Study on the conductivity of proppant in shale reservoir

At present, in the process of developing shale reservoirs by hydraulic fracturing, proppants play a critical role in the overall fracturing effect. Therefore, accurately evaluating the conductivity of different proppants determines the development effect of shale reservoirs. In this paper, proppant screening is first carried out, and the conductivity of four different proppants under laying concentration and closing pressure is studied, including 10-20 mesh quartz sand proppants with non-standard particle size, and the influence of different factors on the embedding degree is analyzed. It is concluded that the bearing capacity of ceramsite proppant is usually 2-3 times stronger than that of quartz sand. The larger the particle size of quartz sand proppant is and the higher the concentration of sand is, the stronger the conductivity is. When the closed pressure of large-size quartz sand is less than 30 MPa, the laying concentration of 14 kg/m2 can obtain higher conductivity, and when it is greater than 30 MPa, 12 kg/m2 is more suitable for field application. The ceramsite proppant has been on the rise with the increase of closing pressure and sand concentration. The embedding depth gradually increases with the increase of closing pressure and the decrease of sand concentration. The embedding depth of shale is greater than that of sandstone, and the flow conductivity of proppant is usually lower than that of sandstone. According to the experimental results, large-size quartz sand has strong conductivity, but it is not easy to migrate and has poor bearing capacity. Therefore, large-size quartz sand proppant can be used in the low-pressure part near the well, supplemented by small-size quartz sand (40-70 mesh) to obtain better fracturing results. This study provides some technical guidance for shale reservoir development and shale fracturing dessert identification.


Introduction
At present, the commonly used proppants are mainly divided into quartz sand proppants and ceramsite proppants, and different types of proppants are usually selected according to the different geological conditions of the fracturing site.In this study, by comparing and analyzing the characteristics of different proppants such as conductivity, the proppants are optimized, and then the shale fracturing development is guided accordingly.
. In 1994, Barree et al. studied the migration velocity of proppant, and thought that when the ratio was less than 10%, the migration velocity of proppant and liquid was almost equal, and when it was more than 10%, the liquid velocity was greater than the migration velocity of proppant [3] .In 1995, Xu and Zhou studied and analyzed the influence of various factors on the settling rate of proppant, including fracturing fluid, proppant type, and pipeline type and size [4] .In 2008, Palisch et al. obtained that the smaller the proppant particle size was, the farther the displacement distance was [5] .In 2010, KING and others put forward the influence of fracture width, proppant properties, and density on proppant migration results [6] .In 2013, Ding e obtained that the conductivity of the proppant decreased with the increase of pressure by simulating the bottom temperature and pressure, and the conductivity of ceramsite proppant was better than quartz sand at higher pressure.In 2014, Zhu et al. calculated the conductivity formula of shale reservoirs through numerical simulation, which reflected the conductivity more intuitively considering the influence of many factors [7][8] .In 2015, Bi et al. considered the influence of pressure change during the well shut-in.By simulating the well shut-in, it was concluded that the cyclic loading of stress led to the decrease of proppant strength, which in turn led to the increase of embedding degree and the decrease of conductivity [9] .In 2017, Peng pointed out that resin-coated sand can slow down the embedding degree of proppant and improve the conductivity, while the conductivity is relatively high when the closing pressure is low.In addition, the laying concentration of proppant has a certain influence on the embedding depth [10] .In 2018, Su analyzed the influence of proppant embedding through experiments and concluded that with the increase of closing pressure, the conductivity of proppant decreased obviously, and the conductivity of proppant with small particle size decreased slightly [11] .In 2020, Liu pointed out that the conductivity of ceramsite proppant is stronger than quartz sand and coated sand among the influencing factors of hydraulic fracturing support fracture in shale reservoirs.At the same time, under the condition of low closing pressure, the conductivity of 20-40 mesh ceramsite is the largest, and it is suggested to use a combined proppant when the closing pressure increases [12] .In 2022, Ma et al. proved that proppant laying can be divided into four stages, namely, early stage, middle stage, middle stage, and equilibrium stage.With the increase of displacement, the disturbance of the flow field becomes more obvious and the collision frequency of proppant particles becomes higher [13] .
According to the literature investigation, it can be seen that at present, the research on the influence of proppant conductivity mainly includes temperature, time, etc., but there is little research on factors such as paving concentration and closing pressure [14][15] .In this study, through the fracture conductivity testing instrument, the differences in conductivity of different types of proppants under different laying concentrations and closing pressures are compared, and the best conductivity conditions are determined.The embedding degree of proppants is studied, and the influence mechanism of proppant conductivity is further analyzed, to improve the conductivity of shale reservoirs after fracturing, thus effectively improving the reservoir exploitation efficiency and increasing economic benefits.

