Experimental Study on Proppant Backflow and Fiber Sand Control in Vertical Fracture Based on the Visual Diversion Chamber Simulation

Abstract

Hydraulic fracturing is a critical technical means for enhancing production in gas fields, and post-fracturing flow-back constitutes a crucial phase of fracturing operations. Proppant backflow during the flow-back process significantly impacts both the effectiveness of stimulation and subsequent production. Particularly for tight gas reservoirs, achieving rapid post-fracturing flow-back while preventing proppant re-flux is essential. To date, domestic and international scholars have conducted extensive research on proppant backflow during flow-back operations, with laboratory experimental studies serving as a vital investigative approach. However, due to limitations in experimental apparatuses, further investigation is required regarding the migration mechanisms of proppants during flow-back, proppant backflow prevention techniques, and associated operational parameters. This paper developed a novel visualized flow chamber capable of simulating proppant migration in vertical fractures under closure stress conditions. Extensive proppant backflow experiments conducted using this device revealed that (1) proppant backflow initiates at weak structural zones near the two-phase interface boundaries; (2) proppant backflow occurs in three distinct stages, with varying fluid erosive capacities on proppant particles at each phase; (3) a multi-stage fiber injection sand control process was optimized; (4) at low proppant concentrations (<10 kg/m²), the fiber concentration should be 0.8%; at high proppant concentrations (>10 kg/m²), the fiber concentration should be 1.2%. The recommended fiber length is 6 mm.

1. Introduction

Hydraulic fracturing is an important technology in gas field development and widely used in the stimulation of various gas fields. Flow-back is an important part of hydraulic fracturing construction, which has an important impact on the overall fracturing effect. According to the current on-site flow-back of tight gas wells after fracturing, there is a common phenomenon of proppant backflow. According to incomplete statistics, the proppant backflow rate of tight gas horizontal wells in the JQ block ranges from 3.7% to 15.3%. The backflow of proppants will produce a fracture-face-skin effect, forming a fracture damage zone near the wellbore, reducing the effective support area of the fracture and its conductivity, thereby affecting the production capacity of the gas well. Related studies have shown that the average gas production reduction rate in proppant backflow gas wells is more than three times that of normal production wells. In addition, the accumulation of backflow proppants at the bottom of the well buries the gas layer or causes erosion of surface pipelines when it is discharged from the wellhead, among other issues, which poses safety hazards in construction and production. Therefore, the study of proppant backflow is of great significance for the development and production of gas wells [1,2,3,4,5].

Laboratory experimentation is an important means to study the law of proppant backflow during the process of flow-back. The existing physical simulation experimental methods to research proppant backflow mainly include the following: (1) the tube-perforation model [6] (Mark P. Understanding Proppant Flow-back[C]. SPE Annual Technical Conference and Exhibition. 1999.); (2) the slot model [7] (Goel N. Experimental Investigation of Proppant Flow-back Phenomena Using a Large Scale Fracturing Simulator[C]. SPE Annual Technical Conference and Exhibition. 1999.); (3) the API standard flow tester [8] (Canon J. Avoiding Proppant Flow-back in Tight-Gas Completions with Improved Fracture Design[C]. SPE Annual Technical Conference and Exhibition. 2003.); (4) and the large-scale flow-back apparatus [9] (Dimitry C. Proppant Flow-back: Can We Mitigate the Risk? [C]. SPE Hydraulic Fracturing Technology Conference and Exhibition held in The Woodlands, Texas, USA, 2020.). In summary, there are some limitations in the existing laboratory physical simulation experiments on proppant backflow [10,11,12,13,14,15]: (1) the influence of sand bank shape on proppant backflow in vertical fractures is ignored; (2) proppant backflow in vertical fractures cannot be simulated under the closure stress condition; (3) the physical simulation of proppant backflow cannot be visualized; (4) the experimental scale is too small, and there is a certain gap between the proppant backflow characteristics under experimental conditions and the actual field conditions; (5) the characterization parameters of critical velocity are too simple to accurately characterize proppant migration during flow-back [16,17,18,19,20,21].

