A Method for Identifying Channeling Paths in Low-Permeability Fractured Reservoirs

Often oilfield fractured horizontal wells produce water flowing in multiple directions.In this study,a method to identify such channeling paths is developed.The dual-medium model is based on the principle of inter-well connectivity and considers the flow characteristics and related channeling terms.The Lorentz curve is drawn to qualitatively discern the geological type of the low-permeability fractured reservoir and determine the channeling direction and size.The practical application of such an approach to a sample oilfield shows that it can accurately identify the channeling paths of the considered low-permeability fractured reservoir and predict production performances according to the inter-well connectivity model.As a result,early detection of water channeling becomes possible,paving the way to real-time production system optimization in low-permeability fractured reservoirs.

Fractal model of spontaneous imbibition in low-permeability reservoirs coupled with heterogeneity of pore seepage channels and threshold pressure

Spontaneous imbibition(SI)is an important mechanism for enhancing oil recovery in low-permeability reservoirs.Due to the strong heterogeneity,and the non-Darcy flow,the construction of SI model for lowpermeability reservoirs is extremely challenging.Commonly,traditional SI models based on single or averaged capillary tortuosity ignore the influence of heterogeneity of pore seepage channels and the threshold pressure(TP)on imbibition.Therefore,in this work,based on capillary model and fractal theory,a mathematical model of characterizing SI considering heterogeneity of pore seepage channels is established.On this basis,the threshold pressure was introduced to determine the pore radius at which the wetted phase can displace oil.The proposed new SI model was verified by imbibition experimental data.The study shows that for weakly heterogeneous cores with permeability of 0-1 m D,the traditional SI model can characterize the imbibition process relatively accurately,and the new imbibition model can increase the coefficient of determination by 1.05 times.However,traditional model has serious deviations in predicting the imbibition recovery for cores with permeability of 10-50 m D.The new SI model coupling with heterogeneity of pore seepage channels and threshold pressure effectively solves this problem,and the determination coefficient is increased from 0.344 to 0.922,which is increased by2.68 times.For low-permeability reservoirs,the production of the oil in transitional pores(0.01-0.1μm)and mesopores(0.1-1μm)significantly affects the imbibition recovery,as the research shows that when the heterogeneity of pore seepage channels is ignored,the oil recovery in transitional pores and mesopores decreases by 7.54%and 4.26%,respectively.Sensitivity analysis shows that increasing interfacial tension,decreasing contact angle,oil-water viscosity ratio and threshold pressure will increase imbibition recovery.In addition,there are critical values for the influence of these factors on the imbibition recovery,which provides theoretical support for surfactant optimization.

Evaluation of Well Spacing for Primary Development of Fractured Horizontal Wells in Tight Sandstone Gas Reservoirs

Methods for horizontal well spacing calculation in tight gas reservoirs are still adversely affected by the complexity of related control factors,such as strong reservoir heterogeneity and seepage mechanisms.In this study,the stress sensitivity and threshold pressure gradient of various types of reservoirs are quantitatively evaluated through reservoir seepage experiments.On the basis of these experiments,a numerical simulation model(based on the special seepage mechanism)and an inverse dynamic reserve algorithm(with different equivalent drainage areas)were developed.The well spacing ranges of Classes I,II,and III wells in the Q gas field are determined to be 802–1,000,600–662,and 285–400 m,respectively,with their average ranges as 901,631,and 342.5 m,respectively.By considering both the pairs of parallel well groups and series well groups as examples,the reliability of the calculation results is verified.It is shown that the combination of the two models can reduce errors and provide accurate results.

