Proppant transport in rough fracture networks using supercritical CO_(2)

Proppant transport within fractures is one of the most critical tasks in oil,gas and geothermal reservoir stimulation,as it largely determines the ultimate performance of the operating well.Proppant transport in rough fracture networks is still a relatively new area of research and the associated transport mechanisms are still unclear.In this study,representative parameters of rough fracture surfaces formed by supercritical CO_(2) fracturing were used to generate a rough fracture network model based on a spectral synthesis method.Computational fluid dynamics(CFD)coupled with the discrete element method(DEM)was used to study proppant transport in this rough fracture network.To reveal the turning transport mechanism of proppants into branching fractures at the intersections of rough fracture networks,a comparison was made with the behavior within smooth fracture networks,and the effect of key pumping parameters on the proppant placement in a secondary fracture was analyzed.The results show that the transport behavior of proppant in rough fracture networks is very different from that of the one in the smooth fracture networks.The turning transport mechanisms of proppant into secondary fractures in rough fracture networks are gravity-driven sliding,high velocity fluid suspension,and fracture structure induction.Under the same injection conditions,supercritical CO_(2)with high flow Reynolds number still has a weaker ability to transport proppant into secondary fractures than water.Thickening of the supercritical CO_(2)needs to be increased beyond a certain value to have a significant effect on proppant carrying,and under the temperature and pressure conditions of this paper,it needs to be increased more than 20 times(about 0.94 m Pa s).Increasing the injection velocity and decreasing the proppant concentration facilitates the entry of proppant into the branching fractures,which in turn results in a larger stimulated reservoir volume.The results help to understand the proppant transport and placement process in rough fracture networks formed by reservoir stimulation,and provide a theoretical reference for the optimization of proppant pumping parameters in hydraulic fracturing.

Proppant transport in rough fractures of unconventional oil and gas reservoirs

A method to generate fractures with rough surfaces was proposed according to the fractal interpolation theory.Considering the particle-particle,particle-wall and particle-fluid interactions,a proppant-fracturing fluid two-phase flow model based on computational fluid dynamics(CFD)-discrete element method(DEM)coupling was established.The simulation results were verified with relevant experimental data.It was proved that the model can match transport and accumulation of proppants in rough fractures well.Several cases of numerical simulations were carried out.Compared with proppant transport in smooth flat fractures,bulge on the rough fracture wall affects transport and settlement of proppants significantly in proppant transportation in rough fractures.The higher the roughness of fracture,the faster the settlement of proppant particles near the fracture inlet,the shorter the horizontal transport distance,and the more likely to accumulate near the fracture inlet to form a sand plugging in a short time.Fracture wall roughness could control the migration path of fracturing fluid to a certain degree and change the path of proppant filling in the fracture.On the one hand,the rough wall bulge raises the proppant transport path and the proppants flow out of the fracture,reducing the proppant sweep area.On the other hand,the sand-carrying fluid is prone to change flow direction near the contact point of bulge,thus expanding the proppant sweep area.

Lattice Boltzmann simulation of solute transport in a single rough fracture

In this study, the lattice Boltzmann method （LBM） was used to simulate the solute transport in a single rough fracture. The self-affine rough fracture wall was generated with the successive random addition method. The ability of the developed LBM to simulate the solute transport was validated by Taylor dispersion. The effect of fluid velocity on the solute transport in a single rough fracture was investigated using the LBM. The breakthrough curves （BTCs） for continuous injection sources in rough fractures were analyzed and discussed with different Reynolds numbers （Re）. The results show that the rough frac~＇e wall leads to a large fluid velocity gradient across the aperture. Consequently, there is a broad distribution of the immobile region along the rough fracture wall. This distribution of the immobile region is very sensitive to the Re and fracture geometry, and the immobile region is enlarged with the increase of Re and roughness. The concentration of the solute front in the mobile region increases with the Re. Furthermore, the Re and roughness have significant effects on BTCs, and the slow solute molecule exchange between the mobile and immobile regions results in a long breakthrough tail for the rough fracture. This study also demonstrates that the developed LBM can be effective in studying the solute transport in a rough fracture.

