HR: 0800h
AN: H11D-1303    [Abstracts]
TI: Modelling of Thermal Advective Reactive Flow in Hydrothermal Mineral Systems Using an Implicit Time-stepped Finite Element Method.
AU: * Hornby, P G
EM: peter.hornby@csiro.au
AF: CSIRO Exploration & Mining, PO Box 1130, Bentley, W.A 6102 Australia
AB: Understanding chemical and thermal processes taking place in hydrothermal mineral deposition systems could well be a key to unlocking new mineral reserves through improved targeting of exploration efforts. To aid in this understanding it is very helpful to be able to model such processes with sufficient fidelity to test process hypotheses. To gain understanding, it is often sufficient to obtain semi-quantitative results that model the broad aspects of the complex set of thermal and chemical effects taking place in hydrothermal systems. For example, it is often sufficient to gain an understanding of where thermal, geometric and chemical factors converge to precipitate gold (say) without being perfectly precise about how much gold is precipitated. The traditional approach is to use incompressible Darcy flow together with the Boussinesq approximation. From the flow field, the heat equation is used to advect-conduct the heat. The flow field is also used to transport solutes by solving an advection-dispersion-diffusion equation. The reactions in the fluid and between fluid and rock act as source terms for these advection-dispersion equations. Many existing modelling systems that are used for simulating such systems use explicit time marching schemes and finite differences. The disadvantage of this approach is the need to work on rectilinear grids and the number of time steps required by the Courant condition in the solute transport step. The second factor can be particularly significant if the chemical system is complex, requiring (at a minimum) an equilibrium calculation at each grid point at each time step. In the approach we describe, we use finite elements rather than finite differences, and the pressure, heat and advection-dispersion equations are solved implicitly. The general idea is to put unconditional numerical stability of the time integration first, and let accuracy assume a secondary role. It is in this sense that the method is semi-quantiative. However, the method does prove quite accurate even when the time step is of order ten greater than the Courant limit. We have even obtained results adequate for a broad understanding of critical factors using time steps hundreds of times larger than the Courant limit. As with many things, the use versus abuse of such an approach depends upon the situation being modelled and good understanding of the nature of the inaccuracies the approch can be expected to generate in that situation. The technology being used to develop the simulations is also novel. Firstly, the Python programming language is used as a computational steering tool. Within this system, the user specifies the partial differential equations and boundary conditions using text strings similar to LaTEX. Consequently adding compressibility through an equation of state for the constituent phases, variable viscosity depending on pressure and temperature, and so on, become a matter of changing constant coefficients to functions and perhaps implementing a Newton iteration for non-linear patial differential equations. A second novel aspect is the manner in which the chemistry is represented and solved. Rather than associating a composition with an element, a reaction vessel is placed at each node, and mineral and fluid molarities assigned. This composition is interpolated across the element using the shape functions, just like any other ``field'' on the mesh. After a transport step, during which the ``vessels'' exchange fluids, each node is re-equilibrated using some form of equilibrium solver.
DE: 1009 Geochemical modeling (3610, 8410)
DE: 1012 Reactions and phase equilibria (3612, 8412)
DE: 1034 Hydrothermal systems (0450, 3017, 3616, 4832, 8135, 8424)
DE: 1849 Numerical approximations and analysis
DE: 1858 Rocks: chemical properties
SC: Hydrology [H]
MN: Fall Meeting 2005