A Unified Mathematical Model for Unconventional Reservoir Simulation
Yu-Shu Wu, Perapon Fakcharoenphol
Source abstract
Abstract Unconventional hydrocarbon resources from low-permeability formation, i.e., tight sands and shales, are currently received great attention because of their potential to supply the entire world with sufficient energy for the decades to come. In the past few years, as a result of industry-wide R&D effort, progresses are being made towards commercial development of gas and oil from such unconventional resources. However, studies, understandings, and effective technologies needed for development of unconventional reservoirs are far behind the industry needs. Unconventional reservoir dynamics is characterized by highly nonlinear behavior of multiphase flow in extremely low- permeability rock, coupled by many co-existing, processes, e.g., non-Darcy flow and rock-fluid interaction within tiny pores or micro-fractures. Quantitative characterization of unconventional reservoirs has been a significant scientific challenge currently. Because of complicated flow behavior, strong interaction between fluid and rock as well as multi-scaled heterogeneity, the traditional Darcy-law-and-REV-based model may not be applicable for describing flow phenomena in unconventional reservoirs. In this paper, we will discuss a general mathematical model proposed for unconventional reservoir simulation. We will present a unified framework model to incorporate various nonlinear flow and transport processes using a multi-domain, multi-continuum concept to handle multi-scaled heterogeneity of unconventional formation. Specifically, we will use extended or modified Darcy law to include the following processes: (1) non-Darcy flow with inertial effects; (2) non-Newtonian behavior (i.e., threshold pressure gradient for flow to occur); (3) adsorption and other reaction effect; and (4) rock deformation. The proposed modeling methodology has been implemented into a general reservoir simulator and will be demonstrated for its application in analyzing well tests in fractured vuggy reservoirs, non-Darcy flow, and non-Newtonian flow in porous and fractured reservoirs.
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