Estimation Of Relative Permeability From Low Rate, Unsteady-State Tests - A Simulation Approach
Authors: Fassihi Mohammad R. 
Published: March 2010

Abstract
When unsteady-state relative permeability tests are conducted in sands containing heavy bitumens, the migration of fines can cause problems. To prevent the migration of fines, lower injection rates are required. These lower rates can cause end effects o become important in the interpretation of the unsteady-state relative permeability tests. Also, the low rates can allow gravitational segregation to occur in the core during the test. A simulator was used to investigate the potential impact of both end effects and gravitational segregation on the interpretation. It was found that the additional pressure drop caused by the end effects shifted the estimated relative permeability curves. Also, for the case investigated, capillary forces act to alleviate the effect of gravitational segregation upon the measurements. Some practical means of reducing the end effects at low rates are also discussed in this paper.

Introduction
Measurement of relative permeability using heavy oil and water in unconsolidated sands is a difficult task. Many problems that require special care exist in such experiments. Conventional techniques of measuring relative permeability may not be appropriate for these heavy oils. A serious problem associated with the flow of heavy oil in unconsolidated sands is core plugging due to fines migration. This has prevented many investigators in the past from completing their relative permeability tests. Even if the effects of fines were minimal, displacement of viscous oil at the high rates normally used in the unsteady-state method may not be practical. At higher rates, the natural wettability of the porous medium existing at equilibrium conditions may not be exhibited(2) (core plug might appear oil-wet). To minimize these problems, the injection rate has to be kept below the critical fines mobilization velocity. At these low rates, capillary pressure can have significant effects on the fluid flow. It can change the shock front into a long smeared front.
The phenomenon of "end effects" whereby the wetting phase builds up at the outlet end of the core due to the capillary discontinuity is also significant under capillary-dominated flow of this smeared front. To better define the problems associated with estimating relative permeability from low rates displacement tests, a simulation study was initiated. The goals of the study included:the validation of numerical simulation as a design tool for relative permeability tests,the quantification of capillary and gravity forces, andthe investigation of ways to minimize the end effects.

Governing Equations
The basic equation describing the displacement of one fluid by another in porous media in one dimension can be written in the following form(3):
Equation Available In Full Paper.....(1)
where. ξ is the dimensionless length, g(s) is the ratio of capillary to viscous forces, h(s) is the derivative of the fractional flow curve and T is the number of pore volumes injected, i.e.
Equation Available In Full Paper.....(2)
Equation Available In Full Paper.....(3)
Equation Available In Full Paper.....(4)
Equation Available In Full Paper.....(5)