Dynamic Displacement Measurements of Three-Phase Relative Permeabilities Using Three Immiscible Liquids

Abstract

SPE Members Abstract The main difficulties to overcome in dynamic displacement relative permeability measurements are capillary end effects and viscous fingering. The latter problem is particularly severe in three-phase systems which include gas. Both of these problems are greatly mitigated in the three liquid system presented here. Water, benzyl alcohol, and decane are the three immiscible liquids which play the role of water, oil, and gas in the conventional three-phase system. The interfacial tensions in this system are about a factor of ten smaller than the comparable tensions for the conventional system, so the capillary end effect is less. Furthermore, viscosity contrasts are diminished, thus lowering the chance of fingering. An extension of the Welge-JBN method to three phases is derived. Each displacement experiment follows a saturation trajectory across the ternary diagram. The method is used to calculate three-phase relative permeabilities along each trajectory. Finally, the data from all trajectories are combined to provide isoperms over a large portion of the ternary diagram. Also included are the two sets of two-phase relative permeabilities needed to apply the interpolative three-phase relative permeabilities needed to apply the interpolative three-phase relative permeability model of Stone. The measured isoperms indicate the model permeability model of Stone. The measured isoperms indicate the model overpredict the relative permeability to oil: oil flows at lower rates than predicted. Introduction Relative permeability is an important concept in the forecasting of field performance. The relative permeability to a given phase is a function of that phase's saturation and possibly a function of other phase saturations as well. The effective permeability is one of the major non-linear (in most cases) factors in the mass transport equations that are used in reservoir models, analytical or numerical. One can imagine determining relative permeabilities by solving the multiphase flow problem from first principles. However, since such an approach is presently untractable, relative permeabilities must necessarily be determined experimentally. The literature presents a vast number of papers relating to the determining of relative permeabilities to fluids in porous media. For a review of the subject see, for example, Honarpour et al. Although many papers discuss absolute permeabilities and two-phase relative permeabilities, few papers deal with three-phase relative permeabilities, few papers deal with three-phase relative permeabilities. Three-phase relative permeabilities are essential in permeabilities. Three-phase relative permeabilities are essential in forecasting the performance of saturated and retrograde condensate reservoirs, and of most tertiary recovery processes. Hence, the importance of understanding and predicting the simultaneous motion of three phases in porous media. There are two major methods involving continuous injection of fluids for determining relative permeabilities: the steady-state method and the unsteady-state method. In the steady-state method, a fixed mixture of fluids is injected into the core, until the same mixture is produced from the core. At this point, steady-state condition is produced from the core. At this point, steady-state condition is assumed and by applying Darcy's law for each individual phase, the relative permeability is determined straightforwardly. In the unsteady-state method, usually (but not necessarily) one fluid is injected. Recovery and pressure drop are measured as a function of pore volumes injected. The relative permeabilities as a function of pore volumes injected. The relative permeabilities as a function of saturation are determined using the combined Welge method and the Johnson Bossler and Naumann method (Welge/JBN). The advantage of the dynamic method over the steady-state method is that the number of the experiments required to map the saturation region is small. In the three-phase case, this advantage is even more significant because the dynamic displacement method yields three-phase relative permeabilities along a continuous saturation trajectory. The main limitation of the dynamic displacement method is that relative permeability data cannot be determined in regions for which there are permeability data cannot be determined in regions for which there are saturation shock fronts. Steady state studies of three-phase flow in porous media are not new in the petroleum literature. As early as 1941, Leverett and Lewis present a study of three-phase flow using the steady-state method. present a study of three-phase flow using the steady-state method. They conclude that the water relative permeability is solely a function of water saturation in an unconsolidated sand pack. However, they conclude that the gas relative permeability depends upon the relative amounts of water and oil, with the gas isoperms being convex in the direction of 100% gas saturation. The oil isoperms are more complex, depending on the amounts of water and gas in the sand pack. pack. P. 325