Estimation of the anisotropy of hydraulic conductivity through 3D fracture networks using the directional geological entropy

With an extension of the geological entropy concept in porous media,the approach called directional entrogram is applied to link hydraulic behavior to the anisotropy of the 3D fracture networks.A metric called directional entropic scale is used to measure the anisotropy of spatial order in different directions.Compared with the traditional connectivity indexes based on the statistics of fracture geometry,the directional entropic scale is capable to quantify the anisotropy of connectivity and hydraulic conductivity in heterogeneous 3D fracture networks.According to the numerical analysis of directional entrogram and fluid flow in a number of the 3D fracture networks,the hydraulic conductivities and entropic scales in different directions both increase with spatial order(i.e.,trace length decreasing and spacing increasing)and are independent of the dip angle.As a result,the nonlinear correlation between the hydraulic conductivities and entropic scales from different directions can be unified as quadratic polynomial function,which can shed light on the anisotropic effect of spatial order and global entropy on the heterogeneous hydraulic behaviors.

Factors Influencing Proppant Transportation and Hydraulic Fracture Conductivity in Deep Coal Methane Reservoirs

The gas production of deep coalbed methane wells in Linxing-Shenfu block decreases rapidly,the water output is high,the supporting effect is poor,the effective supporting fracture size is limited,and the migration mechanism of proppant in deep coal reservoir is not clear at present.To investigate the migration behavior of proppants in complex fractures during the volume reconstruction of deep coal and rock reservoirs,an optimization test on the conductivity of low-density proppants and simulations of proppant migration in complex fractures of deep coal reservoirs were conducted.The study systematically analyzed the impact of various fracture geometries,proppant types and fracturingfluid viscosities on proppant distribution.Furthermore,the study compared the outcomes of dynamic proppant transport experiments with simulation results.The results show that the numerical simulation is consistent with the results of the proppant dynamic sand-carrying experiment.Under the conditions of low viscosity and large pumping-rate,a high ratio of 40/70 mesh proppant can facilitate the movement of the proppant to the depths of fractures at all levels.The technical goal is to create comprehensive fracture support within intricate trapezoidal fractures in deep coal and rock reservoirs without inducing sand plugging.The sand ratio is controlled at 15%–20%,with a proppant combination ratio of 40/70:30/50:20/40=6:3:1.Proppant pumping operations can effectively address the issue of poor support in complex fractures in deep coal formations.The research results have been successfully applied to the development of deep coalbed methane in the Linxing-Shenfu block,Ordos Basin.

Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil-water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

Morphological evolution and flow conduction characteristics of fracture channels in fractured sandstone under cyclic loading and unloading

In coal mining,rock strata are fractured under cyclic loading and unloading to form fracture channels.Fracture channels are the main flow narrows for gas.Therefore,expounding the flow conductivity of fracture channels in rocks on fluids is significant for gas flow in rock strata.In this regard,graded incremental cyclic loading and unloading experiments were conducted on sandstones with different initial stress levels.Then,the three-dimensional models for fracture channels in sandstones were established.Finally,the fracture channel percentages were used to reflect the flow conductivity of fracture channels.The study revealed how the particle size distribution of fractured sandstone affects the formation and expansion of fracture channels.It was found that a smaller proportion of large blocks and a higher proportion of small blocks after sandstone fails contribute more to the formation of fracture channels.The proportion of fracture channels in fractured rock can indicate the flow conductivity of those channels.When the proportion of fracture channels varies gently,fluids flow evenly through those channels.However,if the proportion of fracture channels varies significantly,it can greatly affect the flow rate of fluids.The research results contribute to revealing the morphological evolution and flow conductivity of fracture channels in sandstone and then provide a theoretical basis for clarifying the gas flow pattern in the rock strata of coal mines.

