Mathematical modeling of unconventional reservoirs is a complex and challenging problem. The traditional approach is to construct a SRV based numerical model to predict long-term performance. The glaring limitation of this approach is that the model quickly becomes mathematically expensive if we attempt to capture complex geometries and incorporate non-planar/non-orthogonal induced/natural fractures. Also, these numerical models are generally constrained to planar geometry only, as an exhaustive suite of fracture orientations is not practical. It is done in order to simplify assigning fracture conductivities in the model. The method outlined in this paper eliminates the first limitation with the help of a dual porosity semi-analytical model. The other limitation of knowing fracture conductivity of non-planar fractures is overcome by incorporating the dimensionless fracture conductivity in this dual porosity model by comparing it with an equivalent single porosity planar model during bilinear flow regime.
This new method, based on dimensionless productivity index and its derivative, uses dual porosity constant volume fractures in linear reservoirs. Dimensionless productivity index essentially conveys information regarding area generated due to transient average reservoir pressure over a given drainage area. The resulting horizontal well performance, which contains part natural fracture and part induced hydraulic fracture, is based on well test parameters evaluated from production data. These parameters help freeze the rate transient solution in the time domain. The early time analysis of flowback (fracturing water and gas/oil) gives us the insight into induced fractures. The connectivity issue is addressed with the help slab (planar 1D), cylinder (non-planar 2D) and sphere (non-planar 3D) matrix orientations which encompass all possible ranges of fracture (natural and induced) orientation that impact long-term performance.
The result of this approach brings to light the pressure support and effect of flowback water on longterm performance of hydraulically fractured horizontal wells. This is demonstrated with the help of published literature data and shows how flowback analysis complements the conventional rate transient analysis for finite conductivity fractures in linear reservoirs.
The method outlined here amounts to analyzing various fractures having different fracture conductivities and having different non-orthogonal orientations, with sphere matrix orientations being the maximum limiting case scenario. As opposed to this, the traditional numerical method requires running a large number of scenarios on a numerical simulator making it a prohibitively large problem. Eliminating this need brings out the significance of the approach.