This study develops a mathematical model for the analysis of pressure behavior in fractured lithophysal reservoirs. The lithophysal rock is described as a tri-continuum medium, consisting of fractures, rock matrices, and cavities. In the conceptual model, fractures have homogeneous properties throughout and interact with rock matrices and cavities that have different permeabilities and porosities. Global flow occurs through the fracture network only, while rock matrices and cavities contain the majority of fluid storage and provide fluid drainage to the fractures. Interporosity flows between the triple media are described using a pseudosteady-state concept and the system is characterized by interporosity transmissivity ratios and storativity ratio of each continuum. Pressure behavior is analyzed by examining the pressure drawdown curves, the derivative plots, and the effects of the characteristic parameters. Typical pressure responses from fractures, matrices, and cavities are represented by three semilog straight lines; the transitions by two troughs below the stabilization lines in the derivative plots. The analytical solution to the proposed model is further verified using a numerical simulation.The analytical model has also been applied to a published field-buildup well test and is able to match the pressure buildup data.Keywords: Naturally fractured reservoirs, Dual-porosity model, Triple-porosity model, Warren-Root solution, Well testing analysis, Dual-continuum medium. 2
IntroductionCharacterizing the behavior of naturally fractured reservoirs is important for studying the flow and transport processes in underground natural-resources recovery, waste storage, and contaminant remediation. In general, fractured rock can be considered as a multiporous medium, in which fractures and porous blocks constitute the flow system.Because of their high permeability and connectivity, fractures provide major flow channels for global fluid movement, whereas high-porosity porous blocks contain the majority of fluid storage and provide gradual fluid drainage to the fractures. Fluid flow in fractured rock is of interest in many engineering fields and has been a subject of active research for several decades. Barenblatt et al. (1960) first introduced the dual-porosity model, in which a fractured medium is represented by two completely overlapping continua, porous matrix and fractures. This double-porosity model was further developedby Warren and Root (1963) to represent the naturally fractured reservoir as an idealized system formed by identical rock-matrix blocks, separated by an orthogonally fractures.Any infinitesimal volume of the fractured formation contains a large proportion of the two constitutive media. Each point in the system is therefore assigned with two pressures, one for the fracture and the other for the matrix. Fluid exchange between the two constitutive media has been describeded by various models. A pseudosteady-state interporosity flow concept was proposed by Barenblatt et al (1960) and subsequent...