Direct Approach Through Hall Plot Evaluation Improves The Accuracy of Formation Damage Calculations and Eliminates Pressure Fall-Off Testing

8/18/2019 Direct Approach Through Hall Plot Evaluation Improves The Accuracy of Formation Damage Calculations and Eliminates Pressure Fall-Off Testing

1/25

DI RECT APPROACH THROUGH HALL PLOT EVALUATION

IMPROVES THE ACCURACY OF FORMATION DAMAGE

CALCULATIONS AND ELIMNATES PRESSURE

, FALL-OFF TESTI NG

. .


2/25

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

*

?

?

w

9

*

P

Pege

*

1

*

2

3

. 5

. 6

.<

. 9

9

9

11

11

.

11

11

12

. 12

. . . ..:


3/25

Figure 1 .

Figure2 .

Figure 3 .

Figure4 .

Figure 5 .

)

Figure 6 .

—

. . .

.

.

.

9

e

LIST OF ILLUSTRATIONS

b

*

b

*

b

s

s

9

.

9

9

.

o

4

4

7

10

22

23


4/25

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.

. . . .


5/25

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

. . . .


6/25

.

WHP x time,

psi-months

,,

CUMULATIVEINJECTION,bbls

Figure 1. NormalHall Plot, no apparentdamage.

..,

.. .. .. . . . . . . . . .:


7/25

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:

.,

. .


8/25

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

.,


9/25

.

. . .

,.

R=


10/25

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

-,


11/25

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 ,,.

:\


12/25

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13/25

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)


14/25

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


15/25

,

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


16/25

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-


17/25

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


18/25

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.


19/25

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.

..>

..

.

.


20/25

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


21/25

(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


22/25

(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


23/25

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


24/25

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