Stress Difference Coefficient Research Articles

Fracturability of shale based on rock brittleness and natural fracture tensile reactivation

Exploration and development practices have proved that fracturability evaluation is the primary basis for sucessful fracturing operations. Current studies mainly rely on using traditional physical parameters to evaluate shale fracturability. However, fracture morphology and the extension of natural fractures during fracturing are also crucial for shale fracturability evaluation. In this study, the correlations among factors and rock fracture complexity and natural fracture opening degree were analyzed through 40 sets of related experiments, proposing a new method for shale fracturability evaluation that considers Young's Modulus, shear expansion angle, residual strain, approach angle, and stress variance coefficient. Finally, taking the shale gas field in the Sichuan Basin as an example, a comprehensive evaluation model of shale fracturability was established by using the gray correlation method combined with the core experimental data. One well was selected to compare and analyze the fracturability profile with the stimulated reservoir volume. The results show thatthe peak strain has the most significant influence on the shale fracture complexity, followed by the shear expansion angle and Young's Modulus. The approach angle and the stress difference coefficient affect the degree of natural fracture opening at the same time. The model is accurate because the fractureability values match the study block's stimulated reservoir volume data. This new method of shale fractureability evaluation offers important technology for predicting the fractureability of shale gas reservoirs and optimizing operation schemes.

Experimental study on the influence of horizontal stress difference coefficient on coal rock fracture

Hydraulic fracturing is a pressure-relief and permeability-enhancing technique widely used in the mining of low-permeability coal seams. The horizontal stress difference coefficient is an important factor that affects the fracture propagation during the fracturing. To study the mechanism of the hydraulic fracturing process, in this paper, the initiation and propagation of cracks under horizontal stress difference coefficient are studied by using the developed true triaxial hydraulic fracturing system. The fracture surface morphology was obtained by 3D scanner. The experimental results are verified by the mathematical model. The results show that the fracture pressure and the peak values of AE count rate and b value increase and the cumulative AE count decreases with the increase of the horizontal stress difference coefficient. After the first pressure drop, the “pressure built-up” in the specimen increases and the peak value of AE count rate decreases with the increased horizontal stress difference coefficient. The 3D scanning results show that when the horizontal stress difference coefficient is larger, the hydraulic fracture propagation is straighter and the fracture surface area is smaller. The experimental results are in good agreement with the theoretical values. The experimental results provide a basis for engineering practice.

Fracture-controlled fracturing mechanism and penetration discrimination criteria for thin sand-mud interbedded reservoirs in Sulige gas field, Ordos Basin, China

Considering the problems in the discrimination of fracture penetration and the evaluation of fracturing performance in the stimulation of thin sand-mud interbedded reservoirs in the eighth member of Shihezi Formation of Permian (He-8 Member) in the Sulige gas field, a geomechanical model of thin sand-mud interbedded reservoirs considering interlayer heterogeneity was established. The experiment of hydraulic fracture penetration was performed to reveal the mechanism of initiation–extension–interaction–penetration of hydraulic fractures in the thin sand-mud interbedded reservoirs. The unconventional fracture model was used to clarify the vertical initiation and extension characteristics of fractures in thin interbedded reservoirs through numerical simulation. The fracture penetration discrimination criterion and the fracturing performance evaluation method were developed. The results show that the interlayer stress difference is the main geological factor that directly affects the fracture morphology during hydraulic fracturing. When the interlayer stress difference coefficient is less than 0.4 in the Sulige gas field, the fractures can penetrate the barrier and extend in the target sandstone layer. When the interlayer stress difference coefficient is not less than 0.4 and less than 0.45, the factures can penetrate the barrier but cannot extend in the target sandstone layers. When the interlayer stress difference coefficient is greater than 0.45, the fractures only extend in the perforated reservoir, but not penetrate the layers. Increasing the viscosity and pump rates of the fracturing fluid can compensate for the energy loss and break through the barrier limit. The injection of high viscosity (50–100 mPa·s) fracturing fluid at high pump rates (12–18 m3/min) is conducive to fracture penetration in the thin sand-mud interbedded reservoirs in the Sulige gas field.

