Page 153 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

142 6 Fluid Mixing, Heat Transfer and Non-Equilibrium Redox Chemical Reactions

W fault

0.5W mp

y

L fault x
0

L mp

Fluid A Fluid B

Fig. 6.8 The conceptual model of two fluids mixing and focusing in a fault
precipitation within the fault zone. Two fluids carrying two different solutes, namely
Fluid A and Fluid B, are injected from the left and right sides of the fault axis and are
focused into the fault zone according to the principles discussed by Phillips (1991)
and Zhao et al. (1999d). Since mineral precipitation is dependent on both chemical
equilibrium and the saturation concentration of a mineral, it is assumed that the
starting position of mineral precipitation is coincident with chemical equilibrium
being attained in the following theoretical analysis. This means that for a given
chemical reaction rate, the starting position of mineral precipitation is controlled by
solute advection and is measured from the lower tip of the fault. On the other hand,
since Fluid A flows parallel to Fluid B, the mixing of these two fluids is due solely
to solute diffusion/dispersion in the direction normal to the fault zone. Hence, the
thickness of mineral precipitation is controlled solely by solute diffusion/dispersion.
The starting position of mineral precipitation within the fault zone can be expressed
as follows:
V
chemical
L mp = l = . (6.30)
advection
φk R
Similarly, the thickness of mineral precipitation within the fault zone can be
expressed as

D
chemical
W mp = 2l = 2 . (6.31)
diffusion
k R