| Groundwater modelling with MicroFEM • Lesson 3A: Grid refinement and Well radius |
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Start MicroFEM and load the "Lesson 1" model by clicking the project file "Lesson 1.fpr". The very simple model we built so far was only good enough to explain some basic principles. A realistic well flow model requires much more nodes between the well and the model boundary. In MicroFEM it is simple to refine the grid stepwise. During a refinement step a node is added on each node connection. In this way each element is split up into four smaller ones.
Step 12: Refine grid
Menu bar: Project / Information ... / read Information / [OK] The pop-up window shows that the number of nodes and elements (7 and 6).
[Walking mode] / [Delete marks (Del)] / [Toggle all marks (F9)] In this way all nodes become marked.
[Alter-grid mode] / [Add marked nodes (F5)] / [Yes] / [Walking mode] Check the Project Information again: the number of nodes and elements = 19 and 24. Check that the new nodes on the boundary are automatically set to "fixed head". These nodes have the transmissivities of their neighbouring nodes: 2000 m2/d. The head of the centre node is still –0.144 m. All new nodes halfway the well and the boundary have interpolated heads of –0.072 m.
Menu bar: Calculate / Go calculate The head in the well is lowered to –0.192, and the nodes halfway the boundary are –0.048 m. Note that the difference between the well node and its neighbouring nodes remains 0.144 m.
[Alter-grid mode] / [F5] / [Yes] / [Walking mode] Check that there are now 96 elements and 61 nodes.
Menu bar: Calculate / Go calculate The head in the well is lowered to –0.247.
Do two more refinement steps and calculate. The grid consists of 1536 elements and 817 nodes. Well head is –0.357.
[Walking mode] / [Del] [Drawing mode] / [Del] / [Grey] / [Draw all nodes (F2)] / [Yellow] / select H1 / [F7] / [OK]
The contour lines show the drawdown cone of the well.
Menu bar: Tools / 3D Viewer / Increase the size of the 3D Viewer window. 3D Viewer menu bar: Tools / Options ... / Heads / Uncheck the box next to the green square / [OK] The drawdown cone is nicely represented. Linear interpolation within the elements is only obvious close to the well.
Apart from rotating and zooming (Step 9 Lesson 2A) more mouse movements are available:
Close the 3D Viewer.
Step 13: Relation between element size and well radius
It is obvious that the drawdown (s) in the well is a function of element size. The real drawdown in the well depends on the well radius (r_w). With the Thiem equation s = Q/(2.π.T) ln(r_1/r_2) = 1000/(2.π.2000) ln(5000/r_w) we can compute for each drawdown (and element size) the corresponding well radius that produces the same drawdown as the finite element model. Here r_1 is the distance to the model boundary where the drawdown is assumed zero.
The drawdown values (s) are computed with our MicroFEM model. The r_w values are the well radii that produce the same drawdown when using the Thiem equation. There appears to be a fixed ratio of about 6 between the element size in the model and the well radius that produces the same drawdown in the well. From this we conclude that when we want to compute the drawdown in a well with a MicroFEM model, we have to choose the element size around the well 6 times larger than the well radius. Since we modified the original model we save it with a new name:
Menu bar: Files / Save as ... / "Lesson 3" / [Save]
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