**5. Discussions**

#### *5.1. Classification of Pore Networks Based on Fractal Theory*

Many studies have demonstrated that pore networks of clastic rocks have statistical self-similarity, characterized by their constantness with various scales [51–53]. Pfeifer and Avnir [54] proposed an equation for calculating surface fractal dimension using mercury intrusion data as follows:

$$
\log\left(-\frac{dV\_r}{dr}\right) \ll \left(2 - D\_s\right) \log(r) \tag{7}
$$

where *Vr* is the accumulated mercury intrusion volume when the throat radius larger than *r*, and *Ds* is defined as the surface fractal dimension. By plotting the *dVr*/*dr* vs. *r* under double logarithmic coordinates, *Ds* can be determined through the slope of the fitting line.

The *dVr*/*dr* vs. *r* obtained from RMIP data shows evident linear relationships (Figure 10A–C), illustrating that the pore-throat networks of studied tight rocks are generally fractal. Noticeably, the *dVr*/*dr* vs. *r* curves can be divided into two segments at various throat radii for all tight rock samples, and the fractal dimension (*D*s2) at the low-pressure section is generally greater than that at the high-pressure section (i.e., *D*s1), which is consistent with studies of Lai and Wang [53]. This phenomenon is possibly attributed to (1) the skin impact related to the rough surface, (2) the presence of microfractures, or (3) the oversimplified assumption of cylindrical pores [53,55]. Evidently, the pore-throat networks corresponding to these two fractal segments cover disparate mercury intrusion features.

**Figure 10.** Surface fractal structure of throats (**A**–**C**) and mercury intrusion curves of total (pores + throats), pores and throats (**D**–**F**), derived from the RMIP experiment of three typical tight rock samples. (**A**,**D**): Sample #1, 0.93 mD; (**B**,**E**): sample #2, 2.35 mD; (**C**,**F**): sample #4, 0.26 mD.

In the wider throat part, the total mercury intrusion saturation goes up rapidly covering a confined scope of capillary pressure (Figure 10D–F). For example, the mercury intrusion saturation increases by 32.51%, comprising 49.49% of total mercury intrusion saturation, from 13.12% to 45.63%, when the intrusion pressure rises from 0.27 to 0.96 MPa in sample #1 (Figure 10D). Furthermore, the mercury intrusion process in pores is primarily completed at this stage, and the amount of mercury intruded into the pores in this stage accounts for 76% of total amount of mercury intruded into the pores for sample #1. Sakhaee-Pour and Bryant [56] regarded this type of pore-throat networks as conventional intergranular-dominant networks corresponding to large pores with wide throats (Figure 11A). As demonstrated by the polished SEM image in Figure 11C, intergranular-dominant networks mainly contain intergranular pores and dissolution pores with relatively larger dimensions, and slim pores between grains are treated as throats.

**Figure 11.** Schematic diagrams showing (**A**) conventional pore-throat structures that larger pores are connected by wider throats, and (**B**) tree-like pore structures that the narrower throats are connected to the wider throats like tree branches. (**C**) SEM image of sample #4 exhibiting an intergranular-dominant and intragranular-dominant pore network. P-pore; T-throat.

In the narrower throat part, the total mercury intrusion saturation grows almost exponentially with the capillary pressure at relatively high pressures, displaying nearly a straight line under semilogarithmic coordinates (Figure 10D–F). The intruded mercury in this stage is almost contributed by the mercury intrusion in throats, with nearly no increase of mercury invaded in the pores. For instance, the mercury intrusion saturation of throats makes up 99.28% of the total mercury intrusion in sample #1 at this stage, i.e., there is no longer any significant discrepancy in pores and throats. Intragranular-dominant pore networks were used to depict this region instead of the abovementioned intergranular-dominant networks, and moreover, Sakhaee-Pour and Bryant [56] adopted a tree-like pore network for the intragranular-dominant region. Intragranular-dominant networks mainly consist of throats with different sizes and lengths, and the narrower throats are connected to the wider throats like tree branches (Figure 11B). As shown in the SEM image in Figure 11C, intragranular-dominant networks predominantly correspond to intercrystalline pores within clay minerals.

The proportions of intergranular-dominant pore networks, determined by RMIP analyses using fractal theory, are listed in Table 3. The proportion of intergranular-dominant pore networks of studied tight samples is between 9.44% and 42.21%, with a mean of 27.45%, implying that intragranular-dominant pores contribute more to pore space. The proportion of intragranular-dominant pore networks is relatively high even for samples with a low clay minerals content. For example, the clay mineral contents of sample #1 and #7 are 2 wt.% and 3 wt.%, respectively, however, their intragranular-dominant pore network percentages still exceed 50%, up to 50.79% and 70.1%, respectively. This may be related to the fact that clay minerals are generally distributed in the intergranular and dissolution pores, resulting in a considerable number of pores associated with clay minerals.


