12. spe-15924-ms
TRANSCRIPT
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SPE
SPE 15924
Practical Well Test Analysis Methods for Hydraulically
Fractured Wells in Dual-Porosity Reservoirs
: j
D.E. Lancaster and J.M. Gatens 11 ,
S.A. Holditch & Assocs. Inc.
SPE Members
//
Cofwrbhl 1S86,Sooiefyof PetroleumEngineers
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ASSTRACT
preomure
t ranaient
datak
from dual-porosity
reeezvoira8 to esttite
Succeeeful analysis of poet- frecture well teat
reaervt r propertied.
Gringerten end Ereaghi nd Afleki have preeented
date tn dual-poroelty resewotre ia eeaential to
munmeriea of analyeia methods for dual-porosity
the design and evaluation of stimulation treatment
reservoir well teste.
in theee resenroire. Many methods have been
preseoted for analyzing peat-fracture well test
deta from
Many dual-poroeity reservoirs have sufficient
hydraulically
fractured wells in
permeability to produce at economic flow rates
single-porosity resewofra.
Little information ie
without
requiring attmulation.
However,
vatlable, however,
some
to asaiat the engineer in
dual-poroeity resarvotra, such ae the Eaatern
analyztng preeaure tranaient data from a well
Devonian Gae Shalea,
have low
effective
completed in a dual-porotaity reservoir which has
been fracture stimulated.
parmeabtlity and require some type of stimulation
to
achieve
commercial
production ratee. A
commonly-applied stimulation method is to create a
As part of a study we are conducting of the
Eestern Devonian Gas Shalee, a reeervoir which ia
conductive hydraulic fracture in the resarvoir by
pumping fluid and proppent into tha formation at
uauelly described aa dual-poroafty, we have
high pressures. When succeeeful, theaa hydreulic
anelyzed peat-fracture well teet deta from a number
fracturee can aubetantially imp~ove the performance
of welle for the purpoee of estimating propped
of low-permeability reaarvoirs.
fractura length
and fracture conductivity. The
purpose of this paper ia to present how we have
To optimize the design end implementation of
applied available analytical technique in our
fracture
stimulation
traatmente, it is of:en
analysis of peat-fracture
well
tests for
desirable to determine the effactive propped length
hydraulically fractured welle in a dual-poroeity
and conductivity of
the
hydraulic
fracture
reservoir.
Simulated and field examplea are
following the treatment.
Prassure
transiant
presented to illustrate our approach.
Guidelines
for conducting and analyzing post-fracture well
teatiog has been found to produce characteristic
deta which can be analyzed to estimate the
tests in dual-porosity
reservoirs are also
~~~~~ yf-lpydraultc
fracture properties.
Many
presented.
have been preaanted for analyzing
~NTRODUCTION
these data from hydraulically fractured wells in a
single-porosity reeervoir.
Unfortunately, little
Many
Information is available to help the engineer
oil
and
gaa
fields produce from
analyaa preseure
tranaient date for a well
reaervoira which contain natural fracturea that
contribute to production. Reaervoira of this type
complated in
dual-porosity resenoir which haa
been fracture stimulated,
have been found to
exhiil~~ a
characteristic
preseure transient behavior
and are coumonly
::;:34L9 aB ual-rorOaity eaenoira finy
We hava been c ducting a study of the Eaatern
?9
have been presented for analyzing
Devonian Gas Shales , a reservoir which la usually
naturally fracturad and which ia often found to
;;&18tha
charactariatic
dual-porosity
The Davonian Shales usually hava low
References and illustration at end of paper,
effective permeability, low reeervoir preaeure, or
both, and must be stimulated to chieva comraerciel
.
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PRACTICAL WELLTEST ANALYSIS METHODSFORHYD~ULICALLY
mmAnmrtmunEm r m T.,
m rltl?sfie.m mecom. fi. .
CD= Co Q/.
rtwiub
vn5u W=14UQ &n uutLb-rvIuJDA& 1
K&on
KVULKD
. ,~
production.
Hydraulic fracturing ia often tha We uae
the above definition for if to
praferred method of stimulation in the Shalea. We
diatinguiah it from
the tnterporosity
have analyzed peat-fracture well teat data from a
f low
coeffic.tent,~ , where
number of Devonian Shale wells for the purpose of
eatimeting propped fractura langth and fracture
conductivity. We obaervad that naarly all of these
k2 rw
well teata
A.a
exhibit the characteristic behavior
r =1
(5)
predicted for hydraulically fractured wells in
E w f~
sinsle-porosity reaervoira; therefore, we-analyzed
these data using
Ype 15:~:f6
developed for
k and u ara properties of a dual-~oroaity
single-porosity reservoirs. Unfortunately, resarvoir aa presented by Warran and Root.
this approach haa often yielded what we consider to
not a formation proparty.
It ia a property o;ko~~
be unreasonable estimatea of hydraulic fracture
the formation and the completion (the hydraulic
properties (i.e., very short fracture half-lengths) fractura).
