Table of Contents
This section will provide only the briefest overview of the basic assumptions used in the TOUGH family of codes. The reader is referred to the TOUGH2 User's Guide [Pruess, Oldenburg, and Moridis, 1999], the T2VOC User's Guide [Falta, Pruess, Finsterle, and Battistelli, 1995], the TMVOC User's Guide [Pruess, Oldenburg, and Moridis, 1999], the TOUGHREACT User's Guide [Xu, Sonnenthal, Spycher, and Pruess, 2004], and the TOUGH-Fx/HYDRATE User's Guide [Moridis, Kowalsky, and Pruess, 2005] for detailed information on the TOUGH codes.
A good fundamental reference on flow in porous media is The Physics of Flow Through Porous Media [Scheidegger, 1957].
The TOUGH family of codes (and thus PetraSim) simulate flow in porous media. A basic assumption is that the flow is described by Darcy's law,
where: 
is the seepage velocity vector, 
is total permeability, 
the viscosity, 
the pressure, 
the density, and 
is the gravity vector.
As described by Scheidegger [Scheidegger, 1957], when two (or more) immiscible fluids or phases exist simultaneously in a porous medium one phase will generally wet the solid. There are in general three saturation regimes:
Saturation regime: The porous medium is completely saturated with one phase.
Pendular regime: The porous medium has the lowest possible saturation with one phase. This phase occurs in the form of pendular bodies throughout the porous medium. These pendular bodies do not touch each other so that there is no possibility of flow for that phase, see Figure 2.1.a.
Fenicular regime: The porous medium exhibits an intermediate saturation with both phases. If the pendular bodies of the pendular regime expand through addition of the corresponding fluid, they eventually become so large that they touch each other and merge. The results is a continuous network of both phases across the porous medium. It is thus possible that simultaneous flow of both phases occurs along tortuous paths, see Figure 2.1.b.
Figure 2.1. Illustration of pendular (a) and funicular (b) saturation regime in the case of an idealized porous medium consisting of packed spheres [Versluys, 1931]
For multi-phase flow, Darcy's law is modified to introduce the concept of relative permeability:
Where 
indicates the phase, 
is the relative permeability (between 0 and 1) for the phase, and
is the fluid pressure in the phase, which is the sum of the pressure in a reference phase (usually the gas phase) and the capillary pressure 
(capillary pressure is negative).
The TOUGH codes provide several options for relative permeability. A typical option is the use of Corey's curves [Corey, 1954] as illustrated in Figure 2.2. At low liquid saturation, the gas relative permeability is 1.0 and the liquid permeability is very low. Conversely, at high liquid saturation the gas relative permeability is very low and the liquid permeability is 1.0. This is consistent with the flow regimes as described above.
The TOUGH codes also provide several options for capillary pressure. A typical option is the van Genuchten function [van Genuchten, 1980] as illustrated in Figure 2.3. At low liquid saturation, the capillary pressure is large, but rapidly becomes smaller as liquid saturation increases.
