Page 233 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

224 Summary Statements

to understand the fundamental mechanisms behind the morphological instabil-
ity of a chemical dissolution front during its propagation within fluid-saturated
porous media of critical and supercritical Zhao numbers. The related numeri-
cal results have demonstrated that the proposed segregated algorithm and the
related numerical procedure are useful for and capable of simulating the mor-
phological instability of a chemical dissolution front within the fluid-saturated
porous medium.
(6) Non-equilibrium redox chemical reactions of high orders are ubiquitous in
fluid-saturated porous rocks within the crust of the Earth. The numerical mod-
elling of such high-order chemical reactions becomes a challenging prob-
lem because these chemical reactions are not only produced strong nonlin-
ear source/sink terms for reactive transport equations, but also often coupled
with the fluids mixing, heat transfer and reactive mass transport processes.
In order to solve this problem effectively and efficiently, it is desirable to
reduce the total number of reactive transport equations with strong nonlinear
source/sink terms to a minimum in a computational model. For this purpose,
a decoupling procedure on the basis of the concept of the chemical reaction
rate invariant has been developed for dealing with fluids mixing, heat transfer
and non-equilibrium redox chemical reactions in fluid-saturated porous rocks.
Using the proposed decoupling procedure, only one reactive transport equa-
tion, which is used to describe the distribution of the chemical product and has
a strong nonlinear source/sink term, needs to be solved for each of the non-
equilibrium redox chemical reactions. The original reactive transport equations
of the chemical reactants with strong nonlinear source/sink terms are turned
into the conventional mass transport equations of the chemical reaction rate
invariants without any nonlinear source/sink terms. A testing example, for some
aspects of which the analytical solutions are available, is used to verify the
proposed numerical procedure. The proposed decoupling procedure associated
with the finite element method has been used to investigate mineral precipita-
tion patterns due to two reactive fluids focusing and mixing within permeable
faults within the upper crust of the Earth. The related numerical solutions have
demonstrated that the proposed numerical procedure is useful and applicable for
dealing with the coupled problem between fluids mixing, heat transfer and non-
equilibrium redox chemical reactions of high orders in fluid-saturated porous
rocks.
(7) The solidification of intruded magma in porous rocks can result in the follow-
ing two consequences: (1) heat release due to the solidification of the interface
between the rock and intruded magma and (2) mass release of the volatile fluids
in the region where the intruded magma is solidified into the rock. Traditionally,
the intruded magma solidification problem is treated as a moving interface (i.e.,
the solidification interface between the rock and intruded magma) problem to
consider these consequences in conventional numerical methods. An equivalent
source algorithm has been presented to simulate thermal and chemical conse-
quences/effects of magma intrusion in geological systems, which are composed
of porous rocks. Using the proposed equivalent source algorithm, an original