the role of downhole flow and pressure …€¦ · the role m townhole flow and pressure...
TRANSCRIPT
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The Role m Townhole Flow and Pressure Measurements inReservoir TesJngby J. Joseph and C.A. EhligEconomides, Schlumberger Well Services, and F. Kuchuk,Schlumberger-Doll Research
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ABS.TRACT INTRODUCTION
In practice, 8 reservoir teat that ia Succeeafully executed Dynamic downhole meaeurem enta such ae pru%mre, flow-
~ tos specikd p-k design will provide in- rate, deneity, and temperature, are acquired routinely by
terpretable remdte aatk&ng the teat objective. Uau- production logging and taating devices. Production leg-
ally, there ie an optimal teetdeeign among eeveral op- ging (or PL) surveys vemus depth under stabilized flow-
tionn which will rninimk the coet of the ted+ without ing or shut-in conditions are used to diagnoae and moni-
jeopardiaing the liieliiood that useful interpretatio~ will tor well performance.l Surveys veraua time with the tool
ertaue. Consequently, ae numerous testing con@urationa in a tied poeition in the wellbore yield the reservoir’s
have been introduced, it hae become neceeaary to develop trannient response pattern to rate perturbation. ThM
interpretation procedure whkh are M straightfonvard .responm ie used to help dellne the well/reservoir model
ae the conventional tecldquea while offering a more r~ and to quantify well performance. By production log test-
liable or retied anewer. The uae of downhole flow and ing ia understood the synergy between the ‘vemuE depth’
pmaaure measurements, or even downhole shut-in devices, and ‘vemua time’ acquisition schemes.
are caeea in point. With proper deeign, execution and in-The acquisition and interpretation procedure used in
terpretation, teste which employ theee configuration canthw paper have been extensively employed.2-* Experi-
provide reeemoir propeitiea that could be much more dt-
flcult to obtain by othe: meana.ence with wellbore hvrate and preaaure meaauremente
has meulted in the guideliiee offered herein for deeign-
One objective of this paper ie to present a methodolog~ ing teeti which maximiae the demiuble characteristic of
for reservoir t4M interpretation. Thw detiee the Me?. the downhole senaom. The purpoee of thii paper ia to
archy and sequence for employment of all analysia tech. d=uee when and why a particular teeting con@ration
niqueu, and ie intended to be general enough in ccncept ie preferable over another, and to define a sequence of
to accommodate any type of teat. Field exampke are ueed interpretation steps that accomodatee any type of teet
to illustrate the merits of speciilc acqukkion prccedurea, while ako provid~ a mechardam for consistently correct
aud ako how the methodology carI aid in acldeving the allalyeie.
●%st objective with conaiatent and coherent analyea.
Reference and illuatratiom at end of paper.
2 TNB ROLE OF ~- PLON At@ PRESSURE SPB 18379NBASUREMENTS IN RBSBRWIR TESTING
. .
Five field examples are presented in a progression at-
kmpting to provide ● rationale for why the meaeurs-
ments were conducted in s certain way and what wee
gained in the process. The tit example illuetmtes the
advantage of downhole shut-in during a buildup teett The
second example ehowe how convolved downhole flowrate
and pressure transients during ● buildup test revealed an
●arly-time he ~genous reservoir response that wee par-
tially masked by wellbore ntorage. In the thud example
the measurement of downhole tiowrate allowed straight-
forward anelyeie of data acquired during drawdown, even
though surface rate variation rendered the pressure vir-
tually uninterpretable by itself. The next example
demonstrates the added advantage of a production log
9owrate eurvey in analysis of a partially penetrated reaer-
Voir response. The fiwl example is ● layered reservoir
teat in which permeabilitiee and ekii were determined
for each of four sones in ● commingled well using produc-
tion kg testing measurements over ● total of 30 hours of
teat time.
TESTING AND iNTERPRETATION
METHODOLOGY
Formation evaluation by reservoir tasting has been an
active area of research and developinmt over the last 40
years. Scores of models, metho&, techniques end ap
plicatione that cover● wide spectrum of poaeibfitiee are
today ●vailable in the literature.* Because of new mea-
surements and interpretation techniques, it is neceesary
to erwxe that methods are used in the proper order, that
techniques are applied to jtiet those portions of data over.
which they are valid, and that checking and verification
procedures be instituted where necessary. This is clearly
a practical concern, 10 the objective being a ~yatematic
approach to overall test interpretation in such away that
the most eelf-coneietent and correct resulte would be ok
tainad. A logical sequence in interpretation m.othodo].
ogy, is presented in Figure L
The major entities identifiable in the flowchart of Fig. I
are
● data acquisition
● preprocessing for interpretation
● interpret at ion
● report of results
Thaee entities are gfo6af in the sense that they ●pply to
any reservoir test. Hence no distinction M made in prin-
ciple between eay a eurface shut-in test and ● DST, or
between a ‘single-layer’ teat and ● layered reeemoir teat
(LRT). This %on-dimensional’ or ‘generic’ feature of Fig.
1 in its totality is extremely attractive from several points
of view. Most importantly, it lays the blueprints for
streamlining an entire interpretation effort — from the
school of thought to software implementations thereof.
Data Acquisition
Acquisition procedures and hardware selection should
ideally be decided during the test design phase. The four
major types of raw data acquisition shown in Fig. 1 are
(a) downhole pressure and possibly surface flowrate
(b) downhole pressure (BHP) and downhole flowrate (BHF)
(c) liquid level monitoring for pumping wells
(d) production logging profiles
Configuration (a) has been the most popular for testing
in the traditional fashion (i.e., DST, elickline, etc.). In
(c) an acoustic device at the surface M used to moni-
tor the wellbore liquid level as a function of time during
buildup in a pumping well,~lJ2 Sonic travel-time infor-
mation thus gathered, plus wellhead pressure are con-
verted into BHP and BHF using an appropriate
transform,ll@~14 and theretiter follow the same path
through Fig. 1 M for configuration (b) above.
Although shown as a test acquisition configuration in Fig.
1, production logging is not usually considered as part
of i‘ s well test unless a layered reservoir test ls- 17 is
beink conducted. LRT’s are multi-rate tests in which
stationi+ry measurements are taken above each sone, and
PL surveys are made across all sones just before changes
in the surface rate. A test conducted in this fashion will
be presented with other field examples later. Stabilized
PL information can be ●n important and essential input
to any tranaient interpretation stream, as will be shown
in another of the examples presented. The stabilised PL
survey is an effective means for directly measuring the
actual flowing thickness ht. Quite often this value is
different from th~ formation thickness h read off the well
log. IMrthermore, PL information concerning the entry
points of various fluid phases into the wellbore, or the
S,= 18339 J. A. JOSkli, C. A. I$CONOMXDBS, AND F. J. XUCHUK 3
c
identification of the vertical flow regime, can be eaeential variable-rate dataeet, which is then analyzable es a drn-
to the transient acquisition e.trategy, and to the ultimate ple drawdown. It ie for thw reaao.. that the outlet km
interpretation. the deconvolution box in Fig. 1 k towwd the ‘prCSCUM-
Preproceuing for %terpretat50nonly’ side of the flowchart, since the rate-dependency of
the acquired dataset has been removed.ReaeIvoir teats are often conducted as a series of events
[static, thing) according to a specified flow sequence.FinaI1y, open hole logs, seismic data, or whatever ad-
During interpretation it maybe desirable to analyse just aditional inputs that could subsequently be used to help
particular event individually, or all events simultaneously.in constructing the final answer should be secured and
Fhrtharmore, interpretation techniques rarely invoke theinspected before entering into the interpretation phase
below.actual acquisition meaaure (e.g., time of job, pressure,
$pinner speed, sonic travel time) but rather some trane- Interpretation
formation thereof. It is for these reasons that preprocess- Ovewiew: It is at this point in the flowchart of Fig. 1ing, or data preparation for the main interpretation, is that a methodology really comes into effect. As seen in theneeded on every joblo figure, reservoir test interpretation begins with a diag-
Preprocaaaing phase can be compactly summarised ae fol- noatic plot (and there are several types of these). Entry
10W* into the next Jevel of interpret ●tion — the epecialiaed
analyde plot● Event lkfinition Baaed On Sequence Of Events
— is pern&ted oniy if the pertinent di-
●gnoetice were eeen at the diagnostic level above. If notSegmentation and Data Editting then type-curve analycis could be attempted, but re-
Data Reduction suits may not be conclusive.
