The tight conglomerate reservoirs in Mahu sag, Junggar Basin are fan-delta front deposits with complex lithofacies characteristics, deep burial and high heterogeneity, and extremely difficult to put into production^[1⇓-3]. In recent years, great breakthrough has been made in production by using horizontal well volume fracturing ^{[4⇓⇓⇓-8]}. In 2020, with the goal of reducing cost and increasing efficiency, multi-cluster + temporary plugging fracturing tests in long horizontal stages of horizontal wells were carried out in this area. However, there was a large difference in post-fracturing effects, and the production of most test wells failed to meet expectations. In order to optimize fracturing process parameters and improve productivity, it is necessary to study the initiation law of artificial fractures. Due to the different mineral composition of gravel and matrix in conglomerate, the rock mechanical properties of them are significantly different, and the conglomerate reservoir has strong mechanical properties heterogeneity ^[9⇓-11]. Conglomerate characteristics (gravel size, content, sorting, distribution and mechanical properties difference between gravel and matrix, etc.) and horizontal stress difference significantly affect artificial fracture propagation morphology. When hydraulic fractures encounter conglomerates, they may have a variety of behaviors such as penetration, deflection and fracture arrest ^{[12⇓⇓⇓⇓⇓⇓⇓⇓⇓-22]}. The hydraulic fracture propagation in conglomerate reservoirs is very complex.

Hydraulic fracture field monitoring technique is an effective method for understanding the artificial fracture morphology, including indirect monitoring technology and direct monitoring technology. The indirect monitoring technique includes net pressure analysis, well testing, production analysis, etc. The direct monitoring technology is composed of near-borehole zone monitoring technology and far-field zone monitoring technology. The near-borehole zone monitoring technology includes radioactive tracer, well temperature logging, well diameter logging, fiber optic monitoring (DTS/DAS), downhole video imaging, etc. ^{[23⇓⇓⇓⇓⇓⇓⇓-31]}. The far-field zone monitoring technology includes microseismic monitoring, surface inclinometer monitoring, downhole inclination image monitoring in surrounding wells, deep shear wave imaging monitoring (DSWI), etc. ^[32-33]. With the downhole video imaging technology, we can directly obtain a large number of high-definition perforation images, and the degree of erosion can be reflected by calculating the erosion area of the perforation (the change in perforation area before and after fracturing). It has been found statistically that the degree of erosion is positively correlated with the volume of proppant in the perforation ^[27-28].

For conglomerate reservoirs with strong heterogeneity, the hydraulic fracture monitoring is rarely carried out at present, and the law of fracture initiation and propagation of staged and multi-cluster fractured horizontal wells in such reservoirs is not clear. To solve this problem, several stages with good cementing quality were selected from MaHW26X test well in Mahu tight conglomerate reservoir, Junggar Basin, and downhole video imaging technology was used to monitor perforation erosion. The initiation law and uniformity degree of fractures under different pumping parameters were analyzed to provide theoretical basis for optimizing pumping program.

The MaHW26X test well is located in the fault block of well area Ma 18-Aihu 1 of Mahu sag, Junggar Basin, and the development layer is T₁b₁² of Triassic Baikouquan Formation. The drilling depth is 3920.4 m. The reservoir porosity, permeability, and oil saturation are 7.5%-12.4%, (0.12-20.00)×10^-3 um² and 45.0%-73.4%, respectively. The elastic modulus, Poisson's ratio and tensile strength are 19.3-24.8 GPa, 0.181-0.201 MPa and 1.0-2.3 MPa respectively. The conglomerate composition is mainly igneous rock, followed by metamorphic rock. The gravel size is mainly medium-size gravel (5-70 mm), and mainly filled with sand, mud or fine gravel between the gravels. The overall reservoir is highly heterogeneous ^[9⇓-11].