The Gas Production Characteristics of No. 3 Coal Seam Coalbed Methane Well in the Zhengbei Block and the Optimization of Favorable Development Areas

The characteristics and influencing factors of gas production in CBM wells are analyzed based on the field geological data and the productivity data of coalbed methane (CBM) wells in the Zhengbei block, and then the favorable areas are divided. The results show that the average gas production of No. 3 coal seam CBM wells in the study area is in the range of 0~1793 m3/d, with an average of 250.97 m3/d; 80% of the wells are less than 500 m3/d, and there are fewer wells above 1000 m3/d. The average gas production is positively correlated with gas content, critical desorption pressure, permeability, Young’s modulus, and Schlumberger ratio, and negatively correlated with fracture index, fault fractal dimension, Poisson’s ratio, and horizontal stress difference coefficient. The relationship between coal seam thickness and the minimum horizontal principal stress is not strong. The low-yield wells have the characteristics of multiple pump-stopping disturbances, unstable casing pressure control, overly rapid pressure reduction in the single-phase flow stage, sand and pulverized coal production, and high-yield water in the later stage during the drainage process. It may be caused by the small difference in compressive strength between the roof and floor and the coal seam, and the small difference in the Young’s modulus of the floor. The difference between the two high-yield wells is large, and the fracturing cracks are easily controlled in the coal seam and extend along the level. The production control factors from strong to weak are as follows: critical desorption pressure, permeability, Schlumberger ratio, fault fractal dimension, Young’s modulus, horizontal stress difference coefficient, minimum horizontal principal stress, gas content, Poisson’s ratio, fracture index, coal seam thickness. The type I development unit (development of favorable areas) of the Zhengbei block is interspersed with the north and south of the block on the plane, and the III development unit is mainly located in the east of the block and near the Z-56 well. The comprehensive index has a significant positive correlation with the gas production, and the prediction results are accurate.

Study on the influence of vertical stress difference coefficient on fracture characteristics of shale under high stress

AbstractTo study the effect of vertical stress difference coefficient on fracture characteristics of shale fracturing, high stress true triaxial hydraulic fracturing test was carried out. By analyzing the profile after fracturing, it was found that the area of hydraulic fracture increased with the increase of vertical stress difference coefficient, and the probability of shear fracture will increase when the stress difference coefficient was high. A high vertical stress differential coefficient exerts a strong control over the direction of crack propagation, while a low vertical stress difference coefficient is beneficial to improve the roughness of hydraulic fracture surface and promote the formation of complex fracture network. By analyzing the pump pressure curves of different tests, it was found that with the increase of vertical stress difference coefficient, the formation and expansion of hydraulic fractures were more difficult. The surface characteristics of hydraulic fractures were quantified based on three‐dimensional topography scanning technology, combined with fractal dimension and fracture area calculation method, the results showed that with the increase of vertical stress difference coefficient, the fractal dimension and fracture area decreased. Since shale is stratified, and the transformation of reservoir is mainly reflected in the enhancement of fracture complexity through tensile failure, Xsite discrete grid method was used to study the influence of fracture propagation behavior with different bedding strengths. The results showed that when the bedding tensile strength was high, hydraulic fractures were easy to pass through the bedding, and when the bedding tensile strength was low, hydraulic fractures were easy to be captured by natural fractures. In addition, tensile cracks were easy to form when the tensile strength of bedding was low, shear cracks were easy to form when the strength of bedding was high, and the fracture volume was larger when the strength of bedding was low. This study provides a theoretical basis for hydraulic fracturing in engineering.

Effects of orthogonal cleat structures on hydraulic fracture evolution behavior

Hydraulic fracturing operation as an effective enhancing coalbed gas production method is widely used in ultra-low permeability coal seam. However, complex geo-stresses and high heterogeneity between natural cleats structure lead to difficulty predicting hydraulic fracture patterns. Fracture evolution behavior for fracturing operation in coal seams requires a better understanding. In this study, a 2D model of hydraulic fracture propagation was built based on the cohesive zone model of finite element method. The effect of orthogonal cleat system, in-situ stress, dig angle and construction parameters on fracture geometries were main investigated. The main conclusions were as follows: (1) According to the interaction types between hydraulic fracture and cleat system, ladder-shaped fracture and H-shaped fracture geometry was summarized. The difference between them was whether there were continuous and small pressure fluctuation stages. (2) When the horizontal stress difference coefficient was lower and larger than 3/12, fracture geometry was prone to present Η shape and ladder shape respectively. Besides, the dimensionless fracture length and the dimensionless fracture extension aspect ratio of fracture were increasing with larger horizontal stress difference coefficient. (3) The favorable condition for fracture extension was that the dig angle was 45°. Hydraulic fracture tended to propagate along face cleats direction. (4) Larger fracture fluid displacement was beneficial to form more balanced hydraulic fracture geometry and promote large extension scale. As fracture fluid viscosity increased, the fracture geometries transformed from ladder shape to H shape.

