## 6 Conclusions and Prospects  
Investigation of the gas-water two-phase flow mechanism in reservoir rocks is crucial for UHS. This paper reviews pore structure characterization approaches, two-phase flow models, imaging-based pore-scale flow experiments, and interface tracking methods, offering insights into the migration and transport characteristics of two-phase fluids within porous media.  
1. Accurate characterization of the pore structure in porous media is essential for predicting rock properties and fluid transport behavior. Various testing methods offer qualitative, semi-quantitative, or quantitative insights into the micro-pore structure, but each has limitations. A multi-technique integrated approach is crucial for a more comprehensive and precise analysis of rock properties and fluid flow within porous media.
2. Microscopic seepage experiments using visualization methods provide insights into fluid flow and pore-scale mechanics. Micro-seepage models quantify gas-water two-phase flow, optimizing conditions for improved production. These models aid in studying complex flow phenomena and, combined with 3D simulations, enhance understanding of reservoir seepage patterns and recovery factor research.
3. Recent advances in digital core technology and computational fluid dynamics have improved pore-scale two-phase flow simulations. Eulerian methods like VOF, level set, and phase field track phase interfaces but face challenges in mass conservation and accuracy. Integrating Eulerian and Lagrangian methods and enhancing computational efficiency will benefit applications in oil recovery, carbon sequestration, and hydrogen storage.  
Conceptualization, Y.W.; formal analysis, X.H. and Y.Z.; funding acquisition, Y.W.; investigation, Y.W.; writing--original draft, X.H. and Y.W.; writing--review and editing, W.Z., Y.D., and H.Z. All authors have read and agreed to the published version of the manuscript. This research was funded by the Doctoral Foundation of SWUST, grant number [20 zx7129]. The APC was funded by (20 zx7129). The authors declare that there are no competing financial interests with any other people or groups regarding the publication of this manuscript.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Numerical Methods** & **Formula** & **Scope/Characteristics** \\ \hline VOSET Equation & \(\frac{\partial\overrightarrow{u}}{\partial t}\overset{\rightarrow}{u}\cdot \
abla\overset{\rightarrow}{u}=\frac{1}{p(\phi)}\left\{-\
abla p+\
abla \cdot u(\phi)\left[\
abla\overrightarrow{u}+(\
abla\overrightarrow{u})^{T} \right]+p(\phi)\overset{\rightarrow}{g}+F_{s}(\phi)\right\}\) & Coupling the VOF and LS methods, and using a geometric interface front construction approach to build the phase interface. \\ \hline PNM Method & \(\frac{\partial\overrightarrow{u}}{\partial t}\) & where \(\phi\) is the symbol for the distance function; \(p\) is pressure, in Pa; \(p(\phi)\) and \(u(\phi)\) refer to the gas–liquid mixture density and the mixture viscosity; \(u\) is the velocity; \(g\) represents the acceleration due to gravity. \\ \hline PNM Method & \(\frac{\partial\overrightarrow{u}}{\partial t}\overset{\rightarrow}{u}\cdot \
abla\overset{\rightarrow}{u}=\frac{\partial\overrightarrow{u}}{\partial t} \left\{-\
abla p+\
abla\cdot u(\phi)\left[\
abla\overrightarrow{u}+( \
abla\overrightarrow{u})^{T}\right]+p(\phi)\overset{\rightarrow}{g}+F_{s}( \phi)\right\}\) & where \(j\) refers to all pores connected to pore \(i\); \(q_{ij}\) is the flow rate between pore \(i\) and pore \(j\); \(g_{ij}\) is the conductivity of the throat connecting pore \(i\) and pore \(j\); \(P_{i}\) and \(P_{j}\) are the pressures at pore \(i\) and pore \(j\); \(k\) is the permeability of the pore network model; \(p\) is the applied pressure gradient between the inlet and outlet of the model; \(L\) is the length of the model in the flow direction. \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._