3.2. Particle Size Analysis
The efficacy of plugging agents in controlling fluid loss and enhancing wellbore stability in complex deep coalbed methane (CBM) reservoirs is critically dependent on their particle size distribution. An optimized particle size allows for effective penetration into micro-fractures and pore throats, as well as the formation of a stable, low-permeability filter cake.
Table 1 presents the key statistical parameters (D
10, D
50, D
90) describing the particle size distribution for four different plugging agents. Complementary to the statistical data,
Figure 2 provides the complete volumetric particle size distribution curves, offering a visual representation of their distinct characteristics.
As indicated in
Table 2, MF-1 and MF-2 are characterized by significantly finer particle sizes, consistent with their classification as polymer nano-plugging agents. MF-1 exhibits a remarkably small median particle size (D
50) of 0.210 μm and a D
90 of 0.665 μm. Its particle size distribution curve, shown in
Figure 2a, is sharply peaked, with the vast majority of particles falling below 1 μm, underscoring its nano-scale nature. Moving towards larger particle sizes, MF-2, MF-3 and MF-4 represent micron-sized plugging agents designed for different sealing functions. MF-2 (
Figure 2b) possesses a D
50 of 2.033 μm and a D
90 of 9.522 μm, indicating a distribution primarily within the lower micron range. MF-3 (
Figure 2c) exhibits a broader micron-scale distribution, with a D
50 of 6.330 μm and a D
90 of 18.700 μm. The distribution curve for MF-3 shows a significant volume fraction of particles in the 5–20 μm range. Finally, MF-4, identified as ultrafine calcium carbonate, is the coarsest among the tested agents, with a D
50 of 8.333 μm and a D
90 of 33.800 μm. Its distribution curve (
Figure 2d) displays a prominent peak shifted towards larger particle sizes, reflecting its role in sealing larger pores and fractures.
3.3. Sealing Performance Analysis
Dynamic displacement experiments provide crucial insights into the real-time sealing performance of drilling fluids under simulated downhole conditions. The inlet pressure profiles, as a function of time, directly reflect the resistance to fluid invasion offered by the drilling fluid, with the breakthrough point indicating the duration and pressure-holding capacity of the created seal.
Figure 3 illustrates the inlet pressure variations over time for the base water-based drilling fluid (WBDF) and various WBDF formulations augmented with 5 wt% of different plugging agents. The analysis of these curves, combined with the coal core’s pore size distribution (
Figure 1) and the plugging agents’ particle size characteristics (
Figure 2), allows for a comprehensive understanding of their sealing mechanisms.
The saturated water curve serves as the negative control, representing the inherent flow resistance of the coal core. The pressure increased marginally to a peak of 0.04 MPa at 480 s, followed by a precipitous drop to 0.01 MPa at 490 s. This rapid pressure collapse signifies a complete fluid breakthrough, confirming the presence of open, connected macropores and fractures within the core. The low breakthrough pressure illustrates that, without any solid phase to bridge the throats, the fluid flows through the porous medium with minimal resistance.
The WBDF, which contains basic rheological modifiers but lacks specific bridging particles, exhibited a delayed breakthrough compared to water. It reached a similar peak pressure of 0.04 MPa at 2890 s before sharply declining to 0.01 MPa at 2900 s, indicating breakthrough. The significantly extended time to breakthrough (2890 s vs. 480 s) suggests that the viscosity and hydration capacity of the base fluid polymers provide some resistance to flow and may cause minor internal clogging. However, the fact that the peak pressure did not exceed that of water (0.04 MPa) and eventually failed demonstrates that viscosity alone is insufficient to form a pressure-bearing seal. The fluid ultimately traversed the pore network, proving the necessity of adding discrete plugging agents to establish a physical barrier.
