In order to more accurately restore the proppant transport behaviors in rough fractures created in reservoir fracturing, large-size outcrops of tight sandstone in the Ordos Basin were selected for splitting and fracturing to obtain tensile fractures with the same type and similar characteristics as those of hydraulic fractures. Fig. 1a and 1b give the rough fracture surface of the split rock sample and the height images of the fracture wall surface at different locations obtained by scanning with a high-precision 3D laser scanner, respectively. The fractal dimension of the fracture surface was calculated to be 2.27 using the cubic covering method. Then based on the fracture and using silicone, resin and other materials, the casting process was used on both sidewalls of split fracture to obtain a large visual rough fracture model with the morphological characteristics of the real fracture wall surface. The front and side views of the model are given in Fig. 1c, where the tortuous and rough characteristics of the fracture are remarkable.

The dimensions of experimental fracture model and field hydraulic fracture usually remain geometrically similar in length and height, and identical in width ^[12]. In previous studies, when designing experimental setups to simulate proppant transport with reference to hydraulic fracture dimensions, the ratio of the length to the height of the fracture was usually set to be greater than or equal to 2 ^[7]. In this paper, the rough fracture model was designed with a length of 1 000 mm, a height of 500 mm, and an adjustable width within 1-5 mm, to satisfy the requirement of geometric similarity. Moreover, the experimental fracture model was set with the same Reynolds number of the fluid as in actual hydraulic fracture, and much greater length and height than the width, so that the observed flow pattern of sand-carrying fluid could be kinematically and dynamically similar to the situation of actual fracture ^[27]. In addition, unconventional oil and gas reservoirs are characterized by low to ultra-low permeability, and the rate of fracturing fluid loss in the fracture is low, so the rough fracture model does not consider the fluid loss on the sidewalls.

Fig. 2 shows the experimental setup for visualizing the proppant transport in rough fracture, which was built with reference to real fracture surface. It mainly consists of variable frequency mixer, sand mixing tank, variable frequency screw pump, visualized rough fracture model and pressure acquisition system. The fracture width is adjustable from 1 mm to 5 mm, and four circular holes with a diameter of 15 mm and a spacing of 80 mm are arranged at the inlet and outlet ends of the fracture model, respectively. The proppant was injected from the left side and flowed out from the right side. Two pressure sensors at the inlet and outlet of the model were able to collect and record the change of the pressure difference within the fracture in real time during the proppant pumping process.

In order to study the typical transport characteristics of proppant in rough fractures formed in reservoir fracturing, the fracturing materials and construction parameters commonly used in field operations were selected for experimental scheme design.

Guanidine gum is a popular thickening agent for fracturing fluids in field fracturing operations because of its excellent viscosity increasing and sand-carrying performance. In this study, three fracturing fluids were prepared using tap water and guanidine gum with guanidine gum mass fractions of 0.25%, 0.30% and 0.35%, respectively, and no other additives were used to ensure the transmittance of the experimental working fluids. Since the length and height of the fracture in the model were scaled down proportionally and the width of the fracture was close to the actual one, 425/212 μm (40/70 mesh) quartz sand commonly used in the field was selected as the proppant in the experiment. The selected proppant has the particle size of 212-425 μm, the apparent density of 2.64 g/cm³, the roundness and sphericity of 0.7. The sand ratio in the experiment was 10%.

As mentioned before, in addition to the geometrical similarity between the fracture model and the actual hydraulic fracture in size, the kinetic similarity between the experimental working fluid pumping and the fracturing fluid flow in the actual fracture also needs to be satisfied. Since the flow of fracturing fluid in the fracture is mainly affected by the viscous force, the Reynolds similarity criterion is chosen for the kinetic similarity calculation, and the calculation formula is as follows:

Since the fracture model width is close to the actual fracture width, and the density of the three fracturing fluids prepared is around 1.01 g/cm³, which is close to the density of guanidine gum fracturing fluid actually used in the field, the following equation can be obtained from Eq. (1):

For guanidine gum fracturing fluids used in unconventional oil and gas reservoir stimulation, they can meet sand-carrying requirements generally when their viscosities exceed 80 mPa·s ^[28]. In addition, the average flow velocity of fracturing fluid in the hydraulic fracture is mostly lower than 0.25 m/s ^[29]. Therefore, the fracturing fluid viscosity of 80 mPa·s and the fluid velocity within the fracture of 0.2 m/s were chosen as the reference parameters in actual operations. Taking the fracturing fluid with guanidine gum mass fraction of 0.3% as an example, the viscosity of this fracturing fluid was measured to be 12 mPa·s at room temperature, and the average fluid velocity within the fracture in the experiment was 0.03 m/s from Eq. (2). Then, based on the width and height of the fracture, the pumping rate in the experiment was determined. The experimental parameters obtained according to the similarity criterion are shown in Table 1.