● Data ‘Ihnsformations The procedure just described is repeated for all events
in the testing eequence. Sn this manner initial estimatesGeneration of interpretation functions for parametem are aecqred, and used aa startihg values
● QuaIity Control foi the next level of interpretation — history match-
It is usually poesible to correlate the squence of eventsing — should thw degree of eophutication be required.
with a recent flow history for the wekl so that superposi- Self-consistency checke and analyses are performed at this
tion effects can be rigorously accounted for. Some formstage, and the resultant ver~cation plots produced. In
of transformation is almost univemally applied before a some cases the interpretation is carried into a compl-
diagnostic plot can be viewed or a formation parametertion analysis and/or sensitivity study before genera-
can be computed. For example, the tranefonnation ~tion of the final results.
is known as the Horner time function. 18 Another popu- Diagnostic Plots: A diagnostic plot is a plot of mea-
lar transformation is the pressure derivative.19*20 Certain sured data from which a well or reservoir condition can
types of interpretation quality control are possible at this be inferred; it is also used to eetabliih the validity of a
point if needed, including smoothing for derivativea20 and particular specialised analysie. This implies that when-
tirna-error corrections.21 Further discussion of data pre- ever a new specialized analysin technique is proposed, its
processing is beyond t% scope of the present paper, but engineer should also define the accompanying diagnostic
some of the more commonly used transformations and to ensure that the method will be applied only when, and
corrections may be found in Refs. 21 snd 22, where, it is valid. Because of their generality, diagnostic
According to the flowchart in Fig. 1, all acquired tran-plots often serve more than, one purpoee.
sient data must paM through the preprocessing box. The StabiIiied PL surveys (pressure, flowrate, temperature
data which enter thie box from the right have both BHP and density profiles) constitute an important claea of di-
●nd BIfF channels present, and so deconvolution23 ie op ●gnostic plots.1 They can be used for the determination
tionally poaeible at this stage if desired. In principle, de- of fluid entry points, fiuid type and ito location in the
convolution produces a constant-rate response from the wellbore, and for assessing the effective flowing thickneae
4 THE ROLB OF 00NNNOLB - MO PRESSURE sPq 18379NRASURBNENTS IN RESBRVOIR TESTING ●
of an intarvala’.The latter application can help identify
poeaible partial penetration or completion effects.
Density measurements can be ueed to help determine ei-
ther an optimum tlowrate change or where a PL wnde
could be stationed downhole in order that the data acqui-
sition proceed in a predominantly single-phase environ-
ment.25 For example, gas wells frequently have standing
water present in the wellbore. The water may be Iiited
past the tool in response to a rate increase (see Figs. 14
and 22 in Ref. 25). Density di~gnosie immediately signals
the problem condition, which could be corrected in real
time by a change of rate or relocation of the tool. Finally,
continuous density recordings can be used as an on-site
aid in determining the ●ppropriate drawdown praeaure
(eg. above bubble or dew point pressure), and an indicw
tion that the pm-teat cleiump period can be terminated
(when the density drope to that of the raeervoir fluid).
The log-log praaaura and preaaura derivative praaantat-
ionlg’zo haa rccestly become ● standard diagnostic tool
used in transient analysie. When plotted on quare cy-
clee the data retaintheir aspect and visual diagnoaia of
●ven rather complicated well/raaervoir behaviour is pos-
sible. If, in addition to BHP the downhole flowrate ie also
available, then the appropriate diagnostic plot is the log-
log convolution derivative. 6*26 Th~ triple plot was drat
used in Ref. 26 on sandface flowrates computed based
on the constant storage assumption (it was inadvertently
termed ‘deconvolution’ by the authore).. Itu 6rat appli-
cation in connection with msa8ured downhole %owrates
wss in Ref. 6 (removing any assumptions concerning the
nature of the storage).
The ‘derivatives’ that are used in transient analysis can
be simply described ac the sfoge of the appropriate sp-
cialised plot, plotted vemu~ test time in log-log coordi-
nates. For example, in a buildup test the derivative is the
slope of the Horner plot; if there ~e multiple rate changes
before a buildup, the derivative is the dope of the gener-
alised Horner plot. Similarly, the convolution derivative
is the slope of the sandface rate convolution23*27 (sFRC)
plot.
The main use of the log-log diagnostic plot is to identify
flow regimee or well/reeervoir models that are present in
the transient so that the specialized analysie (usually per-
formed in another coordinate system) can be performed.
As an example, straight lines on ● Horner plot are valid
only where the derivative m fiat (constant). Similarly,
straight line analysia on the SFRCplot ia valid only where
the convolution derivative ie flat.
In addition m the identification of flow ragimea on a lo-
cal basis (e.g., a period of !inear flow in the data), log-
Iog diagnostic plots can provide ● global representation
of the entire system behaviour -- considerably enhanc-
ing the so-called pattern recognition problem28 with the
introduction of the derivative. 10*20Hence, wellbore dom-
inated flow, ‘homogeneous’ systems, heterogeneous (fis-
sured) and layered systems, channels and boundad sys-
tems, etc., may all be recognised by their characteristic
fingerprints on the log-log plot. Such diagnostics ~hould
either be supported by, or used to support external infor-
mation, especially from eeiemic and geological aourcea.
A log-log diagnostic pattern look-up table and general
diecuasion ie found in Ref. 29.
Specialhed Plotw A apecialiaad analysis technique ie
one that ie valid only for a specific flow regime or well/~
servoir geometry. Itusually yielda the moat reliable esti-
mate for the parameter(s) aceociated with that particular
90W regime. As a raault the majority of specialized anal-
vsis techniques are based on straight line picks over data
plotted in the appropriate coordinate system.
The fundamental tenet of the methodology depicted in
Fig. I is that the specialised plot for a particular con-
dition shall not be constructed unlwa the accompanying
diagnostic for that condition indicate its validity. Ra-
stated, a 8peciahed t8chn@e 8hould not be u8ed a8 h
own diagno8tak Specialised analyeaa, once deemed ap
plicable, are preferable to type-curve analyses for local
parameter estimation. Common examples of speciahsed
analyeie for radial flow are Horner,18 MDH30 and SFR@7
plots. Linear, hi-linear, spherical, peeudo-steady, and nu-
merous other flow regimae each have their corresponding
specialised plcts, which can be found elsewhere2i in the
literature.
Type-Curve Analysis: Typecurves are plots of aolu-
tiona to theoretical flow probleme used to repreeant real-
ity. Most often, but not always, the solutions are plotted
in log-log coordinate. Their role in reservoir description
has been continually refined once it wae realised that they
are no panacea.zl!3i!92 A eurvey and discuuion of diffar-
ent type-curves can be found in Refs. 21, 31 and 33.
s~ 18379 J. A. JOSEPH, C. A. BCONOHIDBS, AND F. J. KUCSUK 5
Withii the framework of Fig. 1, itiawan that the PM= There are some caaaa where it may not be poaeible to
farred interpretation hierarchy for properly designed and lower and anchor ● dowrthole shut-in device into ● com-
conductad teats ia the dhgnoatic plot, followed by sp- pleted production or injection well, due to restrictions
cialiaed analyaie plot.. Subeeqaently, type-cwwe match- in the wellbore or to the lack of ● landing nipple ●t the
ing can be used to dnd ● global model of the wel@servoir tubing shoe. Many of the newer well. are quipped with
eystem that rapreaants all of the tramieut data from ●oin- the aeceaaary hudwam for anchoring a downhole shut-
gle flow period. Choice of the model chould draw fmm in tool, without having to pull the tubing. Otherwise,
and consolidate all of the observations from external data surface shut-in may be utilised, This configuration can
(the box in Fig. 1 labeled Additional Info.), the diagnosis sometimes lead to complications during interpretation,
step, and computed parametem from epecialiaed analy- Wrticularly in producing welle where multiphase flow con-
sia. Refining the match may involve the use of nonlinear ditions are Iikely in the weIlbore.
