1438 results about "Fracturing fluid" patented technology

The invention relates to the technical field of data acquisition and data analysis, in particular to a hydraulic fracturing test crack propagation monitoring system which comprises a monitoring system and is used for monitoring crack propagation behaviors in the hydraulic fracturing process in real time. Constant or dynamically changing confining pressure and axial pressure are provided; the pore pressure dynamic regulation and control unit is used for accurately controlling the injection pressure, flow and saturation of fracturing fluid and simulating fracture propagation behaviors under different seepage conditions; the multi-physics field sensing monitoring network unit is used for collecting strain, sound wave signals and a surface displacement field in the crack expansion process in real time; full-scale monitoring of rock fracture propagation is realized, an influence mechanism of pore pressure and time effect on fracture evolution is disclosed, an accurate prediction means is provided for shale gas development and deep engineering, and the fracturing effect and engineering safety are remarkably improved.

The invention discloses a self-crosslinking temperature-resistant salt-resistant emulsion type fracturing fluid thickening agent and a preparation method thereof, and belongs to the technical field of oilfield chemistry. The raw materials adopted by the invention comprise 30 to 50 parts of an oily solvent, 15 to 25 parts of deionized water, 10 to 20 parts of acrylamide, 5 to 10 parts of acrylic acid, 2 to 4 parts of 2-acrylamido-2-methylpropanesulfonic acid, 0.05 to 0.2 part of a crosslinking monomer, 0.5 to 1 part of a quaternary ammonium salt type hydrophobic association monomer, 4 to 8 parts of an emulsifier and 1 to 2 parts of a phase inversion agent. The self-crosslinking emulsion is formed through water phase-oil phase mixing, high-speed emulsification, low-temperature initiation polymerization and phase inversion treatment. Based on physical-chemical double-crosslinking temperature control cooperation, a salt-resistant-hydrophobic double-shielding mechanism and an integrated design without an exogenous crosslinking agent, the contradiction between the temperature-resistant and salt-resistant performance of a traditional thickening agent and the process complexity is broken through, and a technical support is provided for efficient development of high-temperature and high-salt oil and gas reservoirs.

The invention relates to the technical field of rock mechanics and petroleum and natural gas engineering, and particularly discloses a hydraulic fracture fracturing monitoring system, method and device based on optical fiber monitoring, and the system comprises a hydraulic fracturing simulation platform which is used for applying three-dimensional stress to a hydraulic fracturing test piece so as to simulate a stratum stress environment; the fracturing fluid injection device is used for injecting pre-prepared fracturing fluid into the test piece, so that a crack in the test piece expands; a plurality of strain sensor groups embedded in the test piece in the preparation process of the test piece; the optical fiber sensing demodulation device is used for collecting strain data detected by the plurality of strain sensor groups; and the data processing device is in communication connection with the optical fiber sensing demodulation device and is used for acquiring the strain data and processing the strain data so as to determine real-time state data of crack expansion in the test piece. According to the scheme, the fracture strain can be monitored in real time, and the accuracy and controllability of the hydraulic fracturing process are improved.

A compartmentalized hydraulic fracturing (frac) system may include a mono line configured to carry frac fluid into a well. The system may include a plurality of zones, each zone comprising: a set of one or more frac pumps each configured to pump frac fluid into the mono line, an isolation valve configured to control the flow of frac fluid between the set of frac pumps and the mono line; and a bleed valve configured to release pressurized frac fluid from the set of frac pumps when in an open position. The system may include partition walls between the plurality of zones. The system may include a control system configured to deactivate or reactivate a zone of the plurality of zones by controlling the set of frac pumps, the isolation valve, and the bleed valve of the zone.

A method for performing a refracturing operation using coke proppant particles comprises refracturing a subterranean formation that has been previously hydraulically fractured with respect to a hydrocarbon well by injecting a fracturing fluid comprising a carrier fluid and coke proppant particles into the subterranean formation via a wellbore of the hydrocarbon well.