Af was identified by Houze et al. aa an
in light of the size of the fracture treatment
important parametar for hydraulically fractured
pumped.
dual-porosity
reservoirs. Anothar
important
Houzeet al>g
distinction identified by Houze ~ Q. in the
have presented a aet of type
development of their analytical solution was tha
curves spec~fi~lly for hydraulically fractured
Uae Of fracture etoratlvlty (V@c)f rather than
wells in dual-porosity resanoirs.
We have found total storativity (V$c)t in the dimensionless tima
theaa type curves and the general approach outlined
8roupP $f.
by Iiouze et al. useful in analyzing peat-fracture
well teat data to obtatn more reasonable results in ~2Theu = 1 cume in Fig. 1 is the Gringartan~
dual-porosity reaervoira. &* eolutfon for an Infinita-conductivity
vertical hydraulic fracture in a aingla-porosity
ne purpose
of
this paper
ia
demonstrate
reeervoir.
All
teat
data from wella with infinite-
how we have appliad tha Houza et al.
conductivity hydraulic fracturaa, in both single-
as
singl~~;ros;~ raJ~%oir3Y2Z1~d~&{J~N
~~~~o~~~~~~~. ~or~he~ua: ~~~~ai~~i~~~~
raaervoire,
of well testa for hydraulically fractured wells in
dual-porosity reservoirs.
voir, this would repranent the time durlnu which
Simulated and fiald only the natural fracture porosity influences the
examplae are preaanted to illustrate the applica-
reaponaa.
tion of the type curves nd to demonstrate number
When the matrix porozity response
begins, the dual-porosity teat data will begin to
of obearvationa we have made in our work with
deviate from theU - 1 curve and follow
~
hydraulically fractured welle in dual-poroeity
transition curva until the total (natural fractur i
reaervoira.
plus matrix) porosity uniformly influences the
data. At this point, the data will leave the if
HOUZETYPE CURVES
transition curve and follow one of the uc 1 curvee.
Houze et al.lg
preeented type curves for the
Tha Houza type curvae can theoretically be
pressure tr~s~nt behavior of a well produced at
used to dete~ine ~,
Xf, kf, and w from a
constant rate with an Infinite conductivity hydraulically fractured
well teet in a
vertical hydraulic fracture of half-langth Xf in an dual-porosity
infinite-acting
reservoir givan sufficient data.
dual-porosity
reservoir. They Onca a match of the actual teat data is achiavad, ~
aaaumed pseudo-steady atate flow in the matrix and
can be obtained from the pressure match POint~ Xf
used an analytical model to develop these curves,
can ba obtained
from the
time-match point, and A
Figure 1 is a graph of these type curves.
These
can be estimated from the transition curva
curves are plots of dimenaionleaa presaure~ PD~
parameter, h , The value ofu may be read diractly
veraus a dtmensionleas time group, tDf, which we
from the typ~curva.
define below.
We have yet to obae~e the complete transiant
~h ~p
bahavior indicated by Fig. 1 in practice, i.e., a
P~ -
141.2 qpB
(1)
teat which begins on the u = 1 curve, follows a A
transition curve, and finiahea on an (IJ
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PE 15924
D. E. LANCASTERA
Table 1 lists the properties we used in the
simulator to generate tha threa examplea diacuased
in this section.
Note that we used
typical
Devonian Shale properties, i.e.
low effective
permeability and low reservoir preaaure.
Figure 2 is a graph shoving the match of the
simulated drawdown teat data for Example 1 on the
Houze type curve.
A good match of the data waa
obtained. The atmulated drawdown data la plotted
as the logarithm of
the
change in adjuated
pressure, (p ~ - pa f), veraua log adjuated time,
t.
Wheneve$appr ate, we uae adjuated time and
a~juated pressure
These
variab~ arc? ;~pl~l&%i;eWya%
paeudopreaaure multiplied by constanta to obtain
units of time in hr and preaaure In paia.
For
aemilog analysis
of
drawdown teata, time la the
preferred var%able; for type curve analyaia of data
distorted by wellbore storage, adjuated time la
preferred. Adjusted shut-in tiuiea are preferred
for both aemilog and type curve analyata of buildup
tests.
The log-log plot of the simulated drawdowo
data shown in Fig. 2 waa laid over the Bouze type
curves and shifted both horizontally and verticall
to obtain the match. When the match waa found,
E
was calculated from the preaaure match points :f
wae calculated from the time match point, and
wan determined from the A
obtained directly from the ~tc %%~al~la%
drawdowm datg~
A~of 0.05md, an Xf of 100 ft. a A
of 6.25 X 10
and an u of 0.01 wera datarmined for
this teat. Aa shown in Table 1, these were the
same propertied used in the model to generate the
drawdowm teat data. An example procedure for
performing a quantitative analysls uSia8 the llouze
type curves is presented in the Appendix.
This example demonatratea that SUGARII can be
used to simulate the performance of a dual-porosity
reservoir with a hydraulic fracture.
It also
demonatratea the application of the Iiouze type
curves to analyze such data.
As mentioned
previously,
this example illustrates that given
sufficient da~a, the Houze type curves can be used
to determine k, x , A and u from a peat-fracture
tell teat conduc ed in a dual-porosity reaarvoir
with an infinite-conductivity hydraulic fracture.