To solve these problems, a new visual diversion chamber was developed and a new physical simulation experimental method of proppant backflow based on this device was proposed. The advantages compared to previous devices and simulation methods are as follows: (1) The entire process of proppant backflow can be made visible, making it easier to observe the movement rule of the proppants during flow-back. (2) The new device can be equipped with rock plates to simulate the proppant backflow in 200 cm² fractures, which is larger than the API diversion chamber in the scale of simulation. (3) The new experimental method adopts the alternate placement of proppants and fibers and simulates proppant settlement in a vertical diversion chamber after saturation of the fluid, forming a sand bank shape similar to the actual situation. The influence of the sand bank shape on proppant backflow is fully considered during the flow-back. (4) A pressure loading cavity is constructed on one side of the diversion chamber and a piston is embedded in the cavity. The external liquid enters the cavity to push the piston to exert closure stress, which simulates the proppant backflow in vertical fractures under the closure stress condition. (5) The method of step displacement increase was used in the experiment, and the critical flow rate was determined by drawing a relationship curve between liquid flow rate and sand production rate.

2. Methodology

2.1. Experimental Device

A schematic diagram of the new visual diversion chamber is shown in Figure 1. The chamber is composed of 5 parts, which are the chamber body, the visual plate, the piston, and the top and bottom plates. The front and back ends of the chamber body, made of 316 section steel, are respectively provided with a stepped inlet and outlet that can eliminate the jet effect. Two rock slabs (top and bottom plates) with a length of 20 cm and a width of 10 cm can be placed in the middle of the chamber body to simulate actual fractures.

One side of the chamber body consists of a piston and a pressure-loading cavity, which can provide about 39 MPa closure stress for simulated vertical fractures through hydraulic pressure that can simulate the proppant backflow in vertical fractures under the condition of closure stress. On the other side of the chamber body is a transparent convex plate called a visual plate, which can observe the whole process of proppant movement in the flow-back during the experiment.

Figure 2 is a schematic diagram of the experimental process of the device. Firstly, quartz sand is placed between the top and bottom plates (rock slabs) of the chamber body to simulate the proppants in the fracture. Secondly, the visual plate and piston are installed and we saturate the proppants with fluid, then keep the combination of rock slabs and proppants in a vertical state for proppant sedimentation to make the sand bank. Thirdly, we connect the pipeline to the chamber and apply closure stress using the pressure-loading device. Then, using the pump we inject the liquid in the water bath into the chamber through the method of increasing displacement in a stepped manner and record the changes in the flow rate at each moment using a flow meter. The outlet line is connected to the water bath, achieving the recycling of experimental liquid, using the mesh to filter the proppants in the flow-back liquid and record the weight of the proppants under conditions of differing displacement. Finally, the critical flow rate is determined by drawing a curve of the relationship between liquid flow rate and proppant production. Figure 3 shows an actual photograph of the visual diversion chamber and its system device.

2.2. Experimental Design

(1) Displacement design

The laboratory experiment’s displacement design follows the Reynolds number similarity criterion, with the displacement range determined based on actual flow-back fluid data from the Shaximiao Formation in the JQ block. The specific data is shown in

Table 1. The comparison table of experimental displacement and actual displacement.

Qe (mL/min)	Qf (m3/min)	He(mm)	Hf (mm)	We(mm)	Wf (mm)
5330.36	1.00	100	20,000	10	10
1110.49	0.83	100	20,000	10	10
888.39	0.67	100	20,000	10	10
666.29	0.50	100	20,000	10	10
444.20	0.33	100	20,000	10	10
222.10	0.17	100	20,000	10	10
199.89	0.15	100	20,000	10	10
177.68	0.13	100	20,000	10	10
155.47	0.12	100	20,000	10	10
133.26	0.10	100	20,000	10	10
111.05	0.08	100	20,000	10	10
88.84	0.07	100	20,000	10	10
66.63	0.05	100	20,000	10	10
44.42	0.03	100	20,000	10	10
22.21	0.02	100	20,000	10	10

.

