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Analyzing pumped-well impeller logs to ascertain
vertical hydraulic conductivity variations
Alison H. Parker1, L. Jared West, Noelle E.
Odling, Simon H. Bottrell School of Earth and
Environment, University of Leeds, Woodhouse Lane,
Leeds, LS2 9JT 1. a.parker_at_see.leeds.ac.uk
Introduction Horizontal variations in the
hydraulic conductivity of aquifers are generally
well characterized through simple pump test
analyses. However, vertical variations are often
poorly understood and misrepresented in the
regional models used by regulatory bodies and
water companies. Understanding these is key for
predicting flow paths and hence the behavior of
contaminants in the aquifer that might present a
risk to public drinking water supplies.
Methodology A pump is set up at the top of the
borehole. The impeller is a set of vanes whose
rotation is proportional to flow speed. As the
impeller is lowered down the hole, it measures
the flow speed of the water, which decreases as a
producing zone is passed.
Traditionally, packer tests are used to
characterize these variations, but they are time
consuming and costly to perform. However, other
techniques have been developed which can quantify
these variations, including impeller logging
(Jones and Skibitzke, 1956). This study aims to
present new, more rigorous methods of analyzing
impeller flow log data.
If there is no ambient flow, the gradient of this
log is proportional to hydraulic conductivity,
(Molz et al 1989). Absolute hydraulic
conductivity can be attained by multiplying the
values of the log by the transmissivity, obtained
from a pump test.
Field area These tests were carried out in
boreholes in the Chalk aquifer of East Yorkshire,
UK
Results
Casing
A typical flow log
The noisy first derivative of the data, using a
simple finite difference method (note scale!)
The model fit to the flow data (see text)
The model results, with 95 confidence intervals
shown in pale blue
Result of Savitzky-Golay filtering on the first
derivative of the data
Filtering A Savitzky-Golay filter (Savitzky and
Golay 1964) removes high frequency noise, caused
by turbulence on borehole rugosities. However,
some lower frequency noise remains, associated
with turbulence at major borehole diameter
changes.

• Modelling
• Due to the shortcomings on the other methods, it
  was decided to create a physical model of the
  flow regime, consisting of layers. The data was
  fitted to determine the key model parameters.
  Constraints are
• Flow speed cannot increase with depth (assuming
  no ambient flows)
• The flow must be zero at the bottom of the hole
  (there are no inflows below the bottom of the
  hole)
• Flow speed is constant in the casing (there are
  no inflows into the casing)
• 4. The model should be a series of connected
  straight line sections that meet at vertices
  (assumes the hydraulic conductivity is constant
  for each layer)
• 5. The number of model sections is determined by
  the user.

Conclusions Even advanced methods for curve
fitting to noisy data gave unsatisfactory
results, hence the discrete layer model gave the
best results in this case, and thus is a feasible
alternative to packer testing.
Two vertices are fixed by the user. A computer
algorithm was used to perform a search of the
space between the defined vertices to find an
intermediate vertex with the aim of minimising
the root mean square error. This process is
repeated for all vertices. To estimate the
uncertainty in the model parameters, a Monte
Carlo method (Metropolis and Ulam, 1949) was used
to define a 95 confidence interval. The model
showed good correlation with pumped dilution
testing carried out in the same borehole. If
constraint 1 is relaxed, this model can also be
used where there are ambient flows, by completing
the analysis with the methodology of Paillet
(2000).
References Jones, P.H., Skibitzke E.B.,
Subsurface geophysical methods in ground water
hydrology, Advances in Geophysics 3, 241-297,
1956 Metropolis, N., Ulam, S., The Monte Carlo
Method, Journal of the American Statistical
Association 44, 335-341, 1949 Molz, F.J., Morin,
R.H., Hess, A.E., Melville, J.G., Guven, O., The
impeller meter for measuring aquifer permeability
variations Evaluation and comparison with other
tests, Water resources Research 25(7), 1677-1683,
1989 Paillet, F.L., A filed technique for
estimating aquifer parameters using flow log
data. Ground Water 38 (4), 510-521 Savitzky, A.,
Golay, M.J.E. Smoothing and Differentiation of
Data by Simplified Least Squares Procedures,
Analytical Chemistry 36, 1627-1639, 1964
2
Analyzing pumped-well impeller logs to ascertain
vertical hydraulic conductivity variations
Alison H. Parker1, L. Jared West, Noelle E.
Odling, Simon H. Bottrell School of Earth and
Environment, University of Leeds, Woodhouse Lane,
Leeds, LS2 9JT 1. a.parker_at_see.leeds.ac.uk
Abstract Horizontal variations in the hydraulic
conductivity of aquifers are generally well
characterized through simple pump test analyses.
However, vertical variations are often poorly
understood and misrepresented in the regional
models used by regulatory bodies and water
companies. Understanding these is key for
predicting flow paths and hence the behavior of
contaminants in the aquifer that might present a
risk to public drinking water supplies. Traditiona
lly, packer tests were used to characterize these
variations, but they can be time consuming and
costly to perform. However, other techniques have
been developed which can quantify these
variations, including impeller logging. This
study aims to present new, more rigorous methods
of analyzing impeller flow log data. Impeller
logs were taken under pumped conditions in open
wells in a chalk aquifer located in N. England.
Theoretically, hydraulic conductivity can be
obtained from the gradient in flow rate with
depth. However, data are typically noisy due to
turbulent flow and hole diameter variations with
depth so directly converting the flow rate
gradient to hydraulic conductivity leads to rapid
non-physical variation and negative hydraulic
conductivity values. Correcting for hole diameter
variations using caliper logs proved difficult
due to phenomena such as jetting, whereby when
the water enters a widening, it does not
instantly slow down. In order to obtain more
realistic hydraulic conductivity profiles, we
firstly tried a data smoothing algorithm, but
this approach distorted the data and still gave
an unacceptable noise level. Instead, a layered
modeling approach has been developed. A hydraulic
conductivity profile consisting of a discrete
number of uniform layers is constructed, and
layer thicknesses and hydraulic conductivities
are varied until a satisfactory fit to the
observed flow log is achieved. Results from
field sites on the confined Chalk aquifer of East
Yorkshire in the United Kingdom showed good
correlation to packer test analysis. The absence
of significant ambient flows at this test site
made the final analysis relatively simple. By
testing boreholes across the aquifer a pattern of
hydraulic conductivity variation with depth can
be established, and compared to the proposed
geological and climatic reasons for the
variations existence.
References Jones, P.H., Skibitzke E.B.,
Subsurface geophysical methods in ground water
hydrology, Advances in Geophysics 3, 241-297,
1956 Metropolis, N., Ulam, S., The Monte Carlo
Method, Journal of the American Statistical
Association 44, 335-341, 1949 Molz, F.J., Morin,
R.H., Hess, A.E., Melville, J.G., Guven, O., The
impeller meter for measuring aquifer permeability
variations Evaluation and comparison with other
tests, Water resources Research 25(7), 1677-1683,
1989 Paillet, F.L., A filed technique for
estimating aquifer parameters using flow log
data. Ground Water 38 (4), 510-521 Savitzky, A.,
Golay, M.J.E. Smoothing and Differentiation of
Data by Simplified Least Squares Procedures,
Analytical Chemistry 36, 1627-1639, 1964