## 1 Introduction  
The greenhouse effect of methane gas is about 25 times greater than that of carbon dioxide [1]. The leakage of methane, the main component of natural gas, from the oil and gas wells is, therefore, considered to be part of the total fugitive greenhouse gas emissions, which cause global warming [2]. In Alberta, approximately three-quarters of the provincial methane emissions come from the activities of the upstream oil and gas sector. As a result, oil and gas industry activities are considered to be the largest source of methane emissions [1]. Failure of cellulose cement could provide methane leakage pathways. Therefore, it is vital to identify and mitigate potential leakage pathways in oil and gas wells to reduce greenhouse gas emissions. Leakage of gas along a well may occur through the cement-casing interface, the cement-rock interface, or through the pores and microchannels of the cement itself [3, 4, 5]. The leakage pathways may be closely related to cement failure or poor bonding of the cement column. Previous research shows that a good quality bond at the cement interfaces in the well, either at the cement-casing interface or at the cement-rock interface, can prevent the occurrence of micro-annulus [6,7]. Recent research on wellbore integrity mostly focuses on carbon capture and storage (CCS) wells. The objective of these studies was to investigate the influence of CO\({}_{2}\)-cement chemical reactions at the cement-casing interface [8, 9] or the influence of chemical reaction at the cement-rock interface [5, 10, 11]. Several experimental studies have been conducted to investigate microchannels at cement-rock interfaces. Researchers at SINTEF have undertaken some work associated with interface geometry [12] and defects of cement and micro-annular flow paths in the cement-caprock interface [13]. [PERSON] et al. [14] investigated the effect of geochemical and geochemical processes on the fracture permeability of composite Portland cement-basalt caprock core samples. The microstructure of the samples used by both [PERSON] et al. [13] and [PERSON] et al. [14] showed significant defects in the cement zone, which means that flow could have been more influenced by those defects. [PERSON] [15] conducted a comprehensive investigation of wellbore cement integrity at the micron scale, including the study of fractures in the cement matrix, the cement-casing interface, and the cement-rock interface. [PERSON] et al. [16] characterized the cement-casing interface microstructure. [PERSON] et al. [17] investigated the impact of stress-induced fractures on the permeability of wellbore cement. They concluded that by compressing the cement samples up to their uniaxial compressive strength limit, fractures created in the cement matrix by uniaxial compressive strength tests are not likely to form continuous leakage pathways. During these studies, micro-computed tomography or a \"micro-CT\" technique was used to obtain the realistic three-dimensional (3D) geometry and the microstructure of the cement matrix, the cement-formation, and the cement-casing interfaces because of the non-destructive characteristic of the technique. A review of these previous works revealed that there was no information available for the case of fluid flow through the cement-rock samples which considers the effect of microchannels located at the cement-formation interface. So far, not much work has been undertaken to investigate the effects of microchannel shapes and inclination angles on flow though the cement rock interface, mainly because it is difficult to identify the actual microchannel geometry by using the current technology. Instead, widely accepted solutions have been developed by assuming a fixed shape for the fracture surface during the process of creating simulation models. [PERSON] et al. [18] conducted a numerical simulation study of gas seepage through coals by generating a coal model with a single artificial fracture with different shapes and angles.