Numerical Analysis of Perforation during Hydraulic Fracture Initiation Based on Continuous-Discontinuous Element Method

Perforation is a pivotal technique employed to establish main flow channels within the reservoir formation at the outset of hydraulic fracturing operations.Optimizing perforation designs is critical for augmenting the efficacy of hydraulic fracturing and boosting oil or gas production.In this study,we employ a hybrid finite-discrete element method,known as the continuous–discontinuous element method(CDEM),to simulate the initiation of post-perforation hydraulic fractures and to derive enhanced design parameters.The model incorporates the four most prevalent perforation geometries,as delineated in an engineering technical report.Real-world perforations deviate from the ideal cylindrical shape,exhibiting variable cross-sectional profiles that typically manifest as an initial constriction followed by an expansion,a feature consistent across all four perforation types.Our simulations take into account variations in perforation hole geometries,cross-sectional diameters,and perforation lengths.The findings show that perforations generated by the 39g DP3 HMX perforating bullet yield the lowest breakdown pressure,which inversely correlates with increases in sectional diameter and perforation length.Moreover,this study reveals the relationship between breakdown pressure and fracture degree,providing valuable insights for engineers and designers to refine perforation strategies.

Wellbore Cleaning Degree and Hydraulic Extension in Shale Oil Horizontal Wells

The efficient development and exploitation of shale oil depends on long-distance horizontal wells. As the degreeof cleaning of the wellbore plays a key role in these processes, in this study, this problem is investigated experimentallyby focusing on the dimensionless cuttings bed height. A method is proposed to calculate the horizontalwellhydraulic extension taking into account the influence of the wellbore cleaning degree on the wellborepressure distribution and assess the effect of a variety of factors such as the bottom hole pressure, the circulatingpressure drop, the drilling pump performance and the formation properties. The analysis shows that the hydraulicextension of horizontal wells decreases with an increase in the cuttings bed height, and the higher the displacementof drilling fluid, the faster the hydraulic extension declines. The annular pressure drop of the horizontalsection increases with the increase of the cuttings bed height, resulting in a higher bottom-hole pressure. Severalarguments are provided to guide the safe drilling of shale oil horizontal wells and overcome the limits of currenttechnological approaches.

Shear behaviour of a rock bridge sandwiched between incipient joints under the influence of hydraulic pressures

The rock bridges sandwiched in incipiently jointed rock mass were considered as barriers that block the fluid seepage,and provide certain shear strength reservation.For better revealing the influence of hydraulic pressure on the failure behaviour of rock bridges,direct shear tests were carried out through a newly proposed method on rock samples that contain two parallel incipient joints.By developing the gypsum-silicone pad coupling samples,a conventional triaxial test system was qualified to implement direct shear tests with satisfied sealing capability.The results showed that the rock bridges could be failed through the tensile failure,shear failure and mixed failure mechanism.The hydraulic pressure would facilitate the tensile failure mechanism and induce rougher fracture surfaces;while the normal stress would facilitate the shear failure mechanism and induce less rough fracture.The hydraulic pressure reduced the global shear strength of the rock block through reducing the efficient normal stress applied on the rock bridge area,which was highly dependent on the joint persistence,k.Moreover,because of the iterating occurrence of the hydraulic pressure lag with the fracture propagation,the rock bridge failure stage in the shear stress-shear displacement curves displayed a fluctuation trend.

Influence of specific speed on hydraulic performances and pressure fluctuations in mixed-flow pumps

A series of steady and unsteady numerical calculations of the internal flow in mixed-flow pumps with three different specific speeds were carried out based on the N-S equation coupled with the standard k-εturbulence model under different operating conditions to investigate the relationship between the impeller specific speed and the pump performance as well as pressure pulsations.Meanwhile,the pump performance and pressure pulsations inside the mixed-flow pump with three different specific speeds were also analyzed and compared with the corresponding test data.From the results,the averaged deviations between the predicted and tested head among different impellers are below 5%,and with respect to the equivalent impeller specific speeds of 280 and 260,the values are 4.30%and 3.69%,respectively.For all the impeller schemes,the best efficiency point of the mixed-flow pump is found at the flow rate of 1.2 Q_(d) and the higher head deviation occurs at lower flow rates.Especially,it can be found that the specific speed has a slight effect on the pressure fluctuation in the impellers.Eventually,it is determined that the pump performance curves calculated by numerical simu-lations have good agreement with the relevant experimental results,which verifies that the numerical methods used in the present study are accurate to a certain extent.Furthermore,the results also provide some references to the pressure pulsation analysis and the performance improvement of the mixed-flow pump design.

