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Nodal Analysis introduction to inflow and outflow performance - next
1. Copyright 2007, , All rights reserved
Production Engineering for All
Analisis Nodal - Introduction to Inflow and Outflow
Performance
2. 2Copyright 2007, , All rights reserved
NODAL ANALYSIS CONCEPT
QQ
NODE
Pn
OUTFLOWINFLOW
Pu PdUPSTREAM
COMPONENTS
DOWNSTREAM
COMPONENTS
Pnode = Pu – ∆Pupstream components (1) = f1(Q)
∆Pu
∆Pd
∆P = f (Q)
Pnode = Pd + ∆Pdownstream components (2) = f2(Q)
3. 3Copyright 2007, , All rights reserved
GRAPHICAL SOLUTION OF THE PROBLEM
Outflow from node
Inflow to node
SYSTEM FLOW CAPACITY
NODE PRESSURE
(1)
(2)
NODEPRESSURE,Pnode
FLOW RATE, Q
4. 4Copyright 2007, , All rights reserved
EXERCISE # 1
ILUSTRATION OF NODAL ANALYSIS CONCEPT
Calculate:
1) Actual capacity of the system in BPD.
2) Capacity of the system when the diameter of the 2” pipe is increased to 3”.
Select the node at the point where the pipe diameter is reduced from 3” to 2”.
Assume flow rates of 2500, 3000 y 3500, 5000, 5500, 6000 BPD.
2000 feet, Ø= 3” 1000 feet, Ø=2”
P1= 200 psi P3= 60 psi
Pnode
WATER
SOURCE
WATER
SINK
∆P1 ∆P2
Use the following equation to calculate the pressure drop in a pipe
L Q2
∆P = 3.8 x 10 - 7 x ;
D5
where, ∆P is the pressure drop in psi, L is the pipe length in feet, D is the pipe
diameter in inches and Q the flow rate in BPD.
5. 5Copyright 2007, , All rights reserved
GRAPHICAL SOLUTION OF THE PROBLEM
FLOW RATE, Q
NODEPRESSURE,Pnode
Outflow performance
Inflow
performance
Actual system flow capacity
Pnode
(1)
(2)
2”
(1) Pnode = P1-∆P1
(2) Pnode = P3+∆P2
2000 feet, Ø= 3” 1000 feet, Ø=2”
P1= 200 PSI P3= 60 PSI
Pnode
WATER
SOURCE
WATER
SINK
∆P1 ∆P2
6. 6Copyright 2007, , All rights reserved
GRAPHICAL SOLUTION OF THE PROBLEM
FLOW RATE, Q
NODEPRESSURE,Pnode
Outflow performance
Inflow
performance
Actual system flow capacity
Pnode
(1)
(2)
2”
3”
new system flow capacity
(1) Pnode = P1-∆P1
(2) Pnode = P3+∆P2
SOL
2000 feet, Ø= 3” 1000 feet, Ø=2”
P1= 200 PSI P3= 60 PSI
Pnode
WATER
SOURCE
WATER
SINK
∆P1 ∆P2
7. 7Copyright 2007, , All rights reserved
Why ‘Nodal’?
Reservoir
Pr
Pwfs
Pwf
Psep
• As many ‘nodes’ as you want
• The observer can be placed at any node
• Normally, the well is observed from bottom
hole, Pwf
Fluid flows from the reservoir to the stock tank because of the pressure
gradients within the system. The total pressure drop from the reservoir to the
separator is the sum of the individual pressure drops through four different
segments: in the reservoir, across the completion, up the wellbore, and
through the flowline.
But we do not know the flow rate - that is what we are trying to find. How do
we calculate the flow rate, knowing the reservoir and separator
pressures? This is the central question of Nodal Analysis.
Given the reservoir pressure and the separator pressure, along with the
physical properties of each segment, what is the flow rate at which the well will
produce?
Pwh
8. 8Copyright 2007, , All rights reserved
Pressure Losses in Well System
∆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 PePwfsPwf
∆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
9. 9Copyright 2007, , All rights reserved
Nodal Analysis
How do we determine the right flow rate? We know the separator pressure
and the average reservoir pressure.
We start in the reservoir at the average reservoir pressure, Pr, and assume a
flow rate. This lets us calculate the pressure just beyond the completion, Pwfs.
We can then calculate the pressure drop across the completion, and the
bottomhole pressure Pwf. This pressure is valid only for the assumed flow
rate.
Or, we may start at the separator at Psep, and calculate the pressure drop in
the flowline to find the wellhead pressure, Pwh. Then we can calculate the
bottomhole pressure Pwf. Again, this pressure is valid only for the assumed
flow rate.
