A major part of the uncertainty for shale reservoirs comes from the distribution and properties of the fracture network. However, explicit fracture models are rarely used in uncertainty quantification due to their high computational cost. This paper presents a workflow to match the history of reservoirs with complex fracture network with a novel forward model. By taking advantage of the efficiency of the model, fractures can be explicitly characterized, and the corresponding uncertainty about the distribution and properties of fractures can be evaluated. No upscaling of the fracture properties is necessary, which is usually a required step in a traditional workflow.
The embedded discrete fracture model (EDFM) has recently been studied by many researchers due to its high efficiency compared to other explicit fracture models. By assuming a linearly distributed pressure near fractures, EDFM can provide a sub-grid resolution that lifts the requirement to refine near the fractures to a comparable size as the fracture aperture. Although efficient, considerable error is reported when applying this method to simulate flow barriers, especially when dominant flux direction is across instead of along the fractures. In this work, a novel discrete fracture model, compartmental EDFM (cEDFM) is developed based on the original EDFM framework. However, different from the original method, in cEDFM the fracture would split matrix grid blocks when intersecting them. The new model is benchmarked for single phase as well as multi-phase cases, and the accuracy is evaluated by comparing to fine explicit cases. Results indicate the improved model yields much better accuracy even for multi-phase flow simulation with flow barriers.
In the second part of the work, we applied the model in history matching and performed uncertainty quantification to the fracture network for two synthetic cases. We used Ensemble Kalman Filter (EnKF) as the data assimilation algorithm due to its robustness for cases with large uncertainty. The initial state does not need to be close to the truth to achieve convergence. Also EnKF performs well for the history matching of reservoirs with complex fracture network, where the number of parameters can be large. Therefore, it is advantageous compared to using Ensemble Smoother (ES) or Markov Chain Monte Carlo (MCMC) in this case. After the final step of data assimilation, a good match is obtained that can predict the production reasonably well. The proposed cEDFM model shows its robustness to be incorporated into the EnKF workflow, and benefit from the efficiency of the model, this work made it practical to perform history matching with explicit fracture models.