In reviewing Example 1 and tha procedura for
using the Houze type curves, it la important to
note that fracture atorativity, (V$c)f, must be
used rathar than the total atorativity, (V@) , in
1alculating x (ace Eq. 2), If total atorat vity
5{
a used to ca culate x following a match of the
teat data to the Houze ype curve, the value of x
calculated will be incorract. Fractur i
atorativity, hovevav, ie not eaaily measured and,
therefore, (V@c)f muet be aatimeted from other
availabla data.
Total atorativity, (V$c)t, ia defined aa
(v@c)t =
(Wf + (v@)m
(6)
Combining Eq, 3 and Eq, 6, (V@)f can be calculated
at3
(W c)f - (d(vf c)t
(7)
J. M. GATENS III
The quantity (V@)t
can usually be eatimeted
from wells logs and core data, while c
can ba
determined from a fluid sample or fluid properties
correlation.
For gas wells, c may approximate
Cs
naturally
frac$ured
formation
(~l~hou~he~hi~ia not alwaya true).
In Example I,OJ waa obtained directly from the
match. If ~ cannot be readily determined from the
peat-fracture well teat (due to insufficient
early-time data), u obtained from a pre-fractura
well test should ba ueed.
If well logs or core
data are not available,(V@c) may alao be eatimeted
~~,2il Pre-fracture
well teat given sufficient.
When Af ia large, only the final, total ayatem
reaponae may be obaervad in a peat-frecture well
test. Tha natural-fracture-dominated region and
the transition region of the test may occur too
early (within minutes) to be observed or may be
distorted
by
wellbore
atoraga. Example 2
illuatratea such a teat. These simulated data were
generated
using
the reservoir
and fracture
propertiaa presented in Table 1.
The aimulatad
drawdown data for Example 2 beginning,at a time of
about 1 hr into the flow period are plotted in Fig.
3. Note that the data do not exhibit ths complete
doel-poroelty behavior illustrated in Fig. 2.
Because of thie, two equally good metchea of the
teat data could be obtained aa shown in Fig. 3.
Match A would be found if pre-fracture teet had
baan run from which we determined IAI= 0.01.
However, another metch, Match B,l~ould be found on
the w = 1 or Gringarten et al.
type curve (for
aingla-poroatty reaervoira~i~no pre-fracture teat
results were available.
Aa seen in
Fig.
3, although these shulated
data ara from a duel-porosity reservoir with a
hydraulic fracture, they exhibit the aama reaponae
(after only a short time) aa data from a
alngle-porosity reservoir.
To analyze the data
correctly using the Houze type curve, we must uae
Match A with the pre-determined u = 0.01 and the
fracture atorativity, (V$c) . This yielda the
fracture half-length of 100 ff ahown in Table 1.
The teat data can also be snalyzed using the
Gringarten ~ ~. or u = 1 type curve for
single-porosity raaervoira with Netch B provided
the total atorativity, (V$c) , is used in place of
(Vl$lc) .
ihis calculation a ao yields a fracture
lengtfi of 100 ft. Thus, if the final, total system
responaa ia observed in a peat-fractura well teat
in a dual-porosity reservoir with a hydraulic
fractura, tha data can ba analyzed just lika those
from a single-porosity reaarvoir providad the total
atorativity ia used to determine xf.
When
i a
small , only the
natural-fractur -dominated
response may be
obaervad.
This is because it may take a long
testing time to reach the transition and total
ayatem regions. Figure 4 illustrate an example of
thta bahavlor.
These simulated data are for
Exampla 3 in Table 1.
Whan
only
tha
natural-fractura-dominated
response is observed,
we must know that tha
resenoir la dual-porosity nd we must know u (or
I
8s
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PRACTICALWELLTEST ANALYSIS NETHODSFOR HYDRAULICALLY
IU TUIJIJS IN D{
(v@)f) in order to determine Xf correctly. From
the retch shown in Fig. 4 and asauming independent
knowledge of
u from a pre-fracture
teat, we
calculated the correct value for Xf of 100 ft.
If we had interpreted these data to be
single-porosity or to have represented the totel
ayatem response and had used total storativity in
calculating xf, we would have computed an x
{
of
10
ft. Assuming c z c , the Xf estimated us ng the
wrong atoretivit y ie %ff by a factor of TU
For
an u of 0.01 as in this example~ the value of xf
would be undereatimeted by a factor of 10. For u =
0.1 to 0.001, this is a factor of 3.16 to 31.6.
Obviously, in e test such as this, it is important
to know vhether the reservoir is single- or
dusl-porosity and, if dual-porosity, to have an
independent knowledge of 10.
These simulated examples
illustrate
the
supplication of the Houze type curves.
Based on
these examples and our diacuasion of Fig. 1 several
practicsl implications of well
test
anslysia
In
hydraulically fracturad dual-porosity reservoirs
become
evldeut.
These are diacuaaed
in
the
following section.
PRACTICAL IMPLICATIONS
Aa
previously discussed, if ll the
characteriatlc featurea predicted by the Houze typa
curves are observed in a well teat, good match
of the teat data can be used to calculata & x , AS
and W.
Unfortunately, tests of this k%n~ re
rare in our perience. What we have observed Is
data with little or no transit&on which could
eaeily be interpreted a ainSle- or dual-porosity.
