Study on the Mechanism of Fiber Fracturing Fluid Controlling Pulverized Coal Transportation

Abstract

In view of the problems associated with coal powder production in the development of Coalbed Methane (CBM), a fiber fracturing fluid technology is proposed to control pulverized coal production. Based on a force analysis of coal powder in the fracture and the microstructure of fiber-proppant, a critical intercepted particle size model of coal powder is established. This model is primarily related to fiber properties, proppant particle size and flow rate. To verify this, an FCES-100 device (Nantong Yichuang Experimental Instrument Co., Ltd., Nantong, China) was used to study the influence of fibers on the transportation of pulverized coal in the proppant pack. Five groups of comparative experiments were set up using no fiber, 0.25 g undegraded fiber, 0.25 g degradable fiber, 0.5 g undegraded fiber and 0.5 g degraded fiber, with the flow rate and closure pressures controlled, and, finally, particle size analysis of the discharged pulverized coal was performed using a laser particle size analyzer. The experimental results have shown that the space network structure formed by fiber-proppant can effectively intercept coal powder, reduce the coal powder migration and agglomeration, and eventually improve the fracture conductivity. The results further indicate that, with the increase of the flow rate, the coal particle size shows an increasing trend. The comparison between the particle size of the pulverized coal and the model calculation results demonstrate that the average error is 14.3% and the maximum error is 21.4%. Fiber fracturing fluid technology provides new directions for pulverized coal treatment.

1. Introduction

Coalbed Methane (CBM) is an unconventional gas, and its geological features and mining technology are very different from conventional reservoirs. China’s CBM sources are abundant, but most of the reservoirs have the “three low” features, that is, low gas saturation, low permeability and low pressure. It is necessary to carry out hydraulic fracturing and other measures to increase single well production. Currently, active water is mostly used in the coal seams, but the active water approach has problems such as weak proppant-carrying capacity, strong filtration loss, and high sand plugging risk, whilst fiber-based fracturing fluid precisely compensates for these disadvantages.

China’s coal geology is relatively brittle, and fracturing produces a large amount of coal powders. Coal powders are carried by the fluid and migrate in the micro-cracks and proppant packs. It is very easy for coal powders to gather and clog pores and throats, leading to the decrease of the penetration and the conductivity in coal reservoirs, which reduces the production of CBM wells. Therefore, preventing and controlling the transportation of pulverized coal has always been one of the cruxes of coal seam gas [1]. Many researchers have conducted in-depth studies on the mechanisms of pulverized coal transportation. Bai et al. [2,3,4] obtained the actual cleat geometry size and pulverized coal distribution characteristics of coal samples through electron microscopy scan images, and a fluid-solid coupling model was established to verify the production process of micro-scale pulverized coal. A new criterion based on dimensional analysis for evaluating the generation of pulverized coal was established, and the authors studied the effect of pulverized coal production size and pulverized coal on permeability under different flow (single-phase flow or two-phase flow) and pressure conditions. Guo et al. [5,6] found that the coal particles blocked the pore throat and caused the permeability of the coal rock to decrease, and the permeability increased after the blockage was discharged. Zhao et al. [7] obtained coal powder source and mechanical properties by comparing the particle size composition of pulverized coal from different production stages of coalbed methane wells. Yao et al. [8] carried out experiments for the correlation of coal type and pulverized coal output characteristics, and concluded that the former had a serious influence on coal powder output intensity, particle size and morphological characteristics. Lan et al. [9] established an instantaneous model of annulus pulverized coal-fluid two-phase flow using CFD software, aiming to study the impacts of the pulverized coal particle size, liquid inflow velocity and different volume fractions of pulverized coal in the annulus on coal powder production. Shi et al. [10] studied the behavior of different coal powders from Erdos and Qinshui Basin in deionized standard brine and NaHCO₃ suspensions, and Russell et al. [11] investigated the impact of the kaolinite content in rocks on its permeability. Based on this, various measures to prevent and control coal powders were proposed, including the following: mechanically wrapped wire screen [12]; control pressure [13]; coal powder suspension agents [14]; based on dynamometer monitoring, related downhole faults [15]; the ultimate pulverized coal concentration control method [16]; and a screw pump connected sand control pipe combining with oil jacket annulus water injection to dilute the concentration of pulverized coal [17].

