Reliable predictions of well recovery are crucial for designing reservoir development. In the bottom-water naturally-fractured reservoirs (NFRs), comprising a network of distributed fracture “corridors,” spacing (and apertures) of the corridors varies throughout the reservoir. This makes oil well’s recovery a probabilistic variable as it depends upon uncertain well’s location in the network. The uncertainty is two-fold; it concerns well’s location within corridor network and well’s possible intersection with the nearest corridor. In any network’s location (with closely- or sparsely–spaced corridors), wells may intercept fracture corridors (fracture well) or go in-between two corridors in a matrix block (matrix-well). A simplified way of estimating well recovery is to ignore well’s location within corridor network and consider only probability and performance of fracture well and matrix well in a statistically-equivalent reservoir with uniform spacing and aperture equal to their expected values derived from their known statistics. Another (fully probabilistic) method considers the combined probabilities of the well’s location in the network and being a fracture well or matrix well. The study evaluates discrepancy between the two methods, explains its statistical nature, and demonstrates their implementation in a corridor-type NFR described in the literature.
In the study, recovery process is simulated by coupling the inner (near-well) zone’s discrete single-porosity flow model with the outer zone Dual Porosity Dual Permeability (DPDP) simulator. The matrix well’s inner zone extends from the well to the nearest corridor and for the fracture well inner zone covers the corridor and adjacent matrix blocks. In the simulations, matrix and fracture-wells are operated at maximum rate constrained by minimum downhole flowing pressure and the surface handling limit. The study is performed using statistical data from a corridor-type NFR with power-law-distributed spacing size from 19 ft to 153 ft and corridor apertures varying from 8ft to 31ft correlated with the spacing.
The simplified method gives recovery values ranging from 28% to 37%, and the single value of total recovery 33% — normalized by the matrix and corridor size fractions of the total reservoir area. Alternatively, the probabilistic method gives two separate distributions of the fracture and matrix wells’ recoveries that are weighted by their probability and converted to a single distribution of total recovery using statistical concept of weighted average. The probabilistic estimation gives higher values of recovery — from 32% to 38% with the expected value of 36.6%. Moreover, there is a considerable 30% probability of having recovery greater than 36.6%. A mathematical proof provides explanation why the probabilistic method gives recovery estimate greater than that from the simplified method. Another advantage of the method is the cumulative probability plot of well recovery that, in practical applications, would let operators make reservoir development decisions based upon the risk-benefit consideration.