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Tech 101
Well Test Analysis in Practice
Alain C. Gringarten, Imperial College London
Why Do We Test Wells?
The main reason for testing an
exploration well is to take a fluid sample.
Further reasons are to measure the
initial pressure, estimate a minimum
reservoir volume, evaluate the well
permeability and skin effect, and
identify heterogeneities and boundaries.
Testing producing wells aims at
verifying permeability and skin effect,
identifying fluid behavior, estimating the
average reservoir pressure, confi rming
heterogeneities and boundaries, and
assessing hydraulic connectivity.
How Do We Test Wells?
We create a step change in rate—for
instance, by closing a flowing well or
an injection well (buildup or falloff,
respectively); by opening a well
previously shut in (drawdown); or by
injecting in a well previously closed
(injection). This rate change creates a
change in pressure in the same well
(exploration or production testing) or in
a different well (interference testing).
In layered reservoirs, there is also a
change in the rates from each individual
layer, which can be measured with a
production logging tool (PLT).
A change in rate can be created at
the surface by shutting or opening the
master valve or at the bottom of the well
with a special downhole shut-in device.
Wellhead shut-in is commonly used in
wells already in production, whereas
bottomhole shut-in is standard practice
after drilling [a drillstem test (DST)].
The way the rate signal is created is not
important as far as well test analysis
is concerned. The same interpretation
This article contains highlights of paper SPE
102079 “From Straight Lines to Deconvolution:
The Evolution of the State of the Art in Well Test
Analysis,” SPEREE (Feb. 2008), 11-1, pp 41–62.
10
methods are used for production tests,
DSTs, analysis of wireline formation tests,
and now for testing while drilling. What is
most important for analysis is the quality
of the rate input signal—which must be
of the proper shape and duration—and
the quality of the measured pressure
output signal.
How Do We Interpret Well Tests?
We try to identify an interpretation model
that relates the measured pressure
change to the induced rate change and
is consistent with other information
about the well and reservoir. This is
an inverse problem without a unique
solution. Petroleum professionals are
confronted with the inverse problem
whenever they interpret data and
model processes (for instance, in
geophysical interpretation, in geological
interpretation, in log interpretation,
and in the reservoir modeling aspect
of reservoir simulation). The problem
of nonuniqueness is well recognized
in the oil industry and accounts for the
increasing use of stochastic modeling
techniques, which aim at providing
alternative equiprobable representations
of the reservoir to capture the
uncertainty associated with predictions.
Nonuniqueness decreases as the amount
of information increases.
As illustrated in Fig. 1, there are
two possible signals we can use to
identify an interpretation model. One
is the difference Δp=[p(Δt)−p(Δt =0)]
between the pressure p(Δt) at an
elapsed time Δt in a flow period and the
pressure p(Δt =0) at the start of the flow
period (a flow period is a period during
which the rate is constant). This signal
and its derivative with respect to the
superposition time are plotted on a log-
Alain C. Gringarten ([email protected]) holds the
Chair of Petroleum Engineering at Imperial College London,
where he is also director of the Centre for Petroleum Studies.
Before joining Imperial in 1997, he held a variety of senior
technical and management positions with Scientific SoftwareIntercomp; Schlumberger; and the French Geological Survey
in Orléans, France. Gringarten’s research interests include
fi ssured fluid-bearing formations, shale gas, fractured wells,
gas condensate and volatile oil reservoirs, high and low
enthalpy geothermal energy, hot dry rocks, and radioactive waste disposal. He is a
recognized expert in well test analysis and received the Society of Petroleum
Engineers (SPE) Formation Evaluation Award for 2001, the 2003 SPE John Franklin
Carll Award, the 2005 SPE Cedric K. Ferguson certificate for the best technical paper
published in 2004, and the North Sea SPE Regional Service Award for 2009.
