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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