Experimental principles
The permeability of fracture can be reflected by the flow rate of gas seepage.After measuring the flow rate of gas at different inlet and outlet pressures, the conductivity of fracture can be determined by the Darcy formula of gas radial seepage.In this study, four kinds of proppants were selected, including 10-20 mesh quartz sand, 20-40 mesh quartz sand, 40-70 mesh quartz sand, and 20-40 mesh ceramsite.Among 10-20 mesh quartz sand, 10-20 mesh quartz sand accounts for 76.76%.Among 20-40 mesh quartz sand, 20-30 mesh quartz sand accounts for 83.25%, and 30-40 mesh quartz sand accounts for 15.5%.Among 40-70 mesh quartz sand, 40-60 mesh quartz sand accounts for 73.7%, and 60-80 mesh quartz sand accounts for 24.0%.Among 20-40 mesh ceramsite, the proportion of 20-30 mesh ceramsite is 72.95%, and the proportion of 30-40 mesh ceramsite is 26.57%.The particle size distribution of different proppants meets the experimental requirements (Figure 2).

Experimental Steps
1.The flow conductivity of the proppant is tested by cylinder specimen, and a certain weight of the proppant is evenly spread on the core surface wrapped with copper mesh to keep a single layer.The concentration of proppant is calculated and the concentration value is recorded in the table.
2. The upper pellet (hole downward) is placed above the lower pellet, and then the upper and lower pellets are placed in the center of the lower support plate of the testing machine.
3. Through the DLY-III fracture conductivity tester, the proppant conductivity under different closing pressures and laying concentrations is tested respectively.

