Fracture Aperture Variation Research Articles

Numerical study of gas invasion law in fractured reservoirs

Gas invasion during the drilling process in fractured reservoirs poses challenges, affecting drilling efficiency and increasing costs. Therefore, it is crucial to effectively and accurately describe the flow characteristics of subsurface fluids. Addressing the issue of gas invasion in fractured reservoirs, this study considers the influence of matrix deformation and fracture aperture variation on fluid flow and establishes a mathematical model for coupled flow and solid deformation in fractured reservoirs. The numerical formulation of the mathematical model is derived using the finite element method. To better represent real reservoir conditions, discrete fractures are created using MATLAB, and numerical solutions are obtained using the commercial software COMSOL Multiphysics. The accuracy of the model is verified through a comparison between numerical and analytical solutions. This paper first explores the characteristics of fluid flow within a single fracture and rock deformation when encountering a fracture during drilling. It then compares the predictive capability of the coupled model with that of the uncoupled model in estimating gas invasion. Finally, the primary factors influencing gas invasion in fractured reservoirs are analyzed from the perspectives of rock matrix, fractures, and drilling operations.

Experimental Study on the Evolution of Fracture Aperture of Single‐Fracture Granite during Liquid Nitrogen Cold Shock Cycling

Fractures in hot dry rock (HDR) reservoirs are the locations where heating fluid flows exchange heat with the HDR matrix. Cold shock with liquid nitrogen is one method for stimulating cracks. This study investigates the evolution law of fracture aperture under cold shock with liquid nitrogen. The real‐time high‐temperature triaxial servo control rock testing machine was used to conduct permeability experiments to examine the fracture aperture of single‐fracture granite during liquid nitrogen shock cycles at various temperatures. The effects of pore pressure, temperature, and shocking cycles on the fracture aperture are analyzed, and the difference in fracture aperture variation under liquid nitrogen cooling and natural cooling modes is compared. The results showed that (1) during liquid nitrogen cooling, the fracture aperture expands as pore pressure rises; the effect of pore pressure on the fracture aperture becomes more robust as the number of liquid nitrogen shocking cycles and initial temperature increases; (2) under 1‐2 soaking cycles, fracture aperture decreases as the temperature rises. Under two or more soaking cycles, the fracture aperture first increases and then decreases with increasing temperature; (3) when the initial temperature of fractured granite is 100°C, the fracture aperture is not significantly changed by repeated cold soaking cycles. However, with a higher initial temperature, the fracture aperture develops with more liquid nitrogen cold soaking cycles. The liquid nitrogen cooling method is more conducive to increasing the fracture aperture than natural cooling. The experimental results can provide primary experimental data for future research into controlling the evolution of granite cracks.

An IFS-based fractal discrete fracture network for hydraulic fracture behavior of rock mass

The discrete fracture network (DFN) model is applied for fluid flow and transport simulations in fractured rock masses. In this study, a novel two-dimensional fractal DFN generation method was proposed based on the iterative function system (IFS). To achieve the fine mesh for the DFN model, a refinement technique was presented to remove the short edges and small gaps. Subsequently, the zero-thickness flow cohesive element was inserted at the adjacent edge of elements for the hydraulic fracture modeling. The results indicated that the injection pressure of hydraulic fracture had three phases: Sudden increase, rapid drop-off, and stabilization. Compared with the traditional linear DFN model, the injection pressure evolution and fracture propagation of fractal DFN were significantly affected. In addition, the fracture aperture variation was an important factor influencing hydraulic fracturing in the rock mass. Considering the complexity of the hydraulic fracturing process, the effects of mesh sensitivity and fracture aperture size were also analyzed based on two-dimensional simulation results. This study presents a novel 2D DFN model for an accurate description of fracturing and provides a valuable simulation method for hydraulic fracturing.

