Flow pattern effect on the pressure drop of biphasic flow through porous media from a fractal dimension perspective
DOI:
https://doi.org/10.29059/cienciauat.v14i2.1308Keywords:
fractal reservoir, porous bed, complex flow, fractional equation of transport, pressure drop predictionAbstract
The description of the behavior of a biphasic flow through porous beds by means of models based on the equations of transport phenomena is made difficult due to the geometric irregularity of the channels that are formed between the solid particles that make up the bed. Deterministic models developed for single-phase flows require the adjustment of empirical constants and cannot be extrapolated to biphasic flows, where the flow pattern generated in the system significantly influences the behavior of the total flow and the frictional pressure losses. Therefore, in this paper, we present a model to describe the behavior of the biphasic flow in relation to the flow pattern and the morphology, dimensions, and operating conditions of the porous bed, whose obtainment was based on a hierarchy that used the equations for conservation of momentum, fractal geometry and fractional differential calculus jointly. The model predicts that, for the same composition of the biphasic flow, the flow pattern significantly influences friction pressure losses, with an increase when one of the phases is dispersed within the other. On the other hand, the increase in the fractal dimension of the pores, in turn, causes an increase in pressure loss due to friction. The model has limitations associated with the considerations established during its collection, since it is only valid when the effects of surface tension are more significant than the gravitational effects, the effects of the latter being disregarded on the flow pattern, as well as for the stationary state.
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