Page 144 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

6.3 Verification of the Decoupling Procedure 133

In order to verify the proposed decoupling procedure for solving reactive trans-
port equations with strong nonlinear reaction source/sink terms, the redox chemi-
cal reaction due to an equilibrium reaction is considered and solved using the pro-
posed numerical procedure. The equilibrium constant is assumed to be 10 and the
time step used in the simulation is 100 years. Figure 6.4 shows the concentration
distributions of the two chemical reactants at three different time instants, while
Fig. 6.5 shows the comparison of the numerical solutions (which are obtained from
the proposed decoupling procedure) with the analytical solutions (which are derived
mathematically and expressed by Eq. (6.21)) for the chemical product. It can be
observed that with the increase of time, both chemical reactants are transported
into the computational domain from the left half and right half of the bottom. Due
to the fluid flow focusing, both chemical reactants are transported much faster in
the fault zone than in the surrounding rock. As expected, these chemical reactants

(Analytical, t = 1000 years) (Numerical, t = 1000 years)

(Analytical, t = 5000 years) (Numerical, t = 5000 years)

(Analytical, t = 8000 years) (Numerical, t = 8000 years)
Fig. 6.5 Comparison of numerical solutions with analytical ones for the chemical product (Equi-
librium reaction)