Study on "fracturing-sealing" integration technology based on high-energy gas fracturing in single seam with high gas and low air permeability

To improve the gas extraction efficiency of single seam with high gas and low air permeability,we developed the"fracturing-sealing"integration technology,and carried out the engineering experiment in the3305 Tunliu mine.In the experiment,coal seams can achieve the aim of antireflection effect through the following process:First,project main cracks with the high energy pulse jet.Second,break the coal body by delaying the propellant blasting.Next,destroy the dense structure of the hard coal body,and form loose slit rings around the holes.Finally,seal the boreholes with the"strong-weak-strong"pressurized sealing technology.The results are as follows:The average concentration of gas extraction increases from8.3%to 39.5%.The average discharge of gas extraction increases from 0.02 to 0.10 m^3/min.The tunneling speeds up from 49.5 to 130 m/month.And the permeability of coal seams improves nearly tenfold.Under the same conditions,the technology is much more efficient in depressurization and antireflection than common methods.In other words,it will provide a more effective way for the gas extraction of single seam with high gas and low air permeability.

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.

Experimental investigation on coal pore-fracture variation and fractal characteristics synergistically affected by solvents for improving clean gas extraction

Chemical solvents instead of pure water being as hydraulic fracturing fluid could effectively increase permeability and improve clean methane extraction efficiency.However,pore-fracture variation features of lean coal synergistically affected by solvents have not been fully understood.Ultrasonic testing,nuclear magnetic resonance analysis,liquid phase mass spectrometry was adopted to comprehensively analyze pore-fracture change characteristics of lean coal treated by combined solvent(NMP and CS_(2)).Meanwhile,quantitative characterization of above changing properties was conducted using geometric fractal theory.Relationship model between permeability,fractal dimension and porosity were established.Results indicate that the end face fractures of coal are well developed after CS2and combined solvent treatments,of which,end face box-counting fractal dimensions range from 1.1227 to 1.4767.Maximum decreases in ultrasonic longitudinal wave velocity of coal affected by NMP,CS_(2)and combined solvent are 2.700%,20.521%,22.454%,respectively.Solvent treatments could lead to increasing amount of both mesopores and macropores.Decrease ratio of fractal dimension Dsis 0.259%–2.159%,while permeability increases ratio of NMR ranges from 0.1904 to 6.4486.Meanwhile,combined solvent could dissolve coal polar and non-polar small molecules and expand flow space.Results could provide reference for solvent selection and parameter optimization of permeability-enhancement technology.

A Data-Oriented Method to Optimize Hydraulic Fracturing Parameters of Tight Sandstone Reservoirs

Based on the actual data collected from the tight sandstone development zone, correlation analysis using theSpearman method was conducted to determine the main factors influencing the gas production rate of tightsandstone fracturing. An integrated model combining geological engineering and numerical simulation of fracturepropagation and production was completed. Based on data analysis, the hydraulic fracture parameters wereoptimized to develop a differentiated fracturing treatment adjustment plan. The results indicate that the influenceof geological and engineering factors in the X1 and X2 development zones in the study area differs significantly.Therefore, it is challenging to adopt a uniform development strategy to achieve rapid production increase. Thedata analysis reveals that the variation in gas production rate is primarily affected by the reservoir thickness andpermeability parameters as geological factors. On the other hand, the amount of treatment fluid and proppantaddition significantly impact the gas production rate as engineering factors. Among these factors, the influence ofgeological factors is more pronounced in block X1. Therefore, the main focus should be on further optimizing thefracturing interval and adjusting the geological development well location. Given the existing well location, thereis limited potential for further optimizing fracture parameters to increase production. For block X2, the fracturingparameters should be optimized. Data screening was conducted to identify outliers in the entire dataset, and adata-driven fracturing parameter optimization method was employed to determine the basic adjustment directionfor reservoir stimulation in the target block. This approach provides insights into the influence of geological,stimulation, and completion parameters on gas production rate. Consequently, the subsequent fracturing parameteroptimization design can significantly reduce the modeling and simulation workload and guide field operations toimprove and optimize hydraulic fracturing efficiency.

