Increase In Fracture Aperture Research Articles

Steady-state relative permeability measurements in rough-walled fractures: The effects of wettability and aperture

Tight subsurface geosystems provide significant prospects for the recovery and storage of mass and energy. Because of the tightness of these systems, natural and engineered fractures are the main conveyance conduits transporting the fluids from the tight rock matrix to the wellbore or vice versa. During the fracturing process, most of the newly induced fractures are considered water-wet, however during injection/production, the wettability of the fractures gradually changes. These changes are mainly due to the interactions between the resident and injected fluids, or the exposure of the virgin fracture surfaces to the resident fluids during production. This alteration in wettability can affect the trapping and flow dynamics, e.g., relative permeability, of the fluids flowing in the fracture. Furthermore, fluid injection and production into and from these systems impact the fractures pore pressure and hence the effective stress they are exposed to, resulting in variations in the fracture aperture. In this study, we present a comprehensive macro-scale experimental investigation focusing on the impact of wettability and aperture on steady-state two-phase relative permeability in rough-walled fractures. Using the stead-state measurement technique, we meticulously characterized oil-brine relative permeabilities and residual trapping in water-wet, oil-wet, and mixed-wet rough-walled fractures induced in Eagle Ford shale rock samples. Additionally, we assessed the influence of fracture aperture size on these properties during both drainage and imbibition flow processes. Our results indicate significant phase interference in oil-brine flow in non-water-wet rough-walled fractures, which renders the commonly used x-curve and Corey models inadequate to represent the steady-state oil-brine relative permeabilities measured in our study, leading to substantial overestimations. Mixed-wet fractures exhibited reduced relative permeabilities compared to oil-wet fractures, which in turn demonstrated lower relative permeabilities than water-wet counterparts. The observed trends stem from evolving fluid configuration and transport dynamics within the fractures as surface wettability transitions. Furthermore, an increase in fracture aperture corresponded with an increase in relative permeability. This was attributed to a broader flow area, diminished capillarity, attenuated impact of fracture wall roughness and tortuosity effects, and a reduction in bypassing and trapping events, all synergistically contributing to the mitigation of phase interference. Similarly, an increase in fracture aperture led to a marked decrease in post-waterflooding endpoint oil saturation and post-oil flooding endpoint brine saturation. Finally, we provided generalized correlation models based on experimental results from fractures with varying conductivities and wettability, yielding a more accurate representation of fracture relative permeabilities compared to traditional models. The data and correlation models produced in this study improve our understanding and prediction of multiphase flow in subsurface fractures and offer insights into rapid production decline in unconventional shale reservoirs.

The magnitudes of multi-physics effects on geothermal reservoir characteristics during the production of enhanced geothermal system

The multi-physics coupling process during the heat extraction from enhanced geothermal system, encompassing thermo(T)-hydro(H)-mechanical(M)-chemical(C) interactions, plays a pivotal role in changing geothermal reservoir characteristics. However, a comprehensive quantitative assessment of these multi-physics behaviors has been lacking. In this study, a novel approach was proposed to calculate the magnitude of mechanical, chemical, strong mechanical-chemical coupling, and weak mechanical-chemical coupling effects on the variations of reservoir characteristics. In particular, mechanical-chemical coupling effects are quantified for the first time. They are obtained by the fracture aperture difference results across five distinct coupling models (thermo-hydro, thermo-hydro-chemical, thermo-hydro-mechanical, partially-coupled four-field, and fully-coupled four-field models). The findings indicate that mechanical effects lead to an increase in fracture aperture, while chemical effects contribute to its reduction under underbalanced injection conditions. Strong mechanical-chemical coupling effects, exhibiting a negative correlation with chemical effects, conversely result in a diminished fracture aperture. The influences of these effects are investigated from the temporal and spatial perspectives. Temporally, mechanical effects dominate early production while chemical effects become prominent in later stages. Spatially, there mainly exists two zones when stable production: a mechanical-controlled region surrounding injection wells, and a chemical-controlled area distant from the injection wells. Furthermore, sensitivity analysis of injection concentration indicates its alternation changes the reservoir traits and production performance by modifying the magnitudes of chemical and mechanical-chemical coupling effects. This quantification of multi-physics effects offers insights into optimizing injection strategies for better geothermal development. The approach could hold promising potential in other geo-energy scenarios like carbon and hydrogen storage in reservoirs.

