## 2 Materials and Methods
### Determination of Dimensions of the Simulation Model  
In this study, we numerically investigated how the presence of microchannels embedded into physical models of the cement-rock interface would affect flow through this interface. The physical rock-cement interface models were built from CT images of the downscaled sample, shown in Figure 2a. The rock sample shown in Figure 2a was collected from a well located in Alberta. The rock is siltstone collected from a Notikewin formation. The mineral and chemical composition of Notikewin rock is shown in Table 1. The cement used for the preparation of the sample shown in Figure 2a is commercial abandonment well cement. The cemented rock core sample in Figure 2a was conditioned at ambient temperature (\(\sim\)21 \({}^{\circ}\)C) and at 1500 psi for 7 days. Once the sample was taken out of the high-pressure cell, it was stored in sealed plastic bags to prevent water loss and isolate the sample from contact with the air.  
The cement-rock sample was then scanned using micro-CT at a resolution of 11.92 \(\upmu\)m. Figure 2b is an example cross-sectional image of the sample shown in Figure 2a. According to the CT image analysis, no through-going microchannels were observed in the CT images. Figure 2b was then binarized (i.e., converted into an image with black and white colors only) and simplified, as the white color only represents the cement-rock matrix (Figure 2c). Under these circumstances, void structures such as cracks and interface gaps were not considered in this study, and the main void structure is the microchannel which is illustrated in Section 2.2.  
The simplified binarized CT image was further divided into three phases: rock, cement, and the interface between the cement and rock. The corresponding images are shown in Figure 3. All binarized CT images have a size of 200 pixels \(\times\) 201 pixels, which is equal to a physical size of 11.92 mm \(\times\) 11.98 mm. The wall thickness of the hollow cylinder  
\begin{table}
\begin{tabular}{l l} \hline \hline \multicolumn{1}{c}{**Properties**} & \multicolumn{1}{c}{**Details**} \\ \hline Lithology & Quartzose sandy siltstone \\ Mineralogical composition & High amount of quartz with small amounts of dolomite, ankerite, \\  & muscovite, and albite \\  & Major element composition (unit: ppm) & Si (340136), Ca (33333), Al (31364), Fe (14598), K (9092), Mg (6883) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mineral and chemical composition of the Notikewin rock [19].  
Figure 1: Flowchart of the methodology.  
Figure 2: Downscaled cement–rock sample (**a**) and its CT image (**b**) and simplified binarized CT image (**c**).  
rock column is 29 pixels, which is equal to an actual wall thickness size of 1.73 mm. The diameter of the cement column is 123 pixels, which is equal to an actual cylinder diameter of 7.33 mm. The interface region is composed of the cement and its thickness is 14 pixels, which is equal to an actual wall thickness of 0.83 mm. The current study considered the microchannels located at the interface region only and, therefore, the modification works were performed on the CT images of the interface.