Investigation of influence factors on CO_(2) flowback characteristics and optimization of flowback parameters during CO_(2) dry fracturing in tight gas reservoirs

CO_(2) dry fracturing is a promising alternative method to water fracturing in tight gas reservoirs,especially in water-scarce areas such as the Loess Plateau.The CO_(2) flowback efficiency is a critical factor that affects the final gas production effect.However,there have been few studies focusing on the flowback characteristics after CO_(2) dry fracturing.In this study,an extensive core-to-field scale study was conducted to investigate CO_(2) flowback characteristics and CH_(4) production behavior.Firstly,to investigate the impact of core properties and production conditions on CO_(2) flowback,a series of laboratory experiments at the core scale were conducted.Then,the key factors affecting the flowback were analyzed using the grey correlation method based on field data.Finally,taking the construction parameters of Well S60 as an example,a dual-permeability model was used to characterize the different seepage fields in the matrix and fracture for tight gas reservoirs.The production parameters after CO_(2) dry fracturing were then optimized.Experimental results demonstrate that CO_(2) dry fracturing is more effective than slickwater fracturing,with a 9.2%increase in CH_(4) recovery.The increase in core permeability plays a positive role in improving CH_(4) production and CO_(2) flowback.The soaking process is mainly affected by CO_(2) diffusion,and the soaking time should be controlled within 12 h.Increasing the flowback pressure gradient results in a significant increase in both CH_(4) recovery and CO_(2) flowback efficiency.While,an increase in CO_(2) injection is not conducive to CH_(4) production and CO_(2) flowback.Based on the experimental and field data,the important factors affecting flowback and production were comprehensively and effectively discussed.The results show that permeability is the most important factor,followed by porosity and effective thickness.Considering flowback efficiency and the influence of proppant reflux,the injection volume should be the minimum volume that meets the requirements for generating fractures.The soaking time should be short which is 1 day in this study,and the optimal bottom hole flowback pressure should be set at 10 MPa.This study aims to improve the understanding of CO_(2) dry fracturing in tight gas reservoirs and provide valuable insights for optimizing the process parameters.

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

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

Self-sealing of fractures in indurated claystones measured by water and gas flow

Self-sealing of fractures in the indurated Callovo-Oxfordian(COX)and Opalinus(OPA)claystones,which are considered as host rocks for disposal of radioactive waste,was investigated on artificially fractured samples.The samples were extracted from four lithological facies relatively rich in clay mineral,carbonate and quartz,respectively.The self-sealing of fractures was measured by fracture closure,water permeability variation,gas penetration,and recovery of gas-induced pathways.Most of the fractured samples exhibited a dramatic reduction inwater permeability to low levels that is close to that of intact rock,depending on their mineralogical composition,fracture intensity,confining stress,and load duration.The self-sealing capacity of the clay-rich samples is higher than that of the carbonate-rich and sandy ones.Significant effects of sample size and fracture intensity were identified.The sealed fractures become gas-tight for certain in-jection pressures.However,the measured gas breakthrough pressures are still lower than the confining stresses.The gas-induced pathways can recover when contacting water.These important findings imply that fractures in such indurated claystones can effectively recover to hinder water transport but allow gas release under relatively low pressures without compromising the rock integrity.

Complex genesis of multiperiod fractures in the Middle Triassic Leikoupo Formation in the Pengzhou gas field, western Sichuan Basin, China

The cumulative expression of multistage deformation is complex multiperiod fractures,which are commonly seen in tectonic zones.The Middle Triassic Leikoupo Formation in the western Sichuan Basin Depression,China,is a typical marine carbonate reservoir with natural fractures caused mainly by tectonic movements.According to outcrops,drill cores,image logging,and fluid inclusions,the fracture characteristics,types of natural fractures,and interactions of fractures are determined.In total,419 natural fractures in 493.2 m of cores from 7 wells are investigated,which are mainly shear and tensile fractures with a small number of weathering generated fractures.Meanwhile,the results of the stable isotope analysis of δ13C and δ18O,as well as the flow fluid inclusion data,reveal four tectonic periods of fractures with different occurrences.Based on the history of regional tectonic evolution,indicating one period of weathering fractures ascribable to stratal uplift and three periods of structural fractures related to the sequential tectonic movements of the Longmenshan fault belt.By analyzing the interaction relationships of fractures,three types of fracture interaction relationships are observed:cutting,restraining,and overlapping.The four stages fractures are chronologically assigned to(1)the early Indosinian N-S trending compression,(2)the late Indosinian NW-SE compression,(3)the middle Yanshanian NE-SE compression,and(4)the early Himalayan E-W compression.The influence of natural fractures on gas migration and well production in marine carbonates is discussed,and indicates that tectonic fractures could provide seepage channels for gas migration and accumulation from near or distant hydrocarbon source rocks into the Middle Triassic Leikoupo Formation.This study utilizes a pragmatic approach for understanding the fracture genesis mechanism in oil and gas field with multiperiod fractures.

