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Nonsteady gas flow through pipeline systems

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Summary

In this paper a mathematical model is developed to study some problems of fluid mechanics involved in a system of gas transportation over long distance. The flow system is made up of a pipeline and a compressor located along its path. The mathematical solutions in a closed form are obtained for the boundary and initial conditions which currently appear in practice. They are used to describe the flow behaviour in system during the nonsteady flow. A compressor operating policy that meets the delivery objective to satisfy the peak consumption imposed by consumer and all pressure constraints at the pipeline ends is also formulated. The solutions obtained in this investigation suggest how a policy of compressor working with consideration of storage capacity could be used to cover the peak demand in an optimal manner. The useful information to determine the optimum location of the compressor station along the pipeline minimizing the operation and energy expenses could be also obtained. To compare the efficiency of this flow system with a looped pipeline network, an analysis of nonsteady flow through such a flow system is also performed. Several numerical examples taken from the practice are presented in order to illustrate the behaviour of the solutions developed in the paper.

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Abbreviations

a :

Constant

b :

Constant

d :

Pipeline diameter

f :

Friction Coefficient

g 0 :

Mass velocity during the steady flow

g(x,t) :

Mass velocity during the nonsteady flow

g k (t) :

Mass velocity at the supply end during the nonsteady flow

g 0(t) :

Mass velocity at the consumption end during the nonsteady flow

h :

Mass velocity amplitude

L :

Pipeline length

m :

Compressor ratio

p 0 (x) :

Pressure distribution during the steady flow

p(x,t) :

Pressure distribution during the nonsteady flow

p k :

Pressure at the supply end during the steady flow

p 0 :

Pressure at the consumption end during the steady flow

\(\bar p_0 \) :

Integrated average steady state pressure

p a :

Atmospheric pressure

t :

Time

T :

Period

x :

Length variable

\(\bar z\) :

Integrated average compressibility factor

v :

Velocity

p d (t) :

Pressure desired by the consumer

ϱ a :

Gas specific mass at atmospheric conditions

α:

Pressure at distanceL 1 during steady state

π(x, t):

A function of time and distance given by relation (3)

π d (t):

A function of time corresponding to the pressure desired by the consumer, given by relation (15)

References

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Authors and Affiliations

  1. Department of Physics, University of Alberta, T6G 2J1, Edmonton, Alberta, Canada

    H. Pascal

Authors
  1. H. Pascal
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Additional information

With 11 Figures

Subscript 1,2 Downstream and upstream compressor

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Pascal, H. Nonsteady gas flow through pipeline systems. Acta Mechanica 42, 49–69 (1982). https://doi.org/10.1007/BF01176513

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  • DOI: https://doi.org/10.1007/BF01176513

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