**Table 3.** Lists of the contributions of intergranular-dominant pore networks to total pore space and permeability and the contributions of various compositions to SSA calculated from Equation (8) for the studied nine tight rocks.

 *rip* = throat radius at inflection point; InterG.-dominant = intergranular-dominant; SSA = specific surface area; I/S = mixed-layer illite/smectite; FM = framework minerals.

The total clay minerals and various types of clay minerals are also correlated to the proportion of intergranular-dominant pore networks, as shown in Figure 12 and as the contents of total clay minerals, chlorite, illite, and I/S increase, the proportions of intergranular-dominant pore networks drop. Previous studies revealed that clay minerals are commonly derived from terrigenous detritus, namely primary clay minerals, and the chemical reaction between fluids and unstable minerals or the transformation between clay minerals, namely authigenic clay minerals [46,57]. Primary clay minerals are principally distributed in intergranular pores during the initial deposition stage, while authigenic clay minerals are dispersed in intergranular pores and dissolution pores during middle diagenesis stage. The increase of primary or authigenic clay mineral contents will obviously promote the evolution of intergranular-dominant pore networks (intergranular or dissolution pores) to intragranular-dominant pore networks (intercrystalline pores). We also found that chlorite is more closely correlated to the proportion of intergranular-dominant pores compared with illite and I/S (Figure 12B–D), illustrating that chlorite may be more e ffective in promoting the above pore evolution process, and thus may make more contribution to intragranular-dominant porosity. Although the increase of clay mineral content substantially promotes the evolution of intergranular-dominant pore networks to intragranular-dominant pore networks, and also it changes the relative proportions of these two types of pore networks, this does not necessarily result in an evident change in total storage space, due to the fact that there is unclear link between clay mineral content and total porosity (Table 1).

**Figure 12.** Relationships between contents of total clay mineral ( **A**), chlorite (**B**), illite ( **C**), I/S ( **D**), and proportions of intergranular-dominant pores.

The throat radius at inflection point (*rip*), boundary of intergranular-dominant pores and intragranular-dominant pores, ranges from 0.305 to 0.768 μm (Table 3), indicating that intragranulardominant pore networks of different samples correspond to inconsistent throat size distributions due to multiple degrees of diagenesis and different rock compositions [17,58,59]. The values of *rip* are negatively correlated with contents of total clay minerals, chlorite, illite, and I/S (Figure 13), and furthermore, chlorite has the relatively stronger control on *rip* (Figure 13B), while the correlations between *rip* and illite, I/S are fairly poor (Figure 13C,D).This implies that chlorite is more efficient in lowering values of *rip* in relative to illite and I/S, due to the fact that chlorite contributes more to intragranular-dominant pore networks, as evidenced by Figure 12.

**Figure 13.** Throat radius at inflection point (*rip*) vs. contents of total clay minerals (**A**), chlorite (**B**), illite (**C**), and I/S (**D**).

#### *5.2. E*ff*ect of Clay Minerals on Pore Structure Properties*

The positive correlation between total clay minerals and SSA is pretty good, as exhibited in Figure 14A, indicating the strong control of clay minerals on SSA of tight rock samples. Specifically, both illite and I/S contents exhibit fine positive correlations with SSA, with a *R*<sup>2</sup> of 0.81 and 0.94 (Figure 14C,D), respectively, while there is a relatively poor positive relationship between chlorite and SSA (*R*<sup>2</sup> = 0.37, Figure 14B). In contrast to framework particles, such as quartz, feldspar, and calcite, clay minerals generally have colossal surface area due to their lamellar and plate-like crystal structure and small particles [19,20,60]. Thus, clay minerals are the main contributor to SSA of tight rocks, and the greater the clay mineral content, the greater the SSA. Furthermore, due to the existence of internal surface area, smectite usually corresponds to a total SSA of up to 800 m<sup>2</sup>/g, whereas the total SSA of illite and chlorite are relatively low at 30 m<sup>2</sup>/g and 15 m<sup>2</sup>/g, respectively, as reported by Passey et al. [20]. We can speculate that I/S, which is the intermediate product from smectite to illite [61], should also possess a greater SSA than that of illite and chlorite. Thus, the contribution of various clay minerals to the total SSA is distinct, which well interprets the differences in the correlation coefficients between different types of clay minerals and SSA (Figure 14B–D).