A review of reservoir damage during hydraulic fracturing of deep and ultra-deep reservoirs

Deep and ultra-deep reservoirs have gradually become the primary focus of hydrocarbon exploration as a result of a series of significant discoveries in deep hydrocarbon exploration worldwide.These reservoirs present unique challenges due to their deep burial depth(4500-8882 m),low matrix permeability,complex crustal stress conditions,high temperature and pressure(HTHP,150-200℃,105-155 MPa),coupled with high salinity of formation water.Consequently,the costs associated with their exploitation and development are exceptionally high.In deep and ultra-deep reservoirs,hydraulic fracturing is commonly used to achieve high and stable production.During hydraulic fracturing,a substantial volume of fluid is injected into the reservoir.However,statistical analysis reveals that the flowback rate is typically less than 30%,leaving the majority of the fluid trapped within the reservoir.Therefore,hydraulic fracturing in deep reservoirs not only enhances the reservoir permeability by creating artificial fractures but also damages reservoirs due to the fracturing fluids involved.The challenging“three-high”environment of a deep reservoir,characterized by high temperature,high pressure,and high salinity,exacerbates conventional forms of damage,including water sensitivity,retention of fracturing fluids,rock creep,and proppant breakage.In addition,specific damage mechanisms come into play,such as fracturing fluid decomposition at elevated temperatures and proppant diagenetic reactions at HTHP conditions.Presently,the foremost concern in deep oil and gas development lies in effectively assessing the damage inflicted on these reservoirs by hydraulic fracturing,comprehending the underlying mechanisms,and selecting appropriate solutions.It's noteworthy that the majority of existing studies on reservoir damage primarily focus on conventional reservoirs,with limited attention given to deep reservoirs and a lack of systematic summaries.In light of this,our approach entails initially summarizing the current knowledge pertaining to the types of fracturing fluids employed in deep and ultra-deep reservoirs.Subsequently,we delve into a systematic examination of the damage processes and mechanisms caused by fracturing fluids within the context of hydraulic fracturing in deep reservoirs,taking into account the unique reservoir characteristics of high temperature,high pressure,and high in-situ stress.In addition,we provide an overview of research progress related to high-temperature deep reservoir fracturing fluid and the damage of aqueous fracturing fluids to rock matrix,both artificial and natural fractures,and sand-packed fractures.We conclude by offering a summary of current research advancements and future directions,which hold significant potential for facilitating the efficient development of deep oil and gas reservoirs while effectively mitigating reservoir damage.

Extended finite element-based cohesive zone method for modeling simultaneous hydraulic fracture height growth in layered reservoirs

In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.

A Novel Fracturing Fluid with High-Temperature Resistance for Ultra-Deep Reservoirs

Ultra-deep reservoirs play an important role at present in fossil energy exploitation.Due to the related high temperature,high pressure,and high formation fracture pressure,however,methods for oil well stimulation do not produce satisfactory results when conventional fracturing fluids with a low pumping rate are used.In response to the above problem,a fracturing fluid with a density of 1.2~1.4 g/cm^(3)was developed by using Potassium formatted,hydroxypropyl guanidine gum and zirconium crosslinking agents.The fracturing fluid was tested and its ability to maintain a viscosity of 100 mPa.s over more than 60 min was verified under a shear rate of 1701/s and at a temperature of 175℃.This fluid has good sand-carrying performances,a low viscosity after breaking the rubber,and the residue content is less than 200 mg/L.Compared with ordinary reconstruction fluid,it can increase the density by 30%~40%and reduce the wellhead pressure of 8000 m level reconstruction wells.Moreover,the new fracturing fluid can significantly mitigate safety risks.

An Integrated Optimization Method for CO_(2) Pre-Injection during Hydraulic Fracturing in Heavy Oil Reservoirs

CO_(2) pre-injection during hydraulic fracturing is an important method for the development of medium to deep heavy oil reservoirs.It reduces the interfacial tension and viscosity of crude oil,enhances its flowability,maintains reservoir pressure,and increases reservoir drainage capacity.Taking the Badaowan Formation as an example,in this study a detailed three-dimensional geomechanical model based on static data from well logging interpretations is elaborated,which can take into account both vertical and horizontal geological variations and mechanical characteristics.A comprehensive analysis of the impact of key construction parameters on Pre-CO_(2) based fracturing(such as cluster spacing and injection volume),is therefore conducted.Thereafter,using optimized construction parameters,a non-structured grid for dynamic development prediction is introduced,and the capacity variations of different production scenarios are assessed.On the basis of the simulation results,reasonable fracturing parameters are finally determined,including cluster spacing,fracturing fluid volume,proppant concentration,and well spacing.

