Equilibrium and Transfer in Porous Media 2
or engineers who may not be looking specifically to become theoreticians in porous media, but wish to integrate knowledge of porous media with their previous scientific culture, or who may have encountered them when dealing with a technological problem. While avoiding the details of the more mathematical and abstract developments of the theories of macroscopization, the author gives as accurate and rigorous an idea as possible of the methods used to establish the major laws of macroscopic behavior in porous media. He also illustrates the constitutive laws and equations by demonstrating some of their classical applications. Priority is to put forward the constitutive laws in concrete circumstances without going into technical detail.
This second volume in the three-volume series focuses on transport and transfer from homogeneous phases to porous media, and isothermal transport in the pore space.
Equilibrium and Transfer in Porous Media 2
Isothermal Transport in the Pore Space
As with the previous one, this chapter begins with a section on the physical foundations of the laws of isothermal transport in porous media, which need not necessarily be read in detail. In the second section, following some reminders about the constitutive equations and boundary conditions, a classification is put forward for the situations encountered in practice. This is an introduction to the different applications, which will be discussed in Chapter 1 of Volume III.
2.1. Laws of transport in the pore space occupied by one or two phases: additional points
In the previous chapter, three fundamental laws governing transfer in porous media were introduced: Darcy's law for the filtration of a fluid saturating the pore space, Fick's law for isobaric binary diffusion in the gaseous phase saturating the pore space or the diffusion of solutes in the saturating liquid phase, and finally Fourier's law in a composite medium for heat conduction without transport of matter.
With the processes that occur in natural conditions, these three fundamental laws usually act simultaneously and interactively. In order to deal with such situations, we need to supplement these laws with a number of important other points. As far as possible, as we did in the previous chapter, we shall base our discussions on the principles of macroscopization by averaging. However, there are limitations to this method in certain situations, where it will be necessary to turn to semi-empirical elements.
In this chapter, we limit ourselves to isothermal transport within the interstitial fluids. Strictly speaking, the hypothesis of isothermia can only be considered an approximation, even if no temperature gradient is imposed on the porous body. The phase-change accompanying the transport of a volatile liquid spontaneously gives rise, at the scale of the processes within the REV and at the macroscopic scale, to the production of latent heat, the amount of which needs to be evaluated. In this chapter, we accept that there are situations in which the effects of the thermal phenomena associated with transport are negligible at all scales.
The two fundamental laws of isothermal transport will be supplemented by three important extensions:
- Transport by filtration and diffusion in two immiscible fluids occupying the pore space, governed by the laws of capillarity. - Transport in the gaseous phase, totally or partially saturating the pore space, by filtration or diffusion. We stressed the point multiple times in Chapter 1 (sections 188.8.131.52, 184.108.40.206 and 220.127.116.11) that the condition of separation between the scale of the molecular REV and the "scale of the pore", which is crucial to justify the process of macroscopization, is frequently not satisfied in practical situations. This being the case, adjustments need to be made to the coefficients in Darcy's and Fick's laws. - Isothermal transport with phase-change. This is transport in a pore space shared between a volatile liquid and a gaseous phase 1 , with the latter being partly or entirely made up of the vapor of the liquid. 2.1.1. Diffusion and filtration in porous media occupied by two immiscible fluids
18.104.22.168. Two-phase sharing of the pore space and macroscopization
The extensions of the transport laws discussed in this section stem from the process of macroscopization applied in the domain occupied by each of the two immiscible fluids. The wetting fluid (marked with a subscript w ) and the non-wetting fluid (marked n ) share the pore space in accordance the laws of capillarity discussed in Chapters (I)-1 (section 1.2) and (I)-3 (sections 3.1.1 and 3.1.2). These laws of