Description of Flow-Related Material Properties

The entire list of units is presented in section Default Units.

Anisotropy angle

Unit: [°]
Default value: 0

Conductivity may be anisotropic in FEFLOW, i.e., the values can vary with direction. If the model dimension is set to 2D, no matter whether horizontal, cross-sectional or axisymmetric, anisotropy is based on:

• Conductivity/Transmissivity [max]: Maximum conductivity/transmissivity
• Anisotropy of conductivity/transmissivity: Fraction minimum conductivity (transmissivity) / maximum conductivity (transmissivity)
• Anisotropy angle: Angle between the direction of the x axis and the direction of the maximum conductivity/transmissivity in degrees

Anisotropy angles (phi, psi and theta)

Unit: [°]
Default value: 0

The anisotropy in 3D model is prescribed by using three consecutive Euler angles (Phi, Psi and Theta) in case that General anisotropy with user-defined angles is chosen as the anisotropy mode.

In three-dimensional models, anisotropy is based on the input of three different conductivity values that can be applied in one of three ways:

• Anisotropy in axis direction:
  The major principal directions of conductivity are coincident with the Cartesian coordinate axes x, y, and z. Conductivities are input as Conductivity Kxx, Conductivity Kyy, and Conductivity Kzz.
• General anisotropy with computed angles:
  Input of conductivities (Conductivity K1m, Conductivity K2m, and Conductivity K3m) for major principal directions with automatic computation of the anisotropy angles based on the slope of each elements (Springer's method).
• General anisotropy with user-defined angles:
  Input of conductivities (Conductivity K1m, Conductivity K2m, and Conductivity K3m) for major principal directions and input of the three Euler angles for the rotation of the coordinate axes.

To assign properties for more than one conductivity parameter simultaneously (e.g., Kxx, Kyy, and Kzz), hold <Ctrl> and double-click on all the parameters you would like to edit in the Data panel.

Anisotropy of Conductivity/Transmissivity

Unit: [-]
Default value: 1

Conductivity/Transmissivity may be anisotropic in FEFLOW, i.e., the values can vary with direction. If the model dimension is set to 2D, no matter whether horizontal, cross-sectional or axisymmetric, anisotropy is based on:

• Conductivity/Transmissivity [max]: Maximum conductivity/transmissivity
• Anisotropy of conductivity/transmissivity: Fraction minimum conductivity (transmissivity) / maximum conductivity (transmissivity)
• Anisotropy angle: Angle between the direction of the x axis and the direction of the maximum conductivity/transmissivity in degrees

Bottom Elevation

Unit: [L]
Default value: 0 m

Bottom elevation describes the bottom elevation of an unconfined aquifer in 2D horizontal projection as an elemental property. It is required to obtain the current saturated thickness as a basis for transmissivity calculation during the simulation run.

Conductivity

Unit: [L/T]
Default value: 1 m/d

The saturated hydraulic conductivity describes the ease with which water can move through a saturated porous medium. Respective values for a specific soil type may for example be obtained from literature values, from empirical estimations based on grain size distributions, or as results of field methods such as pumping tests.

Anisotropy

Depending on the defined Anisotropy Settings, there are different parameters available:

• Anisotropy in axis direction:
  The major principal directions of conductivity are coincident with the Cartesian coordinate axes x, y, and z. Conductivities are input as Conductivity K_xx, Conductivity K_yy, and Conductivity K_zz .
• General anisotropy with computed angles:
  Input of conductivities (Conductivity K₁^m, Conductivity K₂^m, and Conductivity K₃^m) for major principal directions with automatic computation of the anisotropy angles based on the slope of each elements (Springer's method).
• General anisotropy with user-defined angles:
  Input of conductivities (Conductivity K₁^m, Conductivity K₂^m, and Conductivity K₃^m) for major principal directions and input of the three Euler angles for the rotation of the coordinate axes.

Conductivity can also be heat or mass dependent. Heat or mass influences can be incorporated in the Transport settings. All input conductivity values correspond to the conductivity at the defined reference temperature and concentration.

