HR: 0800h
AN: H11D-1302 [Abstracts]
TI: Temperature-based versus enthalpy-based numerical simulations of non-isothermal subsurface fluid flow
in heterogeneous porous or fractured media
AU: * Geiger, S
EM: geiger@erdw.ethz.ch
AF: Department of Earth Science,
Institute of Isotope Geology and Mineral Resources,
ETH Zurich, Sonneggstr. 5, Zurich, 8005
Switzerland
AU: Driesner, T
EM: driesner@erdw.ethz.ch
AF: Department of Earth Science,
Institute of Isotope Geology and Mineral Resources,
ETH Zurich, Sonneggstr. 5, Zurich, 8005
Switzerland
AU: Coumou, D
EM: coumou@erdw.ethz.ch
AF: Department of Earth Science,
Institute of Isotope Geology and Mineral Resources,
ETH Zurich, Sonneggstr. 5, Zurich, 8005
Switzerland
AB:
We compare temperature-based and enthalpy-based numerical schemes for compressible non-isothermal subsurface fluid flow. We
formulate a diffusion equation for the fluid pressure, a diffusion equation for heat conduction, and an equation for the
advective transport of temperature or enthalpy in the fluid. These equations can readily be solved by a combination of finite
element and higher-order finite volume methods, which are capable of preserving steep temperature gradients in advection
dominated flows and handling complex two- and three-dimensional geologic structures with orders of magnitude variation in
permeability. Since the time-scale of pressure diffusion is slower than the time-scale for advective fluid flow, it is
possible to decouple the equations and use implicit finite element methods for the parabolic (diffusion) equations and
explicit finite volume methods for the hyperbolic (advection) equations.
For single-phase flow, we use the thermal wave speed to compute the advection of the temperature field on the finite volumes.
Since the thermal front is advected at a slower rate than the actual fluid flow, a significant (i.e., a factor 10 at liquid
and a factor 1000 at vapor conditions) computational speedup can be achieved in comparison to the formulation where enthalpy
is advected. The results for temperature-based and enthalpy-based formulations at vapor or liquid conditions, however, are
identical and compare extremely well with results obtained from other codes that use fully coupled solution techniques. Our
results do not improve if we use Picard iteration to couple the pressure, conduction, and advection equations.
For the enthalpy-based transport schemes, we use a Newton iteration to equilibrate the energy in the fluid and rock. This
also allows us to use more modern equation of states for complex multi-component systems, that are formulated in terms of
pressure p, temperature T, and composition X, and hence cannot use the specific enthalpy h to obtain
fluid properties and phase state.
At two-phase conditions, at least for pure H2O, the enthalpy-based transport scheme is preferred, because the volume
fractions of vapor and liquid can be directly calculated for the given enthalpy and pressure, while the temperature is given
by the fluid pressure along the saturation curve. We show, however, that it is possible to approximate the volume fractions
of vapor and liquid in the temperature-based formulation from energy and mass balance considerations and hence avoid flash
boiling (i.e. all liquid immediately transforms to vapor). At two-phase conditions, it is crucial to use upwind weighted
phase mobilities and derive an accurate pressure equation that includes condensation of vapor and boiling of liquid due to
pressure changes in order to obtain numerical results that agree well with results obtained from other computer codes.
DE: 1805 Computational hydrology
DE: 1828 Groundwater hydraulics
DE: 3017 Hydrothermal systems (0450, 1034, 3616, 4832, 8135, 8424)
DE: 3225 Numerical approximations and analysis (4260)
DE: 8424 Hydrothermal systems (0450, 1034, 3017, 3616, 4832, 8135)
SC: Hydrology [H]
MN: Fall Meeting 2005