Empirical Equations for Water/Oil Relative Permeability in Saudi Sandstone Reservoirs

Abstract

Abstract Relative permeability data are essential for almost all calculations of fluid flow in petroleum engineering. Water/oil relative permeability curves play important roles in characterizing the simultaneous two-phase flow in porous rocks and predicting the performance of immiscible displacement processes in oil reservoirs. This paper presents new empirical equations for calculating water/oil imbibition relative permeability curves. The models of relative permeability were developed using experimental data from 46 displacement core tests from sandstone reservoirs of Saudi fields. Three empirical equations are presented to calculate oil relative permeability, water relative permeability, and the endpoint of the water relative permeability curve. The relative permeability models were derived as a function of rock and fluid properties using stepwise linear and nonlinear regression analyses. The new empirical equations were both evaluated using the data utilized in the development and validated using published data, which were not used in the development stage, against previously published equations. Statistical results show that the new empirical equations developed in this study are in better agreement with experimental data than previous empirical equations, for both the data used in the development and validation stages. The new empirical equations can be used to determine water/oil relative permeability curves for other fields provided the reservoir data fall within the range of this study. Introduction Relative permeability1–4 is an important concept in describing the flow of multiphase systems. It is defined as the ratio of the effective permeability of a fluid at a given saturation to the absolute permeability of the rock. Data of relative permeabilities are essential for almost all calculations of fluid flow in petroleum reservoirs. The data are used in making engineering estimates of productivity, injectivity, and ultimate recovery. Some applications of relative permeability data include determination of free water surface, aid in evaluating drill-stem and production tests, determination of residual fluid saturations, fractional flow and frontal advance calculations to determine the fluid distributions, and making future predictions for all types of oil reservoir under different operational schemes. Undoubtedly, these data are considered probably the most valuable information required in reservoir simulation studies. The producing gas-oil ratio and the producing water/oil ratio are two criteria used in history matching, which can be modified by relative permeability changes. More accurate prediction of relative permeability will reduce the trial and errors needed to improve the history matching. Estimates of relative permeabilities are generally obtained from laboratory experiments with reservoir core samples using one of the measurement methods: steady state or unsteady state techniques. The relative permeability data may also be determined from field data using the production history of a reservoir and its fluid properties. However, this approach is not often recommended because it requires complete production history data and provides average values influenced by pressure and saturation gradients, differences in the depletion stage, and saturation variations in stratified reservoirs. In addition, the agreement between laboratory determined relative permeabilities and those calculated from production history is generally poor. Because the laboratory measurement of relative permeabilities is rather delicate and time consuming, empirical correlations are usually employed to reproduce experimentally determined relative permeability curves, or to estimate them when experimental data from core samples are not available. The purpose of this study is to develop new empirical equations to predict imbibition water/oil relative permeability characteristics using experimentally obtained data for sandstone reservoir rocks. Multiple linear and nonlinear least-square regression techniques are applied on the new proposed models utilizing the experimental rock and fluid saturation data. The new empirical equations are evaluated against several empirical equations published in the literature4–11 using the data utilized in the development, and validated using published relative permeability data.