Thermo-poro-elastic analytical model of the heat extraction performance of EGS inlaid with multi-linked fractures

The existing analytical model of the heat extraction performance of EGS ignored the influences of both thermo-poro-elastic effect and multi-linked fractures. Therefore, a thermo-poro-elastic analytical model was proposed to simulate heat extraction performance of EGS inlaid with multi-linked fractures. First, the mathematical models of fluid flow, heat transfer, and fracture aperture variation were established based on the conservation of energy and mass. Second, the partial differential equations were converted to ordinary differential equations by Laplace transformation, and the analytical solutions of water and rock temperatures were obtained. Then, the proposed model was verified with the published single-fracture model, which has been demonstrated to be efficient. Finally, the influencing factors, including geothermal reservoir parameters, production parameters, thermo-poro-elastic effect, and fracture morphology, were systematically analyzed and discussed. The results indicated that both the thermo-poro-elastic effect and multi-linked fractures have significant influence on the heat extraction performance of the EGS. The thermo-poro-elasticity effect tends to cause the fracture aperture to increase. The heat extraction performance of the EGS inlaid with multi-linked fractures is much better than that of single fracture EGS. Compared to the uncoupled situation, the production temperature is lowered and the output energy is increased by the thermo-poro-elastic effect at a constant flow rate in the fracture due to the increase in injection rate caused by the increase in fracture aperture. With the increasing of initial fracture aperture, the production temperature gradually decreases, while the output energy first increases and then decreases, so that the optimal initial fracture aperture is 2 mm. The results can provide important guidance for the design and production of an EGS inlaid with multi-linked fractures.

In-situ flow visualization with Geo-Positron-Emission-Tomography in a granite fracture from Soultz-sous-Forêts, France

We investigate the fluid flow field in a fractured granite core sample. Sequential imaging with Positron-Emission-Tomography (PET) allows direct reconstruction of flow streamlines, thus providing a unique insight into the fluid dynamics of complex fractured crystalline materials. Pulse migration experiments using the positron-emitting radionuclide 18F− as tracer were conducted on a fractured granitic drill core, originating from a depth of 1958 m of the Enhanced Geothermal System (EGS) reference site at Soultz-sous-Forêts, France. The flow field was analyzed as a function of in- and outlet positions across the fracture, as well as applied flow rates. Different flow path characteristics were identified. Both the fracture aperture variation and the topography of the fracture surface affect the flow field with consequences on flow channeling and preferential flow paths. Furthermore, pulse migration experiments were also numerically simulated with a 2.5D model using COMSOL Multiphysics®.While the higher flow rate experiments show wider and higher dispersion of the flow path, lower velocity results in more localized flow and channeling behavior. This type of study thus yields enhanced experimental insights into the hydrodynamics of fracture flow and its relation to the rough structure of a single fracture, compared to input-output experiments. It can help to validate model simulations and experimentally determine hydrodynamic parameters needed for reactive transport modeling that are otherwise estimated with a high degree of uncertainty.

A numerical investigation for the impacts of shale matrix heterogeneity on hydraulic fracturing with a two-dimensional particle assemblage simulation model

A shale gas reservoir has complex mineral components, bedding planes and micro-cracks, thus being of inherent heterogeneity and anisotropy. The roles of bedding planes in hydraulic fracturing performance have been deeply studied, but the effects of rock inherent heterogeneity induced by mineral components are not well understood. This paper establishes a two-dimensional particle assemblage model to investigate the impacts of mineral component heterogeneity on hydraulic fracturing treatments. The impacts of the mass fraction and elastic modulus of low-brittle minerals on fracture initiation pressure, breakdown pressure, fluid injection volume and fracture permeability are comparatively investigated through numerical simulations. It has been found that the mass fraction of low-brittle minerals is closely related to the critical pore water pressure while the elastic modulus of low-brittle minerals plays a significant role in fracture permeability. With the same hydraulic fracturing treatments, the shale gas reservoir with a large mass fraction of clay minerals could decrease the critical pore water pressure, while the shale gas reservoir with a low elastic modulus of clay minerals is conducive to increasing fracture aperture. The shale matrix heterogeneity induced by the fraction coefficient and micro-mechanical properties of clay mineral has a critical role in the fracture initiation and propagation as well as the variation of fracture aperture. This understanding of shale mineral composition can benefit the effectiveness evaluation on hydraulic fracturing and the morphology of fracture networks.

