1. Steady-State Pipeline Linepack Inventory
The total standard gas volume stored in a pipeline of length \(L\) and inner diameter \(D\) is given by:
\[ V_{\text{pack}} = V_{\text{geom}} \cdot \left(\frac{P_{\text{avg}}}{P_{\text{base}}}\right) \cdot \left(\frac{T_{\text{base}}}{T_{\text{avg}}}\right) \cdot \frac{1}{Z(P_{\text{avg}}, T_{\text{avg}})} \]
where \(V_{\text{geom}} = \frac{\pi}{4} D^2 L\), and \(P_{\text{avg}}\) is the parabolic Weymouth mean pressure:
\[ P_{\text{avg}} = \frac{2}{3} \left( P_1 + \frac{P_2^2}{P_1 + P_2} \right) \]
2. Transient Mass Balance & Survival Buffer
During a supply disruption, the rate of linepack depletion is the net imbalance:
\[ \frac{d V_{\text{pack}}}{dt} = Q_{\text{in}} - Q_{\text{out}} \]
The usable linepack buffer represents the inventory above the minimum delivery pressure \(P_{\text{min}}\). The survival time before forced industrial curtailment is:
\[ t_{\text{survival}} = \frac{V_{\text{pack}}(P_{\text{normal}}) - V_{\text{pack}}(P_{\text{contract\_min}})}{Q_{\text{demand}} - Q_{\text{supply}}} \times 24 \text{ hours} \]