Aa shown above. if Af la large, these data are
probably in the total systam response region and
can be correctly analyzed uain8 existing type
cuNes for
single-poroatty ayatema.
However,
finding s reaaonsbly unique-match can be difficult
without prior knowledge of k to fix the vertical
match point and allow only horizontal shifting of
data on the type curve. This la true for moat
post-fracture analysis mathoda.
IfAf ia smell, we have ahown
it
is possible
that only the natural-frscture-dominated response
may be observed. In thess caaes, prior knowledge
of u and (V$c) is critical to correctly astimete
x. Using (V$c) as opposed to (V$C)
~ $h$h::{alyais can lest to eatimstes of x
substantially smeller than the trua .
analyzed several testa where, using (V@) , we
computed x
8
valuea which ware much smellert than
expacted f r the size treatment pumpad.
Howaver,
if we assumad that the data ware reflecting the
natural-fracture-dominated reaponae rathar than the
total system reaponae and ueed (V$c)
anslyaia, a mora reasonable value 0{ ; %
obtained.
In ell peat-fracture well teat analysia,
a ingle-
or dual-porosity, knowledge of ~ from a
pre-fracture teat may ba critically important to
the intarpratation procedure.
The beat sourca
of
this knowledge ia pra-atimulation wall testa,
properly conducted.
In wells which will not flow
prior to atimulationo
smell ballout or breakdown-
typa treatment should be conductad to initiata
flow. Steps must also be taken in dual-porosity
well tests to minimize wellbore storage to maximize
the chancee of computing u. Without knowledge of
a reaenoirs true nature and natural potential, it
may be impossible to properly interpret poat-
fracture well tests to aasesa the effectivene:a of
the treatment uaad. Lack of pre-fracture well teat
data is a common problem in trying to interpret
post-frecture teata. This ia especially true in
the Devonisn Shsles.
FIELD SXANPLES
In
this
section, we
present
two field
sxamples of peat-fracture
well teets in
dual-porosity reaervoira.
Field Example 1
This example is for a Devonian Shale gas well
tn Lincoln County, UV.
This well haa baen
stimulated
twice
with
hydraul%c
frscture
trsatmente. The first treatment was a nitrogen
foam fracturs which used about 1S0,000 gala of 75
quality foam nd 280,000 lb of 20/40 sand. A
pre-fracture taat was
not
conducted for this well.
Following 168 hr flow teat, the well waa shut-in
for
318 hr buildup teat.
The post-fracture
prcaaura buildup taat data are plotted in Fig. 5.
Basic raaarvoir nd completion data for this well
are
shown in Table 2.
Note the flat esrly-time data in Fig. 5. We
%ntarpret these data to be tranaitlon data for SA
of 500 aa ahowo in our match of the
teat
data wit
t
the House type curva in Fig. 5.
The transit ion
data begin at a real time of about 10 min nd span
about 1 hr. Sinca we do not have sufficient early
data to fit the u = 1 curve, u can only be
aatimeted to be less than 0.1. The tranaitioo data
last too long for u to be greater than 0,1.
Lacking pre-fracture teat, we saumed w - 0.01
for the purpoaea of quantitative analyata. Using
the match shown in F&g. 5 we
calculated
a ~ 2$
0.0264 md, an x of 105 ft. and a A of 3.07 x 10
t
s ahovn in Ta le 3.
Our calculation for this
example test are presented in the Appendix.
A second fracture traatmemt conaiating of
about 300,000 gals of 75 quality nitrogan foam snd
610,000 lb of 20/40 sand was parformed on the wall.
Following this treatment, another peat-fracture
butldup
teat waa run
which la shown
in Fig. 6.
We analyzed this teat by aaauming ~,~,
and w (which are resarvoir properties) did not
change from the previously calculated valuea.
Doing this wa obtainad the match shown in Fig. 60
From this match we calculated an Xf of 349 ft and
read a A of 5500 aa shown in Table 3.
f
Tha fit
of
the data in Fis, 6 with the Flouse
type curve is not aa good as the fit obtained
following
the firat fracture treatmant. Tha
early-tires
data do not xhibit tha transition
bahavlor exhibi$ad in Fig. 5.
Sttll, fixing both~
and w
t the valuea
determined from the initisl
peat-fracturs tezt, a raaaonable match of this da ta
w a a obteined.
This field ample,
nd
pecially the first
peat-fractura teat) illuatratea the bahavior pra-
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F
15924
D. E. LANCASTERAND J
. m. G~ 1
dieted by Howe et al.
19
and the application of the TESTING AND ANALYSIS GUIDELINES
Houze type curvet~analyze the data.
Note that
the tesulta we
obtained for Xf are largely
Based on
our
experience in
analyzing
depandent on our assumption of an w of 0.01.
peat-fracture dual-porosity reservoir well teat
ilowever, given the teat data and what we know about
data in the Devonian Shales, we present the
this well, this value of w appeara reasonable. We
following general guidelines for conducting and
plan to gather production data for this veil to analyzing peat-fracture well tests in dual-porosity
confirm our well teat analyaia results.
reaervoira.
Field Example 2 1) Alwsy~ conduct a pre-fracture test to deter-
mina k, A , andw. Since w can be critical to
This exsmple ia for a Devonian Shale gaa well
the post-fracture teat interpretation, ataps
in Mason County, WV.