Numerical analysis of rock fracturing by gas pressure using the extended finite element method

High energy gas fracturing is a simple approach of applying high pressure gas to stimulate wells by gen- erating several radial cracks without creating any other damages to the wells. In this paper, a numerical algorithm is proposed to quantitatively simulate propagation of these fractures around a pressurized hole as a quasi-static phenomenon. The gas flow through the cracks is assumed as a one-dimensional transient flow, governed by equations of conservation of mass and momentum. The fractured medium is modeled with the extended finite element method, and the stress intensity factor is calculated by the simple, though sufficiently accurate, displacement ex- trapolation method. To evaluate the proposed algorithm, two field tests are simulated and the unknown parameters are determined through calibration. Sensitivity analyses are performed on the main effective parameters. Considering that the level of uncertainty is very high in these types of engineering problems, the results show a good agreement with the experimental data. They are also consistent with the theory that the final crack length is mainly determined by the gas pressure rather than the initial crack length produced by the stress waves.

Progress and prospects of horizontal well fracturing technology for shale oil and gas reservoirs

By systematically summarizing horizontal well fracturing technology abroad for shale oil and gas reservoirs since the “13th Five-Year Plan”, this article elaborates new horizontal well fracturing features in 3D development of stacked shale reservoirs, small well spacing and dense well pattern, horizontal well re-fracturing, fracturing parameters optimization and cost control. In light of requirements on horizontal well fracturing technology in China, we have summarized the technological progress in simulation of multi-fracture propagation, horizontal well frac-design, electric-drive fracturing equipment, soluble tools and low-cost downhole materials and factory-like operation. On this basis, combined with the demand analysis of horizontal well fracturing technology in the “14th Five-Year Plan” for unconventional shale oil and gas, we suggest strengthening the research and development in the following 7 aspects:(1) geology-engineering integration;(2) basic theory and design optimization of fracturing for shale oil and gas reservoirs;(3) development of high-power electric-drive fracturing equipment;(4) fracturing tool and supporting equipment for long horizontal section;(5) horizontal well flexible-sidetracking drilling technology for tapping remaining oil;(6) post-frac workover technology for long horizontal well;(7) intelligent fracturing technology.

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

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

Simulation of the Production Performances of Horizontal Wells with a Fractured Shale Gas Reservoir

The production performances of a well with a shale gas reservoir displaying a complex fracture network are simulated.In particular,a micro-seismic cloud diagram is used to describe the fracture network,and accordingly,a production model is introduced based on a multi-scale flow mechanism.A finite volume method is then exploited for the integration of the model equations.The effects of apparent permeability,conductivity,Langmuir volume,and bottom hole pressure on gas well production are studied accordingly.The simulation results show that ignoring the micro-scale flow mechanism of the shale gas leads to underestimating the well gas production.It is shown that after ten years of production,the cumulative gas production difference between the two scenarios with and without considering the micro-scale flow mechanisms is 19.5%.The greater the fracture conductivity,the higher the initial gas production of the gas well and the cumulative gas production.The larger the Langmuir volume,the higher the gas production rate and the cumulative gas production.With the reduction of the bottom hole pressure,the cumulative gas production increases,but the growth rate gradually decreases.

Proppant transport in rough fractures of unconventional oil and gas reservoirs

A method to generate fractures with rough surfaces was proposed according to the fractal interpolation theory.Considering the particle-particle,particle-wall and particle-fluid interactions,a proppant-fracturing fluid two-phase flow model based on computational fluid dynamics(CFD)-discrete element method(DEM)coupling was established.The simulation results were verified with relevant experimental data.It was proved that the model can match transport and accumulation of proppants in rough fractures well.Several cases of numerical simulations were carried out.Compared with proppant transport in smooth flat fractures,bulge on the rough fracture wall affects transport and settlement of proppants significantly in proppant transportation in rough fractures.The higher the roughness of fracture,the faster the settlement of proppant particles near the fracture inlet,the shorter the horizontal transport distance,and the more likely to accumulate near the fracture inlet to form a sand plugging in a short time.Fracture wall roughness could control the migration path of fracturing fluid to a certain degree and change the path of proppant filling in the fracture.On the one hand,the rough wall bulge raises the proppant transport path and the proppants flow out of the fracture,reducing the proppant sweep area.On the other hand,the sand-carrying fluid is prone to change flow direction near the contact point of bulge,thus expanding the proppant sweep area.

