Stress-dependent Fracture Permeability Research Articles

A Connectivity Metrics-Based Approach for the Prediction of Stress-Dependent Fracture Permeability

Rapid and accurate assessment of fracture permeability is critical for subsurface resource and energy development as well as rock engineering stability. Fracture permeability deviates from the classical cubic law under the effect of roughness, geological stress, as well as mining-induced stress. Conventional laboratory tests and numerical simulations are commonly costly and time-consuming, whereas the use of a connectivity metric based on percolation theory can quickly predict fracture permeability, but with relatively low accuracy. For this reason, we selected two static connectivity metrics with the highest and lowest prediction accuracy in previous studies, respectively, and proposed to revise and use them for fracture permeability estimation, considering the effect of isolated large-aperture regions within the fractures under increasing normal stress. Several hundred fractures with different fractal dimensions and mismatch lengths were numerically generated and deformed, and their permeability was calculated by the local cubic law (LCL). Based on the dataset, the connectivity metrics were counted using the revised approach, and the results show that, regardless of the connectivity metrics, the new model greatly improves the accuracy of permeability prediction compared to the pre-improved model, by at least 8% for different cutoff aperture thresholds.

The Role of Heterogeneity on Deformation and Flow in Fractured Coal Slopes

The fractures in brown coal influence fluid flow and deformation in these materials. These fractures display highly heterogeneous characteristics in the distributions of their apertures, separations and orientations. While discrete fracture models have previously been used to analyse the effects of fractures, such models are not feasible for the scales encountered in many brown-coal mines. Instead, here a continuum permeability model is used to capture the effects of the fracture heterogeneity on fractured coal. This paper presents an analysis of the fracture heterogeneity of brown coal at the AGL Loy Yang coal mine in Latrobe Valley and its influence on the fluid flow, dispersion and rock stability. A stress dependent fracture permeability is considered and captures the effects of heterogeneity in the fracture aperture and orientation. Numerical simulations conducted with multiple plasticity models present different flow paths and potential failure modes depending on the the implemented boundary conditions.

Transient Pressure Behavior of a Horizontal Well in a Naturally Fractured Gas Reservoir with Dual-Permeability Flow and Stress Sensitivity Effect

Dual-permeability flow and stress sensitivity effect are two fundamental issues that have been widely investigated in transient pressure analysis for horizontal wells. However, few attempts have been made to simulate the combined effects of dual-permeability flow and stress-dependent fracture permeability on the pressure transient dynamics of a horizontal well in a naturally fractured gas reservoir. In this approach, an analytical model is proposed to integrate the complexities of pressure-dependent PVT properties, dual-permeability flow behavior, and stress-dependent fracture permeability characteristics. The nonlinearity of the mathematical model is weakened by using Pedrosa’s transform formulation. Then, the Laplace integral transformation and separation of variables are applied to solve the model. Based on the solution of the mathematical model, a series of new-type curves are drawn to make a precise observation of different flow regimes. The main differences between the proposed model and the traditional models are discussed, and the effects of the permeability modulus of fractures, storability ratio, interporosity flow factor, and skin factor on transient pressure response are also examined. The results show that there are obvious differences in transient pressure dynamic curves between the proposed model and traditional models. The stress sensitivity effect plays a significant role in the intermediate flow period and the late-time pseudoradial flow period. The dual-permeability flow behavior mainly affects the early transient and interporosity flow stages. The proposed model can accurately simulate the transient pressure behaviors of a horizontal well in a naturally fractured gas reservoir with a dual-permeability flow and stress sensitivity effect. The novel model can be used to interpret pressure signals with accurate matching results and more reasonable interpreted parameters.

