Page 70 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

56 3 Algorithm for Simulating Coupled Problems in Hydrothermal Systems

solutions (from mesh 2 to mesh 1). Clearly, the forwardly transformed solutions in
mesh 2 are exactly the same as the inversely transformed solutions in mesh 1. Fur-
thermore, the inversely transformed solutions in mesh 1 (see Figs. 3.6 and 3.7) also
compare very well with the original solutions in mesh 1 (see Figs. 3.4 and 3.5). This
means that after the original solutions are transformed from mesh 1 to mesh 2, they
can be transformed back exactly from mesh 2 to mesh 1. Such a reversible process
demonstrates the robustness of the proposed consistent point-searching interpola-
tion algorithm.

3.4 Application Examples of the Proposed Consistent
Point-Searching Interpolation Algorithm

3.4.1 Numerical Modelling of Coupled Problems Involving
Deformation, Pore-Fluid Flow and Heat Transfer
in Fluid-Saturated Porous Media

Since the verification example considered in Sect. 3.3 is a coupled problem between
medium deformation, pore-fluid flow and heat transfer processes in a fluid-saturated
porous elastic medium, it can be used as the first application example of the pro-
posed consistent point-searching interpolation algorithm. Thus, we can continue the
simulation of the verification example and use FLAC with the translated/transferred
temperature in mesh 2 to compute thermal deformation and stresses in the fluid-
saturated porous elastic medium. Towards this end, it is assumed that: (1) the bot-
tom boundary of the computational domain is fixed; (2) the top boundary is free; and
(3) the two lateral boundaries are horizontally fixed but vertically free. Except for
the parameters used in Sect. 3.3, the following additional parameters are used in the
10
continued simulation: the elastic modulus of the porous medium is 1×10 Pa; Pois-
o
−4
son’s ratio is 0.25; the volumetric thermal expansion coefficient is 2.07×10 (1/ C)
and the initial porosity is 0.1.
Figures 3.8 and 3.9 show the temperature induced deformation and stresses in
the porous elastic medium respectively. It is observed that the distribution pattern
of the volumetric strain is similar to that of the temperature. That is to say, higher
temperature results in larger volumetric strain, as expected from the physics point
of view. Owing to relatively larger volumetric strain in the left side of the compu-
tational domain, the maximum vertical displacement takes place at the upper left
corner of the domain. This is clearly evidenced in Fig. 3.8. As a direct consequence
of the thermal deformation, the temperature induced horizontal stress dominates in
the porous medium. The maximum horizontal compressive stress due to the thermal
effect takes place in the hottest region of the computational domain, while the max-
imum horizontal tensile stress occurs at the upper left corner of the domain, where
the vertical displacement reaches its maximum value. Apart from a small part of
the top region of the computational domain, the thermal induced vertical stress is