## 3 Results & Discussion  
### Assessment of Impregnation Parameters  
We evaluated the impregnation parameters by understanding the mechanisms controlling resin impregnation in a porous medium. We qualitatively assessed the relative effect of each parameter and later used experiments to properly quantify them, as an explicit theoretical model was beyond the scope of our study. Hence, we assumed an incompressible Newtonian fluid in creeping laminar flow and neglected the time derivative of the fluid velocity and gravity. In this case, the Navier-Stokes equation reduces to  
\[\
abla P=\mu\
abla^{2}v \tag{2}\]  
where \(v\) is the fluid velocity, \(\mu\) is the dynamic viscosity, and \(P\) is the pressure. Based on Equation (2), [PERSON] et al. [45] derived an expression to predict the infiltration distance \((h)\) of polymers with variable viscosity into a porous composite material. In other words, the polymer/epoxy changed its viscosity while curing and loosing its fluidity as described in Equation (1). The derived relationship was  
\[h^{2}=\frac{2k\Delta P}{\phi\mu_{0}k_{n}}(1-e^{-k_{n}t}) \tag{3}\]  
where \(k\) is the permeability, \(\Delta P\) is the differential pressure, and \(\phi\) is the porosity. In the case of epoxy impregnation of a rock sample, the effective pressure was attributed to capillary forces and any external forces acting upon the surface of the epoxy. In Table 2, we show that epoxy wetted the silica surface. Similar behavior for carbonate impregnation has also been reported by others (e.g., [8; 29; 46]), thus, confirming the wetting behavior of epoxy on rock surfaces. Thereby, we can write  
\[\Delta P=\frac{2\gamma}{R}\cos\theta+P_{impreg} \tag{4}\]  
where \(\gamma\) is the surface tension and \(\theta\) is the advancing contact angle. \(\frac{2\gamma}{R}\cos\theta\) represents the capillary pressure and \(P_{impreg}\) is the impregnation pressure imposed on the resin. Now, we can rewrite Equation (3) to estimate the impregnation penetration length \((h)\) as  
\[h=\sqrt{\frac{2k(1-e^{-k_{n}t})}{\phi\mu_{0}k_{n}}(\frac{2\gamma}{R}\cos \theta+P_{impreg})} \tag{5}\]  
Equation (5) was used to evaluate the impregnation of the epoxy system summarized in Table 2, into the Indiana limestone sample described earlier. Figure 5 plots the impregnation penetration length \((h)\) against time for three different pressures: \(P_{impreg}~{}=~{}0\) bar models the behavior of epoxy in spontaneous inhibition, \(P_{impreg}~{}=~{}1\) bar models vacuum impregnation, and \(P_{impreg}~{}=~{}65\) bar models the high-pressure assisted impregnation. The relative effect of the imposed impregnation pressure on the impregnation penetrationlength is demonstrated. In this model, the flow stopped when the resin was too viscous to flow discernibly.  
On top of the simplifications mentioned earlier, this model assumes single-phase flow and an absolute vacuum to be achieved, i.e., no possibility of modeling trapped gases, which is a major concern that we discuss in the following section. Several models have been proposed in the literature to address the limitations of this model [47; 48; 49; 50; 51; 52]. Although the proposed model is a great simplification of the experimental system, it can provide useful insights into the impregnation process and its efficiency, which can be summarized as follows:  
1. Resin should fill the pore space completely by spontaneous imbibition owing to its wetting behavior. However, this typically never happens in practice because of limited impregnation times.
2. The application of high pressure helps resin impregnation, especially at the significant pressures that can be generated in a laboratory. The drastic effect of pressure on the impregnation penetration distance is exemplified in Figure 5, where high-pressure-assisted impregnation is an order of magnitude longer than the other cases.