Mechanisms of Stress Sensitivity on Artiﬁcial Fracture Conductivity in the Flowback Stage of Shale Gas Wells

: The presence of a reasonable ﬂowback system after fracturing is a necessary condition for the high production of shale gas wells. At present, the optimization of the ﬂowback system lacks a relevant theoretical basis. Due to this lack, this study established a new method for evaluating the conductivity of artiﬁcial fractures in shale, which can quantitatively characterize the backﬂow, embedment, and fragmentation of proppant during the ﬂowback process. Then, the mechanism of the stress sensitivity of artiﬁcial fractures on fracture conductivity during the ﬂowback stage of the shale gas well was revealed by performing the artiﬁcial fracture conductivity evaluation experiment. The results show that a large amount of proppant migrates, and the fracture conductivity decreases rapidly in the early stage of ﬂowback, and then the decline gradually slows down. When the effective stress is low, the proppant is mainly plastically deformed, and the degree of fragmentation and embedment is low. When the effective stress exceeds 15.0 MPa, the fragmentation and embedment of the proppant will increase, and the fracture conductivity will be greatly reduced. The broken proppant ratio and embedded proppant ratio are the same under the two choke-management strategies. In the mode of increasing choke size step by step, the backﬂow proppant ratio is lower, and the broken proppant is mainly retained in fractures, so the damage ratio of fracture conductivity is lower. In the mode of decreasing choke size step by step, most of the proppant ﬂows back from fractures, so the damage to fracture conductivity is greater. The research results have important theoretical guiding signiﬁcance for optimizing the ﬂowback system of shale gas wells.


Introduction
As a kind of unconventional gas resource, shale gas has been successfully explored and developed, which is an innovation and leap forward in the theory and technology of the global oil and gas industry.The development of shale gas has broken through the understanding of oil and gas geology, expanded the oil and gas development process, guaranteed national energy, and even changed the world oil pattern [1][2][3].Shale gas is currently an important support for global natural gas production, but its development faces many more challenges than conventional natural gas.Due to developed micro/nano pores and extremely low permeability, shale reservoirs usually have no natural productivity, so they cannot be developed economically and effectively unless the mode of "horizontal well + volumetric fracturing" is adopted [3].In the process of shale reservoir fracturing, a large amount of fluid and proppant is injected into the reservoirs, and a complex artificial fracture network is formed to improve the permeability of the shale reservoir [4][5][6][7].Shale gas wells cannot be formally put into production until soaking, flowback, and testing are performed.At the stage of the flowback test, the early productivity of the gas well is Processes 2023, 11, 2760 2 of 14 determined by changing the size of the choke.At this stage, the proppant can move in fractures and flow back to the wellbore as fracturing fluid is produced.In this situation, the prop effect weakens, so the fractures close, leading to a reduction in fracture conductivity.In addition, the seepage feature is extremely complex due to the two-phase flow of gas fracturing fluid [8][9][10][11].With the continuous production of fracturing fluid and gas, the pressure in fractures drops gradually, and under the action of overlying pressure, proppant embedment and fragmentation are inevitable.Hence, fracture conductivity decreases greatly and irreversibly, which seriously impacts the estimated ultimate recovery (EUR) of shale gas wells [12,13].
To develop shale gas reservoirs reasonably, it is necessary to determine the stress sensitivity characteristics of artificial fractures and the variation characteristics of fracture conductivity in the stage of the flowback test.Several studies have been conducted on the stress sensitivity characteristics of fractures and the change of fracture conductivity caused by stress sensitivity by means of physical simulation experiments [14][15][16][17][18], numerical simulation [19][20][21][22], and theoretical models [23,24].Zhang [16] used Barnett shale samples to make physical models to study the influence of fracture conductivity under different pressures and proppant concentrations.Computational Fluid Dynamics (CFD) software was used for simulation verification, and the results showed that the conductivity reduction was 45-80%.The fracture property in the study is different from that in the actual reservoir.Tan [17] studied the effect of the layer number and type of proppant on fracture permeability and compressibility, and the backflow of the proppant was not considered.Andrei Osiptsov [20] applied a coupled modeling approach considering fluid displacement in a fracture.The results confirmed that the "smooth" scenario of piece-wise constant choke opening is better because it can maintain fracture conductivity and increase well production.John D. [22] studied the deformation and stability of the proppant in the flowback process by means of the DEM-CFD (Discrete Element Method-Computational Fluid Dynamics) coupling method and the results showed that formation fines and crushed proppant caused permeability damage, reducing the fracture width.Mohammed Kaita [24] developed mathematical models for calculating fracture conductivity, fracture aperture reduction, proppant insertion, and deformation of rod-shaped proppant, and the analysis model can match the embedding and fracture conductivity of rod-shaped proppant under different closing pressures.Seismic methods also have great potential in characterizing fractures and evaluating their conductivity.For instance, Bouchaala used seismic attenuation anisotropy to separate open and closed fractures [25].Furthermore, Diaz-Acosta combined shear wave splitting and multicomponent velocity analysis to determine fracture orientations in reservoir zones [26].However, all this research lacked quantitative evaluation on proppant backflow, fragmentation, and embedment.Furthermore, the stress sensitivity characteristics of fractures and the variation characteristics of fracture conductivity under different choke management systems are less researched, so there is no effective guidance for field production.
In this study, a method for evaluating the conductivity of artificial fractures in shale was developed, which can quantitatively evaluate proppant backflow, fragmentation, and embedment.The fracture conductivity evaluation results reveal that the intrinsic conductivity mechanisms vary with the effective stress.The research in this paper provides a theoretical basis for optimizing flowback and production regimes in shale gas wells.

