Numerical simulation of three-dimensional fracturing fracture propagation in radial wells

A fracture propagation model of radial well fracturing is established based on the finite element-meshless method.The model considers the coupling effect of fracturing fluid flow and rock matrix deformation.The fracture geometries of radial well fracturing are simulated,the induction effect of radial well on the fracture is quantitatively characterized,and the influences of azimuth,horizontal principle stress difference,and reservoir matrix permeability on the fracture geometries are revealed.The radial wells can induce the fractures to extend parallel to their axes when two radial wells in the same layer are fractured.When the radial wells are symmetrically distributed along the direction of the minimum horizontal principle stress with the azimuth greater than 15,the extrusion effect reduces the fracture length of radial wells.When the radial wells are symmetrically distributed along the direction of the maximum horizontal principal stress,the extrusion increases the fracture length of the radial wells.The fracture geometries are controlled by the rectification of radial borehole,the extrusion between radial wells in the same layer,and the deflection of the maximum horizontal principal stress.When the radial wells are distributed along the minimum horizontal principal stress symmetrically,the fracture length induced by the radial well decreases with the increase of azimuth;in contrast,when the radial wells are distributed along the maximum horizontal principal stress symmetrically,the fracture length induced by the radial well first decreases and then increases with the increase of azimuth.The fracture length induced by the radial well decreases with the increase of horizontal principal stress difference.The increase of rock matrix permeability and pore pressure of the matrix around radial wells makes the inducing effect of the radial well on fractures increase.

Fracture propagation,proppant transport and parameter optimization of multi-well pad fracturing treatment

This paper establishes a 3D multi-well pad fracturing numerical model coupled with fracture propagation and proppant migration based on the displacement discontinuity method and Eulerian-Eulerian frameworks,and the fracture propagation and proppant distribution during multi-well fracturing are investigated by taking the actual multi-well pad parameters as an example.Fracture initiation and propagation during multi-well pad fracturing are jointly affected by a variety of stress interference mechanisms such as inter-cluster,inter-stage,and inter-well,and the fracture extension is unbalanced among clusters,asymmetric on both wings,and dipping at heels.Due to the significant influence of fracture morphology and width on the migration capacity of proppant in the fracture,proppant is mainly placed in the area near the wellbore with large fracture width,while a high-concentration sandwash may easily occur in the area with narrow fracture width as a result of quick bridging.On the whole,the proppant placement range is limited.Increasing the well-spacing can reduce the stress interference of adjacent wells and promote the uniform distribution of fractures and proppant on both wings.The maximum stimulated reservoir volume or multi-fracture uniform propagation can be achieved by optimizing the well spacing.Although reducing the perforation-cluster spacing also can improve the stimulated reservoir area,a too low cluster spacing is not conducive to effectively increasing the propped fracture area.Since increasing the stage time lag is beneficial to reduce inter-stage stress interference,zipper fracturing produces more uniform fracture propagation and proppant distribution.

Complex fracture propagation model and plugging timing optimization for temporary plugging fracturing in naturally fractured shale

In this paper,a viscoelasticity-plastic damage constitutive equation for naturally fractured shale is deduced,coupling nonlinear tensile-shear mixed fracture mode.Dynamic perforation-erosion on fluid re-distribution among multi-clusters are considered as well.DFN-FEM(discrete fracture network combined with finite element method)was developed to simulate the multi-cluster complex fractures propagation within temporary plugging fracturing(TPF).Numerical results are matched with field injection and micro-seismic monitoring data.Based on geomechanical characteristics of Weiyuan deep shale gas reservoir in Sichuan Basin,SW China,a multi-cluster complex fractures propagation model is built for TPF.To study complex fractures propagation and the permeability-enhanced region evolution,intersecting and competition mechanisms between the fractures before and after TPF treatment are revealed.Simulation results show that:fracture from middle cluster is restricted by the fractures from side-clusters,and side-clusters plugging is benefit for multi fractures propagation in uniformity;optimized TPF timing should be delayed within a higher density or strike of natural fractures;Within a reservoir-featured natural fractures distribution,optimized TPF timing for most clustered method is 2/3 of total fluid injection time as the optimal plugging time under different clustering modes.

