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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

8/10/2019 12. SPE-15924-MS

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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)

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.

15.

16.

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

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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

8/10/2019 12. SPE-15924-MS

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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