optimization aad search achemesio’i’sa’There are clearcut advantage to employing the down-
Hiatory Matching and Verification: This portion of hole shut-in technique. Of foremost importance is the
Fig. 1 i. ueed for performing condatency checkiig ●nd fact that the portion of the buildup data dominated by
global analysia (a. in LRT) for an entire dataaet. wellbore storage effects will be considerably shorter. The
duration of thee. effect. ie proportional to the fluid-filledTkre are award ●pproached to verify an interpretation. “‘ volume below the shut-in valve. For example, in ● 10,000
One of the more popular ia by eelacting just one event ft well, if the top of the interval teated ia ●t 9500 ft andfrom a multi-rate teat aaquence, and rnodelling that event the shut-in valve ie located●t the same depth, then theby type curve matching ae diacueeed dxwe. ThM type storage coetlicient and hence the wellbore storage dur~curve [and its aaaociated parametem) are then extrap tion can be reduced by 95% (in the caee of aero skin).elated baaed on the principle of superposition into the
remaining events in the teat sequence that had not been Furthermore, the duration of wellbore storage ia propor-
analyaed. If the model were correct, then its extrapola- tional to the compresaibiity of the wellbore fluid, At
tion via superposition ohould provide a match for off of depths near the flowing interval, oil produced from an
the transient data. Strictly speaking, this ia not varifica- undematurated reservoir will be in the liquid phase. As
tion of the results of interpretation but rather a verifica- liquid rise. in the wellbore, the pressure may fall below
tion that an adequate model had been choeen. the bubble point and gas originally in solution will be
liberated. When the well ie flowing, produced gas can be
Statistical principles’ have alao been used to assess the mixed with the oil. Following shut-in, gas and oil phacesuncertainty of parameter eatimatea during history match- may segregate leading to a complex pressure behaviour
ing. Thm is a check on the goodnem of the interpretation called wellbore phase redistribution.ss
in terms of some chosen statistic. This approach is ex-
tremely powerful, and is the basis for nonlinear estima-Downhole shut-in is a technique for isolating the pres-
tion procedures used in type curve matchingio and thesure sensor from lengthy and complex wellbore transient
analysis of layered reservoir tests. 17behaviour, Distortion due to the fluid in the volume
below the shut-in vahre are likely to be manifest es a
SELECTED FIELD EXAMPLES (small) constant storage effect, and the compressibility
DiscussioIIof the fluid there will usually be much smaller than the
effective compressibility of the two-phase mixture above
the valve.The most effective way to conduct a buildup test in gen-
eral is to shut the well in near the sandface using a down- For formations in contact with a gas cap or active wa-
hole shut-in valve (wells produced or injected at very high ter drive, the effects of the constant pressure boundary
rates may require special consideration). Newly drilled may be apparent before the end of wellbore dominated
wells are usually tested in this way, with the shut-in valve transient behaviour.3G The same is also possible in com-
i duded in the drill stem test assembly. plex fauhed reservoirs, where the effect of a near planar
6 THE ROLE OF mNNNoLB PLm AND PRBSSURB SPB 18379MEASUREMENTS IN RBSERWIR TESTING #
“
boundary may be missed because of wellbore effects.s’
Dual porosity or layered eystem response patterns can
also be maeked by lengthy wellbore storage. For these
reaeons, there are some testswhich do not offkr conck-
sive results from pressure transient data recorded during
a surface shut-in.
If it is not possible to conduct a brildup test using down-
hole shut-in, one alternative is to measure downhole ilow-
mtea simultaneously with the pressure. Methods such as
convoIutiont27 deconvolution} 2s or rate-normaliiationge
can achieve an analogous reduction in the storage effect.
These techniques work well when the flowmeter sensor
can be positioned in a predominantly single phase envi-
ronment in the wellbore, and the dynamic range of the
measured flowrate is ●bove the threshold level for the
particular tool. Otherwise, special devices’ catering to
the very low flowrate ●pplicationsso may be required.
Several of theee pointe will be demonstrated by examples
later in the paper. Well, fiuid and rock properties for
Examplee 1-4 era contained in Table 1, and for Ex. 5 in
Table 3. Interpretation results for Ex. 1-4 are in Table
2, and for Ex. S in Table 4.
Example 1: Surface/Downhole Shut-Yn
The 6rst field example provides a comparison between
buildups on the same well conducted with surfms and
downhole shut-in. The jobs were performed in West
Africa. A 185 hour surface shut-in test was fimt run
on this producing oil well, Two yeare later a battery
operated downhole shut-in tool wae run in a nipple in
a standard production completion, providing the second
buildu~ of 91 hours duration. Pattern watertlooding was
ongoing in the field during the period between the two
tests.
The log-log diagnostic plot for the pressure transient re-
sponses from the two tests is presented in Figure 2, ‘lMan-
gles and squares represent the pressure change (Ap) and
its derivative for the surface shut-in, while the stare and
plus symbols show Ap and its derivative for the down-
hole shut-in. The data from each buildup have been nor-
malised by the surface flowrate immediately preceding
shut-in. Normalisation in this fashion facilitates superim-
posing all of the data on the same plot for identification
or comparison of the gross well/reservoir behaviour from
test to test.
The drst buildup is eeverly dietorted by wellbore stor-
●ge effects, which last some 100 hours. Them is also
evidence of changing storage probably caused by well-
bore phase segregation during the Scat hour of the first
buildup. Storage becomes essentially constant thereafter,
but another 99 houre are needed for a stabilization to
be evident in the derivative (thie would indicate infinite-
acting radial flow or 2ARF, in the formation).
The downhole shut-in teat, on the other hand, has es-
tablished lARF after just 1 hour of shut-in, based on ite
derivative (plus signs). The duration of wellbore domi-
nated ROWbehaviour was reduced by about 99% in this
exampJe. Whenever IARF ie diagnoeed from the deriva-
tive the pertinent specialized plot (in this case it is the
generalized Homer plot, which accounts for the flow hb
tosy of the well) should be used for reservoir parameter’
estimation.
Itisinstructive to examine the dataeeta on a modikl
MDHgO plot (normalii pressure change versus log At),
as shown in Figure 3. This confirms that the eemilog
slopes are roughly the same (implying the same M),
However, obaeswe that the line for the downhole shut-
in (stare) istarte approximately one cycle in time ●arlier
than for the surface shut-in cask. Fig. 3 also indicates a
slight increase in the slope of the downhole shut-in data
at later time, confirmed also in the diagnostic plot (Fig.
2).
The generalized Homer plot for each test is presented
in Figure 4.The permeability and skin computed from
each are about the same, The difference in the pressures
extrapolated over the two year period is attributed to
pattern water injection.
Deviation from the semi-log line at late time in the 8ec-
ond buildup could be caused by several factom, including
mobility or phase effects associated with the water injec-
tion, or, possibly, a fault. If it were caused by a fault
(and this is a distinct pomibility in this area), the same
deviation should have been evident on the first buildup
test. Hence, the mobility change due to the water in-
jection is the favored explrtnztion, since the oil bank ie
moving toward the producer, and would have been more
distant at the time of the fimt buildup test,
sp 18379 J. A. JOSEPH, C. A. ECONOMIDBS, AND F. J. KUCHUK 7
&emple % Pressure Buildup With Downhole
Flowrate
As a logical continuation of the iirst example, a buildup
test where downhole flowmtea were measured is next pre-
sented. This job was performed on a new gas well in
the thrustbelt region of western USA; tlie well had been
producing for 39,5 hours. A flow profile run just before
shut-in indicated that 20 ft of the 26 ft net pay inter-
val was flowing. This sandstone reservoir is located in a
river bed/channel type of depositional environment; an
active tectonic history has made fissuring (natural frac-
turing) and block faulting not at all uncommon in this
region. Openhole log interpretation revealed essentially
constant formation properties over the pay sone, and so
a singlelayer analysis was justifiable. However, the re-
siativity measured by the spherically focused log wee less
than the reeietivity from the induction log — a qualitative
and empirical indicator of nstrml fruturing.’”
