This article focuses on interpretation of well test data from wells completed in naturally fractured reservoirs. Because of the presence of two distinct types of porous media, the assumption of homogeneous behavior is no longer valid in naturally fractured reservoirs. This article discusses two naturally fractured reservoir models, the physics governing fluid flow in these reservoirs and semilog and type curve analysis techniques for well tests in these reservoirs. Naturally fractured reservoirs are characterized by the presence of two distinct types of porous media: matrix and fracture. Because of the different fluid storage and conductivity characteristics of the matrix and fractures, these reservoirs often are called dual-porosity reservoirs.

Knowledge of the maximum- and minimum-permeability directions in anisotropic reservoirs helps to optimize injector and producer locations and is important for reservoir management, especially under secondary or enhanced recovery of hydrocarbons. The complete paper describes a method using transient-test data rich with dynamic information aiming to provide fieldwide permeability distribution in well-spacing scale, which is relevant for estimating fluid movement and recovery. The knowledge of flow communication between wells is key information for reservoir management, especially in secondary or tertiary recovery. The surveillance methods to collect dynamic data to gain such knowledge include multiple-well pressure-transient tests and tracer tests. The measurements of tracer agents arriving at producing wells provide direct confirmation of flow communication.

The study of pressure transient behavior in fractured-vuggy reservoirs has recently received considerable attention because a number of such reservoirs have been found worldwide with significant oil and gas production and reserves. In recent years, the use of highly deviated wells (HDW) is considered an effective means for developing this type of gas reservoir. However, in many fractured-vuggy reservoirs unexpected high gas production have been observed which cannot be identified with pressure transient models of horizontal well with pseudo state triple-porosity interporosity flow. This paper presents a semi-analytical model that analyzed the pressure transient behavior of HDW in triple-porosity continuum medium which consist of fractures, vugs and matrix. Introducing pseudo-pressure, Laplace transformation and Fourier transformation were employed to establish a point source and line source pseudo-pressure solutions in Laplace space. Then the pseudo-pressure transient curve was got by numerical inversion. Furthermore, the flow characteristics were analyzed thoroughly by examining the curve which is mainly affected by inclination angle of HDW and interporosity flow coefficients between different pore media. Sensitivity analysis on the pressure transient behavior was performed by varying some important parameters such as the inclination angle, fracture storativity ratio and interporosity flow coefficients. Finally, a field case was successfully used to show the application of the presented semi-analytical model. With its high efficiency, this approach will serve as a reliable tool to evaluate the pressure behavior of HDW in fractured-vuggy carbonate gas reservoirs.

In the shale oil reservoirs, the horizontal wells with large-scale fracturing treatments have been the most effective tools to enhance oil productivity. After large-scale fracturing treatments, many micro-seismic data showed that the fracture networks are generated in the reservoir along the wellbore. Understanding the complex fracture properties is the primary step for fracturing evaluation and productivity estimation. Thus, an efficient approach is needed to estimate the fracture properties. To improve this situation, a well-testing approach was proposed in this work to identify the fracture properties. This work was organized as follows: (1) developing a well-testing model of multiple fracture horizontal well (MFHW) including reservoir flow equations, fracture flow equations, and mass balance equations, (2) solving and verifying the proposed model using boundary element method, superposition principle, and numerical approach, (3) applying the well-testing model to investigate the pressure transient behaviors, and (4) estimating the fracture properties of shale oil wells from the Junggar Basin.

