In order to improve the resilience of the integrated electricity and gas system (lEGS), the gas-electric early warning system based on the slow dynamic characteristic of the gas failure has been proposed, which can estimate the available escape time for the power system. In this paper, a linearized time-domain port model of the gas network is constructed, which is suitable for local calculation of the available escape time on the power system side. Firstly, a linearization approximation method for the partial differential-algebraic equation of gas pipelines is presented. Secondly, a linear compensation method for the calculation of internal pressure is proposed based on the systematic finite-difference time-domain iterative scheme. Finally, a single pipeline numerical example is designed to verify and analyze the error of the proposed method. The results show that this method is practical when the prediction of boundary conditions is accurate enough.