Evaluation of the combined influence of geological layer property and in-situ stresses on fracture height growth for layered formations

Fracture geometry is important when stimulating low-permeability reservoirs for natural gas or oil production. The geological layer (GL) properties and contrasts in in-situ stress are the two most important parameters for determination of the vertical fracture growth extent and containment in layered rocks. However, the method for assessing the cumulative impact on growth in height remains ambiguous. In this research, a 3D model based on the cohesive zone method is used to simulate the evolution of hydraulic fracture (HF) height in layered reservoirs. The model incorporates fluid flow and elastic deformation, considering the friction between the contacting fracture surfaces and the interaction between fracture components. First, an analytical solution that was readily available was used to validate the model. Afterwards, a quantitative analysis was performed on the combined impacts of the layer interface strength, coefficient of interlayer stress difference, and coefficient of vertical stress difference. The results indicate that the observed fracture height geometries can be categorized into three distinct regions within the parametric space: blunted fracture, crossed fracture, and T-shaped fracture. Furthermore, the results explained the formation mechanism of the low fracture height in the deep shale reservoir of the Sichuan Basin, China, as well as the distinction between fracture network patterns in mid-depth and deep shale reservoirs.

Experimental study of hydraulic fracturing for deep shale reservoir

Compared with shallow reservoirs of shale gas, the high stress and plasticity of shale reservoirs under deep conditions significantly impact the propagation of hydraulic fractures. The study investigates the characteristics of hydraulic fracture propagation in deep shale reservoirs by conducting true triaxial fracturing tests at different stress levels and combinations under circumstances close to the original in-situ stress of the target reservoir. Specifically, it includes comparative experiments under high and low-stress levels, variable stress combinations with equal stress differences, and experiments on the influence of maximum and minimum horizontal in-situ stress, respectively. Through a series of experimental studies, it has been shown that the fracture roughness is relatively low at high stress levels. Fractures can still generate complex and multiple fractures when subject to high-stress conditions. Amongst, natural fissures or weak surfaces still dominate the complex fracture morphology. In the case of a higher in-situ stress level with the same stress difference value brings about a more complex hydraulic fracture morphology as a result of a smaller stress-difference coefficient. The Intersection of hydraulic fractures with multiple parallel weak surfaces creates hydraulic fractures in stepped shape, which can cause drastic fluctuations in injection pressure. The research results provide a reference for on-site deep shale reservoir stimulation and optimization of a fracturing design.

Tectonic fractures induced by strike-slip faulting in intracratonic ultradeep carbonate rocks: Insights from the finite element method and self-adaptive constraints computational model for boundary conditions

Numerical simulations of the paleostress field during a period of tectonic fracture formation and rock failure criteria are used to quantitatively predict the development and occurrence of tectonic fractures induced by the formation of the SB18 fault zone in the Middle Ordovician Yijianfang Formation of the Shunnan area, Tarim Basin, China. The results of acoustic emission experiments, mechanical property measurements, and tectonic fracture occurrence observations obtained from core descriptions and fullbore formation microimager logs are combined with the Andersonian model of faulting and the finite element method, which is widely used for the numerical simulation of stress fields, to investigate the paleotectonic and in situ stress fields via numerical simulation. The quantitative prediction of the opening pressure and opening sequence of tectonic fractures is based on the occurrence of tectonic fracture, numerical simulation of in situ stresses, and coordinate system conversion. The results show that the width of the fracture zone induced by strike-slip faulting is ∼310 m. The degree of fracture development is significantly increased when the Young’s modulus, paleostress difference, and paleostress difference coefficient of the rock are elevated. The current horizontal principal stress is positively correlated with the distance from the fault, and the elevated areal density of the secondary faults causes a clockwise deflection of the horizontal stress direction. SSE-striking shear fractures with orientations ranging from 140° to 150° and two sets of tensional fractures with orientations ranging from −40° to −35° and 55° to 60° are preferentially opened in the water injection development stage of the reservoir. As the horizontal stress difference, horizontal stress difference coefficient, and angle between the maximum horizontal principal stress and a fracture decrease, the fracture opening pressure decreases. At the structural highs (burial depths <6225 m) and lows (burial depths >6225 m), the fracture burial depth is positively and negatively correlated with the opening pressure, respectively. Quantitative prediction of tectonic fracture developmental characteristics, opening pressure, and the opening sequence and investigation of the main factors that control their development can help to identify and support opportunities for hydrocarbon exploration and development of fractured carbonate reservoirs.