This well ia a relatively
should be taken to minimize wellbore storage
poor well and was fracture treated with about
(bottomhole
shut-in) ~4ao ~u:~e:in;~ nay be
70,000
gals of 90 quality nitrogen foam and 60,000
accurately determined.
lb of aand to improve its performance.
Basic
*ila:
to those presauted by Holgate at al.
reservoir and completion data for this well are
.
recommended for conducting pre-fracture well
shown in Table 4. Pre-fracture test data were not taats in the Devonian Shalee.
available for this well.
2)
Conduct the post-fracture test using standard
Following tha fracture treatment, this well
practices.
If wellbore etorage effects are
waa flow tested for 216 hr and shut-in for a 144 hr expected to be a problem, stepa should be
pressure buildup test.
Thasa data are ahown in
taken to minimize these effects.
Fig. 7.
Aa in the
Wa could not fit these data using the
Houza typa curve.
pre-fracture test, bottomhole shut-in should
However, a reasonable fi\ f the
be considered to minimize wallbore storage
data could be found with a Barker-Ramey
type
diatort$on of the early time data. Conducting
cuwa for infin%te-conductivity vertical fractures long teats and gathering data at very eerly
with wellbore
storaga in
single-porosity
times (minutes In most caeea) meximizea the
reservoir. Wa analyzed these data using the match
shown
chancee of obsarving tranaitton or character-
in Fig.
7 aaauming a single-porosity
istic dual-porosity behavior.
For buildup
reservoir and using (V$c)t in our calculations.
teata, the flow teet should be at least ual
Tha reeulta for E and Xf are shown ID Table 5.
to and preferably longer than tha buildup teat
Nota the short fracturt: length of about 5 feet.
in duration.
Aaauming theaa data are from a dual-porosity
3)
If characteristic dual-porosity behavior ia
reaewotr (which ia reasonable for the Devonisn
observed, uae the appropriate tyms curve to
Shales) and Af ia small, it la poeaible that all
analyze the data. Currently, only the Houze
the tast data could ba dominated by the natural
type
fracture porosity.
curve ia available ap~cifically for
If ao, (V+c)f should have bean
dual-porosity reeervoira. Usa k, A and tAIfrom
used to calculate x .
6
Assuming values for u of
0.1,
0.01,
pre-fracture
teat
and O. 01, we
analy~is to
assist in
calculated fracture
matching the pest-fracture data.
half-lengths of 15 ft, 49 ft and 155 ft.
respectively.
Theee reaulta are alao summarized i~
4)
Until new dual-porosity type curvee ara
Table 5. Without pre-fractura data to determine k
available, if the data exhibit other than
and to, we cannot be certain whtch, if any, of the
infinite-conductivity fracture bahavior with
above results is most reasonable.
However, ve
believe that the dual-poroafty interpretation is
~~n~a~,~e atora6eC use published type
for single-porosity reservoirs to
more consistent with what we know about this
match tha data.
Calculate x aaauming both
reservoir, this well and the stimulation treatment
iotal system and natural-fr ctu:e-dominated
pumped. We will be monitoring the
future
behavtor (( VI$IC)
performance of this
well to
confirm
this
f
or (V$IC) ) and determine
which Interprets ion is moa~ conalstent with
intarpretation.
what is known about the rasarvoir and the
stimulation treatment.
If the reservoir ia
This example ahowa that vhat appears to be
known to ba dual porosity and an independent
conventional single-porosity pressure
tranaient
knowledge of ~ Is availabla, uae (V$c)f to
behavior may, in feet, ba dual-porosity behavior
calculate xf.
vhich requires a different calculation procedure to
yield meaningful results. In ~\is example, we used
5)
Analyze post-fracture production data using
a single-porosity type curve
to make a dual-
the appropriate reservoir model or type curve
porosity intyjpretation.
We believe the work of
to
determine
whether the well
Houze et al.
taat
can be extended in the way shown
interpretation yields a reasonable perfonnsnca
above not only to infinite-conductivity fractures prediction. If not, ra-intarprat the well
with wellbore storage but also to
finite-
test data,
conductivity fractures.
We are working to expand
the Houze type curves and to develop fractured wall 6)
In the atepa 3-6 above, type curves can be
type curves for dual-porosity reservoirs which
replace~O by
a
reservoir
model
such aa
include the effacts of wellbore storage, finite-
SUCARII
to analyze the data. In some casea,
conductivity fractures, and unsteady-state matrix
whare no type curve ia applicable due to
flow.
complex behavior, this may be tha only
analyaie method available.
al
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PRACTICAL WBLLTEST ANALYSISMETNODSFOR HYDRAULICALLY
FRACTUREDWELLSIN D
CONCLUSIONS
Baaed on the work presented in thie paper, we
~ave drawn the following concluaiona.
.)
)
1)
If sufficient data are observed, tncluding
transition from netural-fracture-dominated to
total-system behavior, and the hydraulic
~~~t% fi infinite
conductivity, the Houze
can be used to determine EO xf~ X
end w.
