Characteristic fracture spacing in primary and secondary recovery for naturally fractured reservoirs

If the aperture distribution is broad enough in a naturally fractured reservoir, even one where the fracture network is highly inter-connected, most fractures can be eliminated without significantly affecting the flow through the fracture network. During a waterflood or enhanced-oil-recovery (EOR) process, the production of oil depends on the supply of injected water or EOR agent. This suggests that the characteristic fracture spacing (or shape factor) for the dual-porosity/dual-permeability simulation of waterflood or EOR in a naturally fractured reservoir should account not for all fractures but only the relatively small number of fractures carrying almost all the injected water or EOR agent ("primary," as opposed to "secondary," fractures). In contrast, in primary production even a relatively small fracture represents an effective path for oil to flow to a production well. This distinction suggests that the "shape factor" in dual-permeability reservoir simulations and the repeating unit in homogenization should depend on the process involved: specifically, it should be different for primary and secondary or tertiary recovery. We test this hypothesis in a simple representation of a fractured region with a non-uniform distribution of fracture flow conductivities. We compare oil production, flow patterns in the matrix, and the pattern of oil recovery with and without the "secondary" fractures that carry only a small portion of injected fluid. The role of secondary fractures depends on a dimensionless ratio of characteristic times for matrix and fracture flow (Peclet number), and the ratio of flow carried by the different fractures. In primary production, for a large Peclet number, treating all the fractures equally is a better approximation of the original model, than excluding the secondary fractures; the shape factor should reflect both the primary and the secondary fractures. For a sufficiently small Peclet number, it is more accurate to exclude the secondary fractures in calculation of the shape factor in the dual-porosity/dual-permeability models than to include them and, in effect, assume they play an equally important role in transport to and from the matrix. For waterflood or EOR, in most cases examined, the appropriate shape factor or the repeating-unit size should reflect both the primary and secondary fractures. If the secondary fractures are much narrower than the primary fractures, then it is more accurate to exclude them for calculating the shape factor in a dual-porosity/dual-permeability model. Yet-narrower "tertiary fractures" are not always helpful for oil production, even if they are more permeable than matrix. They can behave as capillary barriers to imbibition, reduce oil recovery. We present a new definition of Peclet number for primary and secondary production in fractured reservoirs that provides a more accurate predictor of the dominant recovery mechanism in fractured reservoirs than the previously published definition.