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101
Why Do We Test Wells?
The main reason for testing anexploration well is to take a fl uid 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 fl uid 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 fl owing 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
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 fl ow period and the pressure p(Δt=0) at the start of the fl ow period (a fl ow 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-Well Test Analysis in Practice
Alain C. Gringarten,
Imperial College London
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 Scientifi c Software-Intercomp; Schlumberger; and the French Geological Survey in Orléans, France. Gringarten’s research interests include fi ssured fl uid-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 certifi cate 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.
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.
log graph. In such a graph, various fl ow 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 fl ow regimes can be verifi ed on fl ow-regime-specialized graphs by plotting Δp=[p(Δt)−p(Δt=0)] vs. f(Δt) on a Cartesian graph (specialized analysis), where f is a fl ow-regime-specifi c
function. f(Δt) is equal to Δt for wellbore storage and pseudosteady-state fl ow, Δ t for linear fl ow, 1 Δ for spherical fl ow, t log(Δt) for radial fl ow, 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 fl ow-regime-specifi c superposition time,
[(q
i–q
i–1)/(q
n–1–q
n)]
f(
1 1 1 1 n n j i − − = = Δtj+Δt)
−f(
Δt),
∑
∑
on a Cartesian plot (Horner analysis).
f(Δt) is the same as for specialized analyses. In both specialized and Horner analyses, a straight line is obtained where the fl ow regime dominates and the straight-line slope and intercept provide the well and reservoir parameters that control this fl ow regime.
What Is a Well Test
Interpretation Model?
The interpretation model is made of the combination of the individual fl ow regime components that dominate the fl ow 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
Fig. 1—Log-log and specialized analysis.
Δ
p
=|
p
(
Δ
t
) –
p
(
Δ
t
=0)|
Δ
t
=
t
(
Δ
t
) –
t
(
Δ
t
=0)
Time from the start of the test
Rat
Δt1 Δt2 ∆ti Δtn–1 tp= Σjn=i–1 Δtj tp+Δt ΔtPr
essure
Time
p
i Δpf
(
Δ
t
)
Specialized analysis
m
derivative
lolog
Δ
t
Log-log analysis
q
1q
iq
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p
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Δ
t
= 0)|
Δ
t
=
t
(
Δ
t
) –
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(
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Time from the start of the test
Rat
e
Δt1 Δt2 ∆ti Δtn–1 tp= Σjn–1 =i Δtj tp+Δt Δtq
nq
2 Flow Period nPr
essure
Time
p
ip
Horner analysism
p*
(
) (
)
[
q q q q]
f(
nj tj t)
f( )
t n i i− i n − n∑
Δ +Δ − Δ∑
− = − = − − 1 1 1 1 1 1Tech
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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.
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 effi ciently. In this respect, the derivative log-log analysis method is much better than the log-log pressure analysis method. Both are signifi cantly better than straight-line-based techniques used in specialized and Horner analyses. Specifi cally, straight-line techniques, although simple to use, are poor at selecting the very straight lines on which they are to beapplied. 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 fl ow regime being analyzed). This is why, when powerful personal computers became
available, the derivative approach superseded log-log pressure analysis, which before had superseded straight-line techniques. This does not mean that new techniques have eliminated previous ones. These are still used, but they are Homogeneous Heterogeneous – 2-Porosity – 2-Permeability – Composite
RESERVOIR
BEHAVIOR
Wellbore Storage Skin Fractures Partial Penetration Horizontal WellNEAR-WELLBORE
EFFECTS
BOUNDARY
EFFECTS
Specified Rates Specified Pressure Leaky BoundaryEARLY TIMES MIDDLE TIMES LATE TIMES
Wellbore Storage Skin Fractures Partial Penetration Horizontal Well NEAR-WELLBORE EFFECTS Specified Rate Specified Pressure Leaky Boundary BOUNDARY EFFECTS Homogeneous Heterogeneous – 2-Porosity – 2-Permeability – Composite RESERVOIR BEHAVIOR
IDENTIFICATION
VERIFICATION
CONSISTENT WELL TEST INTERPRETATION MODEL YES DATA LATE TIMES MIDDLE TIMES EARLY TIMES ANOTHER MODEL? NO ENDWELL TEST INTERPRETATION MODEL
CALCULATE MODEL BEHAVIOR COMPARE WITH DATA CONSISTENT? NO YES
Fig. 3—Components of the well test interpretation model.
integrated in a methodology that allows them to be applied correctly.
Pressure derivatives combine great diagnosis and verifi cation capabilities with the accuracy of straight-line methods. Derivative shapes for various fl ow regimes at early, middle, and late times in a fl ow period are distinctly different, which is not necessarily the case with pressure change. For instance, spherical fl ow 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 identifi ed: 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 fl ow. Others are more diffi cult to see and may affect the analysis. These include end effects (if the last pressure in a fl ow period is too high or too low, the derivative shows an upward or downward
in the reservoir. But the most impact by far comes from the rate history. Oversimplifying the fl ow-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 fl ow 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 104
Fig. 5—Example of deconvolution.
Pr es su re , p si a 0 1,000 2,000 3,000 0 10,000 20,000 30,000 40,000 50,000 60,000
Elapsed Time, hours
0 20 40 60 80 100 120 140 160 FP 203 FP 386 FP 186 Measured rates Analysis rates T o ta l R a te , M M scf /D
Elapsed time, hours
P re s su re D e riv a tiv e , p s i FP66 FP186 FP203 FP386 Deconvolved Derivative 102 10 1 10–1 10–2 10–3 10–3 10–2 10–1 1 10 102 103 104 105 (a) (b)
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hours. This could not be seen from the longest buildups, limited to 103 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 signifi cant improvements in the identifi cation 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 quantifi ed from well test analysis with more-complex interpretation models that represent geological bodies more closely. For instance, vertical permeability and meander information in a fl uvial meandering channel can be found from well test data in the transition between radial fl ow in middle times and channel fl ow 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 mini-DSTs for sampling, permeability, and initial reservoir pressure; core and log analyses for permeability; and geology, seismic analysis, and geochemistry for reservoir heterogeneities, boundaries, and fl uid 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 fl uid samples required for sizing surface processing facilities or for determining the quality of the fl uids 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.
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 fl owmeters 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 5simply 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 diffi cult 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 fi elds we have in the last few years because
they would not allow their exploration teams to work in such a free-fl owing way. However, they are our ideal partners. They have many things we do not have, including massive fi nancial clout.
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 sacrifi ce 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 offi ce but are also happy to go back home. I
sometimes send people home from the offi ce 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?
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
