Well Test Analysis with PIE. Part 4. Analysis Plots in PIE
M. Levitan, M. Wilson
Part 4
Analysis Plots in PIE
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Well Test Analysis with PIE. Part 4. Analysis Plots in PIE
M. Levitan, M. Wilson
4. Analysis Plots in PIE
There are a number of analysis plots provided by PIE. Analysis plots are accessed from
Plots menu. Analysis plots are used to study the character of transient pressure behavior
and to translate this behavior into corresponding reservoir and well characteristics. In
order to highlight and identify specific features of transient pressure behavior during the
test some of these plots use special transforms applied to horizontal and vertical axes of
the plot. Analysis plots are not just graphical representation of the test data. Each
analysis plot in PIE comes with its own set of tools specific to the plots that are used to
translate the features of the pressure behavior into reservoir-well characteristics. The
tools are located in the Graphics Functions panel. The set of tools that appear in the
panel is controlled by user. Some new tools can be placed into the panel depending on
what task a user attempts to achieve. There are a number of items on the Analysis menu
that control the tools on the Graphics Functions panel.
A user selects analysis plot to be displayed from the Plots menu. Several analysis plots
can be displayed in PIE at the same time. However, there is only one Graphics Function
panel that displays the tools of just one plot. It means that among several plots displayed
there is one plot that is an active plot. This plot is identified by the bright bar on the top
of the plot window. To change the focus to another plot and make this other plot active
one needs to click anywhere within the body of this plot.
Among the analysis plots provided by PIE, the most often used plots are: Data Plot,
Superposition Plot, and Derivative Plot.
4.1 Data Plot
Well test data may consist of a sequence of flow periods. A subset of flow periods of the
test sequence may be selected for analysis. This selection is done by using the Period for
Analysis function on the Analysis menu. Normally, the sequence of flow periods
selected for analysis begins from the first period of the test sequence and ends at some
specific flow period during which the transient pressure behavior is to be investigated.
The pressure and the rate data from the sequence of flow periods selected for analysis is
displayed on Data Plot. PIE uses uniform (Cartesian) scales for the time and pressure
axes on this plot. The pressure data during the last flow period displayed on this plot
appear on superposition and derivative plots if these plots are activated from the Plots
menu.
4.2 Superposition Plot
Superposition plot displays the pressure data from the last flow period presented on Data
plot. Superposition plot presents the pressure behavior as pressure vs. superposition time.
The superposition time here is determined based on the sequence of flow periods that
appear on the corresponding Data plot.
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Well Test Analysis with PIE. Part 4. Analysis Plots in PIE
M. Levitan, M. Wilson
Superposition plot is a generalization of the semi-log plot for single flow constant rate
drawdown test to multi-rate test sequences. It is also a generalization of Horner plot used
for analysis of two-flow period drawdown-pressure buildup test sequences.
The pressure behavior that is associated with radial flow geometry near the well appears
on this plot as straight line. The slope of this line is inversely proportional to the
formation permeability-thickness characteristic. This line also defines the well skin
factor.
Superposition time decreases as time increases during pressure buildup period. As a
result, when presented on superposition plots the pressure builds up from right-to-left.
This is not the case for drawdown periods.
In infinite reservoir, extrapolation of the radial flow analysis line trend to infinite time
gives the initial reservoir pressure p i .
4.3 Derivative Plot
Modern well test analysis originates with invention of derivative plot. Derivative plot is
associated with Dominique Bourdet who first introduced it in mid-eighties. Derivative
plot demonstrates the same pressure transient behavior as Superposition plot. However,
Derivative plot is much more sensitive and is able to identify very small changes in the
transient behavior that can not be spotted on Superposition plot. In a way, it serves as a
magnifying glass allowing us to see the things that could not be seen by naked eye. In
addition, the effects of boundaries, heterogeneities, of the geometry of well completion
produce characteristic features on Derivative plot and for this reason derivative plot
became a main diagnostic tool for well test analysis.
Derivative plot is a log-log plot. It means that it uses logarithmic scales along horizontal
and vertical axes. Derivative plot presents two curves reflecting two different
characteristics of pressure behavior during a flow period. The first curve presents  p vs
t , where p is the pressure change from the last pressure value of the previous flow
period and t is the time from the start of the current flow period. The second curve
presents the value of local slope of the pressure data on superposition plot as function of
t . The slope of pressure curve on Superposition plot is equal to the derivative of
pressure with respect to superposition time. Hence, the second curve on Derivative plot
is called derivative curve. One has to remember, however, that this is not the derivative
with respect to time but with respect to superposition time and as such it depends on the
well rate history accounted for in the superposition time.
There is one more specific enhancement in the way how PIE presents these two curves on
Derivative plot. PIE normalizes both  p and derivative by the rate. In the case of a
pressure build-up period, this rate is the rate during the preceding flow period. This
normalization is very important because it allows one to compare the characteristic
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Well Test Analysis with PIE. Part 4. Analysis Plots in PIE
M. Levitan, M. Wilson
features of transient pressure behavior during different flow periods by comparing the
corresponding derivative plots (by overlaying the plots).
A constant slope trend on a superposition plot reflecting radial flow near the well
translates into constant derivative and shows as the horizontal derivative trend on a
corresponding derivative plot. The pressure behavior associated with well-bore storage
effect shows as characteristic hump of the derivative curve at early time. Normally,
following this well-bore storage hump the derivative stabilizes at some constant value
reflecting radial flow near the well. The stabilized derivative reflects the permeabilitythickness characteristic, kh of the formation. The value of the derivative is inversely
proportional to the value of kh .
The vertical separation between the derivative and the  p curves reflects the value of
skin factor. The larger the skin the larger is the vertical separation between the two
curves.
Effects of boundaries cause the derivative curve to deviate upward at later time. The
form of this late-time upward deviation depends on specific configuration of reservoir
boundaries. Geometry of well completion and reservoir heterogeneities also affect the
shape of the derivative curve.
Derivative plot displays differential characteristics of transient pressure behavior (  p ,
and derivative) and as such it does not depend on the absolute value of pressure.
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