Numerical parametric investigation of thermal extraction from the enhanced geothermal system based on the thermal-hydraulic-chemical coupling model

There are chemical dissolution and precipitation in geothermal formations with the long-term exploitation of hot dry rocks, which would induce the remarkable alteration of fracture transmissibility and evolution of thermal performance. The objective of this study is to identify the influence of various parameters incorporating chemical reactions to provide suggestions for the operation of the enhanced geothermal system (EGS). A 3D thermal-hydraulic-chemical coupling model is established for a fractured EGS considering silica-water reaction kinetics at fracture surface. Parametric study and sensitivity analysis are innovatively conducted to investigate the effects of key operation and formation parameters, including injection concentration (cin), injection temperature (Tin), injection rate (Qin) and initial formation silica reactant content (Ci), on thermal extraction performance. Results indicate that undersaturated injection causes chemical dissolution while oversaturated injection leads to silica precipitation. Higher cin relieves the thermal breakout (10 °C) but enhances the injection-production pressure difference (13.5 MPa). The selection of cin is an efficient way to adjust geothermal production, especially for oversaturated injection. The influence degrees of cin on production temperature (Tout) and pressure difference (Δp) under oversaturated injection are 8 times and 2 times larger than those under undersaturated injection. Tin (<80 °C) exerts little influence on the chemical reaction. The remarkable water storage phenomenon will be induced with the increase of Qin when precipitation occurs. Higher Ci results in lower Tout and Δp. The sensitivity analysis provides the rank of major parameters to thermal performance: Qin, Tin, cin and Ci. The standard sensitivities of Qin to Tout, Δp and net thermal power N are 0.78, 0.63, and 0.88 respectively. As for the contribution ratio, cin contributes the most (89%) to the variation of fracture aperture while Tin (<80 °C) contributes the least (nearly 0%). The research will provide a significant reference for the selection of parameters during the development of geothermal energy.

Investigation of Nonlinear Flow in Discrete Fracture Networks Using an Improved Hydro-Mechanical Coupling Model

Fractures commonly exist in rock masses; the coalescence of fractures provides fluid flow pathways in a fractured rock mass and greatly increases the flow capacity of fractured rock. This work aims to study the characteristics of nonlinear flow in fractures. A series of tests were conducted and indicated that the Forchheimer law performed well when describing the nonlinear relationship between hydraulic gradient and flow. The test results also indicate that higher water pressure may induce stronger nonlinearity. Additionally, the linear and nonlinear coefficients of the Forchheimer law increase with a decrease in the particle size of the filling material in fractures. On the basis of the laboratory results, the classical Forchheimer law was modified by considering the influence of stress on the variation of fracture aperture. A hydro-mechanical coupling model for fractured rock masses was built and programmed with a subroutine through ABAQUS. Furthermore, a random discrete fracture network was generated and simulated to prove that a high flow velocity will result in a nonlinear flow, not only in a single fracture, but also in a fracture network. The numerical results from fractured rock masses show that a ratio of the flow to the hydraulc gradient will change the flow from linear to weak nonlinearity and, finally, to strong nonlinearity with an increase in the hydraulic gradient. It also shows that the linear and nonlinear coefficients increase with an increase in the confining pressure and that they decrease with an increase in the aperture. Due to the complexity of fracture channels, a nonlinear flow is likely to occur in a fractured rock mass. Finally, the developed model was applied to simulate the flow behavior of underground engineering; the results show that the smaller the hydraulic aperture is, the higher the water pressure is required to be in order to change the flow regime from linear to nonlinear.

