Application of Mercury Intrusion Porosimetry in Coal Pore Structure Characterization: Conformance Effect and Compression Effect Correction

Abstract

Mercury intrusion porosimetry (MIP) is commonly used to characterize coal pore structures, but conformance effect and compression effect can overestimate pore volume. This study uses MIP data from coal with varying metamorphic degrees in China to compare existing correction methods and propose a new approach based on apparent and true density for pore volume correction under no confining pressure. The study also analyzes the impact of conformance and compression effects on MIP data. Correctly identifying the “actual initial intrusion pressure” and “closure pressure” is essential for accurate data correction. The fractal dimension method offers a more robust theoretical foundation, while the conformance and intrusion pressure identification method is simpler. The stage correction method is reliable but requires repeated MIP tests, adding to the workload. The new method, which corrects both coal matrix and mercury volume compression, provides a simpler and reliable solution. Results show that conformance volume accounts for 9.91–83.26% of the apparent mercury intrusion volume and increases with coal metamorphism. Coal matrix volume compression represents 99.86–99.90% of the corrected total volume, with mercury volume compression being negligible. The corrected pore volume decreases as coal metamorphism increases, indicating the effectiveness and simplicity of the proposed method.

1. Introduction

Precise characterization of the pore structure characteristics and connectivity of oil and gas reservoirs is the foundation for understanding the laws of fluid occurrence, migration, and output in reservoirs. Especially for the unconventional oil and gas reservoirs, the complex genetic types of pores, the wide pore size distribution range, the high development degree of nanoscale (0.1–100 nm) pores, and strong heterogeneity increase the difficulty of pore structure characterization [1,2]. The three main methods for characterizing the pore structure of oil and gas reservoirs are as follows: (microscopic) observation methods, such as optical microscope and electron microscope; ray detection methods, such as nuclear magnetic resonance (NMR), X-ray computed tomography (X-ray CT), small angle X-ray scattering, and neutron small angle scattering; and gas adsorption and fluid penetration methods, such as mercury intrusion porosimetry (MIP) and N₂/CO₂ adsorption tests [3,4,5,6,7,8,9]. Among these methods, MIP is one of the most commonly used pore structure characterization methods and has a fast measurement speed, low sample shape requirements, low cost, ease of use, and mature technology.

MIP determines the pore throat volume and porosity by measuring the mercury injection pressure (up to 60,000 psi or 413.7 MPa); from these data, the pore size distribution, pore specific surface area, and pressure–mercury saturation curve can be calculated, and the sample permeability or relative permeability can be estimated [10,11]. The relationships among the mercury injection pressure, pore throat diameter, and pore specific surface area are characterized by the Washburn equation (Equation (1)) [12].

$$P_{\mathrm{Hg}}={\displaystyle \frac{2\sigma \cos \theta }{r}}$$

(1)

where r is the pore throat radius, μm; P_Hg is the mercury intrusion pressure, MPa; σ is the surface tension of mercury, 0.48 N/m; and θ is the contact angle of mercury and porous medium, typically set to 140° or 130°.

It is believed that there are two errors in the calculation of the pore structure using MIP data. (1) Powder and granular samples (e.g., coal powder) are commonly used in MIP to shorten the mercury injection time, and these samples can cause a “conformance effect” or “surface effect”. Before mercury is injected into the sample pores, it first fills the “spaces” between the sample particles and “holes” on the sample surface, compensating for the irregularity of the sample particles; here, the volume occupied by mercury is not part of the actual pore volume of the sample, resulting in an overestimation of the sample pore volume [13,14,15]. Moreover, with increasing mercury injection pressure, the sample pores are compressed, and a higher injection pressure is needed to fill all the “spaces” and “holes” before mercury enters the sample pores [15]. When samples with larger particle sizes (e.g., coal lumps) are used, the “conformance effect” is relatively small and is often disregarded; however, it still exists [13,14,16]. The samples with larger particle sizes may contain more microfractures, which may not be inherent in the samples and are generated during sample collection and preparation. The mercury injected into these microfractures also leads to a “conformance effect”. Therefore, regardless of whether broken or unbroken samples are used, errors are caused by the “conformance effect” in MIP, and the “actual entry pressure” needs to be corrected; this “actual entry pressure” is the pressure that occurs when mercury begins to enter the real pores. (2) A high mercury injection pressure can compress the experimental samples and lead to an additional mercury intrusion volume that does not belong to the actual pore volume of the samples, resulting in an overestimation of the sample pore volume. This phenomenon is called the “compression effect” [17,18,19], and the mercury injection pressure that causes severe compression of the samples is called the “closure pressure” of the pores [20]. In summary, both the “conformance effect” and the “compression effect” can lead to an overestimation of the sample pore volume, making it necessary to correct the MIP data to obtain a more realistic pore size structure.

MIP data correction has been extensively studied. This study focuses on the identification of “actual entry pressure” and “closure pressure” and the correction of the mercury intrusion volume (or pore volume) [11,21,22]. (1) The main purpose of identifying the “actual entry pressure” and “closure pressure” is to determine the extent of the impact of the “conformance effect” and the “compression effect” and then to clarify the pressure interval of the MIP data correction. The fractal dimension method [18,23,24] and the conformance volume and intrusion volume identification method [13,20] are commonly used for this purpose. The fractal dimension method uses the MIP data to calculate the fractal dimension of the sample pores and determine the “actual entry pressure” and “closure pressure”. The conformance volume and intrusion volume identification method compares the compression coefficient of the pore volume calculated from the MIP data with the linear portion of the mercury injection pressure curve to determine the “actual entry pressure” and “closure pressure”. The initial pressure where the calculated compression coefficient of the pore volume deviates from the linear fitting point at a low mercury injection pressure is considered the “actual entry pressure” or “conformance pressure”, and that at a high mercury injection pressure is considered the “closure pressure” or “mercury intrusion pressure”. (2) To correct the mercury intrusion volume (or pore volume), a direct correction method is predominantly used, or the compressibility of the samples under high pressure is quantified using other experimental methods to correct the actual mercury intrusion volume (or pore volume) under high mercury injection pressure. The direct correction method substitutes the determined “actual entry pressure” or “closure pressure” into the corrected expression of the pore volume compression coefficient to obtain the corrected mercury intrusion volume and pore volume [20]. This method is simple to perform but lacks a theoretical basis. The correction method is based on other experimental methods, generally uses MIP on the samples wrapped in epoxy resin to obtain the volume compression coefficient of the samples under the same experimental conditions and then corrects the errors in the mercury intrusion volume caused by compression effects [17,25]. This correction method has a sufficient theoretical basis but requires repeated MIP tests, greatly increasing the workload. These identification methods for the correction pressure interval and correction methods for the mercury intrusion volume (or pore volume) have been widely used in carbonate rocks, tight sandstone, mudstone, shale, etc. [23,26,27]. However, studies using the correction method for coal MIP data are limited, and most focus on the identification of the correction pressure interval. Moreover, under high mercury injection pressure, the pore structure changes in coal with different degrees of metamorphism are complex, and the applicability of the identification method for the correction pressure interval and the correction method for the mercury intrusion volume (or pore volume) has not yet been determined. In addition, the pore volume obtained from the N₂ adsorption test was used to correct the MIP data of coal. The pore volume obtained from the N₂ adsorption test is considered to be the real accumulated pore volume in the correction pressure interval. This volume is used to calculate the coal matrix compression coefficient (considered a constant) and correct the coal matrix volume and stage mercury intrusion volume [28]. This correction method assumes that the pore volumes obtained from the different testing principles and data processing methods are equivalent; this assumption does not have a sufficient theoretical basis.

