This study presents the application of a new analytical model for analyzing pressure transient data for wells intercepted by a finite-conductivity vertical fracture in a closed square multilayered reservoir using the concept of a dual-porosity system. The solution with the single-layer solution; secondly, to verify the numerical solution with the analytical solution. A set of asymptotic analytical (early-, intermediate-and late-time) solutions is also presented.

In addition, we developed constant rate drawdown type curves applicable for analyzing transient pressure data. These type curves are used to match drawdown and buildup curves to determine fracture half-length, reservoir permeability and fracture conductivity. The results obtained from our type curves indicate that if the reservoir conductivity is known or can be calculated from given data, the estimated values of the aforementioned parameters compared favorably with the value of the designed parameter.

Although this study presents the solution to a two-layered system, it can be extended to a n-layered reservoir system.


The double-porosity models originated by Barenblatt et al and extended by many other are generally used to represent naturally fractured porous systems by superimposing two continua, one for fractured system and another for the porous matrix. In a previous study a double porosity model was used to previous study a double porosity model was used to simulate the behavior of tight multi-layered reservoirs intercepted by hydraulically induced vertical fracture of finite conductivity. Although several studies have been conducted on either wells producing double porosity reservoirs or fractured producing double porosity reservoirs or fractured wells in homogeneous reservoirs there are very few studies that include fractures in double porosity multi-layered reservoirs. Using the work of Barenblatt et al Warren and Root extended the transient pressure analysis of fractured water reservoirs to oil reservoirs and introduced the concept of "two porosity" system. While Warren and Root assumed pseudo-steady state interporosity flow Kazemi's and deSwaan's model allowed for transient interporosity flow. The concepts of wellbore storage and skin were later incorporated by Mavor and Cinco-ley.

Both models have been established to exhibit three well defined flow periods. These periods include: early time, which is dominated by storativity of the natural fractures, the intermediate time, when the fluid transfer from matrix to fractures becomes the dominating factor and the pressure in the network of the fractures tends towards stabilization and lead to transition period, and long time, when the flow is controlled by the storage capacity of the entire system. The behavior of a double porosity system is normally correlated by the fracture storage capacity parameter w and the interporosity flow parameter nf or parameter w and the interporosity flow parameter nf or dimension less matrix hydraulic diffusivity nmaD.

In the absence of fractures and layers, the studies by Cinco-Ley et al and Cinco-Ley and Samaniego-V. provide a complete analysis of the behavior of a well provide a complete analysis of the behavior of a well intersecting a finite conductivity fracture. For double porosity reservoirs Houze et al developed a model to study the behavior of wells intersected by infinite conductivity and uniform flux vertical fractures.

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