The two calculated bottomhole pressures will probably not be the same. If not,
then the assumed rate is wrong.
“Nodal” analysis refers to the fact that we have to choose a point or “node” in
the system at which we evaluate the pressure - in this case, the bottom of the
wellbore. This point is referred to as the solution point or solution node.
11. 11Copyright 2007, , All rights reserved
RESERVOIR INFLOW PERFORMANCE
Psep
Q
Separator
Tubing
Pwf
FlowlinePwh
∆Ptubing
∆P flowline GAS
OIL
+WATER
∆Pres
Pr, IPR, K
Reservoir
∆Pres = f(Q)
NODE (Pwf)
Pwf
Q
INFLOW
12. 12Copyright 2007, , All rights reserved
Types of Outflow Systems
Single / multiple
selective / non-selective
flowing / lifted
– gas-lifted
– pumped
• beam pump
• ESP
• PCP
• Jet Pump
• Hydraulic Pump
13. 13Copyright 2007, , All rights reserved
WELLBORE FLOW PERFORMANCE (OUTFLOW)
Psep
Q
Separator
Tubing
Pwf
FlowlinePwh
∆Ptubing
∆P flowline GAS
OIL
+WATER
∆Pres
Pr, IPR, K
Reservoir
∆Ptbg = f(Q)
NODE (Pwf)
Pwf
Q
OUTFLOW
14. 14Copyright 2007, , All rights reserved
SINGLE PHASE FLOW
BASIC CONCEPTS
FLUID VELOCITY
Is the flow rate (q) divided by the pipe cross sectional area (A)
through which the fluid flows at the pressure and temperature
conditions of the pipe element
q A
v
v = q / A
P,T
15. 15Copyright 2007, , All rights reserved
FUNDAMENTALS OF FLUID FLOW IN PIPES
ZZ
δP/δZ
θ
FLOW GEOMETRY
GENERAL ENERGY EQUATION
∆P ∆P ∆P ∆P
( ) T = ( ) acceleration + ( ) elevation + ( ) friction
∆L ∆L ∆L ∆L
16. 16Copyright 2007, , All rights reserved
FUNDAMENTALS OF FLUID FLOW IN PIPES
∆P
( )elevation =
∆L 144
ρ
∆P ρ v 2
( )friction = f
∆L 2 g d
∆P ρ ∆( v 2)
( )acc =
∆L 2g ∆L
17. 17Copyright 2007, , All rights reserved
FRICTION LOSSES CALCULATION
(single phase flow)
∆P ρ v 2
( )f = f
∆L 2 g d
where f, is the friction factor which is a function of the pipe roughness (ε)
and theReynolds Number (NRe), which is calculated fromthe following
equation:
µ is the viscosity in lbm/ft-sec
1cps= 0.00067197 lbm/ft-sec
dvρ
NR =
µ
e
18. 18Copyright 2007, , All rights reserved
Friction Factor Calculation (single phase flow)
Depends on the flow regime:
For laminar flow NRe < 2000
For turbulent flow NRe > 2000.
64
f =
NRe
ε 2.51
√1/ f = - 2 log ( + )
3.71d NRe√ f
The latest equation requires a trial and error process to calculate f
An intial value to start the iterative process can be obtained from the following equation:
f = 0.0056 + 0.5 NRe
- 0.32
19. 19Copyright 2007, , All rights reserved
Moody Diagram for Friction Factor Calculation
20. 20Copyright 2007, , All rights reserved
EXERCISE 10
SINGLE PHASE FLOW
Calculate the friction pressure drop in a section of horizontal pipeline of
3000 ft length and 3.937 inches internal diameter, where 5000 STB/D of 0.9 sp. gr.
oil with a viscosity of 5 cps oil are flowing. The absolute pipe wall roughness
is 0.006 ft.
