Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil-water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery.In contrast to water,polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening,polymer convection,diffusion,adsorption retention,inaccessible pore volume and reduced effective permeability.Meanwhile,the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution,formation damage,and proppant breakage.In this paper,we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior,and non-uniform fracture characteristics in fractured polymer flooding.The hydraulic fracture is firstly divided into two parts:high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section.A hybrid grid system,including perpendicular bisection(PEBI)and Cartesian grid,is applied to discrete the partial differential flow equations,and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution.The combination of polymer behavior characterizations and numerical flow simulations are applied,resulting in the calculation for the distribution of water saturation,polymer concentration and reservoir pressure.Compared with the polymer flooding well with uniform fracture conductivity,this non-uniform fracture conductivity model exhibits the larger pressure difference,and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section.The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately,and yields fracture half-lengths that better match engineering reality,enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity.The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology,as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

Transient pressure analysis of polymer flooding fractured wells with oil-water two-phase flow

The oil-water two-phase flow pressure-transient analysis model for polymer flooding fractured well is established by considering the comprehensive effects of polymer shear thinning,shear thickening,convection,diffusion,adsorption retention,inaccessible pore volume and effective permeability reduction.The finite volume difference and Newton iteration methods are applied to solve the model,and the effects of fracture conductivity coefficient,injected polymer mass concentration,initial polymer mass concentration and water saturation on the well-test type curves of polymer flooding fractured wells are discussed.The results show that with the increase of fracture conductivity coefficient,the pressure conduction becomes faster and the pressure drop becomes smaller,so the pressure curve of transitional flow goes downward,the duration of bilinear flow becomes shorter,and the linear flow appears earlier and lasts longer.As the injected polymer mass concentration increases,the effective water phase viscosity increases,and the pressure loss increases,so the pressure and pressure derivative curves go upward,and the bilinear flow segment becomes shorter.As the initial polymer mass concentration increases,the effective water phase viscosity increases,so the pressure curve after the wellbore storage segment moves upward as a whole.As the water saturation increases,the relative permeability of water increases,the relative permeability of oil decreases,the total oil-water two-phase mobility becomes larger,and the pressure loss is reduced,so the pressure curve after the wellbore storage segment moves downward as a whole.The reliability and practicability of this new model are verified by the comparison of the results from simplified model and commercial well test software,and the actual well test data.

An approximate analytical solution for transient gas flows in a vertically fractured well of finite fracture conductivity

An analytical solution in physical variable space is presented for transient gas flows during constant-rate production from a vertically-fractured well in an infinite homogeneous reservoir with finite fracture conductivity.The solution is based on the short-time asymptotic solution and a new approximate transient elliptical flow solution,which covers transient flows from the bilinear flow regime to the pseudo-radial flow regime.The solution covers the well-known asymptotic solutions in both short-and long-time limits of bilinear and pseudo-radial flows.The analytical model provides a practical and reliable engineering tool to evaluate the fractured reservoir properties,which can be programmed using a spreadsheet.

A Reinterpretation of Historic Aquifer Tests of Two Hydraulically Fractured Wells by Application of Inverse Analysis, Derivative Analysis, and Diagnostic Plots

Aquifer test methods have greatly improved in recent years with the advent of inverse analysis, derivative analysis, and diagnostic plots. Updated analyses of past aquifer tests allow for improved interpretations of the data to enhance the knowledge and the predictive capabilities of the flow system. This work thoroughly reanalyzes a series of pre- and post-hydraulic fracturing, single-well aquifer tests conducted in two crystalline rock wells in New Hampshire as part of an early 1970’s study. Previous analyses of the data had relied on older manual type-curve methods for predicting the possible effects of hydraulic fracturing. This work applies inverse analysis, derivative analysis, and diagnostic plots to reanalyze the 1970’s aquifer test data. Our results demonstrate that the aquifer tests were affected by changes in flow regimes, dewatering of the aquifer and discrete fractures, and changes due to well development. Increases in transmissivities are related to well development prior to hydraulic fracturing, propagation of a single, vertical fracture hydraulically connecting the two wells after stimulation and expansion of troughs of depression. After hydraulic fracturing, the estimated total yield of the individual wells increased by 2.5 times due to the hydraulic fracturing. However, the wells may be receiving water from the same source, and well interference may affect any significant increase in their combined yield. Our analyses demonstrate the value in applying inverse analysis, derivative analysis, and diagnostic plots over the conventional method of manual type-curve analysis. In addition, our improvement in the aquifer test interpretation of the 1970’s test data has implications for more reliable estimates of sustained well yields.