In this work, the MIP data of coal with different degrees of metamorphism in China was used, and the applicability of the identification methods for the correction pressure interval and correction methods for mercury intrusion volume (or pore volume) were compared and analyzed. Additionally, the correction method for mercury intrusion volume (or pore volume) was improved to obtain more accurate pore structure characteristics in coal and other oil and gas reservoirs.

2. Research Methods

2.1. Experimental Samples

Six coal samples were selected for this study: sub-bituminous coal from the Junggar Basin in Xinjiang; high volatile bituminous coal from coal seam #9 of the Taiyuan Formation in the Bohai Bay Basin; medium volatile bituminous coal from the 2nd coal seam of the Shanxi Formation in the Pigdingshan mining area; and low volatile bituminous coal, semianthracite, and anthracite from coal seam #3 of the Shanxi Formation in the southern Qinshui Basin. These samples are numbered #1–#6 (

Table 1. Coal quality parameters of the test samples.

Number	Sampling Position	Ro, max	Industrial Analysis				φ	ρbulk	ρture
			Mad	Aad	Vdaf	FCad
#1	Saier Energy No.6 mine	0.40	11.04	4.87	43.99	47.10	4.05	1.35	1.41
#2	Yangzhuang mine	0.72	2.05	5.92	39.94	55.28	2.62	1.31	1.35
#3	Shoushan mine	1.35	0.90	13.48	19.44	68.97	3.04	1.31	1.35
#4	Xinyuan mine	1.81	0.96	6.15	15.69	78.31	2.53	1.42	1.46
#5	Yuwu mine	2.19	1.51	12.08	12.47	75.63	2.90	1.43	1.47
#6	Sihe mine	3.33	4.21	11.07	7.14	78.67	2.65	1.57	1.61

Note: R_{o, max} is the mean maximum vitrinite reflectance, %; M_ad is the moisture content, wt.%; A_ad is the ash content, wt.%; V_daf is the volatile content, wt.%; FC_ad is the fixed carbon content, wt.%; the subscript “ad” is air-dried basis; the subscript “daf” is dry ash-free basis; φ is porosity, %; ρ_bulk and ρ_ture are apparent density and true density, respectively, g/cm³.

). The collection, storage, and transportation of the coal samples were conducted in accordance with the national standard GB/T 19222-2003 and the international standard ISO 7404-2:1985. The coal qualities of the samples are provided in Table 1.

2.2. MIP Experiment

In this study, the pore size structure classification system proposed by the International Union of Pure and Applied Chemistry (IUPAC) was adopted: pore sizes less than 2 nm are micropores; pore sizes between 2 and 50 nm are mesopores; and pore sizes greater than 50 nm are macropores [29].

The MIP experiment was conducted using an AutoPore IV 9500 mercury porosimeter manufactured by Micromeritics, Norcross, GA, USA, in accordance with the international standard ISO 15901-1:2005. The samples used were 3–4 cm³ in volume. The mercury injection pressure ranged from 0.0070 to 273.0031 MPa (1.0174–39585.4450 psi). The pore size and pore specific surface area were calculated using the Washburn formula, as expressed in Equations (1) and (2), with a contact angle of 130° between mercury and coal.

3. Correction Methods for the MIP Experimental Data

3.1. Determination of the “Actual Entry Pressure” and “Closure Pressure”

3.1.1. Fractal Dimension Method

Research has demonstrated that the pore systems of coal, sandstone, shale, and mudstone exhibit fractal characteristics. Based on fractal theory, the pore fractal dimension in coal can be calculated using the mercury intrusion porosimetry curve; this curve enables the determination of the “actual entry pressure” and “closure pressure” in the MIP experiment. The calculation method for the pore fractal dimension in coal can be found below [30,31].

According to the scaling law, the relationship between the pore size distribution dV_Hg/dr and the fractal dimension D is as follows:

$${\displaystyle \frac{d{V}_{\mathrm{Hg}}}{dr}}\propto r^{2-D}$$

(2)

Equation (1) can be substituted into Equation (2) to yield the following equation:

$${\displaystyle \frac{d{V}_{\mathrm{Hg}}}{d{P}_{\mathrm{Hg}}}}\propto P_{\mathrm{Hg}}^{D-4}$$

(3)

Thus, the following equation can be obtained:

$$\mathrm{l}\mathrm{g}\left({\displaystyle \frac{d{V}_{\mathrm{Hg}}}{d{P}_{\mathrm{Hg}}}}\right)\propto \left(D-4\right)\mathrm{l}\mathrm{g}\left(P_{\mathrm{Hg}}\right)$$

(4)

where V_Hg is the mercury intrusion volume or the cumulative mercury intrusion volume at the maximum experimental mercury injection pressure, cm³/g; and D is the fractal dimension (dimensionless).

Equation (5) expresses the relationship between the fractal dimension of the coal pores and the fractal dimension fitting curve lg(dV_Hg/dP_Hg) − lg(P_Hg). By using the fractal dimension fitting curve, the fractal dimension of the coal pores can be obtained (Figure 1). The fractal dimension fitting curve of the coal MIP data can generally be divided into three segments, with fractal dimensions D₁, D₂, and D₃ [25,32]. D₁ represents the fractal dimension during the “conformance effect” stage; this stage shows the intrusion characteristics when mercury fills all “voids” and “cavities” in the sample at low pressure. The highest injection pressure in the D₁ segment is P₁ (critical pressure of the filling stage); D₂ represents the actual mercury intrusion characteristics of the coal pores, typically less than 3, and the highest mercury injection pressure at this stage is P₂ (critical pressure for the actual mercury intrusion stage); and D₃ represents the “mercury intrusion characteristic” caused by the compression of coal at high pressure, specifically the “mercury intrusion characteristic” in the “compression effect” stage, typically greater than 3, and the highest mercury injection pressure at this stage is P₃ (critical pressure for the coal compression stage) (Figure 1). When uncrushed samples are used, the performance of D₁ is relatively weak because of the absence of interparticle “voids”. According to previous studies, when the mercury injection pressure exceeds 10 MPa (P₂), the influence of the compressibility of coal on the mercury intrusion volume cannot be disregarded, corresponding to pore sizes ranging from approximately 150 to 180 nm. Furthermore, P₂ is not constant. A higher degree of coal metamorphism correlates with a higher P₂. For example, P₂ is 3.56 MPa for sub-bituminous coal and can reach 44.77 MPa for anthracite coal [13,32]. Significant differences are observed in the mechanical properties of different coal rock samples, and the deformation and destruction characteristics of the samples under high mercury injection pressure are different. If the coal sample is not significantly damaged under high mercury injection pressure and remains in the elastic deformation stage, P₃ is usually equal to the maximum mercury injection pressure in the MIP experiment (Figure 1c–f); if the coal sample undergoes severe plastic deformation and the pore structure is destroyed, it no longer exhibits fractal characteristics, and the fractal dimension fitting curve shows a fourth segment, namely the failure stage (Figure 1a,b).

