A theoretical model of hysteresis and dynamic effects in the capillary relation for two-phase flow in porous media

It is well known that the relationship between capillary pressure and satur ation, in two-phase flow problems demonstrates memory effects and, in parti cular, hysteresis. Explicit representation of full hysteresis with a myriad of scanning curves in models of multiphase flow has been a difficult probl em. A second complication relates to the fact that P-c-S relationships, det ermined under static conditions, are not necessarily valid in dynamics. The re exist P-c-S relationships which take into account dynamic effects. But t he combination of hysteretic and dynamic effects in the capillary relations hip has not been considered yet. In this paper, we have developed new model s of capillary hysteresis which also include dynamic effects. In doing so, thermodynamic considerations are employed to ensure the admissibility of th e new relationships. The simplest model is constructed around main imbibiti on and drainage curves and assumes that all scanning curves are vertical li nes. The dynamic effect is taken into account by introducing a damping coef ficient in P-c-S equation. A second-order model of hysteresis with inclined scanning curves is also developed. The simplest version of proposed models is applied to two-phase incompressible flow and an example problem is solv ed.