Reliable performance assessment of unconventional reservoirs requires accurate modeling of inter-porosity flow characteristics in hydraulic fractures, microfractures and reservoir rock. In addition, phase behavior in nano-porous rocks plays an important role in reservoir performance. High resolution flow simulation incorporating the complex underlying physics and detailed reservoir heterogeneity is computationally expensive. In this paper, we propose a fast and novel approach for field scale compositional simulation and history matching for unconventional reservoirs.
Our proposed simulation approach is based on a high frequency asymptotic solution of the diffusivity equation in heterogeneous and fractured reservoirs. The high frequency solution leads to the Eikonal equation which is solved for a ‘diffusive time of flight’ (DTOF) that governs the propagation of the ‘pressure front’ in the reservoir. Our approach consists of two decoupled steps: calculation of the DTOF using the Fast Marching Method (FMM) and fully-implicit compositional simulation using DTOF as a spatial coordinate. The computational efficiency is achieved by reducing the 3-D compositional flow equation into 1-D equation using the DTOF as spatial coordinate, leading to orders of magnitude faster computation over full 3-D compositional simulation. The savings in computation time increases significantly with grid refinement and for high resolution models.
We demonstrate the power and utility of our method using synthetic and field applications. The field application involves history matching of three-phase production data from a horizontal well with multi-stage hydraulic fractures in a shale reservoir in East Texas. The properties of individual hydraulic fractures, microfractures and the matrix/fracture geometries and the extent of the stimulated reservoir volume were adjusted through history matching using the Genetic Algorithm with the FMM-based compositional simulation. For the history matching, 2,200 simulation runs were required but completed in four days using the FMM-based simulation, at least an order of magnitude savings in computation time over a commercial finite difference simulator. Multiple history-matched models were generated and used for obtaining the bounds of production forecast.
This study shows the novelty and efficiency of the FMM-based compositional simulation for field-scale modeling of shale reservoirs including phase behavior and multi-continua heterogeneity. It also enables systematic history matching and uncertainty analysis that require large number of simulation runs.