Pitch angle (θ) is required in 2D.
Pitch and yaw angles (θ, ψ) are required in 3D.
The entire list of units is presented in section Default Units.
Unit: [1/T]
Default value: 0 * 10-4 1/s
Decay rate allows to specify a first-order decay for the simulated species.
Unit: [L]
Default value:5 m (longitudinal), 0.5 m (transverse)
Dispersivity is introduced in the equations to take into account effects of inhomogeneities not considered in the model properties. On the one hand, these are microscale inhomogeneities such as pore directions not parallel to flow direction, on the other hand also macroscale properties such as layer structures and lenses not considered due to missing knowledge and model discretization. The coefficients of dispersivity come into the formulation of the classical Bear-Scheidegger macro-dispersion tensor together with the coefficient of molecular diffusion (or diffusivity).
Macro-dispersion in FEFLOW is handled by default by a linear Fickian relationship, distinguishing a longitudinal dispersion length (in flow direction) and a transverse dispersivity (perpendicular to the flow direction).
In this case, the material properties are:
As an alternative, there can be an additional directional dependency (anisotropy), following the work of Lichtner et al. (2002) on the formulation of dispersion tensor for axisymmetric porous media. This can be turned on the Anisotropy page of the Problem Settings dialog.
As opposed to the isotropic, standard dispersion tensor of Bear-Scheidegger, Lichtner et al. tensor requires:
Definition of an axisymmetric axis
Definition of dispersivity coefficients in the direction of the axis (denoted as minimum dispersivity coefficients)
For this option, the material properties to be defined are:
The axisymmetric axis definition is as follows:
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Pitch angle (θ) is required in 2D. |
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Pitch and yaw angles (θ, ψ) are required in 3D. |
The anisotropic dispersion tensor reads:
with
Note that the Lichtner et al. formulation can be of great help for these situations where vertical variations of velocity through geological layers of various sizes occur. This is e.g. typical in saltwater intrusion settings with which there is a tendency for over-estimating the effect on dispersion when longitudinal dispersivity can only operate in the direction of velocity with always the same strength (and similarly transverse dispersivity operating in directions perpendicular to velocity).
Note also that the Lichtner et al. formulation can be used to match the so-called Burnett-Frind formulation using a purely vertical axisymmetry axis (θ = 90 degrees and ψ = 0) and by letting the minimum longitudinal dispersivity being equal to the maximum one. The Burnett-Frind tensor actually does not fully match Lichtner et al. tensor, but can be seen as a simplified form of the dispersion tensor for axisymmetric media:
Lichtner et al. report that the Burnett-Frind tensor agrees with their more general formulation for flow perpendicular to the axis of symmetry, and that for small vertical component of velocity, their tensor reduces to the Burnett-Frind tensor.
Practically, estimations for dispersivity are often hard to obtain, so that literature values are used. Dispersivity highly depends on the length scale of the transport phenomenon.
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Low dispersivity values lead to steep gradients at plume fronts. Thus a fine spatial discretization is needed in such cases. |
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Bear J., 1972. Dynamics of Fluids in Porous Media, Dover, p. 764, 1972. Lichtner P. C., Kelkar S., Robinson B., 2002. New form of dispersion tensor for axisymmetric porous media with implementation in particle tracking. Water Resources Reseach 38(8). Burnett R.D., Frind E.O., 1987. Simulation of contaminant transport in three dimensions. 2. Dimensionality effects. Water Resources Reseach 23. |
Unit: [L]
Default value:1 m
Aquifer thickness is only visible in confined two-dimensional horizontal models. For this model type, the aquifer geometry does not have to be defined for the flow simulation as Transmissivity is used as the input parameter. The transport simulation, however, needs pore velocities as a basis. These are calculated by dividing the Darcy velocity by the aquifer thickness. Thus for this model type, aquifer thickness has to be specified separately as a transport-material property.
Unit: [1]
Default value:0.3
For the transport simulation, only the part of total porosity contributing to fluid flow, and thus to advective transport, is relevant. This so-called effective porosity is to be input as porosity for mass transport.