Controlling factors of fracture aperture reduction based on experimental study using proppant pack apparent Young's modulus

The hydraulic fracture aperture packed by proppants determines the fracture conductivity and is pivotal to oil and gas production. After hydraulic fracturing, the fracture width decreases owing to proppant embedment, deformation, and crushing. However, the analysis of fracture width reduction based on the mechanical properties of the proppant pack is limited. In this study, an experiment is designed to obtain the apparent Young's modulus, which represents the rigidity of the entire pack, and steel sheets are used to replace rock samples to eliminate heterogeneity and weaken the effect of proppant embedment. Subsequently, the effects of proppant type, concentration, and size on the apparent Young's modulus are discussed. Finally, the controlling factors and mechanisms of fracture width reduction are determined. The results indicate that the fracture width decreases linearly with increasing closure pressure for the ceramsite pack, and that the apparent Young's modulus is associated with the fracture aperture variation, which is governed by proppant embedment and deformation. The apparent Young's modulus increases as the proppant concentration increases or the proppant size decreases, whereas the proppant size imposes a more prominent effect. However, the mixed-size ceramsite pack shows only slight improvements in terms of propping ability. This study provides new insights into factors governing proppant pack deformation. • The apparent Young's modulus is defined through experimental results to quantitatively characterize mechanical properties of the whole proppant pack. • The proppant pack will experience at least 1 rigid-to-plastic deformation cycle under closure pressure. • The apparent Young's modulus for ceramiste can be inserted into fracture width calculation correlation, of which the fracture width decrease is mainly dominant by proppant embedment and deformation. • Proppant concentration and size both have influence on apparent Young's modulus, but the latter is more profound . The finer the particles are, the higher the modulus of the proppant pack is.

A particle-tracking formulation of advective–diffusive heat transport in deformable fracture networks

Modeling heat transfer in complex heterogeneous fractured system is key for geothermal energy applications. Discrete fracture network (DFN) modeling is the classical framework to reproduce the advective part of the transport, which is determined by the fracture connectivity and heterogeneity. This approach in general sacrifices the representation of the rock matrix, disregarding both its diffusive heat exchange with the fractures and the effects of its thermo-mechanical deformation on the fracture aperture. Here we propose a new semi-analytic formulation that can be implemented in a DFN simulator with particle tracking approach. The contribution of the rock matrix in terms of diffusive heat exchange and thermal contraction/expansion is analytically evaluated, which respectively impact the advective heat transfer and the fracture aperture variation. The method is proved to be accurate and robust. Results from simulations of cold fluid injection show that rock contraction affects the transmissivity, which accelerates the advective transport resulting in a faster recovery of cold fluid at the outlet. The methodology enables investigating the reservoir behavior and optimizing the geothermal performance while keeping the computational effort within reasonable values. This allows exploring the uncertainty in cases when the in situ characterization is poor, which is the spirit of the DFN modeling.

Modelling slurry flowing and analyzing grouting efficiency under hydro-mechanical coupling using numerical manifold method

Grouting is a typical HM (hydro-mechanical) coupling process between slurry and rock and widely used in underground engineering to reinforce the strength of fractured rock mass. In present work, based on numerical manifold method (NMM), an NMM-HM grouting model is proposed to investigate slurry flowing and analyze grouting efficiency. In this NMM-HM grouting model, the slurry flows in fractures and grouting pressure can cause fracture aperture variation and fracture propagation. Then, two numerical examples for central embedded crack and hydraulic fracturing are adopted to validate the presented model. Furthermore, grouting simulations are conducted on a multi-crack and a roadway with fracture networks. Results show that Grouting pressure in fractures can increase fracture aperture, which is beneficial for grouting efficiency. However, fluid pressure could also cause closure of neighboring fractures or even fracture propagation and failure of rock mass, which will weaken grouting effectiveness. Therefore, the coupled HM impacts on grouting efficiency and grouting pressure should be seriously considered and optimized to achieve the expected grouting performance in practice.