The invention discloses a shale oil exploitation method based on cooperation of multistage pulse gas fracturing and nano-catalysis, and belongs to the technical field of oilfield development, and the shale oil exploitation method comprises the following steps: S1, determining an optimal drilling position of a target shale layer, and carrying out drilling operation; s2, 0.1-10 Hz adjustable pulse pressure waves are formed through control of a high-frequency electromagnetic valve, a fracturing medium mixed with the functionalized nanoparticles is injected into the stratum through a fracturing pump, the pulse frequency of the high-frequency electromagnetic valve is adjusted, staged pulse fracturing operation is conducted, and a fracture network is formed; s3, after fracturing of each stage is completed, mixed fluid of a propping agent and fracturing fluid is injected into stratum fractures; and S4, after fracturing operation is completed, a microwave field is applied to the stratum, and the stratum temperature is kept within a set range. According to the method, the gas fracturing medium and the functionalized nanoparticles are mixed and then fractured, so that the influence on the environment is remarkably reduced, and the recovery ratio of shale oil is greatly increased under the combined action of multi-stage pulse fracturing, the composite proppant and the microwave field.

A method for producing hydrocarbon fluids via a hydrocarbon well comprises providing petroleum coke proppant particles having an Amott index for oil of at least 0.02, an Amott index for water of at most 0.1, and a pseudo Amott index of at most 0.35. The method also comprises, for each of a number of stages of the hydrocarbon well, introducing a fracturing fluid comprising a carrier fluid and the petroleum coke proppant particles into a subterranean formation via a wellbore of the hydrocarbon well and then producing hydrocarbon fluids from the subterranean formation via the wellbore of the hydrocarbon well.

The invention discloses a high-performance guanidine gum fracturing fluid system for deep coal rock gas backlog fracturing and application, and relates to the technical field of oil and gas reservoir chemistry, the high-performance guanidine gum fracturing fluid system for deep coal rock gas backlog fracturing comprises the following components: 0.05-0.35% of graft modified guanidine gum, 0-0.3% of multiple cross-linking agent, 0-0.2% of conditioning agent, 0.1-0.3% of functional additive, 0-0.1% of gel breaker, and the balance of water, the grafting modified guanidine gum is prepared by performing functional group modification and side chain grafting polymerization on guanidine gum raw powder, the number of chemical crosslinking groups and branched chains is remarkably increased, after the grafting modified guanidine gum is compounded with a matched multiple crosslinking agent, the chemical and physical synergistic crosslinking effect is remarkably enhanced, and the performance of the fracturing fluid is greatly improved; the high-performance guanidine gum fracturing fluid system for deep coal rock gas backlog fracturing, provided by the invention, has the characteristics of low component dosage, low cost, low residue content, good swelling performance, good resistance reduction performance, good sand carrying performance, controllable mixing construction and controllable online crosslinking, and can effectively meet the construction requirements of coal rock gas backlog fracturing.

A method comprises hydraulically fracturing a subterranean formation by introducing a fracturing fluid comprising coke proppant particles and a carrier fluid into the formation, where the carrier fluid has a base viscosity of at most 0.8 centipoise (cP) at 25 degrees Celsius (° C.). A hydrocarbon well comprises a wellbore that extends within a formation, a production casing string that extends within the wellbore, perforation clusters formed within the production casing string, hydraulic fractures formed in the formation proximate to the perforation clusters, and a fracturing fluid comprising coke proppant particles and a carrier fluid within at least a portion of the hydraulic fractures, where the carrier fluid has a base viscosity of at most 0.8 cP at 25° C. Another method comprises providing a carrier fluid having a viscosity of at most 0.8 cP at 25° C. and forming a fracturing fluid comprising the carrier fluid and coke proppant particles.

A hydraulic fracturing process comprises, during a time interval T1, pumping a first fracturing fluid comprising first coke proppant particles into a subterranean formation, such that a first weight of the first coke proppant particles, WCP1, is pumped into the subterranean formation. The process also comprises, during a time interval T2 that occurs before or after T1, pumping a second fracturing fluid differing from the first fracturing fluid and comprising non-coke proppant particles and optionally second coke proppant particles into the subterranean formation, such that a second weight of the second coke proppant particles, if any, WCP2, is pumped into the subterranean formation, where WCP1 / WCP2≥1.2.

