P.L. Mills

Determination of polymer chain length distributions by numerical inversion of z-transforms

Abstract A numerical technique is presented for evaluation of the polymer chain length distribution in polymerization reaction engineering models whose governing equations can be represented in the z -transform domain. The method is based upon an appropriate z -transform inversion relationship that has the form of an inverse discrete Fourier transform which can be efficiently evaluated by the fast Fourier transform algorithm using various existing computer software. The approach is illustrated through several example problems involving polymerization systems and comparisons are made to other alternate solution methods. One of the example problems includes a complex reaction network for polycarbonate polymerization as a novel application. It is shown that the proposed technique requires an order-of-magnitude less computer time to evaluate the polymer MWD when compared to direct numerical integration.

A new model for assessment of external liquid-solid contacting in trickle-bed reactors from tracer response measurements

Abstract The dynamic response of a trickle-bed reactor is analyzed assuming that the external surface of the catalyst is only partially wetted. This leads to a new type of transient mixed boundary value problem which is solved by a dual series technique. The solution presented in the Laplace transform s-domain provides a method for determining the contacting efficiency without the need for invoking any heuristic arguments as done in the earlier studies

A numerical study of approximation methods for solution of linear and nonlinear diffusion-reaction equations with discontinuous boundary conditions

Abstract Three different approaches based upon the least-square method of weighted residuals, an integral equation method and the finite element method are used to obtain approximate solutions to diffusion-reaction equations in two-space dimensions having d It is shown through a selected example problem having physical significance that all three methods give similar results for the case where regular geom Extension of the finite element method to systems described by nonlinear power-law reaction rate equations where the other methods cannot be used is al

Solution of Mixed Boundary Value Problems by Integral Equations and Methods of Weighted Residuals with Application to Heat Conduction and Diffusion-Reaction Systems

Integral equation methods are considered as an alternate approach for the solution of mixed boundary value problems in heat conduction or diffusion with chemical reaction that can be described by dual or triple series equations. The approach is based upon reduction of the dual or triple series to a single or a set of Fredholm integral equations of the first kind whose kernel

Catalytic amination of methyl tertiary-butyl ether to tertiary-butylamine over pentasil molecular sieves

K(x,y)

Solution methods for a class of linear and nonlinear diffusion—reaction equations with mixed boundary conditions

and forcing function

Analysis of multiphase polycarbonate polymerization in a semibatch reactor

f(x)

Design of semi-batch gas-liquid-liquid polymerization reactors with application to interfacial condensation

are presented in terms of an appropriate infinite series which can be derived from the separation-of-variables solution. The solution of the integral equation for the unknown function

Approximation methods for linear and nonlinear diffusion-reaction equations with discontinuous boundary conditions

g(y)

Catalytic hydrodesulfurization of a specialty agricultural chemical intermediate

is obtained by a modified quadrature method which accounts for the presence of a logarithmic singularity in the kernel for