Abstract
Homogeneous core samples are needed for EOR experiments. We have devised a simple test for detecting the presence of nonuniformities in cores. The test consists of presence of nonuniformities in cores. The test consists of measuring the pressure drop across the core during a two-phase immiscible displacement experiment. We show that for a constant injection rate, the pressure drop will be linear with time provided that the core is homogeneous. In situations for which the initial section of the core is homogeneous, but the properties are not uniform in a latter section of the core, the location of the position where the rock properties fast change may be approximately determined. The effect of heterogeneities on the pressure-drop profile is demonstrated with analytical solutions and profile is demonstrated with analytical solutions and laboratory experiments.
Introduction
Core samples are used routinely for EOR or relative permeability experiments. For such experiments, selection permeability experiments. For such experiments, selection of a homogeneous core sample is necessary. Visual inspection of the core is not sufficient to ensure homogeneity. Often, vugs or shale barriers may be present, which may invalidate experimental results. In this paper, a simple test to detect the presence of core heterogeneities is devised.
The scale of heterogeneities considered corresponds to the usual macroscopic description of porous medium properties. The properties of a porous medium (e.g., the properties. The properties of a porous medium (e.g., the porosity and permeability) at any particular location refer porosity and permeability) at any particular location refer to average quantities for some appropriate (small) representative volume element. In this way, each (locally averaged) property is defined at every point within the medium, the collection of which defines the representation of each property as a function of position. If each macroscopic property has the same value at all positions, the medium is said to be homogeneous. Otherwise, the medium is heterogeneous. A more complete discussion of macroscopic properties and heterogeneities can be found in Refs. 1 through 3.
The macroscopic scale is a natural one to use for core selection because attempts to model coreflood experiments or to estimate properties of the porous medium on the basis of measured flow data generally will use mathematical models that use macroscopic properties. A homogeneous core sample is necessary for the experimental determination of relative permeabilities from displacement experiments. Explicit methods for estimating relative permeabilities from displacement data are based on the permeabilities from displacement data are based on the Buckley-Leverett model, in which the core is assumed to be homogeneous. The absolute permeability generally is determined from a single-phase flow experiment and thus represents an average value for the entire core. If the core is not homogeneous, so that the absolute permeability takes on different values in different locations permeability takes on different values in different locations in the core, errors will appear in the relative permeability estimates. Although the magnitude of the errors will depend on many factors, a macroscopically homogeneous sample is always preferred.
Note that heterogeneities may also be defined on a microscopic scale. A porous medium that is macroscopically homogeneous may be microscopically heterogeneous. In fact, this typically would be the case because few real porous media structures are microscopically homogeneous.
In this paper, we develop a test for detecting the presence of macroscopic heterogeneities in core samples. presence of macroscopic heterogeneities in core samples. The test is conducted by displacing the fluid that initially saturates the porous medium with a second fluid that is immiscible with the displaced fluid. The pressure drop across the core is recorded up to the time of breakthrough of the displacing fluid. The test is based on the observation that, with a constant injection rate and incompressible fluids, the pressure drop will be linear with time provided that the core is homogeneous. It is also shown provided that the core is homogeneous. It is also shown that, if the porosity and permeability for a heterogeneous core may be approximated as functions of the longitudinal spatial dimension, the pressure drop will be linear with time provided that the region in which both fluid phases are flowing simultaneously has uniform properties. The detection of heterogeneities by this method is discussed and illustrated with analytical solutions for the displacement process and with laboratory experimental data.
Theory
We consider here a displacement experiment with two incompressible fluids. Initially, the core is saturated with one fluid and the other fluid is injected at one end. For example, if the core initially contains only oil or air, water might be injected at one end. The core could contain the irreducible saturation of the displacing fluid initially, although this is not experimentally convenient and is not necessary for conducting the test. The pressure drop across the core is recorded through the time of breakthrough of the displacing fluid at the core outlet.
SPEJ
P. 909
Determining Triaxial Stress Sensitivity of Oil Reservoir Rocks without Fluid Flooding