Fast Marching Methods: Application via Integration with Commercial E&P Software

Development and production of unconventional reservoirs, especially shale, are on the rise and so is the need to better understand drainage volumes, reliably estimate reservoir properties, and forecast well performance. Numerical simulation and analytical techniques, like decline curve analysis and pressure transient analysis, have been applied to unconventional resources. However, analytical methods rely on several simplifications and while numerical simulation can account for complex geological models it is computationally expensive. Fast Marching Methods (FMM), being a semi-analytical calculation, is between the two approaches and retains the simplicity of the analytical approach while achieving the desired generality.

The generalization of the concept of depth of investigation to heterogeneous reservoirs utilizes the idea of diffusive time-of-flight and better accounts for the non-uniform pressure fronts that may be distorted due to heterogeneity effects. The pressure front propagation is obtained by solving the Eikonal equation, which is derived from an asymptotic solution of the diffusivity equation. The FMM solves the Eikonal equation very efficiently using a single non-iterative solution, making it very fast. The FMM estimates the drainage volume and the diffusive time of flight can be used as a spatial coordinate to reduce the 3D diffusivity equation into a 1D equation allowing for rapid forecasting of well pressure and rate performance.

In this work, the FMM is implemented into an application plug-in and is integrated with a common commercial E&P software platform. The integration of the FMM Plug-in capitalizes on the simplicity, intuitive appeal, power and utility of the approach, like providing the time-evolution of the drainage volume for visualization, and utilizes the software platform features, like state-of-the-art visualization tools. This work also includes a number of applications that demonstrate the capability of FMM Plug-in to calculate the drainage volume and forecast well pressure or rate performance and validate its results against an industry-reference finite difference simulator. Finally, a study on the scalability of calculations runtime demonstrate the speed advantage that FMM has over finite difference simulators.