In order to reveal the typical characteristics and intrinsic mechanism of proppant transport in rough fracture, Case 1 with an average fracture width of 2 mm was selected for analysis. The process of proppant transport and placement in Case 1 is shown in Fig. 3. In straight smooth fractures, the proppant pumped into the fracture usually moves forward in uniform suspension in the fluid before settling under gravity to form a flat sand dune at the bottom of the fracture ^[11,13]. As can be seen from Fig. 3, the flow pattern of sand-carrying fluid in rough fracture at the early stage of injection (1-3 min) shows streaks, indicating that the proppant suspended in the fracture is not uniformly distributed, which is due to the complex width variation of the rough fracture. Essentially, the proppant particles tend to migrate along the specific dominant flow paths. With the continuous pumping of sand-carrying fluid, the sand dune accumulating in the fracture grows until its height reaches a relative equilibrium state. Unlike the sand dune accumulating in straight smooth fracture, the sand dune in rough fracture is irregular morphologically and with scattered unfilled zones in the center.

The fracture surface morphology has an impact on the fluid flow and the motion behavior of particles in rock fractures. Some typical features of the sand-carrying fluid flow in rough fracture are given in Fig. 4. It can be seen that the fluid flow in rough fracture is more complex, in contrast to the regular and orderly flow in straight smooth fracture. As shown in Fig. 4a, the sand-carrying fluid presents various flow behaviors, such as channeling, reverse flow, and bypass flow, after entering the rough fracture. The fluid flow in the fracture is closely related to the shape of the flow channel, and the spatial structure and width distribution of the fracture flow channel are affected by the roughness of the fracture surface. Thus, the sand-carrying fluid shows complex and variable flow behaviors in the rough hydraulic fracture.

During the flow of the sand-carrying fluid, the proppant may bridge and accumulate in some areas of the rough fracture, forming various shapes of proppant clusters (Fig. 4b), which restricts the flow of the sand-carrying fluid. Fig. 5 gives the flow field distribution in the region around proppant cluster when the sand-carrying fluid flows through. It can be seen that the fracture wall surface roughness significantly affects the fluid flow in the fracture, and the built-up proppant clusters cause the fluid bypassing, which alters the proppant’s state of motion and ultimately results in unfilled zones in the sand dune (Fig. 4c).

Observation of the experimental images shows that the occurrence of bridging and the formation of unfilled zones when the proppant is transported in a rough fracture is the most obvious feature that distinguishes it from its transport and placement behaviors in a straight smooth fracture. The roughness of the fracture surface has the most direct impact on the geometry of the flow channel ^[30]. Taking the fracture with an average width of 2 mm in the experiment as an example, a schematic diagram of the fracture width variation is provided in Fig. 6. For a smooth fracture, local width reduction occurs at the location where the flow channel becomes tortuous, with a greater reduction at a location with increased tortuosity, which causes bridging of the proppant (Fig. 6a). Given the same channel shape, the effective width of the rough fracture at the tortuous position is smaller than that of the smooth fracture (Fig. 6b), increasing the possibility of bridging during the proppant transport. Due to the effect of roughness, the hydraulic aperture of the fracture is usually lower than the mechanical aperture ^[31]. According to the boundary layer theory, it is known that when the sand-carrying fluid flows through the turning of the flow channel, as shown in Fig. 7, there is a favorable pressure gradient at the point S₁, and the pressure force acting on the fluid particle is in the same direction as the flow direction. After the fluid passes through the point S₂, the pressure gradient is positive, and the pressure force acting on the fluid particle is opposite to the flow direction. Under the dual effect of the reverse pressure gradient and viscous resistance, fracturing fluid separation begins to occur at the point S₃, thus causing flow loss, which is not conducive to the transport of proppant. Therefore, the proppant is more prone to generate bridging and buildup at the tortuous location in the rough fracture.

The above analysis indicates that, unlike the simplified straight smooth fracture, the inherent surface roughness characteristics of the hydraulic fracture will bring about changes in the shape of flow channel and flow pattern, resulting in complex fluid flow and proppant bridging buildup, which in turn will impact the motion behavior of the proppant and the placement pattern of the sand dune, and ultimately affect the filling effect of the artificial fracture.

