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.     

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.     

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.     

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.     

pH控制在管状流动反应器中的应用(英文)

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 reactors. In the present work, sodium hydroxide and acetic acid solutions were sent to the tubular flow reactor. The aim was to control pH at 7 in the nonlinear region. The pH control of a tubular flow reactor with high time delay and a highly nonlinear behavior in pH neutralization reaction was investigated experimentally in the face of the various load and set point changes. Firstly, efficiency of conventional Proportional-Integral-Derivative (PID) algorithm in the experiments was tested. Then self-tuning PID (STPID) control system was applied by using the ARMAX model. The model parameters were calculated from input–output data by using PRBS signal as disturbance and Bierman algorithm. Lastly, the experimental fuzzy control of pH based on fuzzy model was achieved to compare the success of fuzzy approach with the performance of other control cases studied.     

Mathematical modelling of a reverse flow reactor with catalytic surface dynamics

This paper studies a system of partial differential equations modelling the behaviour of a reverse flow reactor. For the parameters appropriate for the oxidation of ammonia on a Pt/Al₂O₃ catalyst in a typical laboratory set-up, the reactor may be split into regions where approximate formulas that determine its behaviour are deduced. Numerical calculations are presented and can be used to compare with the analytical formulas. The physical insight gained from the asymptotic analysis suggests a new switching strategy which is the subject of numerical experiments. The switching strategy is found to be efficient at minimising the ammonia exiting the reactor after reversal.     

A model predictive formulation for control of open-loop unstable cascade systems

Cascade control is commonly used in the operation of chemical processes to reject disturbances that have a rapid effect on a secondary measured state, before the primary measured variable is affected. In this paper, we develop a state estimation-based model predictive control approach that has the same general philosophy of cascade control (taking advantage of secondary measurements to aid disturbance rejection), with the additional advantage of the constraint handling capability of model predictive control (MPC). State estimation is achieved by using a Kalman filter and appending modeled disturbances as augmented states to the original system model. The example application is an open-loop unstable jacketed exothermic chemical reactor, where the jacket temperature is used as a secondary measurement in order to infer disturbances in jacket feed temperature and/or reactor feed flow rate. The MPC-based cascade strategy yields significantly better performance than classical cascade control when operating close to constraints on the jacket flow rate.     

Considerations on nonlinear model predictive control techniques

The nonlinear model predictive control (NMPC) is an on-line application based on nonlinear convolution models. It is an appealing control methodology, but it is difficult to implement and its solution is not so performing since it unavoidably means to solve a usually large-scale, constrained, and multidimensional optimization. To increase the difficulty, this optimization problem is subject to computationally heavy differential and algebraic constraints constituting the same convolution model and the least squares nature of the objective function easily leads to narrow valleys and multimodality issues.Beyond a short review of the state-of-the-art, the paper is aimed at highlighting the possibility to exploit at best the intrinsic features of the specific system one is going to control using the NMPC. The idea is to give the NMPC the possibility to automatically select the best combination of algorithms (differential solvers and optimizers) in accordance with the specific problem to be solved. From this perspective, the NMPC could be easily extended to many scientific fields traditionally far from process systems and computer-aided process engineering and the user has not to worry about which specific differential solvers and optimizers are needed to solve his/her problem.     

Infinite horizon model predictive control with no terminal constraint

This paper investigates the constrained infinite horizon linear quadratic regulator (CIHLQR). In particular, it is shown that the terminal set inclusion condition that is associated with this control law introduces limitations into the control system. By relaxing this condition, it is demonstrated that the resulting controller will in many cases remain equivalent to CIHLQR. It is further shown that CIHLQR with a relaxed terminal set inclusion condition offers significant benefits, in terms of computational expense and performance when compared with standard finite horizon model predictive control (MPC) approaches.