Gas Flow in Pipelines

When everything else is specified, Eqs. (6.86) or (6.88) may be solved for the exit specific volume 2- Then P2 may be found from Eq. (6.81) or in the rearrangement 

Although the key equations are transcendental, they are readily solvable with hand calculators, particularly those with rootsolving provisions. Several charts to ease the solutions before the age of calculators have been devised M.B. Powley, Can. J. Chem. Eng., 241-245 (Dec. 1958) C.E. Lapple, reproduced in Perry s Chemical Engineers Handbook, McGraw-Hill, New York, 1973, p. 5.27 O. Levenspiel, reproduced in Perry s Chemical Engineers Handbook, 7th ed., p. 6-24 Hougen, Watson, and Ragatz, Thermodynamics, Wiley, New York, 1959, pp. 710-711. 

In all compressible fluid pressure drop calculations it is usually justifiable to evaluate the friction factor at the inlet conditions and to assume it constant. The variation because of the effect of temperature change on the viscosity and hence on the Reynolds number, at the usual high Reynolds numbers, is rarely appreciable. 

In the isothermal case, any appropriate PVT equation of state may be used to eliminate either P or V from this equation and thus permit integration. Since most of the useful equations of state are pressure-explicit, it is simpler to eliminate P. Take the example of one of the simplest of the non-ideal equations, that of van der Waals 

It is to be expected that the kind of phase distribution will affect such phenomena as heat transfer and friction in pipelines. For the most part, however, these operations have not been correlated yet with flow patterns, and the majority of calculations of two-phase flow are made without reference to them. A partial exception is annular flow which tends to exist at high gas flow rates and has been studied in some detail from the point of view of friction and heat transfer. 

Further substitutions from Eqs. (6.80) and (6.81) and multiplying through by 2kgc/C2V2 result in 

Although integration is possible in closed form, it may be more convenient to perform the integration numerically. With more accurate and necessarily more complicated equations of state, numerical integration will be mandatory. Example 6.13 employs the van der Waals equation of steam, although this is not a particularly suitable one the results show a substantial difference between the ideal and the nonideal pressure drops. At the inlet condition, the compressibility factor of steam is z = PV/RT = 0.88, a substantial deviation from ideality. 

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By the use of extremely simple models for the gas flow in pipelines, it has been demonstrated how important the acceleration term becomes when sonic conditions are approached in a gas network. This term is usually neglected in most design computations, tut the simple examples in this paper show that this may not be justified. 

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