Transient vadose zone flow and Tc-99 transport ---------------------------------------------- This tutorial illustrates *Amanzi* simulation of transient vadose zone flow and non-reactive (tracer) transport in the context of Tc-99 migration at the DOE Hanford BC Cribs and Trenches site. The tutorial involves a two-dimensional heterogeneous three-layer subsurface system with time- and space-varying infiltration at the ground surface. BC Cribs and Trenches site ~~~~~~~~~~~~~~~~~~~~~~~~~~ The two-dimensional geometry and salient features of the Hanford BC Cribs and Trenches site, as represented in this simplified tutorial, are defined in the following schematic diagram: .. image:: Schematic.png :scale: 50 % :align: center General recharge at the site (:math:`U`) increased following development of the Hanford facility in 1956, and Cribs B-17 and B-18 represent localized sources of water infiltration and Tc-99 contamination (:math:`C_{Tc-99}`) to the subsurface: +------------------------+-------------------+------------------------------------------+ | ID | :math:`U` (mm/yr) | :math:`C_{Tc-99}` (mol/m\ :sup:`3`\ ) | +========================+===================+==========================================+ | General site, pre-1956 | 3.5 | N/A | +------------------------+-------------------+------------------------------------------+ | General site, post-1956| 47 | N/A | +------------------------+-------------------+------------------------------------------+ | B-17, Jan 1956 | 8025 | 1.88e-6 | +------------------------+-------------------+------------------------------------------+ | B-18, Feb-Mar 1956 | 10439 | 2.27e-6 | +------------------------+-------------------+------------------------------------------+ The three facies underlying the site have the following material properties: +-------------------------------------------------+---------------+---------------+---------------+ | Material property | Facies 1 | Facies 2 | Facies 3 | +=================================================+===============+===============+===============+ | Porosity | 0.4082 | 0.2206 | 0.2340 | +-------------------------------------------------+---------------+---------------+---------------+ | Particle density (kg/m\ :sup:`3`\ ) | 2720.0 | 2720.0 | 2720.0 | +-------------------------------------------------+---------------+---------------+---------------+ | Horizontal permeability (m\ :sup:`2`\ ) | 1.9976e-12 | 6.9365e-11 | 2.0706e-09 | +-------------------------------------------------+---------------+---------------+---------------+ | Vertical permeability (m\ :sup:`2`\ ) | 1.9976e-13 | 6.9365e-12 | 2.0706e-09 | +-------------------------------------------------+---------------+---------------+---------------+ | Capillary pressure model | van Genuchten | van Genuchten | Brooks-Corey | +-------------------------------------------------+---------------+---------------+---------------+ | Relative permeability model | Mualem | Mualem | Mualem | +-------------------------------------------------+---------------+---------------+---------------+ | :math:`\alpha` (Pa\ :sup:`-1`\ ) | 1.9467e-04 | 2.0260e-03 | 2.0674e-03 | +-------------------------------------------------+---------------+---------------+---------------+ | :math:`S_r` | 0.0 | 0.0 | 0.0 | +-------------------------------------------------+---------------+---------------+---------------+ | van Genuchten :math:`m` | 0.2294 | 0.2136 | N/A | +-------------------------------------------------+---------------+---------------+---------------+ | Brooks-Corey :math:`\lambda` | N/A | N/A | 0.3006 | +-------------------------------------------------+---------------+---------------+---------------+ *Amanzi* input specifications ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ A working *Amanzi* input file for this tutorial simulation is listed in a separate section below. *Amanzi* input file structure and XML element names are intended to be reasonably self-explanatory; however, selective commentary is provided here for further guidance. Currently *Amanzi* requires the SI units indicated in the ``model_description/units`` element. The corresponding units of density, viscosity, pressure, hydraulic conductivity, and permeability are thus kg/m\ :sup:`3`\ , Pa :math:`\cdot` s, Pa, m/s, and m\ :sup:`2`\ , respectively. Simulation outputs also use these dimensional units. The use of named constants in the ``definitions`` element, e.g., ```` allows the user to use a fixed name throughout the input file, but change its numerical value in only one location. Here the time- and space-varying infiltration parameters are input as defined constants. ``time_macro name="Macro 1"`` defines the output times for visualization in seconds; for example, the last time is ``6.33834396E10`` seconds or year 2008.5 for a 365.25 day year. ``Macro 2`` is defined but not used in this example. Under ``process_kernels`` the chemistry kernel is turned off because the simulation involves only non-reactive transport. In the ``phases`` element, equation-of-state (eos) computations are turned off in favor of direct specification of fluid density and viscosity. Under the ``mesh`` element a three-dimensional grid is specified, however, only one cell is specified for the :math:`y`-coordinate (``ny = "1"``) making the simulation effectively 2D in the :math:`(x,z)` coordinates. The grid spacing is 0.5 meters horizontally and 0.42 meters in the vertical dimension. In the ``initial_conditions`` element, a hydrostatic profile is specified through a linear pressure profile with slope/gradient = :math:`- \rho g` = -9789 Pa/m. The reference point for :math:`P = P_{atm}` = 101325 Pa is set to :math:`z` = 0.5 meters rather than the water table elevation of :math:`z` = 0.0 meters to be compatible with a prior benchmarking comparison to a STOMP code model. The boundary conditions at the top surface are defined in the problem statement as a volumetric fluxes [m\ :sup:`3`\ /m\ :sup:`2`\ d = m/d]. *Amanzi* currently requires boundary conditions of this type to be specified as mass fluxes, :math:`\rho U` [kg /m\ :sup:`2`\ s]. The ``inward_mass_flux`` values in the XML input have these units. *Amanzi* execution ~~~~~~~~~~~~~~~~~~ *Amanzi* is executed from the command-line using this or analogous command for the user's specific installation: ``mpirun -n 4 /ascem/amanzi/install/current/bin/amanzi --xml_schema=/ascem/amanzi/install/current/bin/amanzi.xsd --xml_file=dvz_3_layer_2d-isv2.xml`` Here execution using 4 processor cores is specified by ``-n 4``. Successful completion is marked by ``SIMULATION_SUCCESSFUL`` followed by a timing summary :: Amanzi::SIMULATION_SUCCESSFUL ********************************************************** *** Timing Summary *** ********************************************************** *Amanzi* results ~~~~~~~~~~~~~~~~ The figure shows saturation dynamics. Saturation grows underneath the left and right cribs during their operational cycles. Note it takes time for two moving plumes to penetrate into the middle soil which leads to saturation increase on the interface between soils. .. image:: saturation.png :scale: 50 % :align: center The next figure shows concentration of Tc-99. The concentration plumes are moving almost vertically with slight latter interaction due to a non-zero pressure gradient in this direction. The speed of the plumes is reduced significantly in the middle soil. The concentration satisfies the maximum principle. .. image:: concentration.png :scale: 50 % :align: center *Amanzi* XML input file ~~~~~~~~~~~~~~~~~~~~~~~ .. literalinclude:: dvz_3_layer_2d-isv2.xml :language: xml