ABSTRACT

Predictions of the gas flow rate, temperature and pressure profiles along the pipeline under transient conditions are vital to the operation of gas transmission pipelines. Available simplified models for the calculation of these profiles are evaluated. Numerical solution with the method of lines is adopted to allow for estimation of the magnitude of the model terms. Sensitivity of pipeline flow model to the choice of heat transfer model, and to the accuracy of compressibility factor, heat capacity and friction factor calculations is investigated. The influence of the selection of different equations of state on pipeline line-pack results is also demonstrated. Equations of state commonly used in the gas industry were investigated, i.e.: Soave-Redlich-Kwong, Benedict-Webb-Rubin, AGA-8 and SGERG-88. The predictions from the numerical solution are compared to the field data from the Yamal-Europe pipeline.

INTRODUCTION

Predicton of the gas flow-rate, temperature and pressure profiles along the pipelines under transient conditions requires adequate mathematical models from the class of systems with distributed parameters. Numerical methods rather than analytical ones are used for their solution. Discretization of the models is usually carried out through the finite difference methods, leading to the systems of "stiff equations", which need specific numerical methods of solution. In this article, we focus on the accuracy of a non-isothermal transient gas flow model. The impact of heat transfer model on the accuaracy flow parameters is demonstrated. The effect of the selection of different equations of state is also discussed. The results of the model solution are compared to the field data from the Yamal-Europe pipeline.

Heat-transfer model

In the energy equation, the heat transfer term q represents the amount of heat exchanged between unit mass of gas and the surroundings per unit time. Application of Fourier's law to calculate the overall heat-transfer between the gas and the ground for a discretization section of a pipeline yields where U is an overall heat transfer coefficient. There exists an analytical steady-state solution for k for a cylinder near a half-plane, which corresponds to the geometry of a buried pipeline [8]. Nevertheless, it is a common practice to calculate k as for a set of concentric cylindrical layers with the distance between the boundary of an outer layer and the pipe equal to the burial depth of the pipe. The ambient temperature is fixed and equal to the ground temperature at the same horizontal level as the pipe axis, and at a sufficient lateral distance from the pipe. This technique for simplified heat transfer modelling and its applicability to calculate accurate temperature profiles in gas work. The process of heat transfer from the gas to the surrounding environment is described using unsteady heat transfer model so that the description of heat flux could take into consideration the effect of heat capacity of the surroundings of a pipeline.

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