Page 133 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

122 6 Fluid Mixing, Heat Transfer and Non-Equilibrium Redox Chemical Reactions

In terms of numerical modelling of coupled problems between fluids mixing,
heat transfer and chemical reactions in fluid-saturated porous rocks, it is possible to
divide the coupled problems into the following three categories (Zhao et al. 1998a).
In the first category of coupled problem, the time scale of the advective flow is much
smaller than that of the relevant chemical reaction in porous rock masses so that the
rate of the chemical reaction can be essentially taken to be zero in the numerical
analysis. For this reason, the first category of coupled problem is often called the
non-reactive mass transport problem. In contrast, for the second category of cou-
pled problem, the time scale of the advective flow is much larger than that of the
relevant chemical reaction in pore-fluid saturated porous rocks so that the rate of the
chemical reaction can be essentially taken to be infinite, at least from the mathemat-
ical point of view. This means that the equilibrium state of the chemical reaction
involved is always attained in this category of coupled problem. As a result, the
second category of coupled problem is called the quasi-instantaneous equilibrium
problem. The intermediate case between the first and the second category belongs
to the third category of coupled problem, in which the rate of the relevant chemical
reaction is a positive real number of finite value. Another significant characteristic
of the third category of coupled problem is that the detailed kinetics of the chem-
ical reactions must be taken into account. It is the kinetics of a chemical reaction
that describes the reaction term in a reactive species transport equation. If a redox
chemical reaction is considered, both the forward reaction rate and the backward
one need to be included in the reaction term of a reactive species transport equation.
Although significant achievements have been made for the numerical modelling of
non-reactive species and quasi-instantaneous equilibrium reaction transport prob-
lems, research on the numerical modelling of the third category of coupled prob-
lem with redox chemical reactions is rather limited. Considering this fact, we will
develop a numerical procedure to solve coupled problems between fluids mixing,
heat transfer and redox chemical reactions in fluid-saturated porous rocks.
Large geological faults and cracks are favorable locations for fluids carrying dif-
ferent chemical species to focus and mix. For this reason, ore body formation and
mineralization are often associated with geological faults and cracks. When the per-
meability of a fault/crack is much bigger than that of the surrounding rock, the
pore-fluid flow in the fault/crack is much faster than that in the surrounding rock.
This implies that an interaction between the solute diffusion, advection and chemi-
cal kinetics is very strong within and around a fault/crack. Although it is well known
that ore body formation and mineralization are associated with geological faults and
cracks, the major factors controlling the reaction patterns within and around large
faults and cracks remains unclear.
Keeping the above-mentioned considerations in mind, a numerical approach
based on the finite element method is used to solve coupled problems between
fluids mixing, heat transfer and redox chemical reactions in fluid-saturated porous
rocks. In order to improve the efficiency of numerical modelling, the concept of the
chemical reaction rate invariant is used to convert the conventional reactive trans-
port equations with strong chemical reaction terms into the following two different