An efficient embedded discrete fracture model based on the unstructured quadrangular grid

It is important yet challenging to effectively and accurately predict the recovery of fractured reservoirs. Among numerous fractured reservoir simulation models, the embedded discrete fracture model (EDFM) is the most outstanding one for it incorporates the discrete fractures into structured grids of the matrix, which precisely describes the arbitrarily distributed fractures while not increasing the gridding and calculation complexity. However, the current EDFM still possesses drawbacks for its structured grid shows poor adaptivity to irregularly shaped reservoirs, and also causes a sharp pressure gradient between the matrix and fractures and weakens the simulation accuracy. To conquer the drawbacks of the current EDFM, an unstructured quadrangular grid-based EDFM (UnQ-EDFM) is proposed in this paper. In this model, a frontal Delaunay quadrangular grid is adopted that could perfectly adapt to irregular reservoir boundaries without increasing the grid number and gridding complexity; besides, local grid refinement could be achieved flexibly in anywhere of the reservoir, which effectively alleviates the simulation error while not adding too much calculation. Based on the UnQ-EDFM, the production of a multi-stage hydraulic fractured well in irregular shaped naturally fractured shale gas reservoir is simulated, the simulation results under different types of grids are compared. Furthermore, an optimization framework that applies WOA as the optimization algorithm and NPV as the objective function is constructed, the hydraulic fractured well in the above-mentioned reservoir is optimized and the reliability of the UnQ-EDFM is testified through thousands of times of simulation. The results of simulation and optimization demonstrate the reliability and superiority of the UnQ-EDFM over the traditional structured grid-based EDFM, for it adapts to complex-shaped reservoirs, maintains high simulation accuracy, and reduces simulation time, simultaneously. The UnQ-EDFM proposed in this paper severs as an efficient tool and contributes to the precise and efficient simulation for the fractured reservoirs' development.