The experimental results demonstrate a distinct correlation between the particle size of the plugging agents and their sealing behavior. The formulation containing MF-3 exhibited the most rapid and substantial pressure buildup, reaching a peak pressure of 0.56 MPa within a short duration (815 s) before breakthrough. According to the “1/3–2/3 bridging rule”, effective bridging occurs when particle size is comparable to the pore-throat size. Given that the dominant pore-throat diameter of the coal core is approximately 6–8 μm, MF-3 (D50 = 6.330 μm) offers the ideal geometric match. This allows it to quickly form a “primary bridge” at the pore throats, leading to a steep pressure rise. However, the subsequent sharp drop indicates that while these bridges are formed quickly, they are susceptible to failure under increasing differential pressure without the reinforcement of finer particles. MF-4, a rigid ultrafine calcium carbonate with a slightly larger size (D50 = 8.333 μm), also showed a relatively fast pressure increase (0.16 MPa). However, its performance was inferior to the flexible polymer MF-3. This suggests that while size matching is critical, the material deformability of polymeric agents like MF-3 allows for better adaptation to irregular pore shapes, creating a tighter seal than rigid particles, which may leave micro-gaps. In contrast, the finer agents MF-1 (nano-sized, D50 = 0.210 μm) and MF-2 (micro-sized, D50 = 2.033 μm) exhibited very slow pressure accumulation, remaining below 0.11 MPa even after extended periods (up to 8000 s). Their D50 values are significantly smaller than the dominant pore throats. Consequently, these particles largely pass through the pore network rather than bridging them. The gradual pressure rise observed for MF-2 likely results from deep-bed filtration and gradual internal cake buildup rather than surface sealing. The data clearly indicate that single plugging agents are insufficient for establishing a high-pressure seal. Ideally sized particles (MF-3) provide rapid bridging but lack the stability to sustain high pressures (breakthrough occurs). Under-sized particles (MF-1, MF-2) fail to initiate effective bridging. Rigid particles (MF-4) provide moderate bridging but lack the sealing tightness of deformable polymers. Therefore, this baseline analysis confirms the necessity of a multi-modal particle size distribution strategy.
To investigate the particle size matching effect in multi-modal sealing systems, the dynamic pressure responses of two dual-component formulations were evaluated (
Figure 4). Both systems utilized MF-3 (D
50 = 6.330 μm) as the primary bridging agent, targeting the dominant pore throats (6–8 μm). The secondary agents varied in size: MF-2 (micro-sized, D
50 = 2.033 μm) and MF-1 (nano-sized, D
50 = 0.210 μm). The formulation containing WBDF + 2.5% MF-2 + 2.5% MF-3 exhibited superior sealing performance, achieving a peak inlet pressure of 3.0 MPa within approximately 1300 s. This remarkable pressure buildup—significantly higher than any single-agent test—can be attributed to the “ideal packing” synergy between MF-3 and MF-2. According to shielding theories, effective filling particles should be approximately 1/3 to 1/4 the size of the bridging particles to optimally occupy the interstitial voids. The size ratio of MF-2 to MF-3 is approximately 1:3. Once MF-3 establishes the primary structural skeleton across the pore throats, the MF-2 particles are geometrically perfectly sized to jam into the voids between the MF-3 particles. This rapid “bridge-and-fill” process creates a dense, low-permeability filter cake almost immediately, leading to the sharp pressure rise observed.
In contrast, the WBDF + 2.5% MF-1 + 2.5% MF-3 system demonstrated poor sealing kinetics and strength, with a delayed pressure rise starting only after 3000 s and reaching a maximum of only 0.6 MPa. Although MF-1 is a nano-material expected to fill tiny pores, its size is over 30 times smaller than the primary bridging agent MF-3. This extreme size disparity creates a “packing gap”. The nano-particles are too small to be effectively retained by the relatively large voids left by the MF-3 bridge. Instead of filling the gaps, MF-1 particles likely pass through the filter cake or require an excessive amount of time to accumulate via adsorption/aggregation, resulting in the observed sluggish pressure response and a “leaky” seal. The comparative analysis confirms that particle size continuity is critical for filter cake integrity. A stepwise reduction in particle size is more effective than a discontinuous jump. The superior performance of the MF-2/MF-3 combination validates that maximizing packing density requires filler particles that geometrically match the interstitial spaces of the bridging skeleton.
