direct approach through hall plot evaluation improves the accuracy of formation damage calculations...
TRANSCRIPT
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8/18/2019 Direct Approach Through Hall Plot Evaluation Improves The Accuracy of Formation Damage Calculations and Eliminates Pressure Fall-Off Testing
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DI RECT APPROACH THROUGH HALL PLOT EVALUATION
IMPROVES THE ACCURACY OF FORMATION DAMAGE
CALCULATIONS AND ELIMNATES PRESSURE
, FALL-OFF TESTI NG
. .
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TABLE OF CONTENTS
1s
II
111
Iv
v.
LIST OF ILLUS7RATTONS
ABSTRACT e ,
INTRODUCTION
BACKGROUNDOF
PROCEDURE e
FIELD
.,.
EXAMPLE
Step 1
Step 2
Step 3
Step 4
step 5
Step 6
Step 7
step 8
s
.
.
9
s
b
*
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?
w
9
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P
Pege
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1
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2
3
. 5
. 6
.<
. 9
9
9
11
11
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11
11
12
. 12
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Figure 1 .
Figure2 .
Figure 3 .
Figure4 .
Figure 5 .
)
Figure 6 .
—
. . .
.
.
.
9
e
LIST OF ILLUSTRATIONS
b
*
b
*
b
s
s
9
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9
9
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o
4
4
7
10
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1. ABSTRACT
In the operationof a waterfloodprogram, it becomes necessaryto deter-
.
mine injectivecapacitythroughthe evaluationof individualinjectionwell
performance. With the occurrenceof a decreasein a particularwell’s injec-
tivity,the need arises for a direct calculationof capacityloss or well-
bore damage,
I& the courseof norinaloperationsthen, a
test is usuallyrun on the problemwell to determinethe
of damage. These tests are lengthy,time consuming,and
pressure fall-off
.
existenceand extent
costly.
The proposedmethod of evaluationcan yield indicationsofthe extent
and natureof injectivityloss without the use of fall-offtests, The method
presentedinvolvesthe interpretationof routinemonthly injectiondata for
all requiredcalculations and effectivelyeliminatesconventionaltesting
procedure in a normal waterfloodprogram.
. . . .
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11. INTRODUCTION
In 1963,Hall(1) ptesenteda systemof analyzingthe performanceof in-
.
jectionwells using what are,known as
Hall
Plots.” The paper presentsa system
of analyzingthe performanceof injectionwells througha method in which
monthlypressureand injectionvolumes are recordedand plotted.asa summa-
tion of pressur~multipliedby time versus cumulativeinjectionvolume.
. .
Accord-
.’
ing to this article,
the examinationof the ltHalllJlot (see Figure 1) before
or
and after any well stimulation‘ortreatmentcan give indicationsof success
failureof such workovers.
Since that time, various articleshave been published
on
this subject
showinghow this systemhas been used in a particularfield2 or in comparison
with some other method of treatmentevaluation. However, in most cases,
its
only use is for recognizingany formationdamage as evident by the accompany-
ing drop in injectivity.v:hi.chs seen a~ a rise in the slope (see Figure 2).
There is an equationfor the slope of the line
on
the Hall Plot (1) which
. . . .
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.
WHP x time,
psi-months
,,
CUMULATIVEINJECTION,bbls
Figure 1. NormalHall Plot, no apparentdamage.
..,
.. .. .. . . . . . . . . .:
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It is, therefore,the intentionof this paper to show that rather than
using the Hall Plots only as a means to identifya loss of injectivity,it
can be used as a method of determiningtreatmentor workoverprocedures,
.
The conventionalprocedure,once the problem
Plot, is to run a pressure fall-offtest4 to
skin effect. This methodwill eliminatethe
P
allowingdirect calculationof these values.
has been recognizedon the Hall
determineformationdamage or
need for fall-offtestsby
111. BACKGROUNDOF PROCEDURE
In any evaluationof formationdamage, the main purpose is to determine
a loss of injectivityor productivitydueto an additionalpressuredrop
across the skin. Therefore,the Van Everdingenslcinfactor is calculatedin >
order to know
the skin, and
gained. With
the seriousnessof the damage, to find the pressuredrop across
to arriveat some figureof production(or injection)to be re-
these indications,a treatmentproceduremay be written.
