A Triple-Continuum Pressure-Transient Model for a Naturally Fractured Vuggy Reservoir

We present an analytical approach for pressure transient test analysis in naturally fractured vuggy reservoirs. This analysis approach relies on a triple-continuum concept, using observed geological data from carbonate oil formations in western China, to describe transient flow behavior in fracture-vugmatrix reservoirs. In the conceptual mathematical model, fractured vuggy rock is considered as a triple-continuum medium, consisting of fractures, rock matrix, and vugs (or cavities). Similar to the classical double-porosity model, the fracture continuum is assumed to be responsible for the occurrence of global flow, while vuggy and matrix continua (providing primary storage space) interact locally with each other as well as with globally connected fractures. Furthermore, the triple continua of fractures, matrix, and vugs are assumed to have uniform and homogeneous properties throughout, and intercontinuum flows between them are at pseudosteady state. With these assumptions, we derive analytical solutions in Laplace space for transient flow toward a well in an infinite and finite reservoir with wellbore storage and skin effects. The analytical solutions reveal typical pressure responses in a fracture-vug-matrix reservoir and can be used for estimating vug properties, in addition to fracture and matrix parameters, through properly designed and conducted well tests. As application examples, actual well test data from a fractured-vuggy reservoir in Western China are analyzed using the triple continuum model. 1 Funded by National Basic Research Program of China (973 Program), “Studying the Fundamentals of the Carbonate Karst Reservoir Development 2006CB202400.” Introduction Since the 1960s, significant progress has been made towards understanding and modeling of flow processes in fractured rock [Barenblatt et al., 1960; Warren and Root, 1963; Kazemi, 1969; Pruess and Narasimhan, 1985]. However, most of these studies have focused primarily on naturally fractured reservoirs without taking into consideration large 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 oil and gas reserves and production [Kossack and Curpine, 2001; Rivas-Gomez et al., 2001; Lui et al. 2003; Hidajat et al., 2004; Camacho-Velazquez et al., 2005; Kang et al. 2006; Wu et al. 2006]. Among the commonly used mathematical methods for modeling flow through fractured rock, dual-continuum models (i.e., doubleand multi-porosity, and dual-permeability) are perhaps the most popular approaches used in reservoir modeling studies. In addition to the traditional double-porosity concept, a number of triple-porosity or triple-continuum models have been proposed [Closemann, 1975; Wu and Ge, 1983; Abdassah, and Ershaghis, 1986; Bai et al. 1993; Wu et al., 2004; Kang et al. 2006; Wu et al. 2006] to describe flow through fractured rock. In particular, Liu et al. [2003] and Camacho-Velazquez et al. [2005] present several new triplecontinuum models for single-phase flow in a fracture-matrix system that includes cavities within the rock matrix (as an additional porous portion of the matrix). In general, these models have focused on handling the heterogeneity of the rock matrix or fractures, e.g., subdividing the rock matrix or fractures into two or more subdomains with different properties. This study develops an analytical model for analyzing transient pressure behavior in naturally fractured vuggy reservoirs and presents our continuing effort in investigating flow processes in naturally fractured vuggy reservoirs [Kang et al. 2006; Wu et al. 2006]. In this study, we focus on singlephase transient flow and fractured vuggy rock, conceptualized also as a triple-or multiple-continuum medium, consisting of (1) highly permeable fractures, (2) low-permeability rock matrix, and (3) vugs. Similar to the conventional doubleporosity model, the fracture continuum is responsible for global flow, while vuggy and matrix continua, providing storage space, are locally connected to each other and interacting with globally connecting fractures. With these assumptions, we derive a mathematical model and analytical SPE 110044 A Triple-Continuum Pressure-Transient Model for a Naturally Fractured Vuggy Reservoir Yu-Shu Wu, SPE, Lawrence Berkeley National Laboratory; Christine Ehlig-Economides, SPE, and Guan Qin, SPE, Texas A&M University; Zhijiang Kang and Wangming Zhang, Sinopec; and Babatunde Ajayi, SPE, and Qingfeng Tao, SPE, Texas A&M University