Material Balance

RESERVOIR ENGINEERING

Chapter 12 – Material Balance Methods and Water Influx

Leonhard GanzerDrive Indices

1.00

0.70

0.80

0.90

Iw

Ig

0.40

0.50

0.60

Is

0 00

0.10

0.20

0.30

0.000 20 40 60 80 100

T ime, mo nths

Material Balance Methods and Water Influx

INTRODUCTION OUTLINEMATERIAL BALANCE EQUATION

DRIVE INDICESINTRODUCTION

OUTLINE

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

MATERIAL BALANCE EQUATIONTarner’s Formulation

DRIVE INDICESDRIVE INDICES

APPLICATIONSUndersaturated Oil ReservoirGas Reservoirs

GRAPHICAL METHODH l Od h M th dHavlena-Odeh Method

WATER INFLUX

2


INTRODUCTION Property Status Pre-drilling

Period1Well

stB C D E FA

MATERIAL BALANCE EQUATION

DRIVE INDICESStudy Method

Period

Analog

Completed Production OperationsAbandonmentDevelopment

Period

VolumetricPerformance

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

Range of Estimates

PerformanceSimulation Studies

Material Balance StudiesDecline Trend Analyses

Actual Recovery

cove

ry

Range of Recovery Estimates

Production Profile

Ultim

ate R

eco

Production ProfileCumulative

Rateg P

rodu

ction

Rate

mulat

ive P

rodu

ction

Log

Cum

HighRelative Risk Time

Risk

Low

3B C D E FA


INTRODUCTION INTRODUCTIONMATERIAL BALANCE EQUATION

DRIVE INDICES

INTRODUCTION

Material Balance is – Powerful method to estimate OOIP, OGIP

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

,– Estimate Aquifer Influx

Advantage– Independent from Volumetric Methods

• Used to verify volumetric results

Disadvantage– Requires Production from Reservoir– Requires accurate pressure monitoring and production/injectionRequires accurate pressure monitoring and production/injection

measurements– Requires accurate PVT data

4


INTRODUCTION MATERIAL BALANCE EQUATIONMATERIAL BALANCE EQUATION

DRIVE INDICES


– Given the reservoir pore volume under reservoir conditionsAPPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

Given the reservoir pore volume under reservoir conditions • Initial pressure, pi and reservoir temperature Ti

– The tank represents the total pore volume of the reservoir

5



DRIVE INDICES


– Fit all hydrocarbons of the reservoir into the tankAPPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

Fit all hydrocarbons of the reservoir into the tank • 0-dimensional representation

– The size of the potential gas cap is measured relative to the size of the oil volume.

• m is a volume ratiop = pi

oigiF NBmBG

NBoiNB

6



DRIVE INDICES


– Expansion of the reservoir fluids due to decrease in reservoirAPPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

Expansion of the reservoir fluids due to decrease in reservoir pressure

• p < pi– At the lower pressure p, the gas cap expands, the aquifer p p g p p q

expands and the oil volume changes

– At pi: at p:gF BG

oigiF mNBBG

gF BG

oNB

NB

gssi BRRN )(

oiNB

eW

7



DRIVE INDICES


– When trying to fit the expanded fluid volumes back into the reservoir tank, some fluid volume does not fit in

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

,– The superfluous volumes are the produced volumes of oil,

gas and water

P d d V lgspp BRRN )(

opBN

Produced Volume

iiF mNBBG

gF BG wpBW

oigiF mNBBG

gssi

o

BRRNNB

)(

oiNB

eW

8

eW

Initial Volume Expanded Volume Reservoir Content


INTRODUCTION MATHEMATICAL FORMULATIONMATERIAL BALANCE EQUATION

DRIVE INDICES

MATHEMATICAL FORMULATION

Initial volume:mNBNBBGNB

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

Expanded volume at pressure p:

B

oioigiFoi mNBNBBGNB

Produced volume at pressure p:

essigogi

goi WRRNBNB

BB

mNB

M t i l B l E ti

wpspgopwpgsppop BWRRBBNBWBRRNBN )()(

Material Balance Equation:

[Expanded volume] – [initial volume] = [produced volume]

9



DRIVE INDICES


g BNmBNWRRBNBNB

BNm ***)(******APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

oioiessigogi

oi

BWRRBBN

BNmBNWRRBNBNB

BNm

)](*[*

)(

wpspgop BWRRBBN )](*[*

Tarner‘s formula (1944):

)()( wpespgoP BWWRRBBNN

)()(1 ooissiggi

goi BBRRB

BB

mB

N

10

gi


INTRODUCTION EXPLANATION OF TERMS IN EQUATIONMATERIAL BALANCE EQUATION

DRIVE INDICES

EXPLANATION OF TERMS IN EQUATION

All terms in reservoir volume at pressure p

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

produced oil & gas net water influx

)()( wpespgoP

B

BWWRRBBNN

)()(1 ooissiggi

goi BBRRB

BB

mB

expansion of expansion of shrinkage of

gas cap dissolved gas reservoir oil

11


INTRODUCTION DRIVE INDICESMATERIAL BALANCE EQUATION

DRIVE INDICES

DRIVE INDICES

1111

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

1

1111

o

wpegggi

oissioiog

RRBN

BWWBBB

mNBRRBBB

N

spg

op RR

BN

Drive mechanisms– The solution gas drive Is

• two phase expansion (dissolution of gas and shrinkage of the oil)– The gas drive Ig

