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Data & Consulting Services
Schlumberger
1. Importance to Schlumberger
2. The concept of NodalTM Analysis
3. Segments in the reservoir/well system where pressure loss occurs
4. Solution node
5. Inflow performance curve
6. Tubing curve
7. System graph
8. Small Project-Multilayer Nodal Analysis
1. Explain the concept of Nodal Analysis.
2. List the four major segments between the reservoir and the
separator where pressure loss occurs.
3. Give definitions for each of the following terms:
• Inflow performance curve
• Tubing performance curve
• System graph
• Solution node
4. Explain the importance to you and Schlumberger
Stimulation candidate selection
Production prediction
Treatment type and design
More objectives of Nodal analysis
Estimate WHP from IPR, Pr, completions and target rate
Estimate rates from WHP, IPR, Pr, completions
Size completions from IPR, Pr and WHP constraints
Determine choke size for target rate and system description
Design AL system
Predict hydrate formation
…
P1 = Pr - Pwfs = Loss in reservoir
P2 = Pwfs - Pwf = Loss across completion
P3 = Pwf - Pwh = Loss in tubing
P4 = Pwh - Psep = Loss in flowline
Pr Pe Pwfs Pwf
P1 = (Pr - Pwfs)
P2 = (Pwfs - Pwf)
P3 = Pwf - Pwh
P4 = (Pwh - Psep)
Psep
Sales line Gas
Liquid
Stock tank
PT = Pr - Psep = Total pressure loss
Adapted from Mach et al, SPE 8025, 1979.
Pwh
P1 = Pr - Pwfs = Loss in reservoir
P2 = Pwfs - Pwf = Loss across completion
P3 = Pwf - Pwh = Loss in tubing
P4 = Pwh - Psep = Loss in flowline
Pr Pe Pwfs Pwf
P1 = (Pr - Pwfs)
P2 = (Pwfs - Pwf)
P3 = Pwf - Pwh
P4 = (Pwh - Psep)
Psep
Sales line
Gas
Liquid
Stock tank
PT = Pr - Psep = Total pressure loss
Adapted from Mach et al, SPE 8025, 1979.
Pwh
2111 STB/D
1957.1 psi
0
500
1000
1500
2000
2500
3000
3500
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Production rate, STB/D
Flo
win
g b
ott
om
ho
le p
res
su
re, p
si
Inflow (Reservoir) Curve
Tubing Curve
9 Initials
27-Aug-13
10 Initials
27-Aug-13 10
27-Aug-13
qk h
B
P P
nr
rS
o
o
o o
r wf
e
w
0 00708
10 472
.
. '
Inflow Performance
Radial Flow Equation
Flow rate (bpd)
permeability (mD) net pay (ft) average reservoir
pressure (psi)
flowing bottom hole
pressure (psi)
viscosity (cp)
formation volume
factor (rb/stb) wellbore radius (ft) drainage radius (ft)
Total skin
Q: What can we do to really influence the flowrate ?
Single phase liquid:Darcy’s law for radial flow
through a permeable medium as follows:
Productivity Index - Oil Wells - Single phase liquid
4
306.10ln
2
12
wArC
APD
11
27-Aug-13
2
06.10ln
2
1
wArC
APD
DtEiPD
4
1
2
1
2
wrC
ktt
t
D
sPB
kh
pp
qJ
Dwf
2.141
Stabilized rate
Productivity index
Pressure drawdown
Dimensionless pressure
Infinite-Acting Solution Steady State Solution Pseudo steady State Solution
wfPPiP
wfPPP wfPPeP
P
CA = Dietz Shape factor
No-Flow Boundaries:Pseudo steady State Solution
12
27-Aug-13
