An Unsteady-state Technique For Three-phase Relative Permeability Measurements
Authors: Sarma H.K. , Maini B.B. , Jha K.N. N. 
Published: March 2010

Abstract
In-situ recovery of heavy oils and bitumen's often involves simultaneous flow of oil, water and gas in the oil sands. Such multi-phase flow in porous media is a complex process. Mathematical simulation of such recovery processes requires a knowledge of the three-phase relative permeability characteristics of the system. Experimentally measured three-phase relative permeability data for heavy oil reservoirs are not available in the literature. This lack of data is primarily due to the tedious nature of such measurements and shows a need for developing less time consuming methods.
In this study, an unsteady-state technique similar to the Johnson-Bossler-Naumann (JBN) method for two-phase flow was developed and used to estimate three-phase relative permeability data. The method was validated by comparing the oil isoperms with those obtained using the steady-state method. A reasonably good agreement was obtained which suggests that the proposed unsteady-state method could be employed as a faster alternative to obtain three-phase relative permeability data.

Introduction
Petroleum production often involves simultaneous flow of three immiscible fluids through subterranean porous rock formations. Examples of recovery processes involving such three-phase flow include alternating gas and water injection, steam drive, in-situ combustion, and immiscible gas injection in presence of mobile water. Thorough analysis of these processes is impossible without reliable three-phase relative permeability data. Reservoir simulation programs incorporate one or several techniques for estimating three-phase relative permeabilities, which permit three-phase simulation studies m be carried out with input of only two-phase relative permeabilities. However such simulation studies may be no more reliable than me techniques for estimating three-phase relative permeabilites employed in them. Unfortunately, the reliability of these estimation techniques cannot be tested without availability of extensive experimental data on three-phase relative permeabilities.
Compared to the wealth of information available in the literature on two-phase relative permeabilities, there is a dearth of experimental studies on three-phase flow through porous media. Virtually no information is available on three-phase relative permeabilities in intermediately-wet or oil-wet systems. Effects of variables such as contact angles, viscosity ratios, interfacial tension, flood velocity and temperature on three-phase relative permeability have not been investigated. There is an obvious need for more experimental investigations of three-phase relative permeabilities to resolve some of the uncertainties concerning the effects of variables mentioned above.
The reason for this scarcity of experimental dam on three-phase relative permeabilities appears to be the effort and time required for such measurements. The only well accepted technique for such measurements is the steady-state method. Between 50 to 100 steady-state measurements are required to fully define the relative permeability characteristics of a given system for one direction of saturation change. It often takes 24 hours or more to reach steady state conditions for each such measurements. Combined with the time involved in core preparation and periodic extractions to overcome the problem of error accumulation the total effort involved is indeed formidable. If the hysteresis effects corresponding to various possible directions of saturation change are also to be evaluated, the task becomes even more onerous.