Sensitivity Studies of Gas-Water Relative Permeability and Capillarity in Reservoir Modeling

Abstract

Sensitivity Studies of Gas-Water Relative Permeability and Capillarity in Permeability and Capillarity in Reservoir Modeling This paper was prepared for the 44th Annual Fall Meeting of the of the Society of Petroleum Engineers of AIME, to be held in Denver, Colo., Sept. 28-Oct. 1, 1969. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal, provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract Numerical models of hypothetical gas-water reservoir systems were used to investigate the sensitivity of calculated pressure and saturation distributions to relative permeability (RP) and capillary pressure (PC) data. Two types of studies were made: the first type invoked gas injection into virgin aquifers, and the second, gas withdrawal from partially gas saturated reservoir-aquifer systems. RP and PC were represented as semi-empirical PC were represented as semi-empirical functions of a set of saturation states and three Parameters coined interference coefficient, Parameters coined interference coefficient, interference exponent, and linkage factor. Simulation studies showed that: saturation-pressure distributions are sensitive to phase saturation extrema (critical and residual saturations) and to parameters defining the curvature of RP and PC data, the sensitivity to RP and PC data declines rapidly with reservoir or block thickness when dip-normal capillary-gravity equilibrium (or near equilibrium) prevails, and laboratory RP and PC data should be adjusted for use in numerical simulators which employ large dimension grid blocks to simulate actual systems. Introduction In reservoir studies questions arise on the methods of reconciling laboratory measured relative permeability and capillary pressure data with prototype reservoir and model conditions. The purpose of this paper is to show, by numerical simulation of hypothetical reservoirs, how relative permeability and capillary pressure data affect the computation of pressure data affect the computation of pressure and saturation distributions, and to shed pressure and saturation distributions, and to shed light into possible methods of reconciling laboratory data and reservoir conditions. In order to save valuable space the following abbreviations were used throughout this paper: PC = capillary pressure, NWF = non-wetting (gas) phase, WF = wetting (water) phase, RP = relative permeability, RPN = RP to phase, RP = relative permeability, RPN = RP to non-wetting phase, RPW = RP to wetting phase. Excepting a few special applications, the numerical simulators are constructed in a Cartesian coordinate system. The finer is the grid network encompassing a given reservoir region, the closer is the representation of the fundamental flow equations by the difference system. Ideally, grid blocks should be smaller near active wells than farther away.