A Method for Reducing the Rate Effect on Oil and Water Relative Permeabilities Calculated From Dynamic Displacement Data
Authors: Odeh A.S. , Dotson B.J. 
Published: December 2007

A Method for Reducing the Rate Effect on Oil and Water Relative Permeabilities Calculated From Permeabilities Calculated From Dynamic Displacement Data

Summary
A method is described for significantly reducing the effect of fluid flow rate on oil and water relative permeability values calculated from dynamic displacement data permeability values calculated from dynamic displacement data with the Jones and Roszelle technique. 1 The method, which is simple and easy to use, basically corrects the Jones and Roszelle values to account for the end effect. Successful application of the method was achieved over a 10-fold range of displacement rates with data obtained on several core samples of widely varied properties.
This paper describes the method and compares permeability values calculated by the Jones and Roszelle permeability values calculated by the Jones and Roszelle technique and by the new method. It also compares a few relative-permeability values determined from steady-state data with those calculated by the new method. The comparison shows favorable agreement.

Introduction
Relative permeability values are vital in many reservoir engineering calculations. However, it is difficult to measure relative permeabilities in the laboratory. Two methods of measurement are practiced by the industry-steady state and dynamic displacement techniques.
The primary disadvantage of the steady-state technique has been the lengthy time needed to obtain a complete relative permeability curve. Steady-state measurements require stabilization. To achieve this, several days may be required for each relative-permeability/saturation point; thus, several weeks are necessary to obtain the complete curve.
In the dynamic displacement technique, a small core sample is saturated with water then flooded with oil to irreducible water saturation. The cycle is repeated, and the pressure drop across the core, as well as oil and water production as a function of the injected fluid, is recorded. production as a function of the injected fluid, is recorded. These data. together with the oil and water viscosities, the absolute permeability, and PV of the core, are used to calculate oil and water relative permeabilities as functions of saturations at the effluent end of the core.
The theory upon which the interpretation of dynamic displacement data is based assumes that capillary pressure effect on saturation distribution is negligible. pressure effect on saturation distribution is negligible. It does not account for capillary discontinuity, better known as end effect. These shortcomings are minimized by conducting the experiment at a sufficiently high rate. Even if it is feasible to establish this high rate a priori, the experimental setup may not permit it.
We have observed that the oil relative-permeability values calculated from the dynamic displacement data were strong functions of the displacement rates. Furthermore, the critical displacement rate needed to make the end effect insignificant over a wide range of saturation was, for most purposes, unattainable. The inclusion of the end effect in the interpretive theory is difficult because the boundary condition that exists at the effluent end during the experiment is not well-defined. No rigorous analytical solution has been reported. Consequently, we have resorted to deductive reasoning based on flow behavior to arrive at a method to account for the effect of displacement rate. The method has been tried on several displacement data with success.
In this paper, the method and its logic are explained. The results of its application to sets of experiments on four core samples are shown.

Theoretical Considerations
Experimental results by Richardson et al. in 1952 demonstrated that, for two-phase flow in a core, a relatively uniform saturation distribution was obtained toward the inflow end. However, a zone of increasing wetting-phase saturation existed toward the outflow end with the maximum saturation value occurring at the effluent face. The width of the zone decreased with increased flow rate. It appears that a very high flow rate may be required to remove the zone effectively in every case.
Relative permeabilities to oil and water were calculated with the Jones and Roszelle method-which is an industry-accepted procedure. The oil relative permeabilities were plotted as functions of saturations referred to permeabilities were plotted as functions of saturations referred to the effluent end for various displacement rates (Fig. 1). This figure basically shows three regions. At relatively high oil saturation (Region 1), the values are not strong functions of rate and may be considered independent of displacement rate. At relatively low oil saturation (Region 3), the values are strong functions of rate. Connecting these two regions is Region 2, a transitional region where the effect of flow rate decreases as the oil saturation increases.
JPT
P. 2051