Core samples
The Wufeng Formation to Long 1 1 Sub-member is currently the major exploration and development formation in the southern Sichuan Basin.The Long1 1 Sub-member is divided into Long 1 1 1 , Long 1 1 2 , Long 1 1 3 , and Long 1 1 4 layers from bottom to top.The Long 1 1 1 to Long 1 1 2 layers have the best production results at present.Therefore, we selected the cores from the Long 1 1 1 to Long 1 1 2 layers as the experimental samples.A core with a diameter of 2.5 mm was drilled along the bedding direction.Then, the Brazilian splitting method was used to create a fracture in the core.Subsequently, the cores were laid flat after the fractures were filled with proppant quantitatively.Finally, the cores were covered with thermal shrinkable film, and fractures and proppant were fixed.In this experiment, the proppant concentration was 2.0 kg/m 3 , and the fracture width after proppant placement was 2.0 mm.The concentration error of proppant placement is less than 0.5%.

Experimental Fluid
The slickwater provided by the oil company was used as the experimental fluid in this study.

Experimental Unit and Process
Previously, we established an experimental method to test the stress sensitivity of artificial fractures in shale [18].To further study the mechanisms of stress sensitivity on artificial fracture conductivity in the flowback stage, we have upgraded the experimental unit and methods.The new experimental unit mainly includes the physical modeling system of core holding and proppant backflow, ISCO pump, intermediate container, pressure acquisition system, flow rate acquisition system, and back pressure control system (Figure 1).

Core samples
The Wufeng Formation to Long 11 Sub-member is currently the major exploration and development formation in the southern Sichuan Basin.The Long11 Sub-member is divided into Long 11 1 , Long 11 2 , Long 11 3 , and Long 11 4 layers from bottom to top.The Long 11 1 to Long 11 2 layers have the best production results at present.Therefore, we selected the cores from the Long 11 1 to Long 11 2 layers as the experimental samples.A core with a diameter of 2.5 mm was drilled along the bedding direction.Then, the Brazilian splitting method was used to create a fracture in the core.Subsequently, the cores were laid flat after the fractures were filled with proppant quantitatively.Finally, the cores were covered with thermal shrinkable film, and fractures and proppant were fixed.In this experiment, the proppant concentration was 2.0 kg/m 3 , and the fracture width after proppant placement was 2.0 mm.The concentration error of proppant placement is less than 0.5%.

Experimental Fluid
The slickwater provided by the oil company was used as the experimental fluid in this study.

Experimental Unit and Process
Previously, we established an experimental method to test the stress sensitivity of artificial fractures in shale [18].To further study the mechanisms of stress sensitivity on artificial fracture conductivity in the flowback stage, we have upgraded the experimental unit and methods.The new experimental unit mainly includes the physical modeling system of core holding and proppant backflow, ISCO pump, intermediate container, pressure acquisition system, flow rate acquisition system, and back pressure control system (Figure 1). Figure 2 shows the independently developed physical modeling system of core holding and proppant backflow, which can simulate the long-term conductivity of artificial fractures in shale while collecting the backflow proppant, so as to calculate the backflow proppant ratio.There is a cavity at the exit of the traditional core holding system.This cavity is divided into three structures.The structure I is funnel-shaped, which collects the Figure 2 shows the independently developed physical modeling system of core holding and proppant backflow, which can simulate the long-term conductivity of artificial fractures in shale while collecting the backflow proppant, so as to calculate the backflow proppant ratio.There is a cavity at the exit of the traditional core holding system.This cavity is divided into three structures.The structure I is funnel-shaped, which collects the backflow proppant in the process of fracturing fluid flowback.Structure II is used as a flow channel.Structure III is an enlarged cavity, which traps the backflow proppant to ensure that the position of the proppant will not change greatly with the flow of fracturing fluid after it flows back and facilitates its collection and measurement after the experiment.The maximum pressure of the system is 70 MPa.The flow rate accuracy and the pressure accuracy are 0.5% FS.
backflow proppant in the process of fracturing fluid flowback.Structure II is used as a flow channel.Structure III is an enlarged cavity, which traps the backflow proppant to ensure that the position of the proppant will not change greatly with the flow of fracturing fluid after it flows back and facilitates its collection and measurement after the experiment.The maximum pressure of the system is 70 MPa.The flow rate accuracy and the pressure accuracy are 0.5% FS.It can be known from the field process parameters that the variable flow pressure test method can reflect the actual production process more accurately when the proppant concentration is higher than 1 kg/m 3 [16].Therefore, in this paper, the variable flow pressure method was adopted, and the confining pressure was used to simulate the overlying pressure, which was kept constant during the experiment.Back pressure was set at the exit of the core, and it was changed to realize the change of the effective stress on cores and simulate the change of different flow pressures in the production process.

Calculation of Fracture Conductivity
The internal structure of an artificial fracture can be regarded as a porous medium composed of proppant.The fracture conductivity can be calculated based on the upstream and downstream displacement pressure of the core sample, the flow rate of fluid through the core sample, fluid viscosity, core length, and core diameter.The calculation formula is: where,  k•d f is fracture conductivity, D•cm; Q is the flow rate of fluid through the core, cm 3 /s; µ is fluid viscosity under the test conditions, mPa•s; L is core length, cm; d is core diameter, cm; ΔP is difference between upstream and downstream pressure of the core, MPa.

Calculation of Backflow Proppant, Embedded Proppant, and Broken Proppant Ratios
After the experiment was completed, the core was taken out, and the collection part of the physical modeling system of proppant flowback was removed.After that, the cavity was flushed, and the backflow proppant was collected.The backflow proppant was put into the thermostat oven for drying and then weighed, and the backflow proppant ratio was calculated.Then, the core sample was cut slowly and put into the thermostat oven for drying.The proppant was brushed gently.After the unembedded proppant was collected, the embedded proppant was brushed down and weighed, and the embedded proppant It can be known from the field process parameters that the variable flow pressure test method can reflect the actual production process more accurately when the proppant concentration is higher than 1 kg/m 3 [16].Therefore, in this paper, the variable flow pressure method was adopted, and the confining pressure was used to simulate the overlying pressure, which was kept constant during the experiment.Back pressure was set at the exit of the core, and it was changed to realize the change of the effective stress on cores and simulate the change of different flow pressures in the production process.