Formation damage mechanism and control strategy of the compound function of drilling fluid and fracturing fluid in shale reservoirs

For the analysis of the formation damage caused by the compound function of drilling fluid and fracturing fluid,the prediction method for dynamic invasion depth of drilling fluid is developed considering the fracture extension due to shale minerals erosion by oil-based drilling fluid.With the evaluation for the damage of natural and hydraulic fractures caused by mechanical properties weakening of shale fracture surface,fracture closure and rock powder blocking,the formation damage pattern is proposed with consideration of the compound effect of drilling fluid and fracturing fluid.The formation damage mechanism during drilling and completion process in shale reservoir is revealed,and the protection measures are raised.The drilling fluid can deeply invade into the shale formation through natural and induced fractures,erode shale minerals and weaken the mechanical properties of shale during the drilling process.In the process of hydraulic fracturing,the compound effect of drilling fluid and fracturing fluid further weakens the mechanical properties of shale,results in fracture closure and rock powder shedding,and thus induces stress-sensitive damage and solid blocking damage of natural/hydraulic fractures.The damage can yield significant conductivity decrease of fractures,and restrict the high and stable production of shale oil and gas wells.The measures of anti-collapse and anti-blocking to accelerate the drilling of reservoir section,forming chemical membrane to prevent the weakening of the mechanical properties of shale fracture surface,strengthening the plugging of shale fracture and reducing the invasion range of drilling fluid,optimizing fracturing fluid system to protect fracture conductivity are put forward for reservoir protection.

Optimization of Gas-Flooding Fracturing Development in Ultra-Low Permeability Reservoirs

Ultra-low permeability reservoirs are characterized by small pore throats and poor physical properties, which areat the root of well-known problems related to injection and production. In this study, a gas injection floodingapproach is analyzed in the framework of numerical simulations. In particular, the sequence and timing of fracturechanneling and the related impact on production are considered for horizontal wells with different fracturemorphologies. Useful data and information are provided about the regulation of gas channeling and possible strategiesto delay gas channeling and optimize the gas injection volume and fracture parameters. It is shown that inorder to mitigate gas channeling and ensure high production, fracture length on the sides can be controlled andlonger fractures can be created in the middle by which full gas flooding is obtained at the fracture location in themiddle of the horizontal well. A Differential Evolution (DE) algorithm is provided by which the gas injectionvolume and the fracture parameters of gas injection flooding can be optimized. It is shown that an improvedoil recovery factor as high as 6% can be obtained.

Surface-functionalized cellulose nanocrystals(CNC)and synergisms with surfactant for enhanced oil recovery in low-permeability reservoirs

Nanocellulose,a natural polymeric nanomaterial,has attracted significant attention in enhanced oil recovery(EOR)applications due to its abundance,nanoscale,high oil-water interfacial adsorption ef-ficiency.In this study,surface-functionalized cellulose nanocrystals(SF-CNCs)were prepared via hy-drochloric acid hydrolysis and chemical modification,with adaptable nanosize and considerable dispersion stability in low-permeability reservoirs.The SF-CNCs were structurally characterized by FT-IR,Cryo-TEM,which have a diameter of 5-10 nm and a length of 100-200 nm.The SF-CNC dispersions possessed higher stability and stronger salt-tolerance than those of corresponding CNC dispersions,due to the strong hydrophilicity of the sulfonic acid group.It was synergistically used with a non-ionic surfactant(APG1214)to formulate a combined flooding system(0.1 wt%SF-CNC+0.2 wt%APG1214).The combined flooding system exhibits strong emulsification stability,low oil-water interfacial tension of o.03 mN/m,and the ability to alter the wettability for oil-wetting rocks.Furthermore,the combined system was_able to provide an optimum EOR efficiency of 20.2%in low-permeability cores with 30.13×10^(-3)μm^(2).Notably.it can enlarge the sweep volume and increase the displacement efficiency simultaneously.Overall,the newly formulated nanocellulose/surfactant combined system exhibits a remarkable EoR performance in low-permeability reservoirs.