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.

A Semi‐Analytical Solution for Heat Transport in Rock With Parallel Fractures and a Heat Source in Both Fracture and Matrix

AbstractIn recent decades, numerous analytical solutions have been developed to quantify temperature perturbations in fractured rock having mobile and immobile fluid phases. The assumption of one‐dimensional heat conduction in the matrix, or neglecting heat dispersion and storage in fractures, however, are typical simplifications adopted to overcome the difficulties in mathematically representing the problem. In this study, we propose a two‐dimensional semi‐analytical solution framework based on Green's function approach for a flexible heat source definition, including source dimensions, energy delivery strength and duration, and the presence of a heat source in the matrix and/or fracture. The solution fully accounts for heat conduction, advection, dispersion, and transient heat exchange between the fracture fluid and rock matrix in a system of parallel fractures. The solution having a strip heat source extending from a fracture into the matrix indicates that one‐dimensional heat conduction in the matrix underestimates and overestimates temperature responses at early and later times, respectively. Additionally, the temperature peak arrival time is also substantially delayed by simplification. The fracture temperature grows slower near the heat source area as the fracture aperture increases. The fracture temperature growth is enhanced via the overlapped heating areas between the parallel fractures. The transient temperature analyses imply that the spatial temperature variation is strongly associated with heat delivery strength. The early time temperature variances are closely related to the heat source configurations, and the later time temperatures in the domain are mainly determined by the total energy being delivered into the domain.

Analytical model for steady-state solute diffusion in non-isothermal fractured porous media

Mass transfer in non-isothermal fractured porous media have a wide application in many natural phenomena and engineering processes. The current study focuses on developing alternative formulations of steady-state analytical modelling for thermally induced solute diffusion in fractured porous media. The proposed analytical frameworks are validated by two set of experimental data. The varied examples of coupled heat transfer and solute diffusion are evaluated by the proposed solution to discuss the effects of thermal diffusion, flow operational conditions, geometry and thermal properties of fracture and matrix on the overall transport of solute in a fractured porous media. It is found that thermal-diffusion process, or explicitly as a “Soret effect (ST)”, is a non-negligible part for investigating solute transport in non-isothermal fractured porous media. For example, increasing ST from 10-3 K−1 to 10-2 K−1 leads to a reduction of solute concentration by a factor of 1.2. We demonstrate that a larger Peclet number ensures the temperature of the solute along the fracture decreasing while its concentration along the fracture increasing. However, an increase of the temperature difference between the entry and the output shows an opposite trend. An increase in fracture aperture or matrix thickness leads to temperature decreasing and concentration increasing along the fracture and matrix as a larger amount of solute are injected from the inlet boundary. The presented analytical solutions may also serve as a benchmark test tool for alternative numerical studies of coupled heat transfer and solute diffusion in fractured porous media.

Numerical simulation and analysis of thermo-hydro-mechanical behaviors of hydraulic fracturing in naturally fractured formation using a THM-XFEM coupling model

Activation and propagation of natural crack during hydraulic fracturing make an essential contribution to the reservoir stimulation. For the sake of figuring out the impact of thermo-poroelastic deformation in multi-field coupling on natural crack activation, a thermo-hydro-mechanical coupled model is developed in this paper. The thermo-poroelastic deformation and non-isothermal fluid flow in fractured media are all taken into account, and the contact problem for natural crack surfaces are solved by the augmented lagrangian multiplier method. Then the extended finite element method is adopted for the discretization of the coupled model. The developed model is verified against the analytical models of fracture propagation, heat transfer and crack loaded in shear. Sensitive analysis is conducted using the numerical model. Numerical results show that the key factors affecting interaction pattern between hydraulic fracture and natural crack are the geomechanical parameters while thermal effect only contribute to natural crack activation. Thermal stress can lead to an increase in fracture aperture but a reduction in fluid pressure in fracture, and the high reservoir temperature and coefficient of thermal expansion will aggravate this. Besides, the non orthogonal intersection angle will cause an asymmetric distribution of fluid pressure and aperture in activated natural crack.