Calculation of Fracture Conductivity
The internal structure of an artificial fracture can be regarded as a porous medium composed of proppant.The fracture conductivity can be calculated based on the upstream and downstream displacement pressure of the core sample, the flow rate of fluid through the core sample, fluid viscosity, core length, and core diameter.The calculation formula is: where η = k•d f is fracture conductivity, D•cm; Q is the flow rate of fluid through the core, cm 3 /s; µ is fluid viscosity under the test conditions, mPa•s; L is core length, cm; d is core diameter, cm; ∆P is difference between upstream and downstream pressure of the core, MPa.

Calculation of Backflow Proppant, Embedded Proppant, and Broken Proppant Ratios
After the experiment was completed, the core was taken out, and the collection part of the physical modeling system of proppant flowback was removed.After that, the cavity was flushed, and the backflow proppant was collected.The backflow proppant was put into the thermostat oven for drying and then weighed, and the backflow proppant ratio was calculated.Then, the core sample was cut slowly and put into the thermostat oven for drying.The proppant was brushed gently.After the unembedded proppant was collected, the embedded proppant was brushed down and weighed, and the embedded proppant ratio was calculated.Finally, after all the proppant was put on the screen of 120 mesh and shaken for 5 min, the broken proppant was collected and weighed, and the broken proppant ratio was calculated (Table 1).

Parameter Definition Formula
Backflow proppant ratio Percentage of backflow proppant Broken proppant ratio Percentage of broken proppant Note: α is the backflow proppant ratio, %; β is the broken proppant ratio, %; γ is the embedded proppant ratio, %; m 1 is the mass of proppant in fractures, g; m 2 is the mass of backflow proppant, g; m 3 is the mass of broken proppant, g; m 4 is the mass of embedded proppant, g.

Effect of Effective Stresses
Based on the new evaluation method, we studied the variation characteristics of longterm fracture conductivity under different effective stresses and quantitatively evaluated the backflow proppant ratio, broken proppant ratio, and embedded proppant ratio under different stress conditions.To research the variation characteristics of fracture conductivity at different effective stresses, five groups of long-term fracture conductivity experiments were carried out by setting the confining pressure at 30.0 MPa to simulate the overlying pressure and the flow pressure at 0, 5.0, 10.0, 15.0, and 20.0 MPa, corresponding to effective stress of 30.0, 25.0, 20.0, 15.0, and 10.0 MPa, respectively.Figure 3 shows the change in the flow conductivity of artificial fractures in shale over time at different effective stresses.The long-term fracture conductivity drops quickly in the early stage and then slowly, for a large amount of proppant migrates in the early stage.The cores before and after the experiment at the effective stress of 10.0 MPa were CT scanned (see Figure 4).It was found that proppant was obviously absent at the edge of the core after the experiment, indicating that proppant flows back with the flow of fracturing fluid.The proppant at the edge of the core sample flows back to the backflow cavity of the device under the action of lateral drag force (see Figure 5).The same phenomenon was also observed in the stress sensitivity experiments in the previous research conducted by Chen [18].
shaken for 5 min, the broken proppant was collected and weighed, and the broken prop pant ratio was calculated (Table 1).Note: α is the backflow proppant ratio, %; β is the broken proppant ratio, %; γ is the embedde proppant ratio, %; m 1 is the mass of proppant in fractures, g; m 2 is the mass of backflow proppan g; m 3 is the mass of broken proppant, g; m 4 is the mass of embedded proppant, g.