Fracture Distribution Characteristics within Low-Permeability Reservoirs:Cases Studies from Three Types of Oil-bearing Basins,China

The permeability or/and porosity in low-permeability reservoirs mainly depends on fracture system. Wthin this kind of low-permeability reservior, fractures play a very important role on exploration and development. Because there are so many differences, such as basin properties and tectonic characteristics, among the eastern,western and central basins, the types and distribution characteristics of fractures are also obviously different. Quantitative information on fracture distribution is very important. Through the contrastive study of 7 oilfield, the differences and distribution characteristics of fractures in three types of oil-bearing basins are summarized. Due to the different geological conditions and stress state during the formation of fractures, the fracture systems in three types of basins are also different. Fractures are mainly composed of tectonic fractutres related to normal faultes in eastern basins, related to folds and reverse faultes in western basins, and regional fractures which widely distributed not only in outcrops but also at depth of the relatively undeformed strata in central basins. So, besides jointed-fractures, we can often see faulted-fractures similar to normal faults in eastern basins and similar to reverse faults in western basins. According to statistical data, fracture spacing generally has a lognormal distribution and is linearly proportional to layer thickness. The development degree of fractures is controlled by lithology, bed thickness, sedimentary microfacies and faults or folds, etc. The permeability, aperture and connectedness of fractures are related to the modern stress field. Though there are 3-4 sets of fractures in a oilfield, the fractures parallel to the maximum principal stress direction are main for the pattern arrangement of low-permeability reservoirs.

Thermally-induced cracking behaviors of coal reservoirs subjected to cryogenic liquid nitrogen shock

The benefits of using cryogenic liquid nitrogen shock to enhance coal permeability have been confirmed from experimental perspectives.In this paper,we develop a fully coupled thermo-elastic model in combination with the strain-based isotropic damage theory to uncover the cooling-dominated cracking behaviors through three typical cases,i.e.coal reservoirs containing a wellbore,a primary fracture,and a natural fracture network,respectively.The progressive cracking processes,from thermal fracture initiation,propagation or cessation,deflection,bifurcation to multi-fracture interactions,can be well captured by the numerical model.It is observed that two hierarchical levels of thermal fractures are formed,in which the number of shorter thermal fractures consistently exceeds that of the longer ones.The effects of coal properties related to thermal stress levels and thermal diffusivity on the fracture morphology are quantified by the fracture fractal dimension and the statistical fracture number.The induced fracture morphology is most sensitive to changes in the elastic modulus and thermal expansion coefficient,both of which dominate the complexity of the fracture networks.Coal reservoir candidates with preferred thermal-mechanical properties are also recommended for improving the stimulation effect.Further findings are that there exists a critical injection temperature and a critical in-situ stress difference,above which no thermal fractures would be formed.Preexisting natural fractures with higher density and preferred orientations are also essential for the formation of complex fracture networks.The obtained results can provide some theoretical support for cryogenic fracturing design in coal reservoirs.