Experimental results
The trend of conductivity under different proppant particle sizes and closing pressure is compared and analyzed, and the changing trend of conductivity with different influencing factors is clear.
It can be seen from the test results of 10-20 mesh quartz sand (Figure 3) that the conductivity of shale is lower than that of sandstone.With the increase of closing pressure, the conductivity shows a downward trend.When the closing pressure increases to 40 MPa, the downward trend of conductivity slows down with the increase of closing pressure.Compared with the same closing pressure, it can be seen that when the closing pressure is less than 30 MPa and the paving concentration is 14 kg/m 2 , the conductivity is the largest, and when it exceeds 30 MPa, the conductivity of each paving concentration has little difference.According to the test results of 20-40 quartz sand (Figure 4), with the increase of closing pressure, the conductivity shows a downward trend.With the increase of paving concentration, the conductivity tends to increase.However, when the closing pressure is 30 MPa, the conductivity of the sandstone reservoir with a paving concentration of 12 kg/m 2 is the strongest, while that of the shale reservoir with a paving concentration of 12 kg/m 2 and 14 kg/m 2 is similar.The main reason is that when the paving concentration reaches 14 kg/m 2 due to the increase in pressure, the porosity is smaller due to the higher paving concentration, and the quartz sand is blocked after being crushed, resulting in the decline of its conductivity.
Comparing the test results of 40-70 quartz sand (Figure 5), the changing trend of its conductivity is the same as that of 10-20.Generally speaking, the conductivity of sandstone and shale increases with the increase of laying concentration and decreases with the increase of closing pressure.The conductivity of sandstone is higher than that of shale.It can be seen from the test results of 20-40 mesh ceramsite (Figure 6) that with the increase of closing pressure, the conductivity of shale and sandstone has been declining, and it has become larger with the increase of laying concentration, so the laying concentration can be set at 14 kg/m 2 when choosing 20-40 mesh ceramsite proppant.Comparing the conductivity of different proppants under different laying concentrations and closing pressures (Figure 7), when the closing pressure is less than 20 MPa, the conductivity of 10-20 mesh quartz sand is the strongest.When the closing pressure exceeds 20 MPa, the conductivity of 20-40 mesh ceramsite proppants is the strongest, and the trend of shale and sandstone is almost the same.And with the increase of closing pressure, the gap of conductivity of quartz sand with different particle sizes gradually becomes smaller.When the particle size of the proppant is too small, there is little difference in conductivity between sandstone and shale.
The trend of other paving concentrations is generally consistent, and the conductivity of 10-20 mesh quartz sand is greater than that of 20-40 mesh quartz sand and 40-70 mesh quartz sand.However, with the increase of paving concentration, the conductivity of each proppant tends to increase in general, and the trend is generally consistent.The conductivity of quartz sand proppant decreases with the increase of closing pressure.When the closing pressure is less than 40 MPa, the larger the particle size of the proppant is, the stronger the conductivity is.When the closing pressure is greater than 40 MPa, the relative difference in conductivity among the three quartz sands gradually decreases.However, the flow conductivity of the ceramsite proppant is higher than that of quartz sand proppant at high closing pressure, so it can be concluded that ceramsite proppant has a stronger bearing capacity than quartz sand.
Therefore, according to the experimental results, for 10-20 mesh and 20-40 mesh quartz sand proppant, when the closing pressure is less than 30 MPa, the laying concentration should be set at 14 kg/m 2 .When the closing pressure is greater than 30 MPa, there is little difference between 12 kg/m 2 and 14 kg/m 2 , and even 12 kg/m 2 of 20-40 mesh quartz sand has higher conductivity.Therefore, considering factors such as cost and construction difficulty, the laying concentration should be set at 12 kg/m 2 .Others with small particle sizes have too small conductivity, so they need to be supplemented in combination with the site.In comparison between ceramsite and quartz sand, when the closing pressure is lower than 20 MPa, the 10-20 mesh quartz sand has stronger conductivity, and when it is higher than 20 MPa, the 20-40 mesh ceramsite proppant has stronger conductivity.The specific selection should be comprehensively analyzed in combination with the actual closing pressure and economic situation.
Moreover, according to the fracturing characteristics, the near-well zone usually has lower pressure and wider fractures.To obtain greater conductivity, large-particle proppant, such as 10-20 mesh quartz sand proppant, should be selected.As the fracture extends, the distance becomes farther and the pressure increases and the large-particle proppant is difficult to migrate, so it can be supplemented with smallerparticle 40-70 quartz sand proppant.

Study on the particle size distribution of proppant after pressure bearing
After 50 MPa closed pressure, the particle size distribution of three kinds of quartz sand is almost the same at various sand laying concentrations.The particle size distribution range is widened, and the minimum particle size is greater than 180 meshes.After 50 MPa closed pressure, the particle size distribution range of ceramsite becomes wider, and the minimum particle size is more than 140 meshes.According to the experimental results (Figure 8), quartz sand of 10-20 mesh is fractured after pressure, and the particle size becomes smaller, and the particle size of 10-20 mesh becomes smaller, and the particle size of 20-40 mesh becomes the main distribution interval.The main particle size of 20-40 mesh quartz sand has not changed after pressure, but a large number of 40-60 mesh particles have been produced.This part is analyzed as the reason for the decrease in conductivity when the laying concentration is 14 kg/m 2 .After the quartz sand with 40-70 mesh is under pressure, the particle size distribution in the interval of 40-60 mesh decreases, but the change in the interval of 60-80 mesh is not obvious, mainly because the original particle size distribution contains some proppant with 60-70 mesh size, while the interval of 80-180 mesh increases.Only a small part of the ceramsite proppant is crushed into 40-60 mesh after pressure bearing, which further proves that the ceramsite proppant has stronger pressure bearing capacity.