A fracturing fluid comprises a carrier fluid and thermally post-treated fluid coke and / or flexicoke proppant particles, comprising fluid coke and / or flexicoke particles, respectively, that have been thermally post-treated to a temperature in a range from 400° C. to 1200° C. for a predetermined duration. A method of utilizing such fracturing fluid comprises introducing the fracturing fluid into a subterranean formation. A method of making such fracturing fluid comprises producing the thermally post-treated fluid coke and / or flexicoke proppant particles by thermally post-treating the fluid coke and / or flexicoke particles, respectively, to the temperature in the range from 400° C. to 1200° C. for the predetermined duration and mixing the thermally post-treated fluid coke and / or flexicoke proppant particles with the carrier fluid, optionally along with one or more other types of proppant particles and / or one or more additives.

The invention provides slick water fracturing fluid as well as a preparation method and application thereof. The slick water fracturing fluid comprises chitosan, a polymer matrix, paraformaldehyde and a solvent. In the slick water fracturing fluid provided by the invention, the chitosan and the polymer are fully dissolved, and the main chains of the two polymers are physically interpenetrated and wound. In the presence of paraformaldehyde, a polymer main chain is chemically crosslinked with paraformaldehyde to form a primary network structure. Then, chitosan and molybdenum disulfide can form coordination cross-linking sites, a secondary network structure is obtained, then a multi-network structure which cannot be split is formed, and the viscosity is high; moreover, the components have good solubility in the solvent, are easy to mix on line and are relatively low in preparation cost.

The present disclosure may provide a method and a system for optimization of fracture parameters of segmented multi-cluster fracturing in a horizontal well of a continental shale. The method includes: establishing a fracture extension model; performing a layer-crossing extension simulation of a single-cluster hydraulic fracture based on at least one injection displacement and at least one fracturing fluid viscosity to determine engineering parameters for the single-cluster hydraulic fracture; determining engineering parameters for multi-cluster hydraulic fractures based on the engineering parameters for the single-cluster hydraulic fracture; determining, based on the engineering parameters for the multi-cluster hydraulic fractures, an equilibrium expansion index and a ground construction pressure for the multi-cluster hydraulic fractures corresponding to at least one perforation parameter; and filtering an optimal perforation parameter based on the equilibrium expansion index and the ground construction pressure.

The invention discloses a rock pulse fracturing and high-voltage pulse discharge collaborative fracturing simulation device and method.The device comprises a triaxial loading mechanism, a pulse fracturing mechanism, a high-voltage pulse discharge mechanism, a collaborative control part and a monitoring mechanism, and the triaxial loading mechanism is used for loading triaxial pressure to a rock sample; a simulation hole is formed in the upper end surface of the rock sample, and a plug is plugged at the hole opening of the simulation hole; the pulse fracturing mechanism comprises a fracturing fluid storage tank and a pulse pumping assembly; the high-voltage pulse discharge mechanism comprises a Marx generator and a discharge electrode; the monitoring mechanism comprises a plurality of acoustic emission sensors and an acoustic emission data processor. The influence of the synergistic effect of pulse fracturing and high-voltage pulse discharge on the rock fracturing process can be systematically studied, the synergistic effect mechanism of the two is disclosed by accurately controlling the fracturing fluid release rhythm and the high-voltage pulse discharge rhythm, a parameter optimization basis is provided for field fracturing operation, the fracturing effect is improved, and the rock fracturing efficiency is improved. The mining cost is reduced.

The invention discloses a deep learning assisted acceleration fracturing construction parameter intelligent real-time optimization method, and belongs to the field of unconventional oil and gas field development, and the method comprises the steps: constructing a structured sample database covering geological attributes, engineering parameters and fracturing effect responses, and carrying out the unified preprocessing of multi-source data; constructing a multi-modal space-time collaborative prediction model, and combining a multi-expansion time permissible convolutional network, a three-dimensional residual network and a cross attention mechanism; supervised learning training is carried out based on a database, sparse regularization and learning rate scheduling are introduced, and the model precision and generalization ability are improved; a hierarchical collaborative optimization framework of outer-layer Bayesian search-inner-layer CMA-ES refinement is provided, and reservoir transformation volume maximization and construction feasibility are achieved under complex constraints; compared with an existing method, optimization parameters of the method include the cluster distance and the section distance and further include the displacement, the sand concentration, the fracturing fluid type and other construction parameters, and real-time optimization of the fracturing construction parameters can be achieved through the machine learning agent model.