3.1.2. Conformance Volume and Intrusion Volume Identification Method

Bailey [33] proposed a method for determining the “actual entry pressure” and “closure pressure” based on the pore volume compression coefficient. This method was further refined by Comisky [20].

The pore volume compression coefficient can be calculated using Equation (5) [20,33]:

$$C_{\mathrm{pore}}={\displaystyle \frac{1}{V_{\mathrm{Hg}}}}{\displaystyle \frac{d{V}_{\mathrm{Hg}}}{d{P}_{\mathrm{Hg}}}}={\displaystyle \frac{1}{V_{\mathrm{Hg}}}}{\displaystyle \frac{\Delta V_{\mathrm{Hg}}}{\Delta P_{\mathrm{Hg}}}}$$

(5)

where C_pore is the pore volume compression coefficient, MPa⁻¹.

At this point, the pore volume compression coefficient at each mercury injection pressure can be expressed as a power function of the mercury injection pressure (Equation (6)). Under the double logarithmic coordinate axis, the relationship between the pore volume compression coefficient and the mercury injection pressure is linear, as follows:

$$C_{\mathrm{pore}}^{\prime }=m{P}_{\mathrm{Hg}}^n$$

(6)

where C′_pore is the pore volume compression coefficient fitted from the linear curve of the pore volume compression coefficient versus the mercury injection pressure under the double logarithmic coordinate axis, MPa⁻¹; m is the intercept of the linear curve of the pore volume compression coefficient versus the mercury injection pressure under the double logarithmic coordinate axis; and n is the slope of the linear curve of the pore volume compression coefficient versus the mercury injection pressure under the double logarithmic coordinate axis.

As shown in Figure 2, a deviation is observed between C_pore and C′_pore under the double logarithmic coordinate axis. The deviation at the low-pressure stage originates from the “conformance effect”, whereas the deviation at the high-pressure stage is caused by the compression effect [20,33]. By analyzing the deviation between C_pore and C′_pore (ΔC_pore = |lg (C′_pore) − log (C_pore)|), the “actual entry pressure” and the “closure pressure”, also known as the conformance pressure and the mercury intrusion pressure, respectively, can be determined (Figure 2a). Consequently, the conformance volume and the mercury intrusion volume can be obtained (Figure 2b).

3.2. Correction Methods for the Mercury Intrusion Volume and Pore Volume

3.2.1. Conformance Volume and Intrusion Volume Correction Method

The conformance volume and mercury intrusion volume obtained from Equations (5) and (6) are substituted into Equation (7) to correct for the conformance effect and compression effect, yielding the corrected pore volume of the sample, as follows:

$$\left\{\begin{array}{l}{V}_{\mathrm{pore}}=0,P_{\mathrm{Hg}}\le P_{\mathrm{c}}\\ V_{\mathrm{pore}}=V_{\mathrm{Hg}}-V_{\mathrm{c}},P_{\mathrm{c}}<P_{\mathrm{Hg}}\le P_{\mathrm{i}}\\ V_{\mathrm{pore}}=V_{\mathrm{Hg}}-V_{\mathrm{i}},P_{\mathrm{Hg}}>P_{\mathrm{i}}\end{array}\right.$$

(7)

where V_pore is the corrected pore volume or the cumulative mercury intrusion volume, cm³/g; V_c, V_i are the conformance volume and the intrusion volume, respectively, cm³/g; and P_c, P_i are the conformance pressure and the intrusion pressure, respectively, MPa.

Substituting the intrusion volume into Equations (8)–(10) enables the calculation of the corrected apparent density, true density, and porosity of the coal sample [20,23,33], as follows:

$${\rho }_{\mathrm{bulk}}={\displaystyle \frac{W_{\mathrm{s}}}{\left[V_{\mathrm{p}}-\left(\frac{W_{\mathrm{a}}-W_{\mathrm{p}}-W_{\mathrm{s}}}{{\rho }_{\mathrm{Hg}}}\right)-V_{\mathrm{c}}{W}_{\mathrm{s}}\right]}}$$

(8)

$${\rho }_{\mathrm{ture}}={\displaystyle \frac{W_{\mathrm{s}}}{\left(\frac{W_{\mathrm{s}}}{{\rho }_{\mathrm{bulk}}}-V_{\mathrm{pore}, \mathrm{totals}}{W}_{\mathrm{s}}\right)}}={\displaystyle \frac{1}{\left(\frac{1}{{\rho }_{\mathrm{bulk}}}-V_{\mathrm{pore}, \mathrm{totals}}\right)}}$$

(9)

$$\phi ={\displaystyle \frac{V_{\mathrm{pore}, \mathrm{total}}{W}_{\mathrm{s}}}{\left(\frac{W_{\mathrm{s}}}{{\rho }_{\mathrm{bulk}}}\right)}}=V_{\mathrm{pore}, \mathrm{total}}{\rho }_{\mathrm{bulk}}$$

(10)

where ρ_Hg is the density of mercury, g/cm³; V_p is the dilatometer volume of the mercury porosimeter, cm³; W_s, W_a, and W_p are the weights of the test coal sample, the dilatometer with both the sample and mercury, and the dilatometer without the sample and mercury, respectively, g; and V_{pore, total} is the total corrected pore volume of the coal sample, cm³/g.

3.2.2. Stage Correction Method

Based on the force analysis of the samples in the MIP experiment, Peng [15] proposed that the correction of the pore volume compression coefficient in the MIP experiment could be divided into two stages. The first stage occurs before mercury invades the pores of the sample. During this stage, the mercury injection pressure acts as the confining pressure, resulting in compression of the sample skeleton and pores (Figure 3a). The compression of the sample skeleton is mainly observed in the more ductile components, such as organic matter and clay minerals. The second stage occurs after mercury invades the pores of the sample. During this stage, the mercury injection pressure serves as both the confining pressure and the pore pressure, resulting in no pore compression but only skeleton compression occurring (Figure 3b). Based on the above analysis, the volume change rate of the sample (ΔV_HgW_s/V_s) in the first and second stages can be expressed as follows [15]:

$${\left({\displaystyle \frac{\Delta V_{\mathrm{Hg}}{W}_{\mathrm{s}}}{V_{\mathrm{s}}}}\right)}_1={\displaystyle {\int }_{P_0}^{P_{\mathrm{r}}}{f}_{\mathrm{r}}\left(P_{\mathrm{Hg}}\right)}{C}_{\mathrm{obs}}\left(P_{\mathrm{Hg}}\right)d{P}_{\mathrm{Hg}}$$