Upon examinationof the slope equation,it is seen that the slope of the
line is inverselyproportionalto transmissibility(Tin).Where:
.,
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Equation (5)
~= 4.844 Bwln(re/rw)
m
—
Therefore,when the Hall Plot is examined,and an increasein slope is
evide.lt,it can be assumed”that there is some degree of wellboredamage present.
The slopes
damage (ml
slope (ml)
are then found for the conditiontiefore and after‘theappearanceof
and m2). The value of transmissibility(l hq)found from the first
is that of the undamagedportionof the reservoir (seeFigure 3).
This is evidentsince the slope is occurringduring that period of time when
there is no damage.
The value found from the second slope (m2) is the average
of both the damagedand the undamagedzones (see Figure 3). With these two
values (Tml and Tm2), all of the formation,damagecharacteristicsrequired
for treatmentdesign can be found.
The assumptionsthus far include:
‘l’mlfoundfrom ml) = ~
Th2 (foundfromm2) = I’mavg
,.”.
Where:
“
Transmissibilityof undamagedzone
.,
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.
. . .
,.
R=
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This becomes:
Equation (7)
TinaTml In (re/rw)
I Mlavg ‘IW2“
Tmaln(re/ra)+ Tmlln(ra/rw)
Which is solved for Tma
.
into
.
With
l’hisvalue of ‘lha,along with the assumedvalue of ra, is then substituted
Van Everdingen’soriginalequationfor skin effect, symbolS.5
Equation48)
.
S = {ke-ka)
ka
In (ra/rw)
or
~=(Tml- ‘Jhla)n (ra/r~)
Equation (9)
lhla
this value of S, the pressuredrop across the zone of damaged transmissi-
bility can be found from:
Equation (10) AP = qSC2BW5 “
a
0.00707 Tm~
After calculationof these importantparameters,the engineermay want to know:
DamageRatio,Flow Efficiency,Damage Factor, and Minimum InjectionIncrease
(uponskin removal).
To find these,however,the assumptionmust be made of
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This exampledeals with a
North DakotaProducingRegion.
field as a part,of.the Newburg
V. EXAMPLE
well operatedby AmeradaHess Corporation’s
It is an injectionwell located in the Newburg
PressureMaintenanceSystem in Bottineau
County,,NorthDakota. Pertinentdata is given below:
Table 1
Data for D-716i6
.’
Perforationdepth
3423-3440ft.
Effectivepay thickness
14 ft.
Mid-pay at
3432 ft.
Porosity (FieldAverage) ‘
14%
Radius of well bore, rw
7-7/8”hole:
0.328 ft.
Spacing
80 acres
InjectionRate before damage
395 BWPD
InjectionRate after damage 60 B’WPD
re, (radius,ofinvestigation) .. . . ., ... ,. . 910 ft ,,.
:\
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TJ q =
Tq =
~2 1=
TnQ =
3.
The transmissibilityof
(4.844) (1.002)ln(910/O.328)
(0.1136)
339 md - ft/cp
(4.844)(1.002)ln(910/O.328)
(0.7385)
52,1 md-ft/cp
the damagedzone (Tma) is found from Equation
(7).
In this case the assumedra = 2.0 feet,
Equation(7)
Tmz =
52.1 =
Tllla
4.
The Van Everdingenskin
Equation
(9)
s
=
s=
. ’
TmaTmlln(re/rw)
‘iavg =
lklaln(re/ra)+ Tmlln (ra/rw)
lha (339) in (910/0.328)
tia In (910/2.0)+ (339) in (2.0/0.328)
13.48md-ft/cp
factor is then calculatedusing Equation (9).