To elucidate the distinct roles of rigid and flexible bridging agents in multi-scale sealing, two ternary formulations were subjected to dynamic pressure testing (
Figure 5). The experimental design compared a rigid bridging system (WBDF + 1% MF-1 + 2% MF-2 + 2% MF-4) against a flexible bridging system (WBDF + 1% MF-1 + 2% MF-2 + 2% MF-3). Both formulations successfully formed a high-strength pressure seal, withstanding inlet pressures up to 10 MPa. This confirms that regardless of the bridging agent’s mechanical modulus (rigid calcium carbonate vs. flexible polymer), the ternary particle size distribution—incorporating nano (0.210 μm), micro-filling (2.033 μm), and bridging (6–8 μm) particles—effectively shuts off the dominant pore throats. The system containing 2% rigid MF-4 demonstrated significantly faster sealing kinetics, reaching maximum pressure at approximately 2800 s. The D50 of MF-4 is 8.333 μm, which is slightly larger than the upper limit of the coal core’s dominant pore throats (6–8 μm). Unlike flexible particles, the rigid nature of calcium carbonate prevents deformation. Consequently, MF-4 particles physically jam the pore throats immediately upon contact, creating an instantaneous structural skeleton without penetrating deep into the formation. The system containing 2% flexible MF-3 exhibited a prolonged induction period, reaching 10 MPa later at 4100 s. MF-3 has a smaller size (D
50 = 6.330 μm) and possesses viscoelastic properties. Under differential pressure, these flexible microspheres can deform and squeeze through pore throats that are slightly larger or irregularly shaped. This “pass-through” phenomenon delays the establishment of a stable bridge, as the particles migrate deeper into the core before accumulation leads to blockage. The comparison highlights a trade-off between sealing speed and mechanism. The rigid system (MF-4) favors rapid wellbore strengthening through immediate physical jamming due to size exclusion. Conversely, the flexible system (MF-3) seals more slowly due to particle deformation and migration, likely forming a deeper, albeit delayed, internal seal. For rapid leak-off control, the rigid, slightly oversized formulation appears more advantageous in this specific pore-throat configuration.
3.4. NMR Analysis
Figure 6 displays the NMR T
2 relaxation time distribution curves for the coal sample initially saturated with simulated formation water and after dynamic displacement by the WBDF. The T
2 spectrum of the saturated coal sample shows a dominant peak located between 300 ms and 500 ms, indicating a significant presence of larger pores and fractures filled with water. The integral area of this initial T
2 spectrum, which is proportional to the total fluid volume, is 12,275,962.66 arbitrary units. After displacement by the WBDF, the T
2 spectrum undergoes a significant change: the peak’s amplitude substantially decreases, and its position shifts slightly towards shorter T
2 relaxation times. The integral area of the T
2 spectrum after WBDF displacement is reduced to 7,825,523.21 arbitrary units. This reduction in the total signal magnitude signifies that a considerable portion of the original fluid-filled pore volume has been either displaced by the drilling fluid’s components or effectively blocked, preventing further fluid exchange. An Es value of approximately 36.25% indicates that the WBDF has achieved a substantial reduction in the effective pore volume accessible to the simulated formation water, demonstrating its capability to mitigate filtrate invasion. Further insights into this sealing mechanism are provided by the pore-throat distribution analyses presented in
Figure 7.
Figure 7a reveals that the initial coal sample possesses a broad distribution of pore throats, with a dominant proportion residing in the 4–6.3 μm, 6.3–10 μm, and 10–16 μm ranges. This characteristic distribution, particularly the presence of larger pore throats, makes the coal formation susceptible to fluid invasion. Upon comparing
Figure 7a with
Figure 7b, a distinct alteration in the pore-throat distribution is observed after WBDF displacement. The most pronounced effect is the significant reduction in the percentage of larger pore throats, especially those in the 6.3–10 μm and 10–16 μm ranges. While the 4–6.3 μm range still contributes, its relative proportion might appear larger due to the decrease in the larger pore fractions, or its absolute percentage might also be slightly reduced. This indicates that the WBDF components, likely including solid particles and polymers, have successfully entered and physically blocked or partially filled these larger pore throats and micro-fractures. By doing so, the drilling fluid effectively reduces the permeability of the coal formation to filtrate invasion, consolidating the wellbore stability. The shift towards smaller effective pore sizes in the T
2 spectrum is a direct consequence of this physical plugging of the larger pore throats.
To further elucidate the sealing mechanism of nano-sized agents at the pore scale, Nuclear Magnetic Resonance (NMR) T
2 relaxometry and pore-throat size analysis were conducted before and after displacement with WBDF + 5% MF-1. As shown in
Figure 8, the T
2 spectrum of the saturated water exhibits a dominant peak at high relaxation times (300–600 ms), representing fluid residing in macropores and primary fractures. After treatment with WBDF + 5% MF-1, two significant changes occur. The total peak area decreased from 12,440,629.13 to 5,808,034.98, representing a 53.3% reduction in detectable fluid signal. The peak maximum shifted significantly to the left (from 450 ms to 180 ms). A shorter T
2 value signifies that the remaining fluid is confined in smaller effective pore spaces or that the specific surface area of the pores has increased due to particle deposition.