Effect of Effective Stresses
Based on the new evaluation method, we studied the variation characteristics of long term fracture conductivity under different effective stresses and quantitatively evaluated the backflow proppant ratio, broken proppant ratio, and embedded proppant ratio unde different stress conditions.To research the variation characteristics of fracture conductiv ity at different effective stresses, five groups of long-term fracture conductivity experi ments were carried out by setting the confining pressure at 30.0 MPa to simulate the over lying pressure and the flow pressure at 0, 5.0, 10.0, 15.0, and 20.0 MPa, corresponding t effective stress of 30.0, 25.0, 20.0, 15.0, and 10.0 MPa, respectively.Figure 3 shows th change in the flow conductivity of artificial fractures in shale over time at different effec tive stresses.The long-term fracture conductivity drops quickly in the early stage and then slowly, for a large amount of proppant migrates in the early stage.The cores before and after the experiment at the effective stress of 10.0 MPa were CT scanned (see Figure 4).I was found that proppant was obviously absent at the edge of the core after the experiment indicating that proppant flows back with the flow of fracturing fluid.The proppant at th edge of the core sample flows back to the backflow cavity of the device under the action of lateral drag force (see Figure 5).The same phenomenon was also observed in the stres sensitivity experiments in the previous research conducted by Chen [18].The calculation formula of the conductivity damage ratio is: where, ε is the damage ratio, dimensionless;  is the initial conductivity, D•cm;  is the conductivity under different effective stress, D•cm.
Figure 6 shows the damage ratio of the flow conductivity of the artificial fracture in shale at different effective stresses.When the effective stress is 10.0 MPa, the damage ratio of fracture conductivity is only 87.92%.After the effective stress exceeds 15.0 MPa, the damage ratio rises sharply.As the effective stress rises to 25.0 MPa, the damage ratio rises to 93.45%.With the further increase in the effective stress, the damage ratio is unchanged.The calculation formula of the conductivity damage ratio is: where, ε is the damage ratio, dimensionless;  is the initial conductivity, D•cm;  is the conductivity under different effective stress, D•cm.
Figure 6 shows the damage ratio of the flow conductivity of the artificial fracture in shale at different effective stresses.When the effective stress is 10.0 MPa, the damage ratio of fracture conductivity is only 87.92%.After the effective stress exceeds 15.0 MPa, the damage ratio rises sharply.As the effective stress rises to 25.0 MPa, the damage ratio rises to 93.45%.With the further increase in the effective stress, the damage ratio is unchanged.The calculation formula of the conductivity damage ratio is: where ε is the damage ratio, dimensionless; η 0 is the initial conductivity, D•cm; η i is the conductivity under different effective stress, D•cm. Figure 6 shows the damage ratio of the flow conductivity of the artificial fracture in shale at different effective stresses.When the effective stress is 10.0 MPa, the damage ratio of fracture conductivity is only 87.92%.After the effective stress exceeds 15.0 MPa, the damage ratio rises sharply.As the effective stress rises to 25.0 MPa, the damage ratio rises to 93.45%.With the further increase in the effective stress, the damage ratio is unchanged.
To further discuss the influence of proppant migration, fragmentation, and embedment on fracture conductivity, the backflow, embedded, and broken proppant were collected and screened after the experiment, and the broken proppant ratio, embedded proppant ratio and backflow proppant ratio at different effective stresses were calculated, seeing Figure 7.With the increase in the effective stress, the amount of backflow proppant decreases, while the fragmentation and embedment degrees increase greatly.When the effective stress is 10.0 MPa, the proppant mainly suffers plastic deformation, and the fragmentation degree and the embedment degree are lower (embedded proppant ratio 8.43% and broken proppant ratio 3.95%).However, it still can act as a better support.The backflow proppant ratio is higher (20.79%), but the fracture compaction degree is lower, so the fracture conductivity remains higher (0.79 D•cm).After the effective stress reaches or exceeds the critical proppant breaking pressure, a large amount of proppant begins to break and the broken proppant ratio rises quickly.When the effective stress reaches 30.0 MPa, the embedded proppant ratio is 22.79%, the broken proppant ratio is 14.54%, and the support effect of the proppant weakens significantly.The backflow proppant ratio decreases greatly (5.14%), but fracture compaction is obvious due to high effective stress, so the decreasing amplitude of the fracture conductivity is larger.Eventually, the fracture conductivity is only 0.29 D•cm.To further discuss the influence of proppant migration, fragmentation, and embed ment on fracture conductivity, the backflow, embedded, and broken proppant were col lected and screened after the experiment, and the broken proppant ratio, embedded prop pant ratio and backflow proppant ratio at different effective stresses were calculated, see ing Figure 7.With the increase in the effective stress, the amount of backflow proppan decreases, while the fragmentation and embedment degrees increase greatly.When th effective stress is 10.0 MPa, the proppant mainly suffers plastic deformation, and the frag mentation degree and the embedment degree are lower (embedded proppant ratio 8.43% and broken proppant ratio 3.95%).However, it still can act as a better support.The back flow proppant ratio is higher (20.79%), but the fracture compaction degree is lower, so the fracture conductivity remains higher (0.79 D•cm).After the effective stress reaches or ex ceeds the critical proppant breaking pressure, a large amount of proppant begins to break and the broken proppant ratio rises quickly.When the effective stress reaches 30.0 MPa the embedded proppant ratio is 22.79%, the broken proppant ratio is 14.54%, and the sup port effect of the proppant weakens significantly.The backflow proppant ratio decrease greatly (5.14%), but fracture compaction is obvious due to high effective stress, so the de creasing amplitude of the fracture conductivity is larger.Eventually, the fracture conduc tivity is only 0.29 D•cm.To further discuss the influence of proppant migration, fragmentation, and embed ment on fracture conductivity, the backflow, embedded, and broken proppant were col lected and screened after the experiment, and the broken proppant ratio, embedded prop pant ratio and backflow proppant ratio at different effective stresses were calculated, see ing Figure 7.With the increase in the effective stress, the amount of backflow proppan decreases, while the fragmentation and embedment degrees increase greatly.When th effective stress is 10.0 MPa, the proppant mainly suffers plastic deformation, and the frag mentation degree and the embedment degree are lower (embedded proppant ratio 8.43% and broken proppant ratio 3.95%).However, it still can act as a better support.The back flow proppant ratio is higher (20.79%), but the fracture compaction degree is lower, so the fracture conductivity remains higher (0.79 D•cm).After the effective stress reaches or ex ceeds the critical proppant breaking pressure, a large amount of proppant begins to break and the broken proppant ratio rises quickly.When the effective stress reaches 30.0 MPa the embedded proppant ratio is 22.79%, the broken proppant ratio is 14.54%, and the sup port effect of the proppant weakens significantly.The backflow proppant ratio decrease greatly (5.14%), but fracture compaction is obvious due to high effective stress, so the de creasing amplitude of the fracture conductivity is larger.Eventually, the fracture conduc tivity is only 0.29 D•cm.

Effect of the Choke Management System
When different chokes are adopted, the effective stress on fractures is different.The smaller the choke size, the higher the bottom hole flow pressure, and the lower the effective stress on fractures.With the increase in the choke size, the bottom hole flow pressure decreases gradually, and the effective stress on fractures increases gradually.The process of gradually increasing and decreasing the choke size is simulated by gradually increasing and decreasing the effective stress.

