Direct Determination of Relative Permeability from Nonsteady-State Constant Pressure and Rate Displacements

Abstract

Direct interpretation methods for determination of the relative permeability data by linear, non-steady-state, two-phase fluid displacements conducted via constant rate and constant pressure laboratory core tests, are presented. The equations necessary for processing of the displacement test data obtained after the breakthrough of the displacing fluid phase are derived by neglecting the capillary end-effects at sufficiently high flow rates and verified by various experimental data. The total mobility and the mobility ratio of the immiscible fluids are related to the characteristic parameters of the displacement process and the cumulative injected fluid pore volume. The general correlation functions of the characteristic parameters of the immiscible displacement process in porous media are facilitated to conveniently describe the relative permeability functions. These functions allow for accurate determination of the characteristic parameters of immiscible displacement by least-squares linear regression of experimental data. Therefore, the present analytic method determines the relative permeability functions uniquely, rapidly, and more accurately than the previous direct interpretation methods, auxiliary functions, and graphical and analytical methods, and offers a possibility of determining the relative permeability functions from constant pressure and constant rate displacements data. Introduction Relative permeability is an essential petrophysical data required for characterization of multiphase flow in petroleum reservoirs. Frequently, the relative permeability data of the two-phase flow in porous media is determined by interpreting the data of the laboratory displacement tests carried out with cylindrical core plugs extracted from petroleum reservoirs. The Darcy law and the material balance equations, with appropriate initial and boundary conditions, are applied to describe the flow of the various fluid phases in porous media. This theoretical description of flow is used to infer for the relative permeability data by processing of the experimental data using a suitable method. This is an inverse problem and development of better methods for its solution has occupied many researchers. Especially, the achievement of the uniqueness in the calculated relative permeability data is of a great concern. In this respect, direct interpretation methods are favored over the indirect regression or matching methods. Honarpour et al.1 give a comprehensive review of the experimental methods for determination of the values of relative permeability. In general, two basic laboratory methods have been facilitated by the petroleum industry:the steady-state method, where both fluids, usually considered incompressible, are injected simultaneously into the core, andthe non-steady-state method, where only one fluid is injected into the core to displace another fluid present in a core plug. The processing of the steady-state test data is relatively simple, but the experiments are tedious, because attaining a steady average saturation value over the core length after each saturation alteration requires a long time, typically several hours. On the other hand, the laboratory tests of the non-steady-state displacements at different flow conditions can be performed within a relatively short time, but the evaluation of the data is a complex task. In both methods of measurements, the unfavorable capillary end-effects, appearing at the inlet and outlet faces of the core plug, further complicate the processing of the experimental data, unless the displacement can be carried out at a sufficiently high rate to minimize the end-effects. However, a rapid flow is usually difficult to accomplish in core plugs and does not represent the actual flow conditions in typical reservoir displacements. Nevertheless, the end-effects are often neglected for development of simplified interpretation methods.

A study of relative permeability parameters on rock cores using a two-phase flow test

“…To reduce the capillary end effect, the flow rate must be sufficiently high. Toth et al (2001) emphasized that the capillary end-effects will normally affect the measurement accuracy both in a displacement method and a steady state method; however, the effect can be minimized if the injection rate can be increased to some extent in a displacement method. By mercury-injection capillary pressure tests conducted on rock samples, Bennion and Bachu (2006) depicted the impact of interfacial tension and poresize distribution/capillary pressure characteristics on relative permeability with regard to CO 2 within reservoir conditions in a CO 2 -brine system.…”

Determining Relative Permeability From Unsteady-State Radial Fluid Displacements

“…1). In this section, the theoretical foundations of the relative permeability determination from radial flow immiscible displacements are presented by extending the application of the Tóth et al [1][2][3][4][5][6] approach.…”

“…For this purpose, the convenient interpretation formulae elaborated and demonstrated by the authors (Tóth et al [1][2][3][4][5][6] previously for determination of relative permeability from unsteady-state two-phase linear fluid displacements in laboratory core tests under constant rate or pressure conditions are transformed for displacement in the radial distance around a well. Special formulae for laboratory simulation of such radial flow in circular disks of relatively small thickness are also derived for interpretation of laboratory data.…”

Acquisition and analysis of transient data through unsteady-state core flooding experiments

“…After determination of saturation and relative permeability end point values, relative permeability curvatures in mathematical function can be adjusted until the flow behavior match the laboratory observations. Therefore, an automatic history match like method could be developed to optimize curvatures (Sigmund and McCaffery 1979;Kerig and Watson 1987;Bech et al 2000;Toth et al 2001;Jaber 2013). For these relevant references, the determination of relative permeability curves is executed by representing it with two functions, each of which contains one coefficient to be adjusted to match the observations.…”