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
Material Balance Methods and Water Influx
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
Material Balance Methods and Water Influx
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
Material Balance Methods and Water Influx
INTRODUCTION MATERIAL BALANCE EQUATIONMATERIAL BALANCE EQUATION
DRIVE INDICES
MATERIAL BALANCE EQUATION
– 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
Material Balance Methods and Water Influx
INTRODUCTION MATERIAL BALANCE EQUATIONMATERIAL BALANCE EQUATION
DRIVE INDICES
MATERIAL BALANCE EQUATION
– 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
Material Balance Methods and Water Influx
INTRODUCTION MATERIAL BALANCE EQUATIONMATERIAL BALANCE EQUATION
DRIVE INDICES
MATERIAL BALANCE EQUATION
– 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
Material Balance Methods and Water Influx
INTRODUCTION MATERIAL BALANCE EQUATIONMATERIAL BALANCE EQUATION
DRIVE INDICES
MATERIAL BALANCE EQUATION
– 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
Material Balance Methods and Water Influx
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
Material Balance Methods and Water Influx
INTRODUCTION MATERIAL BALANCE EQUATIONMATERIAL BALANCE EQUATION
DRIVE INDICES
MATERIAL BALANCE EQUATION
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
Material Balance Methods and Water Influx
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
Material Balance Methods and Water Influx
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
Material Balance Methods and Water Influx
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
Material Balance Methods and Water Influx
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
Material Balance Methods and Water Influx
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
Material Balance Methods and Water Influx
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
Material Balance Methods and Water Influx
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
Material Balance Methods and Water Influx
INTRODUCTION MATERIAL BALANCE EQUATIONMATERIAL BALANCE EQUATION
DRIVE INDICES
MATERIAL BALANCE EQUATION
– 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
Material Balance Methods and Water Influx
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
Material Balance Methods and Water Influx
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
Material Balance Methods and Water Influx
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
Material Balance Methods and Water Influx
INTRODUCTION GAS RESERVOIRSMATERIAL BALANCE EQUATION
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
Material Balance Methods and Water Influx
INTRODUCTION GAS RESERVOIRSMATERIAL BALANCE EQUATION
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
Material Balance Methods and Water Influx
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