(11)

$${\left({\displaystyle \frac{\Delta V_{\mathrm{Hg}}{W}_{\mathrm{s}}}{V_{\mathrm{s}}}}\right)}_2={\displaystyle {\int }_{P_{\mathrm{r}}}^{P_{\max }}{f}_{\mathrm{r}}\left(P_{\mathrm{Hg}}\right)}{C}_{\mathrm{s}}\left(P_{\mathrm{Hg}}\right)d{P}_{\mathrm{Hg}}$$

(12)

where ΔV_Hg is the stage mercury intrusion volume and can be understood in Equation (11) as the volume change of sample under the mercury injection pressure P_Hg (including both actual pore volume change and volume change induced by sample compression), cm³/g; vs. is the test sample volume, cm³; P_r is the mercury injection pressure when mercury intrudes pores with radius r, MPa; P_max is the experimental maximum mercury injection pressure, MPa; P₀ is the mercury injection pressure when mercury begins to enter the pores, which can be equated to the “actual entry pressure” and the conformance pressure, MPa; f_r (P_Hg) is the function of the stage mercury intrusion volume or sample volume change at mercury pressure P_Hg; C_obs (P_Hg) is the sample (skeleton and pores) volume compression coefficient at the mercury pressure P_Hg, MPa⁻¹; and C_s (P_Hg) is the sample skeleton volume compression coefficient at the mercury pressure P_Hg, MPa⁻¹.

Based on the above analysis, the sample volume change under mercury injection pressure P_Hg is the sum of the changes in the first and second stages. In the first stage, although the sample volume change includes both sample skeleton volume compression and pore volume compression, the compressed pore volume is part of the original pore volume under the initial condition. Therefore, when the pore volume (or actual mercury intrusion volume) is corrected in this stage, only the sample skeleton volume compression needs to be considered. Thus, Equation (11) can be rewritten as follows [15]:

$${\left({\displaystyle \frac{\Delta V_{\mathrm{Hg}}{W}_{\mathrm{s}}}{V_{\mathrm{s}}}}\right)}_1={\displaystyle {\int }_{P_0}^{P_{\mathrm{r}}}{f}_{\mathrm{r}}\left(P_{\mathrm{Hg}}\right)}{C}_{\mathrm{s}}\left(P_{\mathrm{Hg}}\right)d{P}_{\mathrm{Hg}}$$

(13)

The sum of the skeleton volume compression in the first stage and the second stage is the total correction amount [15] as follows:

$$\begin{array}{ll}\hfill {\left({\displaystyle \frac{\Delta V_{\mathrm{Hg}}{W}_{\mathrm{s}}}{V_{\mathrm{s}}}}\right)}_{\mathrm{total}}& ={\displaystyle {\int }_{P_0}^{P_{\mathrm{r}}}{f}_{\mathrm{r}}\left(P_{\mathrm{Hg}}\right)}{C}_{\mathrm{s}}\left(P_{\mathrm{Hg}}\right)d{P}_{\mathrm{Hg}}+{\displaystyle {\int }_{P\mathrm{r}}^{P_{\max }}{f}_{\mathrm{r}}\left(P_{\mathrm{Hg}}\right)}{C}_{\mathrm{s}}\left(P_{\mathrm{Hg}}\right)d{P}_{\mathrm{Hg}}\hfill \\ & ={\displaystyle {\int }_{P_{\mathrm{Hg}}}^{P_{\max }}{f}_{\mathrm{r}}\left(P_{\mathrm{Hg}}\right)}{C}_{\mathrm{s}}\left(P_{\mathrm{Hg}}\right)d{P}_{\mathrm{Hg}}\hfill \end{array}$$

(14)

The (ΔV_HgW_s/V_s) _total (dimensionless) calculated from Equation (14) can be used to correct the pore volume (stage mercury intrusion volume) of a sample under the mercury injection pressure P_Hg (Equation (15)). The corrected stage mercury intrusion volume can subsequently be used to calculate the sample volume compression coefficient and the cumulative mercury intrusion volume under this mercury injection pressure. The cumulative mercury intrusion volume can be used to correct the porosity and pore size distribution characteristics. Moreover, since this method does not consider the pore volume compression, the corrected pore volume and porosity are those without the confining pressure; these can be compared with the results obtained by other methods, such as He testing, without the confining pressure conditions.

$$\Delta V_{\mathrm{pore}}=\Delta V_{\mathrm{Hg}}-{\displaystyle \frac{{\left(\frac{\Delta V_{\mathrm{Hg}}{W}_{\mathrm{s}}}{V_{\mathrm{s}}}\right)}_{\mathrm{total}}}{{\rho }_{\mathrm{bulk}}}}$$

(15)

where ΔV_pore is the corrected stage pore volume or stage mercury intrusion volume, cm³/g.

In this correction method, the sample volume compression coefficient C_obs (P_Hg) under the mercury injection pressure P_Hg can be calculated using Equation (16); however, distinguishing between the changes in mercury intrusion volume caused by skeleton compression and pore compression is difficult. Therefore, the skeleton volume compression coefficient C_s (P_Hg) under mercury injection pressure P_Hg is difficult to obtain using MIP data. Instead, C_s (P_Hg) is often obtained through other experimental methods or by using empirical values. The most common method involves conducting MIP experiments under the same conditions on samples encapsulated with epoxy resin.

$$C_{\mathrm{obs}}={\displaystyle \frac{1}{V_{\mathrm{Hg}}}}{\displaystyle \frac{d{V}_{\mathrm{Hg}}}{d{P}_{\mathrm{Hg}}}}={\displaystyle \frac{1}{V_{\mathrm{Hg}}}}{\displaystyle \frac{\Delta V_{\mathrm{Hg}}}{\Delta P_{\mathrm{Hg}}}}$$

(16)

In this method for pore volume and porosity correction, the compression of the pore volume is not considered. However, the impact of the pore volume compression needs to be considered in the calculation of actual pore size; specifically, the compression of the pore volume before mercury intrusion leads to a reduction in the calculated pore size. Therefore, the original pore size is larger than the pore size measured under mercury injection pressure. For a given sample volume compression coefficient C_obs (P_Hg) and skeleton volume compression coefficient C_s (P_Hg) under the given mercury injection pressure P_Hg, the compression coefficient of the sample pore volume C_pore (P_Hg) can be expressed as follows:

$$C_{\mathrm{pore}}\left(P_{\mathrm{Hg}}\right)=C_{\mathrm{obs}}\left(P_{\mathrm{Hg}}\right)-C_{\mathrm{s}}\left(P_{\mathrm{Hg}}\right)$$

(17)

The pore volume compression can be obtained using Equation (18) [34,35]:

$$\left({\displaystyle \frac{\Delta V_{\mathrm{pore}}}{V_{\mathrm{pore}}}}\right)={\displaystyle {\int }_{P_0}^{P_{\mathrm{r}}}{f}_{\mathrm{r}}\left(P_{\mathrm{Hg}}\right)\left(C_{\mathrm{obs}}-C_{\mathrm{s}}\right)}d{P}_{\mathrm{Hg}}$$

(18)

Assuming that the pores are spherical, the pore volume compression relative to the original pore volume can be written as follows:

$${\displaystyle \frac{\Delta V_{\mathrm{pore}}}{V_{\mathrm{pore}}}}={\displaystyle \frac{{\displaystyle \sum _i\left[\frac{4}{3}\pi r_i^3-\frac{4}{3}\pi {\left(a{r}_i\right)}^3\right]}}{{\displaystyle \sum _i\frac{4}{3}\pi r_i^3}}}$$

(19)

where a is the pore size reduction ratio; and r_i is the pore radius, nm, where i = 1, 2, 3, …, representing the number of pores.

