*3.2. Experimental Method*

XRD analysis was completed at Sichuan Keyuan Engineering Technology Testing Center. XRF analysis, rock mechanics experiments, and reservoir physical properties analysis were completed at the Experimental Research Center of East China Oil and Gas Branch of Sinopec.

#### 3.2.1. XRD and XRF Analysis

The mineral composition of samples was obtained by XRD, which was determined on the premise of deducting background values through the Jade 5.0 software package. The principle of XRD analysis is that di fferent minerals show di fferent XRD di ffraction e ffects. Data calculated by the XRD accurately represents the relative content of each mineral. However, XRD cannot measure the content of amorphous silica because it shows no di ffraction peaks.

The secondary X-rays were emitted when the X-ray irradiated on the material. Di fferent elements show their specific secondary X-ray with certain features or wavelength characteristics. XRF analysis uses secondary X-rays to convert the data into specific elements and their abundance. Elemental Si occurs in quartz, plagioclase, k-feldspar, clay minerals, and amorphous silica.

#### 3.2.2. Rock Mechanics Experiment

Samples were tested using a TAW-2000 computer-controlled electrohydraulic servo testing machine under constant confining pressure conditions. The size of test samples is 25 mm (diameter) × 50 mm (length). In the process of testing, strain rate was controlled by the DUOLI microcomputer control system, mostly 0.01–0.03, which was convenient to obtain smooth stress–strain curves. The compressive strength, Young's modulus, and Poisson's ratio can be calculated by the stress–strain curves.

#### 3.2.3. Reservoir Physical Properties

The total porosity was obtained by calculating the di fference between the bulk density and the skeleton density. Permeability was obtained by calculating the expansion of He with increasing pressure (5 MPa–30 Mpa) at a constant temperature. Oil saturation was measured by nuclear magnetic resonance (NMR).

#### *3.3. A New Method for Calculating the Content of Amorphous SiO2*

In this study, a new method for quantitative analysis of amorphous SiO2 in the Lucaogou Formation of the Jimusar Depression was established by using a combination of XRD and XRF. Through XRD analysis, the shale strata mainly consist of quartz, plagioclase, potash feldspar, dolomite, calcite, pyrite, and clay minerals (Figure 2A). Elemental Si is in quartz, plagioclase, potash feldspar, and clay minerals.

The combination of XRD and XRF can calculate amorphous silica as follows. Suppose the sample mass is *M*, where the mass of amorphous SiO2, quartz, plagioclase, K-feldspar, and clay minerals are respectively represented by *mSiO*2 , *mquartz*, *mplagioclase*, *mK*−*f eldspar*, and *mclay*.

**Figure 2.** Mineral composition of different lithofacies samples in the Lucaogou Formation. (**A**) The mineral content of the different lithofacies; (**B**) clay mineral composition in the different lithofacies.

According to XRD analysis:

$$\frac{m\_{quartz}}{M - m\_{SiO\_2}} = \mathcal{W}\_{quartz}.\tag{1}$$

$$\frac{m\_{\text{plagicclas}}}{M - m\_{\text{SiO}\_2}} = \mathcal{W}\_{\text{plagicclas}} \tag{2}$$

$$\frac{m\_{\rm K-feldspin}}{M - m\_{\rm SiO\_2}} = \mathcal{W}\_{\rm K-feldspin} \tag{3}$$

$$\frac{m\_{clay}}{M - m\_{SiO\_2}} = \mathcal{W}\_{clay} \tag{4}$$

The *Wquartz*, *Wplagioclase*, *WK*−*<sup>f</sup> eldspar*, and *Wclay* represent the percentage of quartz, plagioclase, *k*-feldspar, and clay minerals measured by XRD analysis.

According to XRF analysis:

$$\frac{m\_{SiO\_2} \times P\_{Si-SiO\_2} + m\_{quartz} \times P\_{Si-quartz} + m\_{plagicular} \times P\_{Si-plagicular}}{M} + \frac{m\_{K-feldquur} \times P\_{Si-K} \times P\_{Si-elay} \times P\_{Si-elay}}{M} = \mathcal{W}\_{Si}$$

The mass percentages of Si in amorphous SiO2, quartz, plagioclase, k-feldspar, clay minerals, and the sample are represented by *PSi*−*SiO*<sup>2</sup> , *PSi*−*quartz*, *PSi*−*plagioclase*, *PSi*−*K*−*<sup>f</sup> eldspar*, *PSi*−*clay*, and *WSi*, respectively.