Thermo-Hydro-Mechanical Coupling Processes in Carbonate Geothermal Reservoirs and Their Numerical Simulation

Abstract Reinjecting low-temperature tailwater into geothermal reservoirs leads to complex thermo-hydro-mechanical coupling processes, making it more difficult to predict the thermal breakthrough of the reservoirs. By taking the example of the deep carbonate geothermal reservoirs of karst fissure type in the Xianxian geothermal field in China, this paper studied the thermo-hydro-mechanical coupling processes in the case of reinjection based on previous tracer tests. It established a thermo-hydro-mechanical three-field coupling model based on a two-dimensional discrete fracture network and further verified its suitability through inversion analyses. Moreover, this paper discovered the regularity of the effects of temperature and pressure changes on the deformation of the rock masses in geothermal reservoirs and clarified the mechanisms of the seepage and heat transfer in thermo-hydro-mechanical coupling processes. Meanwhile, it presented the effects of the pressure and temperature on the heat extraction efficiency and production well temperature of the geothermal production-reinjection system in the Xianxian geothermal field. As indicated by the results, the pressure and temperature of geothermal reservoirs increased and decreased, respectively, in the initial phase of the reinjection, leading to an increase in fracture aperture and reservoir permeability. Then, they tended to gradually stabilize, and the amplitude change of the reservoir permeability decreased as the reinjection proceeded. Finally, this paper proposed an optimized reinjection scheme of the study area, aiming to provide scientific support for geothermal reinjection.

Numerical modelling of nitrate transport in fractured porous media under non-isothermal conditions.

Subsurface contamination is a frequent occurrence in fractured porous systems, posing a potential threat for the groundwater contamination. Tracking the movement of these contaminants is an inherent aspect of effective remediation strategy. The non-isothermal conditions prevailing in the subsurface environment further add to the complexity of the existing scenario. The current study focuses on simulating the concentration profiles of nitrogen species in a fracture-matrix system under non-isothermal conditions. The kinetics and biochemical thermodynamics of nitrogen transformation reactions were explicitly modelled in this study by adopting a finite differential numerical scheme. The numerical results clearly depicted the spatial-temporal profiles of the concentration of all the species in response to the observed peak values. Considering the sensitivity of the model parameters, an increase in flow velocity triggered the migration of all nitrogen species in the fracture, while an increase in matrix porosity reduced the concentration by enhancing the chemical reactions. An increase in fracture aperture also could trigger the denitrification process in the fracture to reduce the nitrate-nitrogen contamination in the fracture. The temperature variation between 25 °C and 45 °C in the fracture and the matrix essentially reduced the availability of nitrate-nitrogen and nitrogen gas in the fracture under non-isothermal conditions. Hence, an increase in the temperature coefficient can reduce the spike of nitrate-nitrogen and nitrogen gas in fracture by minimizing such transformation rates.

