A common way to produce hydrocarbons from tight reservoirs is to use horizontal wells with multiple hydraulic fractures. In many cases, fractures do not have a simple bi-wing shape, but are branched. For modeling purposes, branch-fracturing can be represented by a high permeability region near each fracture, while the bulk of the space between the fractures remains unstimulated.

This paper presents an analytical model to simulate the flow rate and pressures for such a reservoir system. The model is a variation on the tri-linear flow solution. It is simple, and flexible enough to be applicable to multi-frac horizontal wells. The model takes into account three linear flow regimes: flow within the fracture (at very early time), flow within the stimulated region towards the fracture and flow within the un-stimulated region towards stimulated region. The model was validated by comparing its results with synthetic data sets generated using numerical simulation; the results showed excellent agreement.

This paper illustrates the various flow regimes and how they are affected by reservoir and completion parameters. The characteristic features of each flow regime are demonstrated using typecurves. History matching of actual field case is presented to illustrate the practicality of the model. The proposed analytical solution provides a practical alternative to numerical solutions, and saves significant computational time.

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