Proppant embedding test
A cylindrical specimen with a diameter of 2.54cm and a height of 2.5 ~ 3.0 cm was drilled by using the outcrop core, and the proppant embedding rule was tested by using the cylindrical specimen.Two shale specimens were stacked up and down, and a certain amount of proppant was placed in the middle.The proppant was selected from 20-40 mesh ceramsite, and the experiment was assembled.After the assembly, the experimental specimen was wrapped with a certain thickness of heat-shrinkable tube and fixed with a steel ring.The uniaxial/triaxial compression test module of the TAW-1000 servo control system is used for the experimental test.Five kinds of closing stresses are considered in the experiment, which are 10.0, 20.0, 30.0, 40.0, and 50.0 MPa respectively, and the corresponding parameters such as stress and displacement are recorded.After the proppant embedding experiment, the end face of the specimen is shown in Figure 9, and the proppant embedding trace can be observed on the end face of the specimen in contact with the proppant.Based on the relationship curve between axial displacement and time obtained from experiments and the elastic modulus of shale, the amount of proppant embedded at different time points can be calculated.With the increase of closing pressure, the embedding depth of the proppant gradually increases, and the increasing rate of embedding depth gradually decreases (Figure 10), mainly because when the closing pressure increases to 30 MPa, most of the proppant has been embedded into the rock, and the corresponding bearing capacity has been improved to some extent.For shale, the embedding depth of proppant is greater than sandstone, and the analysis is mainly because the hardness and rigid mineral content of shale are lower than sandstone.
With the decrease in paving concentration, the embedding depth of the proppant gradually increases (Figure 11).The analysis reason is that when paving concentration is high, the contact area between the proppant and rock is large and the bearing capacity is strong.With the decrease in paving concentration, the difference in embedding depth between shale and sandstone becomes smaller.The main reason is that when paving concentration is low, the influence of rock strength on embedding depth is small, while when paving concentration increases and contact area increases, the influence of sandstone strength on embedding depth becomes stronger, which makes the embedding depth smaller.
According to the conclusion that low closure pressure and high laying concentration have higher conductivity in the conductivity experiment, it corresponds to lower embedding depth in the embedding experiment, and because of the low embedding depth, the crack opening is larger, which further proves that the low embedding depth has higher conductivity.
However, the proppant embedment depth in shale reservoirs is large, so the conductivity of proppant in shale is less than that in sandstone.In the actual engineering selection, we should try to choose a higher paving concentration and improve the conductivity of shale reservoirs as much as possible.

Determination of application scope of proppant
According to the well-logging data in the study area, the confining pressure distribution map is obtained as shown in Figure 12.It can be seen that the confining pressure in the study area is in the range of 25-40 MPa, and the confining pressure in Area B is higher than that in Area A. From the results of the proppant diversion experiment and embedding experiment, it is concluded that the confining pressure in the northwest area (Area A) is greater than 30 MPa, so the 20-40 mesh ceramsite proppant and the laying concentration of 14 kg/m 2 have the strongest diversion ability.However, the confining pressure in the southeast area (area B) is about 25 MPa.According to the results of the diversion experiment and economic analysis, 10-20 mesh quartz sand proppant should be selected, and the laying concentration should be 14 kg/m 2 , which has the best diversion ability.In addition, natural fractures are developed in the middle zone of Area A in the main research area, and micro-cracks can be supported by multi-stage sand addition based on 20-40 mesh ceramsite proppant and smaller particle size quartz sand (40-70 mesh /70-140 mesh).

