This paper presents analytical solutions for interpreting pressure-transient tests for wells producing from a finite composite reservoir system. The paper also includes rate solutions and methods for analyzing long-term production data and forecasting production of oil or gas in a finite composite reservoir.

This paper presents analytical solutions for interpreting pressure transient tests for wells producing from a finite composite reservoir system. We also present rate solutions and methods for analyzing long term production data and forecasting production of oil or gas in a finite composite reservoir.This paper presents three field examples to demonstrate the application of the type curve analysis method to buildup and falloff test data.

In this paper, we present a model of the complete characteristic transient response from a composite reservoir including the effects of skin, wellbore storage and phase redistribution at the well. We present six flow regimes and the combined effects of wellbore storage and phase redistribution on pressure behavior in composite reservoirs.Using an automatic history matching approach, we analyzed three buildup tests and a pressure falloff test.This method eliminated the serious uniqueness problem associated with type curve analysis. We demonstrate that incorrect reservoir parameter estimates and incorrect production performance predictions would result from the use of any model that lacks the capabilities of the model we present in this paper.We also demonstrate possible misinterpretations of pressure data ~at may result from not recognizing the presence of phase redistribution in the buildup test data or not recognizing the composite reservoir behavior.

Summary This paper presents a new analytical model for interpreting pressure-transient tests for wells producing from dual-porosity reservoirs. This model includes unsteady-state matrix flow and incorporates the effects of wellbore storage, skin, and, for gas reservoirs, desorption. The model is applicable to bounded and infinite-acting reservoirs. Introduction Numerous analytical models have been presented recently to describe the transient pressure behavior of dual-porosity reservoirs. Dual-porosity or naturally fractured reservoirs are formations composed of two porous media of different porosities and permeabilities. One medium, the matrix blocks constituting the primary porosity, contains the majority of the fluid stored in the reservoir and possesses a low conductivity. The other medium, the fractured network constituting the secondary porosity, acts as the conductive medium for fluid and possesses a high flow capacity but low storativity. The storativities of the two media usually differ by several orders of magnitude: consequently, these reservoir types are referred to as dual-porosity reservoirs. These types of reservoirs are also characterized by a large permeability contrast between the two media. The basis for the study of dual-porosity media was presented by Barenblatt and Zheltov, who treated the fractured reservoir as a continuum with the fractured network superimposed on the primary porosity. Furthermore, they assumed that the flow of fluid within the matrix occurs under pseudosteady-state conditions. Warren and Root, using a formulation similar to Barenblatt and Zheitov, were the first to present analytical solutions to this model with the assumption of a pseudosteady-state matrix flow and developed a procedure for interpretation of buildup tests without wellbore storage and skin effects. Warren and Root showed that. on a semilog graph, their solution yielded two parallel straight lines with slopes related to formation flow capacity. The existence of two parallel semilog straight lines was disputed by Odeh, who used a model similar to that used by Warren and Root but who investigated different ranges of parameters. Kazemi was the first to consider the effects of unsteady-state matrix flow. He used a numerical model and assumed that the dual-porosity system can be simulated by a layered radial system. His results are similar to those of Warren and Root with the exception of a smooth unsteady-state transition zone between the two parallel semilog straight lines compared with the flat pressure profile characteristic of the pseudosteady-state transition. Later, de Swaa presented analytical unsteady-state solutions for a well producing at a constant rate in naturally fractured reservoirs. He introduced new diffusivity definitions for reservoir characterization. Kucuk and Sawyer presented a comprehensive model for gas flow in a naturally fractured reservoir of the Devonian shale. They investigated the behavior of dual-porosity gas reservoirs including the Klinkenberg effect in the tight shale matrix and the effect of gas desorption from pore surfaces of the shale matrix. Mavor and Cinco-Ley extended Warren and Root's solution to take into account the effects of wellbore storage and skin. Bourdet and Gringarten were the first to identify the existence of a semilog straight line during the transition period. They stated that this line had a slope one-half the classic parallel semilog straight lines and existed if the fracture storativity was not too large. Streltsova and Serra et al. analyzed the transition period in detail and confirmed the existence of the straight line of slope 0.5756, one-half the classic semilog straight line (1.151). Serra et al.'s solution includes unsteady-state matrix flow but not wellbore storage effects. Chen et al. presented an application of classic techniques to bounded dual-porosity systems and discussed flow regimes that may be exhibited by drawdown data. Their work, however, did not include wellbore storage, skin, or the effects of gas desorption. Cinco-Ley and Samaniego-V. presented a model based on the transient matrix flow model formulated by de Swaan-O. and demonstrated that the behavior of dual-porosity reservoirs can be correlated by use of three dimensionless parameters (i.e., w, AFD, and maD). They also established that, regardless of matrix geometry, the transition period might exhibit a straight line with a slope equal to one-half the slope of the classic parallel semilog straight lines. The purpose of this paper is to present an analytical solution for dual-porosity reservoirs, capable of modeling both pseudosteady- and unsteady-state matrix flow, for both finite and infinite-acting reservoirs. The solution includes the effect of gas desorption from the pore surfaces of shale matrix in dual-porosity gas reservoirs with sorbed gas. This is of particular application to the Devonian shale gas reservoirs and any dual-porosity "black shale" reservoir with matrix kerogen. Wellbore storage and skin effects are included in the solution. Furthermore, application of the model to analysis of field pressure-transient data with an automatic parameter-estimation technique is demonstrated. Theoretical Formulation Formulation of Flow Equations. The differential equations governing fluid flow in naturally fractured reservoirs are derived in a manner similar to de Swaan-O. formulation and are presented in Appendix A of the original version of this paper. The derivation is based on the following assumptions:unsteady-state radial flow in an isotropic dual-porosity reservoir at uniform thickness,negligible gravitational forces and small pressure gradients;uniform initial reservoir pressure throughout the reservoir;fluid production through the fracture network with the matrix blocks acting as a uniformly distributed source;one-dimensional (ID) unsteady-state flow in the matrix blocks that are of regular shape;gas-desorption source uniformly distributed within the matrix blocks;gas-desorption rate linear with pressure; andwell producing at a constant rate in a finite reservoir with wellbore storage and skin effects. The diffusivity equations describing flow in the fracture network for both oil and gas reservoirs in dimensionless form are ............(1) for oil reservoirs and ............(2) for gas reservoirs with desorption. The dimensionless pressure, PfD, is defined identically for oil and gas except that adjusted pressure instead of real pressure is used for gas to linearize the gasflow equations. SPEFE P. 384

