We introduce a numerical investigation of the effect of gravity on the problem of two-phase countercurrent imbibition in porous media. We consider three cases of inlet location, namely, from, side, top, and bottom. A 2D rectangular domain is considered for numerical simulation. The results indicate that gravity has a significant effect depending on open-boundary location. 1. Introduction Oil recovery by imbibition mechanism, from fractured reservoirs, is a significant research area in multiphase flow in porous media especially for water-flooding process in fractured oil reservoirs. Fractured reservoirs are composed of the fracture network and matrix. Fractures have a higher permeability and relatively low volume compared to the matrix, whose permeability is very low but it contains the majority of the oil. Water flooding is used to increase oil recovery by increasing water pressure in fractures since water quickly surrounds oil-saturated matrices of lower permeability. The process of water flooding works well when the matrix is water-wet, and imbibition can lead to significant recoveries, while poor recoveries and early water breakthrough occur with oil-wet matrix conditions. Imbibition is defined as the displacement of the nonwetting phase (oil) by the wetting phase (water) with dominant effect of capillary forces. Imbibition can occur in both countercurrent and cocurrent flow modes, depending on the fracture network and the water injection rates. In cocurrent imbibition, water displaces oil out of the matrix; thus both water and oil flows are in the same direction. Countercurrent imbibition, on the other hand, is whereby a wetting phase imbibes into the porous matrix (rock), displacing the non-wetting phase out from one open boundary. In spite of the fact that cocurrent imbibition is faster and more efficient than countercurrent imbibitions, the latter is often the only possible displacement mechanism for cases where a region of the matrix is exposed from one side to water filling the fracture [1–4]. Imbibition has also been investigated by several other authors either for cocurrent or countercurrent flows or both of them together (e.g.,？？[5–8]). Reis and Cil [9] introduced one-dimensional model for oil expulsion by countercurrent water imbibition in rocks. An examination of countercurrent capillary imbibition recovery from single matrix blocks and recovery predictions by analytical matrix/fracture transfer functions was introduced by Cil et al. [10]. Lee and Kang [11] have introduced an experimental analysis of oil recovery in a fracture of variable
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