Conclusion
This paper studies the conductivity and embedding degree of four kinds of proppant in shale and sandstone through macro-proppant conductivity experiment and micro-proppant embedding experiment, and draws the following conclusions: 1.With the increase of closing pressure, the conductivity of the proppant tends to decrease, and it usually tends to increase with the increase of laying concentration.For 10-20 mesh and 20-40 mesh large-particle quartz sand proppant, the conductivity is the strongest when the laying concentration is 14 kg/m 2 when the closing pressure is less than 30 MPa.When the closing pressure is greater than 30 MPa, there is no obvious difference in conductivity.Even when the concentration of 20-40 mesh quartz sand is 12 kg/m 2 , the conductivity is greater than that of 14 kg/m 2 .
2. With the increase of closing pressure, the conductivity of the ceramsite proppant shows a downward trend, and the conductivity is the strongest when the laying concentration is 14 kg/m 2 .After bearing pressure, the large-particle quartz sand proppant is more likely to be crushed into small-particle proppant, while the ceramsite proppant has better bearing capacity, and the particle size distribution has not changed obviously, so it is concluded that the bearing capacity of ceramsite is stronger than that of quartz sand.
3. Comparison between ceramsite and quartz sand, the 10-20 mesh quartz sand has stronger conductivity when the closing pressure is lower than 20 MPa, and the 20-40 mesh ceramsite proppant has stronger conductivity when it is higher than 20 MPa.
4. Due to the large particle size of 10-20 mesh quartz sand, good conductivity can be obtained.However, due to its large particle size, it is difficult to transport at a long distance, and it is easy to be crushed under high closure pressure.Therefore, it is possible to lay 10-20 mesh quartz sand proppant in the low-pressure zone near the well, which can obtain high conductivity, and it can be supplemented with 40-70 quartz sand proppant with smaller particle size along with fracture extension. .With the increase of closing pressure and the decrease of laying concentration, the embedding depth of proppant increases obviously, and the embedding depth of proppant in shale reservoir is greater than that in sandstone.According to the corresponding conductivity test, it can be concluded that the greater the embedding depth is, the lower the conductivity of the proppant is, while the embedding depth of the shale reservoir is usually greater, so the higher laying concentration should be adopted as much as possible in construction.

Figure 3
Figure 3 Test results of conductivity of 10-20 mesh quartz sand.

Figure 7 .
Figure 7. Results of flow conductivity of different types of proppants when laying concentration is 6 kg/m 2 .

Figure 9 .
Figure 9. Example of proppant embedded in the core.The proppant embedment test of sandstone and shale was carried out, and the proppant embedment depth under different closing pressures and different sand concentrations was compared.With the increase of closing pressure, the embedding depth of the proppant gradually increases, and the increasing rate of embedding depth gradually decreases (Figure10), mainly because when the closing pressure increases to 30 MPa, most of the proppant has been embedded into the rock, and the corresponding bearing capacity has been improved to some extent.For shale, the embedding depth of proppant is greater than sandstone, and the analysis is mainly because the hardness and rigid mineral content of shale are lower than sandstone.With the decrease in paving concentration, the embedding depth of the proppant gradually increases (Figure11).The analysis reason is that when paving concentration is high, the contact area between the proppant and rock is large and the bearing capacity is strong.With the decrease in paving concentration, the difference in embedding depth between shale and sandstone becomes smaller.The main reason is that when paving concentration is low, the influence of rock strength on embedding depth is small, while when paving concentration increases and contact area increases, the influence of sandstone strength on embedding depth becomes stronger, which makes the embedding depth smaller.According to the conclusion that low closure pressure and high laying concentration have higher conductivity in the conductivity experiment, it corresponds to lower embedding depth in the embedding experiment, and because of the low embedding depth, the crack opening is larger, which further proves that the low embedding depth has higher conductivity.However, the proppant embedment depth in shale reservoirs is large, so the conductivity of proppant in shale is less than that in sandstone.In the actual engineering selection, we should try to choose a higher paving concentration and improve the conductivity of shale reservoirs as much as possible.

Figure 10 .
Figure 10.Influence of closing pressure on embedment depth.

Figure 11 .
Figure 11.Influence of sand laying concentration on the embedding depth.

Figure 12 .
Figure 12.Distribution of confining pressure in the study area.