Empirical prediction of hydraulic aperture of 2D rough fractures:a systematic numerical study

This study aims to propose an empirical prediction model of hydraulic aperture of 2D rough fractures through numerical simulations by considering the influences of fracture length,average mechanical aperture,minimum mechanical aperture,joint roughness coefficient(JRC)and hydraulic gradient.We generate 600 numerical models using successive random additions(SRA)algorithm and for each model,seven hydraulic gradients spanning from 2.5×10^(-7)to 1 are considered to fully cover both linear and nonlinear flow regimes.As a result,a total of 4200 fluid flow cases are simulated,which can provide sufficient data for the prediction of hydraulic aperture.The results show that as the ratio of average mechanical aperture to fracture length increases from 0.01 to 0.2,the hydraulic aperture increases following logarithm functions.As the hydraulic gradient increases from 2.5×10^(-7)to 1,the hydraulic aperture decreases following logarithm functions.When a relatively low hydraulic gradient(i.e.,5×10^(-7))is applied between the inlet and the outlet boundaries,the streamlines are of parallel distribution within the fractures.However,when a relatively large hydraulic gradient(i.e.,0.5)is applied between the inlet and the outlet boundaries,the streamlines are disturbed and a number of eddies are formed.The hydraulic aperture predicted using the proposed empirical functions agree well with the calculated results and is more reliable than those available in the preceding literature.In practice,the hydraulic aperture can be calculated as a first-order estimation using the proposed prediction model when the associated parameters are given.

Investigations of Water Flow Behaviors Induced by Local Temperature Variations through a Single Rough Fracture for the Enhanced Geothermal Systems

In recent years,Enhanced Geothermal System(EGS)technologies have been applied to the geothermal resources production in the Hot Dry Rock(HDR).The core of EGS technologies is to adopt hydraulic fracturing in the reservoir to create a connected network of discrete fractures with the consideration of water as a working fluid for hydraulic fracturing and heat production.This paper investigates the characteristics of water flow behaviors through a single rough fracture under different temperature and pressure conditions.A single fracture model with rough fracture surfaces is constructed and then characterized,and influences of the anisotropic factor on the average tortuosity and frictional resistance coefficient of water flow through a single fracture with rough surfaces have been compared and analyzed.With consideration of other impacting factors(temperature,pressure,fracture roughness),the impact of mass flow rate has also been presented.Numerical simulation results present that changes of average tortuosity for water flow through a single rough facture are mainly affected by temperature.It can be observed that higher temperature leads to larger average tortuosity but the frictional resistance coefficient shows an opposite trend.As for pressure conditions,it is found that effects of pressure on average tortuosity and frictional resistance coefficient is very small,which can be neglected under high pressure conditions.Furthermore,the average tortuosity shows a progressively linear relationship with the mass flow rate.On the contrary,the frictional resistance coefficient has a negative relationship with the mass flow rate.It is revealed that when the mass flow rate reaches a critical point,the influences of temperature on the frictional resistance coefficient will be negligible.Comparisons of single rough fractures with different anisotropic factors show that values of average tortuosity and frictional resistance coefficient have positive relationships with the increase of anisotropic factors.

Characteristics of proppant transport and placement within rough hydraulic fractures

A three-dimensional reconstruction of rough fracture surfaces of hydraulically fractured rock outcrops is carried out by casting process,a large-scale experimental setup for visualizing rough fractures is built to perform proppant transport experiments.The typical characteristics of proppant transport and placement in rough fractures and its intrinsic mechanisms are investigated,and the influences of fracture inclination,fracture width and fracturing fluid viscosity on proppant transport and placement in rough fractures are analyzed.The results show that the rough fractures cause variations in the shape of the flow channel and the fluid flow pattern,resulting in the bridging buildup during proppant transport to form unfilled zone,the emergence of multiple complex flow patterns such as channeling,reverse flow and bypassing of sand-carrying fluid,and the influence on the stability of the sand dune.The proppant has a higher placement rate in inclined rough fractures,with a maximum increase of 22.16 percentage points in the experiments compared to vertical fractures,but exhibits poor stability of the sand dune.Reduced fracture width aggravates the bridging of proppant and induces higher pumping pressure.Increasing the viscosity of the fracturing fluid can weaken the proppant bridging phenomenon caused by the rough fractures.