3D Lamellar-Structured Graphene Aerogels for Thermal Interface Composites with High Through-Plane Thermal Conductivity and Fracture Toughness

Although thermally conductive graphene sheets are efficient in enhancing in-plane thermal conductivities of polymers,the resulting nanocomposites usually exhibit low through-plane thermal conductivities,limiting their application as thermal interface materials.Herein,lamellarstructured polyamic acid salt/graphene oxide(PAAS/GO)hybrid aerogels are constructed by bidirectional freezing of PAAS/GO suspension followed by lyophilization.Subsequently,PAAS monomers are polymerized to polyimide(PI),while GO is converted to thermally reduced graphene oxide(RGO)during thermal annealing at 300℃.Final graphitization at 2800℃ converts PI to graphitized carbon with the inductive effect of RGO,and simultaneously,RGO is thermally reduced and healed to high-quality graphene.Consequently,lamellar-structured graphene aerogels with superior through-plane thermal conduction capacity are fabricated for the first time,and its superior through-plane thermal conduction capacity results from its vertically aligned and closely stacked high-quality graphene lamellae.After vacuum-assisted impregnation with epoxy,the resultant epoxy composite with 2.30 vol% of graphene exhibits an outstanding through-plane thermal conductivity of as high as 20.0 W m^−1 K^−1,100 times of that of epoxy,with a record-high specific thermal conductivity enhancement of 4310%.Furthermore,the lamellar-structured graphene aerogel endows epoxy with a high fracture toughness,~1.71 times of that of epoxy.

Determination of hydraulic conductivity of fractured rock masses:A case study for a rock cavern project in Singapore

In order to reduce the risk associated with water seepage in an underground rock cavern project inSingapore, a reliable hydro-geological model should be established based on the in situ investigationdata. The key challenging issue in the hydro-geological model building is how to integrate limitedgeological and hydro-geological data to determine the hydraulic conductivity of the fractured rockmasses. Based on the data obtained from different stages （feasibility investigation stage, constructionstage, and post-construction stage）, suitable models and methods are proposed to determine the hydraulicconductivities at different locations and depths, which will be used at other locations in thefuture. 2015 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Numerical well test for well with finite conductivity vertical fracture in coalbed

A new well test model is developed for the hydraulic fractured well in coalbed by considering the following aspects： methane desorption phenomena, finite conductivity vertical fractures, and asymmetry of the fracture about the well. A new parameter is introduced to describe the storage of the fracture, which is named as a combined fracture storage. Another new concept called the fracture asymmetry coefficient is used to define the asymmetry of the fracture about the well. Finite element method （FEM） is used to solve the new mathematical model. The well test type curves and pressure fields are obtained and analyzed. The effects of the combined fracture storage, desorption factor, fracture conductivity, and fracture asymmetry coefficient on the well test type curves are discussed in detail. In order to verify the new model, a set of field well test data is analyzed.

An optimization model for conductivity of hydraulic fracture networks in the Longmaxi shale,Sichuan basin,Southwest China

Shale gas is an important unconventional resource.The economic recovery of shale gas is only possible when a fracture network with sufficient conductivity is created by hydraulic fracturing,that,if effectively propped,connects fracturing fractures and natural fractures.Focusing on the Longmaxi shale in the Sichuan Basin,Southwest China,we built an optimization model for conductivity of multi-grade fractures based on equivalent seepage theory.We then experimentally analyzed the conductivity of self-propped and sand-propped fractures,and optimized the propping patterns of multi-grade hydraulic fractures in shale gas reservoirs.We concluded that the propping effectiveness of fracture networks could be improved by using low concentrations of small-sized sands and by focusing on creating a large number of self-propped fractures.By applying this understanding to the optimization of fracturing designs for the Longmaxi shale,we successfully created networks of well-propped fractures.

Experimental modeling of sanding fracturing and conductivity of propped fractures in conglomerate:A case study of tight conglomerate of Mahu sag in Junggar Basin,NW China

True tri-axial sanding fracturing experiments are carried out on conglomerate samples from the Permian Wuerhe Formation of Mahu sag,Junggar Basin,to study hydraulic fracture propagation geometry and quartz sand transport in ma-trix-supported fine conglomerate and grain-supported medium conglomerate.The effect of rough fracture surface on conduc-tivity is analyzed using the 3D-printing technology to reconstruct the rough surface formed in the fractured conglomerate.The hydraulic fractures formed in the matrix-supported fine conglomerate are fairly straight,and only more tortuous when en-countering large gravels at local parts;thus,proppants can get into the fractures easily with transport distance about 70%–90%of the fracture length.By contrast,in the grain-supported medium conglomerate,hydraulic fractures tend to bypass the gravels to propagate in tortuous paths and frequently change in width;therefore,proppants are difficult to transport in these fractures and only move less than 30%of the fracture length.As the ma trix-supported fine conglomerate has high matrix content and low hardness,proppants embed in the fracture surface severely.In contrast,the grain-supported medium conglomerate has higher gravel content and hardness,so the quartz sand is crushed more severely.Under the high proppant concentration of 5 kg/m^(2),when the closure stress is increased(above 60 MPa),fractures formed in both matrix-supported fine conglomerate and grain-supported medium conglomerate decrease in width significantly,and drop 88%and 92%in conductivity respectively compared with the case under the low closure stress of 20 MPa.The field tests prove that under high closure stress above 60 MPa,using a high proportion of fine proppants with high concentration allow the proppant to move further in the fracture;meanwhile proppant places more uniformly in the ro ugh fracture,resulting in a higher fracture conductivity and an improved well per-formance.