In this table, H_e denotes the simulated fracture height in the experimental setup, while H_f represents the actual fracture height formed during the fracturing process (this fracture height is an average derived from micro-seismic data monitoring of multiple construction wells on-site and post-fracturing fitting). W_e stands for the simulated fracture width in the experimental apparatus, and W_f corresponds to the actual fracture width achieved after the fracturing operation. Q_f indicates the actual volume of fluid expelled per hour during the flow-back phase post-fracturing, and Q_e refers to the laboratory experimental discharge rate that corresponds to the actual flow-back fluid volume. According to the field measurements from the JQ block, the flow-back fluid volume is approximately between 1 and 20 m³/h. When converted, this corresponds to a laboratory discharge rate ranging from 22.21 to 444.2 mL/min. Consequently, the designed discharge rate for the experimental process is set within the range of 20 to 500 mL/min.

(2) Experimental group design

The L₉ (3³) orthogonal experiment takes fiber length, fiber concentration, and sand concentration as the independent variables, with sand production rate and critical flow velocity as indicators. Through range analysis, the impact of these three factors on the sand production rate and critical flow velocity is analyzed to clarify the trend of experimental indicators with each factor. The optimal fiber length, fiber concentration, and sand concentration under the desired conditions of low sand production rate and high critical flow velocity are determined. The specific experimental data are presented in

Table 2. The L₉ (3³) orthogonal experiment data.

Number	Fiber Concentration (%)	Sand Concentration (kg/m2)	Fiber Length (mm)	Cumulative Sand Production Rate (%)	Critical Flow Velocity (mL/min)
1	0.4	5	3	/	/
2	0.4	10	6	/	/
3	0.4	15	9	/	/
4	0.8	5	6	/	/
5	0.8	10	9	/	/
6	0.8	15	3	/	/
7	1.2	5	9	/	/
8	1.2	10	3	/	/
9	1.2	15	6	/	/

.

In conventional proppant flow-back experiments, the critical flow velocity is typically defined as the fluid discharge rate corresponding to the initial sand production or when the sand production reaches a certain threshold. However, this definition of critical flow velocity is subject to significant errors due to a series of uncontrollable factors such as operator intervention during the experiment. The method for determining the critical flow velocity in this experiment represents a substantial innovation over traditional methods. The experiment employs a stepwise increase in discharge rate, collecting data on sand production and the corresponding fluid discharge rate over the same time scale. These data are then plotted to create a relationship curve between fluid flow velocity and sand production rate. The critical flow velocity is comprehensively determined by identifying the inflection point on the curve in conjunction with observations from a visualization device throughout the experimental process. In addition to the aforementioned experiments, we also utilized the apparatus to compare different sand control techniques, which primarily included the tail-end fiber addition, multi-stage fiber, and full fiber injection sand control processes.

(3) Specific experimental operation methods

• Position the chamber body horizontally and shield the inlet and outlet to prevent the spillage of proppants and fibers. Subsequently, place the rock slab into the chamber body, ensuring it fits snugly against the inner wall without any gaps. Then, evenly distribute the pre-weighed proppants and fibers onto the rock slab, making sure the surface of the filling layer formed by the proppants and fibers is level. Finally, cover the visual plate and connect it to the chamber body through threads without any looseness.
• Position the chamber body vertically to simulate a vertical fracture. Then, assemble the piston and connect it to the pressure-loading device, using it to inject liquid into the pressure-loading cavity to provide pressure on the vertical walls, simulating closure pressure. Simultaneously turn on the pump and saturate the proppant/fiber fill layer within the chamber body with liquid at a displacement rate of 10 mL/min.
• After the proppant/fiber fill layer is fully saturated with fluid, remove the shields from the inlet and outlet ends. Begin the flow-back process by incrementally increasing the displacement rate from an initial speed of 20 mL/min up to 700 mL/min to simulate the proppant transport during flow-back. Place a camera at the visualization window to continuously record the state changes of the fill layer within the fracture. Position a collector at the outlet end to gather and weigh the expelled sand.

