**3.2 Numerical measured embedment**

Contact analysis with finite element method has been performed to quantify the conductivity loss due to proppant embedment based on computational contact mechanics. A similar contact analysis has been also investigated between rail/wheel [26]. Initially, the model was developed and validated according to the boundary load as applied in the experimental procedure. As shown in **Figure 9**, the load is

#### **Figure 8.**

*SEM images of proppant (20/40 mesh) embedment on the original core soaked in fracking fluid: (a) bottom of the core and (b) top of the core.*


#### **Table 3.**

*Proppant embedment depth in the shale samples.*