The MaHW26X test well was fractured using a bridge plug staged + temporary plugging fracturing process. The lateral section is 931 m long, and the stimulated section is 483.2 m long. It was divided into six 80-m stages, numbered 1-6 from toe to heel. Each stage was perforated in 6 clusters, with 3 perforations in each cluster except for the fifth stage with 8 perforations. Perforation guns of type 86 and perforating bullets with equal diameter were used for perforating, and the phase angle of perforation was 60°. Variable viscosity fracturing fluid system was used, which have 2% KCl anti-swelling performance. The pre-slug was 0.380 mm/0.212 mm (40/70 mesh) quartz sand and the main slug was 0.550 mm/0.270 mm (30/50 mesh) ceramics. The temporary plugging materials were temporary plugging ball + particle + powder combination. The specific fracturing operation parameters of the test well are shown in Table 1. Due to the insufficient depth of the downhole video imaging equipment, only a small number of perforation hole images were obtained in the first stage. Therefore, this paper focuses on the comparative analysis of the perforation images in the second to sixth stages.

In the process of staged and multi-cluster fracturing of horizontal wells, multi-fractures often appear non-uniform initiation and propagation, which is directly caused by the unbalanced fluid distribution of each cluster. Scholars have conducted a large number of numerical simulation studies on the mechanism of multi-fracture initiation and propagation. They pointed out that the non-uniform propagation of multi-fractures was not only affected by reservoir heterogeneity and stress interference, but also by perforation friction. Improving perforation friction can promote the uniform initiation and propagation of fractures ^[34-35]. However, these studies generally assumed that the perforation friction is constant during fracturing, and ignored the effect of perforation erosion on the perforation friction.

Crump et al. ^[36] obtained the calculation formula of perforation friction based on Bernoulli equation and mass conservation equation, as shown in Eq. (1). In addition, the experimental results showed that the perforation erosion can be divided into two stages: at the first stage, the perforation edge was gradually smooth, but the perforation diameter didn’t increase significantly, and the perforation discharge coefficient (C_p) played a leading role in reducing the perforation friction. At the second stage, C_p was relatively constant, and the perforation diameter increased slowly, leading to further reduction of the perforation friction. For intact perforations, C_p was 0.5-0.6, and for fully worn perforations, C_p was 0.95. According to Eq. (1), the variation curve of perforation friction with perforation diameter of single cluster under different number of perforations was drawn (Fig. 1), where fluid density was 1000 kg/m³, injection rate of single cluster was 0.04 m³/s, the perforation diameter was 10-12 mm, the number of perforations was 3-12, and discharge coefficient was 0.7.

Fluid distribution of each cluster was determined by perforation friction, tortuous friction and in-fracture friction when wellbore friction was ignored. Since both perforation friction and tortuous friction belong to near- wellbore friction, and the flow-limiting mechanism is similar, tortuous friction can be equivalent to perforation friction. That is, the fluid distribution of each cluster satisfies the following fluid flow conservation and pressure balance conditions:

When there are enough perforations, the perforation friction can be regarded as a small constant, and the fluid distribution is mainly determined by the friction in the fracture. The influence of the non-uniform erosion on the fluid distribution is not obvious. When the number of perforations is small, the friction of perforations is large and plays a leading role in fluid distribution, while the perforation friction is very sensitive to the change of the perforation diameter. For example, an increase of 2 mm in perforation diameter can lead to a reduction of about 15 MPa in perforation friction when the number of perforations is 3 (Fig. 1). At this time, the non-uniform erosion of perforations will have a significant influence on flow distribution, and then change the uniformity of multi-fracture initiation. Long et al. ^[37] proposed a relationship between perforation diameter and discharge coefficient, proppant concentration and flow rate, as perforation diameter and discharge coefficient increased continuously, and the degree of perforation erosion was related to the kinetic energy of proppant:

α and β are two independent parameters obtained by empirical fitting method to represent the influence of proppant and casing interaction. In summary, the calculation formula of perforation diameter after erosion can be further obtained:

Eq. (5) indicates that the greater the flow rate, the greater the degree of perforation erosion. By calculating the dynamic change of perforation diameter and discharge coefficient, the dynamic perforation friction under the action of erosion can be obtained. Therefore, some scholars established a multi-fracture propagation model considering the effect of perforation erosion based on the erosion model proposed by Long et al. ^[37⇓-39], and found that there was non-uniform erosion in perforations on each cluster, the perforation diameter of the dominant cluster increased rapidly, and the proportion of fluid flow distribution increased further. However, the perforation diameter of inferior clusters increased slowly, or even did not increase, and the proportion of fluid flow distribution decreased further. Therefore, the effect of perforation erosion aggravated the disequilibrium degree of fluid distribution and leaded to the disequilibrium of initiation and propagation of multi-fractures. The influence of perforation erosion on the initiation and propagation of multi-fractures can be obtained by numerical simulation, but it is difficult to accurately reflect the actual situation of perforation erosion. Since the erosion degree of perforations is positively correlated with the injected proppant volume, and the proppant volume of each cluster can reflect the uniformity of multi-fracture initiation, this paper directly compares the erosion degree of each perforation through downhole video imaging technology to reflect the uniformity of multi-fracture initiation.