∆P ρ v 2
( )f = f
∆L 2 g d
q A
v
1cps= 0.00067197 lbm/ft-sec
1 Bbl=5,615 Ft3
1 day=86400 sec
v = q / A
dvρ
NRe =
µ
f from Moody
ε/D
sol
21. 21Copyright 2007, , All rights reserved
Oil Reservoir Phase Envelop
Temperature
Pressure
GasDew
PointLine
% Liquid
Single Phase Region
(Liquid)
Bubble Point Line
Pb
Two
Phase
Region
C
Pres
Psep
100
75
50
25
20
15
10
5
0
Single Phase Region
(Gas)
22. 22Copyright 2007, , All rights reserved
MULTIPHASE FLOW
PRESSURE GRADIENT EQUATION FOR TWO-PHASE FLOW:
∆P ∆P ∆P ∆P
( ) T = ( ) acceleration + ( ) elevation + ( ) friction
∆L ∆L ∆L ∆L
∆P
( )elevation =
∆L 144
ρm
∆P ρm vm
2
( )friction = f
∆L 2 g d
∆P ρm ∆( vm
2)
( )acc =
∆L 2g ∆L
23. 23Copyright 2007, , All rights reserved
GRAVITY
TERM
∆P
( )elevation =
∆L 144
ρm
Correcting weight of fluid
Dominant term
Single phase simple
Multiphase complex
24. 24Copyright 2007, , All rights reserved
FRICTION
TERM
∆P ρm vm
2
( )friction = f
∆L 2 g d
Increases with rate
Proportional to velocity
Proportional to relative roughness
Laminar vs turbulent flow
Effect of viscosity
Effect of mixture density
Sensitive to gas volumes
25. 25Copyright 2007, , All rights reserved
ACCELERATION
TERM
∆P ρm ∆( vm
2)
( )acc =
∆L 2g ∆L
Expansion of fluid as pressure decreases
Smallest term
Often ignored
Need to account in high rate
26. 26Copyright 2007, , All rights reserved
BASIC CONCEPTS
Mixture Velocity, V (Two-phase flow)
v
L
qg
A
qL
Pipe element with liquid and gas travelling at the same velocity, V
v = (qL+qg) / A
27. 27Copyright 2007, , All rights reserved
No-Slip Liquid Holdup (Input Liquid Content), λ
qL
Ap
v
Ag
AL
L
qg
RATIO OF THE VOLUME OF LIQUID IN A PIPE ELEMENT THAT WOULD EXIST
IF THE GAS AND THE LIQUID TRAVELED AT THE SAME VELOCITY (NO SLIPPAGE)
DIVIDED BY THE VOLUME OF THE PIPE ELEMENT.
P,T
λ = AL /AP = qL / (qL + qg)
28. 28Copyright 2007, , All rights reserved
No-Slip Liquid Holdup (Input Liquid Content), λ
qL
Ap
v
Ag
AL
L
qg
RATIO OF THE VOLUME OF LIQUID IN A PIPE ELEMENT THAT WOULD EXIST
IF THE GAS AND THE LIQUID TRAVELED AT THE SAME VELOCITY (NO SLIPPAGE)
DIVIDED BY THE VOLUME OF THE PIPE ELEMENT.
λ = AL /AP = qL / (qL + qg)
P,T
However, the gas velocity is higher than the liquid velocity and as a consequence the volume
of liquid in the pipe element increases.
This phenomenon is known as “slippage between phases” , and the volumen fraction occuppied
by the liquid in the pipe element under this conditions is known as“Hold-Up Factor” (HL), and is
dependent on flow pattern, gas and liquid properties, pipe diameter and pipe inclination.
29. 29Copyright 2007, , All rights reserved
Superficial Gas Velocity, VSG
qL
Ap
v
Ag
AL
L
qg
Pipe element with liquid and gas travelling at the same velocity, V
vSG = qg / Ap
Is the velocity that the gas phase would exhibit if it flowed through the total cross
sectional area of the pipe alone.
30. 30Copyright 2007, , All rights reserved
Superficial Liquid Velocity, VSL
qL
Ap
v
Ag
AL
L
qg
Pipe element with liquid and gas travelling at the same velocity, V
vSL = qL / Ap
Is the velocity that the liquid phase would exhibit if it flowed through the total cross
sectional area of the pipe alone.
Vm= Vsl + Vsg
31. 31Copyright 2007, , All rights reserved
Vertical Flow Parameters
Temperature Pressure
Approximate
linear
temperature
profile
Depth
oil
Single-
phase
oil
p > pBP
bubble
flow
chum
flow
slug
flow
32. 32Copyright 2007, , All rights reserved
Two-Phase Vertical Flow
Analysis and Calculations are Complex
DecreasingPressure
Flow regime (gas distribution)1
Proportion gas vs liquid changes2
Gas tends to rise faster than liquid
(slippage)
3
Factors affecting ∆Pvert.
Mass flow rate:
Oil Rate
1
Gas Rate (GLR)
Water Rate (CUT)
Physical properties PVT2
Viscosity
Surface tension
Conduit Configuration Size3
Roughness
Concentric?