The use of fiber fracturing fluid has many advantages, such as: low cost; a solution to the problem of proppant flow back [18,19,20]; improved carrying sand capacity; the relative ease and speed at which the fluid returns [21,22]; temporary fiber plugs [23,24,25]; and improved fracture conductivity [26], etc. The above scholars only explain the advantages of its properties from the experimental phenomena of fiber fracturing fluids, and lack the analysis of mechanical mechanisms. Hence fiber fracturing fluid technology is proposed for coal powder treatment. Then, the effect of degradable fibers on the movement of pulverized coal was tested, and the mechanism of mechanical action of fibers on pulverized coal was analyzed to provide a new idea for pulverized coal treatment.

2. Model Establishment

2.1. The Microstructure of Fibers-Proppant

The KTL1 fiber and active water were used to configure the fiber fracturing fluid. A certain amount of 20/40 mesh ceramsite was placed in the fracturing fluid and stirred well. Part of the fracturing fluid was picked up on the slide glass and then placed under a Stemi SV6 stereo microscope. The microstructures of fibers-proppant are shown in Figure 1. From the micrograph, it can be seen that fibers and proppants form a grid structure which can hinder the agglomeration of pulverized coal particles, thereby increasing the permeability of the coal seam.

2.2. The Mechanical Model of Fiber-Proppant Controlling Coal Powder

The fluid-carrying pulverized coal particles migrated in the coal fractures where the pulverized coal meets the fiber barrier, as shown in Figure 1, and the schematic diagram of fiber barrier resisting pulverized coal is shown in Figure 2.

Before the force analysis of the pulverized coal particles was undertaken, the following assumptions were made: (1) the fiber is uniformly anisotropic with elastic thin rods of the same size [27]; (2) single fiber ends are hinged and fixed; (3) pulverized coal particles are equal-diameter rigid spherical, not deformed, not broken; and (4) fiber bending deformation is a small bending deformation. Force analysis of pulverized coal is demonstrated in Figure 3.

Pulverized coal is subjected to force analysis as the following [28]:

$$F_1=2F_2\cos (\frac{\theta }{2})$$

(1)

$$F_1=F_p+F_i+F_r$$

(2)

$$F_r=\frac{\pi R_s^2}{2}{C}_D{\rho }_1{\upsilon }_1^2$$

(3)

where F₁ is the combined force of the fluid, N; F₂ is the force of the fiber on the pulverized coal, N; θ is the angle of the resistance, rad; F_r is the surface force, N; R_s is the coal powder radius, mm; ρ₁ is the fluid density, kg/m³; υ₁ is the fluid velocity, m/s; K is the permeability, 10⁻³ μm²; μ is the fluid viscosity Pa·s; and C_D is the surface coefficient.

The fiber is subjected to the reaction force$F_2^{\text{'}}$ of pulverized coal, the magnitude is the same as F₂ and the direction is opposite. $F_2^{\text{'}}$ is decomposed in the horizontal (F₃) and vertical directions (F₄). Only the influence of the vertical force F₃ is considered, as shown in Figure 4, and the force analysis is as follows:

$$F_3=F_2\sin (\frac{\theta }{2})$$

(4)

Substituting (1) into:

$$F_3=\frac{F_1}{2}\tan (\frac{\theta }{2})$$

(5)

According to the assumptions of (1), (2) and (4), it is assumed that the fiber is a beam subjected to a concentrated load F₃ and hinged at both ends, and the fiber is deformed by the concentrated force.

According to the related theory of material mechanics [29], the force relationship shown in Figure 5, the bending moment equations of AC and CB are:

AC segment

$$\begin{gathered} \mathrm{EI}{\omega }_1^{\text{'}}=-\frac{F_{3}b}{6L}(L^2-b^2-3x_1^2) \\ \mathrm{EI}{\omega }_1=-\frac{F_{3}b{x}_1}{6L}(L^2-b^2-x_1^2) \end{gathered}$$

(6)

CB segment

$$\begin{gathered} \mathrm{EI}{\omega }_2^{\text{'}}=-\frac{F_{3}b}{6L}\left[\left(L^2-b^2-3x_2^2\right)+\frac{3L}{b}{\left(x_2-a\right)}^2\right] \\ \mathrm{EI}{\omega }_2=-\frac{F_{3}b}{6L}\left[\left(L^2-b^2-x_2^2\right)x_2+\frac{L}{b}{\left(x_2-a\right)}^3\right] \end{gathered}$$

(7)

where x is any point on the x-coordinate; L is the length of single fiber, mm; a is the distance of concentrated load from point A, mm; b is the distance of concentrated load from point B, mm; ω is the deflection of single fiber, mm; M is the bending moment of single fiber, N·m; E is a single fiber elastic modulus, GPa; and I is a single fiber moment of inertia, mm⁴.

