Coal sample selection

The Qinshui Basin, rich in coalbed methane resource reserves, is an important coalbed methane-producing area in China. The cleat structure of the coal reservoir with strong permeability is well developed, so the coal sample of a pumping well in mining area III of Shizhuang South Block in Qinshui Basin is selected. The formation and development of cleat are related to coal rank, maceral, and ash contents. First, an industrial analysis experiment of the coal sample was conducted and then, the measured moisture (Mad) content (2.15%), ash (Ad) content (14.73%), volatile (Vad) content (33.26%), and fixed carbon (FCad) content (40.14%) were determined. The organic microcleat of coal was identified using an optical microscope, and the following parameters were measured: exinite content (16%), vitrinite content (57%), and inertinite content (27%). The coal sample was determined to be bituminous coal. Table 1 shows the results in detail.

Microscopic model preparation

The outer part of coal was first peeled off by the wire cleat to obtain the cleat structure in coal, and the samples were cut into sizes of 2 cm × 2 cm × 2 cm. Then, the side that showed cleat development clearly was dissected. Pulverized coal was blown out using a negative ion blower at a low temperature, which prevented the accumulation of pulverized coal and cracking of the original cleat. Finally, the opposite side of the face cleat was polished for observation under a microscope. The coal sample was placed in the observation area of a Leica 3D topography instrument. The magnification was adjusted to 100× according to the cleat opening and length, and effective visual field radius is 300 μm. Then, the whole sample was scanned with tiled coal samples after translation processing. The geometric contour of the channel was obtained on the basis of the starting position of the cleat. Finally, the complete face cleat structure was stitched and restored by the stitching algorithm in ImageJ software.

Figure 1 shows the whole process. The Fractal Box Count function of ImageJ was used to calculate the number of square boxes with side length a occupied by a single cleat image and to describe the morphological characteristics of the irregular cleat in detail. Box side length a was changed to count the N(a) values under different a values and to plot the corresponding data points of N(a) values and a values under different conditions. The slope of the best-fit curve was plotted to obtain the fractal dimension of the fractal surface (1.5).

Photolithography was used to construct a transparent channel model of the extracted cleat structure. The basic principle of photolithography involves the use of a photoresist sensitized to form corrosion resistance due to the photochemical reaction to engrave the desired pattern onto the surface of the object to be processed. This study investigated the effect of local width variation of the zigzag cleat surface on the flow. Based on the principle of minimum pore size to control the flow (Li, Wang, et al., 2022), the depth of the model was uniformly set to 3 mm, which was much larger than the maximum width of the cleat surface. According to the characteristics of the large depth-to-width ratio of the model, a molding processing method based on the SU-8 process was selected.

The preparation process of the model is as follows: (1) A mask version was made on the quartz substrate according to the geometric structure extracted by the surface cleat. The template corresponding to the model channel was partially transparent, and the rest was opaque. (2) The SU-8 photoresist was stirred to remove bubbles and applied to the rotating quartz substrate. (3) The UV irradiation device was set above the mold, which accelerated the curing of the SU-8 photoresist through the light-transmitting part of the mask. The convex mold was formed after the chemical reaction, baking, and cleaning of the residual adhesive. (4) The treated polydimethylsiloxane (PDMS) prepolymer and curing agent were poured on the mold and solidified in the attemperator. (5) The mold was separated from the PDMS polymer and the channel structure of the cleat was transferred to PDMS. (6) The PDMS substrate containing the channel structure was bonded to the cover plate of the same material and a complete micromodel was formed after postprocessing. Figure 2 shows the model preparation process.

Cleat characterization refinement

The channel opening affects the flow capacity, and the model channel in this study represents the real face-cleat structure. Since the openings of plane geometric points are different, the local opening distribution characteristics of the area are quantified. First, the geometric structure background was set to a black rectangular box and binarized. The gray value of the cleat area was 255 (white) and that of the other areas was 0 (black). Then, the image was imported to ImageJ software. The change in the gray values of the survey line was calculated, and the average gray value of the white crack and the black background was determined based on the Plot Profile function. Figure 3a shows the measurement. Finally, the local opening of the cleat was calculated according to the following equation:

(1)

where l is the actual length of the cleat, μm; b the white pixel value on the line; r is the total gray value when the image is assumed to be all white; and h represents the actual length of the line, μm.