The invention provides a hydraulic fracturing fracture net distribution form near-field monitoring method, which comprises the following steps of: arranging a plurality of roof monitoring holes in roadways on two sides of an underground coal mine working surface, installing electromagnetic signal sensors in each roof monitoring hole and on anchor rods of roadway stoping sides, and constructing a full-space monitoring network covering a hydraulic fracturing layer; a data interpretation processing module of the electromagnetic signal time-shifting imaging analysis system comprises a multi-field coupling mathematical model for analyzing and deducing real-time imaging of electromagnetic signals; in the hydraulic fracturing process, an electromagnetic signal sensor is used for monitoring a current field, an electromagnetic field and an ion diffusion field in the rock mass fracture development and expansion process, a monitoring result is substituted into an electromagnetic signal time-shifting imaging analysis system for calculation and feature value extraction, and the fracture net distribution form is deduced through the feature value. According to the invention, the expansion path of the fracturing fluid in the rock stratum can be monitored in real time, the three-dimensional distribution form of the hydraulic fracturing fracture network can be inverted, and a new technical support is provided for the inspection of the hydraulic fracturing pressure relief effect of the underground coal mine.

The invention discloses an ultra-low-density high-strength resin proppant capable of being carried by clear water or low-viscosity slickwater. The proppant is prepared by dispersing, polymerizing and curing a mixture comprising 15 to 50 weight percent of vinyl monomer, 5 to 10 weight percent of acrylate monomer and 50 to 70 weight percent of unsaturated resin. The preparation method comprises the following steps: controlling the resin composition in a water phase by virtue of a dispersing agent and a rotating speed to form spherical liquid drops with the particle size of 12-140 meshes and the sphericity of nearly 100%; then, the temperature ranges from 30 DEG C to 80 DEG C; the propping agent provided by the invention has ultra-low density, can be carried by clear water or low-viscosity slickwater, is suitable for low-viscosity fracturing fluid, low-displacement construction and small-scale fracturing, can realize ultra-far-end seam net support, and greatly increases the oil and gas drainage area. The breaking rate under the closing pressure of 20-90 MPa is lower than 2%, the surface is weakly lipophilic, and the oil-phase flow conductivity is higher than the water-phase flow conductivity.

Provided is a method for determining huff and puff fluid volumes in multi-scale spaces of shale oil reservoirs, including the following steps: rock sample pretreatment; porosity stress sensitivity testing; high pressure hg injection testing and nuclear magnetic resonance testing benchmarking; online nuclear magnetic resonance testing; data processing and analysis. Firstly, a changing law of multi-scale spaces of shale oil reservoirs with an effective stress is characterized through a pore stress sensitivity measurement and online nuclear magnetic resonance measurement combined experiment, and then the huff and puff fluid volumes of multi-scale spaces of shale oil reservoirs under a condition of a certain stimulated reservoir volume are calculated. A usage amount of a fracturing fluid for a fracturing horizontal well in the shale oil reservoir is determined from the perspective of giving full play to the imbibition replacement role of micro-nano pores.

A fracturing fluid comprises a carrier fluid and proppant particles. The proppant particles comprise non-coke proppant particles and coke proppant particles. The coke proppant particles are provided at a concentration of 10 vol % to 67 vol % of the proppant particles within the fracturing fluid, based on a total volume of all proppant particles in the fracturing fluid, on a dry particle basis. A method of making the fracturing fluid comprises providing a first collection of coke proppant particles having a first total particle volume of V1; providing a second collection of non-coke proppant particles having a second total particle volume of V2, wherein 0.1≤V1 / (V1+V2)≤0.67; and mixing the first collection and the second collection with at least a carrier fluid. A hydraulic fracturing method includes hydraulically fracturing a subterranean formation via a wellbore by introducing such fracturing fluid into the subterranean formation via the wellbore.

The invention relates to the technical field of oil and gas field exploitation, and discloses a drag reducer for a multifunctional fracturing fluid and a preparation method thereof.The preparation method of the drag reducer for the multifunctional fracturing fluid comprises the steps that acrylic acid, acrylamide, 2-acrylamido-2-methylpropanesulfonic acid and modified itaconic acid are added into deionized water, stirring and mixing are conducted, and the drag reducer for the multifunctional fracturing fluid is obtained. Nitrogen is introduced for 30-40 min to remove oxygen, then azobis (isobutylamidine) hydrochloride is added, the mixture is stirred to react for 48-72 h at the temperature of 45-50 DEG C, and a polymer solution is obtained; and directly and uniformly mixing the polymer solution, the compatilizer and the modified nano silicon dioxide, and reacting in a magnetic stirrer at 60-70 DEG C for 1.5-2 hours to obtain the drag reducer for the multifunctional fracturing fluid. The drag reducer has a good drag reduction effect, and the hydrophobicity, the temperature resistance, the salt resistance and the shear resistance are improved.

