Model setup

Highlights
Setup of a model for a fractured limestone aquifer Modeling objectives Typical steps of setting up a model for limestone aquifers

Steps to setup a model for flow and transport in fractured limestone aquifers This chapter gives an overview of the recommended steps to setup a model for the simulation of flow and transport in a fractured limestone aquifer. The following list shows the typical steps to setup a model for contaminant transport in a fractured limestone aquifer. Expand an item (button on the right) to get more information about it. Formulation of the modeling objectives Before setting up a model, it is important to define the specific modeling objective(s). The choice of the model concept, model extent, modeling scale and included details should be closely linked to these objectives. One should aim at including the most relevant features in the model, while keeping it as simple as possible to address the modeling objective(s). The following list gives some examples for modeling objectives: Delineate the capture zone of a well Improve risk assessment, e.g. for a contaminant threatening a drinking water well, in order to assess future actions Analyze the distribution and potential spreading of a contaminant plume in an aquifer Test hypotheses related to the origin of a contaminant Interpret observed / measured field data Analyze the influence of transient hydraulic conditions (annual variations, pumping in the area) on plume propagation Develop and optimize a remediation strategy for the source zone of a contaminated site Optimize a remediation strategy for a contaminant plume Conceptualization and setup of a conceptual model including geology and hydrogeology Example geologic profile of a Geoscene3D model. Geologic modeling Borehole data, outcrops, geophysical measurements etc. can give valuable information about the geology at a site. Bits of geologic knowledge can be connected to establish a geologic model, that shows different geologic layers and relevant geologic features (like inclusions or lenses). Typically, these layers are characterized by different hydrogeologic properties. The geometry can be stored as a CAD interpolation of the surfaces, that delineate the geologic layers. Tools like GeoScene3D can be very useful to manage borehole data and to create interpolation surfaces. The surfaces can be imported into the numerical model later on. Definition of the model scope The scale also depends on the modeling objectives. The model scope will, for example, be different for the prediction of the spreading of an entire plume (large scale) and for the planning of source zone remedial actions (local scale). An important aspect when choosing the model extent is to have the boundaries sufficiently far away from the most influential features in the area, such as pumping wells. The model extent has to be big enough, so that the boundaries do not influence the results in the area of interest. It should be chosen based on physically meaningful boundaries (f.e. known head isolines or no-flow boundaries). The modeling of source zone remediation requires a different scale than the risk assessment of a contaminant plume for water works. The following scales can be distinguished: well or borehole scale source zone scale intermediate scale for e.g. pumping tests plume scale Based on available data and modeling objectives, the model complexity has to be chosen. A very complex and detailed model is not appropriate if only little field data is available. Then, a simple model can be applied, which can be improved as soon as new data is measured. Modeling was an integral part in the limestone project and already done at an early stage of the project. Initially, a rough model based on first measurements and available data was setup. It was used for the planning of further field work and measurements. It also helps to identify further data requirements and to plan measurements that support the modeling. These additional measurements and data can then be incorporated in the model. Data acquisition - measurements to obtain relevant model parameters (see list of parameters for each model) See Chapters Data acquisition and Transport parameters and contaminant data. Implementation of parameters for selected units in the model domain (homogeneous/heterogeneous) Based on available data and the chosen model, parameter distributions have to be defined. For a steady-state flow simulation, the hydraulic conductivity (or permeability) is required. For transport, parameters like porosity, (effective) diffusion coefficients, dispersivities and sorption parameters are required. Choice of boundary conditions and sources/sinks Boundary conditions have to be chosen according to known values, like a constant head or a known in-/outflow. The most common boundary conditions are Dirichlet conditions (or first-type boundary conditions), where the primary variable is fixed to a value (e.g. fixed head or fixed concentration). Neumann conditions (or second-type boundary conditions), where the gradient of the primary variable is specified (e.g. flux across the boundary, often no-flow boundaries) Cauchy conditions (or third-type boundary conditions), which sets a condition to the primary variable and it's derivative (used f.e. for the flux through a river bed). The boundary conditions should be chosen according to known boundaries, such as geologic boundaries, known head isolines, known flowlines (these can be used as no-flow condition perpendicular to them). The choice of the boundary condition is a very important step and determines the calculated results. Sources and sinks are employed to include e.g. withdrawal/injection at wells or groundwater recharge due to precipitation. For transient models: definition of initial conditions Steady-state models do not require the definition of initial conditions. Transient problems, however, require to specify the initial value of the primary variables at each location of the model domain. Mesh generation Example a mesh used for discrete-fracture simulations of the Akacievej tracer tests. The mesh is refined at the horizontal fractures and at the wells. When working with complex models it is useful to start with a coarse mesh to test the model and the setup with limited time efforts. When everything is properly setup, a finer grid can be employed. Modern grid generators allow a local mesh refinement at specific parts of the mesh. Especially at heterogeneities and fractures, at wells and at concentration fronts, the mesh should be sufficiently fine to resolve the local gradients (e.g. of concentration or head gradients) appropriately. Locations, where strong gradients of the primary variables (head, concentration) occur, should be resolved at a high resolution, while for the parts of the model domain with only small changes, a coarser mesh resolution may be sufficient. If the applied mesh is sufficiently fine can be tested by a grid refinement study, where the mesh is gradually refined and the results are compared. When the solution does not significantly change with a further grid refinement, the grid resolution is sufficient. Simulation After setting up the geometry, boundary conditions, initial conditions, material parameters and simulation parameters (simulation time, solver settings), the actual simulation can be run. It is always a good idea to start with a test run, f.e. with a coarse mesh and a short duration, to test if everything is set as desired. Critical evaluation of the modeling results Modeling results should always be critically evaluated and the model should be properly tested. It is, for example, helpful, to check the mass balance of a model, i.e. to balance all inflows and outflows and the storage in the model domain. It is also important to visually inspect the results, f.e. by visualizing the hydraulic heads and concentrations in the domain and in special areas of interest. Then, it should be checked, if the results look reasonable and as expected, if the boundary conditions are fulfilled and if there are any disturbances like oscillations in the model domain. Oscillations can be an indication for a too coarse mesh. It is also a good idea to test for grid convergence, i.e. to test if the model results change, when the numerical grid is refined. Model calibration and validation more information will be included soon Model reporting more information will be included soon Example: Setup of a COMSOL Multiphysics model for a contaminated site with a fractured limestone aquifer (Akacievej, Hedehusene) The setup of a discrete-fracture model in 2D in COMSOL Multiphysics using Coefficient Form PDEs is described in the following document: Instructions for setting up a discrete-fracture model in COMSOL Multiphysics (PDF) - DRAFT COMSOL provides also the possibility to include fracture flow in the Darcy's Law interface, while fracture transport can be included in the Transport of Diluted Species in Porous Media interface. We refer to the product documentation for more details. FEFlow provides a tutorial, that describes the steps of setting up a flow and transport model and how to include discrete fractures. DRAFT: The typical workflow for modeling a contaminated site will be demonstrated using an example field site close to Copenhagen. Example: Setup of models for a field site (Akacievej, Hedehusene) Return to Content