Mechanical properties and fracture surface roughness of thermally damaged granite under dynamic splitting

In order to understand the mechanical properties and the fracture surface roughness characteristics of thermally damaged granite under dynamic splitting,dynamic Brazilian splitting tests were conducted on granite samples after thermal treatment at 25,200,400,and 600℃.Results show that the dynamic peak splitting strength of thermally damaged granite samples increases with increasing strain rate,showing obvious strain‐rate sensitivity.With increasing temperature,thermally induced cracks in granite transform from intergranular cracks to intragranular cracks,and to a transgranular crack network.Thermally induced damages reduce the dynamic peak splitting strength and the maximum absorbed energy while increasing the peak radial strain.The fracture mode of the thermally damaged granite under dynamic loads is mode Ⅱ splitting failure.By using the axial roughness index Z2 a,the distribution ranges of the wedge‐shaped failure zones and the tensile failure zones in the fracture surfaces under dynamic Brazilian splitting can be effectively identified.The radial roughness index Z_(2)^(r)is sensitive to the strain rate and temperature.It shows a linear correlation with the peak splitting strength and the maximum absorbed energy and a linear negative correlation with the peak radial strain.Z_(2)^(r)can be used to quantitatively estimate the dynamic parameters based on the models proposed.

Shear sliding of rough-walled fracture surfaces under unloading normal stress

Through high-precision engraving,self-affine sandstone joint surfaces with various joint roughness coefficients(JRC=3.21e12.16)were replicated and the shear sliding tests under unloading normal stress were conducted regarding various initial normal stresses(1e7 MPa)and numbers of shearing cycles(1 e5).The peak shear stress of fractures decreased with shear cycles due to progressively smooth surface morphologies,while increased with both JRC and initial normal stress and could be verified using the nonlinear Barton-Bandis failure criterion.The joint friction angle of fractures exponentially increased by 62.22%e64.87%with JRC while decreased by 22.1%e24.85%with shearing cycles.After unloading normal stress,the sliding initiation time of fractures increased with both JRC and initial normal stress due to more tortuous fracture morphologies and enhanced shearing resistance capacity.The surface resistance index(SRI)of fractures decreased by 4.35%e32.02%with increasing shearing cycles due to a more significant reduction of sliding initiation shear stress than that for sliding initiation normal stress,but increased by a factor of 0.41e1.64 with JRC.After sliding initiation,the shear displacement of fractures showed an increase in power function.By defining a sliding rate threshold of 5105 m/s,transition from“quasi-static”to“dynamic”sliding of fractures was identified,and the increase of sliding acceleration steepened with JRC while slowed down with shearing cycles.The normal displacement experienced a slight increase before shear sliding due to deformation recovery as the unloading stress was unloaded,and then enhanced shear dilation after sliding initiation due to climbing effects of surface asperities.Dilation was positively related to the shear sliding velocity of fractures.Wear characteristics of the fracture surfaces after shearing failure were evaluated using binary calculation,indicating an increasing shear area ratio by 45.24%e91.02%with normal stress.

EXPERIMENTAL STUDY OF FRICTION FACTOR FOR GROUNDWATER FLOW IN A SINGLE ROUGH FRACTURE

To study the relationships between the friction factor f and the flow type in a single rough fracture, the formulae of f for both unconfined and confined flows are deduced based on previous studies. The relationships between f and the Reynolds number （Re） for different relative roughnesses are investigated experimentally. The Moody-type diagram, based on the deduced formula of f, is also plotted and the hydraulic characteristics of the flow in a rough fracture are analyzed. Results show that the Moody-type diagram of the experiment has a similar distribution to that of the conventional Moody diagram. It is found that the value of f in the experiment is much smaller than that of the conventional Moody diagram and turbulent flow appears easier for rough fractures, which can be explained by the separation phenomenon in boundary layers. The critical Re ranging from 650 to 700 in rough fractures is concluded based on the experimental results. It also can be concluded that the friction factor f is related not only with the Re and the relative roughness but also with the absolute roughness.

