%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
W. G. Pritchard Lab Seminar: 4:00-5:00 PM, 320 Whitmore Laboratory
**Tuesday September 14, 2004**
Mathematical model for the productivity index of an oil well
Dinara Khalmanova
Department of Engineering Science & Mechanics
Penn State University
Abstract:
Motivated by the reservoir engineering concept of the productivity index of
a producing oil well in an isolated reservoir, we analyze a time dependent
functional, diffusive capacity, on the solutions to initial boundary value
problems for a parabolic equation. Sufficient conditions providing for time
independent diffusive capacity are given for different boundary conditions.
The dependence of the constant diffusive capacity on the type of the
boundary condition (Dirichlet, Neumann or third-type boundary condition) is
investigated using a known variational principle and confirmed numerically
for various geometrical settings. An important comparison between two
principal constant values of the diffusive capacity is made, leading to the
establishment of criteria when the so-called pseudo-steady-state and
boundary-dominated productivity indices of a well significantly differ from
each other. The third type of boundary condition is shown to model the thin
skin effect for the constant wellbore pressure production regime for a
damaged well. The questions of stabilization and uniqueness of the time
independent values of the diffusive capacity are addressed. The derived
formulas are used to numerically evaluate the productivity index of a well
in a general three-dimensional reservoir for a variety of well
configurations.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%