Numerical Simulation of Fracture Propagation during Temporary Plugging Staged Fracturing in Tight-Oil Horizontal Wells.

Fracture propagation with temporary plugging hydraulic fracturing in tight-oil reservoirs is simulated in this study. The research considers dynamic fluid redistribution, with stress differences among multiple fractures. The fracture morphology during temporary plugging staged fracturing (TPSF) is investigated by using a user-defined perforation element combined with a pore-pressure finite-element model. The precision of the integrated model is verified by using the standard finite-element approach. Then, case studies are presented to investigate the influence of cluster spacing, horizontal stress difference coefficients (SDC), injection rates, and barrier tensile strengths. The simulation results show that central cluster fractures are hampered by side-cluster fractures, while TPSF can alleviate the effect and lead to a more uniform propagation of all fractures. Stress interference weakens as cluster spacing increases, and propagation patterns are minimally influenced once spacing reaches 40 m. Higher injection rates can improve the injection pressure, enlarging fracture width, and potentially increasing the risk of fracture penetration. Barrier tensile strength and horizontal SDC can modify fracture geometries and determine the penetration behavior of multiple fractures.

Hydraulic fracture initiation and propagation in deep coalbed methane reservoirs considering weak plane: CT scan testing

Hydraulic fracturing technology in coal reservoirs helps increase coalbed methane (CBM) production, and the development of hydraulic fractures (HFs) is influenced by in situ stress and original fractures. Therefore, in this study, triaxial HF tests and computed tomography (CT) were used to determine HF initiation and propagation in coal, considering weak structural planes and in situ stress. The experimental results show that weak structural planes control HF initiation and propagation in coal under a deep-stress environment. Most HFs occurred along bedding planes, followed by exogenetic fractures. The influence of the horizontal stress difference coefficient k, which is equal to the maximum horizontal stress minus the minimum horizontal stress and divided by the minimum horizontal stress, on the propagation of the HF was studied. When k increases to 1.04, the HF becomes perpendicular to the direction of the minimum principal stress. When k < 1.04, the main controlling factor of HF propagation is a weak structural plane, and when k ≥ 1.04, the main controlling factor of HF propagation is in situ stress. Based on the CT reconstruction model, the average aperture distributions of the discrete bedding fractures and exogenetic fractures of coal in this experiment were calculated to be 0.0947 mm and 0.1940 mm, respectively. This determines the different strength properties of exogenetic fractures and bedding planes, and determines the priority initiation position of HF in coal. During the HF initiation and propagation, the average energy along the exogenous fracture was lower than that along the bedding planes. On this basis, this study predicts that the main factor controlling HF propagation in a deep coal seam in the Qin-Shui Basin, China, is the weak structural plane in the coal seam.

Quantitative Prediction of the Development and Opening Sequence of Fractures in an Ultradeep Carbonate Reservoir: A Case Study of the Middle Ordovician in the Shunnan Area, Tarim Basin, China