The foregoing discussion is in line with the methodology
proposed in Fig. 1. Before even viewing the transient
diagnostic plots, external information had signalled the
poeeibtity that the dataaet may display the patterns of
● fissured-faulted ayekm. Such information is invaluable
in piecing together a reservoir model,
Following the production surveys, the PL sonde was posi-
tioned 37 ft above the sone of iutere8t before closing the
wel$ 270 ft of rathole remained below the tool, Based
purely on volumetric considerations a 97% reduction in
wellbore storage (volume above tool eliminated) should
be experienced. Fig. 5 presents the transient rate and
pres8ure acquired by a fullbore spinner and quart8 cry8tal
gauge respectively. Density measurements (not shown)
confirmed that the spinner was operating in a single-
phase wellbore environment during the test.
As seen in Fig. 6, when spinners are used during a
buildup test their readings are accurate initially, but then
decline rapidly as the afterflow decays. In this case the
8pinner reading went to zero after 6 minutes. This illus-
trates the problem with measuring transient downhole
flowrates during buildup tests. Once the spinner rota-
tion rate falls below the sensor thre8hold value, acquired
data are no longer accurate, and extrapolation is usually
necessary in practice.
The extrapolated flowrates are usually computed by ae-
suming that the wellbore fluid compressibility is constant
and of small magnitude.zs This is valid and practical as-
sumption, but the observation that often the most infor-
mative featurea in the convolved reeponee are computed
with extrapolated flowratee should be acknowledged. In
contrast, tlowrates measured during drawdown do not
●uffer from such &itations as the test time progresses,.
es will be seen in the third example,
The diagnostic plot for the test is shown in Fig. 6, Convo.
lution derivative based on measured flowrate is shown by
the circlee, and for extrapolated flowrate by the crosses,
The high quality of the crystal gauge pressure measure-
ment (triangles) is reflected in the sharpness of its deriva-
tive curve (squares), which was unemoothed in F@ 6.
The initial oscillation of the pressure derivative is due to
the slow (30 second) closing of the eurface valve, The
convolution derivative, however, is quite smooth during
the same time frame as one would expect (slow closing of
the valve is akin to ● multi-rate effect).
The dip in the pressure derivative after about one hour
is a diagnostic of heterogeneity — in this case it M in-
terpreted u ● 6eaured-system response pattern based on
the external information ●vailable (and discussed above).
The gap in the convolution derivative between 0.01 and
0.1 hours was caused by negative values (unplottable on
the logarithmic scale), brought about first by declining
flowrates and finally by the crossover from measured data
(circles) to extrapolation (crosses). Both pressure and
convolution derivative cumes eventually merge at later
times, On this and all remaining examples, convolution
derivative plots show the responses computed with ex-
trapolated flowrates in a different symbol or line type,
Log-log diagnostic analysis for fi8sured systems (pseudo-
steady state fluid tranefer from fissure to matrix) require8
two stabilisations at the same level in a derivative. The
first stabilisation represents radial flow in the fissures
only, while the second represents radial flow in the to-
t al system (fissures+ matrix). Often, as is the case in the
present example, the first stabilisation is masked on the
pressure derivative by wellbore storage, However, this
level i8 quite clearly indicated by the convolution deriva-
tive in early time. After reconciling all information the
type-curve match shown by the solid lines on the diag-
nostic plot was obtained.
The multiple type-curwe presentation shown in Fig. 6
fixes the pressure match (and hence the permeability) at
8 TNE ROLE OF DOUNSOLE PLW MD PRESSURB SP$ 183?9MEASURBMB~S IN RESERVOIR TSSTING
the lWC1indicated by the convolution derivative (circlae);
semilog analyoie of the preeeura data & not jtwtijied ba-
cauee the prasaura derivative doee not stabilise at this
level. However, ● SFRC pIot wouId be wdid for com-
putations during the time frame where the convolution
derivative ia flat. It is normal to compute negative skins
in caeee such u thw one. Thie ie ueuaIly not an indica-
tion of stimulation but rather aoaociated with the mod-
elling of fiseured systems. It is alsoseen that the final
level ●ttained by both preeaure and convolution derivm
tivee (squarea and croeaee) ia higher than the initial level
of the convolution derivative (circles). This M caused by
a nearby eealing fault, the poseible exiater.ce of which waa
indicated earlier.
The convolution derivative ie matched in Fig. 6 to a
6aeured-aystam type-curve that wee computed with all
of the parameter for the choean model, escept that the
storage coefficient corraeponda to the fluid filled volume
below the tool. In eecuriag the curve match for the praa-
mre data, ● dimenaionleea storage coefficient CD = 456
wae wed. The convolution derivative type=curva match
wae made uaiag ● C~ value of 23.5, whkh represents a
95% d~aaa in the coefficient used to match the preaeure
data alone. The storage reduction effected by measured
data (95%) checks very closely with the anticipated value
(97%) baeed on well completion/tool location considera-
tions.
Even though a rather convincing interpretation was re.
alised from convolution derivative analysis of a buildup, it
should be pointed out that a drawdown test in the same
reservoir would have produced ● response similar to the
lower dotted curve in Fig. 6 without the need for flowrate
extrapolation, The next example will further clarify this
point,
Example S: Pressure Drawdown With Downhole
Flowrate
Buildup or falloff tests are historically more popular than
flowing tests (drawdown or injection) because of practical
difficulties associated with maintaining constant surface
rates, Also, buildups are conducted to determine reser-
voir pressure, However, there are advantages to testing
with the well flowing, For example, if not for the prob-
lems associated with surface flowrate fluctuations during
drawdown, the obvious reason to flow test would be to
avoid loss of production,
The tlowing well ie performing in its n~tural condition.
Changea occur in the near-wellbore and wellbore during
buildup that are nonexistent, or much less extreme, when
the weIl is left flowing. in”buildup these changea can re
suit in transients that are not representative of the reser-
voir but rather of the wellbore, and can be misleading if
wrongly interpreted aa such.ss In the case of water injec-
tore, the well may perform aa if vertically fractured when
in the flowing condition, but may show damage during
falloff as the hydraulic fracture closes.’l
There is therefore ● certain benefit to testing while fiow-
ing the well. This can be fully realizable if downhole
flowrates are meaeured in addition to the praesure. Fur-
thermore, spinner flowmeter actually perform much bet-
ter when the well is flowing. There ie an initial period
where the data are not reliable, but even thie can be
minimised (or avoided altogether) by deeigning teeting
eequencee appropriately. Mechanical problems that could
occur during the initial period include
● inertial effects, in turning the *pinner from a dead stop
(as when a drawdown ia run from the static condition);
typical duration ia 1 to 2.5 eeconda, and even less if rate
changeb ok..er than from static condition are used.
. overcoming the sensor threshold; this is fixed and deter-
mined by calibration for each device.
Problems seen in the previous example (spinner going
to zero and the need for extrapolation) can be largely
avoided by designing the test to include a step-rate change
before the buildup. A steprate drawdown and buildup
sequence can be used to enhance the buildup test analy-
sis. The convolution response during the ftow test min-
imizes the distortions due to wellbore storage or surface
flowrate fluctuations revealing early-time near-wellbore
features and reservoir heterogeneities= In late time, the
characteristic drawdown response patterns to faults and
closed or no-flow boundary effects are more straightfor-
ward to distinguish than the equivalent buildup respons-
es42. By identifying the reservoir model during the tlow-
ing period, the ensuing buildup data can be correctly ex-
trapolated for determination ofp; or p*, and the duration
of the shut-in period may be reduced,
Example 3 was selected to illustrate practical problems
with drawdowns, and how downho]e flowmetering can be
used to enhance the analysis under these conditions, The
-L
SW 18379 J. A. J08EPH, C. A. ECONOl@BS, AND F. J. KUCEUK 9
data c. ,ne from ● producing gee well in Europe. Ae is of-
ten the cam, production wee manifolded directly into the
exietent gathering eystem. No special surface quipment
WM used onsite for controlling the rate during the tmt.