Pressure4
5
Single Phase
Liquid Flow
Bubble Flow
Plug OR
Slug Flow
Churn Flow
Annular
Flow
Mist Flow
Temperature
33. 33Copyright 2007, , All rights reserved
Vertical Flow Paterns
BUBBLY
FLOW
SLUG
FLOW
CHURN
FLOW
ANNULAR
FLOW
34. 34Copyright 2007, , All rights reserved
Horizontal Flow Paterns
Annular
Dispersed
Stratified
Wavy
Slug (Intermitent)
Dispersed
Bubble
35. 35Copyright 2007, , All rights reserved
2-Phase –Gas-Liq) Flow Regimes
Flow regime or Flow Pattern : is a qualitative description of
the phase distribution in a pipe.
4 regimes are generally agreed upon:
1. BUBBLE FLOW: dispersed bubbles of gas in a continuous
liquid phase
2. SLUG FLOW: at higher rates, the bubbles coalesce into
larger bubbles, which eventually fill up the entire pipe section.
Between the large gas bubbles are slugs of liquid that contain
smaller bubbles of gas entrained in the liquid.
36. 36Copyright 2007, , All rights reserved
2-Phase –Gas-Liq) Flow Regimes
3. CHURN FLOW: with further increase in gas rate, the larger
gas bubbles become unstable and collapse, resulting in a
highly turbulent pattern. Both phases are dispersed. Churn
flow is characterized by oscillatory up-and-down motions of
liquid.
4. ANNULAR FLOW: at higher rates, gas becomes the
continuous phase, with liquid flowing in an annulus coating
the surface of the pipe and with liquid droplets entrained in
the gas phase.
37. 37Copyright 2007, , All rights reserved
Flow Regime (Ros)
0.1 0.2 0.3 0.5 0.7 1 2 3 5 7 10 100 1000
RN = Dimensionless Gas Velocity Number
FN = Dimensionless Liquid Velocity Number
0.01
0.02
0.05
0.1
0.2
0.5
1
10
100
BUBBLE FLOW
FROTH FLOW
SLUG FLOW
PLUG FLOW
HEADING
MIST FLOW
RN
FN
As µ, Increases, heading
regime may range up to
TRANSITION
SLUG/MIST
RNTRAN
RNMIST
R
N
B
U
B
RNSLUG*
RNSLUG
*
TR
A
N
SITIO
N
B
U
B
B
LE
/
SLU
G
38. 38Copyright 2007, , All rights reserved
CORRELATIONS
Babson (1934)
Gilbert (1939 / 1952)
Poettmann & Carpenter (1952)
Duns & Ros
Hagedorn & Brown
Orkiszewski
Aziz, Govier and Fogarasi
Chierici et al
Fancher & Brown
Beggs &Brill
Duckler Flannigan
Gray
H.MONA, Asheim
Hasan and Kabir
39. 39Copyright 2007, , All rights reserved
PROCEDURE FOR PRESSURE TRAVERSE CALCULATION
(incrementing pressure drop)
1. Starting with the known pressure value, P1, at location L1, select a length
increment ∆L.
2. Estimate a pressure drop, ∆P, corresponding to the length increment, ∆L.
3. Calculate the average pressure and temperature in the selected pipe
element.
4. Calculate the the fluids PVT properties at the average conditions of P and T.
5. Calculate fluids densities and flow rates at the average conditions.
6. Calculate the input liquid content, λ and the superficial velocities vsl and
vsg.
7. Determine the flow regime pattern.
8. Calculate the hold-up factor, HL, corresponding to the stablished flow
regime pattern.
9. Calculate the mixture properties for the calculated hold-up factor.
10. Calculate the two-phase friction factor.
11. Calculate the total pressure gradient in the increment of pipe at the average
conditions of P and T.
12. Calculate the pressure drop corresponding to the selected length increment.
13. Compare the estimated and calculated pressure drop. If they are not
sufficiently close, estimate a new pressure drop an repeat the procedure
from steps 3 through 13.
14. Repeat steps 3 through 13 until the estimated and calculated values are
sufficiently close.
15. Calculate a new position L2 = L1 + ∆L and the corresponding pressure P2 =
P1 + ∆P.
16. Repeat steps 1 through 15 until the total pipe length is completely covered.
P2
∆L
L1
L2
∆P
P1
40. 40Copyright 2007, , All rights reserved
Outflow Calculation (node at the bottomhole)
Q1
PressurePwh
DepthEquv.
