Fujita, Yusuke (2014-08). Fast Marching Method with Multiphase Flow and Compositional Effects. Master's Thesis.
In current petroleum industry, there is a lack of effective reservoir simulators for modeling shale and tight sand reservoirs. An unconventional resource modeling requires an accurate flow characterization of complex transport mechanisms caused by the interactions among fractures, inorganic matrices, and organic rocks. Pore size in shale and tight sand reservoirs typically ranges in nanometers, which results in ultralow permeability (nanodarcies) and a high capillary pressure in the confined space. In such extremely low permeability reservoirs, adsorption/desorption and diffusive flow processes play important roles for a fluid flow behavior in addition to heterogeneity-driven convective flow.
In this study, the concept of "Diffusive Time of Flight" (DTOF) is generalized for multiphase and multicomponent flow problems on the basis of the asymptotic theory. The proposed approach consists of two decoupled steps - (1) calculation of well drainage volumes along a propagating 'peak' pressure front, and (2) numerical simulation based on the transformed 1-D coordinates. Geological heterogeneities distributed in 3-D space are integrated by tracking the propagation of 'peak' pressure front using a "Fast Marching Method" (FMM), and subsequently, the drainage volumes are evaluated along the outwardly propagation contours. A DTOF-based numerical simulation is performed by treating a series of the DTOF as a spatial coordinate. This approach is analogous to streamline simulation, whereby a multidimensional simulation is transformed into 1-D coordinates resulting in substantial savings in computational time, thus allowing for high resolution simulation. However, instead of using a convective time of flight (CTOF), a diffusive time of flight is introduced in the modeling of a pressure front propagation.
The overall workflow, which consist of the FMM and numerical simulation, is described in detail for single-phase, two-phase, blackoil, and compositional cases. The model validation is firstly performed on single-porosity systems with and without geological heterogeneity, then extended to multi-continuum domains including dual-porosity fractured reservoir and triple-continuum system. The large-scale unconventional models are finally demonstrated in consideration of the permeability correction for shale gas system and capillarity incorporation for confined phase behavior in multiphase shale oil system.