COMPREHENSIVE PRODUCTION ANALYSIS FOR SHALE GAS WELLS CONSIDERING MULTI-NONLINEAR FLOW MECHANISMS AND HETEROGENEOUS SRV

Unlike conventional reservoirs, prediction of production for shale gas wells is hardly reached by analytical models for accurately characterizing nonlinearity caused by multiple transport mechanisms of shale gas and the heterogeneity of stimulated reservoir volume (SRV). Given the limitations of analytical solutions, we adopted the finite difference method (FDM) in this paper to approximate the classic three-region model and obtained an effective numerical solution in which the pressure-dependent dynamic properties, such as gas desorption; pressure, volume, and temperature (PVT) properties; various transport mechanisms; and stress-dependent fracture permeability are considered in the modeling. The results explain that (1) the production predicted with the numerical method is accurate for the nonlinearity in the model being dealt with properly; (2) the field case shows the veracity of the proposed approach, and gas production and estimated ultimate recovery (EUR) can be evaluated with this model; (3) gas viscosity and Z-factor have an important impact on the initial production, which should be emphasized in rate transient analysis (RTA) for early-time production; slippage flow and diffusion of shale gas increase the productivity of gas wells; desorption in shale matrix can enhance middle- and long-term production; and the stress-sensitive effect and heterogeneity of SRV obstruct gas flow and reduce the total gas production; and (4) an optimized production strategy for controlling pressure drawdown is of great importance. Consequently, the refracturing treatment might be an effective measure to alleviating formation pressure drawdown, improving gas desorption and SRV permeability.

Stress-dependent fracture permeability measurements and implications for shale gas production

Stress-dependent fracture permeability could significantly affect oil and gas production, underground CO2 storage, and deep waste disposal containment. Yet, measurements to characterize these effects are lacking. To be most relevant to field conditions, measurements of stress-dependent fracture permeability should target pre-existing fracture features, be completed at high-stress conditions, and enable visualization of the fracture geometry to characterize the in-situ aperture profiles. Here, we employ triaxial direct-shear (TDS) tests, integrated with real-time X-ray imaging, to measure the stress-dependent fracture permeability of Marcellus shale and ‘Western Texas’ shale at subsurface conditions. Our results indicate that the studied shale fractures are characterized by large variation of compressibility factor. We also found that surface roughness can reduce fracture permeability more severely than what literature values would suggest. We then implemented our stress-dependent fracture permeability measurements in a formation-linear flow model to investigate the significance for shale gas production. The model uses the MIP-3H well at the Marcellus Shale Energy and Environment Laboratory (MSEEL) as a base case. The model results reveal a narrow stress-dependent permeability range over which fracture closure can be critical for production and that MSEEL appears to be close to this critical condition, which could be important for reservoir pressure management.

Interactive roles of geometrical distribution and geomechanical deformation of fracture networks in fluid flow through fractured geological media

In this study, the combined effects of geometrical distribution and geomechanical deformation of fracture networks on fluid flow through fractured geological media are investigated numerically. We consider a finite-sized model domain in which the geometry of fracture systems follows a power-law length scaling. The geomechanical response of the fractured rock is simulated using a hybrid finite-discrete element model, which can capture the deformation of intact rocks, the interaction of matrix blocks, the displacement of discrete fractures and the propagation of new cracks. Under far-field stress loading, the locally variable stress distribution in the fractured rock leads to a stress-dependent variable aperture field controlled by compression-induced closure and shear-induced dilatancy of rough fractures. The equivalent permeability of the deformed fractured rock is calculated by solving for the fracture-matrix flow considering the cubic relationship between fracture aperture and flow rate at each local fracture segment. We report that the geometrical connectivity of fracture networks plays a critical role in the hydromechanical processes in fractured rocks. A well-connected fracture system under a high stress ratio condition exhibits intense frictional sliding and large fracture dilation/opening, leading to greater rock mass permeability. However, a disconnected fracture network accommodates much less fracture shearing and opening, and has much lower bulk permeability. We further propose an analytical solution for the relationship between the equivalent permeability of fractured rocks and the connectivity metric (i.e. percolation parameter) of fracture networks, which yields an excellent match to the numerical results. We infer that fluid flow through a well-connected system is governed by traversing channels (forming an “in parallel” architecture) and thus equivalent permeability is sensitive to stress loading (due to stress-dependent fracture permeability), whilst fluid flow through a disconnected system is more ruled by matrix (linking isolated clusters “in series”) and has much less stress dependency.

