A dry gas seal (DGS) is one of the key basic components of natural gas transmission pipeline compressors, and the sealing performance of a DGS dealing with complex multi-component pipeline natural gas is different from that dealing with conventional nitrogen medium. In this paper, a spiral groove DGS of the compressor in natural gas transmission pipeline systems is taken as the research object. The thermal hydrodynamic lubrication model of the DGS is established considering turbulence effect and choking effect. Based on the finite difference method, the temperature and pressure distributions and the steady-state performance of the DGS are obtained by simulating. The influence of unitary impurity compositions such as light hydrocarbon, heavy hydrocarbon, non-hydrocarbon, and their contents on the steady-state performance of the DGS is analyzed. The steady-state performance of the DGS dealing with multi-impurity natural gas such as in the West-East gas transmission is investigated under different operating conditions. The results show that turbulence had a significant effect on the DGS, while choking had a weak effect. Increasing the content of light hydrocarbon such as C2H6 and heavy hydrocarbon such as C5H10 resulted in an increase in the gas film stiffness, leakage rate, and the temperature difference between the inlet and outlet, while non-hydrocarbon, such as N2, reduced the temperature difference between the inlet and outlet. The greatest impact on seal performance was produced by the heavy hydrocarbon, followed by the light hydrocarbon, and the least was produced by the non-hydrocarbon.