4. Slug test for confined aquifer - Dawsonville#

Import packages#

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

import timflow.transient as tft

plt.rcParams["figure.figsize"] = [5, 3]

Introduction and Conceptual Model#

This Slug Test, was reported by Cooper Jr et al. (1967), and it was performed in Dawsonville, Georgia, USA.

A fully penetrated well (Ln-2) is screened in a confined aquifer, located between depths 24 and 122 (98 m thick). The volume of the slug is 10.16 litres. Head change has been recorded at the slug well. Both the well and the casing radii of the slug well is 0.076 m.

../../_images/Dawsonville.png

Load data#

data = np.loadtxt("data/dawsonville_slug.txt")
to = data[:, 0]
ho = data[:, 1]

Parameters and model#

# known parameters
b = 98  # aquifer thickness in m
zt = -24  # top of aquifer in m
zb = zt - b  # bottom of aquifer in m
rw = 0.076  # well radius of Ln-2 Well in m
rc = 0.076  # casing radius of Ln-2 Well in m
Q = 10.16 / 1000  # slug volume in m^3 (10.16 l = 0.01016 m^3)

ml = tft.ModelMaq(kaq=10, z=[zt, zb], Saq=1e-4, tmin=1e-6, tmax=1e-3, topboundary="conf")
w = tft.Well(ml, xw=0, yw=0, rw=rw, rc=rc, tsandQ=[(0, -Q)], layers=0, wbstype="slug")
ml.solve()

self.neq  1
solution complete

Estimate aquifer parameters#

We calibrate hydraulic conductivity and specific storage, as in the KGS model (Hyder et al. 1994).

# unknown parameters: kay, Saq
cal = tft.Calibrate(ml)
cal.set_parameter(name="kaq0", initial=10, pmin=0, layers=0)
cal.set_parameter(name="Saq0", initial=1e-4, layers=0)
cal.seriesinwell(name="obs", element=w, t=to, h=ho)
cal.fit(report=False)

...............................
Fit succeeded.

display(cal.parameters)
print("rmse:", cal.rmse())
layers optimal std perc_std pmin pmax initial inhoms parray
kaq0_0_0 0 0.420908 0.018325 4.353689 0.0 inf 10.0000 None [[0.42090788883700814]]
Saq0_0_0 0 0.000017 0.000005 31.025816 -inf inf 0.0001 None [[1.7004312750679313e-05]] 
rmse: 0.004409616694582213

tm = np.logspace(np.log10(to[0]), np.log10(to[-1]), 100)
hm = ml.head(0, 0, tm)
plt.semilogx(to, ho, ".", label="obs")
plt.semilogx(tm, hm[0], label="timflow")
plt.xlabel("time [d]")
plt.ylabel("drawdown [m]")
plt.title("Model Results - Single-layer model")
plt.legend()
plt.grid()
../../_images/a9c34e3f93890007afd9115fa0e7464c9961399e2910899b27e39fff1040ff05.png

Comparison of results#

We now compare the values in timflow and add the results of the modelling done in MLU (Hemker & Post, 2014). Results are similar between both models. The RMSE of MLU is slightly better than the one from timflow.

Hide code cell source

 
t = pd.DataFrame(
    columns=["k [m/d]", "Ss [1/m]", "RMSE [m]"],
    index=["timflow", "MLU"],
)

t.loc["timflow"] = np.append(cal.parameters["optimal"].values, cal.rmse())
t.loc["MLU"] = [0.4133, 1.9388e-05, 0.004264]

t_formatted = t.style.format(
    {"k [m/d]": "{:.2f}", "Ss [1/m]": "{:.2e}", "RMSE [m]": "{:.3f}"}
)
t_formatted
  k [m/d] Ss [1/m] RMSE [m]
timflow 0.42 1.70e-05 0.004
MLU 0.41 1.94e-05 0.004

References#

  • Cooper Jr, H.H., Bredehoeft, J.D. and Papadopulos, I.S. (1967) Response of a finite diameter well to an instantaneous charge of water, Water Resources Research 3, 263–269

  • Duffield, G.M. (2007), AQTESOLV for Windows Version 4.5 User’s Guide, HydroSOLVE, Inc., Reston, VA.

  • Hemker, K. en Post V. (2014) MLU for Windows: well flow modeling in multilayer aquifer systems; MLU User’s guide. https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fmicrofem.com%2Fdownload%2Fmlu-user.pdf&data=05%7C02%7CMark.Bakker%40tudelft.nl%7Cad7f16364d2d4fd55dbf08de73832eaa%7C096e524d692940308cd38ab42de0887b%7C0%7C0%7C639075204580287861%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=OBoe8seXZUfoat89Dfr4g6lF%2Bn1FdtXqtp%2F18BMXCn0%3D&reserved=0

  • Hyder, Z., Butler Jr, J.J., McElwee, C.D. and Liu, W. (1994) Slug tests in partially penetrating wells, Water Resources Research 30, 2945–2957.