The zero position is determined by the mathematical extreme method, which can obtain the maximum deflection. The maximum deflection expression is:

$${\omega }_{\max }={\omega }_1(x_0)=-\frac{F_{3}b}{9\sqrt{3}EIL}\sqrt{(L^2-b^2{)}^3}$$

(8)

when the pulverized coal particles just pass, according to the geometric relationship.

$${\omega }_{\max }=R_s\left[1-\sin \left(\frac{\theta }{2}\right)\right]$$

(9)

Finished critical coal particle size R_s1 is:

$$\pi R_{s1}{\upsilon }_1({\rho }_1{\upsilon }_1+\frac{4\mu R_{s1}}{3K}+\frac{C_D{\rho }_1{\upsilon }_1}{2})=\frac{9\sqrt{3}EIL[1-\sin (\frac{\theta }{2})]}{b\sqrt{({\mathrm{L}}^2-b^2{)}^3}}$$

(10)

where μ is fluid viscosity, mPa·s; ρ₁ is fluid density, kg/m³; υ₁ is formation fluid velocity, m/s; and C_D is the drag coefficient.

Assuming that the fluid velocity is the same as the pulverized coal velocity and the concentrated load acts on the midpoint of the fiber, the above equation is simplified as:

$$\pi R_{s1}{\upsilon }_1({\rho }_1{\upsilon }_1+\frac{4\mu R_{s1}}{3K}+\frac{C_D{\rho }_1{\upsilon }_1}{2})=\frac{24(2-\sqrt{3})EI}{L^3}$$

(11)

Before establishing the critical particle size model for proppant interception of pulverized coal, the following assumptions are made [30]: (1) the proppant is a rigid spherical body with equal diameter and is not deformed or broken; (2) it is not considered that the proppant is embedded in the formation; (3) the proppant is formed into a diamond shape arrangement; and (4) the proppant pack in the fracture is a capillary model.

The total number of proppants N_mm is:

$$N_{num}=\left\{n\left[\frac{H_f-2R_p}{\sqrt{3}{R}_p}+1\right]-M\right\}\left(\frac{L_f}{2R_p}\right)$$

(12)

where H_f is the height of the fracture, m; L_f is the length of the fracture, m; R_p is the radius of the proppant, mm; n is the number of proppant layers; and M is a constant related to n.

According to Kozeny’s capillary model [31], the pores formed between the proppants in the proppant pack are assumed to be a single diversion beam, and the cross section is composed of N₁ diffusive bundles with a radius R_h. The number of diversion bundles from the geometric relationship is:

$$N_1=(n+1)[\frac{H_f-2R_p}{\sqrt{3}{R}_p}+2]$$

(13)

The following expression can be derived from the capillary model:

$$\pi R_h^2{L}_f{N}_1=L_f{H}_f{W}_f-N_{num}\times \frac{4}{3}\pi R_p^3$$

(14)

The critical particle size of proppant intercepting pulverized coal particles is:

$$R_h=\sqrt{\frac{L_f{H}_f{W}_f-N_{num}\times \frac{4}{3}\pi R_p^3}{\pi L_f{N}_1}}$$

(15)

Pulverized coal moves in fractures filled with fiber-proppants and can be transported through fiber and proppant pores. The critical particle size of the intercepted pulverized coal is derived from the formula above, and is calculated as follows:

$$R_c=\min \left\{R_{s1},R_{\mathrm{h}}\right\}$$

(16)

3. The Experiments of the Influence of Degradable Fiber on Coal Transportation

3.1. Experimental Program

In order to study the effect of fiber addition on coal production, an FCES-100 conductivity measuring instrument was used for optimization and quality control testing of different proppants before fracturing operations. It automatically collects parameters such as pressure difference, displacement, flow rate and temperature, and can automatically process data. It can simulate the temperature and pressure conditions of liquid flowing in the formation during fracturing, and calculate the fracture conductivity under different closing pressures. This instrument was used to conduct the following five groups of comparative experiments with no fiber, 0.25 g fiber, 0.25 g degradable fiber, 0.5 g fiber and 0.5 g degradable fiber, see

Table 1. Experimental program.