Summary Quantitative prediction of reservoir tectonic fracture development characteristics, opening pressures, and opening sequences is critical in the exploration and development of oil- and gas-bearing reservoirs and thus has received widespread attention. Using numerical simulations of the paleostress field during the formation of tectonic fractures and the rock fracture criterion, we predict the development and occurrence of fractures in the Middle Ordovician Yijianfang Formation in the Shunnan region of the Tarim Basin, China. The local paleostress fields reflected by the mechanical properties and occurrence of tectonic fractures obtained from core descriptions, acoustic emission (AE) experiments, paleomagnetic experiments, sound velocity measurements, and borehole breakouts were used to determine the regional paleostress and in-situ stress. We established a geomechanical model by combining the mechanical parameters of the rocks with the finite element method (FEM), optimizing the boundary conditions with a self-adaptive constraint algorithm, and conducting numerical simulations of the in-situ stresses. Fracture occurrence and numerical simulation results of the in-situ stress field were used to determine the opening pressure (Pk) and opening sequence of the fractures. The level of fracture development decreases away from the strike-slip fault in the study area. Fracture development is positively correlated with the Young’s modulus, paleostress difference, and paleostress difference coefficient of the rock. The direction of the maximum horizontal principal stress is from north-northeast (NNE) to northeast (NE). Initially, shear fractures and tensional fractures oriented NNE 30°–35° and NE 40°–45°, respectively, open during the water injection process. Pk is positively correlated with the horizontal stress difference coefficient and the angle between the fracture strike and the maximum horizontal principal stress. At the structural highs (burial depths shallower than 6450 m) and the structural lows (burial depths deeper than 6450 m), the burial depth correlates negatively and positively with Pk, respectively. This investigation of the development, occurrence, Pk, and opening sequence of tectonic fractures and their principal controlling factors will have a positive impact on the future exploration and production opportunities of similar fractured reservoirs.

Laboratory study on acid fracturing performance in high temperature carbonate reservoirs

In this article, we investigate acid fracturing, a promising method to increase the effectiveness of fractures in high temperature carbonate reservoirs. In order to determine the performance of acid fracturing in carbonate reservoirs, we conducted a lab scaled true triaxial acid fracturing experiment on high temperature carbonate rock. The fracture initiation, propagation behavior, and conductivity under the action of acid solution were analyzed. The 3-D micro computed tomography was applied to illuminate the fracture network patterns; coefficient of stress difference, acid etching time, and acid concentration were also analyzed. Results show acidification exhibits the lowest breakdown pressure compared with no-acidification, reduced by 58%.

Analysis of Coalbed Methane Production Characteristics and Influencing Factors of No. 15 Coal Seam in the Shouyang Block

Based on the basic geological data and production data of coalbed methane wells in the Shouyang Block, the characteristics and influencing factors of coalbed methane well production were analyzed, and the primary controlling factors were identified by the grey correlation method. The results show that the average daily gas production of the coalbed methane wells in the study area for the single mining of No. 15 coal ranges from 0 to 604.34 m3/d, with an average of 116.82 m3/d. The overall average gas production is relatively low, with only 7 of the 42 wells having an average gas production greater than 200 m3/d. Gas production tends to increase as the gas content increases. There is a significant positive correlation between gas saturation and average gas production. Burial depth and coal seam thickness also show a positive correlation with average gas production. On the other hand, there is a negative exponential relationship between average gas production and critical desorption pressure. Permeability, as determined by well tests in the area, exhibits a negative correlation with the gas production of coalbed methane wells. The correlation between gas production and the mean three-dimensional stress is weak. As the fractal dimension D value of fractures increases, gas production decreases. A smaller difference in horizontal principal stress is more favorable for the formation of network fractures, facilitating reservoir fracturing and resulting in better reconstructive properties. Moreover, an increase in the sand–mud ratio leads to a decrease in average gas production. The correlation between fault fractal dimension and average gas production is weak. The grey correlation method was employed to determine the controlling factors of coalbed methane production in the study area, ranked from strong to weak, as follows: coal thickness &gt; fracture fractal dimension D value &gt; gas saturation &gt; coal seam gas content &gt; horizontal stress difference coefficient &gt; permeability &gt; critical desorption pressure &gt; mean value of three-dimensional principal stress &gt; coal seam burial depth &gt; sand–mud ratio &gt; fault fractal dimension.

