# iMOD User Manual version 4.4 (html)

#### 12.15HFB Horizontal flow barrier module

Horizontal barriers obstructing flow such as semi- or impermeable fault zone or a sheet pile wall are defined for each model layer by a *.GEN line file. The behaviour of this is twofold:

• Factor $f$
This is used automatically whenever the packages TOP and BOT are omitted in the runfile. By lines that obstruct groundwater with a particular reduction factor $f$ for the hydraulic conductance or permeability, see Figure 12.9a, resulting in variable resistances along the line. The factor $f$ is applied to the computed harmonic conductances in between cells $i$ (icol index) and $j$ (irow index).

\begin{equation} \begin {array}{l} CR_{i,j}=f\frac {2T_2T_1 DY_{j}}{(T_1DX_{i}+T_2DX_{i-1})} \\ \\ CC_{i,j}=f\frac {2T_2T_1 DX_{i}}{(T_1DY_{j}+T_2DX_{j-1})} \end {array} \end{equation}

• Resistance $r$ This is used automatically whenever the packages TOP and BOT are included in the runfile. By lines that obstruct groundwater flow with a variable resistance $r$ in days for that line, see Figure 12.9b, resulting in variable resistances $C^{’}$ along that line. This combined resistance $C^{’}$ (as a sum of the original resistance and the additional fault resistance) is computed internally as:

\begin{equation} \begin {array}{l} CR_{i,j}=\frac {2T_2T_1 DY_{j}}{(T_1DX_{i}+T_2DX_{i-1})} \\ \\ DZ_{i,j}= \frac {1}{2}(TOP_{i,j}-BOT_{i,j})+\frac {1}{2}(TOP_{i+1,j}-BOT_{i+1,j}) \\ \\ C_{i,j} = \frac {1}{2}DX_{i}DX_{i+1}\frac {CR_{i,j}}{DZ_{i,j}} \\ \\ C^{’}_{i,j}=r+C_{i,j} \\ \\ CR_{i,j}=C^{’}_{i,j}\frac {2T_2T_1 DY_{j}}{(T_1DX_{i}+T_2DX_{i-1})} \end {array} \end{equation}

Whenever $r$ is negative, the resulting resistance $C^{’}$ is equal to abs($r$). In that way the resistance between cells can become less than the resistance that is based on the permeability of the geological material.

Note: A Factor $f$ or Resistance $r$ of 0.0, means that the fault is completely impermeable.

In iMOD faults can be simulated by entering GEN files in the runfile directly. iMOD will define automatically at which cell faces the permeabilities need to be adjusted based on the specifications of the fault. Figure 12.10: Example of a horizontal flow barrier parameterization in case of a uniform model network consisting of model cells of 25 x 25 m. Based on the location of an irregular shaped fault line (white line) the cell faces (thick black lines) are identified where the conductance between the cells is adjusted using the parameter values of the fault line. The computed hydraulic heads (thin black contour lines) illustrate the local effects of the barriers on groundwater flow. Figure 12.11: The same example as above, but now for a uniform model network consisting of model cells of 100 x 100 m.

The line *.GEN file defines the location of the barrier. The multiplication factor is used to create the obstruction by reducing the conductance between model cells. The HFB module corresponds with the MODFLOW HFB package.

Whenever GEN files are assigned to layer number 0, iMOD will assign the fault to the appropriate model layers automatically. In that case the GEN file needs to be a 3D GEN (see Section 9.11). Based on the elevation in the 3D GEN file and the TOP and BOT elevations of each model layer, the fault and the nett resistance will be assigned according the following method:

• • Whenever the thickness of the model layer is $< 0.5$ meter:

• – Compute the nett resistance $r$ or factor $f$ of the fault as a weighted arithmetic mean for the thickness of each individual fault along that particular cell.

• • Whenever the thickness of the model layer is $> 0.5$ meter:

• – Each grid cell interface will be filled in until no space is available that can be occupied by a fault line;

• – Each contribution of an individual fault is harmonic ($c^{-1}$);

• – The system number as used in the model, is equal to the fault that contributed mostly to the nett resistance;

• • The final nett resistance is the harmonic mean between:

• 1. the summed resistance weighted to the level of occupation index ($i=0.0 - 1.0$), and

• 2. a resistance of 1 day for the remaining part of the model layer ($1.0-i$).

Be aware that whenever the occupation index is 90 %, the resistance will be already significantly less. An example is demonstrating what the nett resistance are for different settings.

\begin{equation} \begin {array}{r|r|r|r|r|r} \rm {Total} & \rm {Thickness} & \rm {Resistance} & \rm {Weighted} & \rm {Nett} & \rm {Confined} \\ \rm {thickness} & & & \rm {harmonic} & \rm { Resistance} & \rm {Resistance} \\ m & m & d & md^{-1} & c & c \\ \hline & 2.5 & 100 & 0.025 & & \\ & 2.5 & 1,000 & 0.0025 & & \\ \hline 5.0 & 5.0 & & 0.0275 & 181.82 & 181.82 \\ \hline & 2.0 & 100 & 0.02 & & \\ & 2.0 & 1,000 & 0.002 & & \\ \hline 5.0 & 4.0 & & 0.022 & 227.27 & 4.89 \\ \hline \end {array} \end{equation}