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.

This paper presents an analytical model for unconventional reservoirs with multiply-fractured horizontal wells. The model is an extension of the "tri-linear flow" solution, but it subdivides the reservoir into five regions instead of three. This enables it to be used for more complex reservoirs. Accordingly, the model can simulate a fracture that is surrounded by a stimulated region of limited extent (branch-fracturing), while the remaining reservoir is un-stimulated. In addition to modeling flow within the fracture and flow within the stimulated region, the model takes into account flow from the surrounding un-stimulated region, both parallel to and perpendicular to the fracture. The model can be used to simulate the flow in tight reservoirs with multi-frac horizontal wells. In many cases, the fractures do not have a simple bi-wing shape, but are branched. This effectively creates regions of higher permeability around each fracture, which obviously affect the production performance significantly. However, in many tight reservoirs, in spite of their low permeability, the surrounding un-stimulated region can also be a significant contributor to long-term production. The Five-Region Model accounts for this contribution. Thus it is particularly valuable when generating production forecasts for reserves evaluation. The model was validated by comparing its results against numerical simulation. We found that analytical and numerical results are in good agreement only when the geometry of the system falls within certain limitations. However these limitations are met in most cases of interest. Therefore the model is useful for practical engineering purposes.

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