Unsteady-State Response of a Nonlinear Tubular Reactor

8 UNSTEADY-STATE RESPONSE OF A NONLINEAR TUBULAR REACTOR  

Simulation of the adiabatic tubular reactor consists of the solution of the partial differential equations which describe the system. The nonlinear nature of these equations makes solution difficult. A powerful technique developed in recent years for the solution of nonlinear partial differential equations is that of quasilinearization. 

Although the application of quasilinearization requires a detailed and complicated derivation of equations, the basic technique is straightforward. First, one must consider a finite-differenced solution space and a marching-like solution. Here, the solution domain is of two dimensions dimensionless distance from 0 to 1 and open-ended time from the initial 

To initiate the algorithm, a guess for the unknown level solution is needed. The known previous solution level is sufficient. The partial differential equations are linearized about this guess and then finite-differenced and solved. This solution yields an improved estimate to the solution of the nonlinear equations. The linearization is now carried about this new estimate and the process is iterated to desired convergence. The last estimate is taken as the solution for the previously unknown level and used as the initial guess for the next unknown level. The nonlinear solution is marched out in time as fax as desired. 

In order to solve the linearized finite-differenced equations, it is only necessary to invert a high-order coefficient matrix which has a diagonal band form. 

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