(Tlq- lhla)in (ra/rw)
Tma
(339 - 13.48)
in (2.0/0.328)
(13.48)
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Pe =
zs~()-
(395) (1.002) in (910/0.328)
(0.00707(339)
l?e= 1570 psia
7.
Damage ratio is calculatedwith Equation (12). “
Equation(12)
DR~ (Pe
- Pw) / (Pe.-Pw - APa)
DR= (1570-2880)/ (1510
-’2880 -(71095))
DR= 6.09
8.
Flow efficiencyis calculatedfrom Equation (13).
Equation(13)
FE= l/DR
FE= 1/6.09
FE= Oa~64
9. The damage factor is foundwith Equation (14)
Equation(14)
DF=l-FE
DF=l
- 0.164
D~s o.836
10. The
last characteristicto”be
:83.5 )
determinedis the value of minimum
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,
examinationof the HornerPlot for
was not carriedout long enough to
ditions, This results in improper
Parameter
s
AP
a, psia
pe~ Psi.a
DR
FE
DF
I~r,BWPD
t
this fall-offtest, it is seen that the test
allow proper evaluationof steady state con-
wellboredamage calculations.
.
Table 2
Value from Hall Plot
+
43.66
- 1095
1570
6. 09
0. 164
0.836
365
Value from Fall-off
,+
6.04
- 315 “
‘ 2006
1.78
0.56
0.44
107
In comparingthe skin factorsof the two methods, it is reasoned that the
value froundfrom the Hall Plot is a much better indicationas to the true seri-
ousnessof the problem. ‘i’hisssumptionis strengthenedby the fact that the
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Table 3 shows a comparisonof
ation and throughfall-offtesting
NewburgField. ‘,
skin factorscalculatedby Hall Plot evalu-
for two additionalinjectionwells in the
.
In comparingthesevalues,a very close correlationis noted. The fall-off
tests for these exampleswere very good, allowingdirect and accuratecalcula-
tionsof skin factors.
In the previousexample,it was
testwas inadequateand the values of skin factor found
parewith those from the Hall Plot evaluation.
shown that the fall-off
did not favorablycom-
.’
These facts indicatethat the closer the data for a fall-offtest approaches
a classicor textbookHornerPlot, the closerthe value of skin factor will be
to that found throughHall Plot evaluation. Therefore,it can be seen in the
limitedcases studied,that the Hall Piot approachcan consistentlygive accur-
ate indicationsof formationdamage in water injectionwells.
VIII.
SUMMARYAND CONCLUST,ON
This paper has been written to point out that all formationdamage charac-
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IX.
NOMENCLATURE
—
—
—
.
—
water viscosity,centipoise
water formationvolume factor
.
~adfus of injection,feet
radiusof wellbore,feet
water permeability,rnillidarcies
injectionthickness,feet
.’
slope of Hall Plot, psi-months/bbl
transmissibility,md-ft/cp
injectionrate, bbls/day
pressuredrop acrom skin, psi
damage ratio
flow efficiency
damage factor
minimum
injectionincreaseupon skin removal
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x*
REFERENCES
1.
Hall, H.N.: “How to AnalyzeWaterfloodInjectionWell Perfornu:,we”,
WORLD
OIL. (Ott..l963)128-130.
2.
DeMarco,M.: “Simplified
.
WORLD OIL. (April,1969)
.
Method PinpointsInjectionWell Problems”,
96-100.
Q
3.
‘sField Comparisonof Methods of EvaluatingRemedialWork”, JPT. (Ott.1964)
1121*
1
..
.
4. Robertson,D, C., Kelm, C. H.:
“InjectionWell Testing to OptimizeWater-
flood Performance”,JPT (Nov.1975) 1337-1342.
5.
Craft,B. S.,
Hawkins,M. F.: “AppliedPetroleum
PrenticeHall Inc. 1959, 322,332.