Productivity simulation of hydraulically fractured wells based on hybrid local grid refinement and embedded discrete fracture model

Using current Embedded Discrete Fracture Models(EDFM) to predict the productivity of fractured wells has some drawbacks, such as not supporting corner grid, low precision in the near wellbore zone, and disregarding the heterogeneity of conductivity brought by non-uniform sand concentration. An EDFM is developed based on the corner grid, which enables high efficient calculation of the transmissibility between the embedded fractures and matrix grids, and calculation of the permeability of each polygon in the embedded fractures by the lattice data of the artificial fracture aperture. On this basis, a coupling method of local grid refinement(LGR) and embedded discrete fracture model is designed, which is verified by comparing the calculation results with the Discrete Fracture Network(DFN) method and fitting the actual production data of the first hydraulically fractured well in Iraq. By using this method and orthogonal experimental design, the optimization of the parameters of the first multi-stage fractured horizontal well in the same block is completed. The results show the proposed method has theoretical and practical significance for improving the adaptability of EDFM and the accuracy of productivity prediction of fractured wells, and enables the coupling of fracture modeling and numerical productivity simulation at reservoir scale.

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 novel production data analysis method for multi-fractured horizontal wells with infill well-caused fracture interference

Tightening the well spacing for unconventional tight reservoirs is an efficient technique to enhance oil and gas recoveries.Infill well-caused fracture connection between wells is widely reported in the field with small well spacing.This will make it difficult to make formation evaluation and fracture characterization between wells compared to single well cases.In this paper,a novel production data analysis(PDA)method is proposed for fracture characterization with the consideration of interwell fracture connections after the hydraulic fracturing of the infill.The PDA method is based on a semianalytical model,in which the small-scaled fractures are treated with the concept of stimulated reservoir volume(SRV).Thus,the fracture connections between wells are classified into three types,including SRV,fractures,and both SRV and fractures.The physical model is discretized into several linear flow regions,so the mathematical model can be solved semianalytically.An integrated workflow is proposed to analyze the production data for the wellpad,and three steps are mainly included in the workflow,including PDA for the parent well before infill,PDA for the parent well after infill,and PDA for the infill well.In each step,the production performance in the early linear and bilinear flow regimes are analyzed with approximate solutions in the square and fourth root-of-time plots.Because only the relationship between unknown model parameters can be obtained with the approximate solutions,history matching to the production data in log-log plots is further used to determine each unknown parameter.The PDA method is benchmarked with a synthetic case generated by the numerical simulator tNavigator and a field case from Southwestern China.The results show that both good matches and precise parameters can be obtained with the proposed PDA method.The connected fracture number will not be sensitive in PDA when the wells are connected with high-conductive dSRV.The innovation of this paper is that a practical method is provided for PDA analysis of well groups with fracture connection,and it will be a good technique for fracture characterization and well-interference analysis for tight formations.

Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

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.

Revolutionizing Tight Reservoir Production: A Novel Dual-Medium Unsteady Seepage Model for Optimizing Volumetrically Fractured Horizontal Wells

This study presents an avant-garde approach for predicting and optimizing production in tight reservoirs,employing a dual-medium unsteady seepage model specifically fashioned for volumetrically fractured horizontal wells.Traditional models often fail to fully capture the complex dynamics associated with these unconventional reservoirs.In a significant departure from these models,our approach incorporates an initiation pressure gradient and a discrete fracture seepage network,providing a more realistic representation of the seepage process.The model also integrates an enhanced fluid-solid interaction,which allows for a more comprehensive understanding of the fluid-structure interactions in the reservoir.This is achieved through the incorporation of improved permeability and stress coupling,leading to more precise predictions of reservoir behavior.The numerical solutions derived from the model are obtained through the sophisticated finite element method,ensuring high accuracy and computational efficiency.To ensure the model’s reliability and accuracy,the outcomes were tested against a real-world case,with results demonstrating strong alignment.A key revelation from the study is the significant difference between uncoupled and fully coupled volumetrically fractured horizontal wells,challenging conventional wisdom in the field.Additionally,the study delves into the effects of stress,fracture length,and fracture number on reservoir production,contributing valuable insights for the design and optimization of tight reservoirs.The findings from this study have the potential to revolutionize the field of tight reservoir prediction and management,offering significant advancements in petroleum engineering.The proposed approach brings forth a more nuanced understanding of tight reservoir systems and opens up new avenues for optimizing reservoir management and production.