Productivity analysis of horizontal wells intercepted by multiple finite-conductivity fractures

Horizontal wells in the anisotropic reservoirs can be stimulated by hydraulic fracturing in order to create multiple finite-conductivity vertical fractures. Several methods for evaluating the productivity of the horizontal wells have been presented in the literature. With such methods, however, it is still difficult to obtain an accurate result. This paper firstly presents the dimensionless conductivity theory of vertical fractures. Then models for calculating the equivalent wellbore radius and the skin factor due to flow convergence to the well bore are proposed after analyzing the steady-state flow in porous reservoirs. By applying the superposition principle to the pressure drop, a new method for evaluating the productivity of horizontal wells intercepted by multiple finite-conductivity fractures is developed. The influence of fracture conductivity and fracture half length on the horizontal well productivity is quantitatively analyzed with a synthetic case. Optimum fracture number and fracture space are further discussed in this study. The results prove that the method outlined here should be useful to design optimum fracturing of horizontal wells.

Electrical-hydraulic conductivity model for a weatheredfractured aquifer system of Olbanita, Lower Baringo Basin, Kenya Rift

Groundwater yield in the Kenya Rift is highly unsustainable owing to geological variability.In this study,field hydraulic characterization was performed by using geoelectric approaches.The relations between electrical-hydraulic(eh)conductivities were modeled hypothetically and calibrated empirically.Correlations were based on the stochastic models and field-scale hydraulic parameters were contingent on pore-level parameters.By considering variation in pore-size distributions over eh conduction interval,the relations were scaled-up for use at aquifer-level.Material-level electrical conductivities were determined by using Vertical Electrical Survey and hydraulic conductivities by analyzing aquifer tests of eight boreholes in the Olbanita aquifer located in Kenya rift.VES datasets were inverted by using the computer code IP2Win.The main result is that ln T=0.537(ln Fa)+3.695;the positive gradient indicating eh conduction through pore-surface networks and a proxy of weathered and clayey materials.An inverse(1/F-K)correlation is observed.Hydraulic parameters determined using such approaches may possibly contribute significantly towards sustainable yield management and planning of groundwater resources.

Advanced production decline analysis of tight gas wells with variable fracture conductivity

Considering the characteristics that the fracture conductivity formed by hydraulic fracturing varies across space and time, a new mathematical model was established for seepage flow in tight gas fractured vertical wells which takes into account the effects of dual variable conductivity and stress sensitivity. The Blasingame advanced production decline curves of the model were obtained using the finite element method with hybrid elements. On this basis, the effects of fracture space and time dual variable conductivity and stress sensitivity on Blasingame curve were analyzed. The study shows that the space variable conductivity mainly reduces decline curve value at the early stage; the time variable conductivity can result in drops of the production and the production integral curves, leading to a S-shaped curve; dual variable conductivity is the superposition of the effects given by the two variable conductivities; both time and space variable conductivities cannot delay the time with which the formation fluid flow reaches the quasi-steady state. The stress sensitivity reduces the curve value gradually rather than sharply, delaying the time the flow reaching the quasi-steady state. Ignoring the effects of variable conductivity and stress sensitivity will not affect the estimation on well controlled dynamic reserves. However, it can result in large errors in the interpretation of fractures and reservoir parameters. Conventional advanced production decline analyses of a tight gas fractured well in the Sulige gas field showed that the new model is more effective and reliable than the conventional model, and thus it can be widely applied in advanced production decline analysis of wells with the same characteristics in other gas fields.