Ae a result, produced liquids were dumped from the ~ep
arator about e~wy 2 houre, reeulting in ● variable back
preeeure on the well during the transient acquishion.
The raw data plot for thie example, which ie Event No.
5 in a multi-rate flow echedule, is shown in Fig. 7. The
log-log diagnostic plot is ehown in Fig. 8. The effect of
liquid removal at the nmface is to cauee the downhole
preseure (squares in Fig. 7) to stairstep in a periodic
manner. Such effects are greatly exaggerated on the pree-
mre derivative, which in fact oscillates between negative
and poeitive valuee each time the Iiquid knock-out occurs.
However, since the downhole meaeured flowrate wae also
varying u ● meult of the surface rate fluctuation, the
convolution derivative in Fw. 8 ie much emoother than
ie the preaaure derivative, and ia themfom analyzable in
a straightforward manner.
Since the convolution derivative tende to etabb ●bout
the line shown in the figure, the SFRC plot of Fig. 9 wee
ueed for parameter estimation. It was not poeeible, nei-
ther wae it the objective, to reetitute a perfectIy smooth
response after convolution. Yet it ia clear that Figs. 8 and
9 do afford an interpretation even in thie example, where
preeeure by iteelf would have remained uninterpretable,
Example 4: Production Log Test
The test in this example included a production log sur-
vey in the baeic drawdown/buiIdup eequence,’s Preesure,
flowrate, temperature, and density vereus depth were ob-
tained from the PL over the entire producing internal,
and provided considerable ineight when incorporated into
the transient data anafysie. Worn openhole well loge the
interval of interest waa approximately 200 ft thick, con-
sisting of eand beds interlain with aerially discontinuous
shales. Baeed on the log interpretation it wee decided
to analyse the problem as an effectively homogeneous,
single-layered system,
The test sequence wae designed to include one drawdown,
a etabhed PL mrvey, and a buildup. Ii began after a
tw-day shut-in period; the transient, pr.sssure and spin.
ner data acquired are shown in Fig. 10. With the tlowme-
ter positioned above the top of the perforated intenal,
the well wee opened to 16,000 BPD. Real-time surface
readout of the downhole acquisition indicated “kfter 20
minutes tliat the bottomhole preaaure wae about to fall
below bubble point. The flowrate wee decreaeed imme-
diately in order to avoid two-phaee flow in the reservoir.
The test wae then continued for seven hours, and the
well remained flowing for another 10 hours before the
etabilieed flow profiles were taken. The tlowrate at this
point was 13,360 BPD, and the well waa subsequently
shut-in for a 28-hour buildup with the tool above all per-
forations.
The cut-back in the production rate was accompanied by
an increaee in the flowing bottomhole preeeure during the
first flow period, as clearly seen in the Fig. 10. A very
important diagnostic plot in production log teete ie the
stabfied flow profile, Fig. 11, It shows graphically that
just the uppar four eatsof parforatione were contributing
to the total production. PL surveys from eeveral other
welle in the saint field alao showed reduced production,
which wae attributed to ecaling probleme. Siice the lower
(non-productive) intervals were believed to be in com-
munication with the upper producing perforations, the
system wae diagnoeed as one of partial penetration type.
Hence the test could be interpreted using a partial pen-
etration model, with the penetration ratio, b, fixed at a
value of 0.5 as indicated from the flow profile analysie.
The log-log diagnostic plot for the drawdown and buildup
tests is shown in Fig. 12. Observe that the same kind of
normalization ai wee used in the first example (Fig. 2) is
once again employed, and also for the same reason — to
facilitate comparison of data from separate events, The
effect of the reduction in flowrate with consequential re-
duction in overall drawdown was to render the pressure
derivative uninterpretable, as shown by the squares in
Fig, 12. However, since the convolution derivative (cir-
cles) is a continuous superposition of the variable down-
hole flowrate with the pressure, it is seen that a imooth
data trend, comparable to that in the buildup, has been
restituted in the response.
The convohttion derivative exhibits ●n effective reduction
in the wellbore storage to about 3096 of that eeen by the
pressure data alone, corresponding mainly to the rathole
volume extending 1000” ft below the tool. The convolu.
tion derivative for the buildup (asterisks in Fig. 12) wee
computed from measured Bowrates for about 30 minutee.
397
,,
10 TNB RO~ OF DOWNBOLEFWW MO PRESSUREHMSURBMENTS IN RESERVOIR TESTING
SPB 18379. .
Then the remaining computation (shown by the dotted
curve in the Fig.) was performed using 9owrates eztrap-
ofated from the measured values.
Interpretation of this dataaet using analytical techniques
was presented in Ref. 43. Penneabilit y and skin from
the drawdown and buildup using convolution analysis
yielded similar values. A history match using a r-z sin-
gle well numerical simulator was made, and the resultant
verification plot is shown in Figure 13. A nonlinear pa-
rameter estimation scheme iG.17 was used to determine in
the least-square sense global estimates for the effective
horizontal and vertical permeabilities, and the damage
skin opposite the active (upper) perforation. The initial
guesses used in the optimisation procedure were taken
from the earlier analysia,43 and the final answem ohown
in Table 2 are consistent with those obtainedpreviously.
Example S: Lay-d Reservoir llset
Layered reservoir testslG- 17.’4 are designad to maximise
the quantity, and quality, of information obtainable from
downhole pressure and 9owrate measurements. The LRT
is a commingled production test that alternates PL pr-
ofilingimme&ately before a surface flowrate change with
a stationary measurement of the transient induced by
the rate change. The sonde is strategically located above
each of the selected perforated intervals before the new
tlowrate change is induced, and after a profile at the last
prevailing rate has been comp!eted. Permeability, skin
and average pressure can then be determined for each
. zone tested in this fashion.”
The LRT example comes from an oil welI. Seismic data
showed that the well was located in a faulted region.
Openhole logs revealed five distinct sands, each of which
wiu~fully perforated and completed for commingled pro-
duction. The objective of this LRT was to determine
permeabilities and skins in each of the completed cones.
Data needed for the analysis are provided in Table 3.
The sequence of events during the test is shown Fig.
14, with the measured pressure, flowrate, density, and
temperature transients given in Fig, 15, Zones above
which measurements were taken are labelled in both fig-
ures, It is apparent from the density data in Fig. 15 that
the transients for zone E were taken in standing water,
The necessity for measuring transient flowrates below the
standing water level in a well is comman in LRT’s, and
can pose particular difficulty in gas wells. In this well, the -
main problem was that the rates recorded ●bove sone E
appeared to contain much more noise than those recorded
elsewhere in the well, The production log flowrate nur-
veya (not shown) indicated that virtually none of the fluid
was produced from sone C, Hence, sones C and B were
grouped in the analysis.