Hydromechanical Investigations on the Self-propping Potential of Fractures in Tight Sandstones

The hydromechanical properties of single self-propping fractures under stress are of fundamental interest for fractured-rock hydrology and a large number of geotechnical applications. This experimental study investigates fracture closure and hydraulic aperture changes of displaced tensile fractures, aligned tensile fractures, and saw-cut fractures for two types of sandstone (i.e., Flechtinger and Fontainebleau) with contrasting mechanical properties, cycling confining pressure between 5 and 30 MPa. Emphasis is placed on how surface roughness, fracture wall offset, and the mechanical properties of the contact asperities affect the self-propping potential of these fractures under normal stress. A relative fracture wall displacement can significantly increase fracture aperture and hydraulic conductivity, but the degree of increase strongly depends on the fracture surface roughness. For smooth fractures, surface roughness remains scale-independent as long as the fracture area is larger than a roll-off wavelength and thus any further displacement does not affect fracture aperture. For rough tensile fractures, these are self-affine over a larger scale so that an incremental fracture wall offset likely leads to an increase in fracture aperture. X-ray microtomography of the fractures indicates that the contact area ratio of the tensile fractures after the confining pressure cycle inversely correlates with the fracture wall offset yielding values in the range of about 3–25%, depending, first, on the respective surface roughness and, second, on the strength of the asperities in contact. Moreover, the contact asperities mainly occur isolated and tend to be preferentially oriented in the direction perpendicular to the fracture wall displacement which, in turn, may induce flow anisotropy. This, overall, implies that relatively harder sedimentary rocks have a higher self-propping potential for sustainable fluid flow through fractures in comparison to relatively soft rocks when specific conditions regarding surface roughness and fracture wall offset are met.

Numerical simulation on the effect of fractures geometries for shale gas development with discrete fracture network model

The shale gas reservoir is regarded as a dual medium consisting of fracture (hydraulic fracture and discrete natural fracture network) and rock matrix, the seepage process in the fracture and rock matrix is fully considered and a mathematical model of seepage flow in accordance with Darcy's law was established. The results show the influence order of hydraulic fracture geometry on the cumulative production. Compared with the hydraulic fracture aperture of 10–4 m, when the aperture is 10–5 m and 10–6 m, the cumulative production is reduced by 88.0% and 99.7%, respectively. Compared with the hydraulic fracture length is 100 m, when the length is 200 m and 300 m, the cumulative production is increased by 38.2% and 62.4%, respectively. The increase in the natural fracture aperture increases the fracture permeability, which make it more conducive to gas flow into the fracture, thereby increasing the cumulative production. The increase in the number of natural fractures makes the connectivity of the shale reservoir becomes better and the cumulative production increases more.

Mathematical model of the spontaneous imbibition of water into oil-saturated fractured porous media with gravity

Studying the mechanism of spontaneous imbibition into oil-saturated fractures is of great significance for unconventional oil reservoir development. Both theory and experimental observations indicate that SI in fractures is significantly different from that in tight matrix. In this work, the implicit analytical solution of the spontaneous water imbibition into a single oil-saturated fracture with gravity is first proposed. The results show that the difference in imbibition velocity with and without gravity increases with the increase in fracture aperture. There is a critical fracture length for SI in the single oil-saturated fracture. Based on the fractal/normal distribution of fracture apertures, the core-scale mathematical model of spontaneous imbibition in the oil-saturated fractured porous media is proposed. The effect of fracture distribution on the oil imbibition rate is investigated and discussed.

A coupled compressible flow and geomechanics model for dynamic fracture aperture during carbon sequestration in coal

SummaryThis paper presents the development of a discrete fracture model of fully coupled compressible fluid flow, adsorption and geomechanics to investigate the dynamic behaviour of fractures in coal. The model is applied in the study of geological carbon dioxide sequestration and differs from the dual porosity model developed in our previous work, with fractures now represented explicitly using lower‐dimensional interface elements. The model consists of the fracture‐matrix fluid transport model, the matrix deformation model and the stress‐strain model for fracture deformation. A sequential implicit numerical method based on Galerkin finite element is employed to numerically solve the coupled governing equations, and verification is completed using published solutions as benchmarks. To explore the dynamic behaviour of fractures for understanding the process of carbon sequestration in coal, the model is used to investigate the effects of gas injection pressure and composition, adsorption and matrix permeability on the dynamic behaviour of fractures. The numerical results indicate that injecting nonadsorbing gas causes a monotonic increase in fracture aperture; however, the evolution of fracture aperture due to gas adsorption is complex due to the swelling‐induced transition from local swelling to macro swelling. The change of fracture aperture is mainly controlled by the normal stress acting on the fracture surface. The fracture aperture initially increases for smaller matrix permeability and then declines after reaching a maximum value. When the local swelling becomes global, fracture aperture starts to rebound. However, when the matrix permeability is larger, the fracture aperture decreases before recovering to a higher value and remaining constant. Gas mixtures containing more carbon dioxide lead to larger closure of fracture aperture compared with those containing more nitrogen.