Analysis of fracture propagation and shale gas production by intensive volume fracturing

This paper presents an integrated study from fracture propagation modeling to gas flow modeling and a correlation analysis to explore the key controlling factors of intensive volume fracturing.The fracture propagation model takes into account the interaction between hydraulic fracture and natural fracture by means of the displacement discontinuity method(DDM)and the Picard iterative method.The shale gas flow considers multiple transport mechanisms,and the flow in the fracture network is handled by the embedded discrete fracture model(EDFM).A series of numerical simulations are conducted to analyze the effects of the cluster number,stage spacing,stress difference coefficient,and natural fracture distribution on the stimulated fracture area,fractal dimension,and cumulative gas production,and their correlation coefficients are obtained.The results show that the most influential factors to the stimulated fracture area are the stress difference ratio,stage spacing,and natural fracture density,while those to the cumulative gas production are the stress difference ratio,natural fracture density,and cluster number.This indicates that the stress condition dominates the gas production,and employing intensive volume fracturing(by properly increasing the cluster number)is beneficial for improving the final cumulative gas production.

Propagation and sealing efficiency of chemical grouting in a two-dimensional fracture network with flowing water

In this study, an orthogonal array experiment is conducted by using a transparent fracture network replica. Image processing and theoretical analysis are performed to investigate the model sealing efficiency(SE), factors influencing SE, and the effect of flowing water on propagation. The results show that grout propagation can be classified into three patterns in the fracture network: sealing off, partial sealing,and major erosion. The factors controlling the SE in a descending order of the amount of influence are the initial water flow speed, fracture aperture, grout take, and gel time. An optimal value for the combination of the gel time and grout take(artificial factors) can result in a good SE. The grouting and seepage pressures are measured, and the results reveal that their variations can indicate the SE to some extent. The SE is good when the seepage pressure at each point increases overall;the frequent fluctuations in the seepage pressure indicate a moderately poor SE, and an overall decline in the seepage pressure indicates a major erosion type. The deflection effect of grouting shows an approximately elliptical propagation with the long axis expanding along the wider fracture opening, demonstrating further application in grouting design.

Peridynamic Study on Fracture Mode and Crack Propagation Path of a Plate with Multiple Cracks Subjected to Uniaxial Tension

How to simulate fracture mode and crack propagation path in a plate with multiple cracks is an attractive but difficult issue in fracture mechanics.Peridynamics is a recently developed nonlocal continuum formulation that can spontaneously predict the crack nucleation,branch and propagation in materials and structures through a meshfree discrete technique.In this paper,the peridynamic motion equation with boundary traction is improved by simplifying the boundary transfer functions.We calculate the critical cracking load and the fracture angles of the plate with multiple cracks under uniaxial tension.The results are consistent with those predicted by classical fracture mechanics.The fracture mode and crack propagation path are also determined.The calculation shows that the brittle fracture process of the plate with multiple cracks can be conveniently and correctly simulated by the peridynamic motion equation with boundary conditions.

Fracture propagation laws of staged hydraulic fracture in fractured geothermal reservoir based on phase field model

Hydraulic fracturing is widely used in geothermal resource exploitation, and many natural fractures exist in hot dry rock reservoirs due to in-situ stress and faults. However, the infuence of natural fractures on hydraulic fracture propagation is not considered in the current study. In this paper, based on the phase feld model, a thermo-hydro-mechanical coupled hydraulic fracture propagation model was established to reveal the infuence of injection time, fracturing method, injection fow rate, and natural fracture distribution on the fracture propagation mechanism. The results show that fracture complexity increases with an increase in injection time. The stress disturbance causes the fracture initiation pressure of the second cluster signifcantly higher than that of the frst and third clusters. The zipper-type fracturing method can reduce the degree of stress disturbance and increase fracture complexity by 7.2% compared to simultaneous hydraulic fracturing. Both low and high injection fow rate lead to a decrease in fracture propagation time, which is not conducive to an increase in fracture complexity. An increase in the natural fracture angle leads to hydraulic fracture crossing natural fracture, but has a lesser efect on fracture complexity. In this paper, we analyzed the infuence of diferent factors on initiation pressure and fracture complexity, providing valuable guidance for the exploitation of geothermal resources.