Assuming that a is the same for all the compressed pores, all pores are compressed at the same ratio, and Equation (18) can be rewritten as follows:

$${\displaystyle \frac{\Delta V_{\mathrm{pore}}}{V_{\mathrm{pore}}}}=1-a^3$$

(20)

The coefficient a can then be calculated from the pore volume compression and the pore volume at the given mercury injection pressure. The corrected pore size is the pore size calculated at that pressure multiplied by 1/a.

3.3. Analysis of the Correction Results

3.3.1. Identification Results of the Correction Pressure Interval

As described in Section 3.1, the principles for identifying the correction pressure interval differ between the fractal dimension method and the conformance volume and intrusion volume identification method, and the results for identifying “actual entry pressure” and “closure pressure” also differ. The fractal dimension method yields relatively concentrated values for the “actual entry pressure” (P₁), which are distributed from 0.038 to 0.052 MPa, and the corresponding pore size (d₁) is concentrated from 24173.7 to 33008.4 nm; among these, low metamorphic coal (sample #1) has a slightly higher P₁ (0.052 MPa) and a slightly smaller d₁ (24173.7 nm), whereas the medium and high metamorphic coal (samples #2–#6) have nearly identical P₁ and d₁ (

Table 2. Identification results of the corrected pressure interval and the pore diameter interval of the test samples.

Samples	The Fractal Dimension Method									The Conformance Volume and Intrusion Volume Identification Method
	Fractal Dimension			Pressure Interval			Corresponding Pore Diameter			Correction Parameters		Pressure Interval		Corresponding Pore Diameter
	D1	D2	D3	P1, MPa	P2, MPa	P3, MPa	d1	d2	d3	m	n	Pc, MPa	Pi, MPa	dc	di
#1	2.59	2.80	3.91	0.052	10.32	72.89	24173.7	120.8	17.1	0.15	−1.35	0.031	6.81	40304.5	183.1
#2	2.08	3.05	3.83	0.041	8.26	72.89	30198.9	150.9	17.1	0.12	−1.16	0.035	28.45	41675.9	51.7
#3	2.29	2.85	3.97	0.038	6.87	/	33008.4	181.5	/	0.02	−1.10	0.137	8.02	10741.8	183.3
#4	2.39	2.92	3.92	0.041	13.76	/	30270.2	90.6	/	0.03	−1.38	0.066	10.37	22450.5	141.9
#5	2.05	3.06	3.69	0.041	6.87	/	30279.5	181.5	/	0.01	−1.12	0.092	7.69	16028.9	191.3
#6	2.29	2.85	3.97	0.038	6.87	/	33008.4	181.5	/	0.01	−1.07	0.153	13.16	9619.8	111.8

Note: d₁, d₂, and d₃ are the pore sizes corresponding to the critical pressures P₁, P₂, and P₃, respectively, nm; d_c and d_i are the pore sizes corresponding to the P_c and P_i, respectively, nm.

). The conformance volume and intrusion volume identification method yields more significant differences in “actual entry pressure” (P_c) for the test samples, ranging from 0.031 to 0.153 MPa, and the corresponding pore size (d_c) also has a wider distribution range (9619.8–41675.9 nm). Although there is no clear overall trend of P_c and d_c is observed with increasing metamorphic degree of the test samples using conformance volume and intrusion volume identification method, contrary to the fractal dimension method, the samples with higher metamorphic degrees (samples #3–#6) exhibit significantly higher P_c than the samples with lower metamorphic degrees (#1 and #2), and, correspondingly, their d₁ values are also smaller (Table 2).

The “closure pressure” obtained from both the fractal dimension method and the conformance volume and intrusion volume identification method do not show a clear pattern and have significant differences. For example, the “closure pressure” (P₂) for samples #2 and #6 obtained via the fractal dimension method are 8 MPa and 6 MPa, respectively, whereas the “closure pressure”(P_i) obtained from the conformance volume and intrusion volume identification method reaches 28.45 MPa and 13.16 MPa, respectively (Table 2). Correspondingly, the pore size corresponding to the “closure pressure” obtained by the two methods also varies significantly. Additionally, the identification results from the fractal dimension method indicate that the samples with lower metamorphic degrees (#1 and #2) are significantly fragmented and lose their fractal characteristics at the mercury injection pressure of 72.89 MPa (P₃), whereas the samples with higher metamorphic degrees (#3–#6) retain their fractal characteristics even at the highest experimental pressure (Table 2 and Figure 1); these results indicate that the coal with lower metamorphic degrees are more prone to damage during the MIP experiment; in contrast, the conformance volume and intrusion volume identification method does not show the failure characteristics of the samples (Table 2 and Figure 4).

Compared with the two methods of correcting pressure interval identification, we can see that (1) the fractal dimension theory has a more substantial theoretical foundation because it exploits the fractal characteristics of coal pores; this method has been confirmed by numerous scholars. The conformance pressure and intrusion pressure identification method assumes that the pore volume compression coefficient can be expressed as a power function of the mercury injection pressure. Deviations from this power function are attributed to the effect of the “void” or coal matrix compression. (2) Both methods are influenced by human factors. Although the fractal dimension method has a solid theoretical basis, the division of fractal stages still requires human judgment. When the scatter plots of the fractal dimension fitting curve lg(dV_Hg/dP_Hg) − lg(P_Hg) are fitted, including or excluding 2–3 points in the P₁ and P₂ stages can result in a high fitting correlation coefficient; however, the obtained P₁ and P₂ significantly differ (Figure 1). For coal powder samples, the P₁ stage is distinct, leading to relatively small errors, whereas for blocky coal samples, especially those with high metamorphism, the P₁ stage is less apparent, leading to greater errors. This is the reason that many researchers neglect the P₁ stage for blocky coal samples. Nevertheless, as shown in Figure 1, even if blocky coal samples are used, the P₁ and P₂ stages exhibit distinct differences and should not be disregarded. Although subjective judgment occurs with the conformance pressure and intrusion pressure identification method, the fitting curves of the six tested coal samples indicate that the deviation between the C_pore and C′_pore is more significant and easier to determine (Figure 4). (3) For the identification of the sample fracture stage, the sample no longer has fractal characteristics after experiencing damage. Based on the fractal dimension method, we can identify the pressure and pore size stages of a coal sample with significant damage (P₃ stage) and then exclude these stages from influencing the MIP results. While the conformance pressure and intrusion pressure identification method cannot accomplish this, after P_Hg > P_i (corresponding to the P₂ stage in the fractal dimension method), the mercury intrusion volume is considered to originate mainly from the coal matrix volume compression and does not need to be included in the cumulative mercury intrusion volume.