Constant Well Rate Constant Well Pressure
Changing pwf Constant pwf
Radial Pressure Profiles
No-Flow
Boundary t
r3
r2
t2= 1 day
t3= 3 days
t4= 10 days
r4
No-Flow Outer
Boundary
r1
t1= 0.3 day
t5
t5
Fluid at the farthest
boundary starts moving
toward the well
t1
t1
r1 r1 r2
t2
t2
r2
t4
t4
r4 r4
t3
t3
r3 r3
Constant-Pressure Boundaries : Steady State Solution
13
27-Aug-13
r3
r2
t2= 1 day
t3= 3 days
t4= 10 days
r4
Constant-Pressure
Outer Boundary
r1
t1= 0.3 day
Constant Well Rate Constant Well Pressure
Changing pwf Constant pwf
Radial Pressure Profiles
Constant-Pressure
Boundary
Fluid at the farthest
boundary starts moving
toward the well
t1
t1
r1 r1 r2
t2
t2
r2
t4
t4
r4 r4
t3
t3
r3 r3
Shape Factors - Pseudo Steady State Solution
srC
AB
kh
pp
qJ
wA
oo
wf
4
306.10ln
2
1
1008.7
2
3
14
27-Aug-13
Shape Dietz
CA
Odeh
CA, Odeh
Fetkovich
sCA
Shape Dietz
CA
Odeh
CA, Odeh
Fetkovich
sCA
31.62 0.564 0.573
2
1 10.84 0.964 1.108
31.6 0.565 0.573
2
14.51 1.494 1.546
27.6 0.604 0.6412
12.077 2.202 1.934
60° 27.1 0.610 0.6502
13.157 1.786 1.725
1/3{21.9 0.678 0.756
2
1
0.581 4.162 2.571
0.098 10.14 3.4612
1
0.111 9.529 3.399
30.9 0.571 0.584
1
4 5.38 1.368 1.458
13.0 0.881 1.018
1
42.69 1.935 1.805
4.51 1.494 1.546
1
40.232 6.591 3.030
3.34 1.738 1.697
1
4
0.1155 9.337 3.379
1
2
21.8 0.679 0.7581
5
2.361 2.065 1.870
Dietz Shape Factor
sr
ACB
kh
pp
qJ
w
OdehA
oo
wf
4
3ln
1008.7 3
Odeh Shape Factor
ssr
rB
kh
pp
qJ
CA
w
e
oo
wf
4
3ln
1008.7 3
Fetkovich Shape Factor Skin
Are
Combination Single Phase Liquid and Two Phase Flow
15
27-Aug-13
psiDSTBpp
qJ
wf
//
2
8.02.01p
p
p
p
q
q wfwf
max
+ Mathematical model for Vogel’s curve
Two-phase flow in the reservoir when pressure drops
below bubble point pressure
Assumptions: Initial Pr at Pb, Radial flow, undamaged well & pseudo steady state
Multiphase Flow
Combination Darcy/Vogel
16
27-Aug-13
qmax
J pb
1.8
q O
O
qb
Rate
pwf
pb
Pre
ss
ure
p
Multiphase Flow
How to find qmax:
17
27-Aug-13
2
max8.02.01:thenfor
:applieslawsDarcy',for
b
wf
b
wf
bbb
wfb
p
p
p
pqqqqqq
ppJqqq
8.1
pJqq b
bmax
Reservoir Conditions:
Original Pressure = 2150 psi
Bubble Point = 2150 psi
Crude oil PVT. Characteristics
and relative permeability
Characteristics from Ref. 7
Well spacing = 20 acres
Well radius - 0.33 foot
Cumulative recover,
percent of original
oil in place
Producing rate, bopd
Bo
tto
m h
ole
we
ll p
ressu
re,
psi
Multilayer Reservoirs
19
27-Aug-13
Input individual IPR for each layer
Composite IPR node solution at top Layer
Jones’ Gas IPR
Problem -
• Darcy’s law valid for laminar flow only
• High permeability gas wells produce in turbulent flow
near the wellbore
bqaqpp wf 222
Turbulence Term Laminar flow Term
Jones Equation
Assumptions
Darcy’s and Jones’ laws assume that the average
pressure( ) is constant
Drainage radius, re, is constant
These assumptions are true in pseudo-steady
state only, i.e. when all of the outer
boundaries of the reservoir are reached.