Placing Formulas (1)–(4) into Formula (5), thus creating Formula (6)

$$\frac{m\_{SiO\_2} \times P\_{Si-SiO\_2} + \mathcal{W}\_{quartz} \times \left(M - m\_{SiO\_2}\right) \times P\_{Si-quartz} + \mathcal{W}\_{plagiclaw} \times \left(M - m\_{SiO\_2}\right) \times P\_{Si-plagiclaw}}{M} + \frac{\mathcal{W}\_{K-f,cylage} \times \left(M - m\_{SiO\_2}\right) \times P\_{Si-lap} + \mathcal{W}\_{slag} \times \left(M - m\_{SiO\_2}\right) \times P\_{Si-lap}}{M} + \frac{\mathcal{W}\_{L,g} \times \left(M - m\_{Sc,l}\right) \times P\_{Si-lap} + \mathcal{W}\_{slag} \times \left(M - m\_{Sc,l}\right) \times P\_{Si-lap} + \mathcal{W}\_{slag} \times \left(M - m\_{Sc,l}\right) \times P\_{Si-lap}}{M}}{M} + \frac{\mathcal{W}\_{L,g} \times \left(M - m\_{Sc,l}\right) \times P\_{Si-lap} + \mathcal{W}\_{slag} \times \left(M - m\_{Sc,l}\right) \times P\_{Si-lap} + \mathcal{W}\_{slag} \times \left(M - m\_{Sc,l}\right) \times P\_{Si-lap}}{M}}{M} + \frac{\mathcal{W}\_{L,g} \times \left(M - m\_{Sc,l}\right) \times P\_{Si-lap} + \mathcal{W}\_{slag} \times \left(M - m\_{Sc,l}\right) \times P\_{Si-lap} + \mathcal{W}\_{slag} \times \left(M - m\_{Sc,l}\right) \times P\_{Si-lap} + \mathcal{W}\_{slag} \times \left(M - m\_{Sc,l}\right) \times P\_{Si-lap} + \mathcal{W}\_{slag} \times \left(M - m\_{Sc,l}\right) \times P\_{Si-lap} + \mathcal{W}\_{slag} \times \left(M - m\_{Sc,l}\right)$$

Formula (6) can be changed to Formula (7):

$$\begin{array}{l} \mathcal{W}\_{\text{SiO}\_{2}} = \frac{\mathcal{W}\_{\text{SiO}\_{2}}}{\mathcal{M}} = \\ \mathcal{W}\_{\text{Si}} - \mathcal{W}\_{\text{quartz}} \times \mathcal{P}\_{\text{Si}-\text{quartz}} - \mathcal{W}\_{\text{logicular}} \times \mathcal{P}\_{\text{Si}-\text{logicalare}} - \mathcal{W}\_{\text{K}-\text{feldupur}} \times \mathcal{P}\_{\text{Si}-\text{K}-\text{feldupur}} - \mathcal{W}\_{\text{clip}} \times \mathcal{P}\_{\text{Si}-\text{slup}} \\ \mathcal{P}\_{\text{Si}-\text{Si}>\text{O}\_{2}} - \mathcal{W}\_{\text{quantiz}} \times \mathcal{P}\_{\text{Si}-\text{qravking}} \times \mathcal{P}\_{\text{Si}-\text{plajewlaw}} - \mathcal{W}\_{\text{K}-\text{feldupur}} \times \mathcal{P}\_{\text{Si}-\text{K}-\text{feldupur}} - \mathcal{W}\_{\text{cyl}} \times \mathcal{P}\_{\text{Si}-\text{clav}} \end{array} \tag{7}$$

In Formula (7), only the mass percentage of element Si in clay minerals is difficult to determine, because the molecular formulas of other minerals are known. The molecular formulas of clay minerals are variable. Therefore, the ideal molecular formulas of di fferent types of clay minerals are applied in this research. For the mass percentage of Si in mixed clay minerals, it is calculated according to the mixed layer ratio based on XRD measurements. Molecular formulas used for kaolinite, montmorillonite, chlorite, and illite are respectively Al4(Si4O10)(OH)8, Al4Si8O2(OH)2, Al6Si4O10(OH)8, and Al4(Si8O20)(OH)4. The mass percentages of element Si in these are 21.7%, 56.3%, 19.6%, and 31.1%, respectively. The *Pclay* of the tu ffaceous shale lithofacies, transitional lithofacies, and carbonate lithofacies samples can be calculated. Then, the contents of amorphous SiO2 in these samples can be calculated by Formula (7).
