DYNAMIC MODELLING AND CONTROL OF A TUBULAR REACTOR

Abstract

Tubular reactors are widely used in process industries for manufacturing chemicals. A tubular reactor is simply a tube or pipe through which reaction mixture flows and during its passage, chemical reaction takes place to produce valuable products as well as other byproducts. In case of exothermic or endothermic reaction, the tubular reactor is likely to be cooled or heated by a co-currently or countei—currently moving coolant or heating media as the case may be. A comprehensive one-dimensional mathematical model of the tubular reactor, based on axial dispersion flow pattern, consists of three partial differential equations, which are of convection-diffusion type. One equation corresponds to mass balance for the reacting species and the remaining two are for the energy balances in the reactor and coolant/heating section. Increase in number of reactions results in increase in number of model equations due to mass balance for species of each reaction. Besides, it has few constitutive relationships, viz. equation for the rate of reaction and correlations for physical properties. Initial and boundary conditions are naturally associated with the model. In almost last four decades, analysis, modelling and control of tubular reactors have been the interesting and challenging fields of research for chemical and control engineers, and applied mathematicians, Review of literature has revealed that in spite of so much wealth of information on this simple process equipment, there still remains something more which is yet to be explored. In the present thesis, research efforts have been directed towards few of the vital aspects of a tubular reactor, e.g. numerical solution of model equations, estimation of parameters, and control system synthesis along with algorithm development. Salient features of the developments made and results obtained in the thesis have been described in the following paragraphs. i A general algorithm has been developed and programmed in FORTRAN 77 to solve the dynamic model equations of a tubular reactor. It is based upon Control Volume Finite Difference method. It is easy to use and program. In this algorithm, the coefficient matrix of discretized equations is tridiagonal in structure and therefore, the set of equations may easily be solved by Thomas algorithm. Tridiagonal structure requires less storage space even for a large number of grid points. Accuracy of numerical solution obtained by the algorithm has been checked with analytical results available for a linear reaction in tubular reactor, and also with the computed results for a limiting situation under steady state conditions. Its predictions have been found to be correct. Further, the algorithm employs a relaxation parameter(A), but the numerical solution has been observed to be insensitive to this parameter. Its application has been demonstrated with an example. A new parameter estimation method has been developed for estimating the parameters of a general system, modelled by convection-diffusion equations. The method assumes that the measurements of only one dependent variable are available at few locations and at several instants of time. It is also assumed that these are free from any kind of error. Besides, the method utilizes the control volume finite difference method to solve the model equations. In this method, advantage is that the converged solution of model equations results into the values of dependent variables which satisfy them in discretized form at all the grid points. Due to this fact, a novel idea has been proposed for the computation of weight factors on the basis of predicted values of other dependent variables, whose measurements are not available at all. Generalized expression for the weight factor has been derived, which may then be used to minimize the objective function by a suitable optimization method. Applicability of this method has been illustrated by taking an example of nonisothermal tubular chemical reactor operating at steady state, for which experimental data were available in the literature. Further, a control system for the tubular reactor-unit has been 11 synthesized, which is a combination of feedforward, feedback and inferential control configurations. It requires the measurement of disturbance, and temperature at four locations. The example reactor possesses fast dynamics; transient period for a given disturbance varies between 20 and 100 s. Therefore, a control scheme has been developed by using heuristic approach, which does not require much on-line computation. For feedforward control configuration, information obtained by solving the steady state model equations has been utilized. Besides, necessary equations correlating the disturbance, manipulated and control variables have also been developed. Rigorous testing of proposed control scheme has been conducted by numerical simulation. In doing so, step-up and step-down disturbances were introduced in either feed velocity or feed inlet temperature. In order to simulate both the ideal and real situations, studies were carried out with the Instantaneous and Delayed control actions. Control scheme also consists of a relaxation parameter (R ) and it should be selected judiciously. For all the cases, its optimum value varies between 0.4 and 0.9. In feedforward control loop, correlations used are empirical in nature and applicable for certain ranges of variables. Control scheme was also tested under situations for which range of validity of correlations was violated. Nevertheless, reactor-unit could be controlled within acceptable bandwidth in overall percent conversion. Further, effect of change in magnitude of disturbance, and the effect of limiting the range of manipulated variables on the performance of control scheme were also studied, and for almost all cases reactor-unit could be controlled satisfactorily. In summary, developed control scheme is robust in controlling a fast process, provided the proper selection of R is made. It is our view that the research work carried out in the thesis iii has wider scope for its application as many engineering systems are modelled by convection-diffusion equations. Computational algorithm may also be applied to fixed-bed reactors, represented by pseudo-homogeneous model, double pipe and shell and tube heat exchangers. Parameter estimation method is quite general in nature and the definition of weight factor is based upon sound physical logic. Procedure for developing control scheme for a fast process may also be adopted for other similar systems. Experimental implementation of control scheme on the reactor-unit is also recommended for future work.