The fast marching method (FMM) based rapid simulation has offered significant speed-up, commonly two to three orders of magnitude, for modeling unconventional reservoirs. The key concept here is a coordinate transformation from 3-D to 1-D using the ‘Diffusive-Time-of-Flight' (DTOF) as the spatial coordinate. The DTOF represents the travel time for pressure front propagation and generalizes the concept of depth of investigation for heterogeneous reservoirs and hydraulically fractured wells. The DTOF can be efficiently computed by solving the Eikonal equation using the Fast Marching Method (FMM). While the FMM-based simulation has shown great potential for single well problems, application to multi-well problems with well-interference has remained a challenge to date.
Previous efforts to extend the FMM-based simulation to multi-well problems partitioned the flow domain based on well drainage boundaries. Within each of the subdomain, 1-D flow simulations are carried out using DTOF as the spatial coordinate. This method was shown to be a good approximation as long as the drainage boundaries do not change significantly during the simulation period. However, in actual field operations, the well drainage volumes change dynamically because of differences in pressure depletion among producers caused by variations in well productivity and hydraulic fracture network. We propose a novel extension of the FMM-based multi-well simulation that accounts for dynamic changes in drainage boundaries by allowing communications between the sub-domains using inter-partition transmissibility. The inter-partition transmissibilities are computed using analytic pressure solution and inter-partition fluxes are accounted for during flow simulation using non-neighbor connections. Our implementation is benchmarked with a commercial finite difference simulator using a series of synthetic and field scale numerical examples with multiple wells and fracture interference. The results clearly demonstrate the benefits of the proposed approach both in terms of accuracy and computational efficiency.
A unique and novel aspect of this work is generalization of the FMM-based simulation accounting for interferences of multiple wells because of differential depletion. The proposed rapid simulation approach is particularly useful for optimizing well spacing and minimizing frac-hits in unconventional plays.