**Figure 14.** Positive correlations between SSA (specific surface area) derived from N2GA experiments and contents of total clay minerals (**A**), chlorite (**B**), illite (**C**), I/S (**D**).

The total SSA can be regarded as the sum of SSAs contributed by various tight rock compositions, and therefore, this work proposes a mathematical model to quantitatively reveal the contributions of various clay minerals to total SSA based on the study of Wang et al. [62]. The compositions of tight rocks are first simplified to four categories: chlorite, illite, I/S, and framework minerals, considering that the SSAs of clay minerals are generally far greater than those of framework minerals. Then, the mathematical model can be written as follows:

$$\begin{cases} \sum\_{i=1}^{l} \left( SSA\_{Ch}\mathcal{W}\_{(Ch)i} + SSA\_{I}\mathcal{W}\_{(I)i} + SSA\_{I/S}\mathcal{W}\_{(I/S)i} + SSA\_{FM}\mathcal{W}\_{(FM)i} \right) = SSA\_{i} \\ \mathcal{W}\_{(Ch)i} + \mathcal{W}\_{(I)i} + \mathcal{W}\_{(I/S)i} + \mathcal{W}\_{(FM)i} = 1 \\ \left. SSA\_{Ch} > 0, \left. SSA\_{I} > 0, \left. SSA\_{I/S} > 0, \left. SSA\_{FM} > 0 \right. \end{cases} \right. \end{cases} \tag{8}$$

where *SSACh*, *SSAI*, *SSAI*/*S,* and *SSAFM* are the SSAs of chlorite, illite, I/S, and framework minerals per unit weight, respectively; *WCh*, *WI*, *WI*/*S,* and *WFM* are the normalized weights of chlorite, illite, I/S, and framework minerals, respectively; and *SSAi* is the total SSA of the *i*th tight rock samples obtained from the N2GA experiment.

Based on the multiple linear regression method, we can obtain the optimized *SSACh*, *SSAI*, *SSAI*/*S*, and *SSABM* of 7.412 m<sup>2</sup>/g, 6.143 m<sup>2</sup>/g, 15.520 m<sup>2</sup>/g, and 0.0061 m<sup>2</sup>/g, respectively, for the nine studied tight rock samples. The estimated SSAs show fine correlation with measured SSAs, with a *R*<sup>2</sup> of up to 0.92 (Figure 15), indicating that the proposed mathematical model is feasible and reasonable. Specifically, the contribution of I/S to total SSA is the largest, ranging from 0–83.35% with an average of 60.31% (Table 3), consistent with the good correlation between I/S and SSA in Figure 14D. The next is chlorite and illite, corresponding to a proportion of 7.48%–90.83% and 6.55%–10.74%, averaging 29.92% and 8.68% (Table 3), respectively. Framework minerals make the least contribution to total SSA, which is between 0.15% and 2.63%, with a mean of only 1.09% (Table 3).

**Figure 15.** Correlation between measured and calculated SSAs for tight rock samples from the Xujiaweizi Rift. The black solid line represents the best match (1:1 line), and the black dashed line is the fitting line of measured and calculated SSAs. SSA = specific surface area.

Total clay minerals, illite, I/S, and chlorite are all positively associated with pore volumes derived from the N2GA experiments, as evidenced by Figure 16. This is because the N2GA technique can effectively reveal pore networks below 200 nm in diameter, which are dominantly linked with clay minerals, as identified by SEM images. It is worth noting that the *R*<sup>2</sup> of chlorite and pore volume is slightly lower than that of illite and of smectite with their respective pore volumes (Figure 16B–D), indicating that illite and I/S may have a more evident effect on the development of intragranular-dominant pore networks with diameter of smaller than 200 nm [23,59].

**Figure 16.** Positive correlations between pore volume derived from N2GA experiments and contents of total clay minerals (**A**), chlorite (**B**), illite (**C**), I/S (**D**).

Both the average throat radius (*ra*) and maximum connected throat radius (*rd*, throat radius corresponding to displacement pressure) derived from the RMIP experiments are also negatively correlated with three types of clay minerals (Figure 17A–F). Illite usually occurs as pore-bridging in pore-throat space and can effectively segmen<sup>t</sup> pores and throats [21]. Pore-lining chlorite wraps the surface of primary intergranular pores resulting in a significant reduction of the pore-throat radius [21]. I/S distributes in pores/throats with discrete particles and can also block the throats to some extent [21]. Hence, all of these three kinds of clay minerals can lower the value of *rd*. Evidently, chlorite is the most effective one to reduce *ra* and *rd* derived from the RMIP experiments. The RMIP experiment is more suitable for revealing pores larger than 240 nm in diameter in this study, and these pores are more closely related to chlorite comprising relatively larger pores.