Step-by-Step Enlargement of the Choke Size
The confining pressure was fixed at 30.0 MPa, and the flow pressure was gradually decreased from 20.0 MPa to 0 MPa with an interval of 5.0 MPa, whose corresponding effective stress was 10.0, 15.0, 20.0, 25.0, and 30.0 MPa.The displacement at each pressure point lasted for about 720 min.
Figure 8 shows the variation characteristics of fracture conductivity and effective fracture width with the increase in the choke size.In the initial stage, the effective stress on fractures is lower and the immobilization of the proppant to fracture plane is weaker, so the proppant is carried out of fractures by fracturing fluid.Under the action of effective stress, the fractures close and the effective fracture width decreases, leading to a quick decrease in the fracture conductivity.When the effective stress rises to 15.0 MPa, the effective fracture width decreases from 2.0 mm to 0.65 mm, and the fracture conductivity decreases from 1.93 D•cm to 0.24 D•cm.With the increase in the effective stress, the immobilization of the proppant to fracture plane becomes stronger gradually, so little proppant can flow back, and thus fragmentation and embedment increase.As a result, the decreasing amplitudes of effective fracture width and fracture conductivity decrease gradually.When the effective stress rises to 25.0 MPa, the effective fracture width is 0.41 mm and the fracture conductivity is only 0.11 D•cm.
tive stress on fractures.With the increase in the choke size, the bottom hole flow pressur decreases gradually, and the effective stress on fractures increases gradually.The proces of gradually increasing and decreasing the choke size is simulated by gradually increasing and decreasing the effective stress.

Step-by-Step Enlargement of the Choke Size
The confining pressure was fixed at 30.0 MPa, and the flow pressure was gradually decreased from 20.0 MPa to 0 MPa with an interval of 5.0 MPa, whose corresponding ef fective stress was 10.0, 15.0, 20.0, 25.0, and 30.0 MPa.The displacement at each pressur point lasted for about 720 min.
Figure 8 shows the variation characteristics of fracture conductivity and effectiv fracture width with the increase in the choke size.In the initial stage, the effective stres on fractures is lower and the immobilization of the proppant to fracture plane is weaker so the proppant is carried out of fractures by fracturing fluid.Under the action of effectiv stress, the fractures close and the effective fracture width decreases, leading to a quick decrease in the fracture conductivity.When the effective stress rises to 15.0 MPa, the ef fective fracture width decreases from 2.0 mm to 0.65 mm, and the fracture conductivity decreases from 1.93 D•cm to 0.24 D•cm.With the increase in the effective stress, the immo bilization of the proppant to fracture plane becomes stronger gradually, so little proppan can flow back, and thus fragmentation and embedment increase.As a result, the decreas ing amplitudes of effective fracture width and fracture conductivity decrease gradually When the effective stress rises to 25.0 MPa, the effective fracture width is 0.41 mm and th fracture conductivity is only 0.11 D•cm.It should be noted that only one core was adopted for simulation in the experimen of increasing choke size step by step.The displacement pressure difference in the experi ment rose quickly from 0.71 MPa to 3.28 MPa with the increase in the effective stress However, in the fracture conductivity experiment of multiple cores at different effectiv stresses (Section 2.1), the displacement pressure difference rose slowly from 0.23 MPa to It should be noted that only one core was adopted for simulation in the experiment of increasing choke size step by step.The displacement pressure difference in the experiment rose quickly from 0.71 MPa to 3.28 MPa with the increase in the effective stress.However, in the fracture conductivity experiment of multiple cores at different effective stresses (Section 2.1), the displacement pressure difference rose slowly from 0.23 MPa to 1.23 MPa (see Figure 9).In two experiments, the displacement pressure difference increases.When the effective stress is low, the displacement pressure difference in the experiment of increasing choke size step by step is close to the value in the experiment with different effective stresses.With the increase in the effective stress, the displacement pressure difference in both experiments increases, but the increasing amplitude in the experiment of increasing choke size step by step is larger, so at high effective stress, the displacement pressure difference in the two experiments is obviously different.The main reason is that, when only one core is adopted in the experiment, the damage to the core is accumulated, which means the damage to the core in the stage of low effective stress is accumulated to the damage at high effective stress.Furthermore, the displacement time is longer, and the amount of displacement fluid is greater.As a result, the fracture surface and proppant are immersed more, and the core is damaged more seriously.In the fracture conductivity experiment of multiple cores at different effective stresses, each core feeds back only the damage under one certain pressure condition.
different effective stresses.With the increase in the effective stress, the displacement pres sure difference in both experiments increases, but the increasing amplitude in the experi ment of increasing choke size step by step is larger, so at high effective stress, the displace ment pressure difference in the two experiments is obviously different.The main reason is that, when only one core is adopted in the experiment, the damage to the core is accu mulated, which means the damage to the core in the stage of low effective stress is accu mulated to the damage at high effective stress.Furthermore, the displacement time i longer, and the amount of displacement fluid is greater.As a result, the fracture surfac and proppant are immersed more, and the core is damaged more seriously.In the fractur conductivity experiment of multiple cores at different effective stresses, each core feed back only the damage under one certain pressure condition.

Step-by-Step Reduction in the Choke Size
The confining pressure was fixed at 30.0 MPa, and the flow pressure was increased from 0 MPa to 30.0 MPa step by step with an interval of 5.0 MPa, whose corresponding effective stress was 30.0, 25.0, 20.0, 15.0, and 10.0 MPa.The displacement at each pressur point lasted for about 720 min.
Figure 10 shows the variation characteristics of fracture conductivity in the proces of decreasing choke size step by step.In the initial stage, the effective stress is 30 MPa, th backflow degree of the proppant is weaker, the fragmentation degree and the embedmen degree are higher, and most fractures are closed, so the fracture conductivity decrease quickly from 9.46 D•cm to 0.46 D•cm.After 755 min, the effective stress is decreased to 2 MPa by regulating the flow pressure, and the fracture conductivity is recovered to 1.0 D•cm.Afterwards, the fracture conductivity decreases slowly to 0.28 D•cm in the displace ment process.Later, the effective stress is decreased to 20, 15, and 10 MPa at the momen of 1570, 2290, and 3055 min, respectively, and the fracture conductivity increases to 1.28 1.40, and 1.30 D•cm, correspondingly.As the displacement continues, the fracture conduc tivity decreases slowly to about 0.50 D•cm.The reason for this phenomenon is that, with the decrease the effective stress, fractures are opened again, and thus the fracture conduc tivity increases.And then, as proppant is carried out of fractures, the support effect be comes weak, so the fractures close again and the fracture conductivity decreases again.I is indicated that, in the process of decreasing choke size step by step, fractures receiv