Since the downho]e pressure was acquired at different
depths in the wellbore, correction to a datum is neces-
sary as keen in Fig. 16. Pressure transients are used as
the wellbore boundary condition for generation of a si.
multaneous match to ail of the measured flowrates, using
a layered model that is consistent with geology and geom-
etry. Permeability and skin values used by the model am
automaticallyvariedaccording to a non-linear parameter
estimation scheme,17 until the match is optimised in the
least squares sense,
Before a match with a layered model was attempted, iog-
log diagnostic plots as prescribed by Fig. 1 were exami-
ned for each flow period, Each showed behaviour similar
to that seen in Fig, 17, which is normalised in the same
fashion as used earlier in Figs. 2, 6 and 12. Pressure
change, pressure derivative and convolution derivative for
the first drawdown and final buildup periods are super-
imposed on Fig, 17. A half-slope is evident at later times
on both the pressure and convolution derivatives. This is
a diagnostic of Iiraear flow, associated with parallel seal-
ing faults,
In Fig. 17 it appears that the buildup pressure derivative
(plus signs) shows a plateau (upper dashed line in Fig,
17) at a higher level than the other pressure / convolution
derivative curves in the figure, This is not an artifact of
an extrapolated spinner, because afterflow was measura-
ble for about 1 hour, Type curve analysis of the buildup
treating the system as a single hmnogeneous layer yielded
k = 391.4 md. and s = -0,126, together with estimates
of distances to the faults of 122 ft (37.2 m) and 365 ft
(111.3 m),
Analysis of the buildup convolution derivative, or any of
the other derivatives in Fig. 17 would result in perme-
abilities roughly twice ss large as those obtained from
1
Spl! 1837.9 J. A. L7CWBPfi, C. A. BC!ONOMIDBS, AND F. J. KUCHUK 11
the buildup pressure derivative alone. (The approximate on log-log coordinates ea the single layer model used forplateau for the other derivatives is given by the lower the buildup type cu~e match, However the thicknesa-horizontal line in the figure.) Such an analysis could also weighted average permeabilitiea and skim ate different inchange the estimates of the distances to the faults, Eati- each case.mates of the permeability and skin baaed on SFRC anal-
Experience with nearly 40 such tests haa indicated thatysis are indicated in Table 4.
itisquite common for the buildup reeponee of a layered
The estimates from the convolution analysis were refined system to appear, and be interpreted, as a homogeneous
by sequential analysia7’1’.44 ueing a layered model with singhr-layer system. LRT interpretation shows that this
a single fault boundary4s. Thie type of analysis is con- approach to the analysis may yield oversimplified results.
ducted from the bottom layer up. Once the permeability However, this example shows the difficulty of attempting
and skin are determined for the lowest layer, those values to determine both layer properties and the distances to
are fixed, so that the properties of the next layer can be vertical barriers simultaneously with a single well test.
determined using a two-layer model. Each time the next An interference test involving pressure measurements in
higher layer ie analysed, another layer ie added to the observation well(s) might provide more conclusive infor-
model, mation on the locatione of vertical barriem to flow, or
Since each analysis was performed on only one flow pe-altematively, vertical seismic profile data might detect
the images of nearby faults, Then the layered reservoirriod at a time, by matching only the early time transients, test would be used to determine permeabilitiea and skinsthere was no need to model the mom distant fault. Re- only, using a model that includes the boundary effects,cults of the Sequer,tial analysis are also provided in Table
CONCLUSIONS4.
A comprehensive methodology for reservoir test interpre-Flnally, veri6cation of the position of the faults detes- tation was presented with field examples, The follow-mined by the buildup type curve match was attempted ing observations concerning the practicalityy and choiceusing a model for the commingled-layered syetem which of .reeemoir testing procedures were made in this study:
includes the parallel fault boundary conditions4s.4G. In
this case, the verification step proved problematic, as ex- 1. In general, the interpretation of a buildup portion of anyplained in the following paragraphs. teat will be more straightforward and leee error-prone if
The history match shown in Fig. 18 was computed with the data is acquired after downhole shut-in. When com-
the layer permeabilities and skins shown in Table 4, and pletion or other constraints exclude the downhole shut-
with parallel fault boundaries at the dietancee indicated in option, or when the test sequence includes acquiai-
by the buildup analysis. However, it was necessary to in- tion while flowing, then the measurement of downhole
elude an ongoing preesure trend of 3.2 psi/hour to achieve flowrates offers considerable advantage.
this match. Since this was an exploration well and there2. The inclueion in the test sequence of a flowing period
were no nearby wells thought to be interfering, the diffi- with measured downhole fiowrates provides data whichculty in finding a simultaneous match for all of the data may improve the interpretation of a subsequent shut.inis an indication that additional features are needed in period, and possibly shorten its duration, Measurablethe mode). Perhaps there are one or more additonal downhole flowrate and pressure transients can be inducedfaults which are too distant to influence any one tran- by a etep change in the eurface rate. This strategy cansient flow period, but which are evident in production be particularly attractive for reservoir limit testing, andover the nearly 30 hours involved for the total test. motivates installation of a fiowmeter sensor in the DST
The comparison between the model used to match the string.
buildup pressure and derivative and the model that pro-3.Production logging surveys during stabilised flow and
duced the simultaneous match in Fig, 18 is shown induring the buildup, when combined with downhole pree.
Fig. 19. Fig, 19 shows that the layered mo~el used forsure and flowrate transients in the teet sequence, ●dd
the simultaneous match has the same general appearance
1.
information about the location and phase of ffuid entries
that is important and can be essential to the tranaient
data interpretation. The ultimate application for this
measurement combination is the layered reservoir test.
NOMENCLATURE
B=
c=
CD =
Cf =
h =
k =
k,, =
P =
Ap =
q =
Q=ru, =
8 =
W =
t-=P
At =
formation volume factor
storage coefficient
dimensionless storage coefficient
total compressibility
formation thickness
formation permeability
vertical permeability
pressure
pressure change
downhole flowrate
surface 9owrate
wellbore radius
skin factor
damage skin factor
producing time skin
test time
Greek Symbols
7!1 = gas gravity (air=l)
P = viscosity
+ = porosity
ACKNOWLEDGEMENTS
The authors greatfully acknowledge the four anonymous
oil companies for allowing us the use of their data, We
are thankful to the management. of Schlumberger for per-
mission to present this paper. Special thanks are due T.
Bratton, G. Clark, O. Myhrer, C, Ovens, and M, Pearson
for their assistance with the field examples.
REFERENCES
Stewart, G., Wittmann, M,J, and Lefevre, D.: ‘Well Per-
formance Analysis: A Synergetic Approach to Dynamic
Resemoir Description,’ paper SPE 10209 presented ●t the
56th Annual Fall Technical Conference and Exhibition of
the SPE, San Antonio TX,, October S-7, 1981,
2.
3.
4.
5.
6.
7,
8.
9,
lot
11!
Pirard, Y.-M. and Bocock, A.: ‘Pressure Derivative En.
hancea Uaa of Type Curves for the Analysis of Well Tests,’
paper SPE 14101 presented at the SPE International
Meeting on Petroleum Engineering, Beijing, China,
March 17-20,1986.
Ahmed, U,, Xuchuk, F. and Ayestaran, L.: ‘Short-Term
‘&ansient-Rate and Pressure-Buildup Analysis of Low.
Permeability Reservoirs,’ SPEFE, December 1987 (611-
617).
Meunier, D. F,, Kabir, C,S. and Wittmann, M+J.: ‘Gas
Well Test Analysis: Use of Normalized Pseudovariables,’
SPEFE, December 1987 (6X3-636),
Home, R. and Kucuk, F,: ‘The Use of Simultaneous
Flow-Rate and Pressure Meuwements To Replace Is-
chronal Gas Well Tests,’ SPEFE, June 1988 (467470),
Ehlig-Economides, C., Joseph, J,, Erba, M. and Vik, S.:
‘Evaluation of Single-Layer Thwients in ● Multilayered
System,’ paper SPE 15860 presented ●t the SPE Eu.
ropean Petroleum Conference, London, October 20-22,
19860
Kuchuk, F,, Shah, P.C., Ayestaran, L. and Nicholson, B,:
‘Application of Multilayer Testing and Analysis: A Field
Case,’ paper SPE 15419 presented at the 61st Annual
Technical Conference and Exhibition of the SPE, New
Orleans, LA,, October 5-8, 1986.
MorTis, C. W,: ‘Case Study of a Gulf Coast Layered
Resenroir Using Multirate lYansient Testing,’ paper SPE
16762 presented at the 62nd Annual Technical Confer.
ence and Exhibition of the SPE, Dallas, TX,, September
27-30, 1987,
Matthews, C.S,, and Russell, D,G.: Pressure Buildup and
Flow ~C8~6 in Welh, SPE Monograph Volume 1, 1967.