Characteristics of helical flow in slim holes and calculation of hydraulics for ultra-deep wells

Due to the slim hole at the lower part of the ultra-deep and deep wells, the eccentricity and rotation of drill string and drilling fluid properties have great effects on the annular pressure drop. This leads to the fact that conventional computational models for predicting circulating pressure drop are inapplicable to hydraulics design of deep wells. With the adoption of helical flow theory and H-B rheological model, a computational model of velocity and pressure drop of non-Newtonian fluid flow in the eccentric annulus was established for the cases where the drill string rotates. The effects of eccentricity, rotation of the drill string and the dimensions of annulus on pressure drop in the annulus were analyzed. Drilling hydraulics was given for an ultra-deep well. The results show that the annular pressure drop decreases with an increase in eccentricity and rotary speed, and increases with a decrease in annular flow area. There is a great difference between static mud density and equivalent circulating density during deep well drilling.

Modeling, analysis, and screening of cyclic pressure pulsing with nitrogen in hydraulically fractured wells

Cyclic pressure pulsing with nitrogen is studied for hydraulically fractured wells in depleted reservoirs.A compositional simulation model is constructed to represent the hydraulic fractures through local-grid refinement.The process is analyzed from both operational and reservoir/hydraulic-fracture perspectives.Key sensitivity parameters for the operational component are chosen as the injection rate,lengths of injection and soaking periods and the economic rate limit to shut-in the well.For the reservoir/hydraulic fracturing components,reservoir permeability,hydraulic fracture permeability,effective thickness and half-length are used.These parameters are varied at five levels.A full-factorial experimental design is utilized to run 1250 cases.The study shows that within the ranges studied,the gas-injection process is applied successfully for a 20-year project period with net present values based on the incremental recoveries greater than zero.It is observed that the cycle rate limit,injection and soaking periods must be optimized to maximize the efficiency.The simulation results are used to develop a neural network based proxy model that can be used as a screening tool for the process.The proxy model is validated with blind-cases with a correlation coefficient of 0.96.

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.

Hydraulic and volume change behaviors of compacted highly expansive soil under cyclic wetting and drying

The wide engineered application of compacted expansive soils necessitates understanding their behavior under field conditions.The results of this study demonstrate how seasonal climatic variation and stress and boundary conditions individually or collectively influence the hydraulic and volume change behavior of compacted highly expansive soils.The cyclic wetting and drying(CWD)process was applied for two boundary conditions,i.e.constant stress(CS)and constant volume(CV),and for a wide range of axial stress states.The adopted CWD process affected the hydraulic and volume change behaviors of expansive soils,with the first cycle of wetting and drying being the most effective.The CWD process under CS conditions resulted in shrinkage accumulation and reduction in saturated hydraulic conductivity(k sat).On the other hand,CWD under CV conditions caused a reduction of swell pressure while has almost no impact on k sat.An elastic response to CWD was achieved after the third cycle for saturated hydraulic conductivity(k sat),the third to fourth cycle for the volume change potential under the CV conditions,and the fourth to fifth cycle for the volume change potential under the CS conditions.Finally,both swell pressure(s s)and saturated hydraulic conductivity(k sat)are not fundamental parameters of the expansive soil but rather depend on stress,boundary and wetting conditions.