3. Results and Discussion

Based on actual field data, a series of laboratory experiments were conducted using the new visual diversion chamber to investigate the migration law of proppants during the flow-back process. The study identified the appropriate fiber sand control techniques and optimized the technical parameters for fiber sand control. The experimental results and insights are discussed in the following 3 aspects.

3.1. The Migration Law of Proppant Backflow

During the experiment, the entire flow-back process was observed, photographed, and documented using the visualization device. By analyzing the morphology of the sandbank post-experiment, the specific locations of proppant migration during the flow-back process were initially identified. Contrary to prior understanding, the experimental results revealed that proppant migration does not solely occur at the top of the proppant fill layer but rather in structurally weak areas within the proppant fill layer. This phenomenon is primarily characterized by the erosion of these weak structural zones due to high fluid flow rates during flow-back, which creates flow channels and leads to the fluidization of the proppants.

Screenshots from the flow-back experiment video and the morphology of the sandbank formed after flow-back reveal the locations of proppant migration during the flow-back process. In Figure 4a, the yellow outline delineates the void area at the top of the proppant fill layer, while the white outline marks the location where proppants are carried out by the fluid. Observations from the experimental video reveal that, despite the presence of voids at the top of the proppant fill layer, the proppants flow out from a middle section. Analysis indicates that this middle section contains a structurally less stable region, which is unable to withstand the erosion caused by high-flow-rate fluid. This results in the formation of flow channels, allowing the proppants to be transported out from this location.

Figure 4b–d, showing the state of the sandbank after flow-back, further corroborate the aforementioned perspective. Typically, proppants are flushed out of the fracture at the top of the proppant fill layer, causing the height of the sandbank to gradually decrease (as seen in Figure 4b,d). However, there are also instances where proppants are ejected from the middle of the fracture (as seen in Figure 4c). Based on these experimental results, we propose that the instability of proppants at the fracture outlet is no longer the primary cause of sand production. Instead, the instability and fluidization of weak structural zones within the sandbank are the main reasons for sand production. Therefore, the approach to sand control should shift from merely blocking the fracture outlet to enhancing the structural stability of the proppant fill layer.

The sand-carrying capacity of flow-back fluid dynamically changes and is strongly correlated with the size of the flow channel and the morphology of the sand bank. In the early stages of flow-back, as the closure stress increases, the area for fluid flow decreases, causing the fluid velocity to increase, which leads to the sand bank becoming more susceptible to erosion and sand production. The proppant backflow forms the channel within the proppant fill layer, which causes the flow area to increase. Under the same or slightly increased displacement rate, the fluid velocity decreases, the erosion capacity of the fluid on the sand bank weakens, and the backflow of proppants reduces. However, due to the closure stress, the newly formed flow channel will gradually decrease, again leading to an increase in the fluid erosion capacity on the sand bank, resulting in sand production. This process repeats until equilibrium is reached. In experiments, this is manifested as fluctuations in the amount of sand produced at different stages (see Figure 5), and in the field, it is manifested as fluctuations in the amount of sand produced under the same or higher choke settings (see Figure 6).

By analyzing the captured proppant flow-back process with image analysis software, it is concluded that the movement patterns of proppant flow-back can be roughly divided into three stages.

• Channels are formed on the surface of the sand bank or at weak structural points due to erosion by high-speed fluid, and the proppants are carried away by the fluid.
• After the proppants flow back, the flow channel of the liquid becomes larger, the fluid velocity decreases, the sand-carrying capacity weakens, the proppants roll back and the amount of backflow decreases.
• The channel further expands, and the flow velocity decreases to the point where the scouring force on the proppants is less than the interlocking force between the particles, causing the proppants to cease movement. The movement patterns of proppant flow-back can be seen in Figure 7.

3.2. Comparison of Fiber Sand Control Under Different Processes

In the experiment, the impact of different fiber injection methods on sand control effectiveness was investigated, primarily including four approaches: no fiber (NF), tail-end fiber injection (TFI), whole-process fiber injection (WFI), and multi-stage fiber injection (MFI). The final sand bank morphology and critical flow velocity were used as indicators to evaluate the effectiveness of sand control. The experimental results revealed significant differences in sand control effectiveness among the various fiber injection methods. Considering both practicality and cost-effectiveness, the multi-stage fiber injection method was deemed the most effective sand control technique.