The invention relates to the technical field of well site fracturing, and discloses a well site fracturing dynamic analysis method based on the Internet of Things, which comprises the following steps: S1, constructing a multi-level sensor network in a well site for acquiring fracturing equipment operation parameters, underground reservoir dynamic response data, fracturing fluid performance parameters and well site surrounding environment monitoring data in real time to form multi-source data; s2, preprocessing the collected multi-source data through an edge computing node to obtain preprocessed data, uploading the preprocessed data to a cloud analysis platform through an encryption transmission protocol, and constructing a well site fracturing digital twinborn model on the cloud analysis platform; s3, the cloud analysis platform carries out correlation calculation on the preprocessed data and the digital twinborn model through a multi-dimensional analysis model, and a comprehensive evaluation result of the fracture propagation dynamic characteristics, the reservoir flow conductivity and the fracturing equipment operation state is generated; and S4, generating a regulation and control instruction based on a comprehensive evaluation result, and dynamically adjusting the fracturing parameters.

A fracturing fluid comprises a carrier fluid and coke particles. The coke particles include microproppant coke particles (e.g., petroleum coke fines) having particle sizes of at most 105 μm, where the microproppant coke particles have a total concentration of at least 3 wt % based on the total weight of the coke particles. The coke particles also have a total concentration in the fracturing fluid from 14 kilograms per cubic meter to 480 kilograms per cubic meter, based on the volume of the carrier fluid. A method includes introducing such fracturing fluid into a subterranean formation.

The invention discloses a shale oil and gas horizontal well layer-crossing expansion fracturing method and application. The fracturing method comprises a pre-fracturing step and a fracture forming step. The displacement of fracturing fluid used in the pre-fracturing step is gradually increased, and the displacement increasing amplitude is gradually increased; the fracture forming step comprises a four-stage reinforced temporary plugging construction step, and variable displacement temporary plugging construction is adopted when temporary plugging balls are delivered for temporary plugging construction. According to the fracturing method, the space-time form of fracture expansion is reasonably regulated and controlled, fracture diversion and reservoir matrix serious damage caused by too high viscosity of fracturing fluid are avoided while the fracture height completely penetrates through a target small layer, the problems that the fracture is excessively expanded in a non-target layer, centralized transformation and repeated transformation are conducted near a shaft and the like are solved, and the fracturing efficiency is improved. The fracture length is greatly increased, the size and the drainage area are effectively transformed, and the fracturing targets of promoting generation of complex fractures and improving the yield and the efficiency through layer-penetrating body expansion are achieved.

A fracturing fluid for fracturing subterranean formations comprising ascorbic acid. The fracturing fluid can use ascorbic acid to delay increases in viscosity until desired. The viscosity increase can then be maintained over a period of time to perform fracturing operations.

The invention relates to the technical field of oil development, in particular to a shale oil and gas fracturing sliding sleeve capable of being opened and closed repeatedly and a using method. According to the technical scheme, a central pipe fracturing liquid inlet is formed in the upper side of a central pipe, and a reversing rail is arranged on the surface of the outer wall of the middle; a sealing cylinder sleeve and a one-way circulating valve carrier are sleeved outside the central pipe, a fracturing piston, a swivel pressing cap and a reset spring are installed in an annulus, a constant-pressure opening cavity is formed in the inner wall of the fracturing piston, a swivel is installed in the swivel pressing cap, a track pin is installed in the swivel, and the position is moved along a reversing track on the surface of the outer wall of the central pipe through the track pin. The fracturing piston moves downwards to the position of the cylinder sleeve fracturing liquid outlet under the action of pressure, the fracturing function is started, fracturing liquid is sprayed out along the cylinder sleeve fracturing liquid outlet to enter a target fracturing layer, fracturing construction of a plurality of fracturing layers can be achieved through multiple times of fracturing liquid injection and injection stopping, the fracturing sliding sleeve can be repeatedly opened and closed, and the fracturing construction efficiency is improved. And fracturing construction requirements of shale oil and gas with different layers can be met.

