What is it?
IGW-NET provides users with the option to simulate density driven flow (applicable to situations like seawater intrusion) through either the SEAWAT or MODFLOW-6 engines. SEAWAT couples the groundwater flow program MODFLOW-2000 with the 3D transport model MT3DMS, and iteratively solves for flow and transport using a freshwater head formulation. In contrast, MODFLOW-6 has both GWF (groundwater flow) and GWT (groundwater transport) modules and uses a hydraulic head formulation to iteratively solve flow and transport. Both programs convert between concentration and density using a linear relationship specified by the user (see below).A note on initial conditions
If the goal is to evaluate temporal changes in concentration and head, it is important that the initial heads and concentrations are at equilibrium with one another and the boundary conditions. It is also important that when using SEAWAT the initial heads are represented as equivalent freshwater values and that concentrations are represented as total dissolved solids. If initial heads and concentrations are not at equilibrium, they may change at the start of the simulation for reasons other than expected. To produce appropriate initial conditions for this type of transient model, either a SEAWAT model should be run to steady state using representative hydrologic conditions, or a transient SEAWAT model with temporally varying stresses should be run repeatedly, (each time with the initial conditions set from the results of the previous run), until the model produces the same results each time. The user should determine the best approach for the particular problem. (adapted from Guo and Langevin 2002)Parameters
In addition to the parameters in this interface, realtime variable density flow in MAGENT uses flow and transport defaults from either the MODFLOW-2005 LPF package with the PCG solver and MT3D (for SEAWAT), or those for MODFLOW 6 NPF package with the IMS solver (for MODFLOW-6). The user can change parameter values in those interfaces.Parameter lookup tables may be helpful for users familiar with SEAWAT or MODFLOW-6 transport and variable names.
Groundwater Transport
The advective transport solver and dispersion options are set here for MODFLOW-6 or in the MT3D Solver settings for SEAWAT.The SEAWAT solver defaults to using the MMOC method for advection but the best method is usually both problem specific and a compromise between accuracy and computation The FDM solver can allow SEAWAT to take long timesteps, but numerical dispersion can incorrectly represent problems with sharp fronts with large concentration gradients. In contrast, the ULTIMATE TVD solver handles sharp fronts well, but may require short timesteps. Particle tracking schemes may be computationally intensive, but will often provide acceptable results. Users can experiment to find the fastest and most accurate solver for a specific problem.
For MODFLOW-6 advection can be simulated with the finite difference method (using central-in-space weighting, or upstream weighting), or an implicit second-order TVD scheme. Currently MODFLOW-6 does not support any particle-based approaches and for advection dominated systems it may require a higher level of spatial discretization.
- FDM weighting scheme: (MODFLOW-6; FDM) The method used by the FDM solver.
The 'upstream' weighting scheme uses upstream concentrations and results in oscillation-free solutions, however, is only accurate to the first order, leading to numerical dispersion for advection dominated problems (truncation error from the advection solution can overwhelm the physical dispersion term).
The 'central-in-space' weighting scheme calculates concentrations from weighted averages (equivalent to linear interpolation), and is accurate to the second order. While this solution is without numerical dispersion it can develop artificial oscillation (typical of higher-order truncation errors) for advection dominated transport problems.
By default, in MODFLOW-6 dispersion is formulated using the XT3D method (documented for the MODFLOW-6 NPF package). Optionally users can specify that XT3D terms are added to the right-hand-side (which uses less memory, but may require more iterations), or turn off XT3D and use a more traditional faster and less accurate approximation. This approximation may be appropriate when flow aligns with the model grid, there is no mechanical dispersion, or when the longitudinal and transverse dispersivities are equal.
Groundwater Flow
The flow solver is set through the MODFLOW interface. SEAWAT supports MODFLOW flow packages BCF and LPF, with solvers PCG, DE4, GMG, and SIP (MODFLOW-2005 interface), or SOR (MODFLOW-2000 interface) [the default uses the LPF package with the PCG solver]. MODFLOW-6 must use the NPF flow package and the IMS6 solver (MODFLOW-6 interface).SEAWAT Density Flow
These parameters control how density flow is achieved through flow and transport coupling in the SEAWAT engine:- Flow and transport coupling: There are three options, 1) explicit coupling with a one substep lag (with a short substep length, this is a conservative approach and sufficient for most problems). 2) implicit coupling where flow and transport are iteratively solved together until a specified convergence criteria is reached (this is the most rigorous option but particle-tracking advection solvers aren't implemented [only FDM and ULTIMATE-TVD]. FDM is used automatically unless ULTIMATE is specified in the MT3D interface). 3) the auto option calculates the density dependent flow field in the first and last substeps, in addition to whenever the maximum density change is above a specified threshold (this is suitable for situations where concentrations are low and the flow field doesn't need to be updated at each substep).