Step-by-Step Reduction in the Choke Size
The confining pressure was fixed at 30.0 MPa, and the flow pressure was increased from 0 MPa to 30.0 MPa step by step with an interval of 5.0 MPa, whose corresponding effective stress was 30.0, 25.0, 20.0, 15.0, and 10.0 MPa.The displacement at each pressure point lasted for about 720 min.
Figure 10 shows the variation characteristics of fracture conductivity in the process of decreasing choke size step by step.In the initial stage, the effective stress is 30 MPa, the backflow degree of the proppant is weaker, the fragmentation degree and the embedment degree are higher, and most fractures are closed, so the fracture conductivity decreases quickly from 9.46 D•cm to 0.46 D•cm.After 755 min, the effective stress is decreased to 20 MPa by regulating the flow pressure, and the fracture conductivity is recovered to 1.09 D•cm.Afterwards, the fracture conductivity decreases slowly to 0.28 D•cm in the displacement process.Later, the effective stress is decreased to 20, 15, and 10 MPa at the moment of 1570, 2290, and 3055 min, respectively, and the fracture conductivity increases to 1.28, 1.40, and 1.30 D•cm, correspondingly.As the displacement continues, the fracture conductivity decreases slowly to about 0.50 D•cm.The reason for this phenomenon is that, with the decrease the effective stress, fractures are opened again, and thus the fracture conductivity increases.And then, as proppant is carried out of fractures, the support effect becomes weak, so the fractures close again and the fracture conductivity decreases again.It is indicated that, in the process of decreasing choke size step by step, fractures receive more damage of stress sensitivity in the early stage, and later when the effective stress is decreased, the fracture conductivity recovers gradually but the recovery capacity is extremely limited.more damage of stress sensitivity in the early stage, and later when the effective stress is decreased, the fracture conductivity recovers gradually but the recovery capacity is extremely limited.

Comparison of Different Choke Management Systems
The results of two groups of fracture conductivity experiments are normalized to further compare the change characteristics of long-term conductivity under different choke management systems (see Figure 11).The calculation formula of the normalized conductivity is: where, ̅ is the normalized conductivity, dimensionless;  is the fracture conductivity at different times, D•cm;  is the maximum fracture conductivity, D•cm.

Comparison of Different Choke Management Systems
The results of two groups of fracture conductivity experiments are normalized to further compare the change characteristics of long-term conductivity under different choke management systems (see Figure 11).The calculation formula of the normalized conductivity is: where η i is the normalized conductivity, dimensionless; η i is the fracture conductivity at different times, D•cm; η max is the maximum fracture conductivity, D•cm.
Processes 2023, 11, x FOR PEER REVIEW 10 of 14 more damage of stress sensitivity in the early stage, and later when the effective stress is decreased, the fracture conductivity recovers gradually but the recovery capacity is extremely limited.

