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Modeling simultaneous oil and water flow with single-phase analytical solutions
Much computer software used to analyze well test and
production data and to forecast well performance is based on
single-phase analytical liquid or gas solutions. Many
attempts have been made to apply the solutions to model
multiphase flow. Most work, however, has examined only the
simultaneous flow of oil and gas. This dissertation is
intended to apply single-phase analytical liquid solutions to
model multiphase flow of oil and water. Of primary concern
is developing a simple analytical method to forecast the
performance of a well producing oil and water simultaneously
based on the Perrine-Martin approach. Using this approach,
this work critically examines the use of the integral
transformation in oil-water flow problems. Additionally,
this work develops a new single-phase solution using an outer
boundary condition called "the prescribed pressure boundary
condition" that might be more appropriate for reservoirs with
water influx or waterflooding. A specific configuration of
well, cylindrical reservoir, and cylindrical aquifer is used.
The material balance principles are applied to this composite
system such that we can relate the water influx to the well
production variables and reservoir flow properties. The
Fetkovich pseudo-steady state water influx model is used to
relate the cumulative water influx and the reservoir-aquifer
interface pressure. The average reservoir pressure which is
then related to the well performance using single-phase
slightly compressible liquid solutions is calculated using a
material balance equation. The producing water-oil ratio and
the oil and water production rates are obtained from the
total rate using relative permeabilities for oil and water
and Darcy's law assuming zero capillary pressure gradient.
The fluid saturations are computed volumetrically so that the
implicit, Muskat-type relation between saturation and
pressure is not necessary. This volumetric saturation
computation technique does not require knowledge of
saturation distribution in the reservoir. Pre- and post-
breakthrough criteria are based on the application of the
fractional flow principle. Although we consider the
constant-rate production case only, it follows that using the
results of the constant-rate production case, the method can
be readily extended to the constant-pressure production case
using the van Everdingen-Hurst identity and an appropriate
Duhamel's formula (principle of superposition).
Issued also on microfiche from University Microfilms Inc.
Includes bibliographical references: pages 177-180.