The key objective of this paper is to point out that a widely used constitutive relationship between the degrees of saturation and capillary pressures for three-phasefluids over the past twenty five years has resulted in an undue constraint. To our knowledge, this constraint is neither physically justifiable nor is it theoretically supported. The discovery of the undue constraint leads this investigation to develop a viable parametric model to describe the constitutive relationship for a system of multiple fluids. Based on the physical consideration wherein fluid wettability follows a sequence, the proposed parametric model can be easily applied to any system of L arbitrary fluids. Three aspects are presented to confirm the plausibility and completeness of the model. First, the proposed closed-form expression of the saturation-capillary pressure head relationship is identical to van Genuchten's renowned model for two-phasefluid systems. Second, a constraint appearing in the widely used model is alleviated in the proposed model. Third, seven hypothetical examples are used to demonstrate that there is no need to impose the constraint on the sequence of capillary pressures. The results show the plausibility and completeness of the model for systems of multiple fluids. The proposed parametric model is a feasible analytic model which provides a generalized saturation-capillary pressure head relationship for any system with regard to multiple fluids. Hopefully, this study will pave a way for others to conduct experiments to validate the model further or develop other better non-constrained models based on experimental evidence.
- Capillary pressure head relationship
- Constitutive relation
- Van genuchten's model