A review of reservoir damage during hydraulic fracturing of deep and ultra-deep reservoirs

Deep and ultra-deep reservoirs have gradually become the primary focus of hydrocarbon exploration as a result of a series of significant discoveries in deep hydrocarbon exploration worldwide.These reservoirs present unique challenges due to their deep burial depth(4500-8882 m),low matrix permeability,complex crustal stress conditions,high temperature and pressure(HTHP,150-200℃,105-155 MPa),coupled with high salinity of formation water.Consequently,the costs associated with their exploitation and development are exceptionally high.In deep and ultra-deep reservoirs,hydraulic fracturing is commonly used to achieve high and stable production.During hydraulic fracturing,a substantial volume of fluid is injected into the reservoir.However,statistical analysis reveals that the flowback rate is typically less than 30%,leaving the majority of the fluid trapped within the reservoir.Therefore,hydraulic fracturing in deep reservoirs not only enhances the reservoir permeability by creating artificial fractures but also damages reservoirs due to the fracturing fluids involved.The challenging“three-high”environment of a deep reservoir,characterized by high temperature,high pressure,and high salinity,exacerbates conventional forms of damage,including water sensitivity,retention of fracturing fluids,rock creep,and proppant breakage.In addition,specific damage mechanisms come into play,such as fracturing fluid decomposition at elevated temperatures and proppant diagenetic reactions at HTHP conditions.Presently,the foremost concern in deep oil and gas development lies in effectively assessing the damage inflicted on these reservoirs by hydraulic fracturing,comprehending the underlying mechanisms,and selecting appropriate solutions.It's noteworthy that the majority of existing studies on reservoir damage primarily focus on conventional reservoirs,with limited attention given to deep reservoirs and a lack of systematic summaries.In light of this,our approach entails initially summarizing the current knowledge pertaining to the types of fracturing fluids employed in deep and ultra-deep reservoirs.Subsequently,we delve into a systematic examination of the damage processes and mechanisms caused by fracturing fluids within the context of hydraulic fracturing in deep reservoirs,taking into account the unique reservoir characteristics of high temperature,high pressure,and high in-situ stress.In addition,we provide an overview of research progress related to high-temperature deep reservoir fracturing fluid and the damage of aqueous fracturing fluids to rock matrix,both artificial and natural fractures,and sand-packed fractures.We conclude by offering a summary of current research advancements and future directions,which hold significant potential for facilitating the efficient development of deep oil and gas reservoirs while effectively mitigating reservoir damage.

Experimental study on flow heterogeneity of shale bedding fractures based on full-diameter cores

A self-designed full-diameter core experimental facility was used to evaluate the flow heterogeneity of bedding fractures at four radial directions under different closure pressures and injection rates,using full-diameter cores retaining original natural bedding fractures.The distribution morphology of bedding surface affects the conductivity of bedding fractures,and the flow capacity of bedding fractures in four radial directions varies greatly with the closure pressure and injection rate.The rougher the fracture surface,the greater the flow capacity varies with the closure pressure.For unsupported bedding fractures,the mean percentage error(MPE)of the conductivity in four radial directions increase gradually with the increase of the closure pressure.This phenomenon is especially prominent in deep rock samples.It is indicated that the flow heterogeneity of bedding fractures tends to increase with the closure pressure.When proppant is placed in the fracture,at a low closure pressure,due to the combined effects of self-support of rough fracture surface,proppant instability and uneven proppant placement,the flow heterogeneity is greater than that when proppant is not placed at the same closure pressure;however,with the increase of the closure pressure,the proppant becomes compact and stable,and the flow heterogeneity is mitigated gradually.

Effect of α-lipoic acid combined with nerve growth factor on bone metabolism, oxidative stress and nerve conduction function after femoral fracture surgery

Objective: To discuss the effect of α-lipoic acid combined with nerve growth factor on bone metabolism, oxidative stress and nerve conduction function after femoral fracture surgery. Methods: A total of 110 patients with femoral fracture who received surgical treatment in the hospital between January 2015 and January 2017 were collected and divided into the control group (n=55) and study group (n=55) by random number table. Control group received postoperative nerve growth factor therapy, and study group received postoperative α-lipoic acid combined with nerve growth factor therapy. The differences in the contents of bone metabolism and oxidative stress indexes as well as the levels of nerve conduction function indexes were compared between the two groups before and after treatment. Results: Before treatment, the differences in the contents of bone metabolism and oxidative stress indexes as well as the levels of nerve conduction function indexes were not statistically significant between the two groups. After treatment, serum bone metabolism indexes BGP and PⅠNP contents of study group were higher than those of control group while CTX-Ⅰ and TRAP contents were lower than those of control group;serum oxidative stress indexes TAC, CAT and SOD contents of study group were higher than those of control group while MDA content was lower than that of control group;limb nerve conduction velocity SCV and MCV levels of study group were higher than those of control group. Conclusion: α-lipoic acid combined with nerve growth factor therapy after femoral fracture surgery can effectively balance osteoblast/osteoclast activity, reduce oxidative stress and improve limb nerve conduction velocity.