Summary Carbonate reservoirs comprise fractures, vugs, and cavities. Vugs have a large contribution to reserves of oil and gas, and the fractures provide effective paths for fluid flow in the reservoir. The triple‐porosity (TP) model is an effective conceptual method for capturing rock matrix and vugs and the microfractures connecting them. However, these fractures and vugs are always nonhomogeneous. Macrofractures and vugs cannot be handled with a continuum scheme because of their low density and high conductivity. In this approach, the TP conceptual model is implemented to characterize rock matrix, microvugs, and fractures. To capture the heterogeneity of fractures and vugs, macrofractures and vugs are represented explicitly with the discontinuum model. The boundaries of macrovugs and macrofractures are discretized into several elements. The boundary‐element method (BEM) is used to handle flow into macrofractures and vugs. The finite‐difference method is applied to handle flow within macrofractures. The flow within macrovugs is assumed to be pseudosteady state. With a simple discretization of the boundaries of macrovugs and macrofractures, the proposed model is shown to efficiently simulate the behavior of fractured carbonate reservoirs with heterogeneity. The computational accuracy is demonstrated using an analytical model and numerical simulation. On the basis of the proposed model, the effect of the heterogeneity of macrofractures and vugs on pressure‐transient behavior is analyzed. The results show that macrofractures and vugs cannot be handled with triple‐continuum models analytically. There will be several “dips” on the derivative of the pressure curve if macrovugs are discretely handled. Also, discretely handling the fractures and vugs will make the calculated dimensionless pressure and the derivative pressure lower than those calculated with the triple‐continuum models. After increasing the porosity of macrovugs, the pressure and the derivative will go down in the flow regimes dominated by macrovugs. The conductivity of macrofractures has a great impact on almost all the flow regimes except for boundary‐dominated flow. Finally, a field case is used to show the application of the proposed semianalytical model. The novelty of the new model is its ability to model the transient behavior of carbonate reservoirs with nonhomogeneous fractures and vugs. Furthermore, it provides an efficient method for characterizing the heterogeneity of multiscaled fractures and vugs.

Summary The dual-porosity and dual-permeability theory of poroelasticity is used to analyze the wellbore dual-pressure responses of dual-porosity or naturally fractured formations. The pressure decline is analyzed by modeling the dual-pressure regimes of the dual-porosity/dual-permeability medium during the after-closure phase of hydraulic fracturing. The analysis shows that both the matrix and natural-fracture permeability, as well as the developed-fracture length, can be estimated on the basis of the obtained pseudolinear and pseudoradial dual-pressure and dual-flow regimes. The estimations are made by use of the corresponding one-half and −1 slopes in the time-history plots of the wellbore-pressure derivative. The transition period between pseudolinear and pseudoradial regimes is also analyzed. The solution involves three time scales related to the rate of fluid flow through and in between the matrix and fractures network. Findings indicate the possible emergence of an additional −½ slope in the log-log pressure-derivative plot of low-permeability shale formations. It is further shown that the transient-pressure response of the formation could be calibrated by incorporating an appropriate interporosity flow coefficient as a measure of the linear-fluid-exchange capacity between the matrix and fracture porosities. The analytical expressions for the time markers of the upper limit for the pseudolinear regime, lower limit for the pseudoradial regime, and the time at which the dip bases occur in pressure-derivative curves are given to estimate this parameter. The solution is successfully applied to and matched with a published set of field data to provide estimations for the associated reservoir properties. The field-data analysis is elaborated by a corresponding sensitivity analysis, through which the prominent poroelastic parameters of the solution are determined. Last, the definitions of conventional key parameters attributed to solutions of this type, such as formation total compressibility, storage coefficients, and hydraulic diffusivity, are reformulated by use of the presented dual-porosity poroelastic approach to the problem.

Abstract Two-phase flow in shale gas reservoirs is caused by water flowback after multi-stage fractured, this paper presents a two-phase pressure transient analysis model of multi-stage fractured horizontal well in shale gas reservoirs. With the new mathematics model, the two-phase flow characteristics and well testing analysis for early production period can be described. The two-phase flow model is established by material balance law, Langmuir isotherm law and Fick diffusion law. Accurate solution to this flow model is obtained by source function theory, Laplace transform, three-dimensional eigenvalue method and orthogonal transformation. According to the solution, bilogarithmic type curve of the two-phase flow model is illustrated, the pressure transient performance under the effects of hydraulic fractures and shale gas reservoir properties are discussed. It is found that there are seven different flow regimes which have been identified on the type curve of two-phase flow model, initial gas-water saturation, storage ratio and fractured stages have deeply impacted the type curve; absorption index, skin factor and interporosity flow coefficient have lower influence to the curve shape. According to the research results and field data of Lower Paleozoic shale in China, improved well testing analysis and dynamic monitoring have been provided. The research of this paper can make optimization design for the parameters selection of drilling and hydrofracture in shale gas reservoir.