The whole cleat area is divided into 8570 lines with a distance of 1 pixel. Figure 3b shows the frequency distribution histogram and the fitting curve of the cleat opening. The maximum opening is 413 μm, and the minimum opening is 13.7 μm; the area less than 60 μm accounts for 51%, with narrow areas throughout the entire cleat model.

The cleat wall surface has certain undulating characteristics, which results in a tortuous fluid flow path. Specifically, it increases the length of the flow path. Therefore, a straight channel model equivalent to the length of the natural cleat meander is designed, and the parameters of the straight channel are calculated according to the opening, volume, and characteristic width of the cleat using the following equation (Zhou et al., 1999). The cleat channel is divided into several segments according to its orientation, and its local curvature characteristics are characterized by tortuosity (Kong, 1999).

(2)

where τ i denotes the curvature of the cleat contour line in the segment; L Ai is the real length of the cleat; and L i is the apparent length of the cleat.

Then, the real length L A of the cleat theory can be expressed as

(3)

When the total cross-flow area of the cleat theory is constant,

(4)

where h i is the local width of the primary cleat in the ith segment; L B is the length of the flat channel; and h B is the width of the flat channel in model B. Therefore, the channel width of model B is set to 92 μm for the comparison experiment of model A. Figure 4 shows the finished model.

Visualized test system and method

2.4.1 Visualized experimental device

An experimental system (Figure 5) was constructed to perform the visualized experiment of the unsaturated flow of the shear model at the microscale. It was mainly composed of a fluid injection system, a pressure monitoring system, a visualization system, and a data acquisition computer.

Gas–liquid displacement flow-rate characteristics

Complete gas-to-water and water-to-gas flow videos captured by the camera were imported to Phantom Camera Control software. The instantaneous flow rate of the displacement interface was measured at an interval of 1 s. The average instantaneous flow rate in model B was used as the standard flow rate, and the fluctuation of the instantaneous flow rate was calculated using Equation ( 5). The gas–water interface flowed evenly in the smooth channel, and the opening in the roundabout channel changed frequently. As a result, there was leapfrog flow, and the flow rate fluctuated accordingly (Bai et al., 2022). Figure 6 shows the displacement characteristics of different regions.

(5)

where R i is the instantaneous flow-rate change rate under certain displacement conditions, and it represents the ratio of the instantaneous flow rate of the circuited channel to the smooth channel; v Ai is the instantaneous flow rate of the displacement interface in the circuited channel of model A from inlet i, mm/s; and denotes the average flow rate of the displacement interface in the smooth channel of model B, mm/s.

Figure 7a shows the instantaneous flow-rate ratio changes of the water-drive process under three injection flows. The instantaneous flow rate also fluctuates in the roundabout channel due to changes in the opening of the local area. The flow rate of the roundabout channel is closest to that of the smooth channel at a low flow rate (0.3 µL/min), and the standard deviation σ of the instantaneous flow-rate change rate is 4.3. As the injection flow rates increase to 1.5 and 3.0 µL/min, the standard deviation values in turn increase to 4.7 and 7.1, respectively, and the instantaneous flow rate fluctuates more violently. Based on the critical pressure before the breakthrough of the three flow injection fluids, the three injection pressures are as follows in the water flooding experiment: P2 = 0.001 32 MPa, P4 = 0.0103 MPa, and P6 = 0.0388 MPa. Figure 7b shows the instantaneous flow-rate ratio changes of the gas-drive process under the three injection pressures. The instantaneous flow rate shows stronger fluctuations than water flooding, and the standard deviation in turn increases from 5.7 to 6.1 and 8.9.

The hysteresis of the displacement interface in the area of sudden changes in the cleat opening destroys the balance of the gas–liquid displacement interface, which causes additional energy loss. Therefore, the wall surface should be smoothened in the production process (e.g., injection of an acidic dissolved solution [Song et al., 2014]) to ensure the smoothness of the migration space. Besides, the capillary pressure model (Gao et al., 2021) where the dynamic contact angle replaces the static contact angle can better reflect the flow process in the shear structure.