Experimental study and modeling of hydromechanical behavior of concrete fracture

In this study, the hydromechanical behavior of a concrete fracture under coupled compressive and shear stresses was investigated. A special experimental device was designed to create a planar fracture in a cylindrical sample and to carry out different kinds of hydromechanical tests on the fracture. Four series of laboratory tests were performed on an ordinary concrete sample. Hydrostatic compression tests were first conducted to characterize the normal compressibility of the fracture. In the second series, direct shear tests were conducted on the fracture under different normal stresses. The maximal shear stress of the fracture was determined as a function of the normal stress. In the third series, fluid flow tests were carried out in view of characterizing the overall hydraulic conductivity of the fracture as a function of its opening and closure. Shear tests with a constant fluid pressure were finally performed to investigate the influence of fluid pressure on the deformation behavior of concrete fractures. Based on the experimental investigation, an elastoplastic model is proposed. This model takes into account the nonlinear elastic behavior of a fracture under normal compression and the plastic deformation and failure due to shear stress. The model was coupled with the classical Darcy's law to describe the fluid flow along the fracture by considering the variation of permeability with fracture aperture. Numerical results agree with experimental data from various laboratory tests.

EFFECTS OF STATIC ELECTRIC FIELD ON THE FRACTURE BEHAVIOR OF PIEZOELECTRIC CERAMICS

The paper gives an overview on experimental observations of the failure behavior of electrically insulating and conducting cracks in piezoelectric ce- ramics.The experiments include the indentation fracture test,the bending test on smooth samples,and the fracture test on pre-notched(or pre-cracked)compact ten- sion samples.For electrically insulating cracks,the experimental results show a com- plicated fracture behavior under electrical and mechanical loading.Fracture data are much scattered when a static electric field is applied.A statistically based frac- ture criterion is required.For electrically conducting cracks,the experimental results demonstrate that static electric fields can fracture poled and depoled lead zirconate titanate ceramics and that the concepts of fracture mechanics can be used to mea- sure the electrical fracture toughness.Furthermore,the electrical fracture toughness is much higher than the mechanical fracture toughness.The highly electrical fracture toughness arises from the greater energy dissipation around the conductive crack tip under purely electric loading,which is impossible under mechanical loading in the brittle ceramics.

DYNAMIC PRODUCTION PREDICTION AND PARAMETER IDENTIFICATION FOR GAS WELL WITH VERTICAL FRACTURE

In order to devoid the hard work and factitious error in selecting charts while analyzing and interpreting hydraulic fracturing fracture parameters, on the basis of the non-Darcy flow factor, this paper put out the non-Darcy flow mathematical model of real gas in the formation and fracture, established the production history automatic matching model to identify fracture parameters, and offered the numerical solutions of those models, which took the variation of fracture conductivity in production process. These results offered a precise and reliable method to understand formation, analyze and evaluate the fracturing treatment quality of gas well.

A new apparatus for investigating stress,deformation and seepage coupling properties of rock fractures

A true triaxial apparatus which is composed of three units was presented.The apparatus allows for investigations on deformation and seepage behaviors of a single rock fracture subjected to lateral stress and normal stress.The first unit has three jacks which can apply loads independently in three orthogonal directions.The second unit is used to supply water inflow,control seepage pressure and measure flow velocity in real time.The third unit is for measuring the normal deformation of rock fractures.Some tests for investigating the normal deformation and seepage behaviors of rock fractures subjected to normal and lateral loads on hard granite specimens with an artificial persistent fracture,were introduced.The results show that both the normal deformation and the hydraulic conductivity are influenced not only by the normal stress but also by the lateral stress.It is also shown that the aperture and the hydraulic conductivity decrease with the increasing normal stress but increase with the increasing lateral stress and both the aperture and the hydraulic conductivity obey exponential relationships with the normal stress and the lateral stress.