Investigation of thermal-induced damage in fractured rock mass by coupled FEM-DEM method

In this study, a 3D coupled FEM-DEM method was adopted to study the influence of thermal-induced damage on the mechanical properties of fractured rock mass. In this method, the rock matrix was discretized into bulk elements bridged by cohesive elements, and the preexisting fractures were represented by cohesive elements. The thermal-induced damage process was modeled through two parts, i.e., thermal conduction and thermal-mechanical coupling. For thermal conduction process, a proposed 3D thermal-cohesive coupled model with a fracture aperture-dependent interfacial thermal conductivity was adopted to simulate the thermal conduction across the fractures, which make it possible to more precisely predict the temperature distribution. Then, the thermal stress induced by temperature variation was coupled to perform the mechanical-failure calculation. Validation simulations indicated that the proposed model is capable of dealing with the thermal-induced damage problems. Then, the influences of fracture aperture on thermal-induced damage in highly fractured rock mass were numerically investigated by the Brazilian disc tests with multiple randomly distributed fractures. The results indicated that as the fracture aperture increases, the area of thermal-induced damage zone increases and the Brazilian tensile strength (BTS) decreases nonlinearly.

Effects of injection fluid type on pressure-dependent permeability evolution of fractured rocks in geothermal reservoirs: An experimental chemo-mechanical study

In geothermal reservoirs, coupled thermal-hydrological-mechanical-chemical processes lead to gradual closure of fractures and consequent production decline. The objective of this study was to investigate the effects of injected fluid type on the evolution of fracture aperture/permeability at various stress levels through a series of flow-through experiments on a fractured phyllite specimen, retrieved from a production well in the Blue Mountain geothermal field. The injected fluids included deionized water, silica super- and under-saturated fluids, and the geothermal fluid extracted from the Blue Mountain geothermal field. It was found that injection of geothermal and silica super-saturated fluids led to lowest and highest permeability reduction, respectively. In addition, the degree of permeability recovery was lower in the experiment using geothermal fluid compared to the experiment using silica super-saturated fluid. On the other hand, chemical analysis of the effluent samples revealed that injection of deionized water resulted in dissolution of feldspar and quartz, while precipitation of silica occurred in the experiment using geothermal fluid. Post-test observation by scanning electron microscopy of fracture surface area in the test using silica super-saturated fluid indicated some degree of mineral precipitation. A comparison between pre- and post-test computer tomography scan images for the experiment with injected silica super-saturated showed that mostly decrease in fracture aperture occurred, with increase in fracture aperture in a few regions along the fracture surface. Finally, the Three-Element rheological model successfully predicted the fracture permeability decay. The results of this study suggested that precipitation of silica, a major problem in permeability loss of geothermal systems, can be potentially minimized by using an injection fluid that is closer to chemical equilibrium state with the host rock.

