# Aquifer constant rate discharge pumping test example#

This Inversion Test Problem demonstrates a range of solutions for the time-drawdown response at an observation well resulting from the application of a constant rate discharge pumping test at an adjacent production well. Each solution describes the response for a unique aquifer type. These are:

Confined aquifer solution (Theis, 1935)

Leaky aquifer solution featuring no aquitard storage (Hantush and Jacob, 1955)

Leaky aquifer solution featuring aquitard storage (Hantush, 1960)

Fractured rock aquifer solution (Barker, 1988)

These solutions assume full aquifer penetration by both the production and observation wells. All solutions are calculated in the Laplace domain and are inverted to the time domain numerically using the De Hoog et al. (1982) algorithm.

Contribution Metadata for *Aquifer constant rate discharge pumping test*

This example involves the matching of an appropriate forward model to time-drawdown data obtained from a two-well constant rate discharge test.

- Author:
Chris Turnadge

- Contact:
Chris Turnadge (chris.turnadge@csiro.au)

## Example usage for `PumpingTest`

#

Code block below is generated automatically based on our tests and inspection of the example objects. We’d like to also refer you to the API Reference for more about the Espresso API.

```
1import espresso
2
3# Create a PumpingTest object
4my_pumping_test = espresso.PumpingTest(example_number=1)
5
6# Guaranteed API
7model_size = my_pumping_test.model_size
8data_size = my_pumping_test.data_size
9null_model = my_pumping_test.starting_model
10good_model = my_pumping_test.good_model
11given_data = my_pumping_test.data
12synthetic_data = my_pumping_test.forward(good_model)
13
14# Optional API
15example_desc = my_pumping_test.description
16cov_matrix = my_pumping_test.covariance_matrix
17inv_cov_matrix = my_pumping_test.inverse_covariance_matrix
18model_fig = my_pumping_test.plot_model(good_model)
19log_likelihood_val = my_pumping_test.log_likelihood(given_data, synthetic_data)
```

Additional attributes to explore: [`list_capabilities`

].

## LICENCE#

Copyright 2021-2022 The Contributors All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.