화학공학소재연구정보센터
Energy & Fuels, Vol.32, No.8, 8024-8039, 2018
Implications of Molecular Thermal Fluctuations on Fluid Flow in Porous Media and Its Relevance to Absolute Permeability
This paper addresses the challenge related to the understanding of varying absolute permeability when forcing fluid (mostly water is considered) through a porous medium at varying system temperatures. It is assumed that the total energy dissipation splits into two contributions, a viscous part and a thermal part. These two energy dissipation channels will exactly balance the supplied external energy. The thermal part has not been considered previously regarding forced water flow through porous media, and it is substantiated theoretically by comparison with the well-known Ludwig-Soret effect. It is based on a hypothesis that the flowing water is dissipating molecular kinetic energy to heat (thermal dissipation) due to an asymmetric spatial velocity distribution up- and downstream the solid matrix. Based on previous theoretical calculations, an expression can be derived showing that thermal dissipation will increase proportional with the total inner surface area of the porous medium and the square root of absolute temperature. The calculation assumes that the solid matrix in the porous media can be considered as a large collection of large macroscopic "Brownian particles" being stagnant relative to the flowing water phase. The measured total energy dissipated in the porous medium, equal to the supplied pressure, can be used to estimate two fit parameters, a weight factor with respect to viscous/thermal dissipation and a thermal dissipation efficiency factor, using a generalized version of Darcy's law also accounting for changes in temperature reading. Absolute permeability can then be calculated as a function of temperature using a reference permeability. This expression was applied for two sets of experimental data reported in the literature. The calculated results showed excellent fit to the measured absolute permeability values, corroborating the hypothesis proposed. The fractional magnitude of the total viscous and total thermal dissipation terms varied typically from 0.8 to 0.3 and from 0.2 to 0.7, respectively, in the temperature range 20-160 degrees C. Hence, total thermal dissipation constitutes a significant part of the energy required to force fluids through porous media, even at ambient temperature, which may have important consequences for processes where temperature is varying significantly in space and time. The reported data for absolute permeability vs temperature in the literature show large scatter, and many hypotheses have been proposed to explain the data. Hence, further systematic empirical work investigating this challenge is very much encouraged using, e.g., fluids with different molecular weights and polarity and porous media with different mineralogy in addition to performing molecular dynamics simulations. The current paper offers a theoretical explanation for the phenomenon observed related to reduction in absolute permeability for increasing system temperature which hopefully can contribute to improved test design and interpretation of experimental data.