Simulation of the Infiltration of Fractured Rock in the Unsaturated Zone

We study infiltration of rainwater into fractured rock and the accompanying capillary exchange processes between fractures and matrix, hereafter referred to as fracture–matrix transfer (FMT). Its influence on the velocity of the wetting front for uniform and variable aperture fractures is of prime interest because it determines the penetration depth of infiltration pulses. FMT is modelled explicitly in a discrete fracture and matrix (DFM) framework realised using a hybrid finite element–finite volume discretisation with internal boundaries. The latter separate the fracture mesh from the rock matrix mesh with the benefit that the flow that occurs within the minute fracture subvolume can be tracked with great accuracy. A local interface solver deals with the transient nonlinear aspects of FMT, including spontaneous imbibition of the rock matrix. Two- and three-dimensional heuristic test cases are used to illustrate how FMT affects infiltration. For the investigated scenario, we find that—beyond a critical fracture aperture around 5–10-mm—infiltration rate is no longer affected by FMT. Fracture aperture variations promote in-fracture-plane fingering, with counter-current flow of water (downward) and air (upward). Fracture flow interacts with FMT in a complex fashion. For systems with a small fracture porosity (≤0.01%), our results suggest that intense, hour-long rainfall events can give rise to tens-of-meter-deep infiltration, depending on fracture/matrix properties and initial saturation of the fractured rock mass.

A discontinuous discrete fracture model for coupled flow and geomechanics based on FEM

A discontinuous discrete fracture model of coupled flow and geomechanics for fractured reservoirs is presented in this paper. Two problems of hydraulic fracturing and production are solved to prove the feasibility of the proposed model. The same grid nodes are shared by the flow and geomechanics parts, except the fracture junctions. Galerkin finite element method is used to discretize the flow equations and the mechanical equations. The meshing process is divided into two steps to avoid mesh concentration in the vicinity of the fracture. Implementing the discontinuous discrete fracture model is validated for three problems with analytical solutions and numerical solutions. Compared with the discrete fracture network model, the stress singularities in fracture tips can be captured by the discontinuous discrete fracture model. The discontinuous discrete fracture model can be used to simulate the fracture propagation. In this paper, the hydraulic fracturing process of four horizontal wells is simulated, and the production of each well is predicted with simulated hydraulic fractures. The methodology is then applied to simulate the production process of an artificially fractured shale oil reservoir containing intersected fractures. By slightly changing the mechanical condition on the fracture surfaces, we showed the importance of proppants in well production. The discontinuous discrete fracture model provides a more realistic description of the fracture aperture variation during the production process. More importantly, it offers a method to simulate the hydraulic fracturing and production processes in sequence. The design of infill-well fracturing can also be optimized with the proposed model.

Impact of Skin on the Movement of Nitrates in a Fractured Porous Media: Numerical Investigations

The objective of this study is to analyse the movement of nitrates and dissolved oxygen under the effect of denitrification in a fracture–matrix (F–M) system with skin formation. An implicit finite difference scheme is developed to model the coupled nonlinear partial differential equations. A varying grid is considered at the fracture–skin interface to handle the mass transfer from the fracture to the skin. Bacterial growth is taken into account in the fracture. The growth is affected by the presence of electron donor and electron acceptor. Sensitivity analysis is performed for various fluid flow velocities, skin diffusion coefficients, facture dispersion coefficients, skin porosities (S-P), fracture apertures and rock–matrix (R–M) porosities. Outcomes of this study indicate that the occurrence of skin enriches the transport of nitrates as compared to the absence of skin when denitrification process exists in the system. The low fluid velocity (0.5 m/day) reduces the transport of nitrates to a distance of 5 m, whereas a high fluid velocity (5.0 m/day) triggers up to a distance of 30 m from the fracture inlet. The higher skin diffusion coefficient enhances the migration of nitrates and dissolved oxygen compared to the lower skin diffusion coefficients. The fracture aperture variation from 100 to 500 μm increases the movement of nitrates and dissolved oxygen in fracture from 4 to 10 m, respectively. The variation of S-P from 25 to 75% also follows the same trend. Variation in R–M porosity has an insignificant effect on the movement of nitrates and dissolved oxygen.