Borehole stability in naturally fractured rocks with drilling mud intrusion and associated fracture strength weakening:A coupled DFN-DEM approach

Borehole instability in naturally fractured rocks poses significant challenges to drilling.Drilling mud invades the surrounding formations through natural fractures under the difference between the wellbore pressure(P w)and pore pressure(P p)during drilling,which may cause wellbore instability.However,the weakening of fracture strength due to mud intrusion is not considered in most existing borehole stability analyses,which may yield significant errors and misleading predictions.In addition,only limited factors were analyzed,and the fracture distribution was oversimplified.In this paper,the impacts of mud intrusion and associated fracture strength weakening on borehole stability in fractured rocks under both isotropic and anisotropic stress states are investigated using a coupled DEM(distinct element method)and DFN(discrete fracture network)method.It provides estimates of the effect of fracture strength weakening,wellbore pressure,in situ stresses,and sealing efficiency on borehole stability.The results show that mud intrusion and weakening of fracture strength can damage the borehole.This is demonstrated by the large displacement around the borehole,shear displacement on natural fractures,and the generation of fracture at shear limit.Mud intrusion reduces the shear strength of the fracture surface and leads to shear failure,which explains that the increase in mud weight may worsen borehole stability during overbalanced drilling in fractured formations.A higher in situ stress anisotropy exerts a significant influence on the mechanism of shear failure distribution around the wellbore.Moreover,the effect of sealing natural fractures on maintaining borehole stability is verified in this study,and the increase in sealing efficiency reduces the radial invasion distance of drilling mud.This study provides a directly quantitative prediction method of borehole instability in naturally fractured formations,which can consider the discrete fracture network,mud intrusion,and associated weakening of fracture strength.The information provided by the numerical approach(e.g.displacement around the borehole,shear displacement on fracture,and fracture at shear limit)is helpful for managing wellbore stability and designing wellbore-strengthening operations.

Creep constitutive model considering nonlinear creep degradation of fractured rock

Stability analysis of underground constructions requires a model study of rock masses’ long-term performance. Creep tests under different stress conditions was conducted on intact granite and granite samples fractured at 30° and 45° angles. The experimental results indicate that the steady creep strain rates of intact and fractured rock present an exponential increase trend with the increase of stress level. A nonlinear creep model is developed based on the experimental results, in which the initial damage caused by fracture together with the damage caused by constant load have been taken into consideration. The fitting analysis results indicated that the model proposed is more accurate at identifying the full creep regions in fractured granite, especially the accelerated stage of creep deformation. The least-square fit error of the proposed creep model is significantly lower than that of Nishihara model by almost an order of magnitude. An analysis of the effects of elastic modulus, viscosity coefficient, and damage factors on fractured rock strain rate and creep strain is conducted. If no consideration is given to the effects of the damage, the proposed nonlinear creep model can degenerate into to the classical Nishihara model.

Identifying flow regime in the aquifer of fractured rock system in Germi Chai Basin,Iran

Considering the importance of fractured rock aquifers in the hydrogeologic process,this research aimed to analyze the flow regime,internal degree of karstification,and estimate storage volume in fractured rock aquifers of the Germi Chai Basin in northwest Iran,which is attributed to its active tectonics,erosion,and the lithological diversity.Given the geological setting,the hypothesis is that this basin is characterized by a high degree of karstification and diffuse or intermediate flow regime leading to variation in discharge flow rate.The hydrodynamic and hadrochemical analysis was conducted on 9 well distributed springs across the basin from 2019 to 2020.The maximum flow rate in most of the springs appeared in the early wet season despite their different levels of fluctuations on the monthly discharge time series.Analyzing the spring recession curve form revealed an aquifer containing multiple micro-regimes withαrecession coefficients and a degree of karstification ranging between 0.001 to 0.06 and 0.55 to 2.61,respectively.These findings indicated a dominant diffuse and intermediate flow system resulting from the development of a high density of fractures in this area.The electrical conductivity of the spring changes inversely proportional to the change in flow discharge,indicating the reasonable hydrological response of the aquifer to rainfall events.Hydrograph analysis revealed that the delay time of spring discharge after rainfall events mostly varies between 10 to 30 days.The total dynamic storage volume of the spring for a given period(2019-2020)was estimated to be approximately 1324 million cubic meters reflecting the long-term drainage potential and high perdurability of dynamic storage.Estimating the maximum and minimum ratio revealed that the springs recharging system in Germi Chai Basin comes under the slow aquifers category.This finding provides valuable insight into the hydrogeological properties of fractured rock aquifers contributing to effective water management strategy.

