Alcino Resende Almeida

Integral transform methodology for convection-diffusion problems in petroleum reservoir engineering

The convection-diffusion equation is present in the formulation of many petroleum reservoir engineering problems. A representative example, the tracer injection problem, is solved analytically here, through the generalized integral transform technique so as to illustrate the usefulness of this approach, for this class of problems. Classical assumptions, such as steady-state single phase flow and unit mobility ratio, are adopted. Comparisons with alternative analytical (when available) or numerical (finite difference) solutions are performed and benchmark results are established.

A comparison of convergence acceleration schemes for eigenfunction expansions of partial differential equations

Different possibilities for the enhancement of convergence rates in eigenfunction expansions are investigated in the realm of integral transform solutions for partial differential equations. A representative parabolic problem is chosen to illustrate two schemes and their combinations; a filtering technique and an integral balance approach. Numerical results are presented to confirm the relative merits in each proposed procedure.

On the integral transform solution of convection–diffusion problems within unbounded domain

Abstract The solution of convection–diffusion problems, defined within unbounded regions, is investigated by making use of the generalized integral transform technique. This hybrid numerical- analytical approach, widely employed in the solution of various classes of problems within finite domains, is tested in the handling of unbounded domains through two different schemes, namely, a plain domain truncation procedure and a coordinate transformation approach. Numerical results are obtained from a linear Burgers-type model in order to illustrate the relative merits in each proposed solution scheme.