Pressure loss, liquid-holdup calculations

Baker, A., Nielsen, K., and Gabb, A., Pressure loss, liquid-holdup calculations developed. Oil and Gas Journal, March 14, 55-59,1988. 

For a quick first approximation in the case of trickle flow, pressure loss may be expressed by an Ergun-type relationship in which the porosity c is replaced by c(l - /3), the total liquid extraparticle holdup /3 being calculated either by the correlation proposed by Sato et al. for spheres (S7) of diameter 2 mm or larger ... 

The frictional pressure drop may be estimated by subtracting the hydrostatic component (calculated from the holdup) from the total pressure gradient, as shown in Figure 4.19. It will be seen that under certain conditions, particularly at low liquid flow rates, the frictional component appears to approach zero. For the flow of air-water mixtures, negative friction losses are well docmnented in the literature. This anomaly arises because not all of the liquid present in the pipe contributes to the hydrostatic pressure, because some liquid may form a film at the pipe wall. This liquid is sometimes flowing downwards and most of its weight is supported by an upward shear force at the wall. The drag exerted by the gas on the hquid complements the frictional force at the pipe wall. 

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