Page 164 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

154 7 Simulating Thermal and Chemical Effects of Intruded Magma Solidification Problems

magma. If an analytical estimation of the volume of the intruded magma is not
available for most complicated geological situations, the particle numerical method
may be useful to simulate the magma intrusion process alone so that the volume of
the intruded magma can also be estimated. Given the total volume of the intruded
magma, we can use continuum-mechanics-based numerical methods, such as the
finite element method and finite difference method, to simulate its thermal effects
by considering the heat release during the solidification of the intruded magma. This
means that we need to develop an equivalent algorithm to transform the original
magma intrusion problem into a heat transfer problem with the internal heat gener-
ation of the intruded magma. Clearly, the key issue associated with the developed
equivalent algorithm is to determine the heat release rate of the intruded magma dur-
ing its solidification. Once the time history of the heat release rate of the intruded
magma during solidification is obtained, the finite element method can be used to
simulate the thermal effects of the intruded magma in the crust of the Earth. Using
the proposed equivalent algorithm, the moving boundary problem (Crank 1984,
Alexiades and Solomon 1993) associated with the original problem during magma
solidification can be avoided. As a direct result, the efficiency of the finite element
method can be much improved. This may be considered as one of the major advan-
tages of the proposed equivalent algorithm in dealing with the thermal effects of
magma intrusion problems in the crust of the Earth.
Geological problems may involve different time and length scales in the descrip-
tions of their different physical and chemical processes. With magma intrusion into
the Earth’s crust taken as an example, the time scale of the magma intrusion pro-
cess, which includes both the creation of the magma chamber and ascent process for
the intruded magma, is much smaller than that of the magma solidification process,
which includes both the release of volatile fluids from the magma and chemical
reaction processes within the crust due to the release of the volatile fluids. On the
other hand, the volume of the intruded magma is usually much smaller than that of
the Earth’s crust of interest. This means that the whole magma intrusion problem
is, in essence, a problem of multiple time and length scales. Nevertheless, due to
the significant time and length scale differences between the magma intrusion and
solidification processes, it is possible to simulate these two different processes using
different analytical models. This will allow the detailed mechanisms associated with
each of the two processes to be modelled using totally different methodologies. For
example, if the magma intrusion process itself is of particular interest, then particle-
based numerical methods can be used to simulate the initiation and propagation of
random cracks during the ascending of the intruded magma. However, if the thermal
and chemical effects/consequences of the intruded magma are of particular inter-
est, then continuum-mechanics-based numerical methods can be used to simulate
heat transfer and mass (i.e. chemical species) transport within the Earth’s crust. To
the best knowledge of the authors, these methods have not been used to simulate
the release of volatile fluids from the magma and the chemical reaction processes
within the crust due to the release of the volatile fluids. Since both the release of
volatile fluids from the magma and the transport of the released volatile fluids may
have significant effects on ore body formation and mineralization in the upper crust