**Figure 17.** Negative relationships between average throat radius derived from RMIP experiments and contents of chlorite, illite, I/S (**A**–**C**), and negative associations between maximum connected throat radius derived from RMIP experiments and contents of chlorite, illite, I/S (**D**–**F**).

The integration of N2GA and RMIP is more advantageous in uncovering the pore volumes of multiple scales, which can give a more reasonable result for this work (Figure 8). With the rising clay mineral contents from #1 to #8, the pore size distribution curves exhibit an increasing trend in the amplitude of a smaller pores section and a declining trend in that of a larger pores section but no evident change in the coverage areas of pore size distribution curves. This again confirms the evolution from intergranular-dominant pore networks to intragranular-dominant pore networks with increasing clay mineral content discussed in the above section. The diminution in the proportion of larger pores and the elevation in that of smaller pores will obviously damage the connectivity of pore networks, resulting in a worse seepage capacity of tight rocks [53]. Compared with clay mineral cements that give rise to the changes of the proportion of different pore networks, mechanical compaction will obviously reduce the absolute size and volume of all pores. For instance, for samples #7, intensely mechanical compaction results in a less proportion of larger pores (>1 μm in diameter), but the proportion of smaller pores (<0.1 μm in diameter) is comparable with that of tight rock samples with similar clay mineral contents (Figure 8), illustrating that the effect of mechanical compaction on smaller pores (<0.1 μm in diameter) within clay minerals is not significant, due to the protection of rigid particle support [63].

#### *5.3. E*ff*ect of Clay Minerals on Permeability*

Neasham [21] has demonstrated that the presence of clay minerals can significantly block pores and throats, which is considered to obviously reduce the permeability of the samples. Total clay minerals, chlorite, illite, and I/S are all negatively related to permeability for studied tight rock samples, as shown in Figure 18, and the effect of chlorite on the decrease of permeability is more evident, compared with illite and I/S. Previous studies have demonstrated that throat size rather than pore size controls the seepage capacity of tight reservoirs, and the permeability is primarily contributed by a small part of relatively larger pore-throat networks [12]. In addition, chlorite generally has a stronger control on the throat radius (Figure 17), and it makes a higher contribution to the intragranular-dominant pore networks of tight gas reservoirs (Figure 12), and thus, its effect on permeability is more obvious.

**Figure 18.** Relationships between contents of total clay minerals (**A**), chlorite (**B**), illite (**C**), I/S (**D**), and permeability.

Purcell et al. [64] proposed a method that was used to calculate the contribution of various scales of throats to the permeability based on mercury intrusion data, and this equation can be written as:

$$K\_{j} = \frac{\int\_{S\_{j}}^{S\_{j+1}} r\_{(S)}^{2} \, dS}{\int\_{0}^{S\_{\text{max}}} r\_{(S)}^{2} \, dS} \tag{9}$$

where *Kj* is the contribution of throat radius at *rj* to permeability; *Sj* and *Sj* + 1 are the mercury intrusion saturations at *rj* and *rj* + 1, respectively; *<sup>r</sup>*(*S*) is the throat distribution functions; and *dS* represents the mercury intrusion saturation from *rj* to *rj* + 1. *Smax* is the maximum mercury saturation.

The displacement pressure represents the minimum pressure at which the nonwetting phase fluids begin to significantly displace the wetting phase fluids in porous materials. When the mercury intrusion pressure is lower than displacement pressure, mercury will intrude into pores connected to the external surface of rock samples, which cannot form a continuous flow cluster in these isolated and discontinuous pores [65,66]. When the mercury intrusion pressure exceeds displacement pressure, incremental pores will be filled by mercury, generating increasingly continuous flow cluster. Therefore, the throat radii below the maximum connected throat radius are the primary contributors to the permeability of tight rocks.

