Demonstration of WellResponse Class
Notebook to demonstrate using the Well Class to estimate drawdown or stream depletion using the solutions available in the python module.
[1]:
import sys
sys.path.insert(1, '../../')
import pycap
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
Example Depletion
The Well class will estimate depletions for streams. The stream distances and streambed conductances, if needed, are passed through dictionaries keyed by a stream name or ID. In this notebook a table of values will be made manually from Table 2 from Reeves, H.W., Hamilton, D.A., Seelbach, P.W., and Asher, A.J., 2009, Ground-water-withdrawal component of the Michigan water-withdrawal screening tool: U.S. Geological Survey Scientific Investigations Report 2009–5003, 36 p. [https://pubs.usgs.gov/sir/2009/5003/]
[2]:
stream_table = pd.DataFrame(({'id': 8, 'distance': 14802},
{'id': 9, 'distance': 12609.2},
{'id': 11, 'distance': 15750.5},
{'id': 27, 'distance': 22567.6},
{'id': 9741, 'distance': 27565.2},
{'id': 10532, 'distance': 33059.5},
{'id': 11967, 'distance': 14846.3},
{'id': 12515, 'distance': 17042.55},
{'id': 12573, 'distance': 11959.5},
{'id': 12941, 'distance': 19070.8},
{'id': 13925, 'distance': 10028.9}))
[3]:
stream_table.head()
[3]:
| id | distance | |
|---|---|---|
| 0 | 8 | 14802.0 |
| 1 | 9 | 12609.2 |
| 2 | 11 | 15750.5 |
| 3 | 27 | 22567.6 |
| 4 | 9741 | 27565.2 |
Compute apportionment
The Michigan screening tool uses inverse distance weighting apportionment. Other apportionment approaches that may be used as a simple way to extend the analytical solution are discussed by Zipper and others (2019). [https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018WR024403]
[4]:
invers =np.array([1/x for x in stream_table['distance']])
stream_table['apportionment'] = (1./stream_table['distance'])/np.sum(invers)
[5]:
stream_table
[5]:
| id | distance | apportionment | |
|---|---|---|---|
| 0 | 8 | 14802.00 | 0.098916 |
| 1 | 9 | 12609.20 | 0.116118 |
| 2 | 11 | 15750.50 | 0.092959 |
| 3 | 27 | 22567.60 | 0.064878 |
| 4 | 9741 | 27565.20 | 0.053116 |
| 5 | 10532 | 33059.50 | 0.044288 |
| 6 | 11967 | 14846.30 | 0.098621 |
| 7 | 12515 | 17042.55 | 0.085911 |
| 8 | 12573 | 11959.50 | 0.122426 |
| 9 | 12941 | 19070.80 | 0.076774 |
| 10 | 13925 | 10028.90 | 0.145993 |
[6]:
np.sum(stream_table['apportionment'])
[6]:
1.0000000000000002
make dictionaries from the distances and apportionment values
[7]:
distances = dict(zip(stream_table.id.values, stream_table.distance.values))
[8]:
apportion = dict(zip(stream_table.id.values, stream_table.apportionment.values))
set aquifer properties and streambed conductances
[9]:
stream_table = pd.DataFrame(({'id': 8, 'distance': 14802},
{'id': 9, 'distance': 12609.2},
{'id': 11, 'distance': 15750.5},
{'id': 27, 'distance': 22567.6},
{'id': 9741, 'distance': 27565.2},
{'id': 10532, 'distance': 33059.5},
{'id': 11967, 'distance': 14846.3},
{'id': 12515, 'distance': 17042.5},
{'id': 12573, 'distance': 11959.5},
{'id': 12941, 'distance': 19070.8},
{'id': 13925, 'distance': 10028.9}))
[10]:
T= 7211. # ft^2/day
S= 0.01
Q = 70 # 70 gpm in cubic feet per day
well_name = 'demo'
pumpdays = int(5. * 365)
call a utility to convert Q to a series with appropriate formatting
also convert to CFD from GPM
[11]:
Q = pycap.Q2ts(pumpdays, 5, Q) * pycap.GPM2CFD
[12]:
Q
[12]:
1 13475.935829
2 13475.935829
3 13475.935829
4 13475.935829
5 13475.935829
...