With perforation imaging monitoring technology, also known as downhole video imaging technology, we can obtain a large number of perforation images by running a special camera along the casing to the perforated section^[24]. In the test well, we used a downhole video imaging technology by array loop scanning that provided 360° continuous measurement with data transfer rate of up to 25 frames per second, effectively identifying relatively small perforations. In addition, the technology was accompanied by digital image analysis software, which can calculate accurately the area of irregular perforations.

Based on downhole video imaging technology, we found that the perforation erosion in the test well can be divided into two stages (Fig. 2). Firstly, the perforation edge became smooth but the perforation area didn’t increase significantly when the proppant volume was less. Second, the perforation became irregular, and the perforation area increased significantly when the proppant volume was larger, which confirmed the research conclusion of Crump et al.^[36].

The perforation erosion area is equal to the post-fracturing perforation area minus the pre-fracturing perforation area, which can be obtained by downhole video imaging technology. Since the erosion area of perforations is positively correlated with the volume of proppant added, the degree of stimulation of each cluster can be reflected by comparing the erosion area of perforations in each cluster, and the uniformity of fracture initiation of each cluster can be further predicted. It is relatively easy to obtain images of perforations in all clusters after fracturing using downhole video imaging technology, but it is difficult to obtain images of perforations before fracturing because it is uneconomical. Therefore, in order to obtain the actual area of the perforation before fracturing, the end of the second stage was reperforated without fracturing. Because the reservoir conditions and completion method are consistent, the reperforated perforation area can represent accurately the area of the pre-fracturing perforations. However, due to the movement of the bridge plug in the test well, the pre-fracturing perforation area can no longer be represented. Therefore, the average area of the perforation without erosion after fracturing was used to approximate the area before fracturing in the study, and then the perforation erosion area was obtained.

The test well has 120 perforations at stages 2-6, and 16 supplementary perforations at the end of Stage 2 for a total of 136 perforations. Only 133 images of the perforations were obtained through downhole video imaging technology due to 3 perforations were blocked by sand deposition at the lower edge of second stage, including 31 perforations without erosion and 102 eroded perforations, with an erosion ratio of 76.7%. The ratio of the change of perforation diameter to the initial diameter of the perforation, namely, the erosion degree is 15%-352%.

The number of perforations of single cluster at each stage in the test well was small. Therefore, the effect of perforation erosion on flow distribution and uniform initiation of multi-fractures cannot be ignored. The perforation erosion area of each cluster was greatly different, reflecting that the initiation of multi-fractures was extremely uneven (Fig. 3). The supplementary perforations at the end of the second stage were only perforated without fracturing, and the perforation erosion area was zero. However, the statistical results show that the erosion area of the supplementary perforations was 2181 mm², indicating that the bridge plug moved during the fracturing of the third stage, so that the fractures of the supplementary cluster were stimulated, and the perforations were eroded. Therefore, the perforation erosion area of the supplementary cluster was divided into Stage 3 for calculation, and its cluster number was defined as 0. At the fourth stage, the designed sanding volume was 60 m³, the total liquid volume was 2183.2 m³, and the perforation erosion area of this stage was 657 mm². At the sixth stage, the number of clusters and perforations was the same as that at the fourth stage, the designed sanding volume (180 m³) and the total liquid volume (3567.3 m³) were greater than those in Stage 4, but the perforation erosion area of Stage 6 was less than Stage 4, only 557 mm², and the perforation erosion area in the Cluster 5 of fifth stage was also abnormally large. Therefore, it is believed that the bridge plug also moved during Stage 6 fracturing, resulting in a significant amount of fracturing fluid and proppant entering the perforations of Cluster 5 of fifth stage, which resulted in a significant erosion area in the cluster.