In summary, the fractal dimension method has a more substantial theoretical basis for the identification of the correction pressure interval, while the conformance pressure and intrusion pressure identification method is simpler, and both methods have their own advantages and disadvantages. Since the mercury intrusion (or pore volume) correction method described in Section 3.2 uses the conformance pressure and intrusion pressure identification method as the basis for the correction pressure interval identification, the results of this method are used for comparison and analysis in the following section.

3.3.2. Pore Size Structure Correction Results

As observed from the pore size structure correction results, the differences between the corrected pore size structure of the conformance volume and the intrusion volume correction method and the original MIP data are mainly in the “conformance effect” stage and the “compression effect” stage (Figure 5). According to Equation (8), this correction method is relatively rough with respect to pore volume adjustment. In the “conformance effect” stage, the conformance volume is the mercury intrusion volume error caused by the “void”. Therefore, when P_Hg ≤ P_c, the actual mercury intrusion volume is 0 (Figure 5); in the “compression effect” stage, the apparent mercury intrusion volume is attributed mainly to the volume compression of the coal matrix. Consequently, when P_Hg ≥ P_i, the actual mercury intrusion volume can be neglected, and the stage mercury intrusion amount is also considered 0 (Figure 5); however, when P_c < P_Hg < P_i, the apparent mercury intrusion volume change caused by coal matrix compression is relatively minor and can be disregarded. Therefore, the apparent stage mercury intrusion volume can be considered the actual stage mercury intrusion volume (Figure 5). This correction method also results in a lower cumulative mercury intrusion volume after correction, especially when P_Hg ≥ P_i; here, the corrected cumulative mercury intrusion volume remains constant (Figure 6).

The stage correction method also considers that the actual mercury intrusion volume should be 0 during the “conformance effect” stage (Figure 5). However, the stage correction method posits that the compressed pore volume is part of the inherent pore volume of coal. Regardless of whether the mercury injection pressure exceeds the conformance pressure, the correction only needs to correct the error caused by the compression of the coal matrix volume. Therefore, when P_Hg > P_c, the corrected pore volume is the apparent mercury intrusion volume minus the coal matrix volume compression. This corrected volume is slightly less than the apparent mercury intrusion volume (Figure 5). In terms of the cumulative mercury intrusion volume, the trend after correction is basically consistent with the MIP data, and the differences are as follows: (1) Since the conformance volume is deducted, the corrected cumulative mercury intrusion volume is much less than the MIP data. (2) The volume compression coefficient of the coal matrix is not a fixed value and increases with the mercury injection pressure; thus, the volume compression of the coal matrix under high mercury injection pressure is larger, and the corrected pore volume is smaller. Consequently, when P_Hg > P_c, the increase in the cumulative mercury intrusion volume after correction is slightly less than that in the MIP data; this is reflected in the slightly lower slope of the straight line on the cumulative mercury intrusion curve (Figure 6).

3.3.3. Correction Results for Porosity, Apparent Density, and True Density

The corrected apparent densities from both methods are obtained by using the calculation of mercury intrusion volume after the conformance volume is deducted; thus, the corrected apparent densities from both methods are identical and higher than the MIP data, aligning more closely with the measured apparent density (Table 1 and

Table 3. Porosity, apparent density, and true density of test samples.

Sample	Uncorrected			Conformance Volume and Intrusion Volume Correction Method			Stage Correction Method
	φ, %	ρbulk, g/cm3	ρture, g/cm3	φ, %	ρbulk, g/cm3	ρture, g/cm3	φ, %	ρbulk, g/cm3	ρture, g/cm3
#1	6.34	1.22	1.25	1.59	1.23	1.25	3.45	1.23	1.27
#2	4.63	1.25	1.28	2.42	1.29	1.33	2.41	1.29	1.33
#3	5.96	1.30	1.34	0.22	1.35	1.36	1.35	1.35	1.37
#4	4.73	1.19	1.22	0.44	1.27	1.27	1.38	1.27	1.28
#5	5.02	1.28	1.31	0.36	1.45	1.46	1.97	1.45	1.48
#6	4.85	1.26	1.29	0.3	1.45	1.46	1.46	1.45	1.47

). The corrected porosities from both methods are significantly lower than those from the MIP data, and the porosity corrected using the stage correction method generally is greater than that obtained using the conformance volume and intrusion volume correction method (Table 1 and Table 3). When the porosity is corrected using the stage correction method, only the conformance volume and coal matrix volume compression are subtracted, whereas the conformance volume and intrusion volume correction method subtracts both the conformance volume and the apparent mercury intrusion volume during the “compression effect” stage; this results in a lower corrected pore volume. Compared with the measured porosity, the MIP data tends to be greater because of errors caused by the conformance volume and the compression of the coal matrix. Therefore, the porosity corrected using the stage correction method is closer to the measured values. Similarly, because the corrected porosities are lower than the MIP data, the true density calculated and obtained from these methods are greater than the MIP data, and the true density corrected by the stage correction method is slightly greater than that corrected by the conformance volume and intrusion volume correction method; thus, these data are closer to the measured values (Table 1 and Table 3).

In summary, compared with the conformance volume and intrusion volume correction method, the stage correction method has a more solid theoretical basis, and the pore size structure correction results exhibit better regularity, reflecting the compressibility of the coal matrix skeleton at different metamorphic degrees; moreover, the corrected porosity, apparent density, and true density are closer to the measured values. Therefore, the stage correction method is considered more reliable.

4. New MIP Experimental Data Correction Method

Based on this analysis, the stage correction method is reliable for the correction results of the MIP data. However, this method requires repeated MIP experiments with epoxy resin-encapsulated samples to obtain the coal matrix volume compression coefficient under the same experimental conditions. Although the MIP experiment is a routine experiment, the test cost of the experiment is relatively high and time-consuming, significantly increasing the research workload. Additionally, although the compression coefficient of mercury is low, it still has a certain impact on the test results under high pressure; the stage correction method does not account for the compression coefficient of mercury. In view of this, a new MIP data correction method that considers the effects of both coal matrix volume compression and mercury volume compression under high mercury injection pressure is proposed. This method does not require repeated MIP experiments and can correct MIP data using MIP data combined with true density, apparent density, and porosity obtained by using conventional methods.

