Reservoirs With Spatially Varying Properties: Estimation of Volume From Late Transient Pressure Data

Abstract

The transient pressure in a reservoir of arbitrary shape and spatially varying properties is expressed in terms of the eigenvalues and eigenfunctions of the region. Although these eigenvalues and eigenfunctions cannot be obtained analytically, except in homogeneous reservoirs of regular shape, the structure of the solution allows the estimation of the pore volume in the general case using data in the pseudosteady or the late-transient period. A least-squares analysis of late transient data is presented which yields, in addition to the pore presented which yields, in addition to the pore volume, the first eigenvalue, which can often be related to reservoir properties. Numerical examples are given using simulated data from a rectangular 4 x 1 reservoir with constant permeability and with spatially varying permeability.

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