Fast Marching Method: A New Paradigm for Rapid Modeling of Subsurface Flow and Transport

Abstract:

In this talk I will discuss a novel approach for rapid field-scale modeling of subsurface flow and transport and its application to CO2 injection in conventional and unconventional oil reservoirs for enhanced oil recovery and carbon sequestration. The proposed approach is based on a high frequency asymptotic solution of the diffusivity equation in heterogeneous reservoirs and serves as a bridge between simplified analytical tools and complex numerical simulation. The high frequency solution leads to the Eikonal equation which is solved for a ‘diffusive time of flight (DTOF)’ using the Fast Marching Method (FMM). The DTOF represents the propagation of the ‘pressure front’ in the subsurface and generalizes the concept of ‘depth of investigation’ to heterogeneous and fractured reservoirs. More importantly, the ‘diffusive time of flight’ can be used as spatial coordinate to reduce the 3-D diffusivity equation into an equivalent 1-D equation which can be solved efficiently accounting for the relevant physics related to multi-continuum and compositional flow and transport in hydrocarbon reservoirs.

Our approach consists of two decoupled steps (Figure.1): calculation of the DTOF using the Fast Marching Method and fully-implicit compositional simulation using DTOF as spatial coordinate. The computational efficiency is achieved by reducing the 3-D compositional flow equation into equivalent 1-D equation using the DTOF as spatial coordinate, leading to orders of magnitude faster computation over full 3-D simulation. The savings in computation time increases significantly with grid refinement and for high resolution models.

The speed and versatility of the proposed method makes it ideally suited for high resolution reservoir characterization through integration of static and dynamic data. The major advantages of the proposed approach are its simplicity, intuitive appeal and computational efficiency. We demonstrate the power and utility of our method using synthetic and field examples.