Page 159 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

148 6 Fluid Mixing, Heat Transfer and Non-Equilibrium Redox Chemical Reactions

reaction rates used in the simulation, the thickness of the chemical equilibrium
within the fault zone is much smaller than the width of the fault zone itself. The
theoretical estimate of the thickness of chemical equilibrium within the fault zone
is 10.95 m for a controlling chemical reaction rate of 10 –11 (1/s), and 0.11 m for a
–7
controlling chemical reaction rate of 10 (1/s). Hence, the maximum concentration
distribution of the chemical product comprises a very thin membrane; that is, min-
eral precipitation comprises a thin lenticular shape within the fault zone and starting
at the lower tip of the fault. This is the fundamental characteristic of the first type of
chemical reaction pattern.

6.4.4.2 The Second Type of Chemical Reaction Pattern

The second type of chemical reaction pattern is defined as an approximate
representation of Type 2 in the previous section. In this example, the background
fluid pressure gradient within the surrounding rock is set equal to a lithostatic
pressure gradient. Two controlling chemical reaction rates, namely k R =∞ and
k R = 10 −11 (1/s), are considered to investigate the effects of different chemical
kinetics on chemical reaction patterns. From a chemical kinetics point of view,
k R =∞ represents an equilibrium chemical reaction. Due to flow focusing, the
maximum vertical flow velocity within the fault zone is about 3.02 × 10 –8 m/s.
Figure 6.10 shows the concentration distributions for the two chemical reac-
tants and the corresponding chemical product at two time instants of t = 5000
and t = 8000 years. Both chemical reactants are transported into the computational
domain from the left half and right half of the base of the model. Due to fluid flow
focusing, both chemical reactants are transported much faster within the fault zone
than in the surrounding rock. There is a strong interaction between solute advec-
tion, diffusion/dispersion and chemical reaction rate (i.e. k R =∞). Although both
reactants are transported into the fault zone, the mixing of the two fluids carrying
them is controlled by solute diffusion and dispersion. Since the chemical reaction
rate is infinite, the corresponding chemical equilibrium length due to solute diffu-
sion/dispersion is identical to zero normal to the fault zone. This implies that the
controlling chemical reaction rate is too fast to allow both the reactants to diffuse
across their common boundary so that fluid mixing cannot effectively take place
within the fault zone. However, around the exit region of the fault zone, the fluid
flow decreases and, more importantly, diverges so that a high concentration of the
chemical product is produced around the exit region of the fault zone.
In the case of a non-equilibrium chemical reaction characterized by a slow chemi-
cal reaction rate (e.g. k R = 10 −11 (1/s)), the theoretical chemical equilibrium length
calculated from Eq. (6.28) is 5.48 m, while the theoretical chemical equilibrium
length calculated from Equation (6.25) is 8630 m in the direction of the fault axis.
Thus the chemical equilibrium length due to solute advection is greater than the
length of the fault itself, so that the chemical product distribution within the fault
zone is controlled by solute advection. Because the chemical equilibrium length due
to the solute advection is greater than the total length of the fault zone plus its exit
region (i.e. 5000 m plus 2500 m), chemical equilibrium cannot be reached within the