Unit: [M/(L2*T)] (2D), [M/(L3*T)] (3D)
Default value:0 g/m2/d (2D), 0 g/m3/d (3D)
The source/sink parameter for mass transport simulation describes a source (positive) or sink (negative) of mass per area (2D) or per volume (3D). Typical applications include purely volume-based biological decay.
Unit: [L2/T] (2D confined), [L/T] (other 2D / 3D)
Default value: 0 m2/d (2D confined), 0 m/d (other 2D, 3D)
The inflow/outflow of mass at mass-transfer boundary conditions is calculated from the relevant area, the transfer rate, and the difference between reference and groundwater concentration:
Qmass = AΦ(Cref-C)
where
Qmass: inflow or outflow of mass to/from the model
A: relevant area
Φ : transfer rate
Cref: reference concentration
C: current concentration in groundwater
The transfer rate for mass transport is a conductance term describing the transfer of mass from an (external) reference concentration to groundwater.
FEFLOW distinguishes between two different transfer rates for infiltration from the external concentration (Transfer rate in) and exfiltration to the outside (Transfer rate out). According to the gradient direction, FEFLOW automatically chooses the correct value.
The transfer rate as a material property is defined on an elemental basis. It is typically set to all elements whose edges (2D) or faces (3D) are covered by the transfer boundary condition.
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Transfer rates set to elements without a transfer boundary condition do not influence the simulation results. In some simple models transfer rate can therefore easily be set as a parameter for all the elements, avoiding detailed element selection. |
Unit: vm: [M/L³/T], Km: [M/L³]
Default values: vm: 0*10-4 mg/l/s, Km: 0 mg/l
vm and Km represent the two Michaelis-Menten constants, vm being the maximum velocity of enzymolysis, and Km the Michaelis (Monod) constant.
These parameters are available in mass transport models for species whose reaction type is set to Michaelis-Menten on the Chemical Species page of the Problem Settings dialog.
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White Paper Vol. I, Chapter 10.4.3 |
Unit: [L2/T]
Default value: 10-9 m2/s
The molecular diffusion coefficient describes the diffusivity of the solute in the fluid.
Unit: [L²T/M]
Default value: 0.001 m²d/g
Besides a standard linear Fickian Bear-Scheidegger dispersion, FEFLOW supports a nonlinear dispersion relation. The parameter nonlinear dispersion describes the exponent for this.
To switch from linear to nonlinear dispersion, the settings in Transport Settings have to be changed.
Default value: 0
Equilibrium sorption processes can be taken into account using either the linear Henry isotherm or the non-linear Freundlich or Langmuir isotherms. The concentrations shown in FEFLOW will always represent the dissolved mass.
The settings for equilibrium sorption can be found on the Transport Settings page in the Problem Settings dialog.
The Henry sorption isotherm is defined as
Cs= κCf
where
Cs: Concentration of absorbed species (species mass per solid volume)
Cf: Concentration of dissolved species (species mass per fluid volume)
κ: Henry constant (dimensionless)
Input parameter is κ (Henry constant).
Unit: [-]
Default value: 0
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The Henry coefficient used in FEFLOW is not the Kd value often derived from lab experiments. Kd has to be multiplied with the density of solid to get the coefficient for FEFLOW. |
The Freundlich sorption isotherm is defined as
Cs= b1(κCf)b2
where
Cs: Concentration of absorbed species (species mass per solid volume)
Cf: Concentration of dissolved species (species mass per fluid volume)
b1: Fitting parameter (units of concentration)
b2: Fitting parameter (dimensionless)
κ: Unit-cancelling coefficient, fixed 1 l/mg
Input parameters are
b_1 (Freundlich coefficient)
Unit: [M/L³]
Default value: 0 mg/l
b_2 (Freundlich exponent)
Unit: [-]
Default value: 0
The Langmuir sorption isotherm is defined as
Cs= k1Cf/(1 + k2Cf)
where
Cs: Concentration of absorbed species (species mass per solid volume)
Cf: Concentration of dissolved species (species mass per fluid volume)
k1: Fitting parameter (dimensionless)
k2: Fitting parameter (units of inverse concentration)
Input parameters are
k_1 (Langmuir constant)
Unit: [-]
Default value: 0
k_2 (Langmuir constant)
Unit: [L³/M]
Default value: 0 l/mg