Density Ratio

Unit: [-]
Default value: 0

The density ratio α describes the ratio between maximum and minimum density in a density-dependent transport model. It is defined as the density difference in the model divided by the density at reference concentration/temperature.

α = (ρ_max-ρ₀)/ρ₀

It relates concentrations in the model to density differences. By default, FEFLOW assumes ρ_max to be the density at maximum concentration in initial or boundary conditions and ρ₀ as the density at a concentration of 0 mg/l.

By default, FEFLOW uses one single Density Ratio for the sum of all concentrations in multi-species simulations. By applying the corresponding setting in Transport Settings in the Problem Settings dialog the density ratio can be specified separately for each single species. In this case, the parameter shows up separately for each species.

 

Density ratio has to be 0 except for density-dependent models.

Drain-/Fillable Porosity

Unit: [-]
Default value: 0.2

Drain-/fillable porosity (storativity in earlier versions), sometimes also referred to as  specific yield, describes the fraction of the bulk volume that can be drained under the forces of gravity. This parameter is often also called drainable porosity. In FEFLOW, specific yield is used as a storage parameter in addition to specific storage. Specific yield is only applied for unconfined aquifers, i.e., for models with a phreatic surface, where it typically forms the major storage component.

Expansion Coefficient

Unit: [1/T]
Default value: 0 1/K

The expansion coefficient is defined as the density difference in the model divided by the water density at reference temperature:

β = (ρ_max-ρ₀)/ρ₀

It relates temperatures in the model to density differences. By default, FEFLOW assumes ρ_max to be the density at maximum temperature in initial or boundary conditions and ρ₀ as the density at reference temperature.

The expansion coefficient has to be 0 except for density-dependent models. In many cases, a linear relationship for temperature versus density is not sufficient. In this case, a variable dependency of fluid density on temperature should be chosen in Transport Settings.

Source/Sink (Fluid)

Unit: [L/T], [1/T]
Default value: 0 m/d, 0 [1/d]

In 2D Domains

In two-dimensional models, the source/sink parameter describes a source (positive) or sink (negative) of water per area. In horizontal projections, the main application is the definition of groundwater recharge.

In 3D Domains

In three-dimensional models, source/sink is used to define a source (positive) or sink (negative) of water per volume of the porous medium.

Source/sink can be linked to a user-defined expression. This expression is evaluated at every time-step during a simulation and the parameter values are updated accordingly. To link Source/sink to an expression, use the context menu of the parameter in the Data panel.

 

As source/sink relates to the volume of an element in 3D models, it can typically not be used for the description of groundwater recharge, which is an area-related property. The material property In/outflow on top/bottom is to be preferred in this case.

Transfer Rate (Fluid)

Unit: [L/T] (2D), [1/T)] (3D)
Default value: 0 m/d (2D), 0 1/d (3D)

The inflow/outflow at transfer boundary conditions is calculated from the relevant area, the transfer rate, and the difference between reference and groundwater head:

Q = AΦ(h_ref-h)

where

Q: inflow or outflow to/from the model
A: relevant area
Φ : transfer rate
h_ref: reference water level
h: current hydraulic head in groundwater

The transfer rate is a conductance term describing the properties of a clogging layer. It is defined as

Φ = K/d

where

K: hydraulic conductivity of the clogging layer
d: thickness of the clogging layer

FEFLOW distinguishes between two different transfer rates for infiltration from surface water (Transfer rate in) and exfiltration to surface water (Transfer rate out). According to the gradient direction, FEFLOW automatically chooses the correct value. Typically the transfer rate out (left image) is larger than the transfer rate in (right image) as clean groundwater 'flushes' the pore space in the clogging layer. In contrast, infiltrating surface water that is typically rich in suspended material tends to clog the pore space.

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.

 

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.

In/Outflow on Top/Bottom

Unit: [L/T]
Default value: 0 m/d

This parameter is applied to describe the net infiltration into the model area from the top or bottom. The main applications are the definition of groundwater recharge on the top layer and of areal inflow into the model from underlying aquifers.