The transformation of the pore-throat distribution (
Figure 9) provides direct evidence of the “Nano-Coating and Pore-Refining” mechanism. The core is characterized by a “macropore-dominant” structure before displacement, with the largest fraction of throats concentrated in the 6.3–10 μm range. The 6.3–10 μm peak nearly disappears, while new peaks emerge in the 1.6–2.5 μm and 2.5–4 μm ranges. This indicates that MF-1 did not simply “plug” the large throats but rather subdivided or lined them.
Correlating these microscopic findings with the previously discussed pressure curves reveals a distinct sealing mechanism. Given that the particle size of MF-1 (0.210 μm) is significantly smaller than the primary throats (6–10 μm), it cannot form a stable “bridge” according to the 1/3 rule. Instead, the 53.3% reduction in NMR signal and the shift toward smaller throat sizes suggest that MF-1 particles form a thick adsorption layer on the pore walls. This adsorption layer reduces the effective hydraulic diameter of the macropores. While this “pore refining” increases flow resistance and delays fluid breakthrough, the resulting structure is mechanically unstable under high pressure. Without the structural “skeleton” provided by larger bridging agents, the nano-particles only offer a “soft seal” via surface adsorption and deep-bed filtration. This explains why, despite a significant reduction in microscopic porosity, the MF-1 system alone cannot achieve the “zero-invasion” 10 MPa seal observed in the ternary hierarchical systems.
The microscopic evaluation via NMR and pore-throat distribution analysis further elucidates the differentiated roles of nano- and micro-sized agents in the hierarchical sealing process. As shown in
Figure 10, compared to the 53.3% signal reduction observed with MF-1, the treatment with WBDF + 5% MF-2 resulted in a more pronounced 72.3% reduction in the T2 integral area (from 12,440,629.13 to 3,447,819.14), indicating superior volumetric occupancy of the movable fluid space. The shift in the T2 peak from 450 ms to approximately 100 ms, coupled with the emergence of sub-micron pore throats (0.1–0.16 μm) in
Figure 11b, demonstrates a significant “pore-refining” effect. While MF-1 primarily forms a surface adsorption layer, the micro-sized MF-2 acts through deep-bed filtration and physical jamming, subdividing the original 4–10 μm dominant throats into high-tortuosity micro-channels. However, a critical synthesis of these microscopic findings with the dynamic pressure curves reveals that high volumetric plugging does not inherently translate to high-pressure seal integrity. Despite the 72.3% reduction in porosity, the MF-2 system alone remains unable to sustain differential pressures above 1 MPa. This suggests that the refined pore network, while effective at restricting fluid flow at low pressures, lacks the mechanical skeleton necessary to resist erosive breakthrough.
As shown in
Figure 12, the microscopic analysis of the WBDF + 5% MF-3 system reveals the highest volumetric plugging efficiency among the single-component agents, with the NMR T
2 integral area decreasing by 80.5% (from 12,440,629.13 to 2,426,825.96). This superior reduction, compared to MF-1 (53.3%) and MF-2 (72.3%), stems from the ideal size match between the flexible polymer microspheres and the dominant pore throats of the coal core. As shown in the pore-throat distribution (
Figure 13b), MF-3 effectively “shuts off” the primary flow channels, shifting the dominant throat size from 8 μm down to 1.6–2.5 μm. Unlike the rigid jamming of MF-4 or the simple filling of MF-2, the viscoelastic nature of MF-3 allows it to deform and tightly wedge into the pore throats, creating a robust structural “bridge.” However, when synthesized with the dynamic pressure results, even this 80.5% reduction in detectable porosity is insufficient for high-pressure integrity when used in isolation. The remaining 1.6–2.5 μm micro-channels act as high-permeability pathways that lead to seal failure under multi-MPa differentials. This confirms that while MF-3 provides the indispensable structural skeleton of the seal, the achievement of the 10 MPa “zero-invasion” state observed in ternary systems requires the synergistic addition of MF-2 and MF-1, collectively transforming a bridged pore network into a truly impermeable composite filter cake.