ReservoirEngineering”,
6. Interoffice Memo: Amerada Hess Corp.
“PressureFall-offon D-716i (NSCU)
S. J. Hunter, July, 1975.
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xl
ACKNOWLEDGEMENTS
I would like to thank Mr. Alex Chaky and the engineeringstaff of AMEWDA
HESS CORPORATIONin,Williston,North Dakota for their help. I would also like
to expressmy gratitudeto Mr.
RobertD. Grace for his assistancethroughout
the courseof this paper.
..>
..
.
.
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XII. APPENDIX
PressureFall-offTest on JI-716i
Perforations- 3423’ - 3440’
EffectivePay Thickness- 14’
Mid-pay@ 3432’
Porosity-
14% (FieldAverage)
Yw = (7-7/8’’)/2~0,328’
Spacing- 80 acres
InjectionRate = qi
= 60 BWPD (stable,prior to shut-in)
Wellheadinjectionpressure= 1220 psig
At, hrs.
o
20.5
48
68.5
214.6
92.2
64.9
~wS(@ surface)(ps%)
1220
680
540
513
Pws (@mid-pay)
2723 (PV7f)
2183
2043
2016
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8/18/2019 Direct Approach Through Hall Plot Evaluation Improves The Accuracy of Formation Damage Calculations and Eliminates Pressure Fall-Off Testing
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(B) Injectionwater density:
~w = (11,000ppm) (8.345x 10-6 ppg/ppm)+ 8.345 ppg
~w= 8.437ppg
.
(C) InjectionWater SpecificGravity:
VW = 8.437 ppg/8.435ppg
yw = 1.011
(D) Water Gr~diant+ (Wellbore):
(1.011)(0.433psi/ft) = 0.438psi/ft
(E) Water Compressibility:
11,000 ppm NaCl
*
~= 2,93 ~ 10-6 Ps
(F) UndersaturatedResidualOil Compressibility:
r. (36’’API)
0.8448 @ STP
rO (f 60°F and 1924 psia) = 0.8448 + 0.01
+ 0.8548
~c = 345 psia
~c= 10550.R
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8/18/2019 Direct Approach Through Hall Plot Evaluation Improves The Accuracy of Formation Damage Calculations and Eliminates Pressure Fall-Off Testing
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(J)
Slope of HornerPlot:
m = (-) 60
pSi/
(K) TotalMobilityt
.
(K/v)~=
, i 62. 6/mh~ ~q~~~
=
[(162.6);(160)(14% $60) (1.002)}
= 11.64 md/Cp
(L)
Radius of~investigation:
0.03[(K/P)t (t)/ $ Ct
$
0.5
tin =
0.03[(11.64) (141)/(0.14)(0.22x 10-6)
3
0.5
=
.,
‘in
= 1070 feet
(M) Skin Van Everdingen:
s= 1.15
i
‘Plhr
- Pwe)/m -
log (K/lI)t/$t (rw)*
3
3.23
-.
= Iils
z
(2127 -
2723)/(-60) -
3
og (11.64)/(0.14)(9.22 X 10-6 “
(0.328)2 *3.23
.f
1.~5 9.94 - 7.92 + 3.231
.,
S = + 6.-4 Formation-damage
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8/18/2019 Direct Approach Through Hall Plot Evaluation Improves The Accuracy of Formation Damage Calculations and Eliminates Pressure Fall-Off Testing
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Q)
(R)
..
(s)
(T)
Flow Efficiency:
FE =
Damage Factor:
DF =
l/DR= 1/1.78 = 0.56
l-FE = (1-0.56)= 0.44 (or 44%)
*
MinimumInjectionIncrease“(Uponskin removal):
DR (Q) =
(1.78) (60) = i07 BWpl’)
Darcy Injqction:
.’
Q= 0.00707 (K/p)th AP/B in (re/rw)
= 0.00707 (11.64) (14) (2723-2006)/in(745/0.328)(1.002)
= 107 BWPD
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8/18/2019 Direct Approach Through Hall Plot Evaluation Improves The Accuracy of Formation Damage Calculations and Eliminates Pressure Fall-Off Testing
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