The present disclosure relates to a method for evaluating a temporary plugging effect of fracturing in a low-permeability oil-gas reservoir based on monitoring pressure. The method comprises: calculating a wellbore friction resistance along a way from a wellhead to a target fracturing segment; calculating, based on a wellhead pressure monitored at the wellhead in real time, a wellbore pressure at the target fracturing segment; calculating a fluid pressure at a crack opening of each perforation cluster; calculating a perforation friction resistance coefficient of each perforation cluster; calculating a fracturing fluid instantaneous displacement of each perforation cluster; calculating, based on the fracturing fluid instantaneous displacement of each perforation cluster, a variation coefficient of a fracturing fluid displacement distribution after a fracturing construction is completed; and evaluating the temporary plugging effect of fracturing based on the variation coefficient.

The invention discloses a quantitative evaluation method for complexity of shale oil and gas horizontal well reservoir reconstruction cracks, which comprises the following steps: determining a crack development strength factor representing reservoir inherent crack development potential by calculating a mineral heterogeneous coefficient based on rock sample mineral component data at each perforation cluster position in a target fracturing section; determining the optimal fracture length by combining reservoir numerical simulation, determining the total fracturing fluid amount, performing non-uniform distribution according to the heterogeneity of each cluster, and determining a fracture propagation complexity factor representing the dynamic propagation complexity of the hydraulic fracture; weighting the two factors to obtain a crack complexity index for comprehensively evaluating the reservoir transformation effect, and performing grading; according to the method, static geological evaluation and dynamic engineering evaluation are combined, quantification of inter-cluster transformation differences is achieved, the defects that a traditional method is one-sided in evaluation and low in precision are overcome, and a reliable quantitative basis is provided for optimal design of a shale oil and gas reservoir fracturing scheme and accurate evaluation of the transformation effect.

A method for performing a refracturing operation using coke proppant particles comprises refracturing a subterranean formation that has been previously hydraulically fractured with respect to a hydrocarbon well by injecting a fracturing fluid comprising a carrier fluid and coke proppant particles into the subterranean formation via a wellbore of the hydrocarbon well.

The invention provides a fracturing fluid performance online detection regulation and control method and a regulation and control system thereof, relates to the technical field of fracturing fluid performance detection, can realize online detection of key performance parameters such as pH, viscosity, mineralization degree and resistance reduction rate of fracturing fluid on a fracturing construction site, transmits the key performance parameters to a control center through acquisition, automatically evaluates and judges whether the key performance parameters meet requirements or not, and improves the working efficiency of the fracturing fluid. The performance of the fracturing fluid can be remotely controlled and adjusted according to technical requirements, commanders can conveniently master the performance of the fracturing fluid in time, the timeliness is high, the accuracy is high, the fracturing construction quality and the intelligent level are effectively improved, and the problems that in the prior art, performance testing of fracturing fluid samples is poor in timeliness, low in accuracy and low in cost are solved. Real-time on-line tracking evaluation cannot be carried out, and fracturing fluid performance cannot be timely and accurately mastered and fracturing construction cannot be guided.

The invention discloses a horizontal well fracturing perforation parameter optimization method and device considering non-uniform crustal stress and a medium, and relates to the field of unconventional oil and gas reservoir yield increase renovation. The method comprises the steps that a three-dimensional non-uniform crustal stress field of reservoir fracturing is constructed; the method comprises the following steps of: performing grid division on a hydraulic fracture by using a fracture unit, acting a three-dimensional non-uniform ground stress field on a divided grid, and establishing a constitutive model of reservoir rock deformation and stress in a hydraulic fracturing process; according to the constitutive model, establishing a flow model of the fracturing fluid in the horizontal shaft, the perforation hole and the hydraulic fracture; establishing an expansion criterion of the hydraulic fracture in the fracture length and fracture height directions; according to the expansion criterion and the flow model, the expansion results of the horizontal well fracturing cracks under different perforation parameters are simulated; and the horizontal well fracturing perforation parameters are optimized according to the expansion result. According to the method, the defects of a uniform crustal stress field assumption and a plane crack propagation assumption in the prior art are overcome, and the optimization of the horizontal well fracturing perforation parameters in the non-uniform crustal stress field is realized.