As shown in
Figure 14, the microscopic evaluation of the WBDF + 5% MF-4 system reveals a substantial volumetric plugging efficiency, characterized by a 75.2% reduction in the NMR
$T_2
$ integral area (from 12,440,629.13 to 3,085,490.56). While this performance is markedly superior to the nano-adsorption of MF-1 (53.3%) and the micro-filling of MF-2 (72.3%), it falls short of the 80.5% reduction achieved by the flexible MF-3, illustrating the inherent limitations of rigid bridging agents. As shown in the pore-throat distribution (
Figure 15b), the rigid calcium carbonate particles effectively target the coal core’s dominant throats through size exclusion and physical jamming, successfully refining the network into micro-channels below 2.5 μm. However, the inability of MF-4 to deform means it cannot perfectly conform to the irregular coal pore geometries, leaving microscopic “point-to-surface” contact gaps that act as high-permeability bypasses. This explains why, despite achieving over 75% volumetric plugging, the MF-4 system alone cannot sustain high differential pressures in dynamic tests.
Microscopic characterization based on Nuclear Magnetic Resonance and pore-throat distribution confirms that the introduction of binary composite systems significantly enhances the compactness and spatial occupancy of the sealing layer. As shown in
Figure 16, the T
2 spectrum integral areas for the WBDF + 2.5% MF-1 + 2.5% MF-3 and WBDF + 2.5% MF-2 + 2.5% MF-3 systems decreased to 1,516,034.57 and 894,764.08, respectively. The corresponding pore space plugging rates reached 87.82% and 92.81%, both of which are significantly superior to the maximum value achieved by single-agent systems. Comparative analysis indicates that the synergistic effect of MF-2 and MF-3 is superior to that of MF-1 and MF-3, a result primarily attributed to the “size matching” between particle dimensions and the pore structure. Specifically, after MF-3 forms a primary bridge at the dominant pore throats, micron-scale inter-particle interstices are generated. The micro-sized filling agent MF-2 effectively fills these interstices, substantially reducing filter cake permeability. Conversely, the nano-sized MF-1, due to its insufficient size, fails to form effective packing within these micron-scale voids, allowing partial interconnected channels to persist. However, synthesizing these findings with macroscopic pressure-bearing test results reveals that although the MF-2 + MF-3 system achieves a volumetric plugging rate of 92.81%, it fails to attain a complete “zero-invasion” state under a differential pressure of 10 MPa. This indicates that binary systems still possess structural defects: the MF-2 + MF-3 combination lacks nano-particles for the further sealing of sub-micron pores, while the MF-1 + MF-3 combination lacks intermediate-sized particles for dense filling (
Figure 17). Consequently, the microscopic experimental data fully demonstrate the necessity of constructing a “bridging–filling–densifying” ternary multi-level sealing architecture. It is essential to simultaneously introduce intermediate-sized particles and nano-particles to eliminate residual hydraulic conductive pathways within the multi-scale pore space, thereby achieving absolute sealing under high-pressure conditions.
Quantitative characterization based on Nuclear Magnetic Resonance T
2 spectra and pore-throat distribution confirms that the ternary composite systems achieve ultimate sealing of the deep coal pore network by constructing a “full-scale multi-level dense packing” architecture. As shown in
Figure 18, the T
2 spectrum peak areas for the WBDF + 1% MF-1 + 2% MF-2 + 2% MF-3 and WBDF + 1% MF-1 + 2% MF-2 + 2% MF-4 systems plummeted to 22,273.52 and 21,204.81, respectively. Compared to the saturated water baseline (12,440,629.13), the plugging efficiency for both systems exceeded 99.8%. Notably, the pore-throat distribution signal for the ternary system containing rigid MF-4 particles dropped below the instrument’s detection limit after displacement, indicating that the system completely blocked fluid invasion channels. Mechanism analysis attributes this superior performance to the precise matching between particle sizes and pore structures: large skeletal particles (MF-3/MF-4) form primary pressure-bearing bridges at the dominant pore throats, medium-sized MF-2 tightly fills the geometric voids between the skeletal particles, and nano-sized MF-1 further seals sub-micron defects and modifies the filter cake surface, creating a synergistic “bridging–filling–sealing” mechanism (
Figure 19). It is noteworthy that the rigid MF-4 system exhibits comparable ultimate sealing efficiency, with MF-4 showing a marginally lower residual low-T2 signal than the flexible MF-3 system. This suggests that once the voids are completely filled by micro/nano particles, the high-modulus of the rigid skeleton is more effective in resisting filter cake creep and compressive deformation under a 10 MPa differential pressure, thereby maintaining the structural integrity and zero permeability of the sealing layer, ultimately achieving the “zero-invasion” objective for deep coalbed methane drilling fluids.