**4. Results**

#### *4.1. Mineralogical Compositions of Tight Sandstone*

The XRD analysis results of samples are shown in Table 1. Overall, the studied P1t tight sandstone samples mainly consist of quartz and clay. Therein, quartz content ranges from 58.9% to 74.1% average as 68.42%, and clay content varies from 16.3% to 35.8%, with an average of 24.32%. The clay minerals are dominated by the mixed illite/smectite (I/S) and illite, attended by a few kaolinites, and chlorites (Table 1). The high content of clay minerals may result from the grea<sup>t</sup> heterogenous composition and strong alteration of detrital feldspars in the tight sandstones [45]. There is only trace amount of feldspar (0.9–8.3%, averaging 5.22%). The lack of feldspar content is possibly due to the dissolution caused by factors such as basin subsidence, thermal events and acid produced by coal-bearing strata [46]. Other minerals, including ankerite, pyrite and calcite, can be identified only in individual samples, and their contents are extremely low (<2.5%).

**Table 1.** The compositions of minerals from the P1t tight sandstone samples.


I/S: Illite/Smectite mixed layer; I: Illite; K: Kaolinite; C: Chlorite.

#### *4.2. Pore Type and Characteristics*

Casting thin section and SEM image analysis results show that there are three dominant pore types in the P1t tight sandstone samples, including micropores associated with clay minerals, secondary intergranular and intragranular dissolution pores (Figure 3). Primary intergranular pores are rarely observed. Quartz overgrowth and authigenic quartz grains are commonly developed in P1t tight sandstones (Figure 3a,b,d), and pyrite crystals are also observed in some pores (Figure 3e). Secondary dissolution pores mostly occur on detrital feldspars, as a result of partial to complete dissolution (Figure 3a,b). These dissolution pores are typically enveloped by authigenic clay minerals derived from the dissolution of detrital feldspars (Figure 3f). Additionally, a few dissolution pores occur on detrital grain boundaries (Figure 3c).

**Figure 3.** Photomicrographs showing the microscopic pore structure characteristics of P1t tight sandstone. (**a**) sandstones with intergranular and intragranular dissolution pores (red arrow) and extensive quartz overgrowths; (**b**) intragranular dissolution pores (red arrow) and quartz overgrowths (blue arrow); (**c**) dissolution pores occur on detrital grain edges (red arrow); (**d**) fine authigenic quartz grains; (**e**) pore-filling pyrites; (**f**) authigenic clay minerals fill the dissolution pores; (**g**) slablike kaolinite filling in the pore; (**h**) flaky illite filling in pore; (**i**) hair-like illite/smectite mixed layers filling in pore (yellow arrow, micropores associated with clay minerals).

The pore structures of samples are severely impacted from clay cementation, because the pore throat system is mainly filled by a large amount of authigenic clay minerals such as the slablike or booklet kaolinite (Figure 3g), and the flaky illite and hair-like mixed illite/smectite (I/S) (Figure 3h,i). SEM image analysis showed that abundant micropores are developed within these clay minerals (Figure 3g–i). These micropores are continuously distributed with a multi-scale pore size (mainly < 1 μm), which provide the necessary percolation path, connecting other relatively larger pores for tight sandstone reservoirs to a certain extent.

#### *4.3. Petrophysical Properties and NMR T2 Distributions*

The porosity of the five samples ranges from 1.95% to 3.41%, with an average of 2.7%, and permeability varies from 0.037 mD to 0.494 mD (Table 2). The petrophysical properties of samples are lower than those observed in the Chang 7 reservoir, with an average value of porosity of 7.2% and permeability of 0.18 mD. The Chang 7 reservoir is an important tight oil reservoir from Yanchang Formation in the Ordos basin [47]. This indicates that the samples have relatively poorer pore structures and reservoir quality. Nevertheless, a positive exponential relationship can be observed between porosity and permeability of samples (Figure 4).

**Table 2.** The petrophysical parameters and pore structure parameters of the tight sandstone samples from NMR measurements.


**Figure 4.** The correlation between porosity and permeability of P1t sandstone.

Reservoir quality index (RQI) and flow zone indicator (FZI) are two ideal macroscopic petrophysical parameters used to evaluate the micro pore structure and reservoir properties of tight sandstone [48]. RQI and FZI were calculated by the following formulas, respectively [33]:

RQI = 0.0316 × \$Kϕ, (12)

$$\text{FZI} = \text{RQI} \times \frac{100 - \text{q}}{\text{q}},\tag{13}$$

where K is the permeability, mD; ϕ is the porosity, %.

As shown in Table 2, the values of RQI vary from 0.0041 μm to 0.012 μm, while FZI values range from 0.1498 μm to 0.341 μm, averaging as 0.228 μm. These values are close to the tight oil reservoir researched by Zhao et al., 2017, whereas they are lower than the Chang 7 tight reservoir [47].

For the fully water-saturated rock, the T2 distributions provide information about the pore size distributions. The T2 relaxation time is in proportion to the pore size [15,49], and the signal amplitude of T2 distributions reflect the pore fluid content and pore volume. The 100% brine-saturated T2 spectra of five samples are shown in Figure 5. Except for sample 1 (unimodal T2 spectrum), all samples show the bimodal characteristics of T2 spectra, and almost all pore sizes of tight sandstones present in the range from 0.1 to 100 ms. There are no pores with the relaxation time larger than 100 ms, attributed to the absence of residually large intergranular pores. The main peaks are distributed between 0.1 ms and 10 ms, and their signal amplitudes are far larger than the secondary peak. The relative amplitudes

of T2 peaks indicate that sample porosities are dominated by smaller pore sizes, and the larger porosity are relatively few. The pores of sample 1 are all smaller pores.