If the peat-fracture well teat data do not
exhibit complete dual-porosity behavior, the
data
can be analyzad using type cmvea
developed for single-poroatty reservoirs. To
uae single-poroatty,
fractured-well
type
curves in
dual-poroeity reservoirs,
the
atoretivity, total ayatem or natural frectura,
which dominetaa the observed behavior must be
diatinguiehed
to
obtain
a correct
interpretation.
If total-system dominated
(late-time) bahavior is observed and matched
on a a%ngle-porosity type curve, the correct
value of Xf will be calculated only if (V$C)
is used. Conversely, if the teat data ar~
dominated by the natural fracture ayatem and
matchad on a single-porosity type curve, the
correct value of Xf will be calculated
only if
V@ f ie used.
Pre-fractura wall teat data are important to
proper peat-frecture well teat interpretation.
Pre-fracture teat data can be used to obtain
estimatea of ~, A, nd u which can be critical
to
the
corract interpratatlon of the
peat-fracture teet.
W2W2WXATURB
symbol
B
B
av
c
Cll
Ct
c
t,av
c
cDf
h
hf
hm
E
Meaning
Formation volume factor, RB/14SCF
Formation volume factor at pav, RB/MSCF
Compreaaibility, llpaia
Gaa compreaaibility, Ifpaia
Total compreaaibility, l/paie
Total compreasibllity
at
pav, l/peia
Wellbore storage coefficient, bbllpat
0.8936 C
*
, matching parameter for
$h
Net
Net
Net
Barker-Rarney type curva;
Ctxf
dimensionleaa wellbore
storage coefficient,
pay thickneaa, ft
fracture thickneaa, ft
matrix thickness, ft
(kh)m+ (kh)f
hf + hm
, effactive
etem
permeability,
md
K
m
~
?a
?~
?i
Pwf
P
wa
P
av
F
ip
1
r
w
r
ta
Matrix permeability, md
Pressure, paia
z
~pav Ip$, adjusted preaaure,
av o
psia
~ , dimenaion~eas we~~bore
.
pressure
Inttial reservoir preaaure, paia
Flowing wallbore pressure, paia
Shut-in wellbore pressure, psia
Reference preaaure for calculating
adjusted time and adjuated preeaure, paia
Average dreinage area praasure, paia
Change in preaaure, (pi - pw ) for
dravdown
taeta, (p
-pwf a t=O) for
buildup tests, pai s
Flow rate, 14SCklDay
Wellbore radiue, ft
Reservoir temperature, F
Time, hr
t ~, adjuated time, hr
r
av ct,av o Bc
t
Ata
Df
Atae
v
f
z
av
~
a
P
~- adjuated shut-in
av Ct,av
o
t
time,
hr
0.000264 Et
~, dimenaionleas time group
(v$c)f Mxf
At /(1 + At /t ), effective adjusted
ah~t-in tim~, R
Bulk volume fraction of tha reservoir,
fraction
racture half-length, ft
Gaa compressibility factor at pav
Interporoslty
Interporoaity
flow
flow
ahape factor, l/ft2
k2
coefficient, a
~r
rKw
k
Fracture trenafer coaffictent, a
2X
E f2
COa g ra v it y (air = 1.0)
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8/10/2019 12. SPE-15924-MS
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E 15924
D. E. LANCASTER
IJ
viscosity, Cp
B
Viscosity at pav, cp
av
@
Porosity, fraction
(v@c)f
u
(v@c)f+ (V$c)m
, storativity ratio
Superscripts and Subscripts
a
Adjusted
D
Dimensionless
e
Effective
f Fracture
6
Gaa
i
Iuitial
m
Matrix
r
Reaervo%r
t Total
w
Wellbore
Wf
Flowing wellbore
wa Shut-in wellbore
ACKNOWLEDG~TS
We would like to acknowledge the Gaa Research
Institute (GRI) which aponaored much of this work
under GRI Contract No. 5084-213-0980, Analysis of
Eaatern Devontan Gas Shales Production Data.
REFERENCES
1.
2,
3.
4.
5,
Barenblatt, G. I.,
and
Zeltov, Y. P.:
Fundamental Equationa of Homogeneous Liquids
In Fissured Rocks, Dokl, Akad. Nauk SSR, 132
(3) (Juna 1960), 545-548,
Warran, J. E. and Root, P, S.:
The Behavior
of Nsturally Fractured Reservoirs, Sot, Pet.
Eng. J., (Sept. 1963) 245-255; Trana., AIME,
249.
Odah, A. S.:
Unateady-State Behavior of
Naturally Fractured Reservoirs, cqc. Pet.
~ (Maieh 1965) 60-640
.
Bourdet, 1).
and
Gringarten, A.:
ltDet.erminatiOn
of Fiaaure Volume and Block
Size in Fractured Reaarvoira by Type-Curve
Analyais,
papar SPE 9293 prasented at the
1980 SPE Annual Technical Conference and
Exhibition, Dallas, September 21-24,
Serra, K., Reynolds, A. C,, and Reahavan, R.;
l~New preaeure- Tranalent A~alyaie ~ethod; for
Naturally Fractured Reservoirs, J,
Pet. Tach,
(Dec. 1983) 2271-2283.
6.
7.
B.
9.
10.
11.
12.
13.
14.
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17.
