A mathematical model of the productivity index of a well

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Title: A mathematical model of the productivity index of a well
Author: Khalmanova, Dinara Khabilovna
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 a 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 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 in numerical study of evaluating the productivity index of a well in a general three -dimensional reservoir for a variety of well configurations .
URI: http : / /hdl .handle .net /1969 .1 /301
Date: 2004-09-30

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A mathematical model of the productivity index of a well. Available electronically from http : / /hdl .handle .net /1969 .1 /301 .

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