Three-dimensional acoustic propagation model for shallow waters based on an indirect boundary element method

This work has a two-fold purpose.On the one hand,the theoretical formulation of a three-dimensional(3D)acoustic propagation model for shallow waters with a constant sound speed is presented,based on the boundary element method(BEM),which uses a half-space Green function instead of the more conventional free-space Green function.On the other hand,a numerical implementation is illustrated to explore the formulation in simple idealized cases,controlled by a few parameters,which provides necessary tests for the accuracy and performance of the model.The half-space Green's function,which has been previously used in scattering and diffraction,adds terms to the usual expressions of the integral operators without altering their continuity properties.Verifications against the wavenumber integration solution of the Pekeris waveguide suggest that the model allows an adequate prediction for the acoustic field.Likewise,numerical experiments in relation to the necessary mesh size for the description of the water-marine sediment interface lead to the conclusion that a transmission loss prediction with acceptable accuracy can be obtained with the use of a limited mesh around the desired evaluation region.

Fracture geometry and breakdown pressure of radial borehole fracturing in multiple layers

Radial borehole fracturing that combines radial boreholes with hydraulic fracturing is anticipated to improve the output of tight oil and gas reservoirs.This paper aims to investigate fracture propagation and pressure characteristics of radial borehole fracturing in multiple layers.A series of laboratory experiments with artificial rock samples(395 mm×395 mm×395 mm)was conducted using a true triaxial fracturing device.Three crucial factors corresponding to the vertical distance of adjacent radial borehole layers(vertical distance),the azimuth and diameter of the radial borehole are examined.Experimental results show that radial borehole fracturing in multiple layers generates diverse fracture geometries.Four types of fractures are identified based on the connectivity between hydraulic fractures and radial boreholes.The vertical distance significantly influences fracture propagation perpendicular to the radial borehole axis.An increase in the vertical distance impedes fracture connection across multiple radial borehole layers and reduces the fracture propagation distance along the radial borehole axis.The azimuth also influences fracture propagation along the radial borehole axis.Increasing the azimuth reduces the guiding ability of radial boreholes,which makes the fracture quickly curve to the maximum horizontal stress direction.The breakdown pressure correlates with diverse fracture geometries observed.When the fractures connect multi-layer radial boreholes,increasing the vertical distance decreases the breakdown pressure.Decreasing the azimuth and increasing the diameter also decrease the breakdown pressure.The extrusion force exists between the adjacent fractures generated in radial boreholes in multiple rows,which plays a crucial role in enhancing the guiding ability of radial boreholes and results in higher breakdown pressure.The research provides valuable theoretical insights for the field application of radial borehole fracturing technology in tight oil and gas reservoirs.

Visualization and characterization of experimental hydraulic fractures interacting with karst fracture-cavity distributions

Karst fracture-cavity carbonate reservoirs,in which natural cavities are connected by natural fractures to form cavity clusters in many circumstances,have become significant fields of oil and gas exploration and exploitation.Proppant fracturing is considered as the best method for exploiting carbonate reservoirs;however,previous studies primarily focused on the effects of individual types of geological formations,such as natural fractures or cavities,on fracture propagation.In this study,true-triaxial physical simulation experiments were systematically performed under four types of stress difference conditions after the accurate prefabrication of four types of different fracture-cavity distributions in artificial samples.Subsequently,the interaction mechanism between the hydraulic fractures and fracture-cavity structures was systematically analyzed in combination with the stress distribution,cross-sectional morphology of the main propagation path,and three-dimensional visualization of the overall fracture network.It was found that the propagation of hydraulic fractures near the cavity was inhibited by the stress concentration surrounding the cavity.In contrast,a natural fracture with a smaller approach angle(0°and 30°)around the cavity can alleviate the stress concentration and significantly facilitate the connection with the cavity.In addition,the hydraulic fracture crossed the natural fracture at the 45°approach angle and bypassed the cavity under higher stress difference conditions.A new stimulation effectiveness evaluation index was established based on the stimulated reservoir area(SRA),tortuosity of the hydraulic fractures(T),and connectivity index(CI)of the cavities.These findings provide new insights into the fracturing design of carbonate reservoirs.