Study of Fracture Aperture Variation in a Fracture Network on Heat Production from an Enhanced Geothermal System (EGS)

With the development of the Enhanced Geothermal System (EGS) technology, extensive geothermal energy applications have become feasible. To simulate fluid migration and heat propagation within a fractured geothermal reservoir, discrete fracture models (DFMs) of the TH processes are widely used. However, the variability of aperture size from one fracture to another is typically ignored in these models. In this work, a discrete fracture model considering variable aperture fractures is applied to investigate the performance of a geothermal reservoir in EGS. The fracture apertures are randomly distributed within the networks, but constant for one single fracture. The simulation results show that the heat production rate and outlet temperature can be divided into three stages based on the value of coefficient of variation of fracture apertures. The higher variability results in the low heat production rate but high outlet temperature. On the other hand, the average heat production rate is proportional to the fracture density. However, the effect of fracture density is reduced with an increase of coefficient of variation. Furthermore, the comparison between fracture aperture and density shows that, the increase in mean fracture aperture leads to a higher increase in average heat production rate than an increase in fracture density.

A Thermal-Hydraulic-Mechanical Coupling Study of Heat Extraction from the Geothermal Reservoir with a Discrete Fracture Network

The complex thermal-hydraulic-mechanical (THM) coupling is the key issue to the energy extraction from a geothermal reservoir, where fractures are the main channels for fluid circulation and heat transfer. However, the effects of matrix deformation-induced aperture variation and fracture roughness on heat recovery efficiency are unclear. In this paper, a fully coupling THM model based on a discrete fracture network is proposed to explore these coupling effects. First, the fracture roughness and the fracture aperture variation with effective stress are introduced. Second, the water flow and heat transfer in the matrix and fractures as well as the deformation of the geothermal reservoir are individually formulated for a fractured geothermal reservoir. Third, the model is validated with analytical solution for its thermal-hydraulic (TH) coupling effect and literature data for its hydraulic-mechanical (HM) coupling effect. Finally, the features of heat transfer and fluid flow in the fractured geothermal reservoir are comparatively analyzed through four scenarios. The simulation results indicate that the discrete fracture network severely impacts the pressure distribution and temperature advance. The aperture variation induced by solid deformation can enhance heat transfer efficiency, and the fracture roughness can reduce the heat transfer efficiency.

The Sealing Mechanisms of a Fracture in Opalinus Clay as Revealed by in situ Synchrotron X-Ray Micro-Tomography

Author(s): Voltolini, M; Ajo-Franklin, JB | Abstract: The detailed mechanisms of the sealing of a single fracture, from hydration to almost complete closure by increase of confining pressure, as monitored from in situ synchrotron X-ray microtomography during the flow of carbonated water, is here shown for the first time. Different mechanisms play the key role at different stages in the evolution of the fracture. Hydration mechanically weakens the surfaces of the fracture and induces a first closure due to microcracking at the asperity contacts, increasing their size and creating choke points. Increase in confining stress promptly hydraulically seals the fracture by closing the main choke point, with a relative small deformation of the sample. Finally, the more pervasive mechanical deformation observed at higher stresses almost completely seals the whole fracture. The evolution of the sample has been described and quantified using 4D image processing, focusing on the evolution of aperture and digital volume correlation. Hydraulic properties of the sample at different stages have been modeled via Stokes flow simulation, and the results compared to the morphometric analysis, finding positive correlations with the average fracture aperture variation along the flowpath in function of confining pressure. Opalinus Clay is found to be a rock markedly prone to sealing in case of flow with carbonated water; this behavior is the result of the large fraction of clays and of its microstructure, lacking both cementing phases and large stiff particles. CO2 in this sample has no evident role in the evolution of the fracture; chemically induced weathering on the surface has not been detected, in contrast with the behavior observed in samples with carbonates as cementing phase.

