A Multiple-Continuum Approach for Modeling Multiphase Flow in Naturally Fractured Vuggy Petroleum Reservoirs

The existence of vugs or cavities in naturally fractured reservoirs has long been observed. Even though these vugs can be largely attributed to reserves of oil, natural gas, and groundwater, few investigations of vuggy fractured reservoirs have been conducted. In this paper, a new multiple-continuum conceptual model is developed, based on geological data and observations of core samples from carbonate formations in China, to investigate multiphase flow behavior in such vuggy fractured reservoirs. The conceptual model has been implemented into a three-dimensional, three-phase reservoir simulator with a generalized multiple-continuum modeling approach. The conceptual model considers vuggy fractured rock as a tripleor multiple-continuum medium, consisting of (1) highly permeable fractures, (2) low-permeability rock matrix, and (3) various-sized vugs. The matrix system may contain a large number of small or isolated cavities (of centimeters or millimeters in diameter), whereas vugs are larger cavities, with sizes from centimeters to meters in diameter, indirectly connected to fractures through small fractures or microfractures. Similar to the conventional double-porosity model, the fracture continuum is responsible for the occurrence of global flow, while vuggy and matrix continua, providing storage space, are locally connected to each other (and interacting with globally connecting fractures). For practical application of the multi-continuum concept in reservoir simulation, we propose a novel upscaling method for computing equivalent gridblock permeabilities of coarse blocks containing large isolated vugs, in which the local problems consisting of Darcy and Stokes flows are solved. In addition, we describe an efficient boundary condition for accurate computation of upscaled permeabilities. In the numerical implementation, a control-volume, integral finite-difference method is used for spatial discretization, and a first-order finite-difference scheme is adapted for temporal discretization of governing flow equations in each continuum. The resulting discrete nonlinear equations are solved fully implicitly by Newton iteration. The numerical scheme is verified and applied to simulate water-oil flow through the fractured vuggy reservoirs of the Tahe Oil Field in China. Introduction Since the 1960s, investigation of flow and transport processes in fractured reservoirs has received much attention with significant progress being made. Driven by the increasing need to develop petroleum and geothermal reservoirs (as well as to resolve subsurface contamination problems), many numerical modeling approaches and techniques have been developed [6, 25, 15, 21]. The petroleum industry is currently facing a growing demand for oil and natural gas, while at the same time fewer new oil reserves exist worldwide. The efficient development of naturally fractured reservoirs, possessing a large portion of current world oil and gas reserves, has become a top priority. Thanks to the known low oil recovery rates from these reservoirs, interest in enhancing oil and gas recovery from such reservoirs has grown, with more investigations conducted for multiphase flow and transport phenomena in fractured reservoirs [2, 19, 4, 12]. Also, environmental concerns over subsurface contamination have motivated many related, similar studies [31, 26, 7]. Even though significant progress has been made towards understanding and modeling of flow and transport processes in fractured rock since the 1960s [6, 25, 15, 16, 21], most studies have focused primarily on naturally fractured reservoirs without taking into consideration of cavities. Recently, characterizing vuggy fractured rock has received attention, because a number of fractured vuggy reservoirs have been found worldwide that can significantly contribute to reserves and the production of oil and gas [17, 23, 18, 13, 9]. Mathematical approaches developed for modeling flow through fractured reservoirs rely in general on continuum approaches, involving developing conceptual models, incorporating the geometrical information of a given fracturematrix system, setting up mass and energy conservation equations for fracture-matrix domains, and then solving discrete nonlinear algebraic equations of mass and energy conservation. The commonly used mathematical methods for modeling flow through fractured rock include: (1) an explicit discrete-fracture and matrix model [24], (2) a dual-continuum method, including doubleand multi-porosity, dual-