Stages 2, 5 and 6 show a obvious trend of sands entering clusters at the heel end (heel bias), that is, the perforation erosion area of heel clusters is more than other clusters, indicating that more proppant flow into the heel clusters, as shown in Fig. 3a, 3d and 3e. But stages 3, 4 show a obvious trend of sands entering clusters at the toe end (Toe bias), that is, the perforation erosion area of toe clusters is more than other clusters, indicating that more proppant flow into the toe clusters, as shown in Fig. 3b and 3c. The variance coefficient of the perforation erosion area of each cluster was used to characterize the uniformity of the perforation erosion area of each cluster. The larger the variance coefficient is, the less uniform the perforation erosion area of each cluster is. The smaller the variance coefficient is, the more uniform the perforation erosion area of each cluster is. The variance coefficient is equal to zero, indicating that the erosion area of perforations in each cluster is completely uniform. The variance coefficient of the stages 2-6 was 1.47, 1.54, 0.39, 1.93, 0.90 respectively. The variance coefficient of the fourth stage is relatively small, indicating that the erosion area distribution of perforations in each cluster was relatively uniform, reflecting that the fracture initiation of each cluster was relatively even. However, the variance coefficient in stages 2, 3, 5 and 6 was obviously larger, indicating that the erosion area of perforations in each cluster was not uniform, reflecting that the fracture initiation of each cluster fracture was uneven.

The change in perforation diameter can reflect the degree of erosion directly. The larger the perforation diameter after fracturing, the greater the erosion degree, and the larger the volume of proppant is. The perforation diameter shows an obvious “phase bias” (Fig. 4). That is, the perforation diameter on the high side of the wellbore (about 0° in phase angle) is smaller, while the perforation diameter on the low side of the wellbore (about 180° in phase angle) is larger.

For the perforations without erosion (Fig. 5a, 5b), the perforation diameter was 8-12 mm, with an average diameter of 10.5 mm. The perforations with phase angle of 0° have the smallest diameter, with an average diameter of 9.6 mm. The perforations with phase angle of 180° have the largest diameter, with an average diameter of 11.3 mm. The average diameter range of perforations without erosion (the difference between the largest average diameter and the smallest average diameter) is 1.7 mm. This is mainly because the perforating gun pipe deviated from the center of the wellbore under the action of gravity and stick to the lower side of the wellbore. As a result, when the perforating gun perforated on the high side of the wellbore, the annular was larger, the energy loss was more serious, and the perforation diameter was smaller. Although with the use of equal-diameter perforating gun, this adverse effect cannot be completely avoided in the field. For the eroded perforations (Fig. 5c, 5d), the perforation diameter was 9-47 mm, with an average diameter of 15.8 mm. The perforations with phase angle of 0° have the smallest diameter, with an average diameter of 11.0 mm. The perforations with phase angle of 180° have the largest diameter, with an average diameter of 18.0 mm. The average diameter range of eroded perforations is 7.0 mm, much larger than that of perforations without erosion. Because of the larger diameter of the perforation on the lower side of the wellbore before fracturing, fracturing fluids and proppant are more likely to enter the large perforations during fracturing, which increases the erosion of the large perforations and further exacerbates the perforation diameter difference between the different phases, so the phase bias of the eroded perforations is more severe than that of the perforations without erosion. Due to the phase bias, the eroded perforation area on the lower side of the wellbore is generally large. The difference of the eroded degree is most significant for perforations with phase angles of 0° and 180° (the upper side and lower side of the wellbore), while the difference of the eroded degree is small (Fig. 4) for perforations phase angles of near 90° and 270° (near the horizontal central axis of the wellbore). Therefore, perforating with 180° in phase angle (horizontal direction) can reduce the phase bias of perforation erosion, promoting uniform perforation erosion and fluid distribution, and avoiding the formation of large perforations in the lower side of wellbore.

The total eroded perforation area of the fracturing stage was positively correlated with the proppant volume added ^[27]. Data of proppant volume and erosion area of each stage are shown in Table 2.