Effect of navigation endoscopy combined with threedimensional printing technology in the treatment of orbital blowout fractures

●AIM:To explore the combined application of surgical navigation nasal endoscopy(NNE)and three-dimensional printing technology(3DPT)for the adjunctive treatment of orbital blowout fractures(OBF).●METHODS:Retrospective analysis was conducted on the data of patients with OBF who underwent surgical treatment at the Affiliated Eye Hospital of Nanchang University between July 2012 and November 2022.The control group consisted of patients who received traditional surgical treatment(n=43),while the new surgical group(n=52)consisted of patients who received NNE with 3DPT.The difference in therapeutic effects between the two groups was evaluated by comparing the duration of the operation,best corrected visual acuity(BCVA),enophthalmos difference,recovery rate of eye movement disorder,recovery rate of diplopia,and incidence of postoperative complications.●RESULTS:The study included 95 cases(95 eyes),with 63 men and 32 women.The patients’age ranged from 5 to 67y(35.21±15.75y).The new surgical group and the control group exhibited no statistically significant differences in the duration of the operation,BCVA and enophthalmos difference.The recovery rates of diplopia in the new surgical group were significantly higher than those in the control group at 1mo[OR=0.03,95%CI(0.01–0.15),P<0.0000]and 3mo[OR=0.11,95%CI(0.03–0.36),P<0.0000]postoperation.Additionally,the recovery rates of eye movement disorders at 1 and 3mo after surgery were OR=0.08,95%CI(0.03–0.24),P<0.0000;and OR=0.01,95%CI(0.00–0.18),P<0.0000.The incidence of postoperative complications was lower in the new surgical group compared to the control group[OR=4.86,95%CI(0.95–24.78),P<0.05].●CONCLUSION:The combination of NNE and 3DPT can shorten the recovery time of diplopia and eye movement disorder in patients with OBF.

Effects of thawing-induced softening on fracture behaviors of frozen rock

Due to the presence of ice and unfrozen water in pores of frozen rock,the rock fracture behaviors are susceptible to temperature.In this study,the potential thawing-induced softening effects on the fracture behaviors of frozen rock is evaluated by testing the tension fracture toughness(KIC)of frozen rock at different temperatures(i.e.-20℃,-15℃,-12℃,-10℃,-8℃,-6℃,-4℃,-2℃,and 0℃).Acoustic emission(AE)and digital image correlation(DIC)methods are utilized to analyze the microcrack propagation during fracturing.The melting of pore ice is measured using nuclear magnetic resonance(NMR)method.The results indicate that:(1)The KIC of frozen rock decreases moderately between-20℃ and-4℃,and rapidly between-4℃ and 0℃.(2)At-20℃ to-4℃,the fracturing process,deduced from the DIC results at the notch tip,exhibits three stages:elastic deformation,microcrack propagation and microcrack coalescence.However,at-4℃e0℃,only the latter two stages are observed.(3)At-4℃e0℃,the AE activities during fracturing are less than that at-20℃ to-4℃,while more small events are reported.(4)The NMR results demonstrate a reverse variation trend in pore ice content with increasing temperature,that is,a moderate decrease is followed by a sharp decrease and-4℃ is exactly the critical temperature.Next,we interpret the thawing-induced softening effect by linking the evolution in microscopic structure of frozen rock with its macroscopic fracture behaviors as follow:from-20℃ to-4℃,the thickening of the unfrozen water film diminishes the cementation strength between ice and rock skeleton,leading to the decrease in fracture parameters.From-4℃ to 0℃,the cementation effect of ice almost vanishes,and the filling effect of pore ice is reduced significantly,which facilitates microcrack propagation and thus the easier fracture of frozen rocks.

