Theoretical Development of a Novel Equation for Dynamic Spontaneous Imbibition with Variable Inlet Saturation and Interfacial Coupling Effects

Abstract

In oil recovery from fractured reservoirs, dynamic spontaneous imbibition (DSI) plays an important role. Conventional equations used for characterizing dynamic spontaneous imbibition neglect the effects of the driving forces acting across the wetting and non-wetting phases which are flowing in opposite directions. Such effects, defined as interfacial coupling effects (ICE), are known to cause a decrease in the calculated flow rate in drainage processes. Moreover, none of the numerical models have considered a variable inlet saturation (S*) for DSI. A new theoretical model has been developed using generalized transport equations to describe dynamic spontaneous imbibition for immiscible two-phase flow processes. The inclusion of interfacial coupling effects provides a more accurate way to describe dynamic spontaneous imbibition. Furthermore, the addition of variable inlet saturation allows one to establish whether the inlet-face saturation (S*) increases from the initial saturation to 1−Sro, or whether it can remain constant and equal to one minus the residual saturation to the non-wetting phase (1−Sro).

Numerical Solution of Equation for Dynamic, Spontaneous Imbibition with Variable Inlet Saturation and Interfacial Coupling Effects

“…However, none of the previous models have included either the effect of the interfacial coupling or the option of variable inlet saturation. Yazzan et al (2010) constructed a novel equation that invalidates the assumption that the interfaces (fluid/fluid and rock/fluid) act in the same way. Moreover, the formulation of the equation permits the inclusion of variable inlet saturation.…”

“…Bentsen (1998;2005b), Ayub and Bentsen (1999), Ayub (2000), and Ayodele (2004 developed a set of modified transport equations that incorporate interfacial coupling and hydrodynamic effects. Yazzan et al (2010) used these equations to develop a novel equation with appropriate initial, boundary, and ancillary conditions to describe the dynamic spontaneous imbibition process. Based on direct observations, it is also commonly assumed that the saturation of the wetting phase at the inlet-outlet face of the rock is close to one minus the residual non-wetting saturation (1 − S ro ) (Li et al 2003).…”

“…Based on direct observations, it is also commonly assumed that the saturation of the wetting phase at the inlet-outlet face of the rock is close to one minus the residual non-wetting saturation (1 − S ro ) (Li et al 2003). However, Yazzan et al (2010) incorporated variable inlet saturation into the analysis, which allows the saturation to increase from its initial value to the maximum saturation (1 − S ro ), to study the effect of variable inlet saturation on the dynamic spontaneous imbibition process.…”

“…As noted above, besides Yazzan et al (2010), previous theoretical approaches to this problem have not included the effect of interfacial coupling on spontaneous counter-current imbibition, nor have they taken into account variable inlet saturation. Thus, the first goal of this article is to develop a numerical solution for the Lagrangian formulation of the differential equation constructed by Yazzan et al (2010), which can be used to study the effect of variable inlet saturation and interfacial coupling on counter-current spontaneous imbibition.…”

“…Thus, the first goal of this article is to develop a numerical solution for the Lagrangian formulation of the differential equation constructed by Yazzan et al (2010), which can be used to study the effect of variable inlet saturation and interfacial coupling on counter-current spontaneous imbibition. The second goal of the study is the construction of an efficient iterative procedure for determining simultaneously the pseudo initial condition and the inlet saturation.…”