## 4 Limitations of the Study  
The models used in this simulation study were built on some simplifying assumptions; therefore, the application of the results should be considered to have some limitations. Mud cakes are formed by the deposition of solid particles in mud under the effect of differential pressure during drilling [34]. They act as physical barriers with low permeability for fluid flow [35]. The model developed in this simulation study did not consider the existence of mud cakes, which in reality may be a major factor affecting fluid flow through the interface, as mud cake permeability is significantly different from rock, cement, and interface permeability. However, in real field applications, a filter cake may not always be present even with good cementing practices (e.g., using a spacer/pre-flush before sending the cement downhole). Conditions like sufficient volume, velocity, and contact time of a well-designed spacer/preflush should remove the mud filter cake. Microchannels are assumed to be located at the cement-rock interface and they are extended all the way from the top to the bottom of the model. The five shapes considered in the study are simple and basic shapes. In reality, the microchannels may consist of irregular shapes and have different cross-sectional areas. When forming microchannels with different inclination angles, it was difficult to precisely control the location and pathway of the microchannels. In other words, the simulation study only considered the \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Section**} & \multicolumn{3}{c}{**Volume Flow Rate (m3/s)**} \\ \cline{2-4}  & **k1 (Krock \textless{} Kinterface)** & **k2 (Krock \textless{} Kinterface)** & **k3 (Krock \textgreater{} Kinterface)** \\ \hline Cement & \(5.12\times 10^{-13}\) & \(9.02\times 10^{-13}\) & \(1.02\times 10^{-12}\) \\ Interface & \(1.81\times 10^{-10}\) & \(3.50\times 10^{-10}\) & \(4.13\times 10^{-10}\) \\ Rock & \(3.56\times 10^{-10}\) & \(2.73\times 10^{-9}\) & \(9.70\times 10^{-9}\) \\ Microchannel & \(9.60\times 10^{-11}\) & \(3.28\times 10^{-10}\) & \(5.75\times 10^{-10}\) \\ Total & \(6.34\times 10^{-10}\) & \(3.41\times 10^{-9}\) & \(1.07\times 10^{-8}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Volume flow rate through cement–rock samples with microchannels and variable rock permeability. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Section**} & \multicolumn{3}{c}{**Average Outflow Velocity (m/s)**} \\ \cline{2-4}  & **k1 (Krock \textless{} Kinterface)** & **k2 (Krock \textless{} Kinterface)** & **k3 (Krock \textgreater{} Kinterface)** \\ \hline Cement & \(1.19\times 10^{-8}\) & \(2.11\times 10^{-8}\) & \(2.39\times 10^{-8}\) \\ Interface & \(7.72\times 10^{-6}\) & \(1.49\times 10^{-5}\) & \(1.76\times 10^{-5}\) \\ Rock & \(6.32\times 10^{-6}\) & \(4.84\times 10^{-5}\) & \(1.72\times 10^{-4}\) \\ Microchannel & \(3.94\times 10^{-4}\) & \(1.35\times 10^{-3}\) & \(2.36\times 10^{-3}\) \\ Total & \(5.16\times 10^{-6}\) & \(2.77\times 10^{-5}\) & \(8.70\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Average outflow velocity through a cement–rock sample with microchannels and variable rock permeability. ideal cases and controlled variables to determine the effect on the overall volume flow rate. Unfortunately, we do not have the relevant facilities to 3D-print the samples to conduct comparison experiments. For further validation of the model predictions, a 3D printing technique, such as 3D-printed samples, could be used to validate the simulation results. [PERSON] [36] proposed that 3D-printed rock could provide novel ways to visualize rock microstructure and fluid-rock interactions at the rock surface. Such 3D-printed rock might be used to create idealized rock samples with microchannels that can be used to validate the model's results from simulation studies like the one presented here. For all simulation models, we assumed that there were no existing defects in the cement-rock sample.