Page 148 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

6.4 Applications of the Proposed Decoupling Procedure 137

Zhao et al. 1998a, 2007a) have demonstrated that ore formation is not only depen-
dent on fluid flow, but also upon solute diffusion/dispersion and chemical kinetics.
Mineralisation is commonly associated with the spatial distribution of chemical
reactions in permeable rocks (Steefel and Lasaga 1990, Phillips 1991, Raffensperger
and Garven 1995, Zhao et al. 1998a). These chemical reaction patterns are strongly
influenced by fluid flow, heat transfer and the transport of reactive chemical species.
Since fluid flow is an important agent for transporting aqueous chemical species
from one location into another (Garven and Freeze 1984, Peacock 1989, Ord and
Oliver 1997, Connolly 1997, Zhao et al. 1999d, Oliver 2001, Braun et al. 2003),
fluid flow patterns can also influence the positions where different chemical species
may meet and mix and hence where chemical reactions may take place (Yardley and
Bottrell 1992, Yardley and Lloyd 1995). In addition, heat transfer processes influ-
ence the thermal structure of the Earth’s crust and hence the spatial distribution of
chemical reaction patterns through the temperature-dependence of the equilibrium
constant and of the reaction rate (Steefel and Lasaga 1994, Xu et al. 1999, Zhao
et al. 2000b).
For aqueous species, whether chemical equilibrium is or is not attained controls
the possibility of precipitation of mineral assemblages in permeable rocks. If an
aqueous species, produced by a chemical reaction, reaches equilibrium, then that
species is saturated within the fluid and hence its concentration reaches a maxi-
mum value for a given mineralizing environment. In most cases, the solubility of
an aqueous species is directly proportional to the ambient temperature. It follows
that in cooling hydrothermal systems the saturated aqueous species becomes over-
saturated and is therefore precipitated in the porous rock. Another process caus-
ing mineral precipitation is transport within the pore-fluid of the saturated aqueous
species from a high temperature region to a low temperature region. The aqueous
species can also become oversaturated and is precipitated in the porous rock. For a
given ore formation environment, flow rates can control the total process of solute
advection. In such a case, a redox controlled chemical reaction can only reach equi-
librium through optimal coupling of solute advection, solute diffusion/dispersion
and chemical kinetics. With parallel flows taken as an example, if the solute dif-
fusion/dispersion in the direction perpendicular to the interface between the flows
is much slower than the chemical reaction rate, the chemical product cannot attain
equilibrium, even though the two fluids are perfectly miscible. On the other hand,
if the flow rate is much faster than the chemical reaction rate, the chemical product
can only attain equilibrium at a distance large with respect to a chemical equilib-
rium length-scale, which we introduce below, in the flow direction. This implies
that for a permeable fault zone with a given chemical reaction, there exists an opti-
mal flow rate resulting in chemical equilibrium being attained between two fluids
that mix and focus within the fault zone. However, for parallel flows, such as those
resulting from vertical super-hydrostatic pressure gradients, chemical equilibrium
may or may not be attained when two fluids of different origins are brought together
through focusing within a permeable vertical fault. In this case, strong interactions
occur between solute advection, diffusion/dispersion and chemical kinetics. It is
this interaction that controls the equilibrium distribution of the resulting chemical