Performance of enhanced geothermal system (EGS) in fractured geothermal reservoirs with CO2 as working fluid

Creating an open, connected fracture by hydraulic stimulation is vital to heat mining in an enhanced geothermal system (EGS). The existence of natural fractures, which seriously affects the development pattern, can complicate the hydraulic fractures. Different fracture propagation patterns of hydraulic fracturing can be achieved through different fracturing processes under certain natural fracture scales. Besides, CO2 has attracted a lot of attention as working fluid because of its superior hydrothermal properties and CO2 geological storage. At present, the study of EGS for fractured geothermal reservoirs with CO2 as working fluid is quite limited. In this paper, we firstly presented a three-dimensional (3D) thermal–hydraulic-mechanical (THM) coupled model to analyze performance of EGS in fractured geothermal reservoirs with different natural fractures scales, reservoir stimulation scales, and working fluids (water and CO2), aimed to guide reservoir stimulation and fracture parameter design. The results are showed as follows: If not forming connected fractures, the existence of natural fractures would cause fluid loss, an increase in natural fracture density by 0.4%, and the heat extraction rate decreases 0.06 MW on average; Forming connected fractures in the foundation of natural fractures would increase the output flow rate, so the reservoir stimulation scale increases by 0.85% and the heat extraction rate increases 0.2 MW; CO2 has better heat extraction properties than water due to its lower viscosity, greatly improving the production efficiency. Combining the hydraulic fracture conductivity tests creatively, the sensitivity analysis of fracturing parameters is studied. The heat extraction rate decreases with the increase in fracture aperture and fracture permeability. Under certain closure pressure (40 MPa in this paper), the best ceramsite proppant concentration and proppant size are 5 kg/m2 and 100 mesh, respectively, and the corresponding fracture conductivity is 1.6 μm2•cm.

Thermo-poroelastic effects on reservoir seismicity and permeability change

In this paper we study the role of thermo-poromechanical processes on reservoir seismicity and permeability enhancement using theoretical/numerical analysis. The numerical model is fully coupled, considering non-isothermal compressible single-phase fluid flow in fractured porous rock. It combines the thermo-poroelastic displacement discontinuity method, a nonlinear joint deformation model, and a finite difference method for solving the fluid and heat transport in a fracture network. The model is applied to simulate cool water injection into fracture/matrix systems to examine the role of coupled processes on fracture deformation, matrix pore pressure and stress redistributions to assess their role in induced seismicity and permeability variations. The simulation results are analyzed to draw conclusions regarding injection rate dependence of seismicity, and its transience due to coupled processes. Thermal influence on pore pressure and stress tend to promote delayed seismicity. In presence of coupled processes, rock matrix stress perturbations due to natural fracture deformation can be an influencing mechanism for seismicity. Our results show the induced normal stress in the vicinity of the fracture center where injected water enters, can be significant for higher cooling levels in low permeability matrix, and induces additional pore pressure perturbations in the matrix. These couplings have implications for reservoir stimulation and induced seismicity in geothermal reservoirs. The reservoirrock can experience a series of induced stress/pore pressure regimes with continued cooling (under injection). A potentially destabilizing regime is followed by a stabilizing one, and subsequently the rock approaches a destabilizing state. Each situation can result in potentially different levels of MEQ activity. Finally, the impact of thermo-poroelastic stresses on injection/extraction pressure profiles in a fractured rock is illustrated. Injection pressure tends to initially increase in response to poroelastic stress, but with time the thermal effect dominates resulting in fracture aperture increases and lowering of injection pressure.

Numerical Investigation of Influence of In-Situ Stress Ratio, Injection Rate and Fluid Viscosity on Hydraulic Fracture Propagation Using a Distinct Element Approach

Numerical simulation is very useful for understanding the hydraulic fracturing mechanism. In this paper, we simulate the hydraulic fracturing using the distinct element approach, to investigate the effect of some critical parameters on hydraulic fracturing characteristics. The breakdown pressure obtained by the distinct element approach is consistent with the analytical solution. This indicates that the distinct element approach is feasible on modeling the hydraulic fracturing. We independently examine the influence of in-situ stress ratio, injection rate and fluid viscosity on hydraulic fracturing. We further emphasize the relationship between these three factors and their contributions to the hydraulic fracturing. With the increase of stress ratio, the fracture aperture increases almost linearly; with the increase of injection rate and fluid viscosity, the fracture aperture and breakdown pressure increase obviously. A low value of product of injection rate and fluid viscosity (i.e., Qμ) will lead to narrow fracture aperture, low breakdown pressure, and complex or dispersional hydraulic fractures. A high value of Qμ would lead wide fracture aperture, high breakdown pressure, and simple hydraulic fractures (e.g., straight or wing shape). With low viscosity fluid, the hydraulic fracture geometry is not sensitive to stress ratio, and thus becomes a complex fracture network.

