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

Abstract

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-vug-matrix 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. IntroductionSince 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 Among the commonly used mathematical methods for modeling flow through fractured rock, dual-continuum models (i.e., double-and 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 triple-continuum 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 m...

Flow Modeling of Well Test Analysis for Porous–Vuggy Carbonate Reservoirs

“…The last is matching the numerical results with field data to estimate property parameters. Wu et al (2004Wu et al ( , 2007Wu et al ( , 2011) examined their numerical solutions using analytical solutions of single-phase flow by ignoring wellbore storage and skin effects (note that their numerical models did not consider the wellbore storage and skin effects). Numerical method can be used to study both multiple-and single-phase flows, however, analytical method for unsaturated reservoirs is more convenient than numerical method in real applications.…”

“…The pressure derivative curve is fluctuant. In fact, many well testing data are irregular (Carnegie et al 2009;Setiawan et al 2011;Wu et al 2007) possibly due to unidentifiable noise. Therefore, we smoothed the pressure derivative curve using a General least-squares smoothing technique (McDonald et al 2009;Nisbet et al 2009).…”

“…Reservoirs composed of matrix, fracture, and vug systems are called "matrix-fracture-vug triple porosity reservoirs" (Liu et al 2003;Camacho-Velázquez et al 2006). Matrix-fracture dual-porosity and matrix-fracture-vug triple-porosity reservoirs are the most commonly studied (Lai et al 1983;Rasmussen and Civan 2003;Wu et al 2004Wu et al , 2007Wu et al , 2011Camacho-Velázquez et al 2006;Corbett et al 2010, for example). However, reservoirs mainly composed of matrix and vug systems, like porous-vuggy carbonate reservoirs in Tahe oilfield of China, do exist.…”

“…The flow problem in carbonate reservoirs has been well researched: (i) theory and applications on dual porosity flow model for well test analysis of fractured reservoirs (Al-Ghamdi and Ershaghi 1996;Bourdet and Gringarten 1980;Braester 1984;Bui et al 2000;Izadi and Yildiz 2007;Lai et al 1983;Liu et al 2003;Jalali and Ershaghi 1987;Rasmussen and Civan 2003;Wijesinghe and Culham 1984;Wijesinghe and Kececioglu 1985) and (ii) theory and applications on triple porosity flow model for well test analysis of fractured-vuggy reservoirs (Bai and Roegiers 1997;Camacho-Velázquez et al 2006;Nie et al 2011Nie et al , 2012aPulido et al 2006;Veling 2002;Wu et al 2004Wu et al , 2007Wu et al , 2011. Both the medium connected to the wellbore and the interporosity of fluid from the matrix or vug systems into the fracture system were considered as the fracture system.…”

“…Both the medium connected to the wellbore and the interporosity of fluid from the matrix or vug systems into the fracture system were considered as the fracture system. Pseudo-steady interporosity flow characteristics were commonly assumed by considering arbitrarily shaped matrix blocks and vugs (Camacho-Velázquez et al 2006;Wu et al 2004Wu et al , 2007Wu et al , 2011. Unsteady interporosity manner was assumed by considering spherical shaped matrix blocks and vugs (Nie et al 2011(Nie et al , 2012a.…”