Numerical simulation on proppant migration and placement within the rough and complex fractures

Hydraulic fracturing is a key technology for the development of unconventional hydrocarbon resources.The proppant placement morphology determines the fracture conductivity,thus affecting the reservoir stimulation effect.In this paper,the proppant migration and placement within complex fractures was studied by considering the fracture wall roughness through computational fluid mechanics-discrete element method(CFD-DEM)in numerical simulation,which is a key approach to study the proppant migration and placement.The results show that the proppant placement non-uniformity,proppant migration capacity,and proppant volume filled in the far-end and the secondary branched fracture are enhanced within the rough fracture compared with those within smooth fractures.The proppant migration capacity is increased within the fracture at low inclination angles(<60°)and low approach angles(<90°),and the proppant placement area is larger in the inclined fracture than that in the vertical fracture.The rise of injection rate and fracturing fluid viscosity causes more proppants migrate to far-end or secondary fractures,resulting in a non-proppant area within the near-wellbore fracture.An increase by 1.3 times in the injection rate and 3 times in the fracturing fluid viscosity leads to a decrease by 26.6%and 27%,respectively,in the proppant placement area within the near-wellbore fracture.The staged injection with small size proppants followed by large size proppants increases the proppant placement area in the primary fracture by 13%-26%,and that with large size proppants followed by small size proppants increases the proppant placement area by 19%-25%,which is due to that the latter method facilitates filling of the secondary branched fracture.The injection location mainly affects the proppant filling degree within the near-wellbore fractures.Compared with the upper injection,the middle and lower injection is not beneficial to filling of proppants within the near-wellbore fracture.

Influence of fracture roughness on shear strength,slip stability and permeability:A mechanistic analysis by three-dimensional digital rock modeling

Subsurface fluid injections can disturb the effective stress regime by elevating pore pressure and potentially reactivate faults and fractures.Laboratory studies indicate that fracture rheology and permeability in such reactivation events are linked to the roughness of the fracture surfaces.In this study,we construct numerical models using discrete element method(DEM)to explore the influence of fracture surface roughness on the shear strength,slip stability,and permeability evolution during such slip events.For each simulation,a pair of analog rock coupons(three-dimensional bonded quartz particle analogs)representing a mated fracture is sheared under a velocity-stepping scheme.The roughness of the fracture is defined in terms of asperity height and asperity wavelength.Results show that(1)Samples with larger asperity heights(rougher),when sheared,exhibit a higher peak strength which quickly devolves to a residual strength after reaching a threshold shear displacement;(2)These rougher samples also exhibit greater slip stability due to a high degree of asperity wear and resultant production of wear products;(3)Long-term suppression of permeability is observed with rougher fractures,possibly due to the removal of asperities and redistribution of wear products,which locally reduces porosity in the dilating fracture;and(4)Increasing shear-parallel asperity wavelength reduces magnitudes of stress drops after peak strength and enhances fracture permeability,while increasing shear-perpendicular asperity wavelength results in sequential stress drops and a delay in permeability enhancement.This study provides insights into understanding of the mechanisms of frictional and rheological evolution of rough fractures anticipated during reactivation events.

Frictional behavior of planar and rough granite fractures subjected to normal load oscillations of different amplitudes

The dynamic frictional behaviors of natural discontinuities(joints,fractures,faults)play an important role in geohazards assessment;however,the mechanisms of the dynamic fault weakening/strengthening are still unclear.In this paper,a dynamic shear box was used to perform direct shear tests on saw-cut(planar)and natural(rough)granite fractures,with different normal load oscillation amplitudes.Based on the recorded shear forces and normal displacements,the shear forces,apparent friction coefficients and normal displacements are found to change periodically with oscillated normal loads and are characterized by a series of time shifts.The observed changing patterns are similar for the rough and planar fractures.Compared with the test data under constant normal load(CNL),small/large normal load oscillation amplitude enhances/reduces the peak shear strength,with a critical point.The magnitude of critical normal load oscillation for the rough fractures is smaller than the planer fractures.The results imply that dynamic fault weakening/strengthening can be achieved by both normal load oscillation amplitudes and slip surface topography.The rough fractures with larger normal oscillation amplitude can easily cause frictional weakening under stress disturbance.