Experimental study of the transition from non-Darcian to Darcy behavior for flow through a single fracture

Laboratory experiments are designed in this paper using single fractures made of cement and coarse sand for a series of hydraulic tests under the conditions of different fracture apertures, and for the simulation of the evolution of the flow pattern at places far from the outlet. The relationship between the hydraulic gradient and the flow velocity at different points, and the proportion evolution of the linear and nonlinear portions in the Forchheimer formula are then discussed. Three major conclusions are obtained. First, the non-Darcian flow exists in a single fracture in different laboratory tests. Better fitting accuracy is obtained by using the Forchheimer formula than by using the Darcy law. Second, the proportion of the Darcy flow increases with the increase of the observation scale. In places far enough, the Darcy flow prevails, and the critical velocity between the non-Darcian flow and the Darcy flow decreases as the fracture aperture increases. Third, when the fracture aperture increases, the critical Reynolds number between the non-Darcian flow and the Darcy flow decreases.

Numerical simulation of high-resolution azimuthal resistivity laterolog response in fractured reservoirs

The high-resolution azimuthal resistivity laterolog response in a fractured formation was numerically simulated using a three-dimensional finite element method. Simulation results show that the azimuthal resistivity is determined by fracture dipping as well as dipping direction, while the amplitude differences between deep and shallow laterolog resistivities are mainly controlled by the former. A linear relationship exists between the corrected apparent conductivities and fracture aperture. With the same fracture aperture, the deep and shallow laterolog resistivities present small values with negative separations for low-angle fractures, while azimuthal resistivities have large variations with positive separations for high-angle fractures that intersect the borehole. For dipping fractures, the variation of the azimuthal resistivity becomes larger when the fracture aperture increases. In addition, for high-angle fractures far from the borehole, a negative separation between the deep and shallow resistivities exists when fracture aperture is large as well as high resistivity contrast exists between bedrock and fracture fluid. The decreasing amplitude of dual laterolog resistivity can indicate the aperture of low-angle fractures, and the variation of the deep azimuthal resistivity can give information of the aperture of high-angle fractures and their position relative to the borehole.

Effect of groundwater flow in vertical and horizontal fractures on borehole heat exchanger temperatures

Vertical closed loop systems, also known as borehole heat exchangers (BHEs), are a popular way of extracting the ground source heat energy. Primary factors affecting the performance of BHEs are the thermal and hydrogeological properties of the subsurface. Groundwater flow is known to potentially influence heat transport and system performance. The effect of groundwater movement is more commonly studied under homogeneous conditions. However, in heterogeneous fractured rocks, BHEs are more common than horizontal or open loops due to lack of sufficient soil layers and productive aquifers. The finite-element modelling shows that fractures can play an important role in BHE functioning. Especially, vertical open fractures (≥1 mm) near the borehole (≤10 m) can have a considerable impact. Although increase in fracture aperture continuously affects the subsurface and BHE temperatures, the increase in its effect progressively lessens. Depending on the distance and aperture, one major fracture influencing the BHE operation performance can be identified; yet a larger number of fractures may govern heat transport (thermal plume outline) and thermal recovery. Individually, horizontal fractures may have less influence than vertical fractures. However, as the density of horizontal fractures increases, their impact can be major, exceeding that of fracture aperture. In particular, we propose that measurements of rock thermal properties be combined with fracture mapping, to better analyse the thermal response testing results and integrate the configuration of fractures in design and layout of the BHE(s). This is particularly valid for (vertical) fractures not intersecting with the borehole.