1. Compressible Flow in Gas Gathering Networks
In high-pressure gathering laterals, the Weymouth equation is the worldwide standard for line sizing and hydraulic rating:
\[ Q = 433.5 \, E \, \left(\frac{T_b}{P_b}\right) \left[ \frac{P_1^2 - P_2^2}{S_g \, T_{\text{avg}} \, L \, Z_{\text{avg}}} \right]^{0.5} D^{8/3} \]
Solving backwards from the delivery manifold pressure \(P_{\text{manifold}}\), the intermediate junction header pressure \(P_{\text{junction}}\) and wellhead nodal pressures \(P_{\text{wh}, i}\) are iteratively determined.
2. API RP 14E Erosional Velocity Limits
High gas velocities carry severe risk of solid particle impingement, pipe wall thinning, and catastrophic rupture at elbows and tees. The maximum allowable velocity is governed by:
\[ v_e = \frac{C}{\sqrt{\rho_g}} \]
where \(C = 100\) for continuous solids-free gas service (\(C = 125\) for intermittent), and \(\rho_g\) is in-situ gas density. Best practice maintains \(v / v_e \le 0.70\) to ensure long-term pipeline asset integrity.