Abstract
We develop a physically-motivated approach to modeling displacement processes in fractured reservoirs. To find matrix/fracture transfer functions in a dual porosity model we use analytical expressions for the average recovery as a function of time for gas gravity drainage and counter-current imbibition. For capillary-controlled displacement the recovery tends to its ultimate value with an approximately exponential decay.1 When gravity dominates the approach to ultimate recovery is slower and varies as a power-law with time.2 We apply transfer functions based on these expressions for core-scale recovery in field-scale simulation.
To account for heterogeneity in wettability, matrix permeability and fracture geometry within a single grid block we propose a multi-rate model.3 We allow the matrix to be composed of a series of separate domains in communication with different fracture sets with different rate constants in the transfer function.
We use this methodology to simulate recovery in a Chinese oil field to assess the efficiency of different injection processes. We use a streamline-based formulation that elegantly allows the transfer between fracture and matrix to be accommodated as source terms in the one-dimensional transport equations along streamlines that capture the flow in the fractures.4–6