Gringarten, A.C,: ‘Computer-Aided Well Test Analy.
sis,’ paper SPE 14099 presented at the SPE Interna-
tional Meeting on Petroleum Engineering, Beijing, China,
March 17-20, 1986,
Godbey, J,K, and Dimon, C, A,: ‘The Automatic Liquid
Level Monitor for Pumping Wells,’ JPT, August 1977
(1019-1024),
spB 18339 J. A. JOSEPS9 C. A. 7---”2i41DBS , AND F. J, KUCSUK 13
12. Podio, A.L., Mc@y, J.N. and Iiuddleston, K.L.: ‘Au- 23. Kucuk, F, and Ayaetaran, L.: ‘Analysis of Simdtane=
matic Praeeura Buildup Data Acqutittion and Interpreta- oudy Measured Preeeura and Sandface Flow Rate in
tioa Using a Microcomptttar-Baaed Acoustic Liquid Level lhnsient Weil Testing,’ JPT, Febru&y 1985 (S23-334).
Instrument,’ p~per l?PE 10228 presented at the Produc-
tion Operations Symposium of the SPE, Oklahoma City, 24, SchJumberger Production Log Interpretation, Schlumber=
OK., March -11,1987. ger Weli Services, Houston, TX., 1979.
13, Haaan, A.R. and Kabir, C.S.: ‘Determinhg Bottomhole 2&, Kabir, C.S., Kucuk, F, :nd Gomes-Angulo, J,: ‘Well Test
Pressures in Pumping Wells,’ SPEJ, December 1985 Interpretation in Faulted Resewoirs,’ paper SPE 14008(828-838). previ%a.i at the 6th offshore South Eaet Asia Technical
14, Hasaa, A. R., Kabw, C.S. and Rahman, R.: ‘PredictingConference of the SPE, Singapore, January 28-31, 1986.
Liquid Gradient in a Pumping-Well Annulus,’ SPEPE, 26. Bourdet, J), and Alagoa, A.: ‘New Method EnhanceaFebruary 1988 (113-120). Well Test Interpretation,’ World Oil, September, 1984,
15, Kacuk, F., Xarakae, M. and Ayestaran, L.: ‘Well Test-27, Meunier, D,, Wittmann, M.J. and Stewart, G,: ‘Interpre
iug and Analysis Techniques for Layered Reservoire,$
SPEFE, August 1986 (S42-354).tation of Pressure Buildup Test Using In-Situ Measure=
ment of Aftefiow,’ JPT, “January 1985 (143-152).
16. Ehli@conomides, G.A. and Joseph, J. A.: ‘A New Teat
for Determhmtion of Individual Layer Properties in a 28. Gringarten, A.C.: ‘Interpretation of Teats in Fissured
Multiiayerad Reaarvoir,’ SPEFE, September 1987 (261- Reaervoirs and Multiiayerad Reservoirs with Double Por-
282). osity Behavior: Theory and Practice,’ paper SPE 10044
presented ●t the International Petroleum Exhibition and
17. Shah, P.C., Kuakas, M., Xucuk, F. and Ayestaran, L.: Technical Symposium of the SPE, Beijing, China, March
‘IMmation of the Permeabiiitias and Skin Factors in 18-26, 1982.
Layered Reservoira Using Downhole Rate and Pressure
Data,’ paper SPE 14131 presented at the International 29, Ehlig-Economides, C, A.: ‘Use of the Pressure Derivative
Petroleum Exhibition ●nd Technical Symposium of the for Diagnosing Pressure ‘hansient Behavior,’ accepted for
SPE, Beijing, China, March 17-20,1986. publication in JPT, 1988.
18. Horner, D. R,: ‘Pressure Build-Up in Wells,’ E. J. BriJJ, 30, Miller, C, C,, Dyes, A.B. and Hutchison, C. A,, Jr.: ‘Es-
Leiden, Netherlands H, 1951 (503-521), timation of Permeability and Reservoir Pressure from
Bottom-Hole Pressure Build-Up Characteristics,’19. Bourdet, D,, Whittle, T.M,, Douglas, A,A, and Pirard,
Petroleum ‘lkans,, AlME, Vol. 189,1950 (91-104).Y.-M.: ‘A New Set of Type Curves Simplifies Well Test
Analysis,’ World Oil, May 1983, 31, Ramey, H, J,, Jr,: ‘Practical Use of Modern Well Test
20. Bourdet, D., Ayoub, J,A, and Pirard, Y.-M,: ‘Use ofAnalysis,’ paper SPE 6878 presented at the 46th Annual
Pressure Derivative in Well Test Interpretation,’ paperCalifornia Regional Meeting of the SPE, Long Beach,
SPE 12777 presented at the California Regional MeetingCA., April 8-9, 1976,
of the SPE, Long Beach, CA,, April 11-13, 1984,32, Gringarten, A. C,: ‘Type-Curve Analysis: What It Can
21. Earlougher, R, C,, Jr,: Advances in WeJl Test Anafysis, and Cannot Do,’ JPT, January 1987 (11-13),
SPE Monograph Volume S, 1977.33, Gringarten, A,C,, Bourdet, D, P,, Landel, P.-A, and Kni.
22. Govier, G. W,: Theory and Practice of the Testing of Gae azeff, V. J.: ‘A Comparison Between Different Skin and
WeJis, Energy Resources Conservation Board, Alberta, Wellbore Storage Type.Curves for Early-Time ‘IYansient
Canada, 4th Ed,, 1979. Analysis, r paper SPE 8205 presented at the S4th Annual
401
14 TliERoLE oFrlOHuBoLB FLcn?Alm -SURE SPS 18379MSRSURE’MENTS IH RESERVOIR TESTING
. .
34.
35.
36.
37.
38.
39.
40.
41,
42.
43,
Technical Conference and Exhibition of the SPE, Laa Va-
gae, Nevada, Septen.ber 23-26, 1979.
Shah, P.C., Gavaiaa, G.R. and Seinfeld, J.H.: Wrror
Anaiysis in History Matching The Optimum Level of
Parametrization,’ SPEJ, June 1978 (219-228).
Fair, W.B., Jr.: ‘Pressure BuiIdup Anaiysia With Well-
bore Phaae Redistribution,’ SPEJ, April 1981 (259-270).
Strelteova-Adams, T. D,: ‘PreMure lhnsient Analysia for
After80w Dominated Wells Producing from a Reservoir
with a Gaa Cap,’ JPT, April 1981 (743-754).
Chen, H.K and Brigham, W.E.: ‘Preeeure Buiidup for a
Well With Storage and Skin in a Closed Square,’ JPT,
January 1978 (141-146).
Fetkovitch, M.J. and Vlenot, M.E,: ‘Rate Normaiiaation
of Buildup Preaaura By Using After!low Data,’ JPT, h
cember1984 (2211-2224).
Piers, G. E., Perkins, J. and Eacott, D.: ‘A New Fbwme-
ter for Production Logging and Well Taating,’ paper SPE
16819 presented at the 62nd Annual Technical Confer-
ence and Exhibition of the SPE~ Daliaa, TX., September
27-30, 1987.
Boyeldieu, C, and Martin, C.: ‘Ihcture Detection and
Evaluation,’ paper No. 21, 9th European International
Formation Evaluation ‘hansactions of the SPWLA,
Faris, 1984,
Koning, E.J.L. and Niko, H.: ‘i%actured ‘Water-Injection
Wells: A Pressure Falloff Test for Determining Ikacture
Dimensions,’ paper SPE 14458presented at the 60th An-
nual Fall Technical Conference and Exhibition of the
SPE, Las Vegas, Nevada, September 22-25, 1985.
Proano, E, A,, and Lilley, I. J.: ‘Derivative of Pressure:
Application to Bounded Reservoir Interpretation,’ paper
SPE 15861 presented at the SPE European Petroleum
Conference, London, (jctober 20-22, 1986.