A comprehensive model for simulating gas flow in shale formation with complex fracture networks and multiple nonlinearities

Shale gas reservoirs are characterized by gas adsorption and multiple flow mechanisms in shale matrix and complex fracture networks after hydraulic fracturing stimulation. It is of significance to capture the dynamic pressure-dependent properties, including gas PVT properties, gas desorption, flow mechanisms, and stress-dependent fracture permeability. In this paper, this problem is handled by proposing a novel Green element method, which is a good extension of the traditional boundary element method. The domain is discretized into many Cartesian grids, and boundary element method is applied to each element. Discrete fractures are flexibly handled by embedding the fractures into the background grids for the domain, and finite difference method is applied to model flow within the fracture system. The flow between the fracture system and matrix system is coupled to obtain the eventual matrix equation, and Picard successive approximation method is applied to obtain the solution of the nonlinear system. The solution of the novel Green element method is validated by the commercial simulator Eclipse for a fractured tight gas well model. A field case from Longmaxi formation in Southwestern China is used to verify the utility of the model. Moreover, the effects of nonlinear parameters on the performance of the well are analyzed. The results show that the nonlinear factors in shale gas flow model have a great impact on the eventual results of gas production forecasts, especially gas PVT properties and stress-sensitive fracture conductivity.

Experimental and modeling study of the stress-dependent permeability of a single fracture in shale under high effective stress

It is of great importance to investigate the change in the permeability of stimulated shale gas reservoirs under high effective stress because the depths of producing shale gas reservoirs in China have gradually exceeded 3500 m. In this study, a series of permeability measurements were performed on two fractured Longmaxi shale samples under confining pressures from 5 to 80 MPa. Experimental results show that the measured apparent permeability of the fractured samples sharply decreases with effective stress. The intrinsic permeability of fractured shale decreases with increasing effective stress, and the Klinkenberg constant is almost invariable. Then, a stress-dependent fracture permeability model was derived based on the fracture compressibility models. The modeling results indicate that the permeability model derived in this study can accurately describe the experimental data, with errors of 5.63% and 2.24% for samples I and II, respectively. A comparison of the modeling results using this model to those using permeability models available in the literature indicates that the model derived in this study is preferable, especially for a broad effective stress range. Moreover, the average compressibility of fractured Longmaxi shale decreases from 0.077 to 0.014 MPa−1 with effective stress increasing from 4.13 to 79.65 MPa, showing that fracture compressibility is strongly stress-dependent. The results in this paper will be important for the prediction of permeability change and gas production behavior for the development of deep shale gas.

A Semi-Analytical Method for Modeling Two-Phase Flow Behavior in Fractured Carbonate Oil Reservoirs

It is quite common for oil/gas two-phase flow in developing fractured carbonate oil reservoirs. Many analytical models proposed for black oil wells in fractured carbonate reservoirs are limited to single-phase flow cases and conventional methods have been the use of numerical simulations for this problem. In this approach, a novel semi-analytical method is proposed to integrate the complexities of phase change, pressure-dependent pressure-volume-temperature (PVT) properties, two-phase flow behavior, and stress-dependent fracture permeability characteristics. A dual-porosity, black oil model considering the phase change and two-phase flow is applied to model the fractured carbonate reservoirs. To linearize the model, only flow equations of oil phase are used to develop the mathematical model. Nonlinear parameters and producing gas–oil ratio (GOR) are updated with coupled flowing material balance equations, followed by a novel proposed procedure for history matching of field production data and making forecasts. The semi-analytical method is validated with a commercial simulator Eclipse. The results show that both of the production rate curves of oil and gas phase using the proposed model coincide with the numerical simulator. The results also show that the effects of pressure-dependent fracture permeability, fracture porosity, and exterior boundary on production rate are significant. Stress sensitivity influences production rate during the whole process, reducing the cumulative production. Fracture porosity influences production rate during the intermediate flow periods. The exterior boundary affects production rate mainly in the early and intermediate production periods. Finally, a field example from the eastern Pre-Caspian basin is used to demonstrate the practicability of the method. Acceptable history match is achieved and the interpreted parameters are all reasonable.

Effect of in-situ Stress Alterations on Flow through Faults and Fractures in the Cap Rock

Cap-rock integrity is of paramount importance during injection and subsequent long-term storage of CO2 in the subsurface. Pre-existing (natural) and man-induced fractures in the cap rock represent potential flow paths out of the storage formation. In this study, a first-order semi-analytical model of flow through a vertical fracture penetrating cap rock is constructed taking the stress-dependent fracture permeability into account. The model is then applied to study the effects of in-situ stress normal to fracture on the flow rate through the fracture. The flow rate increases nonlinearly with the reservoir pressure, which is due to a combined effect of nonlinear fracture deformation law and the cubic law governing the flow rate.

