1_introduction to nodal analysis
TRANSCRIPT
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Introduction to NODAL Analysis
April 2003
Instructor: Felipe Montoya
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Objective
The objective of this course is to give the engineer the basic tools and knowledge of Nodal Analysis for him/her to understand its benefits, usefulness and limitations and help him/her apply it to his/her work for production optimization.
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Outline
• Explain the concept of Nodal Analysis.• List the four major segments between the reservoir and the
separator where pressure loss occurs.• Give definitions for each of the following terms:
– Inflow performance curve– Tubing Intake curve– System graph– Solution node
• Benefits of NODAL Analysis
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Agenda
1. The concept of Nodal Analysis2. Segments in the reservoir/well system where
pressure loss occurs3. Fluid Properties4. Solution node5. Inflow performance curve6. Outflow performance curve7. System graph
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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 lineGas
Liquid
Stock tank
PT = Pr - Psep = Total pressure loss
Adapted from Mach et al, SPE 8025, 1979.
Pwh
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Nodal Analysis
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 lineGas
LiquidStock tank
PT = Pr - Psep = Total pressure loss
Adapted from Mach et al, SPE 8025, 1979.
Pwh
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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
Flo
win
g b
ott
om
ho
le p
ress
ure
, p
si Inflow (Reservoir) Curve
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Tubing Intake Curve
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
ressu
re,
psi
Tubing Curve
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System Graph
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
ress
ure
, p
si
Inflow (Reservoir) Curve
Tubing Curve
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Solution Node At Wellhead
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 lineGas
Liquid
Stock tank
PT = Pr - Psep = Total pressure loss
Adapted from Mach et al, SPE 8025, 1979.
Pwh
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Fluid Physical Properties• Oil Properties
– Oil in the absence of gas in solution is called dead oil. The physical properties of dead oil are a function of the API gravity of the oil, pressure and temperature. The API gravity of oil is defined as:
5.131F60@SpGr
5.141gravity API
o
– With gas in solution, oil properties also depend on gas solubility. Gas solubility is normally represented by Rs.
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• Gas Solubility:– Gas solubility is defined as
the volume of gas dissolved in one stock tank barrel of oil at a fixed pressure and temperature.
– There are several correlations for gas solubility such as:
• Standing
• Lassater
• and others …
Fluid Physical Properties
2.1
T00091.0
API0125.0
gs 10
10x
18
p
STB
scfR
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• Formation Volume Factor (o):– Is the volume in barrels occupied by one stock tank barrel
of oil with the dissolved gas at any elevated pressure and temperature. It measures the volumetric shrinkage of oil from the reservoir to surface conditions.
– There are different correlations for calculating the formation volume factor. They are empirical and based on oil from different areas. The Standing correlation was developed for California crude and can be written as follows:
o = 0.972+0.000147 x F1.175
Fluid Physical Properties
T25.1RF
5.0
o
gS
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Example
Required
Formation volume at 200o F of a bubble point liquid having a gas/oil ratio of 350 CFB, a gas gravity of 0.75, and a tank oil gravity of 30o API
Procedure
Starting at the left side of the chart, proceed horizontally along the 350 CFB line to a gas gravity of 0.75 . From this point, drop vertically to the 30o API line. Proceed horizontally from the tank oil gravity scale to the 200o F line. The required formation volume is found to be 1.22 barrel per barrel of tank oil.
Properties of natural mixtures of hydrocarbon gas and liquids, formation volume of bubble-point liquids after Standing.
Copyright 1952
Chevron Research Company
Reprinted by Permission
Graphical Form of Standing’s Correlation, Bo
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• Standing’s or any other correlation for formation volume factor cannot be used above the bubble point pressure Pb. Above the bubble point:
Fluid Physical Properties
bo PPCobo e
Where Pb and Bob are calculated from Standing’s or Lassater’s correlation using Rs=Rp, Rp being the produced GOR. The parameter Co is not a constant and can be calculated by Trube’s correlation as follows:
5
gso 10 x P
API61.12180,1T2.17R5433,1C
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Properties of Natural Hydrocarbon Mixtures of Gas and Liquid Bubble Point Pressure
Example:
RequiredBubble point pressure at 200oF of a liquid having a gas-oil ratio of 350 CFB, a gas gravity of 0.75, and a tank oil gravity of 30o API.Procedure:Starting at the left side of the chart, proceed horizontally along the 350o CFB line to a gas gravity of 0.75. From this point drop vertically to the 30o API line. Proceed horizontally from the tank oil gravity scale to the 200o F line. The required pressure is found to be 1930 PSIA.
