The fast marching method (FMM)-based rapid reservoir simulation workflow has proven to be effective for various applications in unconventional reservoirs. The FMM-based simulation relies on the concept of the ‘Diffusive-Time-of-Flight’ (DTOF) that represents the travel time of pressure front propagation and captures geological heterogeneity as a 1-D spatial coordinate. It is challenging to model gravity in the FMM-based approach because the 1-D DTOF coordinate is not necessarily aligned with the physical direction of gravity.
We present a novel FMM-based simulation workflow that can account for gravity segregation in the fracture planes. The DTOF is first obtained by solving the Eikonal equation using the FMM assuming that gravity segregation is negligible in the ultra-tight matrix domain. Next, the 3-D transport problems in the matrix domain are transformed into a 1-D problem using the DTOF as a spatial coordinate. The hydraulic fractures are treated as gridded 2D planes to allow for gravity segregation and are connected to the 1-D matrix domain through non-neighbor connections (NNCs). A critical aspect here is computing the matrix-fracture transmissibilities based on the surface area of the DTOF contour. The proposed approach retains the speed of the FMM-based simulation while incorporating additional dominant physical mechanisms.
The FMM based model is benchmarked with a commercial finite volume simulator using a series of synthetic and field scale numerical examples encompassing different levels of geologic complexity to illustrate the accuracy and efficiency of the approach. We applied our proposed model and the standard FMM-based approach to synthetic cases and a field scale example with multi-million gridblocks and over 100 hydraulic fractures and compared flow responses and CPU time. It is found that the proposed approach effectively captures gravity effects and the results are in close agreement with 3-D finite volume simulation compared to the standard FMM-based approach. The FMM-based approaches are orders of magnitude faster in CPU time than the 3-D finite volume simulation. These numerical examples clearly demonstrate that our proposed approach is able to adequately model gravity effects while retaining computational efficiency.
The uniqueness of this work is incorporating gravity effects for the first time in the FMM-based reservoir simulation framework. The proposed approach is relatively simple and easy to implement, and the rapid workflow is capable of performing field scale history matching and optimization much faster and within realistic time frame.