ABSTRACT

The transient flow of gas in pipes can be adequately described by a one dimensional approach. The basic equations describing the transient flow of gas in pipes are derived from an equation of motion (or momentum), an equation of continuity, equation of energy and state equation. In practice the form of the mathematical models varies with the assumptions made as regards the conditions of operation of the networks. In much of the literature, either an isothermal or an adiabatic approach is adopted. For the case of slow transients caused by fluctuations in demand, it is assumed that the gas in the pipe has sufficient time to reach thermal equilibrium with its constant - temperature surroundings. Similarly, when rapid transients were under consideration, it was assumed that the pressure changes occurred instantaneously, allowing no time for heat transfer to take place between the gas in the pipe and the surroundings. Adiabatic flow relates to fast dynamic changes in the gas. In this case heat conduction effects can not be neglected. Isothermal flow relates to slow dynamic changes. Changes of temperature within the gas due to heat conduction between the pipe and the soil are sufficiently slow to be neglected. For many dynamic gas applications this assumption that a process has a constant temperature or is adiabative is not valid. In this case, temperature of gas is a function of distance and is calculated using a mathematical model which includes energy equation. In the paper comparison of different (isothermal and non-isothermal) models is presented. Practical examples have been used to emphasize differences between models.

1. Introduction

It is a well established fact that flow in gas pipelines is unsteady. Conditions are always changing with time, no matter how small some of the changes may be. When modeling systems, however, it is sometimes convenient to make the simplifying assumption that flow is steady. Under many conditions, this assumption produces adequate engineering results. On the other hand, there are many situations where an assumption of steady flow and its attendant ramifications produce unacceptable results. Dynamic models are just a particular class of a differential equation model in which time derivatives are present. During transport of gas in pipelines the gas stream loses a part of its initial energy due to frictional resistance which results in a loss of pressure. This is compensated for by compressors installed in compressor stations. Compression of the gas has the undesired side effect of heating the gas. The gas may have to be cooled to prevent damage to the main transmission pipeline. If cooler is installed heat from the gas is passed to the air in a force draught heat exchanger in which one or more fans operate, depending on the number of compressors in service. Cooling of the gas is desirable because it improves the efficiency of the overall compression process. As always it is a matter of balancing capital and maintenance costs against operating costs.

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