Abstract As indicated by Kazemi et al1 and Dean and Lo2, when dual porosity methods are used for reservoir forecasting purposes in naturally fractured reservoirs, a shape factor is needed for representing the block geometry and as a measure of matrix-fracture communication. Warren and Root3 in 1963 suggested a dimensionless parameter λ for the representation of the interporosity coefficient in naturally fractured reservoirs. Shape factor may be obtained from the estimation of λ. The interporosity coefficientλ, defines the extent of the communication between the matrix and fractures. Warren and Root offered no solutions for estimation of λ. Later on, solutions were proposed by several authors. A methodology suggested by the Gringarten3 method has been widely included in textbooks. In our study, we have demonstrated that this technique may result in errors of several orders of magnitude. This of course creates significant uncertainties in the estimation of the shape factor. Examples are included to highlight the errors, and it is emphasized that various other techniques including non-linear parameter estimations should be tried to ascertain the estimated values for λ.

Abstract Predicting the performance of individual oil wells is of great importance to petroleum engineering for continuous production optimization in the field. This study proposes a new Inflow Performance Relationships (IPR) for naturally fractured gas condensate reservoirs. Existing IPR models are commonly used for conventional solution gas drive reservoirs. The purpose will be to generate inflow performance relationships (well flowing pressure vs. flow rate) for naturally fractured condensate reservoirs as a function of the average reservoir pressure and fractured reservoir parameters including storage capacity (fracture storativity) and inter porosity flow parameter (interporosity flow coefficient). A dual porosity/dual permeability compositional equation of state simulator is used in this study. A regression program is used to fit the IPR curves and to obtain the corresponding equations. As a result, rational functions have been developed for the IPR curves for gas and oil phases. These correlations are functions of pressure drawdown and reservoir depletion. Additional correlations for predicting future maximum gas and oil rates were developed. The behavior of the future gas rate shows linear relationships between average reservoir pressure ratio and the maximum gas rate ratio. However, a highly non-linear behavior was observed for the oil phase. Additionally, fluid representing extreme types of condensates were also considered. Condensates with high fraction of light composition shows a hump and three distinct regions with different slopes in future maximum rate curves. In the other case where the composition of the condensate contains heavy components has shown nonlinear curves.

Abstract The formations of DaQing gas field are mainly volcanic reservoirs which have the characteristics of low permittivity and complex formation structures. Most of these wells need fracturing remodeling to meet the standards of industrial gas stream, and also, the gas productivity tests as well as the pressure recovery tests conducted on these wells are different from other regular gas reservoirs. Considering the nature of the volcanic reservoir, such as dissolution pores, karsts caves, natural fracture development, we built two mathematical models of dissolution pores development and natural fracture development under both of the Darcy flow conditions and Non-Darcy flow conditions separately to predict the production of triple porosity reservoir after gas reservoir well fractures. By using the Laplace transform and numerical inversion, the equation to calculate production of complex volcanic gas wells is obtained. Based on these researches, law of volcanic reservoir productivity is investigated. The theoretical data are compared with the practical data collected from the field operation. The comparison results reveal how the parameter of the fluid volume, proppant indexes, and conductivity of artificial fracturing induced fractures and length of fractures change affect the productivity. The research work reported in this paper provides theoretical support on the optimization method of fractured wells design of volcanic gas reservoir.