**Figure 5.** The saturated NMR T2 spectra of samples.

By analyzing NMR T2 data, some NMR pore structure parameters, including movable-fluid porosity (ϕ**m**), bound-fluid porosity (ϕ**b**), T2cutoff, T2gm (amplitude weighted logarithmic mean), T35 and T50, are also summarized in Table 2. Porosity in the rock can be separated into bound-fluid porosity (T2 < T2cutoff) and movable-fluid porosity (T2 > T2cutoff) in the cumulative T2 spectrum by T2cutoff value (Figure 6). The bound-fluid porosity of tight sandstone usually exists in clay-dominated micropores, which contain capillary and clay-bound water, while movable-fluid porosity tends to reside in large pores which are connected by effective pore throat [18]. Then, the movable-fluid porosity is determined by removing the proportion of the bound fluid from the 100% brine-saturated NMR signal, varying from 0.38% to 1.85%. Compared to movable-fluid porosity, bound-fluid porosity is commonly high, with the range of 1.08%–2.25%, indicating that the sandstone samples have the complex pore structure with poor pore connectivity. T35, T50 are corresponding to the T2 value, where the samples reach 35% and 50% brine saturation in the cumulative T2 distributions, respectively [3]. Overall, compared to Chang 7 and Xujiahe tight sandstone reservoirs [48,50], T2cutoff, T2lm, T35, and T50 of samples are characterized by relatively lower values, indicating a narrower pore size distribution in the samples.

**Figure 6.** The cumulative and incremental T2 spectrum of sample 5.

## *4.4. Multifractal Characteristics*

In this study, multifractal characteristics of pore structures were obtained from 100% brine-saturated T2 spectra. The range of moments *q* is defined in the interval from −10 to 10. The generalize dimension spectra (*Dq~q*) and the relationship of mass exponent τ(*q*) versus *q* are presented in Figures 7 and 8, respectively. The *Dq* with respect to variable *q* shows an inverse S-shaped curve. *Dq* has a larger variation for *q* < 0, while a minor variation for *q* > 0. Moreover, τ(*q*) follows a monotone increase as *q* increase, and the increasing trend gradually becomes smoother with increasing *q*. Figure 9 represents the multifractal spectra or singularity spectra of samples, where α(*q*) are also strongly correlated to the variable *q*. Overall, these spectra of different samples all show two different variation trends, that reveal that the pore size distributions of tight sandstone samples are multifractal. Therefore, the heterogeneity of pore volume distribution can be represented via the generalized dimension and singularity spectra shape and its characteristic parameters, which further reveal the local di fferences in the whole.

Generally, the heterogeneity of the whole pore size distribution is assessed by the total width of singularity spectra α−10*–*α10 and generalized dimension spectra *D*−10–*D*<sup>10</sup> [19]. Higher values of α−10*–*α10 and *D*−10–*D*<sup>10</sup> usually sugges<sup>t</sup> a more heterogeneous pore size distribution within samples, and vice versa. The right part of the generalized dimension spectra and the singular spectra (*q* > 0) corresponds to the areas with higher probability density of porosity distribution (concentrated areas). However, the left part of the generalized dimension spectra and the singular spectra (*q* < 0) represent the areas with lower probability density (sparse areas) [32,51]. Therefore, multifractality parameters *D*10, *D0*–*D*10, α10, and α*0*–α*1*0 can describe the pore characteristics in higher probability areas, and the parameters *D*−10, *D*−10–*D0*, α−10, and α−10–α*0* play the same role in lower probability areas. For the studied sandstone samples, the porosities in higher probability density areas mainly consist of the smaller pores, such as clay-dominated micropores, whereas the porosities in lower probability density areas mainly refer to the larger pores, such as intergranular dissolution pores, with a relatively larger pore size.

**Figure 7.** Generalized multifractal dimension spectra.

**Figure 8.** Generalized mass exponent τ(q) versus variable q.

**Figure 9.** Multifractal spectra of five samples.

*D0* is defined as a capacity dimension or box-counting dimension. *D1*, as an information dimension, is a measure of concentration degree of pore size distribution [28]. *D2* is the correlation dimension, which explains the scaling behavior of the second sampling moments [25]. For a monofractal structure, *D0* = *D1* = *D2* [44]. However, as shown in Table 3, all samples show a same order of *D0* > *D1* > *D2*, suggesting that the pore size distribution of every studied tight sandstone sample has a tendency toward a multifractal type of scaling. Additionally, the calculated *D*−10, *D*10, *D*−10–*D0*, *D0*–*D*<sup>10</sup> and *D*−10–*D*<sup>10</sup> are also listed in Table 3. For all samples, *D*−<sup>10</sup> > *D*10 and *D*−10–*D0* > *D0*–*D*10, indicating that the pore distributions of higher probability areas may be more homogeneous than that of lower probability areas.


**Table 3.** The generalized dimensions of samples.

For singularity parameters, the similar trend, α−10 > α10 and α−10–α*0* > α*0*–α10, are also found in Table 4, indicating that the pore system in lower probability density areas owns more obvious multifractal characteristics than that in a higher probability density area. As presented in Table 4, the values of α10–α−10 are in the range of 1.15–3.69, indicating that the pore structures of samples are highly heterogeneous. The parameter *A* = (<sup>α</sup>*0*–<sup>α</sup>10)/(<sup>α</sup>−10–α*0*) is referred to express the asymmetry of singularity spectrum, and *A* > 1 demonstrates a strong fluctuation in pore size distribution. The values of A for sample 1 and sample 2 are lower than 1, which exhibit more stable pore size distributions compared to those of other samples. The multifractal analysis of tight sandstone pores shows that the pore distribution is complicated, multifractal and heterogeneous.

**Table 4.** The singularity parameters of samples.