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.

Discontinuity development patterns and the challenges for 3D discrete fracture network modeling on complicated exposed rock surfaces

Natural slopes usually display complicated exposed rock surfaces that are characterized by complex and substantial terrain undulation and ubiquitous undesirable phenomena such as vegetation cover and rockfalls.This study presents a systematic outcrop research of fracture pattern variations in a complicated rock slope,and the qualitative and quantitative study of the complex phenomena impact on threedimensional(3D)discrete fracture network(DFN)modeling.As the studies of the outcrop fracture pattern have been so far focused on local variations,thus,we put forward a statistical analysis of global variations.The entire outcrop is partitioned into several subzones,and the subzone-scale variability of fracture geometric properties is analyzed(including the orientation,the density,and the trace length).The results reveal significant variations in fracture characteristics(such as the concentrative degree,the average orientation,the density,and the trace length)among different subzones.Moreover,the density of fracture sets,which is approximately parallel to the slope surface,exhibits a notably higher value compared to other fracture sets across all subzones.To improve the accuracy of the DFN modeling,the effects of three common phenomena resulting from vegetation and rockfalls are qualitatively analyzed and the corresponding quantitative data processing solutions are proposed.Subsequently,the 3D fracture geometric parameters are determined for different areas of the high-steep rock slope in terms of the subzone dimensions.The results show significant variations in the same set of 3D fracture parameters across different regions with density differing by up to tenfold and mean trace length exhibiting differences of 3e4 times.The study results present precise geological structural information,improve modeling accuracy,and provide practical solutions for addressing complex outcrop issues.

Understanding hydraulic fracture propagation behavior in tight sandstone–coal interbedded formations: an experimentalinvestigation

Whether hydraulic fractures could connect multiple gas zones in the vertical plane is the key to fracturing treatment to jointly exploit coalbed methane and tight sandstone gas through integrative hydraulic fracturing in tight sandstone–coal interbedded formations. Laboratory true triaxial hydraulic fracturing experiments were conducted on layered specimens with di erent combination types of natural sandstone and coal to simulate the propagation behavior of hydraulic fractures. The effects of the fracture initiation position, fracturing fluid viscosity and injection rate were discussed. The results showed that di erent fracture morphologies could be found. When initiating from coal seams, three patterns of fracture initiation and propagation were obtained:(1) The main hydraulic fracture initiated and propagated along the natural fractures and then diverged due to the effects of in situ stress and formed secondary fractures.(2) The hydraulic fracture initiated and propagated in the direction of the maximum horizontal stress.(3) Multiple fractures initiated and propagated at the same time. With the same fracturing fluid viscosity and injection rate, the hydraulic fractures initiating in sandstones had greater chances than those in coal seams to penetrate interfaces and enter neighboring layers. Excessively small or large fracturing fluid viscosity and injection rate would do harm to the vertical extension height of the induced fracture and improvement of the stimulated reservoir volume. Compared with operation parameters(fracturing fluid viscosity and injection rate), the natural weak planes in coals were considered to be the key factor that a ected the fracture propagation path. The experimental results would make some contributions to the development of tight sandstone–coal interbedded reservoirs.

Experimental investigation of propagation mechanisms and fracture morphology for coalbed methane reservoirs

Fracture propagation mechanisms in coalbed methane(CBM) reservoirs are very complex due to the development of the internal cleat system. In this paper, the characteristics of initiation and propagation of hydraulic fractures in coal specimens at different angles between the face cleat and the maximum horizontal principal stress were investigated with hydraulic fracturing tests. The results indicate that the interactions between the hydraulic fractures and the cleat system have a major effect on fracture networks. "Step-like’’ fractures were formed in most experiments due to the existence of discontinuous butt cleats. The hydraulic fractures were more likely to divert or propagate along the butt cleat with an increase in the angles and a decrease in the horizontal principal stress difference. An increase in the injection rate and a decrease in the fracturing fluid viscosity were more conducive to fracture networks. In addition, the influence on fracture propagation of the residual coal fines in the wellbore was also studied. The existence of coal fines was an obstacle in fracturing, and no effective connection can be formed between fractures. The experimental investigation revealed the fracture propagation mechanisms and can provide guidance for hydraulic fracturing design of CBM reservoirs.

