|Groundwater modelling with MicroFEM • Lesson 10B: Transient modelling|
When head changes with time (as in all natural situations) we are dealing with transient (time dependent, unsteady, nonsteady state) flow. We can simulate such flow for a given period. It requires an additional aquifer parameter: (elastic) storativity (for confined aquifers) or specific yield (unconfined aquifers).
The total simulation period must be subdivided into a number of (one or more) stress periods. Within a stress period the boundary conditions do not change. A stress period is subdivided into a number of time steps. For each time step the heads are computed for all nodes in all aquifers. The results of a transient model also depend on the initial condition, the heads at the start of the first stress period. We usually start with a steady-state model:
When you run this we are back to our original model with precipitation and no well. Maximum height of water table = 24.741. This will be our initial condition.
Save the model.
When running a transient model, MicroFEM does not save all computed heads and fluxes for each time step, but only the data that you ask for. When we are only interested in the simulated transient heads at the nodes that represent observation wells around the pumping well, then we have to assign labels to those nodes. The smart way is to use labels that have some text in common, such as: obs.1, obs.2, obs.a, and obs.b3, or we can use whatever names we like and end for example with the number sign # (e.g. observ# , old_well# and forest-lake#).
Seleect six nodes close to and further from the well and assign a different label to each of them, all ending with the # sign.
Add the following text to the batch-file
The OPEN-H command opens a file "Lesson 10.fth" and writes for the start (t=0) and at the end of each time step a line with the time (in days) and the computed heads for each node that has a label with a #-sign.
Run the model.
When ready the total running time is displayed.
Close the blue and black windows.
Menu bar: Tools / Time curves ... / [Open file] (second button upper left) / Click FTH file
The Selection Tab can be used to make a section of nodes (observation wells) and times. The Option Tab can be used for a few settings of the Time graph. The Time-Head curve displays the resulting time-graph.
Menu bar: Export / Copy to clipboard / Time-curve
A copy of the time-graph can now be pasted into Word or other windows software for presentation purposes.
Although a black background, white axes and yellow curves work fine on the screen, a white background, black axes and darker curves are better for presentations. The same applies to maps, profiles and sections.
When it is not the well discharge but the recharge by precipitation that changes in time, then the batch-file could look like:
At the end or in between stress periods you can also save files or copy results, e.g.:
SAVE fem=”lesson 10a”
to save the fem-file: lesson 10.fem
to copy the computed heads (water table heights) to X4 of the Xtra worksheet.
Another interesting command is DRAW. When you start the batch-file with DRAW and draw a contour map before you run the model, the map will be updated each time step. You have to shift the blue and black screen to the right for a better view of the map. Any section (or profile) on the screen will also be updated.
This lesson is only a simple introduction to the batch-file commands. See the online Help texts and the MicroFEM website for further information.