In sand control experiments, it can be observed that when the mechanical strength of the proppant fill layer is insufficient to withstand fluid erosion, both fibers and proppants are flushed out of the fracture by high-speed fluid. In such cases, the fibers of TFI are extensively washed out of the fracture, leading to the failure of the fracture outlet blockage in the proppant fill layer and resulting in a larger-scale back-flow of proppants.

Figure 8 shows the morphology of sand banks under different sand control techniques before and after flow-back. Images a to d simulate various fiber injection methods (NF, TFI, WFI, MFI) prior to flow-back, while images e to h depict the sand bank morphology after flow-back for each corresponding fiber injection method. As can be discerned from the figures, the sand bank configurations resulting from TFI and NF are remarkably similar. The partial failure of the fracture outlet blockage formed by fibers leads to significant erosion of the proppants at the top of the sand bank, resulting in a reduction in the height of the sand bank and a decrease in effective support in the fracture by the proppants. The sand bank formations after flow-back for the WFI and MFI are alike. Due to the reinforcement of the structure of the entire proppant fill layer by fibers, compared to the former two fiber injection methods, the sand banks exhibit greater height and thickness, with less proppants flowing out from the fractures.

By inputting the experimental data into the sand bank strength increase calculation model, the forces acting on the proppants under different fiber injection methods were computed to characterize the ability of the proppant fill layer to resist fluid erosion. The calculation results (see Figure 9) indicate that the WFI and MFI significantly enhance the structural strength of the proppant fill layer, far surpassing the TFI. Taking into account all experimental results, it is concluded that the MFI is the optimal choice for fiber-based sand control.

3.3. Optimization of Construction Parameters for Sand Control Technology

The previous section demonstrated that the MFI is the most effective sand control technique. In this section, orthogonal experiments are conducted based on the MFI to investigate the sand control performance under different operational parameters. The specific experiments were conducted based on the experimental protocol outlined in Section 2.2 and the experimental results observed in

Table 3. Orthogonal experimental results of sand production rate and critical flow velocity under multi-factorial influences.

Number	Fiber Concentration (%)	Sand Concentration (kg/m2)	Fiber Length (mm)	Cumulative Sand Production Rate (%)	Critical Flow Velocity (mL/min)
1	0.4	5	3	0.06	110
2	0.4	10	6	0.13	140
3	0.4	15	9	0.12	110
4	0.8	5	6	0.04	140
5	0.8	10	9	0.18	190
6	0.8	15	3	0.20	140
7	1.2	5	9	0.04	190
8	1.2	10	3	0.10	230
9	1.2	15	6	0.05	400

and

Table 4. Comprehensive analysis of orthogonal experiments.

Main Effect Values	Indicators	Fiber Concentration (%)	Sand Concentration (kg/m2)	Fiber Length (mm)
K1	sand production rate	0.30	0.14	0.36
K2		0.41	0.40	0.22
K3		0.19	0.37	0.33
k1		0.10	0.05	0.12
k2		0.14	0.13	0.07
k3		0.06	0.12	0.11
R		0.07	0.09	0.05
K1	critical flow velocity	360	440	480
K2		470	560	680
K3		820	650	490
k1		120	146.67	160
k2		156.67	186.67	226.67
k3		273.33	216.67	163.33
R		153.33	70.00	66.67

.

Using sand production rate and critical flow velocity as evaluation metrics, the main effect values (K₁, K₂, K₃) and range (R) were calculated. Under the sand production rate criterion, the ranges (R) for the three influencing factors (fiber concentration, sand concentration, and fiber length) were 0.07, 0.09, and 0.05, respectively. For the critical flow velocity criterion, the corresponding ranges were 153.3, 70.4, and 66.7. The results indicate that, in the MFI, sand concentration has the greatest impact on sand production rate, while fiber concentration predominantly influences critical flow velocity.