Gringarten was an SPE Distinguished Lecturer for 2003–04. He has published more
than 90 technical papers and was responsible for many advances in well test
interpretation. A member of SPE since 1969, he was elected a Distinguished Member
in 2002 and an Honorary Member in 2009. Gringarten has chaired or organized many
SPE Advanced Technology Workshops, and is currently a member of the following
SPE International committees: R&D; Information and Management; Carll-Uren-Lester
Awards; Honorary and Distinguished Members Selection Committee; and SPE PE
Faculty Pipeline Award Committee; and was 2011 chair of the SPE Talent Council. He
holds MS and PhD degrees in petroleum engineering from Stanford University and an
engineering degree from École Centrale Paris, France.
qi
Rate
q2
Δt 1
Flow Period n
q n–1
pressure
qn
log Δp
q1
Δt
Δt 2
∆t i
derivative
Δt n–1
Time from the start of the test
log Δt
tp = Σ jn–1
=i Δtj
tp+Δt
Log-log analysis
pi
Pressure
Δp
m
Δp=|p(Δt) – p(Δt =0)|
Time
Δt = t(Δt) – t(Δt =0)
f (Δt)
Specialized analysis
Fig. 1—Log-log and specialized analysis.
log graph. In such a graph, various flow
regimes (e.g., linear, bilinear, spherical,
radial) exhibit distinctive shapes and
occur at different times, and this is used
to identify them (log-log pressure and
derivative analysis). The existence of
the flow regimes can be verified on
flow-regime-specialized graphs by
plotting Δp=[p(Δt)−p(Δt =0)] vs. f (Δt) on
a Cartesian graph (specialized analysis),
where f is a flow-regime-specific
q1
function. f (Δt) is equal to Δt for wellbore
storage and pseudosteady-state flow, Δt
for linear flow, 1 Δt for spherical flow,
log(Δt) for radial flow, etc.
The other signal is [pi−p(Δt)], where
pi is the initial pressure (Fig. 2). Because
pi is usually not known, the signal is
actually p(Δt), to be plotted against a
flow-regime-specific superposition time,
n −1
n −1
∑ i =1 [(qi –qi –1)/(qn –1–qn )]f ( ∑ j =1 Δtj +Δt)−f (Δt),
on a Cartesian plot (Horner analysis).
qi
q n–1
Rate
q2
Δt 1
Δt 2
∆t i
p*
Δt n–1
i
− qi −1 ) (qn−1 − qn )] f
(∑
n−1
j =1
Horner analysis
Fig. 2—Horner analysis.
)
Δt j + Δt − f (Δt )
Pressure
n−1
tp = Σ jn–1
=i Δtj
pi
m
p
i =1
qn
Δt
Time from the start of the test
∑ [(q
Flow Period n
tp+Δt
pi – p(Δt = 0)|
Time
Δt = t(Δt) – t(Δt =0)
f (Δt) is the same as for specialized
analyses. In both specialized and Horner
analyses, a straight line is obtained
where the flow regime dominates and the
straight-line slope and intercept provide
the well and reservoir parameters that
control this flow regime.
What Is a Well Test
Interpretation Model?
The interpretation model is made of the
combination of the individual flow regime
components that dominate the flow
period at different times. The number
of interpretation model components is
limited to three types (Fig. 3), namely
• The basic dynamic behavior of the
reservoir during middle times, which
is usually the same for all the wells in a
given reservoir
• Near-wellbore effects at early times
resulting from the well completion that
may vary from well to well or from test
to test
• Boundary effects at late times,
determined by the nature of the reservoir
boundaries, which is the same for all
the wells in a given reservoir, and by
the distance from the well to these
boundaries, which may differ from well
to well
Although there are few possible
interpretation model components, their
Vol. 8 // No. 2 // 2012
11
Tech 101
combination can yield several thousand
different interpretation models to
match all observed well behavior. The
challenge for the well test interpreter
is to diagnose from the observed well
behavior which components should be
included in the interpretation model. A
schematic of the complete interpretation
process is shown in Fig. 4.
NEAR-WELLBORE
EFFECTS
RESERVOIR
BEHAVIOR
BOUNDARY
EFFECTS
Wellbore
Storage
Homogeneous
Specified
Rates
Skin
Heterogeneous
Specified
Pressure
– 2-Porosity
Leaky
Boundary
Fractures
Partial
Penetration
What Is the Difference
Between the Various
Interpretation Methods?