Simulation Method and Feature Analysis of Shutdown Pressure Evolution During Multi-Cluster Fracturing Stimulation

Multistage multi-cluster hydraulic fracturing has enabled the economic exploitation of shale reservoirs,but the interpretation of hydraulic fracture parameters is challenging.The pressure signals after pump shutdown are influenced by hydraulic fractures,which can reflect the geometric features of hydraulic fracture.The shutdown pressure can be used to interpret the hydraulic fracture parameters in a real-time and cost-effective manner.In this paper,a mathematical model for shutdown pressure evolution is developed considering the effects of wellbore friction,perforation friction and fluid loss in fractures.An efficient numerical simulation method is established by using the method of characteristics.Based on this method,the impacts of fracture half-length,fracture height,opened cluster and perforation number,and filtration coefficient on the evolution of shutdown pressure are analyzed.The results indicate that a larger fracture half-length may hasten the decay of shutdown pressure,while a larger fracture height can slow down the decay of shutdown pressure.A smaller number of opened clusters and perforations can significantly increase the perforation friction and decrease the overall level of shutdown pressure.A larger filtration coefficient may accelerate the fluid filtration in the fracture and hasten the drop of the shutdown pressure.The simulation method of shutdown pressure,as well as the analysis results,has important implications for the interpretation of hydraulic fracture parameters.

Reliability Design for Impact Vibration of Hydraulic Pressure Pipeline Systems

The research of reliability design for impact vibration of hydraulic pressure pipeline systems is still in the primary stage,and the research of quantitative reliability of hydraulic components and system is still incomplete.On the condition of having obtained the numerical characteristics of basic random parameters,several techniques and methods including the probability statistical theory,hydraulic technique and stochastic perturbation method are employed to carry out the reliability design for impact vibration of the hydraulic pressure system.Considering the instantaneous pressure pulse of hydraulic impact in pipeline,the reliability analysis model of hydraulic pipeline system is established,and the reliability-based optimization design method is presented.The proposed method can reflect the inherent reliability of hydraulic pipe system exactly,and the desired result is obtained.The reliability design of hydraulic pipeline system is achieved by computer programs and the reliability design information of hydraulic pipeline system is obtained.This research proposes a reliability design method,which can solve the problem of the reliability-based optimization design for the hydraulic pressure system with impact vibration practically and effectively,and enhance the quantitative research on the reliability design of hydraulic pipeline system.The proposed method has generality for the reliability optimization design of hydraulic pipeline system.

Effects of Loading Paths on Hydrodynamic Deep Drawing with Independent Radial Hydraulic Pressure of Aluminum Alloy Based on Numerical Simulation

In order to meet the forming demands for low plasticity materials and large height-diameter ratio parts, a new process of hydrodynamic deep drawing （HDD） with independent radial hydraulic pressure is proposed. To investigate the effects of loading paths on the HDD with independent radial hydraulic pressure, the forming process of 5A06 aluminum alloy cylindrical cup with a hemispherical bottom was studied by numerical simulation. By employing the dynamic explicit analytical software ETA/Dynaform based on LS-DYNA3D, the effects of loading paths on the sheet-thickness distribution and surface quality were analyzed. The corresponding relations of the radial hydraulic pressure loading paths and the part＇s strain status on the forming limit diagram （FLD） were also discussed. The results indicated that a sound match between liquid chamber pressure and independent radial hydraulic pressure could restrain the serious thinning at the hemisphere bottom and that through adjusting radial hydraulic pressure could reduce the radial tensile strain and change the strain paths. Therefore, the drawing limit of the aluminum cylindrical cup with a hemispherical bottom could be increased significantly.

Hydraulic calculation of gravity transportation pipeline system for backfill slurry

Taking cemented coal gangue pipeline transportation system in Suncun Coal Mine, Xinwen Mining Group, Shandong Province, China, as an example, the hydraulic calculation approaches and process about gravity pipeline transportation of backfill slurry were investigated. The results show that the backfill capability of the backfill system should be higher than 74.4 m3/h according to the mining production and backfill times in the mine; the minimum velocity (critical velocity) and practical working velocity of the backfill slurry are 1.44 and 3.82 m/s, respectively. Various formulae give the maximum ratio of total length to vertical height of pipeline (L/H ratio) of the backfill system of 5.4, and then the reliability and capability of the system can be evaluated.