Stages 2-6 were designed with pumped proppant volume of 111, 122, 60, 180, 180 m³. At Stage 3, the bridge plug moved, and downhole imaging showed scratches on the casing wall caused by the plug movement, indicating that the perforations in the supplementary cluster were eroded. Therefore, the actual perforation eroded area of Stage 3 was equal to the total eroded area of all clusters at Stage 3 plus the supplementary clusters. In addition, the bridge plug was moved to Stage 5 during fracturing in Stage 6, resulting in less designed proppant volume at Stage 6 and more designed proppant volume at Stage 5. Since it is difficult to obtain the actual proppant volume at Stage 6 directly, it can only be obtained by extrapolation fitting. The designed proppant volume is the actual value at Stage 4 because the plug didn’t move, so the erosion area per cubic meter of sand at Stage 4 can be calculated (the ratio of the total erosion area to the total proppant volume). Given the erosion area of Stage 6, the proppant volume required for Stage 6 can be calculated from the erosion area generated per cubic meter of sand at Stage 4, which is called the fitted proppant volume. The proppant volume reduction at Stage 6 is equal to the proppant volume increase at Stage 5, and then the fitted proppant volume of Stage 5 can be calculated.

The linear fitting of the fitted proppant volume and the erosion area at each stage (Fig. 6) shows that the correlation is as high as 94.2%, proving that there is indeed a good positive correlation between the two. This is also consistent with the numerical simulation results. That is, the greater the degree of perforations erosion, the more fluid flow and proppant volume ^[37⇓-39], which also shows that the hypothesis of plug movement is valid.

The common methods for judging the effectiveness of temporary plugging fracturing are as follows: when the operation pressure increased after temporary plugging at the same injection rate, or when the injection rate was lower than that before temporary plugging, the operation pressure remained unchanged or increased after temporary plugging, which qualitatively indicates that temporary plugging was effective ^[40⇓-42]. By combining the pumping pressure curves before and after temporary plugging (Fig. 7), the variation range of operation pressure, injection rate and other parameters can be determined, and then the effectiveness of temporary plugging fracturing can be judged. As shown in Fig. 7, the operation pressure after temporary plugging is significantly increased at almost the same injection rate, and the positive differential pressure (the operation pressure increases after temporary plugging) is dominant, indicating that temporary plugging fracturing is effective. Three stages of temporary plugging fracturing were analyzed by the above method, and the results show that temporary plugging fracturing is effective in all stages. However, this method is to judge the effectiveness of temporary plugging fracturing qualitatively, and it mainly reflects whether the temporary plugging material has blocked up the large perforations or fractures, but does not accurately reflect the stimulated uniformity of each cluster. Therefore, based on the monitoring data of perforation imaging, the variance coefficient of eroded perforation area of each stage of temporary plugging fracturing was calculated to reflect quantitatively the effective of temporary plugging fracturing. The smaller the variance coefficient is, the more uniform the eroded perforation area of each cluster is. In other words, the more uniform the fluid and proppant distributed in each cluster is, the higher the effectiveness of temporary plugging fracturing is.

It can be seen from the above that the temporary plugging stages are stages 2, 5 and 6, and the variance coefficients of eroded perforation area are 1.47, 1.93 and 0.90, respectively. In the stages 3 and 4 without temporary plugging, the variance coefficients of erosion area were 1.54 and 0.39, respectively. Since the Stage 4 was not affected by bridge plug movement, and its variance coefficient value can better represent the stimulated uniformity of various clusters in the stages without temporary plugging fracturing. It is worth noting that the variance coefficients of other temporary plugging stages should theoretically be lower than Stage 4 (without temporary plugging), but the result is the opposite. The possible reason is that the bridge plug movement occurred in stages 5 and 6, and affecting the Stage 2, so that the fracturing fluid flew into single cluster. In addition, the volume of proppant also has a direct influence on the perforation erosion. The designed sand volume in stages 5 and 6 was three times than that at the Stage 4, and the designed sand volume in the Stage 2 was almost twice than that at the Stage 4. Comparing the two unplugged stages, the variance coefficient of the Stage 3 is also significantly higher than that of the Stage 4, which is due to the movement of the bridge plug and the designed sand volume in the Stage 3 is twice as much as that in the Stage 4.

