Streamlit Apps for the topic

05 Applied Hydrogeology

Aquifer Testing

Theis, Neuman, and Hantush Jacob parameter estimation

Fitting formation parameter to REAL measured data


This variant of the app allows to choose real measured data

This interactive document allows to apply the Theis and Neuman principle for pumping test evaluation in unconfined, leaky, and confined transient setups. The notebook is based on an Spreadsheet from Prof. Rudolf Liedl.

General situation

We consider a aquifer with constant transmissivity. If a well is pumping water out of the aquifer, radial flow towards the well is induced. To calculate the hydraulic situation, the following simplified flow equation can be used. This equation accounts for 1D radial transient flow towards a fully penetrating well within a confined aquifer without further sinks and sources:

\[\frac{\partial^2 h}{\partial r^2} + \frac{1}{r} \frac{\partial h}{\partial r} = \frac{S}{T} \frac{\partial h}{\partial t}\]

Mathematical model and solution

Theis solution for confined aquifers

Charles V. Theis presented a solution for this by deriving

\[s(r, t) = \frac{Q}{4 \pi T} W(u)\]

with the well function

\[W(u) = \int_u^{+\infty} \frac{e^{-\tilde{u}}}{\tilde{u}} d\tilde{u}\]

and the dimensionless variable

\[u = \frac{S r^2}{4 T t}\]

Neuman solution for unconfined aquifers

ToDo: Provide explanation and theory here

This equations are not easy to solve. Historically, values for the well function were provided by tables or as so called type-curve. The type-curve matching with experimental data for pumping test analysis can be considered as one of the basic hydrogeological methods. However, modern computer provide an easier and more convinient way to solve the 1D radial flow equation based on the Theis approach. Subsequently, the Theis equation is solved with Python routines. The results for the measured data are graphically presented in an interactive plot.

Screenshot of the app

You can access the app here: https://theis-neuman-hantush.streamlit.app/

Theis parameter estimation and drawdown prediction

Fitting formation parameter to REAL measured data


Screenshot of the app

You can access the app here: https://theis-inverse-drawdown-random.streamlit.app/