Analysis of dynamic changes in contact angles

The instantaneous flow-rate characteristics of the gas–liquid displacement show that the displacement interface is affected by changes in the local channel opening and shows obvious hysteresis. The dynamic contact angle is used to characterize the degree of obstruction of the channel to the fluid (Eral et al., 2013). The monocular electron microscope is adjusted to capture the enlarged gas–water displacement interface at all times, and the entire dynamic process is divided into images at intervals of 1 s. According to the five-point measurement method (Chen et al., 2022), the dynamic contact angle of the partial displacement interface is calculated in ImageJ software.

The contact angle (θi = 127°) hardly changes throughout the entire flow process in a smooth channel (Figure 8a). The meniscus is found to be concave θii = 68°, θiii = 107°, θiv = 114°, and θv = 118° in the tortuous channel. An obvious difference exists in the contact angle on both sides (θvil = 102° and θviu = 151°) in areas with uneven wall openings. The curvature of the gas-to-water interface is greater than that of the water-to-gas interface, and both are concave to the driven phase; the curvature of the contact angle interface is stable (θi = 56°) in the smooth channel (Figure 8b). The dynamic contact angle in the roundabout channel is generally smaller than that of the smooth channel, and the contact angle of the upper and lower walls is consistent in the area where the opening changes evenly (θii = 26°, θiii = 12°, and θiv = 47°). The contact angle is not identical on both sides (θvu = 32°, θvl = 28°, θviu = 26°, and θvil = 59°) in areas where the wall opening is uneven.

The displacement interface advances with a symmetrical meniscus in the partially flat channel area. Influenced by the undulation of the wall, the contact line on the side of the first contact inflection point comes to a halt. An obvious stick phenomenon occurs when the displacement interface advances to the vicinity of the partially curved channel. The other side of the contact line continues to advance and the meniscus rotates around the contact line stagnation point. The curvature of the gas–liquid interface increases until the meniscus bends around the stagnation point side of the channel wall to encounter the single-phase contact angle conditions on the channel wall. The contact line reaches a new equilibrium position so that the flow can continue. The water-drive interface shows concave and convex changes greatly affected by the pinning effect in the zigzag channel. By contrast, the gas-drive interface maintains a relatively stable concave surface. The capillary pressure model with a dynamic contact angle instead of a static contact angle reflects the flow process in the cut-off structure.

Characteristics of the gas-drive residual phase

The desorbed gases of coalbed methane are transported from the pores to the space of saturated water. Free water away from the wellhead also invades the cleat space occupied by the gas phase (Sander et al., 2018). Therefore, the process of gas–water mutual displacement often occurs in the cleat, with the small structure of the pore throat on the microscale and obvious constraints between the gas and the liquid (Li et al., 2017). Figure 9 shows the distribution of residual fluids under different displacement pressures. The displacement interface moves slowly under the low displacement pressure, and the residual liquid is mainly distributed in the cleat groove (Figure 9a). The liquid level bends to the wall surface under pressure, and only a small amount of liquid film exists in the smooth channel. As the pressure increases, the effusion at the groove increases and the residual liquid film on the smooth wall is also significant (Figure 9b). Figure 9c shows the residual liquid distribution when the gas-drive pressure increases to 0.0103 MPa. The groove is almost filled with effusion, and the thickness of the liquid film at the smooth wall surface significantly increases.

As the injection pressure increases (P6 = 0.0388 MPa), the relative flow rates of the displacement gas and the displacement liquid phase also increase. The gas–water interface fluctuates drastically, and the shear effect between the gas and liquid phases is enhanced, which thickens the liquid film on the wall with an uneven distribution. Groove effusions and liquid films occupy the cleat migration channel, which reduces the effective open area of subsequent fluids. Therefore, this factor should be considered in the capillary force model. Meanwhile, the stability of the pressure should be maintained during the production process to prevent the residual liquid from occupying the seepage channel and thus reducing the permeability of the reservoir.