Series	Proppant	Sand Concentration	Pulverized Coal Concentration	Flow Rate/Closure Pressure	Group	Variable
A	Ceramsite 20/40	5 kg/m2	10%	200 mL/min	1	no fiber
					2	0.25 g fiber
					3	0.25 g degradable fiber
					4	0.5 g fiber
					5	0.5 g degradable fiber
B	Ceramsite 20/40	5 kg/m2	10%	5 MPa	1	no fiber
					2	0.25 g fiber
					3	0.25 g degradable fiber
					4	0.5 g fiber
					5	0.5 g degradable fiber

. The closure pressure or flow rates were changed, and the pulverized coal was collected for 1 h, then the collected coal slurry filtered, dried and its particle size distributions measured.

3.2. Experimental Procedure

(1) Lay a section of 16/20 mesh quartz sand at the inlet end of the diversion chamber of the FCES-100 fracture deflector, and uniformly mix a certain concentration of pulverized coal to simulate the coal reservoir. Changing the pulverized coal concentration can simulate reservoirs with different pulverized coal production capabilities. In the present study, pulverized coal was sourced from the Qinshui Basin.

(2) Mix a certain amount of fiber with ceramic particles of a slightly smaller particle size and then lay it on the remaining part of the diversion chamber up to the outlet end to simulate the filling layer. The steel plate is used to simulate the wall of the fracture, and the proppant embedding is not considered, as shown in Figure 6.

(3) Closure pressure is applied, and the advection pump is used to pump fluid (water or fracturing fluid) at a constant flow rate to simulate the flowback process of the fracturing fluid.

(4) Pulverized coal is collected at the outlet end, filtered, dried and weighed, and the fracture conductivity is measured when the flow rate is stable.

(5) The particle size distribution of the collected pulverized coal is finally measured by a laser particle size analyzer.

3.3. Experimental Results and Analysis

As shown in Figure 7, the pulverized coal output decreased with the increase of closure pressure. When the closure pressure was fixed, the output of coal powder after adding fiber reduced. With greater amounts of fiber added, the output of pulverized coal was lower; this primarily contributes to the space network formed by fiber and proppant, and can easily trap coal powder and reduce the movement of pulverized coal, thereby reducing the damage of pulverized coal transportation to the fracture throat. However, due to the partial degradation of the fiber, the smooth surface of the fiber became rough. In addition to the physical barrier, the rough surface is more likely to adsorb coal powder, which meant that the destructive fiber had a better effect on intercepting the coal powder.

Figure 8 shows a general downward trend in conductivity. This is likely because as the closure pressure increased, the proppant broke down to varying degrees until, finally, it caused the pore throat to become smaller. Clogging is more likely to occur when the pulverized coal migrates. As a result, the conductivity is decreased with the increase of closure pressure; the A1 group had the lowest conductivity under the same closure pressure, and the A5 group had the highest conductivity. This may be predominantly because the A1 group did not have any fiber added. The pulverized coal moved easily with the water flow and blocked the pores of the coal seam, leading the conductivity to decrease. The fibers could form a spatial network structure with the proppant, which would block the migration of coal powder and reduce its damage to the fracture conductivity. Therefore, the addition of fibers helped to increase the fracture conductivity.

As shown in Figure 9, as the flow rate increased, the pulverized coal output gradually increased, which prevented the coal powder from adhering and depositing. However, some coal powder was still clogged in the proppant pore throat because of the hydrophobicity of pulverized coal. When the flow rate was the same, the output of pulverized coal after the addition of fiber significantly reduced, and the greater the amount of fiber added, the lower the output of pulverized coal.