Effect of persistent high intraocular pressure on microstructure and hydraulic permeability of trabecular meshwork

As the aqueous humor leaves the eye, it first passes through the trabecular meshwork （TM）. Increased flow resistance in this region causes elevation of intraocular pressure （IOP）, which leads to the occurrence of glaucoma. To quantitatively evaluate the effect of high IOP on the configuration and hydraulic permeability of the TM, second harmonic generation （SHG） microscopy was used to image the microstructures of the TM and adjacent tissues in control （normal） and high IOP conditions. Enucleated rabbit eyes were perfused at a pressure of 60 mmHg to achieve the high lOP. Through the anterior chamber of the eye, in situ images were obtained from different depths beneath the surface of the TM. Porosity and specific surface area of the TM in control and high IOP conditions were then calculated to estimate the effect of the high pressure on the permeability of tissue in different depths. We further photographed the histological sections of the TM and compared the in situ images. The following results were obtained in the control condition, where the region of depth was less than 55 μm with crossed branching beams and large pores in the superficial TM. The deeper meshwork is a silk-like tissue with abundant fluorescence separating the small size of pores. The total thickness of pathway tissues composed of TM and juxtacanalicular （JCT） is more than 100 p.m. After putting a high pressure on the inner wall of the eye, the TM region progressively collapses and decreases to be less than 40 μm. Fibers of the TM became dense, and the porosity at 34 μm in the high IOP condition is comparable to that at 105 μm in the control condition. As a consequent result, the permeability of the superficial TM decreases rapidly from 120 μm2 to 49.6 μm2 and that of deeper TM decreases from 1.66 μm2 to 0.57 μm2. Heterogeneity reflected by descent in permeability reduces from 12.4 μm of the control condition to 3.74 μm of the high IOP condition. The persistently high IOP makes the TM region collapse from its normal state, in which the collagen fibers of the TM are arranged in regular to maintain the physiological permeability of the outflow pathway. In the scope of pathologically high IOP, the microstructure of the TM is sensitive to pressure and hydraulic permeability can be significantly affected by IOP.

Hydraulic calculation and dynamic analysis of columnar reversing gate

According to the hydraulic calculation principles of the orifice outflow, the discharge capacity of the columnar reversing gate under the partial opening condition was calculated and checked. Using ANSYS, a large finite element analysis software, the discharge process was simulated. The distribution rule of the velocities in the gate chamber and downstream channel was obtained. An FEM model of the columnar reversing gate was built, and the natural vibration properties of the gate were analyzed. Based on the Westergaard added mass method, the added mass caused by the fluid-structure coupling motion was taken into account, and the effects of the coupling interaction were discussed. The results show that the size of the small gates meets the demand for discharge capacity, the current in the gate chamber is quite turbulent, the trunnion and arms are obviously impacted by flow, and the effects of water on vibration characteristics are remarkable. The study provides a reference for the design and calculation of gates of the same type.

Effects of shifting time on pressure impact in hydraulic systems

The limitations in existing measures for absorbing pressure impact in hydraulic systems were summarized in this paper. Based on the forming principle of the oil in a hydrostatic closed pressure chamber, the underlying reasons of the pressure impact were analyzed theoretically, the intrinsic laws that the extent of the pressure impact in hydraulic oil lines are affected by some factors, such as oil elastic modulus, oil line's geometrical volume, and changing rate of oil volume versus time etc, were discussed. Experimental investigations into pressure impact in all pressure chambers because of shifting were conducted under different working conditions by employing a special experimental system. The effects of shifting time on pressure impact were studied. A new concept with universal meaning, i.e. optimal shifting time, and its characterizing parameter and the methods of shifting at optimal shifting time were also proposed. The results show that shifting time lag △t is of rationality and maneuverablility. The higher the working pressure, the shorter the shifting time.