Application of fracturing technology to increase gas production in low-permeability hydrate reservoir:A numerical study

Low temperature and low permeability are the challenges for the development of hydrate reservoirs in permafrost.The ice produced around the production well caused by high depressurization driving force reduces the gas production,and it is necessary to reduce the effect of ice production on gas production.In this work,a new combination of fracturing technology and depressurization method was proposed to evaluate the gas production potential at the site DK-2 in Qinghai-Tibet Plateau Permafrost.A relatively higher intrinsic permeability of the fracture zone surround the horizontal production well was created by the fracturing technology.The simulation results showed that the fracture zone reduced the blocking of production ice to production wells and promoted the propagation of production pressure.And the gas production increased by 2.1 times as the radius of the fracture zone increased from 0 to 4 m in 30 years.Nearly half of the hydrate reservoirs were dissociated in 30 years,and greater than 51.7%of the gas production was produced during the first 10 years.Moreover,production behaviours were sensitive to the depressurization driving force but not to the thermal conductivity.The growth of gas production was not obvious with the intrinsic permeability of the fracture zone higher than 100 m D.The effect of ice production on gas production by fracturing technology and depressurization method was limited.

Growth behavior and resource potential evaluation of gas hydrate in core fractures in Qilian Mountain permafrost area, Qinghai-Tibet Plateau

The Qilian Mountain permafrost area located in the northern of Qinghai-Tibet Plateau is a favorable place for natural gas hydrate formation and enrichment,due to its well-developed fractures and abundant gas sources.Understanding the formation and distribution of multi-component gas hydrates in fractures is crucial in accurately evaluating the hydrate reservoir resources in this area.The hydrate formation experiments were carried out using the core samples drilled from hydrate-bearing sediments in Qilian Mountain permafrost area and the multi-component gas with similar composition to natural gas hydrates in Qilian Mountain permafrost area.The formation and distribution characteristics of multi-component gas hydrates in core samples were observed in situ by X-ray Computed Tomography(X-CT)under high pressure and low temperature conditions.Results show that hydrates are mainly formed and distributed in the fractures with good connectivity.The ratios of volume of hydrates formed in fractures to the volume of fractures are about 96.8%and 60.67%in two different core samples.This indicates that the fracture surface may act as a favorable reaction site for hydrate formation in core samples.Based on the field geological data and the experimental results,it is preliminarily estimated that the inventory of methane stored in the fractured gas hydrate in Qilian Mountain permafrost area is about 8.67×1013 m3,with a resource abundance of 8.67×108 m3/km2.This study demonstrates the great resource potential of fractured gas hydrate and also provides a new way to further understand the prospect of natural gas hydrate and other oil and gas resources in Qilian Mountain permafrost area.

Analysis of Emissions Profiles of Hydraulic Fracturing Engine Technologies

Today, the oil and gas industry, and in particular hydraulic fracturing operations, have come under increasing pressure from regulators and the public to reduce emissions. As the industry evolves, oil and gas producers are in the position of evaluating alternative technologies which will support their objectives of reducing their overall emissions profile and carbon footprint. As a response, the deployment of technology and solutions to reduce emissions related to hydraulic fracturing applications has recently accelerated, creating various options to address these industry challenges. BJ Energy Solutions and West Virginia University have been working on the application and emissions characterization of various hydraulic fracturing technologies. A study was conducted to evaluate the efficiency and resultant emissions from various technologies, including natural gas reciprocating engines, diesel-natural gas dual-fuel engines, large (>24 MW) gas turbines, and direct drive turbines. The study involved the development of an emissions model with the purpose of estimating total emissions of carbon dioxide (CO2), nitrous oxide (N2O) and exhaust methane (CH4) slip, all Greenhouse Gases (GHGs), and converted to tons of CO2 equivalent emissions per day of operation. The model inputs are the required Hydraulic Horsepower (HHP) based on pumping rate and pressure for various shale play scenarios. The model calculates emissions from the TITAN, which is a direct-drive turbine model fielded by BJ, using data collected following U.S. Environmental Protection Agency (EPA) testing protocols. The model also calculates and compares other hydraulic fracturing technologies utilizing published Original Equipment Manufacturer (OEM) data. Relevant EPA-regulated criteria emissions of oxides of nitrogen (NOx), Carbon Monoxide (CO) and Particulate Matter (PM) are also reported. Modeling results demonstrated that in most cases, the TITAN gas turbine system has lower total GHG emissions than conventional diesel and other next-generation technologies, and also has lower criteria emissions. The benefits of the TITAN gas turbine system compared to the other technologies stems from significantly lower methane slip, and the high-power transfer efficiency resulting from directly connecting a turbine to a reciprocating pump, despite the comparatively lower thermal efficiency.