• i f h• expansion of the gas cap– The water drive Iw

• expansion of the aquifer

Is+ Ig+ Iw= 1

12


INTRODUCTION SOLUTION GAS DRIVE INDEX - IsMATERIAL BALANCE EQUATION

DRIVE INDICES

SOLUTION GAS DRIVE INDEX Is

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

1

1111

wpe

gggioissioio

g

B

BWWBBB

mNBRRBBB

N

sp

g

op RR

BBN

1

ssioio

gs

RRBBB

NI

1

sp

g

op

s

RRBBN

13


INTRODUCTION GAS DRIVE INDEX - IgMATERIAL BALANCE EQUATION

DRIVE INDICES

GAS DRIVE INDEX Ig

1111 APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

1

1111

wpe

gggioissioio

g

B

BWWBBB

mNBRRBBB

N

sp

g

op RR

BBN

oi BB

mNB 11

spo

p

ggig

RRBN

BBI

spg

p B

14


INTRODUCTION WATER DRIVE INDEX - IwMATERIAL BALANCE EQUATION

DRIVE INDICES

WATER DRIVE INDEX Iw

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

1

1111

wpe

gggioissioio

g

B

BWWBBB

mNBRRBBB

N

sp

g

op RR

BBN

wpe BWWB1

spo

p

gw

RRBBN

BI

spg

p B

15


INTRODUCTION DRIVE INDICES VARY WITH TIMEMATERIAL BALANCE EQUATION

DRIVE INDICES

DRIVE INDICES VARY WITH TIME

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

Source: Clark, Elements of Petroleum Reservoirs, 1969

16


INTRODUCTION DRIVE INDICES SUMMARYMATERIAL BALANCE EQUATION

DRIVE INDICES

DRIVE INDICES SUMMARY

Solution Gas Drive Index

1APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

ssioio

gs

B

RRBBB

NI

1

Gas Cap Drive Index

spg

op RR

BBN

11

o

ggioi

g

RRBN

BBmNB

I

11

Water Drive Index BWW1

spg

op RR

BN

spo

p

wpeg

w

RRBBN

BWWB

I

17

spg

p B



DRIVE INDICES


– Solving the MB-equation

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

)()(1

)()(

g

wpespgoP

BBRRBB

B

BWWRRBBNN

– for water influx We yields

)()(1 ooissiggi

goi BBRRB

BmB

– for water influx, We, yields

)( wpspgoPe BWRRBBNW

)()(1

)(

ooissigg

oi

wpspgoPe

BBRRBBB

mBN

giB

18


INTRODUCTION UNDERSATURATED OIL RESERVOIRSMATERIAL BALANCE EQUATION

DRIVE INDICES

UNDERSATURATED OIL RESERVOIRS

g mNBNBWRRNBNBB

mNB )(APPLICATIONS

GRAPHICAL METHOD

WATER INFLUXwpspgop

oioiessigogi

oi

BWRRBBN

mNBNBWRRNBNBB

mNB

)]([

)(

– In undersaturated reservoirs, there is no gas cap (m = 0)– Hence:

– The Rs function is constant above the bubble point pressure

wpspgopoiessigo BWRRBBNNBWRRNBNB )]([)(

– Therefore:

wpopoieo BWBNNBWNB – Or:

wpopeoio BWBNWBBN

19


INTRODUCTION UNDERSATURATED OIL RESERVOIRSMATERIAL BALANCE EQUATION

DRIVE INDICES– The compressibility of the connate water and rock have an

important role in undersaturated reservoirs:

UNDERSATURATED OIL RESERVOIRS

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX pVcpVc

VVV

pww

pw

cSc

pS

NBcpS

SNBcwi

oiwi

wioiw

1

11

– If entered into the following equation

pS

cScNB

wi

wwioi

1

g q

wpopeoio BWBNWBBN

– yields

wwioi BWBNWpcScB

BBN

20

wpope

wi

wwioioio BWBNW

Sp

BBN

1


INTRODUCTION GAS RESERVOIRSMATERIAL BALANCE EQUATION

DRIVE INDICES

GAS RESERVOIRS

– The compressibility of the connate water and rock can be neglected

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

g

– The reservoir initial volume: GBgi– The expanded reservoir volume: GBg+WeThe expanded reservoir volume: GBg We– The produced volume: GpBg+Wp

– Then the material balance equation is:Then, the material balance equation is:

pgpgieg WBGGBWGB

WWBG

epgpgig WWBGBBG

gig

pe

gig

gp

BBWW

BBBG

G

21



DRIVE INDICES

GAS RESERVOIRS

pegp TZCZTPBWWBG

G

0

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

ggiggig

Z

Tp

CzpT

BBBBB

G

: thenconstant, are T and C if00

gig

pep BB

WWZZ

pZ

GG

– If there is no water influx, then We and Wp are zero:

ipp

pp

i

GCCGG

Zp

Zp

211

– Then, a plot of Gp versus p/Z will show a linear function!

22



DRIVE INDICES

– Plot of cumulative Gas Production (Gp) versus p/Z will show linear function, if no water influx.

GAS RESERVOIRS

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

23 Source: Craft & Hawkins, Applied Petroleum Reservoir Engineering, 1991


INTRODUCTION MATERIAL BALANCE FORECAST METHOD (p/Z)MATERIAL BALANCE EQUATION

DRIVE INDICES ZCZTB 02830

MATERIAL BALANCE FORECAST METHOD (p/Z)

APPLICATIONS

GRAPHICAL METHOD

WATER INFLUX

ZZZ

BBGBGp

Cp

B

giggp

g

)(

0283.0

ZGZGZG

pZ

CpZCG

pZCG

i

i

ip

PZ

GPZGG

pG

pG

pG

i

ip

ip

G

GGZp

Zp

GGG

pZ

pZ p

i

i

pi

i

i

GG

Zp

Zp p

i

i 1

24

Material Balance

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