Figure 10 shows curves reflecting the relationship between fiber concentration and critical flow velocity under different sand concentrations. It can be found that at low sand concentrations (5, 10 kg/m²), the critical flow velocity exhibits a logarithmic increase with rising fiber concentration. When the fiber concentration exceeds 0.8%, the enhancement effect on critical flow velocity diminishes. At high sand concentrations (15 kg/m²), the critical flow velocity shows exponential growth with increasing fiber concentration, and the improvement becomes more pronounced when fiber concentration surpasses 0.8%. From the structural analysis of fiber–proppant composites,

• Under low sand concentrations, excessive fiber concentration may reduce dispersion within the composite structure and cause overflow, thereby compromising structural stability.
• At high sand concentrations, the proppant-dominated composite structure effectively prevents fiber overflow, enabling fibers to consistently enhance structural strength.
• Experimental results recommend 0.8% fiber concentration for low sand concentrations and 1.2% fiber concentration for high sand concentrations.

Figure 11 shows the relationship between fiber length and critical flow velocity under different sand concentrations. The experimental results demonstrate that increasing fiber length can enhance the critical flow velocity, but this effect is limited. When the fiber length becomes excessively long, its dispersion capability significantly deteriorates, which adversely affects the structural stability of the fiber–proppant composite system.

From the perspective of mechanical property enhancement mechanisms, increasing fiber length improves critical flow velocity by strengthening fluid–fiber interaction forces. The physical essence stems from a modified Stokes law: as the fiber aspect ratio (L/d) increases, the viscous resistance generated by fluid circumfluence significantly increases, manifesting as enhanced critical velocity. However, this growth follows a logarithmic curve characteristic, with diminishing critical velocity increments when fiber length exceeds 6 mm. Analyzing the dispersion deterioration threshold, excessive fiber length induces the following issues: (1) the entanglement probability increases exponentially; (2) local aggregation occurs, with micro-CT revealing fiber clusters >50 μm in diameter when fiber length ≥9 mm. Structural stability optimization modeling demonstrates that the system achieves Pareto optimality at 6 mm fiber length, delivering 32% critical velocity improvement while maintaining over 85% dispersion degree. Therefore, 6 mm fiber length is recommended for this process.

4. Field Application

This technology was applied in well QL220-8-H2 on the QL platform, with two other wells (H1 and H3) from the same platform serving as control groups for sand control effectiveness comparison. Specific operational parameters are shown in

Table 5. The construction parameter statistics.

Well	Proppants	Injection Method	Total Sand Volume (t)	Total Liquid Volume (m3)	Fiber Concentration (%)	Fiber Length (mm)	Sand Production (m3)
QL220-8-H2	sand	MFI	5804	22,925.8	0.8	6	40
QL220-8-H1	sand + resin-coated sand	tail-end resin-coated sand injection	5628	20,542.2	/	/	104
QL220-8-H3	sand + resin-coated sand	tail-end resin-coated sand injection	5488	19,070.8	/	/	150

.

Post-fracturing flow-back results indicated that well H2 produced 40 m³ of sand with a sand production rate of 1%, while wells H1 and H3 produced 104 m³ and 150 m³ of sand, respectively, corresponding to sand production rates of 2.8% and 4.1%. Compared with traditional resin-coated sand technology, this technology achieved 61.5% and 73.3% reductions in sand production, respectively. The application of this technology at the QL220 platform has fully demonstrated its effectiveness.

5. Conclusions

This study has reached the following conclusions:

• Proppant flow-back occurs at the interface between two phases (i.e., irregular voids or structurally weak zones at the top of the proppant fill layer). The essence of proppant flow-back is the erosion of proppant particles in structurally weak areas of the proppant fill layer by backflow fluids.
• The movement of proppants during flow-back can be divided into three stages. Its resistance to fluid erosion varies with each stage, and this capability is strongly correlated with fluid flow channels and sand bank morphology.
• The optimal sand control technique identified in the experiments is MFI, with the following recommended parameters:
• At low proppant concentrations (<10 kg/m²), the fiber concentration should be 0.8%;
• At high proppant concentrations (>10 kg/m²), the fiber concentration should be 1.2%;
• The recommended fiber length is 6 mm.