Comparison of Different Choke Management Systems
The results of two groups of fracture conductivity experiments are normalized to further compare the change characteristics of long-term conductivity under different choke management systems (see Figure 11).The calculation formula of the normalized conductivity is: where, ̅ is the normalized conductivity, dimensionless;  is the fracture conductivity at different times, D•cm;  is the maximum fracture conductivity, D•cm.The damage to fractures accumulates and increases gradually as the choke size (the effective stress) increases.When the effective stress is increased to 30.0 MPa, the normalized conductivity is only 0.10.When the choke size is decreased step by step, the normalized fracture conductivity decreases quickly to 0.04 at the effective stress of 30.0 MPa.With the decrease in the effective stress, the normalized conductivity increases quickly and then decreases slowly.When the effective stress is 10.0 MPa, the normalized conductivity is only 0.05, which is much lower than the value in the mode of increasing choke size step by step.To sum up, if the objective external conditions are not taken into consideration, as for the same reservoir, the reservoir damage is increased gradually in the flowback test mode of increasing choke size step by step, but the fracture conductivity is always higher than the value in the mode of decreasing choke size.In the mode of decreasing choke step by step, the initial reservoir damage is stronger, and later with the decrease in the effective stress, the fracture conductivity can be recovered in a way, but the recovery capacity is limited.As the production goes on, the fracture conductivity will continue to decrease.
Two choke size adjustment modes are obviously different in the changing trend of the conductivity damage ratio caused by fracture stress sensitivity.Figure 12 shows that, in the flowback test mode of increasing choke size step by step, the damage ratio of fracture conductivity is 78% when the initial effective stress is 10.0 MPa.As the effective stress rises to 20.0-25.0MPa, the damage ratio increases to about 90%.With the further increase in the effective stress, the damage ratio of fracture conductivity is basically unchanged.The process of increasing choke size step by step is the increasing process of effective stress, and its damage to fractures is accumulated and increased gradually.In the early stage, the effective stress is low, so the backflow of proppant leads to a quick increase in damage ratio.In the late stage, the effective stress is high and proppant fragmentation and embedment are dominant, so the increasing amplitude of the damage ratio is not large.In the mode of decreasing choke size step by step, the damage ratio of fracture conductivity is as high as 96% when the initial effective stress is 30 MPa.As the effective stress is decreased to 20 MPa, the damage ratio decreases to about 94%.With the further decrease in the effective stress, the damage ratio is basically maintained at 94% and can be hardly recovered.In the early stage, the effective stress is high enough to bring unrecoverable damage to reservoirs.With the decrease in the effective stress in the late stage, the fracture conductivity recovers slightly in a short period, but it will decrease quickly.
Processes 2023, 11, x FOR PEER REVIEW 11 of 14 The damage to fractures accumulates and increases gradually as the choke size (the effective stress) increases.When the effective stress is increased to 30.0 MPa, the normalized conductivity is only 0.10.When the choke size is decreased step by step, the normalized fracture conductivity decreases quickly to 0.04 at the effective stress of 30.0 MPa.With the decrease in the effective stress, the normalized conductivity increases quickly and then decreases slowly.When the effective stress is 10.0 MPa, the normalized conductivity is only 0.05, which is much lower than the value in the mode of increasing choke size step by step.To sum up, if the objective external conditions are not taken into consideration, as for the same reservoir, the reservoir damage is increased gradually in the flowback test mode of increasing choke size step by step, but the fracture conductivity is always higher than the value in the mode of decreasing choke size.In the mode of decreasing choke step by step, the initial reservoir damage is stronger, and later with the decrease in the effective stress, the fracture conductivity can be recovered in a way, but the recovery capacity is limited.As the production goes on, the fracture conductivity will continue to decrease.
Two choke size adjustment modes are obviously different in the changing trend of the conductivity damage ratio caused by fracture stress sensitivity.Figure 12 shows that, in the flowback test mode of increasing choke size step by step, the damage ratio of fracture conductivity is 78% when the initial effective stress is 10.0 MPa.As the effective stress rises to 20.0-25.0MPa, the damage ratio increases to about 90%.With the further increase in the effective stress, the damage ratio of fracture conductivity is basically unchanged.The process of increasing choke size step by step is the increasing process of effective stress, and its damage to fractures is accumulated and increased gradually.In the early stage, the effective stress is low, so the backflow of proppant leads to a quick increase in damage ratio.In the late stage, the effective stress is high and proppant fragmentation and embedment are dominant, so the increasing amplitude of the damage ratio is not large.In the mode of decreasing choke size step by step, the damage ratio of fracture conductivity is as high as 96% when the initial effective stress is 30 MPa.As the effective stress is decreased to 20 MPa, the damage ratio decreases to about 94%.With the further decrease in the effective stress, the damage ratio is basically maintained at 94% and can be hardly recovered.In the early stage, the effective stress is high enough to bring unrecoverable damage to reservoirs.With the decrease in the effective stress in the late stage, the fracture conductivity recovers slightly in a short period, but it will decrease quickly.To compare the characteristics of proppant backflow, embedment, and fragmentation under different choke management systems, the backflow proppant ratio, broken proppant ratio, and embedded proppant ratio were statistically calculated and analyzed after each group of experiments (see Figure 13).In the process of increasing choke size, the effective stress on fractures is lower in the initial stage, the proppant fragmentation and embedment are weaker, and the immobilization of proppant is also weaker, so proppant tends to flow back.The backflow proppant is mainly unbroken, and the backflow proppant ratio is 7.90%.In the process of decreasing choke size step by step, the effective stress on fractures is higher in the initial stage, so the proppant can hardly flow and fragmentation and embedment are dominant.Subsequently, as the effective stress decreases, the fracture opens, and the proppant begins to migrate.The migration degree is high, up to 12.17%, because the proppant has been broken.The displacement time is long, and the amount of displacement fluid and the effective stress are basically similar.Hence, the broken proppant ratio and embedded proppant ratio in the two choke adjustment modes are relatively close.It should be noted that in the experiment of increasing choke size step by step, the broken proppant is mainly retained in fractures.In the experiment of decreasing choke size step by step, the broken proppant is mainly in the "cavity" of the holder, which means it flows back from fractures.
To compare the characteristics of proppant backflow, embedment, and fragmentation under different choke management systems, the backflow proppant ratio, broken proppant ratio, and embedded proppant ratio were statistically calculated and analyzed after each group of experiments (see Figure 13).In the process of increasing choke size, the effective stress on fractures is lower in the initial stage, the proppant fragmentation and embedment are weaker, and the immobilization of proppant is also weaker, so proppant tends to flow back.The backflow proppant is mainly unbroken, and the backflow proppant ratio is 7.90%.In the process of decreasing choke size step by step, the effective stress on fractures is higher in the initial stage, so the proppant can hardly flow and fragmentation and embedment are dominant.Subsequently, as the effective stress decreases, the fracture opens, and the proppant begins to migrate.The migration degree is high, up to 12.17%, because the proppant has been broken.The displacement time is long, and the amount of displacement fluid and the effective stress are basically similar.Hence, the broken proppant ratio and embedded proppant ratio in the two choke adjustment modes are relatively close.It should be noted that in the experiment of increasing choke size step by step, the broken proppant is mainly retained in fractures.In the experiment of decreasing choke size step by step, the broken proppant is mainly in the "cavity" of the holder, which means it flows back from fractures.