Enhancing hydraulic fracturing for in-situ remediation in low-permeability soils: A comprehensive investigation of fracture propagation

Enhancing the complexity of the hydraulic fractures to provide a wide channel for the injection of the agent is crucial for remediating low-permeability contaminated sites. This study involved a physical simulation experiment of large-scale true triaxial hydraulic fracturing in undisturbed soil, as well as field fracturing tests, to investigate fracture initiation mechanisms and the influence of different factors on fracture propagation. The study revealed a unique failure mode for low-permeability soils characterized by impact splitting, involving simultaneous tensile and shear failure. Three typical fracture propagation patterns emerged: (1) horizontal fracture, (2) parallel fracture, and (3) complex fracture. Silty clay predominantly exhibited horizontal fractures, while mucky clay facilitated the formation of complex fractures dominated by multiple transverse fractures. As the vertical stress difference coefficient increased from 1.0 to 1.5, the pressure on the fracture surface enhanced the connection between hydraulic fractures and natural fractures. Hydraulic fracturing in low-permeability soils necessitated large displacements and high-viscosity fracturing fluids to sustain fracture propagation. The field fracturing test results underscored that soil type and in-situ stress were the primary factors governing hydraulic fracture initiation and propagation. Identifying the optimal fracturing location was critical for achieving the maximum stimulated formation volume.

Experimental investigation on fracture growth for integrated hydraulic fracturing in multiple gas bearing formations

The key to extracting multiple natural gases from coalbed methane, shale and other tight gases through integrated hydraulic fracturing in coal measure strata (CMS) is determining whether hydraulic fracture can connect different gas-bearing zones. In this paper, several groups of combination samples comprised of artificial rocks were prepared. True triaxial hydraulic fracturing experiments were conducted to stimulate the hydraulic fracture propagation and penetration behavior. The effects of in-situ stress, injection rate, natural fracture and well type on fracture growth were studied. The main results were as follows: (1) Fracture geometries in CMS exhibited strong asymmetric, nonplanar extension and unilateral expansion features in the vertical plane. (2) Higher values of the vertical stress difference coefficient and injection rate led to larger vertical fracture extension and an increased likelihood of fracture connection to adjacent gas-bearing layers. (3) The behavior of the hydraulic fracture varied significantly between vertical and horizontal wells. In vertical wells, the main fracture presented a "+” shape and fully communicated natural coal cleats system, while in horizontal wells, fracture height growth was limited, resulting in fracture patterns that presented vertically as “H” or “T” shape due to the hydraulic fracture's tendency to turn direction when propagating to natural weak planes. The study found that the fracture vertical extension ability increased with rising vertical stress difference coefficient. (4) Natural fractures could induce fracture turning and branching, which improved fracture network complexity but also caused fracturing fluid loss and hydraulic energy dissipation. Therefore, choosing shale or coal layer with developed natural fractures as fracturing layer was unhelpful for integrated fracturing operation. Finally, higher fracturing fluid viscosity, injection rate and gradient sanding could enhance fracturing operation efficiency. These results could provide theoretical guidance for integrated fracturing operation in CMS.

Preferred Selection of Fractured Sweet Spot Section for Horizontal Shale Oil Well in West 233 Area

Six parameters, which can effectively reflect the reservoir quality and the completion quality, have been selected, including the sand structure index, the physical parameters, the oil content index, the brittleness index reflecting, the stress difference coefficient and the fracture pressure. The evaluation index of fracturing sweet spots in shale oil horizontal wells was constructed, and the fracturing sweet spot selection criteria for shale oil horizontal wells in the study area were established. Combined with dynamic production data, the fracturing sweet spots were classified into Class I (high quality reservoir), Class II (secondary reservoir) and Class II (non-fracturing sweet spot), which provided technical support for the preferential selection of fracturing formations in shale oil horizontal well.

Evaluation of Tight Sandstone Mechanical Properties and Fracability: An Experimental Study of Reservoir Sand−Stones from Lufeng Sag, Pearl River Mouth Basin, Northern South China Sea

Reservoir rocks of the Pearl River Mouth Basin’s Lufeng Sag have low porosity (average porosity 12.6%) and low permeability (average permeability 16.5 mD), requiring hydraulic fracturing to obtain economic production of oil and gas. To contribute to the understanding of these reservoirs, and to promote successful production in the region, we analyzed the mechanical properties of tight sandstone. Moreover, we introduced the shear/tensile strength factor, in combination with the fracture toughness and horizontal stress difference coefficient, as an innovative approach to characterize the ease of forming a complex fracture network after reservoir fracturing. Based on this, we established a fracability evaluation model suitable for offshore low-permeability sandstone reservoirs by an analytic hierarchy process from the perspective of whether the reservoir can form an effective transformation volume and complex fracture network after fracturing. The results indicate that the primary minerals of the target reservoir are quartz and clay minerals, and the natural fractures are not developed. The mechanical properties exhibit a high Young’s modulus (ranging from 30.4 to 34.4 GPa) and high compressive strength (with cohesion between 41 and 45 MPa and an angle of internal friction between 31.0 and 33.5°). The relatively low tensile strength and fracture toughness values are conducive to fracture initiation and extension during the fracturing process. Through the fracability evaluation model constructed in this paper, the depth interval at 4155.1–4172.1 m is identified as a high-quality fractured layer. The results of this study not only provide theoretical guidance for target well and formation selection in the Lufeng Sag, but also have important practical implications for increasing oil and gas production from tight sandstone reservoirs.

