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0.2. Reactions and Transport in Porous Media 5

by x i /x i,ref , t/t ref ,and u/u ref ,where x i,ref , t ref ,and u ref are fixed reference
values of the same dimension as x i , t,and u, respectively. These reference
values are considered to be of typical size for the problems under investiga-
tion. This procedure has two advantages: On the one hand, the typical size
is now 1, such that there is an absolute scale for (an error in) a quantity
to be small or large. On the other hand, if the reference values are chosen
appropriately a reduction in the number of equation parameters like K
and c in (0.7) might be possible, having only fewer algebraic expressions of
the original material parameters in the equation. This facilitates numerical
parameter studies.

0.2 Reactions and Transport in Porous Media

A porous medium is a heterogeneous material consisting of a solid matrix
and a pore space contained therein. We consider the pore space (of the
porous medium) as connected; otherwise, the transport of fluids in the
pore space would not be possible. Porous media occur in nature and man-
ufactured materials. Soils and aquifers are examples in geosciences; porous
catalysts, chromatographic columns, and ceramic foams play important
roles in chemical engineering. Even the human skin can be considered a
porous medium. In the following we focus on applications in the geosciences.
Thus we use a terminology referring to the natural soil as a porous medium.
On the micro or pore scale of a single grain or pore, i.e., in a range of µm
to mm, the fluids constitute different phases in the thermodynamic sense.
Thus we name this system in the case of k fluids including the solid matrix
as (k +1)-phase system or we speak of k-phase flow.
We distinguish three classes of fluids with different affinities to the solid
matrix. These are an aqueous phase, marked with the index “w” for water,
a nonaqueous phase liquid (like oil or gasoline as natural resources or con-
taminants), marked with the index “o,” and a gaseous phase, marked with
the index “g” (e.g., soil air). Locally, at least one of these phases has al-
ways to be present; during a transient process phases can locally disappear
or be generated. These fluid phases are in turn mixtures of several com-
ponents. In applications of the earth sciences, for example, we do not deal
with pure water but encounter different species in true or colloidal solu-
tion in the solvent water. The wide range of chemical components includes
plant nutrients, mineral nutrients from salt domes, organic decomposition
products, and various organic and inorganic chemicals. These substances
are normally not inert, but are subject to reactions and transformation
processes. Along with diffusion, forced convection induced by the motion
of the fluid is the essential driving mechanism for the transport of solutes.
But we also encounter natural convection by the coupling of the dynamics
of the substance to the fluid flow. The description level at the microscale