Page 145 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

134 6 Fluid Mixing, Heat Transfer and Non-Equilibrium Redox Chemical Reactions

are divergent around the exit region of the fault. The comparison of the numer-
ical solutions with the analytical ones for the chemical product clearly demon-
strates that the proposed decoupling procedure can produce accurate numerical
solutions for simulating the equilibrium chemical reaction, in which the chemi-
cal reaction rate approaches infinite. It is interesting to note that there is a strong
interaction between solute advection, diffusion and chemical reaction rate in the
considered equilibrium chemical system. Although two reactants are well trans-
ported into the fault zone, the mixing of the two fluids carrying them is controlled
by the solute diffusion. Since the chemical reaction rate is infinite for the equilib-
rium reaction, the corresponding chemical equilibrium length is identical to zero
due to the solute diffusion. This implies that the chemical reaction rate is too fast
to allow both the reactants to diffuse across the common boundary between them
so that fluid mixing cannot effectively take place within the fault zone. This is the
reason why both chemical reactants are abundant but no chemical product is pro-
duced within the fault zone in the computational model. However, around the exit
region of the fault zone, the flow of the fluids is slowed and divergent so that the
fluids carrying two different reactants can be mixed. Consequently, a high con-
centration of the chemical product is produced around the exit region of the fault
zone.

6.4 Applications of the Proposed Decoupling Procedure
to Predict Mineral Precipitation Patterns in a Focusing
and Mixing System Involving Two Reactive Fluids

Mixing of two or more fluids is commonly suggested as a mechanism for precipi-
tating minerals from solution in porous rocks. Examples include uranium deposits
(Wilde and Wall 1987), MVT deposits (Appold and Garven 2000, Garven et al.
1999), Irish Pb-Zn deposits (Hitzmann, 1995, Everett et al. 1999, Murphy et al.
2008), vein gold deposits (Matthai et al. 1995, Cox et al. 1995) and Carlin gold
deposits (Cline and Hofstra 2000). The mixing process is attractive because it
enables two fluids of contrasting Eh-pH conditions to mix and hence generate chem-
ical conditions conducive to mineral precipitation. Clearly rock-fluid(s) interactions
must be involved as well as the fluid mixing process but in depth exploration of such
multi-fluid-rock reaction processes awaits robust and computationally fast ways of
handling realistic kinetic-reaction-transport phenomena.
There are three end member geometries that promote the mixing of two miscible
fluids (Fig. 6.1). The first we refer to as parallel-flow geometries of the first kind
(Figs. 6.6a, b) where two contrasting fluids are brought alongside each other by
convection or focusing in a highly permeable fault or sedimentary lens (Phillips
1991). The second involves the production of a new fluid within an existing fluid
flow system by thermal or chemical reactions with a mineral assemblage within the
flow stream (Fig. 6.6c). An example is the production of CO 2 or of hydrocarbons
from carbonates or carbonaceous material within a fluid stream that is hot, acid and