Kuchuk, F.: ‘New Method for Estimating Parameters
of Low Permeability ReseNok,’ paper SPE 16394 pre-
sented at the SPE/DOE Low Permeability Symposium,
Denver, CO., April 18-19, 1987.
44. Ehiig-Economidaa, C. A.: ‘Taating and Interpretationin
Layered Reservoirs,’ JPT, September 1987 (1087-1OW).
45. Chen, T.: ‘Preaaure Drawdown in a Layered Raaervoir
With Linear Boundaries,’ paper SPE 16767 presented at
the 62nd Armuai Technical Conference and Exhibition of
the SPE, Khllaa, TX., September 27-30, 1987.
46. EHig-Economides, C,A. and Economidee, M. J.: ‘Pres-
sure fiansient Analysie in an Elongated Linear Flow Sys-
tem,’ SPEJ, December 1985 (839-847).
.
-It
\*J(cp)
tt(pd -1)rw(ft)
B(%TC)Pt[ft]
19l(v)
I
.21
5
5.Ex1o-S.4
1.1462.1
TMLE 1: IPP1l. Flui& S * FraPs?th6f6r EAMPIW 1-4
2 3 4
:2: .12 .21
.0’..1 .0192 .s6
I.52x10-4 *Q-4 ,0.5
.33 .292 .35s
a 200
.69 .618
163 236
TMLE 3: wI1, FIufd. t Reek Fropwtios for Exmplt 6
Zwm A 8 c B
* .29 .264 .23 ,18
h(ft] 21.3 49.2 21.3 21.3
% 0.3 0.26 03 0.6
Q(P$!-1) 1.39X1O-5 I.42X10-5 i 39X1O-5 0.66xlCr5
r#(ft) .51
B(RV31B) 1.4
Il[cp) 0.42
TA6LE2: Intcrpmtat!m R6sults for QIc$ 3.:.
EX6V1* 1 z J 4
kb(d) 28.7 100.9
kv(d 6.5
kh(mi-ft) 12.3 63.5
s -2.43 -2.9 0.71
u 0.1
A 4. SX1O-5
P*(P$i) 2222 4663
TA6LE4: Results for F.x+lt 6
SFRC
Zom A l-c D
k(~) 172 665 585
s 7.2 2.4 2.8
SEC4KFSTIALA16ALWS
Z6M A B-c D
k(md) 606 100 690
s 1.1 2.8 5.1
SWLTPHEWS H1STD6YPL4TCPI
zon6 A 8-c D
k(md) 513 746 720
s 2.3 1.s 2.1
E
44
-1.2
E
70
0.9
E
84
2.1
Parallel Fwlt Oistances (rt) 122 365
, ~-$
sPE M@)-
1I J
F@ l-Rowtvolr to8t [ntwpmtatlon IWUWMOW.
SURFACE/DOWNHOLE SHUT-IN EXAMPLEhrmha.ti 07cn n,mhrncnr mnr,.V,. ”.,... L”L” “,,.”,. v., ,,e . ~v,
–=**@__>.:.
A PRESSURE CHANCE-SURFACE SHUT-IND PRE+J.IRE DERIVATIVE-SURFACE SWT-IN* PRESSURE CIUNCE-0i3WNHOLE SHUT-IN+ PRcssURE lJERN/AT!UE-OOWNHO+.ESHUT-IN
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St-iUT-lN TIME, HOURS
Fig. 2-NOrmAl@d log-lag dlwnoatlc plot for Sxamplo 1.
SURFACE/DOWNHOLE SHUT-lN ExAMPLENORMUIZEO SEW-LOG ~ol
i .8A wWSSUR[CI+ANCE-SUWA?E SW! -IN● iWCSSUUECMANff-WMOLE SHU:-IN
16-
1,4-
12-
1,o-
08 -
06 -
04 -
02 -
00 -
, @
SHUT-IN TIM:, HOURS
SURFACE/DOWNHOLE SHUT-IN EXAMPLEG131EWJZCD HORNER-W
2500’@!@mlm’
2000-
Z0.
w-3 1500 -!/lyJ
aa
1000
5000 400 800 1200 1600 2000 2400 2800 3
SUPERPOSITION TIME FUNCTION
EXAMPLE WITH EARLY-TIME HETEROGENEIWDIAGNOSTICPLOT UAICHEO TO FISSUREOS=TEUWTM FNJL7AT 122 ~
y0
~
z
21 lo’-
w“g
<
E
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,V, I .,;.. ,& ,:., ,:.. I I
100 10’
SHUT-IN TIME. HOURS
D
8-
5.70
555
5,40
3525 1 435000 100 200 3GQ 4CU SW 603 700
TKIW (hews)
Flq.7_Fawdsm fwE8M#D’3.
60
4.60
4,65
4,50
DRAw~”’: I wlTH MEASURED DOWNHOLE FLOWRATE EXAMPLE
,25 !A NoRwmo w?swl CW22 V5K,, I
200-
175-
150-
125-
1oo-
75-
50-
25-
0,”–2.4 -2.0 -1.6 -1,2 -0,8 -0.4 0.0 0.4 0.8
RATE- CONVOLVEO TIME FUNCTION
DRAWDOWN WITH MEASUREO OOWNI+OLE fLOW::ATE EXAMPLEoAoNosTK PLOT
mm. Iojy w
2
3K0
—
y
~ 1o1-
$ ●
0~. #’0 00: ~o
❑
✌✎✎✌
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1O* 10’ 1Oa
FLOW TIME, HOURS
bm’
..”
.+
.
.E -0 “0
Isd “sdnoW 3AILvAIti3d ‘39NvH2 3MfK.S3tid
A-
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LAYERED RESERVOIR TEST EXAMPLE
—$Al!ooo -
SEOUENCE OF EVENTS
co : A.10000-
9000-
80C@
~ ,Ir r,.$,000$ ‘“D60001 “’
L--$.c
u-: 5ooo -
~ 4ooo -
b. L*E3000-
2000-: RfXRATESLMWY
000- A-E RESHW4RIAYERS
0-+ , , , ,
0 3 6 9 24
ELA~:ED T’lfiE. &JRS2’
4–LAYERS, PARALLEL FAULT BOUNDARIES
27 3
LAyEREO RESERVOIR TEST FXAMPLE
5380wELLBORE EOUNOARY CONOITION
a #
5220
1L!!
5200 ~03691215 IB 212427
Time, hrs
1 2000CO01+ I
I
Time (hours)
Fl#.13-88w48tmiw Eum#@s.
LAYEREO RESERVOIR TEST EXAMPLE
, ~—l
~o->y:~oT’*4”...................K . . . .. .. ..OK*J ❑ ~. ●
. . . . . . . . . . . . . . . . . . . . . . . . .. . .. . . . . .. . . . . . . . . . . . . . . . . . . . .
0
.“. : 0
0 I1 I I
4
10-” 1o“’ , ;-l ,;., 1o“
FLOW TIME, SHUT-IN TIME. HOURS
... -
LAYEREDRESERVOIRTESTEXAMPLEVERIFICATIONPLOT
HISTORY MATCH WITH ZONE FLOWWES3~o ~ *ucl A&ovezoneofnuwmd
-Above Zono DedCIM~Aba9z8n98m908Wd-Abovozw Bit Abovo ZWAmo8wrodxAbOWzw EfnOOsUd;#JWUJ ;O& ~ phlot
_ Abov8 ZOM A COkUbtu I I ‘1
-5000 ! v 1 , w 1 u v , 9 {
O 3 6 9 12 15 18 21 24 27 soTime, hrs
f@W-valsmsm #ottumnolmle@Mf=m~.
LAYERED RESERVOIR TEST EXAMPLECOMPARISONBETWEENPRESSURE MATCH IYPE CURVES
g 102; Em!EiE5<~Ewo
g
u
~ 1o’- .
;v-lw
~z~EIL ----
mIny= 10°0!3 ..-—g
6
10-’ II I 1
1Oz 10’, ~., , ;s 10’ 10’
DIMENSIONLESS TIME
SPE 18379