## 5 Conclusions  
The presence of microchannels in the cement-rock interface is of significant concern as these channels may form possible gas leakage pathways in oil and gas wells. The main objective of this study was to investigate the effect of microchannels (>11.92 \(\upmu\)m) present in the cement-rock interface on the volume flow rate of formation fluid leakage in oil and gas wells. Idealized models of cement-rock samples containing microchannels with different shapes, cross-sectional areas, quantities, and inclination angles were developed, and the CFD modeling technique was used to study the fluid flow characteristics through these idealized models. According to the simulation results, the following conclusions can be offered:  
1. Compared with the cement-rock interface containing no microchannels (i.e., base case), all the cases with simulated microchannels have a relatively higher overall volume flow rate of formation fluid leakage.
2. The main factors affecting the overall volume flow rate of formation fluid are the microchannel cross-sectional and contact areas. Increasing the magnitude of both factors would cause the overall volume flow rate to also increase.
3. For microchannels that have the same cross-sectional area, microchannels of different shapes will have different perimeter values, which directly affects the contact area of a microchannel. As the number of sides of a polygonal shape decreases (from circular to triangular shape), there is a relative increase in the overall volume flow rate.
4. For microchannels that have the same shape, as the cross-sectional area of the microchannel increases, the overall volume flow rate also increases.
5. For microchannels that have the same shape and cross-sectional area, an increasing number of microchannels increases the volume flow rate significantly because both the cross-sectional area and contact area increase simultaneously.
6. For microchannels that have the same shape and cross-sectional area, a higher inclination angle of microchannels (measured from the vertical direction) yields a relatively higher overall volume flow rate, due to the higher contact area of the microchannel.
7. The relative magnitude of rock permeability (as compared to cement matrix and cement-rock interface permeabilities) may influence the volume flow rate through each section.  
This study also provides a new perspective on the wellbore integrity study: the 3D reconstruction method, which was used to build the geometry shown in Figure 9, can be presented as a solution for the \"complex geometry\" that involves interactions between artificial microchannels and realistic microstructures (such as geometries in [18]), as a reconstruction method is the only way to generate the \"complex geometry\".  
Future research should focus on refining the current physical model by considering in situ conditions (e.g., using samples that are exposed to compressive stress), and establishing physical samples that contain artificial microchannels. The application of micro-PIV in characterizing microchannel flow will be also considered. The effect of microchannels beyond the resolution of the micro-CT remains to be elucidated.  
Conceptualization, methodology, visualization, X.Y.; software, validation, formal analysis, investigation, writing--original draft preparation, S.G.; resources, data curation, supervision, project administration, funding acquisition, E.K.; writing--review and editing, X.Y. and E.K. All authors have read and agreed to the published version of the manuscript.  
This work is supported by the Science Foundation of Zhejiang Ocean University (1102509222). This work also received funding from the Natural Sciences and Engineering Research Council of Canada and Sanjel Energy Services (NSERC CRDPJ 531509-18 Kuru and SESINC CRD 531509 Kuru).  
Not applicable.  
The first author would like to thank [PERSON] and [PERSON] for their technical help.  
The authors declare no conflict of interest.