Reservoir Rock Characteristics - Three-Phase Imbibition Relative Permeability

An equation for three-phase (water, oil, gas) imbibition oil permeability is developed, assuming the water to be the dominant wetting fluid. Oil isoperms are obtained for consolidated sandstones characterized by 1/pc2 = CS*. The evolution of an oil-gas system imbibing water from Swi to(Sw,imb )max is shown to proceed along a line of constant oil saturation with increasing oil permeability and decreasing gas saturation. When the gas satuation cannot be reduced further, the system evolves along a line of constant Sg with decreasing oil saturation and permeability. The initial gas saturation is shown to reduce markedly the effect of complete wetting by either oil or water on flow performance. INTRODUCTION Imbibition oil isoperms are required for performance prediction when a well is producing water, oil and gas. This situation occurs in multiphase displacements such as underground combustion, steam injection and the water flooding of highly depleted reservoirs. In a recent paper,1 a model was presented for the prediction of two-phase imbibition characteristics. This paper extends the imbibition model to the case of three phases by assuming that the water is the dominant wetting fluid. The following results were obtained from the model: (1) an analytical expression of oil isoperms; (2) oil isoperrns as functions of reduced water, oil and gas saturations, valid for all sandstones having a capillary pressure curve which can be approximated by 1/PC = CS*; and (3) evaluation of the three-phase flow performance as dictated by complete wetting by either oil or water. The agreement between predicted and observed oil recovery in the presence of a gas phase, reported in Ref. 1, is a partial support for the present development. However, experimental data are not available at this time to check fully the model predictions. Perhaps this paper will stimulate the collection of such data. The imbibition model of a porous medium has been described previously, and the reader is referred to the paper of Naar and Henderson1 for details. In brief, the model is formed by the random interconnection of straight capillaries, with a provision for the blocking of the non-wetting phase by the invading wetting fluid. The following expressions were derived from the model. 1. The amount of oil blocked by the invading water is