Study on the Impact of Massive Refracturing on the Fracture Network in Tight Oil Reservoir Horizontal Wells

Class III tight oil reservoirs have low porosity and permeability,which are often responsible for low production rates and limited recovery.Extensive repeated fracturing is a well-known technique to fix some of these issues.With such methods,existing fractures are refractured,and/or new fractures are created to facilitate communication with natural fractures.This study explored how different refracturing methods affect horizontal well fracture networks,with a special focus on morphology and related fluid flow changes.In particular,the study relied on the unconventional fracture model(UFM).The evolution of fracture morphology and flow field after the initial fracturing were analyzed accordingly.The simulation results indicated that increased formation energy and reduced reservoir stress differences can promote fracture expansion.It was shown that the length of the fracture network,the width of the fracture network,and the complexity of the fracture can be improved,the oil drainage area can be increased,the distance of oil and gas seepage can be reduced,and the production of a single well can be significantly increased.

Impacts of proppant distribution on development of tight oil reservoirs with threshold pressure gradient

Field evidence indicates that proppant distribution and threshold pressure gradient have great impacts on well productivity.Aiming at the development of unconventional oil reservoirs in Triassic Chang-7 Unit,Ordos Basin of China,we presented an integrated workflow to investigate how(1)proppant placement in induced fracture and(2)non-linear flow in reservoir matrix would affect well productivity and fluid flow in the reservoir.Compared with our research before(Yue et al.,2020),here we extended this study into the development of multi-stage fractured horizontal wells(MFHWs)with large-scale complicated fracture geometry.The integrated workflow is based on the finite element method and consists of simulation models for proppant-laden fluid flow,fracture flow,and non-linear seepage flow,respectively.Simulation results indicate that the distribution of proppant inside the induced cracks significantly affects the productivity of the MFHW.When we assign an idealized proppant distribution instead of the real distribution,there will be an overestimation of 44.98%in daily oil rate and 30.63%in cumulative oil production after continuous development of 1000 days.Besides,threshold pressure gradient(TPG)also significantly affects the well performance in tight oil reservoirs.If we simply apply linear Darcy’s law to the reservoir matrix,the overall cumulative oil production can be overrated by 77%after 1000 days of development.In general,this research provides new insights into the development of tight oil reservoirs with TPG and meanwhile reveals the significance of proppant distribution and non-linear fluid flow in the production scenario design.

Hydrocarbon gas huff-n-puff optimization of multiple horizontal wells with complex fracture networks in the M unconventional reservoir

The oil production of the multi-fractured horizontal wells(MFHWs) declines quickly in unconventional oil reservoirs due to the fast depletion of natural energy. Gas injection has been acknowledged as an effective method to improve oil recovery factor from unconventional oil reservoirs. Hydrocarbon gas huff-n-puff becomes preferable when the CO_(2) source is limited. However, the impact of complex fracture networks and well interference on the EOR performance of multiple MFHWs is still unclear. The optimal gas huff-n-puff parameters are significant for enhancing oil recovery. This work aims to optimize the hydrocarbon gas injection and production parameters for multiple MFHWs with complex fracture networks in unconventional oil reservoirs. Firstly, the numerical model based on unstructured grids is developed to characterize the complex fracture networks and capture the dynamic fracture features.Secondly, the PVT phase behavior simulation was carried out to provide the fluid model for numerical simulation. Thirdly, the optimal parameters for hydrocarbon gas huff-n-puff were obtained. Finally, the dominant factors of hydrocarbon gas huff-n-puff under complex fracture networks are obtained by fuzzy mathematical method. Results reveal that the current pressure of hydrocarbon gas injection can achieve miscible displacement. The optimal injection and production parameters are obtained by single-factor analysis to analyze the effect of individual parameter. Gas injection time is the dominant factor of hydrocarbon gas huff-n-puff in unconventional oil reservoirs with complex fracture networks. This work can offer engineers guidance for hydrocarbon gas huff-n-puff of multiple MFHWs considering the complex fracture networks.

