Page 143 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

132 6 Fluid Mixing, Heat Transfer and Non-Equilibrium Redox Chemical Reactions

vertical velocity within the fault is equal to 3.02 × 10 –8 m/s, the corresponding
flow-focusing factor of the fault is equal to the ratio of the maximum velocity
within the fault to that of the injected fluids at the bottom of the computational
model. This results in a flow-focusing factor of 18.88 for the rectangular fault
within the computational model. The analytical value of the flow-focusing fac-
tor for the rectangular fault can be calculated from Eq. (6.23). Substituting the
related parameters into Eq. (6.23) yields the analytical flow-focusing factor of 18.25.
Since the relative error of the flow-focusing factor from the numerical simulation
is within 3.5%, it quantitatively demonstrates that the proposed numerical proce-
dure used in the computational model can produce accurate numerical solutions
for fluid focusing and mixing within the fault. These processes are very impor-
tant for accurately simulating the chemical species transport and reaction within the
fault.

(Reactant A, t = 1000 years) (Reactant B, t = 1000 years)

(Reactant A, t = 5000 years) (Reactant B, t = 5000 years)

(Reactant A, t = 8000 years) (Reactant B, t = 8000 years)
Fig. 6.4 Concentration distributions of the chemical reactants at different time instants (Equilib-
rium reaction)