Determination of Three-Phase Relative Permeabilities From Displacement Experiments

Abstract

Summary We describe a novel methodology for the determination of three-phase relative permeability functions at reservoir conditions. Two- and three-phase displacement experiments are conducted on a low-permeability chalk sample, and estimates of the three-phase relative permeability and capillary pressure functions are obtained. Three-phase relative permeabilities are also calculated using the Stone correlation, and they are evaluated by simulating the experimental data. Introduction Determination of relative permeability functions from displacement experiments has received a lot of attention over the past 50 years. The vast majority of the work has been directed towards determination of two-phase properties from laboratory experiments. Most applications involving three- phase relative permeabilities have utilized correlations in which two-phase relative permeability data are extrapolated into three-phase regions. Although this would be tractable, if accurate, these correlations have largely remained untested due to the lack of sufficient measurements of three-phase relative permeability functions. Analysis of three-phase experimental data has often been based on several generally unsupported simplifications (e.g.. the neglect of capillary pressure, incompressible fluids, uniform saturation profiles, and each relative permeability being a function of its own saturation only). In an effort to meet such simplifications, experiments have frequently been conducted under flowing conditions that are unrepresentative of those encountered within the reservoir. Consequently, the estimated three-phase properties may not be suitable for describing reservoir flow. We report here the application of a methodology to overcome these problems. We have constructed an experimental apparatus whereby two- and three-phase displacement experiments may be performed at reservoir conditions. The experimental process is modeled by a general purpose three-phase simulator which includes all the pertinent physical effects. We then choose the appropriate relative permeability and capillary pressure functions, through solution of a series of optimization problems, so that the quantities calculated with the simulator are consistent with the measured values. This methodology is demonstrated with a low-permeability chalk sample. We also calculate three-phase relative permeabilities from the two-phase data using the Stone model, and evaluate the effectiveness of that model by simulating the data collected during the experiment. The estimates of the three-phase relative permeabilities obtained with the Stone model do not accurately reconcile the experimental data. Three-Phase Flow Apparatus The schematic of the flow apparatus is shown in Fig. 1. It consists of a pumping system, a three-phase separator, a core holder and a X-ray scanner system for in-situ saturation measurements. Each of these components is described below. For further details on experimental set-up, see Ebeltoft et al. Pumping system. The pumping system consist of eight computer controlled cylinders that pumps reservoir fluids into the core sample at reservoir conditions. Cylinders are paired to act as a pump.

A New Design of Steady-State Type Experiments for Simultaneous Estimation of Two-Phase Flow Functions

“…This type of experimental design for estimating flow functions has also been used for estimating three-phase relative permeability functions. 23,24 Experimental Results. The proposed method to determine relative permeability and capillary pressure functions was used with experimental data.…”

Metodología experimental para la estimación de permeabilidades relativas en dos y tres fases por medio de ajuste histórico

“…Como se menciona en trabajos previos (Helset, Norvdtvedt, Skjaeveland y Virnovsky, 1998) (Nordtvedt, et al, 1997), las representaciones funcionales seleccionadas para describir las permeabilidades relativas, son importantes debido a que definen, el número de parámetros a usar para buscar el ajuste, y la flexibilidad que tienen las curvas y superficies a estimar. Un número mayor de parámetros, generalmente, permite mayor flexibilidad para que las curvas puedan describir mejor las permeabilidades relativas, pero incrementa el número de variables a optimizar y por lo tanto los tiempos de computo (Kreig y Watson, 1986).…”

“…Es importante señalar los métodos de optimización de gradiente han sido usados eficazmente por diversos autores para estimar permeabilidades relativas (Fassihi, 1989) (Grattoni y Bidner, 1990) (Chavent, Jaffré y Jan, 1998) (Nordtvedt, et al, 1997).…”

Simulation-enhanced fracture detection: research and demonstration in U.S. basins

“…There is a vast amount of experimental data on relative permeabilities and capillary pressure relations (Brooks & Corey 1964;Nordtvedt et al 1997;Liu et al 1998). In the absence of experimental data, expressions provided by Brooks & Corey (1964) and Van Genuchten (1980) are the most commonly used ones (see Lenhard et al 1989b for a comparison).…”