## Aquifer test interpretation with special emphasis on the drawdown evaluation for wells within fracture networks smaller than the representative elementary volume (rev)

##### Abstract

Fractured aquifers are characterized by the fact that most of the water flows along
fractures, faults, open bedding planes, or other geological features. These features are
embedded in a matrix that has either porous nature, like in sandstone, or is almost
impermeable (inert), as in the case of granite.
It is often observed that in fractured aquifers the measured air lift yield is a strong
overestimation of the long-term sustainable yield of the well. The explanation for this
effect is that the water extracted initially is provided by a geological feature that is
high yielding but limited in its extension, while the long-term sustainable yield is the
response of the matrix. Such a geological feature can be among others, a single
vertical fracture or a fracture network, which usually acts as a preferential flow path.
Pumping tests in primary and secondary aquifers are widely used by the ground
water industry because they provide important information on the reservoir and the
well performance. Various researches in the oil and ground water industries have
found that the presence of single preferential flow paths results in characteristic
drawdown curves. However, a lack of research is encountered, when it comes to more
complex fracture networks. This work investigates the behavior of drawdown curves
in fracture set ups below the representative elementary volume (REV), which is
defined as the smallest volume of aquifer that can be considered as a homogeneous
fractured unit. Emphasis is given to the importance of a thorough diagnosis of the data
to be able to adequately estimate the aquifer properties.
Chapter 2 of the present work summarizes the basic knowledge on ground water
flow in fractured reservoirs, where the REV, fracture connectivity, and conductivity
contrast between fracture and matrix are defined and explained. Thereafter, the flow
behavior in fractured media (linear, radial, and spherical) are described. This chapter
ends with the review of various well and reservoir boundary effects, such as well bore
storage, well bore skin, partial penetration skin, fracture skin, pseudo-skin, fracture
dewatering, and reservoir boundaries.
Chapter 3 gives practical advice for the planning and performance of pumping tests
and stresses the necessity of time correction in the case of variable discharge rate
during the test. The importance of the pseudo-skin effect originated by the presence of
a single vertical fracture is highlighted. It is shown that pseudo-skin effects are the
reason for the apparent dependence of the storage coefficient (S) on the distance
between the observation borehole and the single vertical feature, when the common
evaluation methods are used for the estimation of S. Furthermore, the radial-acting
flow phase and in relation to the REV is explained. This chapter ends with the
description of various diagnosis tools, which allow, among others, the determination
of the flow phases from pumping test data influenced by preferential flow paths.
These tools are included in the computer program Test Pumping Analysis (TPA),
which was compiled under the umbrella of this thesis. It is explained that data
consistency can be rapidly analysed with the comparison between drawdown and
recovery data and any discrepancy must be investigated additionally. The use of
straight-lines, especial plots, and curves derivatives is described.
Chapter 4 presents the most important analytical and semi-analytical available
solutions for the analysis of pumping test data in fractured aquifers, which are
included in TPA. For each case, the mathematical solution is first described. The
influence of well bore and reservoir effects are explained using TPA, based on
theoretical and field examples. Special emphasis is given to the various skin analyses
and to the possible misinterpretation of drawdown curves. The solutions presented
are: double porosity model of Moeneh (1984)
• single vertical fracture with infinite conductivity and finite extent of Gringarten et
al. (1974)
• single vertical fracture with finite conductivity and finite extent of Cinco-Ley et
al. (1978)
• single vertical dike with finite conductivity and infinite extent of Boonstra &
Boehmer (1986)
• bedding plane fracture with infinite conductivity and finite extent of Gringarten &
Ramey (1974)
• generalized radial flow model for fractured reservoirs of Barker (1988)
Chapter 5 investigates more complex fracture situations with help of numerical
modelling based on the Darcian law. Synthetic pumping tests are simulated and their
drawdown behavior is analysed. The single vertical fracture case is first computed to
ensure that the model set up leads to the analytical and semi-analytical solutions of
Gringarten et al. (1974) and Cinco-Ley et al. (1978), respectively. To investigate the
influence of wider fault zones, which are assumed as a homogeneous fractured zone,
faults with increasing width are modelled. It is found that:
• for large storage capacities and finite conductivity, the drawdown at early time
shows a radial-acting flow phase within the fault, which could be easily
misinterpreted as double porosity. However, this effect occurs most likely under
unconfined conditions
The model is then modified to include parallel vertical fractures. It is found that:
• parallel vertical structures with infinite conductivity have no influence on the
drawdown at the well
• parallel vertical structures with finite conductivity show minor influences at early
time, if the dimensionless relative separation Sr (Sr = df/xf) is less than 0.125
Thereafter, the model is modified to represent a crossed fracture case and a bend
fracture case, both vertical and with infinite conductivity. The computed drawdown
differs significantly from the drawdown measured in the single straight fracture. It is
found that:
• this drawdown is comparable to that obtained with the uniform flux solution of
Gringarten et al. (1974), although the influx along the fracture is not uniform.
However, the authors mentioned that some field data from hydraulic fracturing fit
better to the uniform flux solution. The results of this work give reasons to believe
that such field data are attributed to more complex fracture networks similar to
those studied here.
The horizontal bedding plane case is also investigated. First, the model is run to
compute the infinite and finite flux solutions from Valkó & Economides (1997). The
modelled curves fit adequately the data for their solutions, although a labelling error
in the published data is identified. Further, the influence of the fracture geometry is
analysed. It is found that:
• horizontal penny-shape fractures and square features with equivalent influx area
have the same drawdown
• rectangular horizontal features have a significant influence on the drawdown
behavior
The investigation of parallel bedding planes shows that:
• the shape of the drawdown curve in parallel horizontal fractures is equivalent to
that of the single horizontal bedding plane. Therefore, without additional on-site
investigations (e.g. fluid logging or flow meter measurements) it is impossible to
determine whether the drawdown belongs to a single fracture or to a series of
parallel features
• The analysis of drawdown curves produced by parallel horizontal fractures using
type curves for single horizontal fractures leads to an over estimation of the
fracture radius. This effect is important among others, for the design of protection
zones
Finally, intersections of a single vertical fracture and a single horizontal bedding
plane are modelled. It is found that:
• the obtained drawdown curves could be misinterpreted with drawdown curves of
single cases. Therefore, it is concluded that additional information is necessary to
correctly identify the geological set up. This issue is highly important for both the
design of well protection zones and the estimation of the transport time

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