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