Development and Application of Fast Simulation Based on the PSS Pressure as a Spatial Coordinate

Rapid modeling of multi-well interactions is extremely useful for infill drilling optimization and in the determination of optimal well spacing in reservoir development. In the case of unconventional reservoirs, especially, the requirement is especially acute for the low permeabilities, since the period of transient flow is large and the amount of historical data showing well interactions is limited. This research starts by examining and extending previous applications of the Fast Marching Method (FMM) and the diffusive time of flight (DTOF). The previous study applied the 1D DTOF coordinate to numerical simulation (FMM-SIM), but the current approach enables pressure approximation without the need to solve numerical finite difference matrix system (FMM-DTOF), and this can be extendable to multi-well interaction through superposition. Although FMM has the strength in its fast computational time due to the dimensional reduction, it is based on the underlying assumption that the pressure drop should be well-aligned with the DTOF coordinate. As an alternative 1D coordinate, we propose the fast simulation based on the PSS as a spatial coordinate, which can overcome the limitations which FMM has and still hold the same benefit. First, we derive the 1D coordinate based on the PSS pressure under a 3D reservoir model and construct its discrete form. Next, we develop both a numerical system (PSS-SIM) and semi-analytic pressure solution (PSS-DTOF) under the PSS coordinate to analyse benefits of each approach. While a numerical simulation has its own strength in its accuracy, semi-analytic approximation has its benefit in that it does not require solving computationally heavy non-linear matrix problems. We validate the approaches against both an analytical solution and a commercial reservoir simulator. First, PSS-SIM provides excellent approximations to the flow simulation results under both early-mid and late time transient, which is an indicator of a well-aligned 1D coordinate along actual pressure drop of the entire reservoir. Secondly, PSS-DTOF also shows accurate performance in forecasting early-mid time transient of reservoirs, although it has a little mismatch in late time solution due to its pressure/flux approximation. Based on their strength and shortcoming, we concluded that PSS-DTOF is more suitable for early-mid time reservoir development, such as well spacing optimization problems, while PSS-SIM is a useful tool for late time transient analysis