A Temperature- and Elevation-Dependent Continuation Method for Loadability Analysis of Gas Transmission Networks Under Variable Gas Composition

A new Temperature- and Elevation-dependent Gas Continuation Method (TE-GCM) is proposed for steady-state loadability analysis of gas transmission networks under coupled thermophysical and topographic conditions with variable gas composition. Building on the signed-flow continuation backbone of the preceding GCM, the present formulation generalizes the traced equilibrium map through coupled state-dependent gas properties, endpoint elevation effects, specified steady-state temperature fields, and composition-dependent bulk inputs. The inherited pseudo-arclength continuation procedure traces the resulting load–pressure branches through turning and weak-conditioning regions, enabling the last operationally admissible solution, termination at the physical pressure boundary, and the weakest-conditioned solution to be distinguished. The resulting branches are then assessed using the established local turning, rank-separation, transversality, and nondegeneracy indicators to determine whether the weakest-conditioned solution is consistent with a saddle-node bifurcation (SNB). Applications to three-node, Belgian, and 40-node systems show that elevation and specified temperature fields can shift the operational boundary in opposite directions depending on network topology, the spatial distributions of elevation and temperature, and loading direction. In the three-node system, the temperature field relocates the operational and critical solutions even though the corresponding branches remain nearly superimposed. Hydrogen-enriched gas scenarios consistently shift the branches toward higher standard volumetric demands, with the largest increase occurring in the 40-node binary methane–hydrogen case. In the elevation–temperature study, the three-node critical solutions are SNB-consistent, whereas termination at the physical pressure boundary prevents conclusive diagnosis in the larger systems. These results demonstrate that the proposed TE-GCM provides a unified framework for capturing how terrain, temperature, and gas composition reshape gas-network loadability and its operational and mathematical limits.