## 2 Materials and Methods
### Establishment of a Three-Dimensional Model and Basic Settings of the Simulation  
The first step of the numerical simulation was to create a physical model. In this study, the modified CT images were imported into the ScanIP software to generate the finite element mesh. Readers can refer to references [24; 25] for detailed principles of the finite element simulation method. Simulation of flow through a combined cement-rock sample was then conducted using the ANSYS CFX program, which has been widely used to solve 3D engineering problems [26; 27; 28; 29]. The microchannel was configured as the isothermal fluid domain, while cement, interface, and rock were considered as isothermal porous domains with isotropic porosity of 0.011, 0.014 and 0.04, respectively. The isotropic loss model was applied to all porous domains, and the corresponding permeability valves of each can be found in Section 2.7. As the simulation focused on single-phase flow in porous media, the most basic control equation was used. Without a change in fluid density, the simulated flow can be treated  
Figure 8: Moving distances of the microchannel to form different inclination angles. as an incompressible viscous flow, which could be described by Navier-Stokes equation, whose vector formula is given below,  
\[\rho\bigg{[}\frac{\partial\mathbf{v}}{\partial t}+(\mathbf{v}\cdot\
abla)\mathbf{v}\bigg{]}= \rho\mathbf{f}-\
abla p+\mu\
abla^{2}\mathbf{v} \tag{1}\]  
The left side of Equation (1) denotes the inertial force, while _of,_\(\
abla p\), and \(\mu\
abla^{2}\mathbf{v}\) on the right side are the inertial force, body force, and viscous force, respectively. According to a previous study [14], pressure differentials should be carefully selected to make sure the Reynolds number is less than 10. As such, the Darcy law could be used when calculating permeability in the post-process stage. Based on experimental measurements, [PERSON] et al. [13] reported that the bulk permeability of the interface was much higher than the permeabilities of the cement matrix and the rock. Therefore, for the initial selection of permeability values, we have assumed that the permeability of the interface is higher than those of the cement and the rock. Considering the Klinkenberg effect, the fluid type was set as water. The values of the primary settings of the simulation parameters are listed in Table 2.  
As for boundary conditions, we assumed that the inlet was the entire lateral surface of the rock phase while the outlet was the top surface of the 3D model. The bottom surface of the sample was set as the no-flow boundary. Under these conditions, the whole 3D model was developed by assuming the fluid was flowing from the reservoir towards the top of the well. The inlet pressure was set at 10 psi and the outlet pressure was set as atmospheric pressure. Assuming that the average distance between inlet and outlet was equal to the height of the model, this setting would lead to a pressure gradient equivalent of 12.5 MPa/m. A previous study measuring the permeability of dry Class G cement sample with a length of 1 inch reported that the breakthrough pressure was varied from 30 to 110 psi [30], which corresponds to the pressure gradient ranging from 8 MPa/m to 30 MPa/m. The pressure gradient assumed in our simulation study was within this pressure gradient range and could therefore be realistically considered to match the experimental results. Moreover, when conducting flow through cement modeling studies, [PERSON] et al. [31] used a pressure gradient ranging from 0 MPa/m to 5 MPa/m, and [PERSON] et al. [14] assumed a pressure gradient of 0.4 MPa/m. In our simulation study, we also assumed a similar magnitude of pressure gradient to these two previous studies. Sample physical geometry and boundary conditions for a 3D cement-rock model with an embedded circular