The purpose of temporary plugging is to promote the uniform initiation and propagation of multi-fractures, and the variance coefficient of eroded perforation area is to reflect the uniform degree of fractures initiation on the whole. Therefore, it is a feasible method to judge the effective of temporary plugging quantitatively. In order to improve the reliability of the judgment of temporary plugging effectiveness, the two methods can be combined to judge qualitatively whether the temporary plugging is successful or not based on the superposition pressure curve, and then judge quantitatively the effective degree of temporary plugging through the variance coefficient of eroded perforation area.

The test well MaHW26X and most horizontal wells in North America have a small number of perforations in single cluster. Therefore, the perforation friction and perforation erosion have important influence on fluid distribution and fracture initiation of multi-clusters. The test well was compared with perforation erosion in North America. First of all, in terms of reservoir properties, the reservoirs in North America are mainly shale reservoirs, while the Mahu Oilfield is mainly conglomerate reservoirs, which have stronger heterogeneity and are more prone to have non-uniform initiation of fractures. Second, in terms of fracturing parameters, the horizontal wells in North America are more than 10 clusters at a stage with 4-5 m cluster spacing, while the test well is 6 clusters in each stage with 11-18 m cluster spacing. Downhole video imaging in North America showed that there were “heel bias” and “phase bias” of perforation erosion, and the perforation erosion area was positively correlated with proppant volume pumped, as shown in Fig. 8^{[24⇓⇓⇓⇓⇓-30,43]}. The fracturing parameters of the test well MaHW26X and horizontal wells in North America are shown in Table 3.

The difference and similarity of perforation erosion between the test well MaHW26X and horizontal wells in North America are as follows.

(1) The degree of perforation erosion in North America ranged from 5% to 120%, while that in the test well ranged from 15% to 352%. The maximum erosion degree of the test well was significantly higher, possibly due to the stronger heterogeneity of the conglomerate reservoir in which the test well was located, and the occurrence of bridge plug movement, the fracturing fluid flowing into partial perforation clusters.

(2) Horizontal wells in North America have a higher percentage of heel bias stages, compared with a lower percentage in the test well. Both the test well and horizontal wells in North America showed phase bias of perforation erosion, that is, the perforation erosion of the lower side of the wellbore (around 180° phase) is more obvious.

(3) There is a clear positive correlation between the cumulative eroded perforation area and proppant volume pumped at each stage of the test well and horizontal wells in North America.

Proppant was pumped into 76.7% of perforations across the five stages in the test well MaHW26X. But in most clusters, only a very limited amount of proppant entered. The proppant was concentrated in a few clusters, and distributed unevenly across clusters. Proppant distribution and multi-fractures initiation were uniform at Stage 4, and uneven at stages 2, 3, 5 and 6. The purpose of promoting uniform initiation of hydraulic fractures and sanding was not achieved after the addition of temporary plugging agent. The proppant volume pumped into cluster 5 of Stage 5 accounted for 90% of the total proppant amount in Stage 5, while that pumped into Cluster 6 of Stage 2 accounted for more than 70% of the total proppant amount in Stage 6, showing obvious heel bias of proppant distribution.

The volume of proppant pumped is positively correlated with the area of perforation erosion. The erosion degree in the test well ranges from 15% to 352%, with an average of 74.5%, which is much larger than the statistical results of some horizontal wells in North American shale reservoirs.

The perforation erosion has obvious phase bias, and the erosion is more serious in the lower side of wellbore. Using perforation with phase angle of 180° (horizontal direction) can alleviate the phase bias of perforation erosion, promote uniform perforation erosion and fluid distribution, and avoid the formation of large perforation in the lower side of wellbore.

C—proppant concentration, kg/m³;

C_p—discharge coefficient, dimensionless;

C_p,max—maximum discharge coefficient, dimensionless;

D—perforation diameter, m;

D₀—initial perforation diameter, m;

D_f—perforation diameter after erosion, m;

N—the number of clusters;

N_p—the number of perforations;

p_fi—intra-fracture friction of cluster i, Pa;

p_pf—perforation friction, Pa;

p_pfi—perforation friction of cluster i, Pa;

q—injection rate of a cluster, m³/s;

q_i—injection rate of cluster i, m³/s;

Q—total injection rate, m³/s;

t—time, s;

v—average fluid velocity at the perforation, m/s;

α—fitting coefficient, (m²·s)/kg;

β—fitting coefficient, (m·s)/kg;

ρ—fluid density, kg/m³.