## 5 Field Data Matching  
In order to prove the practical application of the proposed model, the production data of an actual case from Moxi gas field in Sichuan Basin was used. The well was partially penetrated and a schedule of constant well bottom-hole pressure was adopted at the initial production stage. Thus, the gas flow rate was characterized by a decreasing trend for a long time. The following equation was used to describe the relationship between porosity and reservoir pressure:  
Figure 12: The effect of well perforation height on production performance curves.  
Figure 13: The effect of well perforation height on pseudotime factor.  
\[\varphi=\varphi_{i}e^{-c_{\varphi}(p_{i}-p)} \tag{16}\]  
where, \(\varphi_{i}\) and \(\varphi\) denote porosity at initial and current reservoir pressure, respectively, following Equation (3); \(c_{\varphi}\) denotes formation compressibility, and it can be calculated by the following equation:  
\[c_{\varphi}=\frac{\varphi_{m}c_{m}+\varphi_{f}c_{f}}{\varphi_{m}+\varphi_{f}} \tag{17}\]  
where, \(c_{m}\) and \(c_{f}\) denote matrix and fracture system compressibility, respectively, following Equation (4); \(\varphi_{m}\) and \(\varphi_{f}\) denote matrix and fracture system compressibility, respectively.  
All input parameters are listed in Table 3. Figure 14 illustrates a comparison between the field production rate data and the matching results obtained from the proposed model. In Figure 14, the solid line represents the matching result considering formation compressibility. The dash line represents the matching result not considering formation compressibility. That is, the formation compressibility equals to zero and the porosity is constant. As we can see from Figure 14, the real field data represented by the red circles is in good agreement with the result considering formation compressibility. The matching data is not good for the model without considering formation compressibility at late time. Therefore, it is necessary to consider formation compressibility and porosity stress-sensitivity in abnormally high-pressure gas reservoir production performance analysis.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value (Field Case)** \\ \hline Reservoir temperature, T (K) & 347 \\ Initial reservoir pressure, \(p_{i}\) (MPa) & 48.6 \\ Inner region radius, \(R_{1}\) (m) & 102 \\ Reservoir radius, \(R_{e}\) (m) & 783 \\ Reservoir thickness, \(h\) (m) & 32 \\ Formation compressibility, \(c_{\varphi}\) (MPa\({}^{-1}\)) & 0.001 \\ Initial fracture horizontal permeability, \(k_{\text{Hsi}}\) (10\({}^{-3}\)\(\upmu\)m\({}^{2}\)) & 1.097 \\ Initial matrix horizontal permeability, \(k_{\text{m2 hi}}\) (10\({}^{-3}\)\(\upmu\)m\({}^{2}\)) & 0.2 \\ Interporosity flow coefficient between fracture and matrix, \(\lambda\) & 0.01 \\ Storativity ratio of natural fracture, \(\omega\) & 0.05 \\ Mobility ratio between outer and inner regions, \(M\) & 0.18 \\ Diffusivity ratio between outer and inner regions, \(\delta\) & 0.05 \\ Permeability anisotropy factor for fracture, \(\kappa_{1}\) & 36 \\ Permeability anisotropy factor for matrix in outer region, \(\kappa_{2}\) & 20 \\ Permeability stress-sensitivity coefficient, \(\gamma_{k}\) (MPa\({}^{-1}\)) & 0.01 \\ Specific gravity, \(\gamma_{g}\) & 0.596 \\ Critical pressure, \(p_{\text{c}}\) (MPa) & 4.67 \\ Critical temperature, \(T_{\text{c}}\) (K) & 195.12 \\ Wellbore radius, \(r_{\text{w}}\) (m) & 0.1 \\ Well bottom-hole pressure, \(p_{\text{wf}}\) (MPa) & 31 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The reservoir, fluid, and well parameters of the real gas field.