Nodal Analysis introduction to inflow and outflow performance - next

Copyright 2007, , All rights reserved
Production Engineering for All
Analisis Nodal - Introduction to Inflow and Outflow
Performance

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)

GRAPHICAL SOLUTION OF THE PROBLEM
Outflow from node
Inflow to node
SYSTEM FLOW CAPACITY
NODE PRESSURE
(1)
(2)
NODEPRESSURE,Pnode
FLOW RATE, Q

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.

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

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

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

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

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.

Copyright 2007, , All rights reserved
Well Outflow Performance

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

Types of Outflow Systems
Single / multiple
selective / non-selective
flowing / lifted
– gas-lifted
– pumped
• beam pump
• ESP
• PCP
• Jet Pump
• Hydraulic Pump

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

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

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

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

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

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

Moody Diagram for Friction Factor Calculation

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

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)

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

GRAVITY
TERM
∆P
( )elevation =
∆L 144
ρm
Correcting weight of fluid
Dominant term
Single phase simple
Multiphase complex

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

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

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

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)

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.

Superficial Gas Velocity, VSG
qL
Ap
v
Ag
AL
L
qg
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.

Superficial Liquid Velocity, VSL
qL
Ap
v
Ag
AL
L
qg
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

Vertical Flow Parameters
Temperature Pressure
Approximate
linear
temperature
profile
Depth
oil
Single-
phase
oil
p > pBP
bubble
flow
chum
flow
slug
flow

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

Vertical Flow Paterns
BUBBLY
FLOW
SLUG
FLOW
CHURN
FLOW
ANNULAR
FLOW

Horizontal Flow Paterns
Annular
Dispersed
Stratified
Wavy
Slug (Intermitent)
Dispersed
Bubble

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.

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.

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

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

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

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

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.

EFFECT OF THE TUBING SIZE
(NODE SELECTED AT THE BOTTOMHOLE)
FLOWRATE, Q
BOTTOMHOLEFLOWINGPRESSURE,Pwf
INFLOW
IPR
0
OUTFLOW
d1
d2>d1
Pr
0

FINDING OPTIMUM TUBING SIZE
UNSTABLE REGION
DIAMETER FOR
MAXIMUM FLOW RATE
FLOWRATE,Q
TUBING DIAMETER, d

Tubing Size in Depleting Reservoir
Pinitial
Tubing
Intake
Pressure
Q
1 “
2 3/8 “
3 1/2 “
5 “
4 1/2 “
P5
P10
Pwf

Effect of Gas Injection Rate
P
Qmax
IPR
250
200
150
100
50
0
400
300

Gas Lift Performance Curve
∆x
∆x
∆x
∆x
∆x
∆x
∆x
∆x
∆x
∆x
LIFT-GAS INJECTION RATE
OR PRODUCTION COSTS
NETOILPRODUCTION
ORREVENUE
2
1
3
4
SLOPE = 1.0
Economic Limit
Technical
Optimum
1
Kick-Off
Lift-Gas Requirement
2 Initial Oil Rate at Kick-off
3 Technical cut-off limit
4 Max. Oil Rate
∆x Incremental
Lift-Gas Volume

Inflow Performance Curve
0
500
1000
1500
2000
2500
3000
3500
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Production rate, STB/D
Flowingbottomholepressure,psi
Inflow (Reservoir) Curve
AOFP
Performance of an ideal OH
well, no damage, no
completion, no friction
losses from reservoir to
wellhead
Pr

Outflow Performance Curve
0
500
1000
1500
2000
2500
3000
3500
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Outflow (Tubing) Curve
Tubing Performance Curve

System Graph
0
500
1000
1500
2000
2500
3000
3500
0 500 1000 1500 2000 2500 3000 3500 4000 4500
Inflow (Reservoir) Curve
Outflow (Tubing) Curve
2111 STB/D
1957.1 psi

System Graph – Wellhead Node
0
200
400
600
800
1000
1200
1400
1600
0 500 1000 1500 2000 2500 3000
Flowingwellheadpressure,psi
Inflow Curve
Outflow Curve
2050 STB/D
500 psi

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

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

Nodal Analysis
Inflow Operating Point
OutflowPressure PWF
Operating Flowrate
Flowrate (stb/d)
PressureatNode
Reservoir Pressure

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

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

Effect of Pressure Depletion in IPR
Outflow
Flowrate
PressureatNode
8 04
Oil Recovery (% STOIIP)
12
Reservoir with no pressure support
Inflow

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

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”

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