In the reservoir stimulation, reservoir geological features (e.g. stress distribution, natural fractures and beddings) may cause the extension trajectory of hydraulic fracture to deflect in the vertical direction, forming inclined fractures. In Case 1, Case 2 and Case 3, three fractures with different angles to the vertical direction, i.e. 0°, 10° and 20°, were set to study the transport and placement of proppant in inclined hydraulic fractures. Fig. 8 shows the experimental proppant transport and placement process in fractures with different degrees of inclination. It can be observed that the inclination of the fracture has a noticeable impact on the proppant transport behavior and the sand dune distribution pattern. Compared to a vertical fracture, proppant is transported over longer distance and placed in a larger area in an inclined fracture under the same injection time. Essentially, the inclination of the fracture in the direction of gravity enhances the particle-wall contact (collision, friction, etc.) (Fig. 9), and the effect of this contact on particle settling becomes more pronounced in rough fractures, which leads to a reduction in the rate of proppant settling and increases the proppant transport distance and distribution range.

It is also observed in Fig. 8 that as the fracture inclination increases, the sand dunes placed in the fracture are more prone to breakthrough and form a new proppant transport channel. However, such phenomenon did not occur in the experiments on proppant transport inside smooth inclined fractures carried out by Chun et al. ^[32]. This suggests that the fracture wall surface roughness affects the flow path of sand-carrying fluid, but also controls the stability of proppant placement.

Fig. 10 illustrates the variation of pumping pressure with time at different degrees of fractures in Fig. 8. It can be seen that the pumping pressure of sand-carrying fluid in the inclined fracture gradually increases and exceeds that in the vertical fracture before the channeling breakthrough in the sand dunes, whereas the pumping pressure decreases sharply after the channeling breakthrough, and changes more drastically with the increasing fracture inclination. This indicates that the instability of the sand dune in the fracture increases as the inclination of the rough fracture increases. When the proppant is fully filled inside the fracture, after the pumping pressure increases to a certain value, a new flow channel is possibly formed in the sand dune, and thus the pressure curve will fluctuate.

The proppant placement rate in the fracture can be obtained by calculating the ratio of the projected area of the front view of the sand dune in the fracture to the projected area of the front view of the fracture model. Fig. 11 illustrates the variation of proppant placement rate with time at different fracture inclination degrees. It can be seen that the proppant placement rate increases and then becomes gentle with the time. Both the rate and efficiency of proppant placement in the fracture are positively correlated with the inclination of the fracture. The placement rate in 10° and 20° inclined fractures increases by 14.69 and 22.16 percentage points, respectively, in comparison with that in the vertical fracture. In addition, the placement rate in the 20° inclined fracture decreases to some extent after 10 min of pumping, which can be attributed to partial proppant carrying-out of the fracture model along with the significant channeling breakthrough of the sand dune in the fracture, as evidenced in combination with Fig. 8 and Fig. 10. The proppant has a higher placement rate and also is able to reach a smooth state more quickly in inclined rough fractures, suggesting that inclined fractures created during reservoir stimulation are more readily propped.

Fig. 12 shows the process of proppant transport and placement in rough fractures with different widths in Case 1, Case 4, and Case 5. The proppant used in all three cases was 425/212 μm quartz sand. It can be seen that when the fracture width is 1.5 mm, the proppant shows a remarkable local bridging, which is manifested by the presence of unfilled zones in the sand dunes. As the fracture width increases, the bridging points in the fracture decrease, and the proppant is able to build up tightly in the fracture when the fracture width is 3 mm. Since the same proppant particle size is used in all cases, the fracture wall surface roughness has a weak impact on the proppant transport and placement when the ratio of the proppant particle size to the fracture width is small, which is conducive to the proppant transportation; however, a bridging is likely to occur when the ratio is large, which hinders the proppant transport.

Fig. 13 illustrates the variation of the pumping pressure of sand-carrying fluid with time in fractures with different widths. It can be seen that the pumping pressure in the fracture with width of 1.5 mm (the ratio of proppant particle size to fracture width is large) is obviously higher, and presents a more fluctuant curve, than that in the fractures with widths of 2 mm and 3 mm (the ratio of proppant particle size to fracture width is small). This phenomenon is attributed to two factors. First, for a narrow fracture, its inherently rough wall surface may cause complex fluid flow, thus inducing a greater flow resistance. Second, the proppant bridging occurs at more locations inside the fracture as the ratio of proppant particle size to fracture width increases, which further increases the hydraulic energy required for sand-carrying fluid flow. From the variation of proppant placement rate with time in rough fractures with different widths, it can be seen that the lowest proppant placement rate occurs in the fracture with width of 1.5 mm, and the placement rate increases by 9.66 and 15.02 percentage points, respectively, when the fracture width increases to 2 mm and 3 mm (Fig. 14).