A Fully Coupled XFEM-EDFM Model for Multiphase Flow and Geomechanics in Fractured Tight Gas Reservoirs

Unconventional reservoirs are typically comprised of a multicontinuum stimulated formation, with complex fracture networks that have a wide range of length scales and geometries. A timely topic in the simulation of unconventional petroleum resources is in coupling the geomechanics of the fractured media to multiphase fluid flow and transport.We propose a XFEM-EDFM method which couples geomechanics with multiphase flow in fractured tight gas reservoirs. A proppant model is developed to simulate propped hydraulic fractures. The method is verified by analytical solutions. A simulation example with the configuration of two multiple-fractured horizontal wells is investigated. The influence of stress-dependent fracture permeability on cumulative production is analyzed.

Importance of rock properties on the producibility of gas shales

Abstract As the development of unconventional gas resources has progressed, the heterogeneity and complexity of shales as gas and oil reservoirs have become apparent. The production histories from shales, both within a sequence of interbedded strata and from adjacent wells, commonly exhibit inexplicable variations and predictions from numerical modeling are rarely accurate. As a result of the variability in the reservoir and rock parameters of gas shales, the complex interaction between the shale properties and the producibility of the reservoir is seldom apparent. One of the most difficult parameters to quantify is the fabric. This study compares the relative importance of the fabric parameters of gas shales on their producibility using a commercial numerical simulator and field and laboratory determined rock properties. The fabric parameters include the stress-dependent fracture permeability, which controls the gas transport through the fracture network, as well as the effective fracture spacing, which controls the path length for gas transport through the matrix, and the stress-dependent matrix permeability, which controls the gas transport through the matrix. The results of the numerical simulations show that for a wide range of stress-dependent fracture permeabilities, stress-dependent matrix permeabilities, and fracture spacings, the productivity of a gas shale reservoir is limited by inefficient gas transport through the matrix. The matrix permeability below which gas production is subeconomic is not a specific value, but varies with the effective fracture spacing and with fracture permeability. The matrix permeability and effective fracture spacing have a greater impact on the producibility of strata with larger fracture permeabilities. The influence of the effective fracture spacing on production is greater than the influence of the matrix permeability. The lower production associated with a large fracture spacing (or a small matrix permeability) can be offset by a large matrix permeability (or a small fracture spacing). The production simulations also show the strong dependence on the geomechanical properties of the rock, which affect how the gas transport through the matrix and fractures changes with stress. The influence of the geomechanical properties on the producibility depends on whether the production is limited by the gas transport through the matrix. When the fabric parameters result in a matrix-independent production (small fracture spacing, large matrix permeability, small fracture permeability), the production is solely controlled by the stress-dependent fracture permeability, with larger initial fracture permeability, larger Young's modulus, and larger Poisson's ratio resulting in higher production. In this case, Young's modulus is much more influential than the Poisson's ratio. When the fabric parameters result in a matrix-limited production, the rock mechanics parameter α , which relates the exponential decline of matrix permeability with effective stress, has the strongest influence on the producibility. The influence of Poisson's ratio on producibility not only varies with the fabric parameters, but also with the Young's modulus and α . When the production is matrix-limited, a smaller Poisson's ratio results in a higher production for all cases except when both α and Young's modulus are small.

Simulation of Hydraulic Fracturing in Low-Permeability Reservoirs

AbstractComputer-based numerical simulation can be used as a tool for analysis of fracturing treatments and prediction of postfracturing well performance. The physical problem studied involves fracture mechanics, fluid flow, and heat transfer both in the fracture and in the reservoir. The numerical model predicts fracture extension, length, and width; proppant transport and settlement; fracture closure; cleanup; and postfracturing performance under different producing conditions.The number of physical features that are customarily neglected in fracture designs have been incorporated in the present model. These include stress-sensitive reservoir properties, proper two-phase calculation of leakoff and cleanup, stress-dependent fracture permeability and temperature- and time-dependent fracturing fluid rheology.The utility and a priori predictive capability of the model is illustrated with two examples of fracturing jobs. The first example is a marginal gas well stimulated by a medium-size gelled-water fracturing job. The second example is a massive foam fracture in the Elm worth basin. In both cases, the simulator predicted results that are in good agreement with the observed productivity.