Analytical Approximate Expression for Cocurrent Imbibition during Immiscible Two-Phase Flow through Porous Media

Cocurrent and countercurrent imbibitions are the crucial mechanism in many multiphase flow processes. In cocurrent imbibition wetting phase displaces nonwetting phase such that the nonwetting phase moves in the same direction to the wetting phase, whereas in countercurrent imbibitions wetting and non-wetting phase flow in opposite directions. However for cocurrent imbibitions, mathematical models need total flux condition as both phases flow in the same direction. Thus cocurrent imbibitions have been considered neglecting pressure gradient of nonwetting phase and only pressure gradient of displacing phase is considered which gives additional velocity to the displacing phase. An approximate analytical solution is derived by the method of small parameter; an approximate expression for the wetting phase saturation has been obtained. From analytical expression graphical presentation of saturation of wetting phase shows that cocurrent imbibition is faster than countercurrent imbibition. Also, the small parameter is chosen from initial wetting phase saturation and wetting phase saturation at imbibition phase, thus giving comparative behavior of imbibition at initial and later stage. It is shown that cocurrent imbibition proceeds faster with more amount of wetting phase present in porous matrix.