Every application of the theory of superposition applied to well interference and boundaries I have seen involves the Theis solution. Is there any reason superposition cannot be used to evaluate drawdown with "leaky" aquifer solutions (e.g. Hantush) or unconfined aquifers (e.g. Neuman, assuming the appropriate use of type A and B curves)?
I don't see any obvious reason superposition cannot be used in those cases, but I may be missing something.
I agree with you, the principle of superposition can be used universally.
For instance when you superpose :
- a piezometric map resulting from the natural flow in an aquifer and the drawdown induced by a pumping (computed with the Theis slution or any other one, with or without boundariy effect, etc.).
Best regards
PL
As long as the problem is linear (in the sense of being a linear PDE), then you can superpose solutions for any individual source to result in the net impact, yes. Both of the well solutions you mention are linear, so they should be applicable.
Also, if you are using this to simulate boundaries with imaginary "image" wells, you should see the right behavior using these solutions.
I agree with Michael Cardiff. The superposition principle is valid for any solutions that are considered as linear. The Hantush solution is a development of the Theis solution with the integration of sink/source term (the leakage flux). So it is already a direct application of the superposition principle.
The extension of superposition principle to unconfined aquifers is only possible if the aquifer can be considered as confined. In this case, the PDE equation cans be linearized. From a practical point of view, it can be done if the drawdown induced by a pumping well remains limited compared to the saturated thickness of he aquifer.
I agree with Francois. The superposition is considered if the governing equation and the boundary condition are linear in term of state variable (this will be head). I just need to add thing for unconfined aquifer. The governing equation for unconfined is not linear. Still we can apply the superposition principle by considering h2 quantity and not h.
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