In/outflow on top/bottom can only be defined on the top and bottom layer of the model. During the simulation, the flows will be applied to the corresponding nodes on the top/bottom slice only.

In/outflow on top/bottom can be linked to a user-defined expression. This expression is evaluated at every time-step during a simulation and the parameter values are updated accordingly. To link In/outflow on top/bottom to an expression, use the context menu of the parameter in the Data panel.

 

This parameter is only applied to the top and bottom faces of the model (even when defining it for all elements). In one-layer models, the parameter is only applied on the top faces of the model elements. In case that there are holes within the model, with model elements above or below, the parameter can also be applied to the top and bottom faces of the hole by defining it for the corresponding elements.

 

When using Inactive elements on the top layer (s) of a layered 3D model, groundwater recharge defined by the In-/Outflow on Top/Bottom parameter is automatically inherited to the uppermost active element at any given time. In partially or fully unstructured meshes, there is no inheritance, and in-/outflow on top/bottom is ignored where the top elements are inactive.

 

For non-layered (partially or fully unstructured) meshes, top or bottom faces are identified by their orientation with respect to the horizontal X-Y plane (taken as reference to define which faces are top and which are bottom). Boundary faces of elements having non-zero values for In-/Outflow on Top/Bottom are analysed and if they appear to be perpendicular to the X-Y plane (at the 1% angular threshold limit) they are considered to be "vertical" and are thus not accounted for. If not, they are or top or bottom faces and integration of the in-/outflow is performed

Maximum Saturation (S_s)

Unit: [-]
Default value: 1

The maximum saturation describes the saturation of a porous medium that is attainable as a maximum. Respective values for a specific soil type may for example be obtained from literature values, from empirical estimations based on grain size distributions, or as results of field or laboratory methods.

Residual Saturation (S_r)

Unit: [-]
Default value: 0.0025

The residual saturation describes the remaining saturation of a porous medium at an infinitely high suction pressure. Respective values for a specific soil type may for example be obtained from literature values, from empirical estimations based on grain size distributions, or as results of field or laboratory methods.

Specific Storage (Compressibility)

Unit: [-] (2D confined), [1/L] (other 2D, 3D)
Default value: 10^-4 1/m

Specific storage (storage compressibility in earlier FEFLOW versions) describes the change in volumetric water content in an aquifer induced per unit change in hydraulic head under saturated conditions. Along with specific yield, specific storage describes the storage properties of an aquifer. As in unconfined layers specific yield typically exceeds specific storage by far, the influence of this parameter in aquifers with phreatic surfaces is usually negligible.

Top Elevation

Unit: [L]
Default value: 1000 m

Top elevation describes the top elevation of an unconfined aquifer in 2D horizontal projection as an elemental property. It is required as an upper limit in cases where partially confined aquifers are simulated in two dimensions. For fully unconfined aquifers, this parameter can be set higher than the actual top elevation.

Transmissivity

Unit: [L²/T]
Default value:m²/d

The saturated transmissivity is a measure of how much water can be transmitted horizontally in an aquifer. Transmissivity is defined as hydraulic conductivity multiplied with the saturated thickness of the aquifer:

T = K * d

FEFLOW applies transmissivity to two-dimensional horizontal confined models only, otherwise hydraulic conductivity is used for the input.

Transmissivity may be anisotropic in FEFLOW, i.e., the values can vary with direction. In this case, the following three parameters need to be defined:

 

Transmissivity [max]: Maximum transmissivity Anisotropy of transmissivity: Fraction minimum transmissivity / maximum transmissivity Anisotropy Angle: Angle between the direction of the x axis and the direction of the maximum transmissivity in degrees

Unsaturated-Flow Porosity

Unit: [-]
Default value: 0.3

The unsaturated flow porosity describes the fraction of the bulk volume that can be drained under the forces of gravity (drain-/fillable porosity) plus the adhesive water volume fraction.

If Richards' equation is used to simulate flow (unsaturated or variably saturated media), this parameter is applied instead of Drain-/fillable porosity which is only used for phreatic simulations with the Darcy equation