Analytical Model for Unconventional Multifractured Composite Systems

This paper presents an analytical model for unconventional reservoirs with horizontal wells with multiple fractures. The model is an extension of the trilinear 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 (fracture branching), whereas the remaining reservoir is nonstimulated. In addition to modeling flow within the fracture and flow within the stimulated region, the model takes into account flow from the surrounding nonstimulated region, both parallel to and perpendicular to the fracture. The model can be used to simulate the flow in tight reservoirs with multifractured horizontal wells. In many cases, the fractures do not have a simple biwing 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 nonstimulated 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 with 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.