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This paper presents a model that takes into account the transient nature of the imbibition process and the effect of variation in fracture saturation. Gravity effect is included in the calculation of the matrix equilibrium water saturation. This simple method requires only one equation per block per component. This is attained by an analytical transfer function that depends only on the fracture variables and by the assumption of instantaneous pressure equilibrium. The transfer function assumes that capillary pressure is the only driving force of the process and eliminates the matrix saturation from the fracture flow equations. The assumption of instantaneous pressure equilibrium eliminates the matrix pressure. The resulting model has the same form as standard single-porosity models. Results of the new model are compared with those from published laboratory experiments, very fine-grid simulations of matrix/fracture transfer for a single matrix block, and simulation of field-scale water-injection problems by standard double-porosity models. These results demonstrate that the new model provides an economical and accurate means of predicting the performance of fractured reservoirs.

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