Modeling of flow behavior through porous media by fractal geometry and fractional calculus

Abstract

Introduction: The use of models in the equations of transport phenomena in the flow of fluids in porous beds, is made difficult due to the highly complex nature of the geometry of the systems of the links, in which the liquid moves through the irregular channels formed between the solid particles that form the bed. In this context, the deterministic models applied to these systems are based on the determination of the empirical constants, which considers these factors that are not considered explicitly.                       

Method: In this work, it is presented a model that describes the flow behavior as a function of the bed dimensions and the properties of the fluid as laminar regime, whose obtention is based on a formalism in which they are used together the equations of conservancy of motion quantity, fractal geometry, and differential fractional calculus.                       

Results: The model obtained is equal to that proposed by Blake and Kozeny, differentiated by the fact that all the parameters are theoretically determined from the images that show the real morphology of the porous bed.                       

Discussion or Conclusion: Results show that the model proposed predicts, for the same pressure gradient, an increase in velocity profile as the diameter particles and porosity increase, and a decrease of the velocity as the fractal dimension increase. These predictions correspond each other in magnitude order and tendency with those estimated by the Blake and Kozeny model.