Failure mechanism and fracture aperture characteristics of hard thick main roof based on voussoir beam structure in longwall coal mining

AbstractThe mechanism and fracture aperture of thick hard roof failure were theoretically analyzed from the perspective of elastoplastic mechanics. A uniform load cantilever beam was established by considering the voussoir beam structure and stress condition. According to the stress inverse principle in solving the plane strain problem, the internal stress component analytic solution was deduced. Considering the lateral thrust and shear force and by applying the Mohr‐Coulomb failure criterion, the plastic zone boundary equation was obtained. Further analysis of the equivalent stress, equivalent strain, elastic energy density, distortion energy density, and strain energy density was studied with blocks of four different lengths, combined with the rotation angles after failure, to analyze the fissure aperture between straight and curved fracture traces. The theoretical analysis reveals that the deviatoric effect plays the lead role in rupture initiation and propagation; the cracks will deflect during failure, and the fracture trace presents a curved shape. The variation of fracture aperture exhibits a tendency to increase first, then decrease, and then increase along the fracture trace. The analytical approach presented in this paper provides a theoretical basis for determining the main seepage channel flow in underground mining.

Thermally driven fracture aperture variation in naturally fractured granites

Temperature variations often trigger coupled thermal, hydrological, mechanical, and chemical (THMC) processes that can significantly alter the permeability/impedance of fracture-dominated deep geological reservoirs. It is thus necessary to quantitatively explore the associated phenomena during fracture opening and closure as a result of temperature change. In this work, we report near-field experimental results of the effect of temperature on the hydraulic properties of natural fractures under stressed conditions (effective normal stresses of 5–25 MPa). Two specimens of naturally fractured granodiorite cores from the Grimsel Test Site in Switzerland were subjected to flow-through experiments with a temperature variation of 25–140 °C to characterize the evolution of fracture aperture/permeability. The fracture surfaces of the studied specimens were morphologically characterized using photogrammetry scanning. Periodic measurements of the efflux of dissolved minerals yield the net removal mass, which is correlated to the inferred rates of fracture closure. Changes measured in hydraulic aperture are significant, exhibiting reductions of 20–75% over the heating/cooling cycles. Under higher confining stresses, the effects in fracture permeability are irreversible and notably time-dependent. Thermally driven fracture aperture variation was more pronounced in the specimen with the largest mean aperture width and spatial correlation length. Gradual fracture compaction is likely controlled by thermal dilation, mechanical grinding, and pressure dissolution due to increased thermal stresses exerted over the contacting asperities, as confirmed by the analyses of hydraulic properties and efflux mass.

Numerical simulation of borehole Stoneley wave reflection by a fracture based on variable grid spacing method

In this paper, the finite difference method is used to model the Stoneley wave reflection by a horizontal fracture in a borehole. The fracture shape is described by some finite difference grids. Therefore, the fracture aperture can be varied in the radial direction, thus extending previous researches on the assumption that the fracture aperture is constant throughout the fracture. Finite difference grids can also be used to describe a fracture which extends a finite distance in the radial direction. In addition, the finite difference algorithm can deal with the problem of inhomogeneous formation. Therefore, it allows the variation of formation elasticity in the model. Fine grids are needed to describe the small fracture aperture, and variable grid spacing is employed by finite difference method to improve computational efficiency. The Stoneley wave propagation is simulated by the variable grid spacing finite difference method in several models with variable fracture aperture, finite extension fracture and models with heterogeneous formation. The variable grid spacing finite difference method is validated through a comparison with real axis integration method and the analytical method. We get some conclusions by simulating and investigating effects of the variation of fracture aperture, the fracture of finite extension and inhomogeneity of formation on the Stoneley wave reflection. Although the fracture aperture changes along the fracture extension direction, the reflection coefficient of Stoneley wave is mainly controlled by the fracture aperture near the borehole. The Stoneley wave in the fracture is reflected back into the borehole, by the tip of finite extension fracture, which results in some notches in the reflection coefficient curve. If the Stoneley wave propagates from the formation with small elastic modulus to the formation with large elastic modulus, the reflection coefficient of Stoneley wave will be larger than that of homogeneous model with small elastic modulus. And if Stoneley wave propagates from the formation with large elastic modulus to the formation with small elastic modulus, the reflection coefficient of Stoneley wave will be smaller that of homogeneous model with large elastic modulus. These results provide some basis for the use of Stoneley wave to detect the fracture properties in formation.