Extreme massive hydraulic fracturing in deep coalbed methane horizontal wells:A case study of the Linxing Block,eastern Ordos Basin,NW China

Deep coal seams show low permeability,low elastic modulus,high Poisson’s ratio,strong plasticity,high fracture initiation pressure,difficulty in fracture extension,and difficulty in proppants addition.We proposed the concept of large-scale stimulation by fracture network,balanced propagation and effective support of fracture network in fracturing design and developed the extreme massive hydraulic fracturing technique for deep coalbed methane(CBM)horizontal wells.This technique involves massive injection with high pumping rate+high-intensity proppant injection+perforation with equal apertures and limited flow+temporary plugging and diverting fractures+slick water with integrated variable viscosity+graded proppants with multiple sizes.The technique was applied in the pioneering test of a multi-stage fracturing horizontal well in deep CBM of Linxing Block,eastern margin of the Ordos Basin.The injection flow rate is 18 m^(3)/min,proppant intensity is 2.1 m^(3)/m,and fracturing fluid intensity is 16.5 m^(3)/m.After fracturing,a complex fracture network was formed,with an average fracture length of 205 m.The stimulated reservoir volume was 1987×10^(4)m^(3),and the peak gas production rate reached 6.0×10^(4)m^(3)/d,which achieved efficient development of deep CBM.

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.

Development of an experimental method for well-controlled blast induced traumatic limb fracture in rats

Heterotopic ossification(HO)is a consequence of traumatic bone and tissue damage,which occurs in 65%of military casualties with blast-associated amputations.However,the mechanisms behind blast-induced HO remain unclear.Animal models are used to study blast-induced HO,but developing such models is challenging,particularly in how to use a pure blast wave(primary blast)to induce limb fracture that then requires an amputation.Several studies,including our recent study,have developed platforms to induce limb fractures in rats with blast loading or a mixture of blast and impact loading.However,these models are limited by the survivability of the animal and repeatability of the model.In this study,we developed an improved platform,aiming to improve the animal's survivability and injury repeatability as well as focusing on primary blast only.The platform exposed only one limb of the rat to a blast wave while providing proper protection to the rest of the rat's body.We obtained very consistent fracture outcome in the tibia(location and pattern)in cadaveric rats with a large range of size and weight.Importantly,the rats did not obviously move during the test,where movement is a potential cause of uncontrolled injury.We further conducted parametric studies by varying the features of the design of the platform.These factors,such as how the limb is fixed and how the cavity through which the limb is placed is sealed,significantly affect the resulting injury.This platform and test setups enable well-controlled limb fracture induced directly by pure blast wave,which is the fundamental step towards a complete in vivo animal model for blast-induced HO induced by primary blast alone,excluding secondary and tertiary blast injury.In addition,the platform design and the findings presented here,particularly regarding the proper protection of the animal,have implications for future studies investigating localized blast injuries,such as blast induced brain and lung injuries.

A phase-field model for simulating the propagation behavior of mixed-mode cracks during the hydraulic fracturing process in fractured reservoirs

A novel phase-field model for the propagation of mixed-mode hydraulic fractures,characterized by the formation of mixed-mode fractures due to the interactions between fluids and solids,is proposed.In this model,the driving force for the phase field consists of both tensile and shear components,with the fluid contribution primarily manifesting in the tension driving force.The displacement and pressure are solved simultaneously by an implicit method.The numerical solution's iterative format is established by the finite element discretization and Newton-Raphson(NR)iterative methods.The correctness of the model is verified through the uniaxial compression physical experiments on fluid-pressurized rocks,and the limitations of the hydraulic fracture expansion phase-field model,which only considers mode I fractures,are revealed.In addition,the influence of matrix mode II fracture toughness value,natural fracture mode II toughness value,and fracturing fluid injection rate on the hydraulic fracture propagation in porous media with natural fractures is studied.

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.

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.

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.