Principles of Three Phase Capillary Pressures
Authors: Kantzas A. , Nikakhtar B. , Pow M. 
Published: March 2010

Abstract
In porous media, there are a variety of configurations in which three immiscible fluids can be distributed within a single body. For example, the fluids may be distributed as concentric rings. Alternatively, two fluids may be dispersed as separate blobs within the third fluid. The configuration governs the mobility of each fluid, and under equilibrium conditions is dictated by the three phase capillary pressure of the system. If the capillary pressure is altered, the configuration will change. Capillary pressure can be altered by flow of any phase through the pore body. However, in a three phase system flow cannot be described as simply "drainage" or "imbibition." Rather, flow must be described as "drainage/drainage," "drainage/imbibition: or "imbibition/imbibition" to account for the change in saturation of all three phases. This paper elaborates on the issues governing three phase capillary pressures and presents some first experimental results on oil/water/gas capillary pressures in a drainage/drainage mode.

Literature Review
Three phase capillary pressure data were first presented in a ternary plot format by Leverett(1). Details of how the data were obtained were not discussed. Another effort to present quantitative information on three phase capillary pressure systems was recently initiated in the field of hydrology.
Lenhard and Parker(2) developed an experimental apparatus to directly measure monotonic capillary pressure curves for water/oil/air systems in unconsolidated media. Treated ceramic disks were used to create semi-permeable membranes for the free flow of water and oil from different ports. Direct measurements of water and total liquid saturations in three phase systems as functions of oil/water and air/oil capillary heads, respectively, were compared to saturation-pressure measurements in two-phase air/oil and oil/water systems for monotonic drainage saturation paths. Excellent agreement was observed between total liquid saturations in an air/oil/water system and oil saturations in an air/oil system as functions of air/oil capillary head. Excellent agreement was also found between water saturations in air/oil/water and oil/water fluid systems versus oil/water capillary head.
The concept of three phase capillary pressures in enhanced oil recovery was recently revisited by Kantzas et al.(3,4) and Chatzis et al.(5) Three phase interactions (water/oil/gas) were evaluated in the course of investigating gravity assisted immiscible gas injection (GAIGI). Three phase capillary interactions were studied visually in regular geometry pores, but were not quantified.
This was done by Kalaydjian(6) who performed both drainage and imbibition capillary pressure measurements using a multi porous membrane apparatus. Clashach sandstone cores were used. Measurements showed that both drainage and imbibition curves are dependent on the three saturations. This conclusion contradicts the results of Leverett as well as the hydrology models presented earlier.
Kalaydjian(6) and Kalaydjian and Tixier(7) demonstrated the effect of the spreading coefficient on drainage capillary pressures (gas/oil) in the presence of connate water. It was found that the residual oil saturation was lower in the case of positive spreading coefficient than in the case of a negative one. Except for the low saturation values, the capillary pressure was higher in the case of a positive spreading coefficient than in the case of a negative one.