Page 147 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

136 6 Fluid Mixing, Heat Transfer and Non-Equilibrium Redox Chemical Reactions

second flow. This situation has been considered by Phillips (1991) and analytical
solutions for the composition of the resulting mixing plume presented.

6.4.1 Key Factors Controlling Mineral Precipitation Patterns
in a Focusing and Mixing System Involving
Two Reactive Fluids

We consider the first of these parallel flow geometries in some detail. The classical
approach (see Phillips 1991) is to assume that chemical equilibrium has been estab-
lished within the mixing plume so that the equilibrium concentration of a particular
chemical species is expressed as a function of the environmental parameters, namely
temperature, fluid pressure and the concentration of other chemical species. The fun-
damental point we explore here is that the overall pattern of mineralization in these
mixing systems results from intimate interactions between solute advection, solute
diffusion and/or dispersion and chemical kinetics. Thus, chemical equilibrium in
some cases may never be attained in these mixing systems.
In this section we concentrate solely on parallel flows of the first kind and show
that the patterns of chemical precipitation for such flows result from intimate rela-
tions between fluid flow (which is a first order control on solute advection), chem-
ical reaction rates, and solute diffusion and dispersion. We show, for instance, that
even for a situation where two fluids are brought together by fluid focusing within
a permeable fault zone, chemical reaction between the two fluids may never occur
even if chemical equilibrium prevails so long as the advection of solute is large with
respect to solute diffusion/dispersion. In order to focus on the principles involved for
parallel flows of the first kind we idealise the situation by considering a vertical per-
meable fault within a less permeable rock mass. The whole model is fully saturated
with fluids of different chemical compositions at different points on the system. We
consider only systems where the fluids are miscible whilst noting for future inves-
tigation that multi-phase systems, that is, fluid systems in which two or more fluids
are present that are immiscible, comprise yet another hydraulic-chemical system
where intimate mixing of contrasting chemistries is possible at the pore scale. We
need to emphasise here that although we are considering only vertical permeable
faults the discussion is just as relevant to permeable sedimentary lenses or to any
other geometry that brings two chemically contrasted fluids together. The vertical
geometry here allows simple boundary conditions to be imposed for the hydraulic
potential driving fluid flow. The discussion is equally relevant for any other orienta-
tion of the focusing “lens”.
Ore formation in the Earth’s crust is commonly considered to be a consequence
of the reaction of large fluxes of one or more fluids with rock. In many situations,
fluid flow is focused within fault zones and the important issue becomes the spatial
control exerted by the fault on the resultant mineralization. It is commonly assumed
that either fluid mixing or fluid/rock reactions or a combination of both are impor-
tant processes associated with permeable fault zones, due to the large fluid fluxes
typically inferred for such zones. However, recent extensive studies (Phillips 1991,