This paper demonstrates the novelty and practical feasibility of the FMM-based multi-phase simulation for rapid field-scale modeling of shale reservoirs with multi-continua heterogeneity.
Modeling of unconventional reservoirs requires accurate characterization of complex flow mechanisms in multi-continua because of the interactions between reservoir rocks, microfractures and hydraulic fractures. It is also essential to account for the complicated geometry of well completion, the reservoir heterogeneity and multi-phase flow effects. Currently, such multi-phase numerical simulation for multi-continua reservoirs needs substantial computational time that hinders efficient history matching and uncertainty analysis. In this paper, we propose an efficient approach for field scale application and performance assessment of shale reservoirs using rapid multi-phase simulation with the Fast Marching Method (FMM).
The key idea of the reservoir simulation using the FMM is to recast the 3-D flow equation into 1-D equation along the ‘diffusive time of flight’ (DTOF) coordinate, which embeds the 3-D spatial heterogeneity. The DTOF is a representation of the travel time of pressure propagation in the reservoir. The pressure propagation is governed by the Eikonal equation which can be solved efficiently using the FMM. The 1-D formulation leads to orders of magnitude faster computation than the 3-D finite difference simulation. The use of FMM-based simulation also enables systematic history matching and uncertainty analysis using population-based techniques that require substantial simulation runs.
We first validate the accuracy and computational efficiency of the FMM-based multi-phase simulation using synthetic reservoir models and comparison with a commercial finite-difference simulator. Next, we apply our proposed approach to a field example in Texas for a multi-stage hydraulically fractured horizontal well. The 3-D heterogeneous reservoir model was built and history matched for oil, gas and water production using the Genetic Algorithm with the FMM-based flow simulation. Multiple history-matched models were obtained to examine uncertainties in the production forecast associated with respect to the properties related to hydraulic fractures, microfractures and the matrix.