Bubble Point Pressure -
- Pounds p
er square
inch
Abso
lute
Graphical Form of Standing’s Correlation, Pb
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• The fluid viscosity of reservoir oil containing solution gas decreases with pressure up to the bubble point pressure
Oil Viscosity
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Oil Viscosity
• In the absence of lab data the Beal correlation is used.
Rate of increase of oil viscosity above bubble-point pressure. After Beal.
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Dead Oil Viscosity
Abs
olu
te V
isco
sity
of
Gas
-Fre
e O
il (c
p)
Oil Gravity o API at 60oF and Atmospheric PressureDead oil viscosity at reservoir temperature and
atmospheric pressure. After Beal.
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Gas Viscosity• Carr, Kobayashi and Burrows presented a correlation for
estimating natural gas viscosity as a function of gas gravity, pressure and temperature
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Gas Deviation Factor
• Variable used in calculating the gas density and gas formation volume factor.
• To determine this parameter, the law of corresponding states is used:– This law states that at the same reduced pressure
and reduced temperature, all hydrocarbon gases have the same gas deviation factor.
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Gas Deviation Factor
As a function of Ppr and Tpr, After Standing and Katz
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Inflow Performance Relationship
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Inflow Performance Relationship
Inflow Performance is the ability of the reservoir to deliver oil or gas through the formation and is described by the pressure / rate response of the reservoir. The IPR depends on reservoir parameters and reservoir fluid characteristics.
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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
ress
ure
, p
si Inflow (Reservoir) Curve
Inflow Performance Relationship
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Inflow Performance Relationship
Progressive deterioration of IPR’s as depletion proceeds with time.
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 footCumulative recover,
percent of original
oil in place
Producing rate, bopd
Bo
tto
m h
ole
we
ll p
ress
ure
, p
si
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o oBr
rs
e
wln .
0 75
7.08 x 10-3 kh (Pr - Pwf)qo =
Inflow Performance Relationship
For single phase oil or liquids, the IPR shown below is stated by Darcy’s law for radial flow as follows:
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Productivity Index (PI)
On the IPR curve the PI is defined as the negative inverse of the slope of the line:
For PI calculations, q = surface production of fluids, and Pr-Pwf = reservoir pressure drawdown.
q = qmax when Pwf = 0
APws
Pwf
00 q B
TAN = = J = PIOBOA
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Productivity Index (PI)
The Productivity Index of a well is defined as the total liquid production per day per psi of pressure drawdown.
or, PI = J = , BPD/psi(qo + qw)
(Pr - Pwf)
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Example Problem No.1
• For the following oil-well data, calculate:a) The absolute open flow potential, AOF and draw the IPR curveb) Calculate the Productivity Index
Permeability, Ko = 30 mD Pay thickness, h = 40 ft Avg reservoir pressure, Pr = 3,000 psi Reservoir Temperature, T = 200o F Well Spacing, A = 160 Acres (43,560 ft2/acre) OH size, D = 12 ¼” Formation Volume factor, o = 1.2 bbl/stb Oil viscosity, o = 0.8 cp Assume skin, St = 0 and no turbulence
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1. Drainage radius = A x 43,560 , ft = 1,490 ft
2. Applying Darcy’s law , qo = 26,550 = 3,672 bopd
7.23
3. PI = = 1.22 bopd/psi
Answers to Example Problem No.1
BPD/psi qo
(Pr - Pwf)
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Darcy Equation for Gas Wells
gtw
eg
wfrgg
DqSr
rTZ
PPhkEq
75.0ln
03.7 224
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Skin factor
• The Skin Factor (St) is a constant which relates the pressure drop in the skin to the flow rate and transmissibility of the formation. Thus:
Kh
q
PS
oo
skint 2.141
wfwfskin PPP '
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Skin Factor – graphical representation
Pr
P’wf
Pwf
rw
rd
Positive skin ~ Damaged wellbore or Reduced wellbore radius
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......, 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 -)