p
The time to reach pseudo-steady state (pss), tstab, can be
calculated with the following equation
k
rc948t
2et
stab
t-hrs Ct-1/psi
K-md re-feet
U-cp Porosity-fraction
t1
t2
t3
tstab
q
pwf
p tstab > t3 > t2 > t1
tstab = Pseudosteady
State (PSS) IPR
(Darcy) @ Time
to PSS
Oil Reservoir IPR’s Well PI (Pwf > PB)
• For undersaturated oil
• Can also be applied to flow below bubble
point with minor changes
Vogel’s* (Pwf < PB) • Empirical relationship
• C = 0.8 by default
Fetkovich/Backpressure • where n which ranges from 0.5 to 1
represents degree of turbulence
Jones* • modified PI and Darcy equation accounting
for turbulent flow
Pseudo-steady-state (Pwf > PB) : • based on Darcy IARF
)( wfR PPJq
2
max
)1(1
R
wf
R
wf
P
PC
P
PC
q
q
n
wfR PPCq )(22
2BqAqPP wfR
Sr
rB
PPkhq
w
e
wfR
75.0ln
00708.0
Gas Reservoirs IPR Well PI
Backpressure* • n = 0.5 to 1
Jones* • modified PI equation accounting for
turbulent flow
Pseudo-steady-state (based on
Darcy IARF)
• pseudo-pressure (for all P)
• OR pressure squared (for low P)
222BqAqPP wfR
)(22
wfR PPJq
n
wfR PPCq )(22
Sr
rTZ
PPkhq
w
e
wfR
75.0ln
10703226
wfR PmPmCq
dPZ
PPm
2 where
27 Initials
27-Aug-13
dZ
dv
g
v
dg
vf
g
g
dZ
dP m
c
mm
c
mmmm
ctot
2sin
2
Elevation
Friction
Acceleration
Vg
VL
gL
LL
VV
VH
gLLLm HH 1
Based on dimensional analysis by Duns and Ros
Duns and Ros (1963)
Hagedorn and Brown (1963)
Orkiszewski (1967)
Beggs and Brill (1973)
Mukherjee and Brill (1983)
Suggested application of correlations
Duns and Ros (1963) (vertical upflow)
Orkiszewski (1967) (vertical upflow)
Hagerdorn and Brown (1965) (vertical upflow)
Beggs and Brill (1973) (vertical or inclined,
upflow or downflow)
Mukherjee and Brill (1985) (vertical or inclined,
upflow or downflow)
Dukler (1964) (only horizontal flow)
Pressure Gradient
Factors affecting Pressure
Gradient Profile include:
Producing Rate
GOR
WCT
Tubing Size
Tubing geometry
Skin factor The Skin Factor (St) is a constant which relates the
pressure drop due to skin to the flow rate and
transmissibility of the formation. Thus:
Kh
q
PS
oo
skin
t2.141
wfwfskin PPP '
The Concept of Skin Damage Skin is an additional pressure drop through a zone of reduced
permeability (kd) in the near wellbore region
rw rd
re
k
kd
What causes this damage skin?
Pwf (no skin)
Pwf (with skin)
pskin
r (distance from wellbore)
rd
kd
rw
kPwf (no skin)
Pwf (with skin)
pskin
r (distance from wellbore)
rd
kd
rw
k
Skin Factor – graphical representation
Pr
P’wf
Pwf
rw
rd
Positive skin ~ Damaged wellbore or
Reduced wellbore radius
The Skin Equation
75.0ln
00708.075.0ln
00708.0 w
doo
w
d
d
ooskin
r
r
kh
Bq
r
r
hk
BqP
rw rd
re
k
kd
75.0ln
00708.0
w
eoo
wfRo
o
r
rB
PPhkq
skin
oo
PBq
khS
2.141
1ln
00708.0 dw
dooskin
k
k
r
r
kh
BqP
S
1ln
dw
d
k
k
r
rS
Skh
BqP oo
skin00708.0
Recalling the original Darcy equation
Sources of Skin
Positive skin
Drilling-induced or other formation damage
Migration of formation fines.
Perforation skin
Partial completions (and partial penetration) cases.
Gravel packs.
Reservoir flow turbulence
Negative skin:
Stimulated formations.
High density perforated completions.
Flow Efficiency:
FE < 1 for Damaged well
FE >1 for a Stimulated well
......, soturbpppdt SSSSSSS
Skin factor
St = total skin effect, (+ damaged; - stimulated)
Sd = skin effect due to formation damage (+)
Spp = skin due to partial penetration (+)
Sp = skin effect due to perforation (+)
Sturb = Dq, skin effect due to turbulence (+)
So = skin effect due to slanting of well (-)
Ss = skin effect due to stimulation (generally -)
Pressure Loss in Perforations
The effect of perforations on productivity can be
quite substantial.
It is generally believed that if the reservoir pressure
is below the bubble point, causing 2 phase flow
through the perforations, the pressure loss may be
an order of magnitude higher.
2 Methods for calculating presssure loss in
perforations, McLeod (1983) and Karakas &Tariq
(1988).
Are you ready?
Given the surface _____ pressure and the _____ pressure, along with the
physical properties of each system segment, we can calculate the
______ at which the well will produce.
(i) Flow rate
(ii) Separator
(iii) Water salinity
(iv) Reservoir
(v) API gravity
(vi) Tubing ID
43
27-Aug-13
Pre
ssure
Before After Incremental
Q1=250 BPD Q2=300 BPD
Pwf1=1750 Psia Pwf2=1900 psia
J1(pss)=1.0 BPD/psia J2(pss)=3.0 BPD/psia J=2 times
Q1, Pwf1
Q2, Pwf2
What is the productivity index before and after the stimulation?
For the same bottom hole flowing pressure(1750), what is the expected incremental oil?
Exercise 3 : Before and after Stimulated well Pr=2000 psia. Assume Pwf1>Pb
Tell me…
How do you see this
class benefiting your
daily job?