In reservoir stimulation, the main fractures created are commonly large in width, while the opened natural fractures or bedding-induced branch fractures are small in width. The analysis of the pumping pressure curve indicates that improper proppant size may lead to pumping overpressure, which may damage the injection pipes and equipment to various extents and may negatively affect the placement rate of the proppant in the fracture, which is not conducive to the effective propping of for the artificial fracture. Therefore, it is crucial to choose an appropriate proppant size when pumping. Considering the influence of the ratio of proppant particle size to fracture width on the placement of sand dunes in the fracture, it can be considered to first pump small-size proppant to support the branch fracture with small width, and then the proppant with appropriate size to fill the main fracture, so that the branch fractures can be motivated to maximize the stimulated reservoir volume.

Adding thickener to adjust the viscosity of fracturing fluid is the main way to improve the sand-carrying capacity of the fracturing fluid. In Case 6, Case 1 and Case 7, fracturing fluids with viscosities of 5, 12, 19 mPa·s were prepared by adding 0.25%, 0.30% and 0.35% guanidine gum, respectively, to study the proppant transport and placement in rough fracture at different fracturing fluid viscosities. Fig. 15 shows the proppant transport and placement process at different fracturing fluid viscosities. It can be seen that, in Case 6 where a low fracturing fluid viscosity (5 mPa·s) is used, the injected proppant prefers to accumulate at the inlet and can be placed throughout the fracture at the early stage of injection. In studies related to proppant transport in straight smooth fractures, the placement of proppant throughout the fracture was rare even when a low-viscosity fracturing fluid was pumped at low velocity, and there was always a flow channel at some height between the top of the sand dune and the top of the fracture ^[12-13]. This paper suggests that in the actual transport of proppant, the fracture roughness may cause a complete plugging of fracture channel in the near-wellbore zone, which will lead to sand plugging. In addition, in the experiment with a fracturing fluid viscosity of 5 mPa·s, after the proppant completely plugged the fracture channel, the pumping pressure increased greatly. When the pumping pressure exceeded a certain value, the sand dune broke through, and then the pumping pressure decreased sharply (Fig. 16), which formed the dominant flow channel for the sand-carrying fluid. Moreover, the path of the flow channel varied with time, suggesting that the dominant flow path in the rough fracture is not fixed.

For the experiment cases with fracturing fluid viscosity of 12 mPa·s and 19 mPa·s as shown in Fig. 15, the increase in the fracturing fluid viscosity enhanced the suspension ability of the proppant, allowing it to be transported farther in the fracture. Also, increasing the viscosity of the fracturing fluid weakened the bridging buildup of the proppant in zones with greater fracture roughness and tortuosity, with a more homogeneous distribution of the sand dunes, as well as a lower pressure required for pumping the sand-carrying fluid, i.e., less hydraulic energy consumption (Fig. 16). This suggests that increasing the viscosity of the fracturing fluid can inhibit the proppant bridging and blockage caused by the rough fracture wall surface to a certain extent, thus facilitating the proppant transport and placement in the fracture.

Fig. 17 illustrates the variation of proppant placement rate in rough fracture with time at different fracturing fluid viscosities. For the low-viscosity fracturing fluid (5 mPa·s), the proppant placement rate is high at the early stage of injection, and increases by an average of 30.13 percentage points compared with that of the fracturing fluid with a viscosity of 12 mPa·s before channeling breakthrough occurs in the sand dune (10 min). As for the high-viscosity fracturing fluids (12 mPa·s and 19 mPa·s), their better sand-carrying capacity makes partial proppant flow out of the fracture model, resulting in a relatively low placement rate in the experiment. Therefore, high-viscosity fracturing fluid can be used in the early stage of hydraulic fracturing to avoid excessive buildup of proppant in the vicinity of the wellbore and to enhance the proppant transport distance. On the other hand, the high-viscosity fracturing fluid consumes relatively low hydraulic energy during transport with carried sand, so that more hydraulic energy pumped underground, if certain in quantity, can be used for fracture extension. In the late stage of fracturing, low-viscosity fracturing fluid can be used to fill fractures near the wellbore, thereby forming effective, highly conductive propped fractures.