Effect of ground stress on hydraulic fracturing of methane well

Most of the coal reservoirs in China are of low-permeability, so hydraulic fracturing is widely used to improve the per- meability in the extraction of gas by ground drilling. The ground stress around the well was analyzed by using theory of elasticity. The pressure when the well fractured is formulated and the effect of ground stress on pressure is discussed. The effect of ground-stress-differences on hydraulic fracturing was analyzed by using the numerical software RFPA2D-Flow in reference to the tectonic stress in Jincheng coal area. The results show that: 1) the position where initial fracture appears is random and fracture branches emerge when the fractures expand if ground stresses in any two directions within a horizontal plane are equal; 2) other- wise, the fractures expand in general along the direction of maximum ground stress and the critical pressure decreases with in- creasing ground-stress-differences and 3) the preferred well-disposition pattern is diamond shaped. The preferred well spacing is 250 m×300 m. This study can provide a reference for the design of wells.

Research Status, Critical Technologies, and Development Trends of Hydraulic Pressure Pulsation Attenuator

Hydraulic pumps are a positive displacement pump whose working principle causes inherent output flow pulsation.Flow pulsation produces pressure pulsation when encountering liquid resistance.Pressure pulsation spreads in the pipeline and causes vibration,noise,damage,and even pipeline rupture and major safety accidents.With the development of airborne hydraulic systems with high pressure,power,and flow rate,the hazards of vibration and noise caused by pressure pulsation are also amplified,severely restricting the application and development of hydraulic systems.In this review paper,the mechanism,harm,and suppression method of pressure pulsation in hydraulic systems are analyzed.Then,the classification and characteristics of pulsation attenuators according to different working principles are described.Furthermore,the critical technology of simulation design,matching method with airborne piston pumps,and preliminary design method of pulsation attenuators are proposed.Finally,the development trend of pulsation attenuators is prospected.This paper provides a reference for the research and application of pressure pulsation attenuators.

ESTIMATION OF RESIDUAL CONTACT PRESSURE IN HYDRAULICALLY EXPANDED CRA-LINED PIPE

The mechanically bonded CRA-lined pipe is developed to meet the need forcorrosion-resistant alloy steel pipe. Residual contact pressure at the interface of lined pipe isimportant factor that governs the quality of lined pipe. A simplified theoretical method ispresented to predict the residual contact pressure created by hydraulic pressure. The calculatingequation related hydro-forming pressure to the residual contact pressure between two metal faces isderived. And the validation of the proposed equation is accomplished by comparing its result tothose obtained by experimental investigation.

Stress characteristics of surrounding rocks for inner water exosmosis in high-pressure hydraulic tunnels

Seepage and stress redistribution are the main factors affecting the stability of surrounding rock in high-pressure hydraulic tunnels.In this work,the effects of the seepage field were firstly simplified as a seepage factor acting on the stress field,and the equilibrium equation of high pressure inner water exosmosis was established based on physical theory.Then,the plane strain theory was used to solve the problem of elasticity,and the analytic expression of surrounding rock stress was obtained.On the basis of criterion of Norway,the influences of seepage,pore water pressure and buried depth on the characteristics of the stress distribution of surrounding rocks were studied.The analyses show that the first water-filling plays a decisive role in the stability of the surrounding rock; the influence of seepage on the stress field around the tunnel is the greatest,and the change of the seepage factor is approximately consistent with the logarithm divergence.With the effects of the rock pore water pressure,the circumferential stress shows the exchange between large and small,but the radial stress does not.Increasing the buried depth can enhance the arching effect of the surrounding rock,thus improving the stability.

Sliding Mode Control of Hydraulic Pressure in Electro-Hydraulic Brake System Based on the Linearization of Higher-Order Model

The possibility to enhance the stability and robustness of electrohydraulic brake(EHB)systems is considered a subject of great importance in the automotive field.In such a context,the present study focuses on an actuator with a four-way sliding valve and a hydraulic cylinder.A 4-order nonlinear mathematical model is introduced accordingly.Through the linearization of the feedback law of the high order EHB model,a sliding mode control method is proposed for the hydraulic pressure.The hydraulic pressure tracking controls are simulated and analyzed by MATLAB/Simulink soft considering separately different conditions,i.e.,a sine wave,a square wave and a square wave with superimposed sine disturbance.The results show that the proposed strategy can track the target within 0.25 s,and the mean observed error is less than 1.2 bar.Moreover,with such a strategy,faster response and less overshoot are possible,which should be regarded as significant advantages.