A Numerical Gas Fracturing Model of Coupled Thermal,Flowing and Mechanical Effects

Gas fracturing,which overcomes the limitation of hydraulic fracturing,is a potential alternative technology for the development of unconventional gas and oil resources.However,the mechanical principle of gas fracturing has not been learned comprehensively when the fluid is injected into the borehole.In this paper,a damage-based model of coupled thermal-flowing-mechanical effects was adopted to illustrate the mechanical principle of gas fracturing.Numerical simulation tools Comsol Multiphysics and Matlab were integrated to simulate the coupled process during the gas fracturing.Besides,the damage evolution of drilling areas under several conditions was fully analyzed.Simulation results indicate that the maximum tensile stress,which occurs in the upper and lower of the injection hole,decreases with the increase of the tectonic stress coefficient(TSC).As the TSC increases,shear fractures increase,a crushed area is gradually formed and the seepage area increases rapidly.The influence of TSC on fracture expansion is concluded as follows:with the decrease of TSC,the relative width of fractures decreases whilst the depth increases.It indicates that thermal stress and pore pressure promote the expansion of tensile fractures but restrain the expansion of shear fractures.Therefore,a relatively lower injection gas pressure is required to obtain the same degree of fracturing with a coupled thermal gradient.

Advances of nanotechnologies for hydraulic fracturing of coal seam gas reservoirs:potential applications and some limitations in Australia

Some of the most promising potential applications of nanotechnology to hydraulic fracturing of coal seam gas(CSG)are reviewed with a focus on Australian CSG wells.Three propitious applications were identifed:(1)Nanoparticle enhanced viscoelastic surfactants(VES)fracturing fuids to prevent fuid loss by up to 30%,made possible by the formation of pseudo-flter cakes and reducing the viscosity of the VES fuids.Besides,there is no requirement of clay control additives or biocides.(2)Nano-proppants to extend fracture networks and reduce proppant embedment by introducing them prior to the emplacement of larger proppants.Fly Ash nanoparticles can be particularly efective because of their high sphericity and mechanical strength.(3)Nanoparticle-coated proppants,to mitigate the migration of particle fnes by restricting them close to their source by adsorption,with MgO being the most efective.The use of nanotechnology in hydraulic fracturing applications is currently hindered due to a discordant regulatory environment compounded by the cost of the nanoparticles themselves,as well as,a lack of feld data to validate the technology under real downhole conditions.Although the necessary feld tests are unlikely to be conducted for as long as abundant natural gas is available,exploratory studies could pave the way for future applications.

Enlightenment of calcite veins in deep Ordovician Wufeng-Silurian Longmaxi shales fractures to migration and enrichment of shale gas in southern Sichuan Basin, SW China

The relationship between fracture calcite veins and shale gas enrichment in the deep Ordovician Wufeng Formation-Silurian Longmaxi Formation (Wufeng-Longmaxi) shales in southern Sichuan Basin was investigated through core and thin section observations, cathodoluminescence analysis, isotopic geochemistry analysis, fluid inclusion testing, and basin simulation. Tectonic fracture calcite veins mainly in the undulating part of the structure and non-tectonic fracture calcite veins are mainly formed in the gentle part of the structure. The latter, mainly induced by hydrocarbon generation, occurred at the stage of peak oil and gas generation, while the former turned up with the formation of Luzhou paleouplift during the Indosinian. Under the influence of hydrocarbon generation pressurization process, fractures were opened and closed frequently, and oil and gas episodic activities are recorded by veins. The formation pressure coefficient at the maximum paleodepth exceeds 2.0. The formation uplift stage after the Late Yanshanian is the key period for shale gas migration. Shale gas migrates along the bedding to the high part of the structure. The greater the structural fluctuation is, the more intense the shale gas migration activity is, and the loss is more. The gentler the formation is, the weaker the shale gas migration activity is, and the loss is less. The shale gas enrichment in the core of gentle anticlines and gentle synclines is relatively higher.

Optimizing the Diameter of Plugging Balls in Deep Shale Gas Wells

Deep shale gas reserves that have been fractured typically have many relatively close perforation holes. Due to theproximity of each fracture during the formation of the fracture network, there is significant stress interference,which results in uneven fracture propagation. It is common practice to use “balls” to temporarily plug fractureopenings in order to lessen liquid intake and achieve uniform propagation in each cluster. In this study, a diameteroptimization model is introduced for these plugging balls based on a multi-cluster fracture propagationmodel and a perforation dynamic abrasion model. This approach relies on proper consideration of the multiphasenature of the considered problem and the interaction force between the involved fluid and solid phases. Accordingly,it can take into account the behavior of the gradually changing hole diameter due to proppant continuousperforation erosion. Moreover, it can provide useful information about the fluid-dynamic behavior of the consideredsystem before and after plugging. It is shown that when the diameter of the temporary plugging ball is1.2 times that of the perforation hole, the perforation holes of each cluster can be effectively blocked.