Page 86 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

Chapter 4
A Term Splitting Algorithm for Simulating

Fluid-Rock Interaction Problems
in Fluid-Saturated Hydrothermal Systems
of Subcritical Zhao Numbers

In recent years, we have been making efforts to develop a practical and predictive
tool to explore for giant ore deposits in the upper crust of the Earth. Towards this
goal, significant progress has been made towards a better understanding of the basic
physical and chemical processes behind ore body formation and mineralization in
hydrothermal systems. On the scientific development side, we have developed ana-
lytical solutions to answer the following scientific questions (Zhao et al. 1998e,
1999b): (1) Can the pore-fluid pressure gradient be maintained at the value of the
lithostatic pressure gradient in the upper crust of the Earth? and, (2) Can convec-
tive pore-fluid flow take place in the upper crust of the Earth if there is a fluid/mass
leakage from the mantle to the upper crust of the Earth? On the modelling develop-
ment side, we have developed numerical methods to model the following problems:
(1) convective pore-fluid flow in hydrothermal systems (Zhao et al. 1997a, 1998b);
(2) coupled reactive pore-fluid flow and species transport in porous media (Zhao
et al. 1999a); (3) precipitation and dissolution of minerals in the upper crust of
the Earth (Zhao et al. 1998a, 2000a); (4) double diffusion driven pore-fluid flow in
hydrothermal systems (Zhao et al. 2000b); (5) pore-fluid flow patterns near geologi-
cal lenses in hydrodynamic and hydrothermal systems (Zhao et al. 1999d); (6) vari-
ous aspects of the fully coupled problem involving material deformation, pore-fluid
flow, heat transfer and species transport/chemical reactions in pore-fluid saturated
porous rock masses (Zhao et al. 1999c, 1999f, 1999g). The above-mentioned work
has significantly enriched our knowledge about the physical and chemical processes
related to ore body formation and mineralization in the upper crust of the Earth.
Since fluid-rock interaction is another potential mechanism of ore body formation
and mineralization in the upper crust of the Earth, it is necessary to extend further the
developed numerical tools to solve fluid-rock interaction problems. This requires us
to deal with coupled reactive species transport phenomenon, which is the direct con-
sequence of the chemical reactions that take place between aqueous reactive species
in pore-fluid and solid minerals in pore-fluid saturated porous rock masses.
For a natural fluid-rock interaction system, the reactant chemical species consti-
tutes only a small fraction of the whole matrix in a porous rock (Phillips 1991). In
this case, the chemical dissolution front is stable if the Zhao number of the system
is subcritical, while it becomes unstable otherwise. Based on the concept of the

C. Zhao et al., Fundamentals of Computational Geoscience, 73
Lecture Notes in Earth Sciences 122, DOI 10.1007/978-3-540-89743-9 4,
C Springer-Verlag Berlin Heidelberg 2009