Interfacing of two-phase fluid filtration basic mathematical models

The interface problem of two basic two-phase fluid filtration models is decided theoretically and numerically: Masket–Leverette model (ML model), that takes into account a capillary saltus of phase pressures and Buckley–Leverett one (BL model) with coinsiding phase pressures. The necessity in reviewing of such problems arises while simulating stages of displacement petroleum with water out of porous medium, various on time and space. For example, in watered part of a petroleum layer, from which the mobile petroleum is in fact already displaced, the capillary forces render weak influence on the two-phase fluid filtration process, and BL model with common pressure for both phases is usually used in this domain. In weakly watered part of petroleum layer the role of capillar forces appears rather essential for displacement of petroleum with water, that leads to the necessity of using more sophisticated ML model. Another example of interface problem between ML and BL models is the so-called “end effect” problem, consisting in improperly stipulated standard (“rigid”) boundary conditions on an operational slit. Use of a hypothesis about coincidense of phase pressures in zone of influence of an operational slit has a good reputation in a solution of this problem. If not to neglect, as it is usually done, by sizes of this nearwell zone, we come as well as above to an interface problem between ML and BL of models.