18,
Bourdet, D., Ayoub, J. A. and Pirard, Y. M.:
Use of Preaaure Derivative in Well Teat
Interpretation ,
SPE paper 12777 presented at
the SPE California Regional Meeting,
Long
Beach, April 11-13, 1984.
Bourdet, D., Alagoa, A., Ayoub, J. A. and
Pirard Y. M.:
New Type-Curvaa for Tests of
Fiaaured Formation, World Oil (April 1984).
Gringarten, A. C.:
Interpretation of Teats
in Fiaaured and Multilayered Reservoirs With
Double-Poroatty
Bahevior: Theory
and
Practice,t J, pet. Tech. (April 1984) 549-564
Eraaght,
I. and Aflaki, R.:
Problems in
Characterization of
Naturally
Fractured
Reaervoira From Well Test Data, Sot. Pet.
Eng. J. (June 1985) 445-450.
Holditch, S. A. and Morse, R. A.:
Large
Fracture Treatments May
Unlock
Tight
Reservoirs, Oil & Gaa Journal (Nay 19, 1971)
57-60 and (April 5, 1971) 84-89.
Ruaeall, D. G. and Truitt, N. E.: Trsnsient
Preaaure Behavior in Vertically Fractured
Reaervoira, J.
Pet. Tech. (Oct. 1964)
1159-1170.
Gringarten, A. C., Ramey, H. J. Jr., and
Raghavan, R.:
Unsteady-State Preeaure
Distributions Created by a Well With a Single
Infinf.te-Conductivity Vertical Fracture,: Sot.
Pet. Eng. J. (August 1974).
ClnCO. E., Samanlego, F. and Dominquez, N.:
Tranalent Preaaure Behavior for a Well With a
Finite-Conductivity Vertical Fracture, Sot.
Pet. En.g. J. (Aug. 1978) 253-264.
Cinco, H.
and Samaniego, F: Effect of
Wellbore Storaga and Damage on the Tranaient
Preaaure Behavior of Vertically Fractured
Wells,
paper SPE 6752 presented at the 1977
SPE
Annual Technical Conference and
Exhibition, Denver, October 9-12.
Agamal, R. G., Cartar, R. D., and Pollock, C.
B.:
Evaluation and Prediction of Performance
of Low Permeability Gaa Well Stimulated by
Maaaive Hydraulic Fracturing, paper SPE 6838
presented at the 1977 SPE Annual Technical
Conference and Exhibition, Denver, October
9-12.
Bsrker, B, J.
and Ramey, R. J. Jr.:
Trsnsient
Flow to
Finite-Conductivity
Vertical Fracture,
paper SPE 7489 praaented
at the 1978 SpE Annual Technical Conference
and Exhibition, Houston, October 1-3.
Lee, W, J. and Gatens, J. M. III:
Analyais
of Eastern Devonian Gaa Shalea Production
Data, paper SPE 14506 preaentad at the 1985
SPE Eaetern Regional Meeting, Morgantown,
November 6-8,
Gatens, J. M. III, Olarewaju, J. S., and Lee,
W. J,:
llAn Integrated Reaemoir DeocriPtiOn
Method for Naturally Frectured Raaervoirs,
-
8/10/2019 12. SPE-15924-MS
8/10
PRACTICAL WELLTEST ANALYSIS NETHODSFOR HYDRAULICALLY
FRACTURNDWELLS IN DU
paper S PE 15235 presented at the 1986 SPE
Unconventional Gas
Technology symposium,
Louisville, Ney 18-21,
19.
20.
21.
22.
23.
24
25.
Houze, O. P., Ilorne, R., and Remey, B. J. Jr.:
?*Infinite Conductivity vertical Fracture n a
Reservoir
With Double Porosity Behavior,
paper SPE 12778 presented at the 1984 SPE
California Regional Meettng, Long Beach, April
11-13.
Science Applications, Inc.: Simulator for
Unconvent ional Gas Reaourcea Multi-Dimensional
Model SUGAR-ND, Vol. 1 and 2, NTIS Report No.
DOE/MC/08216-1440, September 1983.
Lee, W. J.: Pressure Buildup
and Drawdown
Analyaia, SPE Short Course Notae, 1984.
Aga~al, R. G.: Reel Gaa Pseudo-Time - A New
Function for Pressure Buildup Analyaia of
MS ?
Gaa Wane,
paper SPE 8279 presented at the
1979 SPE Technical Conference and Exhibition,
La s Vega a,
September 23-26.
A1-lluaaainy, R., Nemey, H. J. Jr., and
Crawford, P. B.: The Flow
Raal Gaaea
Through Porous
Ifadfa,
J.
Pet.
Tech. (Mey
1966) 624-636.
Wataon, A. T.. Gatena, J. M. 111,
nd Lane, Il.
s. :
Nodel Selection or Well Teat nd
Production Data Analyals, papar SPE 15926
presented
t the 1986 SPE Eaetern Regional
Meeting, Columbus, Nov. 12-14.
Flolgate. K. E., Lancaster. D. E.. and Lea. W.
J-
kalyain of Dr%liatem T-sat Data- in:
Devonian Shale Reaervotra, papar SPZ 15925
presented at the 1986 SPE Eestern Regional
Maeting, Columbus, Nov. 12-14.