From the results displayed in Figure 10, under the same conditions, group B1 produced the most pulverized coal whilst its conductivity was the lowest, and group B3 produced the least pulverized coal production with the highest conductivity. The reason for this result is that B1 had a large number of coal powder outputs. At the same time as producing pulverized coal, the transporting amount of pulverized coal increased and the clogging of the pore throat increased, resulting in a decrease in conductivity. The space network formed by fibers with proppants can easily capture pulverized coal and reduce the pulverized coal transportation. As a result, only a small amount of pulverized coal was produced. The suitable pulverized coal production theory is beneficial to the formation of channels with high conductivity and, here, the optimal addition of fiber was seen in the group B3; exceeding this value would reduce the fracture conductivity.

Figure 11, Figure 12 and Figure 13 show the particle size analysis of pulverized coal produced at flow rates of 100, 200 or 300 mL/min, and closure pressure 5 MPa, using a laser particle size analyzer Mastersizer2000 (Malvern Instruments Ltd. UK, Malvern, UK). Figure 12 shows that when the flow rate was 200 mL/min, the pulverized coal particle size distribution curve took the form of a bimodal right polar peak, and the particle size value N varied from 1 to 464 μm. In five controlled trials, B1 had no fiber added. Pulverized coal migrated in large quantities and aggregated into clusters, which resulted in the production of larger particle-sized pulverized coal and increased the probability of plugging the pores of the proppant pack, which would result in lower conductivity; while the remaining four groups had a certain amount of fibers added, the space network structure formed fiber (with the proppant) could easily capture the coal powder, eventually reducing the coal powder migration and agglomeration. The particle size of the producing pulverized coal was relatively small, thereby obtaining a higher conductivity. At a flow rate 300 mL/min, the pulverized coal particle size distribution range was wide, and the particle size value varied from 1 to 1015 μm. The increase of flow rate caused a large amount of pulverized coal to change from a rest to migration state.

4. Model Validation

According to the results of the experiments, the values of related parameters are as follows, see

Table 2. Related calculation parameters.

Parameter Name	Value
Fiber diameter/µm	20
Fiber length/mm	8
Fiber elastic modulus/GPa	4.9
Fracture length/cm	17.7
Crack height/cm	3.8
Proppant particle size/10−3 m	0.3
Fluid density/(g/cm3)	1.016
Fluid viscosity/(mPa·s)	0.79
Surface coefficient	0.44

:

According to the results of the laser particle size analyzer, as shown in Figure 14, the maximum particle size of the producing pulverized coal was obtained. The experimental results were compared with the theoretical values of the model. The overall average error was 14.3%, and the maximum error was 21.4%. The model provides a theoretical reference for the calculation of critical coal particle size.

5. Outlook

Based on the properties of coal and rock, this paper studied the properties of fiber fracturing fluid and the influence of degradable fiber on pulverized coal transport from the aspects of compatibility between fiber and proppant, static sand suspension experiments and reservoir damage, and analyzed the mechanical action mechanism of fiber on pulverized coal. However, without extensive field applications, the practical significance of fiber fracturing fluid has not been fully demonstrated. Therefore, the author will actively contact relevant oil, gas and coal fields and adopt the fracturing fluid developed in this paper to test its practical effect in actual fracturing engineering.

6. Conclusions

(1) By analyzing the particle size distribution of coal seam produced at different flow rates, it was found that when the flow rate was 100 mL/min, the distribution curve of coal particle size was in the form of double peak right pole peak, and the particle size value varied from 1 to 337 µm. At 200 mL/min and 300 mL/ min, the particle size ranged from 1 to 464 µm and from 1 to 1015 µm. Therefore, at larger flow rates, the particle size distribution was wider and the particle size was larger.

(2) Based on the force analysis of coal powder in coal fractures and the microstructure of fiber-proppant, a critical particle size model for coal powder was established. The average error between theoretical and experimental values was 14.3%. The maximum error was 21.4%.

(3) The effect of fiber addition on the coal production and fracture conductivity was investigated by the FCES-100 fracture deflector, and the particle size distribution of the pulverized coal was analyzed. Experiments demonstrated that the addition of fiber reduced the probability of pulverized coal migration and coalescence and improved the fracture conductivity. As the flow velocity increased, the particle size distribution of pulverized coal showed an increasing trend. Fiber fracturing fluid provides a potential opportunity for the treatment of coal powder.