4.1. Proposal for the Correction Method

Based on MIP data, the sample volume (skeleton and pore) compression coefficient, pore volume compression coefficient, coal matrix volume compression coefficient, and mercury volume compression coefficient can be calculated using Equations (7), (18), (21) and (22), respectively:

$$C_{\mathrm{pore}}={\displaystyle \frac{1}{V_{\mathrm{Pore}}}}{\displaystyle \frac{d{V}_{\mathrm{Pore}}}{d{P}_{\mathrm{Hg}}}}={\displaystyle \frac{1}{V_{\mathrm{Pore}}}}{\displaystyle \frac{\Delta V_{\mathrm{Pore}}}{\Delta P_{\mathrm{Hg}}}}$$

(21)

$$C_{\mathrm{s}}={\displaystyle \frac{1}{V_{\mathrm{s}}}}{\displaystyle \frac{d{V}_{\mathrm{s}}}{d{P}_{\mathrm{Hg}}}}={\displaystyle \frac{1}{V_{\mathrm{s}}}}{\displaystyle \frac{\Delta V_{\mathrm{s}}}{\Delta P_{\mathrm{Hg}}}}$$

(22)

$$C_{\mathrm{Hg}}={\displaystyle \frac{1}{\Delta V_{\mathrm{Hg}}}}{\displaystyle \frac{d{V}_{\Delta \mathrm{Hg},}}{d{P}_{\mathrm{Hg}}}}={\displaystyle \frac{1}{\Delta V_{\mathrm{Hg}}}}{\displaystyle \frac{\Delta V_{\Delta \mathrm{Hg}}}{\Delta P_{\mathrm{Hg}}}}$$

(23)

where V_ΔHg is the change of mercury volume caused by compression at the mercury injection pressure P_Hg, cm³/g.

For the given mercury injection pressure P_Hg, the relationships between the pore volume compression coefficient, coal matrix volume compression coefficient, mercury compression coefficient, and sample volume compression coefficient are as follows:

$$C_{\mathrm{obs}}=C_{\mathrm{pore}}+C_{\mathrm{s}}+C_{\mathrm{Hg}}$$

(24)

For the given mercury intrusion pressure P_Hg, the apparent mercury intrusion volume, actual pore volume, matrix volume compression, and mercury volume compression are balanced by the following equation:

$$\Delta V_{\mathrm{Hg}}=\Delta V_{\mathrm{pore}}+\Delta V_{\mathrm{s}}+\Delta V_{\Delta \mathrm{Hg}}$$

(25)

Thus, from Equation (21), the following equation can be obtained:

$$\begin{array}{ll}\hfill {\displaystyle \frac{\Delta V_{\mathrm{pore}}}{V_{\mathrm{pore}}}}& =C_{\mathrm{pore}}•\Delta P_{\mathrm{Hg}}\hfill \\ & =\left(C_{\mathrm{obs}}-C_{\mathrm{s}}-C_{\mathrm{Hg}}\right)•\Delta P_{\mathrm{Hg}}\hfill \\ & =\left({\displaystyle \frac{1}{V_{\mathrm{Hg}}}}{\displaystyle \frac{\Delta V_{\mathrm{Hg}}}{\Delta P_{\mathrm{Hg}}}}-{\displaystyle \frac{1}{V_{\mathrm{s}}}}{\displaystyle \frac{\Delta V_{\mathrm{s}}}{\Delta P_{\mathrm{Hg}}}}-C_{\mathrm{Hg}}\right)•\Delta P_{\mathrm{Hg}}\hfill \\ & ={\displaystyle \frac{\Delta V_{\mathrm{Hg}}}{V_{\mathrm{Hg}}}}-{\displaystyle \frac{\Delta V_{\mathrm{Hg}}-\Delta V_{\mathrm{pore}}-\Delta V_{\Delta \mathrm{Hg}}}{V_{\mathrm{s}}}}-C_{\mathrm{Hg}}•\Delta P_{\mathrm{Hg}}\hfill \end{array}$$

(26)

Assuming that the volume compression coefficient of mercury is a fixed value, namely, 0.4 × 10⁻¹⁰ m²/N or 4.0 × 10⁻⁵ MPa⁻¹, the following equation can be obtained:

$$\Delta V_{\Delta \mathrm{Hg}}=C_{\mathrm{Hg}}\Delta V_{\mathrm{Hg}}\Delta P_{\mathrm{Hg}}=4.0\times {10}^{-5}\Delta V_{\mathrm{Hg}}\Delta P_{\mathrm{Hg}}$$

(27)

Then, the following equation applies:

$$\begin{array}{ll}\hfill \Delta V_{\mathrm{pore}}& ={\displaystyle \frac{\Delta V_{\mathrm{Hg}}\left(V_{\mathrm{s}}-V_{\mathrm{Hg}}\right)+V_{\mathrm{Hg}}\Delta V_{\Delta \mathrm{Hg}}-C_{\mathrm{Hg}}\Delta P_{\mathrm{Hg}}{V}_{\mathrm{Hg}}{V}_{\mathrm{s}}}{V_{\mathrm{Hg}}\left(V_{\mathrm{s}}-V_{\mathrm{pore}}\right)}}{V}_{\mathrm{pore}}\hfill \\ & ={\displaystyle \frac{\Delta V_{\mathrm{Hg}}{V}_{\mathrm{pore}}\left(V_{\mathrm{s}}-V_{\mathrm{Hg}}+4.0\times {10}^{-5}{V}_{\mathrm{Hg}}\Delta P_{\mathrm{Hg}}\right)-4.0\times {10}^{-5}\Delta P_{\mathrm{Hg}}{V}_{\mathrm{Hg}}{V}_{\mathrm{s}}{V}_{\mathrm{pore}}}{V_{\mathrm{Hg}}\left(V_{\mathrm{s}}-V_{\mathrm{pore}}\right)}}\hfill \end{array}$$

(28)

In Equation (28), V_Hg, ΔV_Hg, and ΔP_Hg are the known quantities. Before ΔV_pore is calculated, vs. and V_pore need to be calculated and can be obtained through the measurement of the apparent density and true density of the sample.

ρ_bulk and ρ_true can be obtained according to “Methods for Determining the Physical and Mechanical Properties of Coal and Rock-Part 2: Methods for Determining the True Density of Coal and Rock” (GB/T 23561.2-2009) and “Methods for Determining the Physical and Mechanical Properties of Coal and Rock-Part 3: Methods for Determining the Block Density of Coal and Rock” (GB/T 23561.3-2009). Since the tests for the apparent density and true density of coal are relatively simple and inexpensive, correcting MIP data using the apparent density and true density of coal is easier and less expensive. Theoretically, regardless of the testing method used, if the heterogeneity of coal is not considered, the apparent density and true density of coal without the confining pressure should be identical. Similar to the stage correction method, this method does not consider the compression of the pore volume. The corrected pore volume represents the pore volume without the confining pressure; this enables a comparison with results obtained from the other methods without the confining pressure. Therefore, this correction method has a solid theoretical foundation, and is also applicable to other porous media or oil and gas reservoirs.

4.2. Pore Structure Correction Analysis

The pore volume and cumulative mercury intrusion volume for each pore size segment are corrected using the new method, and their values are slightly lower than those corrected by the stage correction method. The results exhibit a very high degree of consistency with those of the stage correction method (Figure 7 and Figure 8). Among them, except for the sub-bituminous coal (sample #1), low volatile bituminous coal (sample #4) and anthracite (sample #6), where the measured true density and apparent density are significantly greater than the values calculated by the stage correction method (Table 1 and Table 3), resulting in a relatively more noticeable reduction in the corrected pore volume and cumulative mercury intrusion volume for each pore size segment, the measured true density and apparent density of the other test samples show minimal differences from the calculated values of the stage correction method, and the corrected pore volume and cumulative mercury intrusion volume are also in high agreement. In addition, the new method considers the impact of mercury volume compression at high mercury injection pressure on the correction results, which also slightly lowers the corrected pore volume and the cumulative mercury intrusion volume compared with those of the stage correction method. Moreover, the differences between the results of the new method and the stage correction method are mainly concentrated in the high mercury intrusion pressure stage; specifically, when P_Hg exceeds 50 MPa, the corrected results are more significant, and the corresponding pore size is approximately 27 nm (Figure 7 and Figure 8).

