocity, reactor diameter, insulation thickness, thermal mass and thermal conductivity of the inert sections are studied using a computer model of the system. The effects on the transient behaviour of the reactor are shown. Emphasis is placed on the effects of geometry from a scale-up perspective. The most stable system is obtained when the thermal mass of the inert sections is highest, while thermal conductivity has only a minor effect on reactor temperature. For a given operation, the stationary state depends on the combination of velocity and switch time. Provided that complete conversion is achieved, highest reactor temperature is achieved with the highest switch time. The role of the insulation is not only to prevent heat loss to the environment, but also to provide additional thermal mass. During operation heat is transfer to and from the insulation. The insulation effect leads to higher reactor temperature up to a maximum thickness. The insulation effect diminishes as the reactor diameter increases, and results in higher temperatures at the centreline.     

Combustion of toluene-hexane binary mixtures in a reverse flow catalytic reactor

This work is focused on the application of reverse flow reactors to the combustion of lean mixtures of aliphatic and aromatic hydrocarbons in air. For this purpose, hexane and toluene were chosen as model compounds. The combustion of binary mixtures of these compounds (up to 500 ppmV total hydrocarbon concentration) over a commercial Pt/Al₂O₃ catalyst in reverse flow reactors has been studied both experimentally, in a bench-scale unit, and by simulations, using a heterogeneous mono-dimensional dynamic model, good correspondence being observed between both approaches.As general trend, it was observed that the behaviour of the reactor is determined mainly by the combustion enthalpies and reactivities of toluene and hexane. Hence, increasing total concentration and increasing fraction of toluene (the most reactive compound) lead to more stable operation. Regarding the kinetic inhibition effects, in the conditions studied no influence on the reactor performance was observed, probably because the hydrocarbons combust in different reactor zones. This behaviour can be extended to the combustion of aromatic and C₅-C₈ alkanes, characterised by their relatively low concentrations (determined by their vapour pressure) and high reaction rates.     

A dynamic programming based approach for explicit model predictive control of hybrid systems

This work presents an algorithm for explicit model predictive control of hybrid systems based on recent developments in constrained dynamic programming and multi-parametric programming. By using the proposed approach, suitable for problems with linear cost function, the original model predictive control formulation is disassembled into a set of smaller problems, which can be efficiently solved using multi-parametric mixed-integer programming algorithms. It is also shown how the methodology is applied in the context of explicit robust model predictive control of hybrid systems, where model uncertainty is taken into account. The proposed developments are demonstrated through a numerical example where the methodology is applied to the optimal control of a piece-wise affine system with linear cost function.     

A Monte-Carlo based model approximation technique for linear model predictive control of nonlinear systems

In this paper we present a model approximation technique based on N-step-ahead affine representations obtained via Monte-Carlo integrations. The approach enables simultaneous linearization and model order reduction of nonlinear systems in the original state space thus allowing the application of linear MPC algorithms to nonlinear systems. The methodology is detailed through its application to benchmark model examples.     

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.     

Long range predictive control of a polymerization reactor

This paper examines the application of generalized predictive control (GPC), one in the class of long-range predictive algorithms, to the control of conversion of methyl methacrylate (MMA) monomer in a simulated CSTR, and to the control of temperature in a pilot plant batch polymer reactor. The control objective is regulation in the presence of (i) stochastic disturbances due to impurities (in the case of the CSTR), and (ii) pulse disturbances from the addition of cold solvent and initiator (in the case of the batch reactor). The role of the observer polynomial as a detuning parameter for trading off performance against variability in the control action is emphasized. Also, the role of data prefiltering, prior to model parameter estimation, is examined. A frequency domain interpretation of the least squares estimation algorithm is used to clarify the role of the filter.     

Flow reversal reactor for the catalytic combustion of lean methane mixtures

This paper describes an experimental investigation of a pilot scale reverse flow reactor for the catalytic destruction of lean mixtures of methane in air. It was found that using reverse flow it was possible maintain elevated reactor temperatures which were capable of achieving high methane conversion of methane in air streams at methane concentrations as low as 0.19% by volume. The space velocity, cycle time and feed concentration are all important parameters that govern the operation of the reactor. Control of these parameters is important to prevent the trapping of the thermal energy within the catalyst bed, which can limit the amount of energy that can be usefully extracted from the reactor.     

Stability of model predictive control with time-varying weights

In this paper, we show that the stability of constrained Model Predictive Control (MPC) systems can be guaranteed by using time-varying weights. It unifies two popular MPC algorithms with guaranteed stability - Infinite Horizon MPC and MPC with End Constraint. Use of time-varying weights may also be useful in analyzing stability properties of MPC for linear time-varying systems as well as uncertain linear systems.     

Control of a solution copolymerization reactor using multi-model predictive control

We study the control of a solution copolymerization reactor using a model predictive control algorithm based on multiple piecewise linear models. The control algorithm is a receding horizon scheme with a quasi-infinite horizon objective function which has finite and infinite horizon cost components and uses multiple linear models in its predictions. The finite horizon cost consists of free input variables that direct the system towards a terminal region which contains the desired operating point. The infinite horizon cost has an upper bound and takes the system to the final operating point. Simulation results on an industrial scale methyl methacrylate vinyl acetate solution copolymerization reactor model demonstrate the ability of the algorithm to rapidly transition the process between different operating points.     

Simulation of a Reverse Flow Reactor for the Catalytic Combustion of Lean Methane Emissions

This work is focused on the performance prediction of pilot scale catalytic reverse flow reactors used for combustion of lean methane-air mixtures. An unsteady one-dimensional heterogeneous model for t...     

Analysis of linear programming in model predictive control

The linear programming formulations of model predictive control are known to exhibit degenerate solution behavior. In this work, a multi-parametric linear programming technique is utilized to analyze the control laws that are generated from various linear programming based MPC routines. These various routines explore a number of factors, including objective function selection and constraint handling on the control laws generated from LP based MPC. A single input single output system is used to demonstrate that the use of input velocity penalties, input blocking, and ∞-norm objective functions can limit or eliminate this undesirable behavior. Finally, a paper machine cross directional control problem is used to demonstrate the control laws generated from LP based MPC for a multivariable example.     

Application of pH control to a tubular flow reactor

Tubular flow reactors are mainly used in chemical industry and waste water discharged units. Control of output variables is very difficult because of the existence of high dead-time in these types of r...