Page 161 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

150 6 Fluid Mixing, Heat Transfer and Non-Equilibrium Redox Chemical Reactions

height of the model, indicating that two fluids cannot mix to produce an extensive
mixing region due to the fast advection of the fluids within the fault.
Thus, for the two end-members of chemical reaction rates, namely a very fast
equilibrium reaction and a slow reaction with a controlling chemical reaction rate of
10 –11 (1/s), chemical equilibrium cannot be attained within the fault, implying that
mineral precipitation cannot take place within a permeable vertical fault zone for
the chemical reaction considered here. This is the fundamental characteristic of the
second type of chemical reaction pattern considered in this investigation.

6.4.4.3 The Third Type of Chemical Reaction Pattern
The third type of chemical reaction pattern is a representation of Type 3 in the
previous section. The fundamental characteristic of this type of chemical reaction
pattern is that chemical equilibrium, which results in a considerable equilibrium
thickness in the direction normal to the fault zone, can be achieved within the fault
zone. In order to enable the starting position of chemical equilibrium to be close to
the lower tip of the vertical fault, the background fluid pressure gradient within the
surrounding rock is one percent of the lithostatic pressure gradient minus the hydro-
static gradient. Due to flow focusing, the maximum vertical flow velocity within the
fault zone is about 4.68 × 10 –10 m/s in the numerical simulation. Since the optimal
reaction rate is directly proportional to the solute diffusion/dispersion coefficient, it
is desirable to select the value of a solute diffusion/dispersion coefficient as large as
possible, so that the total CPU time in the simulation can be significantly reduced.
For this reason, the solute diffusion/dispersion coefficient is assumed to be 3 × 10 –8
2
m /s in the numerical simulation. If the thickness of chemical equilibrium in the lat-
eral direction of the fault zone is 80 m, the optimal chemical reaction rate is about
1.9 × 10 –11 (1/s), as can be calculated from Eq. (6.37).
Figure 6.11 shows concentration distributions of the two chemical reactants
and the corresponding chemical product at two time instants of t = 500,000 and
t = 800,000 years. The maximum concentration distribution of the chemical prod-
uct generates considerable thickness within the fault zone. This agrees well with
what is expected from the previous theoretical analysis given in Sect. 6.4.3. Due
to the low fluid velocity, a chemical equilibrium zone is also generated in the flow
convergent region just in front of the fault zone. It is noted that this chemical equilib-
rium zone is almost separated from the chemical equilibrium zone within the fault.
This phenomenon results from the distribution of fluid velocity vectors arising from
fluid flow focusing just outside and within the fault zone.
The geological implication of the third type of chemical reaction pattern is that if
a mineral precipitation pattern of a certain thickness and length within a permeable
vertical fault zone is observed, then it is possible to estimate both the optimal flow
rate and the optimal reaction rate during the formation of this precipitation pattern.
On the other hand, if the flow rate and reaction rate are known, then it is possible to
estimate the width of the potential mineral precipitation pattern within a permeable
vertical fault zone.