Numerical modeling of the effects of roughness on flow and eddy formation in fractures

The effect of roughness on flow in fractures was investigated using lattice Boltzmann method(LBM).Simulations were conducted for both statistically generated hypothetical fractures and a natural dolomite fracture. The effect of increasing roughness on effective hydraulic aperture, Izbash and Forchheimer parameters with increasing Reynolds number(Re) ranging from 0.01 to 500 was examined. The growth of complex flow features, such as eddies arising near the fracture surface, was directly associated with changes in surface roughness. Rapid eddy growth above Re values of 1, followed by less rapid growth at higher Re values, suggested a three-zone nonlinear model for flow in rough fractures. This three-zone model, relating effective hydraulic conductivity to Re, was also found to be appropriate for the simulation of water flow in the natural dolomite fracture. Increasing fracture roughness led to greater eddy volumes and lower effective hydraulic conductivities for the same Re values.

Meso-mechanical anisotropy and fracture evolution of reef limestones from the Maldives Islands and the South China Sea

Reef limestone is a biogenic sedimentary rock widely distributed in coral reef areas, acting as an important foundation for coast construction. Due to its special biogenic origin, reef limestone is different from conventional rocks both in terms of rock structure and mechanical properties. In this study, mesoscale uniaxial compression experiments with five different loading directions were conducted on two kinds of reef limestones from the Maldives Islands and the South China Sea, respectively. The real-time high-resolution videos and images of failure processes were recorded simultaneously to investigate the fracture evolution and fracture surface roughness of reef limestones. It demonstrated that the reef limestones belonged to extremely soft to soft rocks, and their uniaxial compressive strength (UCS) values fluctuated with high discreteness. The mesoscale mechanical properties of reef limestones were highly anisotropic and mainly controlled by pore structure. The occurrence of dissolution pores in reef limestone tended to intensify mechanical anisotropy. With the integration of the fracture initiation and propagation features of reef limestones, it is supposed that the intrinsic mechanism of anisotropy was probably attributed to the differences in coral growth direction and dissolution. Furthermore, the quantified fracture surface roughness was revealed to have a good consistency with density and UCS for the reef limestones from the South China Sea. The findings are helpful for providing theoretical and experimental references for engineering construction in coral reef areas.

Convective heat transfer of water flow in intersected rock fractures for enhanced geothermal extraction

Numerous intersected rock fractures constitute the fracture network in enhanced geothermal systems.The complicated convective heat transfer behavior in intersected fractures is critical to the heat recovery in fractured geothermal reservoirs.A series of three-dimensional intersected fracture models is constructed to perform the flow-through heat transfer simulations.The geometry effects of dead-end fractures(DEFs)on the heat transfer are evaluated in terms of intersected angles,apertures,lengths,and the connectivity.The results indicate that annular streamlines appear in the rough DEF and cause an ellipse distribution of the cold front.Compared to plate DEFs,the fluid flow in the rough DEF enhances the heat transfer.Both the increment of outlet water temperatureΔToutand the ratio of heat production Qrpresent the largest at the intersected angle of 90°while decline with the decrease of the intersected angle between the main flow fracture(MFF)and the DEFs.The extension of the length of intersected DEFs is beneficial to heat production while enhancing its aperture is not needed.Solely increasing the number of intersected DEFs induces a little increase of heat extraction,and more significant heat production can be obtained through connecting these DEFs with the MFF forming the flow network.