.ToPwh
TubingDepth
Pwf1 Q Q1 Q2 Q3
Pwf Pwf1
Q2
Pwf2
Pwf2
Q3
Pwf3
Pwf3
Pwf1
Pwf3
Pwf2
Q
Pwf
q1 q2 q3
Outflow
41. 41Copyright 2007, , All rights reserved
Well Performance Software
The most noteworthy well performance programs on the market
today are:
Prosper (Petroleum Experts)
WellFlo (Edinburgh Petroleum Services)
Perform (Dwight’s / IHS Energy Services)
PipeSim (Schlumberger)
WEM (P.E. Mosely & Associates)
In addition to these programs, numerous other well performance
programs have been developed for commercial or private use.
42. 42Copyright 2007, , All rights reserved
EFFECT OF THE TUBING SIZE
(NODE SELECTED AT THE BOTTOMHOLE)
FLOWRATE, Q
BOTTOMHOLEFLOWINGPRESSURE,Pwf
INFLOW
IPR
0
OUTFLOW
d1
d2>d1
Pr
0
43. 43Copyright 2007, , All rights reserved
FINDING OPTIMUM TUBING SIZE
UNSTABLE REGION
DIAMETER FOR
MAXIMUM FLOW RATE
FLOWRATE,Q
TUBING DIAMETER, d
50. 50Copyright 2007, , All rights reserved
System Graph – Wellhead Node
0
200
400
600
800
1000
1200
1400
1600
0 500 1000 1500 2000 2500 3000
Production rate, STB/D
Flowingwellheadpressure,psi
Inflow Curve
Outflow Curve
2050 STB/D
500 psi
51. 51Copyright 2007, , All rights reserved
Nodal Analysis: Uses
Estimation of Reservoir Parameters
– Skin
– Permeability
– Reservoir Pressure
– Note : Non unique solutions unless only one unknown
Evaluation of Potential Stimulation Treatments
– Primarily through reduction in skin
– Parameter sensitivity studies are important
52. 52Copyright 2007, , All rights reserved
Nodal Analysis
Two Main Components
Inflow Performance Curve/Relationship (IPR)
– Oil or Gas Flowrate vs Bottomhole Flowing Pressure
– Ordinate Origin = Reservoir Pressure (∆P = 0 q = 0)
– Abscissa Intercept = Absolute Open Flow Potential (∆P = Pr q = Max)
Outflow Curve (Tubing Intake)
– Function of Hydrostatic, Friction & Acceleration Components
– Curves Shifted by Wellhead Pressure & Artificial Lift
Intercept of Curves Gives FBHP (psi) & Flowrate
53. 53Copyright 2007, , All rights reserved
Nodal Analysis
Inflow Operating Point
OutflowPressure PWF
Operating Flowrate
Flowrate (stb/d)
PressureatNode
Reservoir Pressure
54. 54Copyright 2007, , All rights reserved
The Inflow Performance Relationship
Dependent On:
Fluid Properties
– Oil
• Viscosity, Gas oil Ratio, Bubble Point
• Formation Volume Factor, Density
– Gas
• Viscosity, Z Factor, Compressibility
• Density
Inflow Correlation Used e.g. Oil - Darcy, Vogel, Gas - Jones, Darcy
Well Geometry i.e. Vertical or Horizontal
Formation Properties
– Reservoir Pressure
– Permeability
– Skin (Includes deviation, perforation, damage etc)
– Net Pay Height
55. 55Copyright 2007, , All rights reserved
Effect of Skin in IPR
Outflow
Flowrate
PressureatNode
5 0 -1 -3
SKIN
Inflow
(IPR)
Note : Log effect
10
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+ s
r
r
ln
1
αq
w
e
O
56. 56Copyright 2007, , All rights reserved
Effect of Pressure Depletion in IPR
Outflow
Flowrate
PressureatNode
8 04
Oil Recovery (% STOIIP)
12
Reservoir with no pressure support
Inflow
57. 57Copyright 2007, , All rights reserved
The Outflow Performance Relationship
Dependent On:
Fluid Properties
– Oil
• Viscosity, Gas oil Ratio, Bubble Point
• Formation Volume Factor, Density
– Gas
• Viscosity, Z Factor, Compressibility
• Density
Outflow Correlation Used e.g. Oil - Duns & Ross, Gas - Gray
Friction
Completion Properties
• Tubing Size
• Tubing Restrictions
• Tubing Roughness
58. 58Copyright 2007, , All rights reserved
Effect of Tubing Size in Outflow
Inflow
(IPR)
Outflow
Flowrate (stb/d)
PressureatNode
For a Tubing Restricted Well
2 3/8”
2 7/8”
4 1/2”
3 1/2”