1821 13475.935829
1822 13475.935829
1823 13475.935829
1824 13475.935829
1825 13475.935829
Length: 1825, dtype: float64
[13]:
stream_table['conductance'] = 7.11855 # example uses constant streambed_conductance
[14]:
stream_table.head()
[14]:
| id | distance | conductance | |
|---|---|---|---|
| 0 | 8 | 14802.0 | 7.11855 |
| 1 | 9 | 12609.2 | 7.11855 |
| 2 | 11 | 15750.5 | 7.11855 |
| 3 | 27 | 22567.6 | 7.11855 |
| 4 | 9741 | 27565.2 | 7.11855 |
[15]:
cond = dict(zip(stream_table.id.values, stream_table.conductance.values))
[16]:
test_well = pycap.Well(T=T,
S=S,
Q=Q,
depletion_years=5,
depl_method='hunt99',
drawdown_dist={'test0':50.},
streambed_conductance=cond,
stream_dist=distances,
stream_apportionment=apportion)
[17]:
test_well.drawdown
/home/runner/work/pycap-dss/pycap-dss/source/examples/../../pycap/solutions.py:66: RuntimeWarning: divide by zero encountered in divide
u = dist**2.0 * S / (4.0 * T * time)
[17]:
{'test0': array([0. , 0.96284254, 1.06585921, ..., 2.07921679, 2.07929839,
2.07937994])}
[18]:
deltaQ = pycap._calc_deltaQ(Q)
deltaQ
[18]:
1 13475.935829
dtype: float64
[19]:
test_well.depletion
/home/runner/work/pycap-dss/pycap-dss/source/examples/../../pycap/solutions.py:561: RuntimeWarning: divide by zero encountered in divide
a = np.sqrt(S * dist**2 / (4.0 * T * time))
[19]:
{8: array([0.00000000e+00, 3.98636452e-33, 3.31204669e-16, ...,
9.90280807e+02, 9.90371342e+02, 9.90461805e+02]),
9: array([0.00000000e+00, 7.13367383e-24, 1.74727419e-11, ...,
1.21340842e+03, 1.21350207e+03, 1.21359564e+03]),
11: array([0.00000000e+00, 1.44038609e-37, 1.82588316e-18, ...,
9.13187370e+02, 9.13276691e+02, 9.13365942e+02]),
27: array([0.00000000e+00, 2.33569680e-77, 1.39682712e-38, ...,
5.52264289e+02, 5.52345936e+02, 5.52427521e+02]),
9741: array([0.00000000e+000, 2.44245084e-115, 1.07059588e-057, ...,
4.03755855e+002, 4.03832253e+002, 4.03908595e+002]),
10532: array([0.00000000e+000, 1.00292409e-165, 5.26758880e-083, ...,
2.94853678e+002, 2.94924279e+002, 2.94994832e+002]),
11967: array([0.00000000e+00, 2.50629102e-33, 2.61529655e-16, ...,
9.86458285e+02, 9.86548762e+02, 9.86639167e+02]),
12515: array([0.00000000e+00, 4.77131258e-44, 9.40917849e-22, ...,
8.22143476e+02, 8.22231229e+02, 8.22318914e+02]),
12573: array([0.00000000e+00, 2.10485259e-21, 3.22528609e-10, ...,
1.29536178e+03, 1.29545646e+03, 1.29555107e+03]),
12941: array([0.00000000e+00, 3.21102915e-55, 2.08239385e-27, ...,
7.04476694e+02, 7.04562126e+02, 7.04647491e+02]),