Anisotropic characteristics of electrical responses of fractured reservoir with multiple sets of fractures

In fractured reservoirs, the fractures not but also form the main flow channels which connect productivity of reservoirs. However, because of the only provide the storage space for hydrocarbons, the pores of the matrix, so fractures dominate the heterogeneity and randomness of the distribution of fractures, exploration and evaluation of fractured reservoirs is still one of the most difficult problems in the oil industry. In recent years, seismic anisotropy has been applied to the assessment of fractured formations, whereas electrical anisotropy which is more intense in fractured formations than seismic anisotropy has not been studied or used so extensively. In this study, fractured reservoir models which considered multiple sets of fractures with smooth and partly closed, rough surfaces were established based on the fractures and pore network, and the vertical and horizontal electrical resistivities were derived as a function of the matrix and fracture porosities according to Ohm＇s law. By using the anisotropic resistivity equations, variations of the electrical anisotropy of three types of fractured models under the conditions of free pressure and confining pressure were analyzed through the variations of the exerted pressure, matrix porosity, fracture aperture and formation water resistivity. The differences of the vertical and horizontal resistivities and the anisotropy between the connected and non-connected fractures were also analyzed. It is known from the simulated results that an increase of the confining pressure causes a decrease of electrical anisotropy because of the elasticity of the closed fractures and the decrease of the fracture aperture. For a fixed fracture porosity, the higher the matrix porosity, the weaker the electrical anisotropy in the rock formation.

Shear testing on rock tunnel models under constant normal stress conditions

Large shear deformation problems are frequently encountered in geotechnical engineering.To expose the shear failure mechanism of rock tunnels,compression-shear tests for rock models with circular tunnel were carried out,including single tunnel and adjacent double tunnels.The failure process is recorded by the external video and miniature cameras around the tunnel,accompanied by real-time acoustic emission monitoring.The experiments indicate that the shearing processes of rock tunnel can be divided into four steps:(i)cracks appeared around tunnels,(ii)shear cracks and spalling ejection developed,(iii)floor warping occurred,and(iv)shear cracks ran through the tunnel model.Besides,the roughness of the sheared fracture surface decreased with the increase in normal stress.Corresponding numerical simulation indicates that there are tensile stress concentrations and compressive stress concentrations around the tunnel during the shearing process,while the compressive stress concentration areas are under high risk of failure and the existence of adjacent tunnels will increase the degree of stress concentration.

New model of propagation rates of long crack due to structure fatigue

By comparison of the characteristics of existing models for long fatigue crack propagation rates, a new model, called the generalized passivation-lancet model for long fatigue crack propagation rates （GPLFCPR）, and a general formula for characterizing the process of crack growth rates are proposed based on the passivation-lancet theory. The GPLFCPR model overcomes disadvantages of the existing models and can describe the rules of the entire fatigue crack growth process from the cracking threshold to the critical fracturing point effectively with explicit physical meaning. It also reflects the influence of material characteristics, such as strength parameters, fracture parameters and heat treatment. Experimental results obtained by testing LZ50 steel, AlZnMgCu0.5, 0.5Cr0.5Mo0.25V steel, etc., show good consistency with the new model. The GPLFCPR model is valuable in theoretical research and practical applications.

Fractal in Fatigue Fractography

Fracture profile roughnesses and fractal dimensions of fracture traces were measured on a fatigued Ti-6Al-4V alloy.It is found that although fractal dimension can well reflect the variation of fracture traces with the measuring units,it is difficult to apply it to quantitative analysis of fractured surfaces because of the dependence of the meas- ured profile roughness on the measuring units.Based on fractal concept.an alternative equation lgR_l(η)=lgR_o-(D-1)lgη was obtained.in which we intro- duced a parameter of intrinsic profile roughness to evalu- ate fracture profile roughness without restriction of the measuring units employed.

SIMULATION OF SOLUTE TRANSPORT IN A PARALLEL SINGLE FRACTURE WITH LBM/MMP MIXED METHOD

This article deals with the solute transport in a single fracture with the combination of the Lattice Boltzmann Method （LBM） and Modified Moment Propagation （MMP） method, and this mixed method is proved to have several advantages over the LBM and Moment Propagation （MP） mixed method which leads to negative concentrations under some conditions in computation. The disadvantage of LBM/MP has been overcome to a certain extent. Also, this work presents an LBM solution of modeling single fractures with uniformly or randomly distributed grains, which can provide a new path of applying the LBM in solute transport simulation in fractures.