The characteristic pressure behavior of naturally fractured reservoir systems has been extensively researched in petroleum engineering literature. In a naturally fractured system, reservoir fluids exist in two interconnected systems, the matrix system which provides the bulk of the reservoir volume, and the fracture network which provides the conductive pathway for transmitting fluids to the producing wells. If the flow between adjacent matrix blocks and fluid transport from the matrix blocks to the wellbore is only through the fracture network, then the system is considered dual-porosity. When there is possibility of fluid flow directly between the neighboring matrix blocks and to the well through the matrix in the unfractured region, the system is considered to be dual-permeability. However, the pressure responses from actual field data display similar characteristics for both dual-porosity and dual-permeability reservoirs. Field data that display the classical dual permeability behavior are not very common in the petroleum literature. This paper presents some field pressure transient tests from a naturally fractured Saudi Arabian reservoir that display the classical dual-permeability characteristics and the analyses performed on them. Introduction The significance of natural fractures and fracture related production in the Hanifa reservoir has been reported by earlier investigators. They found that this reservoir has low matrix permeability between 0.01 and 5md and yet during production testing, anomalously high flow rates such that could not be produced from such low permeability matrix systems were recorded on the flowmeter log. It was also noticed that over half of the flow could be attributed to only one or two 10ft thick stratigraphic intervals. The large disparity between core derived permeabilities and well test permeabilities also indicated that there must be another enhanced permeability system in this reservoir. It was reported that on the average, permeability from well test was 40 times greater than the permeability determined from core plugs. This was attributed to the presence of fractures which have also been observed in several cores from Hanifa wells and were also seen on borehole imaging logs. Most of the fractures in the cores are open and less than 2 mm wide. In a recent detailed study by Luthy and Grover, they concluded that the fractures and stylolites form the essential fluid permeability system of the reservoir. From these previous efforts on the Hanifa reservoir, it was established that the Hanifa is a dual-permeability system consisting of a matrix permeability system and a fracture permeability system. The fracture permeability system accounts for the majority of the fluid flow in this reservoir. However the matrix could contribute some production, however small, in some unfractured intervals. The main objectives of this analytical pressure transient work were to seek for reservoir engineering evidence to confirm the dual-permeability characteristics of this naturally fractured reservoir from the behavior of the pressure transient and to estimate flow capacities. The resulting flow capacities would be used in generating permeability distribution for numerical flow simulation. Reservoir Concepts The term dual porosity, often used to describe naturally fractured reservoirs, stands for a reservoir with a primary and a secondary porosity. The primary porosity usually refers to a matrix system which was formed when the reservoir was originally deposited. This matrix system is made up of fine pores and a low permeability. The secondary porosity was formed later by geological processes which modified the primary porosity. In our case, the secondary porosity is a set of interconnecting fractures, fissures or vugs which have high permeabilities. The matrix system serves as the fluid storage medium for the entire system since more than 90 percent of the total fluid reserve is contained in the matrix pore spaces. P. 357^