APPENDIX
Example Calculations
Field Exampla 1
This appendix demonstrates the procedure for
analyzing peat-fracture well teat data in 9
dual-poroeity raaemoir using tha Houza et al.
type curve. To obtain a match, plot the w~ll~aat
data aa Ap varaus t (At
for buildup tests) on
log-log co~dinatea t%a aa~~ size aa tha Rouze typa
curve.
Overlay this plot on tha type curve and
move the data vertically and horizontally on the
typa curve
until a good fit ta found.
If E is
known, a pressure metch point can be pra-calculated
and only horizontal shifting la needed to find a
match.
For Fiald Example 1,
the
metch la shown in
Fig. 5 and the match point data racorded balow.
Ataa =
10 hr
ba
4 paia
;Df ;
0.7
hr
pD =
O*OI
0.01
(aaaumed) Af ~
500
~ can be calculated from
the
praaaure match
point.
)-POROSITY RESERVOIRS
SPE 15924
141 2 B
E - ~ u (+)
a
21
Whan using adjusted timee and pr~ssuree , we
evaluate B, P and c
at pav
=1/2(p+p) In
this case, p is 17 paia and Bav, Vav, a~~ Ct av
ara shown bef~w,
s
B
m
15.5 RB/M8CF
av
IJ
.
av
0.011 Cp
Ct,av =
4.10 x 10-3 paia-l
Using thaae values, we calculated ~,
~.
141,2(90)(0.011)(15.5) ~0.01
205 T)
~- O.0264 md
x can be calculated from the time metch, but
fractu~e atorativity, (V@c)fi must first be
calculated using Eq. 7. Aaaum g u - 0.O1O
(Wc)f
(V c)t
vwf
0.01(0.02)(4.IOX 10-3)
V lc )f =
8.2 x 10-7 paia-l
Xf can then be calculated using the time metch
point.
0.000264(0.0264
Xf-(
) ( )) 1/
(8.2x
10-7) 0.011)
=
10s ft
f
A can then ba calculated using Eq. 5.
A
0,26 )2
- 500 (~
A
- 3.07X
10-3
The reaulta are aunmisrized below.
E=
0.0264 md
k - 3.07 x 10-3
f =
105 ft
u
= 0.01
asaumed)
I
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9/10
T; , I } I
, 1 , ,: . ::, . ;1 1:) Pl opby;,, l-.
,. [ ; IT IN :l :ll[, ir,l~ D.t,t rl l-s
I>::-J,-::_
f
km
.. _.. -
.__i . . .
..
(md~
)
Q
{,.$5 y, 10-~
4.167 x 10
-4
1
1WI(I
h.?5 Y 1[)-~
.
L,167 Y
10-
1
Il. I
6.25 x 10
-7
4,167 x
10
-6
Prrp.rt lcs commm ,, HI 1 ax, .nples
include the fol lm ng:
E
= 0.05 nd
rw - 0., 5 ft
h = l[:fI ft
x=
f
00 fc
Ap = 0,7
: I . ,,
l~,,, . ,, .,, ,. . ,,
.,
. . r r.,,.,,,.
,:\,,,,,.,,,,
95
-
8/10/2019 12. SPE-15924-MS
10/10
/1 /1
I I I 1 I I I
IO-3 10-2 lo-l
100
101
Ioz I(y 104
106 106 I
lm4
.,
, , ,J t I ,p, . L ., w, t ., mlmn,. conrl ,,clw, ly hyf lr ,whc fracture m a d.a l. pmos,ty Ieservotr (al ter Houzec1
,,,
1
10-f
.. -
Iof
~b. -?YPWUWO
IIMtth.,
01
mn lohd d,,wdown tt data-E,m@8 1.
Af.
500
I
I
I
1
1
1
I
1
1
lo.~ K@ 10-~ lo~ 100 101
@
@
104
10s II
EFFEC TI VE A DJ USTEO TI ME , hr
FIII,
6-TVPHUWO
match 01Ilml POM.IMCIW buildup lent dma-Field Emmple 1,
~ 15924
ADJUSTED TIME, hr
Fig. 2-Tvpe.cuwe malch cdslmulatad drawdown test dMn-Example 1,
10+
I
I
1
I
1
I
I
I
1
104 10- ID+ @ @
I01
lot @ 10
10S I
ADJUSTED TIME, hr
% 4-TwMum mtl ch 01
bMkFSd dmwdown WI dmbemmpla a.
MATCH POINT
tof 80,98
poml
+
/
h f 95500
+
.
---
--- Af m1000
co
o
t
I
o
I
I
I
I
I
I
1
)-4 lo-~ 10.2 ,04 100
Iol lot lo~
104 lo~ 1(
EFFECTIVE A DJ USTED TI ME , hr
~lg.6-TWIO.CUWOmolch01
mwd p0 9t .l rm tu r b ui ld up I *9 d da -kld Compk 1,
Go
o
10-t
Io.1
I00
lot
i@
I
EFFECTIVE A DJ USTED TIME, hr
Fh, ?.-TYP*,cUWC mMCh 01 P09ttmclure blldp 1081dala--tlold
EIIDIFWIC,
96