# Studies of Fracture Damage Caused by the Proppant Embedment Phenomenon in Shale Rock
## Materials and Methods
### Methodology for Studying the Embedment Phenomenon  
The research methodology developed in the Oil and Gas Institute - NRI was used [7; 10; 20; 21; 28]. It allowed an initial determination of the primary roughness of the fracture face. It was determined for several selected areas, and then the average roughness was calculated from the roughness profiles along the selected measurement sections. The method of determination of the surface roughness and the measurements are presented in Figure 5[7; 10; 20; 21]. Equation (1) was used [7; 10; 20; 21; 28]. \[R=\frac{\sum_{i=0}^{n}H_{p_{i}}+\sum_{i=0}^{n}H_{v_{i}}}{n_{p}+n_{v}} \tag{1}\]  
where \(R\) is the roughness of the profile surface along the measurement section (mm), \(H_{p}\) is the peak height (mm), \(H_{v}\) is the valley depth (mm), \(n_{p}\) is the total number of peaks (-), \(n_{v}\) is the total number of valleys (-). The average primary roughness \(R_{a}\) for the entire surface of the fracture face was determined as an arithmetic average of the roughness of the profiles determined for the individually selected areas. Laboratory simulation of the embedment phenomenon consisted of placing a proppant between two cylindrical core plugs and then exposing it to the set axial compression stress, at the set temperature, for the set period of time (Figure 6a,b) [7; 10; 21; 22]. Figure 4: Materials used for testing: (a) Shale rock; (b) Proppant. Figure 5: An example of the surface roughness profile along the measurement section for the selected area on the surface of the fracture face. The amount of the proppant material needed to pack the fracture and obtain the specified surface concentration was determined according to Equation (2) [10; 28; 29]:  
\[m_{p}=A_{f}\cdot 10^{-1}\cdot C \tag{2}\]  
where \(m_{p}\) is the weight of the proppant (g), \(C\) is the surface concentration of the proppant (kg/m\({}^{2}\)), \(A_{f}\) is the surface area of the fracture face subjected to compression stress (cm\({}^{2}\)). The analysis of the fracture face after simulation of the embedment phenomenon consisted in the determination of the average depth of embedment of the proppant grains and of the damage of its surface. The method of determination of embedment depth and damage of the fracture face along the measurement section is presented in Figure 7 [7; 10; 20; 21; 26] and in Equation (3) [7; 10; 20; 21; 28]. \[H_{e}=\frac{\sum_{i=0}^{n}H_{e_{i}}}{n_{e}} \tag{3}\]  
where \(He\) is the average depth of proppant embedment in the fracture face of the profile along the measurement section (mm), \(He_{i}\) is the valley depth (embedment of a proppant grain in the fracture face) (mm), \(n_{e}\) is the total number of valleys (embedment of proppant grains in the fracture face) (-). The total average depth \(He_{t}\) of proppant embedment in the fracture faces (rock), expressed in mm, was determined according to Equation (4) [7; 10; 20; 21; 28]:  
\[H_{e_{t}}=H_{e_{Ta}}+H_{e_{Ba}} \tag{4}\]  
Figure 6: Test unit: (**a**) Arrangement of cores and proppant into the chamber; (**b**) Hydraulic press with heating chamber for the simulation of the embedment phenomenon. Figure 7: Sample profile of the depth and width of grain embedment (valleys) along the measurement section in the selected area, on the surface of the fracture face. where \(He_{T,a}\) is the average depth of proppant embedment in the top fracture face, corresponding to the arithmetic average of the obtained values for individually specified areas (mm), \(He_{\cdot B,a}\) is the average depth of proppant embedment in the bottom fracture face, corresponding to the arithmetic average of the obtained values for individually specified areas (mm).