13925: array([0.00000000e+00, 8.60822413e-15, 8.25718576e-07, ...,
1.60192335e+03, 1.60202161e+03, 1.60211978e+03])}
[20]:
stream_depl = pd.DataFrame(test_well.depletion)
need to convert to GPM to compare results to Table 2
[21]:
stream_depl = stream_depl/pycap.GPM2CFD
stream_depl
[21]:
| 8 | 9 | 11 | 27 | 9741 | 10532 | 11967 | 12515 | 12573 | 12941 | 13925 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 | 0.000000e+00 |
| 1 | 2.070695e-35 | 3.705547e-26 | 7.482006e-40 | 1.213265e-79 | 1.268718e-117 | 5.209633e-168 | 1.301879e-35 | 2.478432e-46 | 1.093354e-23 | 1.667951e-57 | 4.471494e-17 |
| 2 | 1.720424e-18 | 9.076119e-14 | 9.484449e-21 | 7.255741e-41 | 5.561151e-60 | 2.736220e-85 | 1.358501e-18 | 4.887545e-24 | 1.675357e-12 | 1.081688e-29 | 4.289149e-09 |
| 3 | 9.397226e-13 | 1.521286e-09 | 2.774686e-14 | 7.755022e-28 | 1.159869e-40 | 1.310323e-57 | 8.006897e-13 | 1.661375e-16 | 1.112081e-08 | 2.547071e-20 | 2.414180e-06 |
| 4 | 7.690155e-10 | 2.171820e-07 | 5.262710e-11 | 2.831779e-21 | 5.934766e-31 | 1.018311e-43 | 6.806930e-10 | 1.076022e-12 | 9.976385e-07 | 1.376230e-15 | 6.273796e-05 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 1820 | 5.143017e+00 | 6.302009e+00 | 4.742572e+00 | 2.867857e+00 | 2.096493e+00 | 1.530867e+00 | 5.123162e+00 | 4.269666e+00 | 6.727700e+00 | 3.658476e+00 | 8.320080e+00 |
| 1821 | 5.143488e+00 | 6.302496e+00 | 4.743037e+00 | 2.868282e+00 | 2.096890e+00 | 1.531234e+00 | 5.123632e+00 | 4.270122e+00 | 6.728193e+00 | 3.658921e+00 | 8.320591e+00 |
| 1822 | 5.143959e+00 | 6.302983e+00 | 4.743501e+00 | 2.868706e+00 | 2.097287e+00 | 1.531601e+00 | 5.124103e+00 | 4.270579e+00 | 6.728685e+00 | 3.659365e+00 | 8.321102e+00 |
| 1823 | 5.144429e+00 | 6.303469e+00 | 4.743965e+00 | 2.869130e+00 | 2.097684e+00 | 1.531968e+00 | 5.124573e+00 | 4.271034e+00 | 6.729177e+00 | 3.659809e+00 | 8.321612e+00 |
| 1824 | 5.144899e+00 | 6.303955e+00 | 4.744429e+00 | 2.869554e+00 | 2.098081e+00 | 1.532334e+00 | 5.125042e+00 | 4.271490e+00 | 6.729668e+00 | 3.660252e+00 | 8.322122e+00 |
1825 rows × 11 columns
[22]:
five_year= pd.DataFrame(stream_depl.loc[1824].T)
[23]:
five_year.rename(columns={1824: 'Depletion'}, inplace=True)
[24]:
pd.options.display.float_format = '{:,.2f}'.format
five_year
[24]:
| Depletion | |
|---|---|
| 8 | 5.14 |
| 9 | 6.30 |
| 11 | 4.74 |
| 27 | 2.87 |
| 9741 | 2.10 |
| 10532 | 1.53 |
| 11967 | 5.13 |
| 12515 | 4.27 |
| 12573 | 6.73 |
| 12941 | 3.66 |
| 13925 | 8.32 |
Matches Table 2
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