Conclusions
In this paper, we proposed a new method for evaluating the flow conductivity of artificial fractures in shale and developed a new type of core holder which can quantitatively evaluate the amount of proppant backflow, embedment, and fragmentation.In addition, the mechanisms of stress sensitivity on fracture conductivity under different choke adjustment modes were revealed.The main conclusions are as follows.
(1) The proppant backflow is dominant and proppant fragmentation and embedment degrees are low when the effective stress is lower.After the effective stress exceeds 15.0 MPa, proppant backflow reduces, and fragmentation and embedment degrees increase.
(2) In the mode of increasing choke size step by step, with the increase in the effective stress, the damage to fracture conductivity increases gradually.In the mode of decreasing choke size step by step, the effective stress is the largest and the damage ratio of fracture conductivity is the highest at the initial moment.With the gradual decrease in the effective stress, fracture conductivity is recovered in a way, but the recovery capacity is limited.And as production goes on, fracture conductivity will continue to decrease.
(3) The broken proppant ratio and embedded proppant ratio are basically the same in both modes.In the mode of increasing choke size step by step, the backflow proppant

Conclusions
In this paper, we proposed a new method for evaluating the flow conductivity of artificial fractures in shale and developed a new type of core holder which can quantitatively evaluate the amount of proppant backflow, embedment, and fragmentation.In addition, the mechanisms of stress sensitivity on fracture conductivity under different choke adjustment modes were revealed.The main conclusions are as follows.
(1) The proppant backflow is dominant and proppant fragmentation and embedment degrees are low when the effective stress is lower.After the effective stress exceeds 15.0 MPa, proppant backflow reduces, and fragmentation and embedment degrees increase.
(2) In the mode of increasing choke size step by step, with the increase in the effective stress, the damage to fracture conductivity increases gradually.In the mode of decreasing choke size step by step, the effective stress is the largest and the damage ratio of fracture conductivity is the highest at the initial moment.With the gradual decrease in the effective stress, fracture conductivity is recovered in a way, but the recovery capacity is limited.And as production goes on, fracture conductivity will continue to decrease.
(3) The broken proppant ratio and embedded proppant ratio are basically the same in both modes.In the mode of increasing choke size step by step, the backflow proppant ratio is lower, the broken proppant is mainly retained in fractures and the damage ratio of fracture conductivity is lower.In the mode of decreasing choke size step by step, most of the broken proppant flows back from fractures and the damage to fracture conductivity is greater.

Figure 1 .
Figure 1.Experimental unit for long-term fracture conductivity.

Figure 1 .
Figure 1.Experimental unit for long-term fracture conductivity.

Figure 2 .
Figure 2. The physical modeling system of core holding and proppant backflow and its photo.(a) Core holder; (b) top view of the proppant collection device; (c) side view.

Figure 2 .
Figure 2. The physical modeling system of core holding and proppant backflow and its photo.(a) Core holder; (b) top view of the proppant collection device; (c) side view.

Figure 3 .
Figure 3.Long-term conductivity of artificial fracture at different effective stresses.

Figure 3 .
Figure 3.Long-term conductivity of artificial fracture at different effective stresses.

Figure 4 .
Figure 4. Proppant migration monitored by CT scanning (confining pressure 30 MPa; flow pressure 20 Mpa; flow direction from left to right; there is much less proppant at the exit after the experiment).(a) Before the experiment.(b) After the experiment.

Figure 5 .
Figure 5. Distribution of proppant on fracture surface under different effective stress (The confining pressure is 30 MPa, and the flow pressures in the left and right figures are 20 MPa and 10 MPa, respectively).

Figure 4 .
Figure 4. Proppant migration monitored by CT scanning (confining pressure 30 MPa; flow pressure 20 Mpa; flow direction from left to right; there is much less proppant at the exit after the experiment).(a) Before the experiment.(b) After the experiment.

Figure 4 .
Figure 4. Proppant migration monitored by CT scanning (confining pressure 30 MPa; flow pressure 20 Mpa; flow direction from left to right; there is much less proppant at the exit after the experiment).(a) Before the experiment.(b) After the experiment.

Figure 5 .
Figure 5. Distribution of proppant on fracture surface under different effective stress (The confining pressure is 30 MPa, and the flow pressures in the left and right figures are 20 MPa and 10 MPa, respectively).

Figure 5 .
Figure 5. Distribution of proppant on fracture surface under different effective stress (The confining pressure is 30 MPa, and the flow pressures in the left and right figures are 20 MPa and 10 MPa, respectively).

Processes 2023 , 1 Figure 6 .
Figure 6.Damage ratio of fracture conductivity at different effective stresses.

Figure 6 .
Figure 6.Damage ratio of fracture conductivity different effective stresses.

Figure 6 .
Figure 6.Damage ratio of fracture conductivity at different effective stresses.

Figure 8 .
Figure 8. Fracture conductivity vs. time in the process of choke size increasing step by step.

Figure 8 .
Figure 8. Fracture conductivity vs. time in the process of choke size increasing step by step.

Figure 9 .
Figure 9.Comparison of the displacement pressure difference between the experiment of choke siz increasing step by step and the experiment at different effective stresses.

Figure 9 .
Figure 9.Comparison of the displacement pressure difference between the experiment of choke size increasing step by step and the experiment at different effective stresses.

Figure 10 .
Figure 10.Fracture conductivity vs. time in the process of decreasing choke size step by step.

Figure 11 .
Figure 11.Conductivity vs. time under different choke management systems.

Figure 10 .
Figure 10.Fracture conductivity vs. time in the process of decreasing choke size step by step.

Figure 10 .
Figure 10.Fracture conductivity vs. time in the process of decreasing choke size step by step.

Figure 11 .
Figure 11.Conductivity vs. time under different choke management systems.Figure 11.Conductivity vs. time under different choke management systems.

Figure 11 .
Figure 11.Conductivity vs. time under different choke management systems.Figure 11.Conductivity vs. time under different choke management systems.

Figure 12 .
Figure 12.Conductivity damage ratio under different choke management systems.Figure 12. Conductivity damage ratio under different choke management systems.

Figure 12 .
Figure 12.Conductivity damage ratio under different choke management systems.Figure 12. Conductivity damage ratio under different choke management systems.

Figure 13 .
Figure 13.Influence of different choke management systems on support effect of proppant.

Figure 13 .
Figure 13.Influence of different choke management systems on support effect of proppant.