Three-dimensional(3D) Printing Technology Assisted by Minimally Invasive Surgery for Pubic Rami Fractures

The feasibility of three-dimensional (3D) printing technology cgmbined with minimally invasive surgery in the treatment of pubic rami fractures was explored.From August 2015 to October 2017,a series of 30 patients who underwent surgical stabilization of their anterior pelvic ring (all utilizing the 3D printing technology)by one surgeon at a single hospital were studied.The minimally invasive incisions were made through anterior inferior cilia spine and pubic nodule.Data collected included the operative duration,the blood loss,the damage of the important tissue,the biographic union and therecovery of the function after the operation.Measurements on inlet and outlet pelvic cardiograph were made immediately post-operation and at all follow-up clinic visits.The scores of reduction and function were measured during follow-up.Results showed that the wounds of 30 patients were healed in the first stage,and there was no injury of important structures such as blood vessels and nerves.According to the Matta criteria,excellent effectiveness was obtained in 22 cases and good in 8 cases.According to the functional evaluation criteria of Majeed,excellent effectiveness was obtained in 21 cases and good in 9 cases.It was suggested that the 3D printing technology assisted by minimally invasive surgery can better evaluate the pelvic fracture before operation,which was helpful in plate modeling, and can shorten surgery duration and reduce intraoperative blood loss and complications. The positioning accuracy was improved,and better surgical result was finally achieved.

A three-dimensional solution of hydraulic fracture width for wellbore strengthening applications

Determining the width of an induced hydraulic fracture is the first step for applying wellbore strengthening and hydraulic fracturing techniques. However, current 2-D analytical solutions obtained from the plane strain assumption may have large uncertainties when the fracture height is small. To solve this problem, a 3-D finite element method(FEM) is used to model wellbore strengthening and calculate the fracture width. Comparisons show that the 2-D plane strain solution is the asymptote of the 3-D FEM solution. Therefore, the 2-D solution may overestimate the fracture width. This indicates that the2-D solution may not be applicable in 3-D conditions. Based on the FEM modeling, a new 3-D semi-analytical solution for determining the fracture width is proposed, which accounts for the e ects of 3-D fracture dimensions, stress anisotropy and borehole inclination. Compared to the 2-D solution, this new 3-D semi-analytical solution predicts a smaller fracture width.This implies that the 2-D-based old design for wellbore strengthening may overestimate the fracture width, which can be reduced using the proposed 3-D solution. It also allows an easy way to calculate the fracture width in complex geometrical and geological conditions. This solution has been verified against 3-D finite element calculations for field applications.

HIGH TEMPERATURE CRACK PROPAGATION AND FRACTURE OF SUPERALLOYS

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Stability of the formation interface under the impact of hydraulic fracture propagation in the vicinity of the formation interface

Unconventional hydrocarbon reservoirs in layered formations,such as tight sandstones and shales,are continually being developed.Hydraulic fracturing is a critical technology for the high-efficiency development of hydrocarbon reservoirs.Understanding the stress field and stability of the formation interface is vital to understanding stress propagation,preferably before the growing hydraulic fracture contacts the formation interface.In this study,models are developed for computing the stress field of hydraulic fracture propagation near the formation interface,and the stress fields within and at the two sides of the formation interface are analyzed.Four failure modes of the interface under the impact of hydraulic fracture propagation in its vicinity are identified,and the corresponding failure criteria are proposed.By simulating the magnitude and direction of peak stress at different parameters,the failure mode and stability of the formation interface are analyzed.Results reveal that when the interface strength is weak,the formation interface fails before the growing hydraulic fracture contacts it,and its stability is significantly related to a variety of factors,including the type of formation interface,rock mechanical properties,far-field stress,structural parameters,distance between the hydraulic fracture and formation interface,and fracturing execution parameters.