The main difference between the
available analysis techniques is their
ability to diagnose and verify an
interpretation model efficiently. In this
respect, the derivative log-log analysis
method is much better than the log-log
pressure analysis method. Both are
significantly better than straight-linebased techniques used in specialized
and Horner analyses. Specifically,
straight-line techniques, although simple
to use, are poor at selecting the very
straight lines on which they are to be
– 2-Permeability
– Composite
Horizontal
Well
EARLY TIMES
MIDDLE TIMES
LATE TIMES
Fig. 3—Components of the well test interpretation model.
applied. And, once a straight line has
been selected, there is no rule to indicate
if it is indeed the correct one (i.e., the
one corresponding to the flow regime
being analyzed). This is why, when
powerful personal computers became
IDENTIFICATION
available, the derivative approach
superseded log-log pressure analysis,
which before had superseded straightline techniques. This does not mean that
new techniques have eliminated previous
ones. These are still used, but they are
VERIFICATION
DATA
EARLY TIMES
Wellbore Storage
Skin
Fractures
Partial Penetration
Horizontal Well
NEAR-WELLBORE
EFFECTS
MIDDLE TIMES
LATE TIMES
Homogeneous
Specified Rate
Heterogeneous
Specified Pressure
– 2-Porosity
– 2-Permeability
– Composite
Leaky Boundary
RESERVOIR
BEHAVIOR
BOUNDARY
EFFECTS
WELL TEST INTERPRETATION MODEL
NO
COMPARE
WITH
DATA
CONSISTENT?
YES
CONSISTENT
WELL TEST
INTERPRETATION
MODEL
CALCULATE
MODEL
BEHAVIOR
ANOTHER
MODEL?
NO
Fig. 4—Interpretation model identification process.
12
END
YES
4,000
200
FP 66
180
FP 186
FP 203
160
Pressure, psia
140
120
2,000
100
FP 386
80
60
Total Rate, MMscf/D
3,000
1,000
40
20
Measured rates
Analysis rates
0
0
10,000
20,000
30,000
40,000
50,000
0
60,000
Elapsed Time, hours
(a)
102
FP66
FP186
FP203
FP386
Pressure Derivative, psi
10
1
10–1
10–2
Deconvolved Derivative
10–3
10–3
10–2
10–1
1
(b)
10
102
103
104
105
Elapsed time, hours
Fig. 5—Example of deconvolution.
integrated in a methodology that allows
them to be applied correctly.
Pressure derivatives combine great
diagnosis and verification capabilities
with the accuracy of straight-line
methods. Derivative shapes for various
flow regimes at early, middle, and late
times in a flow period are distinctly
different, which is not necessarily the
case with pressure change. For instance,
spherical flow is easy to identify on the
derivative, whereas it is invisible on the
pressure drop curve. The main drawback
of derivatives, however, is that, contrary to
pressure data, they are not measured but
must be calculated. A number of factors
can affect the shape of the derivative
curve and, therefore, mislead the
interpreter. Some can be easily identified:
derivation algorithm, sampling frequency
of the data acquisition, gauge resolution,
time or pressure errors at the start of
the period, erratic raw data points, or
multiphase flow. Others are more difficult
to see and may affect the analysis. These
include end effects (if the last pressure
in a flow period is too high or too low, the
derivative shows an upward or downward
trend, which must not be confused with
a boundary effect), phase redistribution
in the wellbore, and a pressure trend
in the reservoir. But the most impact
by far comes from the rate history.
Oversimplifying the flow-rate history can
jeopardize the reliability of the pressure
derivative as a diagnostic tool (this holds
true also for Horner analysis).
What Is Well Test Deconvolution?
Deconvolution transforms variable-rate
pressure data into a constant-rate initial
drawdown with a duration equal to the
total duration of the test and directly
yields the corresponding pressure
derivative, normalized to a unit rate. This
derivative is free from the distortions
caused by the pressure-derivative
calculation algorithm and from errors
introduced by incomplete or truncated
rate histories.
Deconvolution is not a new
interpretation method but rather is a new
tool to process pressure and rate data
in order to increase the amount of data
that can be analyzed with derivative,
pressure, and straight-line analyses. The
gain is clearly greater in long tests, such
as with permanent downhole pressure
gauges, in which the total test duration is
one or two orders of magnitude greater
than the duration of the longest flow
period at constant rate. Deconvolution,
however, is also useful in short tests
such as DSTs because it gives access
to a greater radius of investigation
and enables differentiation between
true test behavior and artifacts of the
derivative calculation.
An example of deconvolution is shown
in Fig. 5. The red curve in Fig. 5b is
the deconvolved derivative obtained by
deconvolution of the entire rate history
shown in Fig. 5a. Its duration, equal to
the total production time, is two orders
of magnitude greater than the longest
buildups, represented by discrete
points in Fig. 5b. The shift between
the deconvolved derivative and the
buildup data in Fig. 5b is from the rate
history before the respective buildups.
In this particular example, the extended
derivative showed contribution to
production from a lower layer after 10 4
Vol. 8 // No. 2 // 2012
13
Tech 101
hours. This could not be seen from the
longest buildups, limited to 10 3 hours.