The contribution of intergranular-dominant pore networks to the permeability of studied tight rock samples employing Equation (9) is listed in Table 3. For all samples except #9, intergranular-dominant pore networks rather than intragranular-dominant pore networks are the primary contributor to permeability, with a contribution ranging from 62.73% to 93.40%, which agrees with the study of Xi et al. [12]. We also found that with an increasing clay mineral content, the permeability of tight rocks decreases rapidly, while the contribution of intragranular-dominant pore networks to permeability rises speedily. The existence of excess clay minerals will bring about a quick decline of the number of interconnected intergranular-dominant pores, and the fluid has to select the intragranular-dominant pores as their main flow path. This will induce intragranular-dominant pores to play an increasingly significant role in the seepage process, but the absolute permeability value of tight rocks will decrease obviously. For example, the clay mineral content of sample #9 is up to 22 wt.%, with an intergranular-dominant pore proportion of 9.44% (Tables 1 and 3). Although the contribution of intragranular-dominant pore networks to permeability can reach 85.55%, its absolute permeability is only 0.0352 mD (Tables 1 and 3). Thus, compared with intragranular-dominant pore networks, intergranular-dominant pore networks are more crucial in generating a high permeability of tight gas reservoirs.

Based on the above discussion, clay minerals, especially authigenic clay minerals precipitated in intergranular pores and dissolution pores, significantly decreases the permeability of tight gas reservoirs. Nadeau et al. [67] proposed that less than 5% of authigenic I/S can e ffectively block the pore network and thus obviously reduce the reservoir permeability. Another possible consequence of the precipitation of authigenic clay minerals is that the relatively poor pore networks will result in an increasing risk of formation overpressure, especially for fine-grained sandstone and shale reservoirs. Formation overpressure can help preserve pore space of tight gas reservoirs to some extent, which may contribute to the relatively high porosity of studied tight rock samples with a burial depth of >3500 m (Table 1).

Many permeability prediction equations have been established based on pore structure parameters [68–70], which were obtained from PMIP (pressure-controlled mercury injection porosimetry) and NMR methods, and these prediction equations can be summarized as the following formula:

$$\text{Log}(\text{K}) = \text{A} + \text{BL}\text{log}(\rho) + \text{CL}\text{log}(r\_i) \tag{10}$$

where *K* is permeability; ϕ is porosity; and *ri* is throat radius corresponding to the various total mercury saturation (*i* = 10%–50%). A, B, and C can be determined according to multiple linear regression.

Evidently, there is no significant correlation between total porosity and permeability for the studied tight rocks (Figure 19A). According to the above discussions, permeability of tight rock samples is dominantly contributed by intergranular-dominant pore networks (Table 3), and the positive relationship between intergranular-dominant porosity ( ϕ*interG.*), and permeability is closer (Figure 19A). In addition, for tight rocks with various pore structures, the throat dimension corresponding to the same mercury intrusion saturation is significantly di fferent, and it has di fferent control levels on permeability. Thus, *rip* (throat radius at inflection point), instead of *rm* (maximum connected throat radius), and *ra* (average throat radius) were selected to substitute *ri* mentioned above to estimate permeability, due to their well positive correlations with permeability (Figure 19B). Based on the multiple linear regression, the permeability estimation results are shown as follows:

$$\text{Log(K)} = 0.076 + 0.689 \text{Log(}\varphi\_{\text{interG.}}\text{)} + 2.841 \text{Log(}\mathbf{r}\_{ip}\text{)}\qquad R^2 = 0.91\tag{11}$$

$$\text{Log(K)} = -0.823 + 0.349 \text{Log(}\varphi\_{\text{interC.}}\text{)} + 1.293 \text{Log(}r\_{\text{m}}\text{)}\qquad R^2 = 0.77\tag{12}$$

$$\text{Log(K)} = -0.96 + 0.991 \text{Log(}\rho\_{\text{inter\%}}\text{)} + 1.451 \text{Log(}r\_a\text{)}\qquad R^2 = 0.81\tag{13}$$

**Figure 19.** Correlations between permeability and porosity (**A**) and throat radius (**B**) parameters. InterG.-dominant = intergranular-dominant.

These three permeability estimation equations, Equations (11) to (13), indicate that *rip* is more appropriate than *ra* and *rm* in predicting permeability, as shown in Figure 20. Evidently, *rip* is the throat size boundary of intergranular-dominant and intragranular-dominant pore networks, as discussed in Section 5.1, representing the change from conventional pore-throat structures to tree-like pore structures of tight rocks, and the seepage capability of tight sandstones worsens rapidly. *rm* and *ra* also can reflect throat size distribution characteristic of tight rocks to some extent, and can also be applied to estimated permeability, with a *R*<sup>2</sup> of 0.77 and 0.81, respectively. However, these two parameters fail to reveal the critical throat size that changes pore structure and the permeability of tight rocks, and thus, their estimation accuracy is worse than that of *rip* (Figure 20).

**Figure 20.** Measured permeability versus estimated permeability using *rip*, *rm*, and *ra*, respectively. The 1:1 line (black dashed line) exhibits the perfect match.