The effects of various factors on spontaneous imbibition in tight oil reservoirs

Slickwater fracturing fluids have gained widespread application in the development of tight oil reservoirs. After the fracturing process, the active components present in slickwater can directly induce spontaneous imbibition within the reservoir. Several variables influence the eventual recovery rate within this procedure, including slickwater composition, formation temperature, degree of reservoir fracture development, and the reservoir characteristics. Nonetheless, the underlying mechanisms governing these influences remain relatively understudied. In this investigation, using the Chang-7 block of the Changqing Oilfield as the study site, we employ EM-30 slickwater fracturing fluid to explore the effects of the drag-reducing agent concentration, imbibition temperature, core permeability, and core fracture development on spontaneous imbibition. An elevated drag-reducing agent concentration is observed to diminish the degree of medium and small pore utilization. Furthermore, higher temperatures and an augmented permeability enhance the fluid flow properties, thereby contributing to an increased utilization rate across all pore sizes. Reduced fracture development results in a lower fluid utilization across diverse pore types. This study deepens our understanding of the pivotal factors affecting spontaneous imbibition in tight reservoirs following fracturing. The findings act as theoretical, technical, and scientific foundations for optimizing fracturing strategies in tight oil reservoir transformations.

Exploring pore-scale production characteristics of oil shale after CO_(2) huff‘n’puff in fractured shale with varied permeability

Recent studies have indicated that the injection of carbon dioxide(CO_(2))can lead to increased oil recovery in fractured shale reservoirs following natural depletion.Despite advancements in understanding mass exchange processes in subsurface formations,there remains a knowledge gap concerning the disparities in these processes between the matrix and fractures at the pore scale in formations with varying permeability.This study aims to experimentally investigate the CO_(2) diffusion behaviors and in situ oil recovery through a CO_(2) huff‘n’puff process in the Jimsar shale oil reservoir.To achieve this,we designed three matrix-fracture models with different permeabilities(0.074 mD,0.170 mD,and 0.466 mD)and experimented at 30 MPa and 91°C.The oil concentration in both the matrix and fracture was monitored using a low-field nuclear magnetic resonance(LF-NMR)technique to quantify in situ oil recovery and elucidate mass-exchange behaviors.The results showed that after three cycles of CO_(2) huff‘n’puff,the total recovery degree increased from 30.28%to 34.95%as the matrix permeability of the core samples increased from 0.074 to 0.466 mD,indicating a positive correlation between CO_(2) extraction efficiency and matrix permeability.Under similar fracture conditions,the increase in matrix permeability further promoted CO_(2) extraction efficiency during CO_(2) huff‘n’puff.Specifically,the increase in matrix permeability of the core had the greatest effect on the extraction of the first-cycle injection in large pores,which increased from 16.42%to 36.64%.The findings from our research provide valuable insights into the CO_(2) huff‘n’puff effects in different pore sizes following fracturing under varying permeability conditions,shedding light on the mechanisms of CO_(2)-enhanced oil recovery in fractured shale oil reservoirs.

Gas-Water Production of a Continental Tight-Sandstone Gas Reservoir under Different Fracturing Conditions

A numerical model of hydraulic fracture propagation is introduced for a representative reservoir(Yuanba continental tight sandstone gas reservoir in Northeast Sichuan).Different parameters are considered,i.e.,the interlayer stress difference,the fracturing discharge rate and the fracturing fluid viscosity.The results show that these factors affect the gas and water production by influencing the fracture size.The interlayer stress difference can effectively control the fracture height.The greater the stress difference,the smaller the dimensionless reconstruction volume of the reservoir,while the flowback rate and gas production are lower.A large displacement fracturing construction increases the fracture-forming efficiency and expands the fracture size.The larger the displacement of fracturing construction,the larger the dimensionless reconstruction volume of the reservoir,and the higher the fracture-forming efficiency of fracturing fluid,the flowback rate,and the gas production.Low viscosity fracturing fluid is suitable for long fractures,while high viscosity fracturing fluid is suitable for wide fractures.With an increase in the fracturing fluid viscosity,the dimensionless reconstruction volume and flowback rate of the reservoir display a non-monotonic behavior,however,their changes are relatively small.

Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method

In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.