Deconvolution actually blurs the
difference between conventional well
test and production-data analysis.
During the course of many years,
several methods have been proposed to
analyze production data to extract all the
information that is usually obtained from
conventional well test analysis without
the constraint of shutting in wells. These
methods have been attempting to convert
variable rate and pressure into variable
pressure at constant rate or into variable
rate at constant pressure. Examples
are the decline curve analysis by use
of material balance time, the reciprocal
productivity index method, and the rate/
time type curve. The aim of all these
methods is achieved with deconvolution,
which produces much cleaner
transformed data and much better results
when estimating permeability and
distances to boundaries.
What’s Next?
Improvements in well test analysis will
essentially come from three areas:
richer signals (i.e., those containing
more information), better interpretation
techniques (providing significant
improvements in the identification and
validation of the interpretation model),
and more-complex models that represent
the geology better. Reservoir geology
is very complex, whereas well test
interpretation models are rather simple.
Some of the geological complexity
can be seen and quantified from
well test analysis with more-complex
interpretation models that represent
geological bodies more closely. For
instance, vertical permeability and
meander information in a fluvial
meandering channel can be found from
well test data in the transition between
radial flow in middle times and channel
flow at late times. The corresponding
data are ignored when the analysis
is performed with the usual simple
interpretation models.
Efforts to reduce costs and
environmental impact are also likely to
impose additional changes. Well testing
in exploration and appraisal wells has
become increasingly unpopular in recent
years. Reasons include cost, safety,
and environmental impact. Well testing
also has become rare in production
wells because of the potential revenue
loss during buildups. Whether suitable
alternatives can be found is the subject
of regular debate. Alternatives to DSTs
include wireline formation tests and miniDSTs for sampling, permeability, and
initial reservoir pressure; core and log
analyses for permeability; and geology,
seismic analysis, and geochemistry for
reservoir heterogeneities, boundaries,
and fluid contacts. However, there is no
suitable well-testing replacement for
fi nding skin (well damage), effective
permeability, and hydraulic connectivity
throughout large reservoir volumes
and obtaining the large fluid samples
required for sizing surface processing
facilities or for determining the quality of
the fluids from a commercial viewpoint.
Production tests, on the other hand, tend
to be replaced by continuous recording
with permanent pressure and rate
gauges in production wells. These data
are particularly well suited for analysis
with deconvolution.
they would not allow their exploration
teams to work in such a free-flowing way.
However, they are our ideal partners.
They have many things we do not have,
including massive fi nancial clout.
sometimes send people home from the
office if I think they are working too late.
Life is very short. Do not stick your head
in the books all the time. You have to
enjoy yourself. You do not want to get to
the age of 60 and think: What I have done
with my life?
Conclusions
Well test analysis has come a long
way since the 1950s when the
interpretation methods on the basis of
straight lines gave unreliable results.
We now have a methodology that
provides repeatability and techniques
with derivatives and deconvolution that
enable a high level of confi dence in
interpretation results.
It can be safely predicted that the
importance of well test analysis in
reservoir characterization will continue
to increase as new tools such as
permanent downhole pressure gauges
and downhole flowmeters become more
widely used and as the scale relationship
with the interpretation of other data from
geophysics, geology, and petrophysics
becomes better understood. TWA
Interview... Continued from page 5
simply looking at the next step they have
to follow to get from A to B. I challenge
processes all the time.
What is the main competitive
advantage of independent-based oil
companies vs. the majors?
The majors are very different. We
only compete with the majors’ E&P
divisions. Their E&P divisions are small
parts of huge organizations with a lot
of bureaucracy. It is very difficult for
them to compete with us. We are a small
organization based on what we do. They
cannot move at the pace we do. There is
no way they could have found the fields
we have in the last few years because
14
Free time is often scarce in a career
like yours. How do you keep a good
work and family life balance? Do you
have any advice for YPs?
Easy! Family comes fi rst. You have to
balance your personal life with your work
life. I would never sacrifice my family for
my business. Once you do that, you do
not have a clear head. You need to have
people who want to come to the office
but are also happy to go back home. I
Have you had professional
interaction with SPE in the past? Has
your workforce had the opportunity
to leverage company activities with
SPE expertise?
Personally, I haven’t, but I know that
our professionals here have had a lot of
interaction with SPE and they use it on a
regular basis. TWA