31 May 2021 to 4 June 2021
Europe/Berlin timezone

Data-Driven Finite Element Method, Energy Conservation approach for temperature, water isotope ($\delta D, \delta ^{18}O$), and $[SiO_{2}]_{sat.}$ conc. distributions of the Culex Basin terrestrial hydrothermal system-Yellowstone, WY.

1 Jun 2021, 19:00
1h
Poster (+) Presentation (MS7) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes Poster +

Speaker

Mr Anthony P. Sorensen II (Washington State University-School of the Environment)

Description

The thermal energy distribution of the Yellowstone terrestrial hydrothermal system is driven by a mantle-derived magmatic plume which has both Iron-Magnesium rich and Aluminum-Silicate rich phases and supplies thermal energy to the surface (Crough, 1978). The Yellowstone hydrothermal system is in steady-state within neighborhood of geologic time (10's Ka) and steady-state diffusive nature predominates as the hydrothermal system marches closer towards eruption(Faust, C.R. and Mercer, J.W., 1977). The Yellowstone Plateau Volcanic Field (YPVF) with area on the order of 90,000$km^{2}$ is the location of numerous active thermal areas. Since the domains observed during field reconnaissance (2019 and 2020) were relatively small ( \approx $1.6km^{2}$) compared to the overall area impacted by thermal energy within the global system (i.e. 90,000$km^{2}$), care was taken to ensure energy minimization $1/2||\bigtriangledown(u)||^{2}\approx0$ within the spatial domain was satisfied during numerical model's implementation of the coupled set of nonlinear hydrodynamic governing euqations (i.e. advection-diffusion-reaction) for the observed domain (i.e. Cule Basin). The FEniCS-Dolfin-PETSc numerical libraries were used in the implementaiton of numerical simulations of spatial distributions for heat, water isotopes (i.e. $\delta D, \delta ^{18}O$), and saturation silica ($SiO_{2}$) concentration estimations of the fluid-rock interface observed from Culex Basin hydrothermal features. Energy distributions, thermal and chemical gradient($\bigtriangledown (u)$)/numerical flux ($-K \bigtriangledown (u)$) fields estimated within the observed fluid-rock interface domain ($\Omega_{CB}$) are the result of the local buoyancy forces (Smith and Chapman, 1983).

If the locally observed hydrothermal systems at Yellowstone interact as energy conservative space time balances, that minimize the distribution of spatial potential energy in the observed phases, then this could be numerical evidence that the global Yellowstone hydrothermal system is in steady-state diffusive energy flux. This would imply that the fluid-rock interface of a terrestrial hydrothermal system is driven by buoyancy forces which determine fluid velocity fields and thus the elliptic plane of thermal energy distribution decoupled from the physical ground surface (Smith and Chapman, 1983). The finite element numerical results of the nonlinear Lagrange-Galerkin diffusive model for variables measured during field reconnaissance will be discussed for temperature based estimations, and measured spatial distributions and associated flux fields (Sorey et al., 1978).

On terrestrial hydrothermal systems found on Earth, this approach could reduce the amount of exploration drilling needed during geothermal development. Less drilling during said geothermal development could reduces the cost ($\$$) on the order of hundreds of thousands of dollars. Additionally less drilling could reduce the environmental impact in the surrounding biomes. Integrated with LiDar, and other types of spatially distributed signal data taken as discrete points, this approach completes the data driven approach to the numerical conservation of energy in natural systems. Upon further development, if Peclet convergence can be determined for the Lagrange-Galerkin methods presented, terrestrial hydrothermal system models could be used to compare the data collected from other terrestrial hydrothermal systems where drilling might be a challenge such as other planetary bodies (i.e. Titan, I.O. Venus, Europa, Triton, etc.) since it would take an observation based approach with respect to the overall system.

References

Crough, S. T. (1979). Hotspot epeirogeny. Tectonophysics, 61(1-3), 321-333.
Faust, C. R., and Mercer, J. W. (1977). Theoretical analysis of
uid
ow and energy transport in
hydrothermal systems, Open File Report 77-60, 85pp. US Geological Survey, Reston.
Smith, L., & Chapman, D. S. (1983). On the thermal e?ects of groundwater
ow: 1. Regional scale
systems. Journal of Geophysical Research: Solid Earth, 88(B1), 593-608.
Sorey, M. L., Lewis, R. E., & Olmsted, F. H. (1978). Hydrothermal system of Long Valley caldera,
California (No. USGS-PP-1044-A). Geological Survey, Sacramento, CA (USA).

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Primary author

Mr Anthony P. Sorensen II (Washington State University-School of the Environment)

Co-authors

Dr Peter B. Larson (School of the Environment-Washington State University) Dr Sergey Lapin (Department of Mathematics and Statistics-Washington State University) Mr Jarred L. Zimmerman (School of the Environment-Washington State University)

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