Rheology of non-Brownian particle suspensions in viscoelastic solutions. Part 1: Effect of the polymer concentration

We study the effect of varying polymer concentration, measured by the dimensionless polymer viscosity partition function β, on the steady shear rheology of rigid particle suspensions using direct numerical simulation of the Oldroyd-B model. We compare the bulk rheology using immersed boundary simulations at Φ=2.5% and 5% to body-fitted single-particle simulations and find that the per-particle viscosity and first normal stress difference coefficient are always shear-thickening at all values of β considered. However, as β decreases, the polymer stress transforms the flow field near each particle from closed concentric streamlines to helical streamlines that advect stretched polymers away from the particle surface. At low β, the polymer stress is diffuse, where the distribution of the particle induced fluid stress (PIFS) caused by the stretched polymers is spread out in the simulation domain rather than concentrated near the particle surface. Therefore in multiparticle simulations, the polymer stress can be significantly affected by particle-particle interactions. The stress generated by a given particle is disrupted by the presence of particles in its vicinity, leading to a significantly lower PIFS than that of the single-particle simulation. In addition, at increased volume fractions and low values of β, the polymer stress distribution on the particle surface shifts so as to increase the magnitude of the polymer stress moments, resulting in a shear-thickening stresslet contribution to the viscosity that is not seen in single particle or high β simulations. This result indicates that for suspensions in highly viscoelastic suspending fluids that are characterized by a low β parameter, hydrodynamic interactions are significant even at modest particle concentrations and fully resolved multiparticle simulations are necessary to understand the rheological behavior.

Rheology of non-Brownian particle suspensions in viscoelastic solutions. Part II: Effect of a shear thinning suspending fluid

The shear rheology of particle suspensions in shear-thinning polymeric fluids is studied experimentally using parallel plate measurements and numerically using fully resolved, 3D finite volume simulations with the Giesekus fluid model. We show in our experiments that the steady shear viscosity and first normal stress difference coefficient of the suspension evolve from shear-thickening to substantially shear-thinning as the degree of shear-thinning of the suspending fluid increases. Moreover, in highly shear-thinning fluids, the suspension exhibits greater shear-thinning of the viscosity than the suspending fluid itself. Our dilute body-fitted simulations show that in the absence of hydrodynamic interactions, shear-thinning can arise from the particle-induced fluid stress (PIFS), which ceases to grow with increasing shear rate at low values of β (solvent viscosity ratio) and finite values of α (the Giesekus drag coefficient). In a Giesekus suspending fluid, the polymers surrounding the suspended particle are unable to stretch sufficiently at high Weissenberg numbers (Wi) and the reduced polymer stress results in a lower PIFS. When coupled with the shear-thinning stresslet, this effect creates an overall shear-thinning of the viscosity. We then explore the effects of particle-particle interactions on the suspension rheology using immersed boundary simulations. We show that multiparticle simulations are necessary to obtain the shear-thinning behavior of the per-particle viscosity of suspensions in shear-thinning fluids at moderate values of β. Particle-particle interactions lead to a substantial decrease in the PIFS and an enhancement of the shear-thinning of the stresslet compared to the single particle simulations. This combination leads to the shear-thinning of the per-particle viscosity seen in experiments. We also find that very low values of β and finite values of α have opposing effects on the per-particle viscosity that can lead to a nonmonotonic per-particle viscosity versus shear rate in a highly shear-thinning fluid. Overall, the addition of rigid particles to highly shear-thinning fluids, such as joint synovial fluid, leads to increased viscosity and also increased shear-thinning at high shear rates.