- Density criteria [decimal]: specifies the convergence requirement when implicit coupling is enabled, or the threshold to trigger flow calculation when automatic coupling is enabled.
- Initial transport substep [decimal]: the length for the first substep in SEAWAT [default 0.01 days]. Subsequent substep lengths are determined by inputs to the MT3D interface for stability constraints and substep length. This value should be less than the timestep length specified in IGW-NET. If using the explicit coupling mode, substep lengths are particularly important as they can significantly alter the solution. Note, this parameter is replaced by SEAWAT with the 'Initial MT3D substep length' from the MT3D interface if that value is smaller (but not 0).
- Conductance scheme: the method for calculating the internodal density values to conserve fluid mass.
- Apply variable-density water table corrections: if enabled, this option uses water table elevations to compute flow between adjacent cells rather than cell centers. This should be used for problems with dewatered unconfined layers, however it adds nonlinearity to the flow equation, and may cause convergence issues for complicated water-table conditions.
- Min density[decimal]: minimum fluid density. If the calculated density is less than this value, it is assigned this value. Use zero to ignore this limit [default 0].
- Max density[decimal]: maximum fluid density. If the calculated density is greater than this value, it is assigned this value. Use zero to ignore this limit [default 0].
- Reference pressure head [decimal]: reference pressure head. This value should normally be set to zero [default 0 meters].
- Slope of density-pressure line [decimal] the relationship between fluid density and pressure head (in terms of the reference density). This can be calculated from the volumetric expansion coefficient for pressure approximately 4.46e-3 kg/m4. A value of zero simulates incompressible flow [default 0 kg/m4].
MODFLOW 6 Density Flow
These parameters control how density flow is achieved through flow and transport coupling in the MODFLOW-6 engine:- Flow and transport coupling: MODFLOW-6 couples groundwater flow and transport explicitly with a one substep timestep lag.
- Number of substeps [integer]: This is the number of transport substeps MODFLOW 6 will use within the specified IGW-NET timestep. The number of substeps should be increased if the IGW-NET timestep is large and density driven flows are significant overwise unrealistic flow patterns can develop [default 10].
- Add off diagonal terms to the right-hand-side: This option will keep asymmetric terms on the right-hand side and prevent the Buoyancy Package from adding them to the flow matrix. Initial testing (Langevin and others 2020) has suggested this option is generally slower.
Density-Concentration Relationship
These parameters are used in both engines to build the equation of state relating concentration and density.density = densityref + slope (concentration - concentrationref)
- Slope of density-concentration line [decimal]: this is the linear relationship between concentration and density. For seawater-freshwater interactions this value is approximately 0.0007 kg/m3 / ppm. To use SEAWAT or MODFLOW-6 to solve non-density dependent transport, a value of 0.0 can be entered. If the slope is not known, a known concentration and density can be used instead.
- Known concentration and density [decimals]: these values can be entered as an alternative to slope (and slope will be computed). Seawater has a concentration of about 35,000 ppm and a density of 1025 kg/m3.
- Reference density [density]: this is the density of the reference fluid, typically "freshwater" set to 1000 kg/m3.
- Reference concentration [density]: this is the concentration of solute in the reference fluid, typically set to 0.0 ppm.
External Links
USGS Documentation for the programs and their parameters.- SEAWAT and MODFLOW-6 FloPy documentation.
- SEAWAT
SEAWAT V4 documentation - Langevin and others (2008)
SEAWAT 2000 documentation Guo & Langevin (2002)
- MODFLOW-6
MODFLOW-6 input documentation - Version mf6.2.0—October 22, 2020
MODFLOW-6 groundwater flow model documentation - Langevin and others (2017)
MODFLOW-6 framework documentation - Hughes and others (2017)
Hydraulic-head formulation for density-dependent flow and transport - Langevin and others (2020)