4.3. Impact of the Conformance Effect and Compression Effect on the Correction Results

4.3.1. Impact of the Conformance Volume on the Correction Results

As shown in Figure 9, the corrected mercury intrusion volume includes two parts: the conformance volume and the compression volume of the coal matrix and mercury. Despite the use of blocky coal samples in the MIP experiment, the proportion of conformance volume of the test samples is still high and accounts for 9.91–83.26% of the apparent mercury intrusion volume of the samples; additionally, the conformance volume of the test samples increase with the degree of coal metamorphism (Figure 9). For the high metamorphic coal samples (#5 and #6), the apparent mercury intrusion volume is attributed mainly to the conformance volume, with proportions reaching 78.79% and 83.26%, respectively; however, for the low metamorphic coal (sample #1) and medium metamorphic coal (samples #2–#4), the conformance volume proportion is much lower than that of the high metamorphic coal (Figure 9). The actual mercury intrusion volume (actual pore volume + coal matrix compression volume + mercury compression volume) accounts for approximately 16.77–90.09% of the apparent mercury intrusion volume (Figure 9). As the degree of coal metamorphism increases, both the actual mercury intrusion volume and its proportion relative to the apparent mercury intrusion volume generally decrease. Among them, the actual mercury intrusion volume (0.0468 cm³/g) of low metamorphic coal (sample #1) and its proportion accounting for the apparent mercury intrusion volume (90.09%) are greater than those of medium metamorphic coal (samples #2–#4) and high metamorphic coal (samples #5 and #6) (16.77–58.33% and 0.0209–0.0350 cm³/g, respectively). The actual mercury intrusion volume of medium metamorphic coal (0.0160–0.0214 cm³/g) is slightly lower than that of highly metamorphic coal; however, the actual proportion of mercury intrusion volume (31.33–34.93%) is greater because of the relatively lower apparent intrusion volume of medium metamorphic coal (Figure 9). In addition, after the conformance volume is corrected, the pore size distribution of the test samples shows a significant reduction in the development of macropores, especially those with pore sizes greater than 10 μm, which tend to approach 0, and the test pore size sections are mainly mesopores and macropores with diameters ≤ 1 μm (Figure 7).

Based on the above phenomenon, even when blocky samples are used for the MIP experiment, the influence of the conformance effect cannot be disregarded, especially for highly metamorphic coal samples, and the influence of the conformance volume on the experimental results needs to be considered. The conformance volume is also the reason for the abnormally developed macropores in the highly metamorphic coal in the MIP experiment. The reason for the large conformance volume of highly metamorphic coal is as follows: (1) High metamorphic coal often has high hardness, and it is more likely to form microcracks and irregular crushing during sample collection and preparation. (2) High metamorphic coal often has well-developed cleats and microcracks. Regardless of whether the fractal dimension method or the conformance volume and intrusion volume identification method is used, the mercury intrusion volume caused by cleats and microcracks is still considered part of the conformance volume. Thus, correcting for the conformance volume effectively eliminates the influence of cleats and microcracks larger than d₁ or d_c.

4.3.2. Impact of the Coal Matrix Volume Compression on the Correction Results

In the actual mercury intrusion volume of the test samples, the corrected pore volume consists of two parts: the coal matrix volume compression and the mercury volume compression. The coal matrix volume compression is the dominant component, accounting for 99.86–99.90% of the total corrected volume, 38.27–55.63% of the actual mercury intrusion volume, and 9.33–39.77% of the uncorrected MIP data (Figure 9). Significant differences are observed in coal matrix volume compression among the coal with different degrees of metamorphism. Sub-bituminous coal (sample #1) and high volatile bituminous coal (sample #2) exhibit significantly greater coal matrix volume compression than the other samples; these results indicate that lower metamorphic coal has greater compressibility. For the low volatile bituminous coal to anthracite (samples #4–#6), the coal matrix volume compression and its proportion to the total corrected volume show no significant differences. However, compared with those of sub-bituminous coal (sample #1) and high volatile bituminous coal (sample #2), their coal matrix volume compression values are significantly lower, and their proportions to their total corrected volumes are significantly greater; thus, these results indicate that higher metamorphic coals are less compressible. The medium volatile bituminous coal (sample #3) has the lowest coal matrix volume compression and the smallest proportion of coal matrix volume compression to the total corrected volume, showing the weakest compressibility. With increasing mercury injection pressure, the coal matrix volume compression increases, indicating that a greater coal matrix volume compression occurs under a high mercury injection pressure (Figure 10). The corrected total pore volume and its proportion to the total corrected volume decrease with increasing of coal metamorphism. Among them, sub-bituminous coal (sample #1) and high volatile bituminous coal (sample #2) have significantly greater corrected pore volumes than medium volatile bituminous coal to anthracite (samples #3–#6); the differences in the corrected pore volumes between medium volatile bituminous coal and anthracite are not significant (Figure 9); these results indicate that lower metamorphic coals have greater pore development in the test pore size section.

In addition, the mercury volume compression is much lower than that of the coal matrix (5.8810⁻⁶–2.82 × 10⁻⁵ cm³/g); this compression accounts for a very low proportion of the total corrected volume (0.02~0.06%), and can be considered negligible.

5. Conclusions

(1) The identification of “actual entry pressure” and “closure pressure” is crucial for MIP data correction. The fractal dimension method is more theoretically robust, while the conformance and intrusion pressure identification method is simpler. The conformance volume and intrusion volume correction method assumes that mercury intrusion during the conformance and compression effect stages is mainly due to conformance volume and coal matrix volume compression, leading to an actual mercury intrusion volume of 0, resulting in a lower corrected pore volume. In contrast, the stage correction method treats the compressed pore volume as part of the inherent coal pore volume, correcting only for coal matrix volume compression. This method yields more reliable results but requires repeated MIP experiments on epoxy resin-encased samples to determine the coal matrix volume compression coefficient, increasing the research workload.

(2) A method for correcting mercury intrusion volume and pore volume based on apparent density and true density of coal has been proposed, providing reliable and simple results for pore volume under no confining pressure. The corrected results show that the conformance volume accounts for 9.91% to 83.26% of the apparent mercury intrusion volume, increasing with coal maturation. Coal matrix volume compression accounts for 99.86% to 99.90% of the corrected total volume, while mercury volume compression is negligible. For highly metamorphosed coal, pore development in the tested pore size section is lower, resulting in a lower corrected pore volume. As mercury injection pressure increases, coal matrix volume compression also increases, with correction mainly focused on the high-pressure stage, particularly when pressure exceeds 50 MPa.