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Subsea Boosting Day 2
November 2014 Jørgen Wessel
November 2013 UiO MEK4450
2
Compressor Modeling
L
The Polytropic Analysis of Centrifugal Compressors
John M. Schultz, Trans. Of the ASME, ASME J. of Engineering for Power, Jan 1962 pp 69-82
The real-gas equations of polytropic analysis are derived in terms of compressibility functions X and Y which supplement the familiar compressibility factor, Z. A polytropic head factor, f, is introduced to adjust test results for deviations from perfect-gas behavior. Functions X and Y are generalized and plotted for gases in corresponding states.
The thermodynamic design and test evaluation of centrifugal compressors is frequently based upon a polytropic analysis employing perfect-gas relations. In many instances real-gas relations would be more accurate, but these are virtually unknown. The purpose of this paper is to derive the real-gas equations of polytropic analysis and to show their application to centrifugal compressor testing and design.
November 2013 UiO MEK4450
3
Back to Classical Thermodynamics
𝐻 −𝐻𝑜 = 𝐶𝑝∗𝑑𝑇 +
𝑇
𝑇0
𝑇𝜕𝑉
𝜕𝑇𝑃
− 𝑉 𝑑𝑃𝑃
0
𝑆 − 𝑆𝑜 = 𝐶𝑝∗
𝑇𝑑𝑇 +
𝑇
𝑇0
𝜕𝑉
𝜕𝑇𝑃
𝑑𝑃𝑃
0
Where C*p is the ideal gas state heat capacity
Question: Compressible fluid?
s
h
Entropy
En
tha
lpy
dh dhi
P+dp
p
November 2013 UiO MEK4450
5
The problem in 1962
• Schultz needed a convenient model for the fluid
• Little General Access to Process Simulation Tools • Limitations in Equations of State Methods
• BWR 1940, complex solution • RK 1949, limited application to mixtures • NGA 1958, Equilibrium Ratio Data for Computers
Needed an alternative which could be handled using a slide rule • I.e.: Simple log-log relationships • Utilize Corresponding States Models
November 2013 UiO MEK4450
6
Compressor Modeling
Classic Compressor Algorithm: Polytropic
• 𝑃𝑉𝑛 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
•𝑃𝑚
𝑇= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
•𝑃𝑛−1𝑛−𝑚
𝑍= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
Solving Bernoulli’s equation
*
1
212
1
2
1
2* lnlnpC
R
pP
PTT
P
PR
T
TC
2
1
2
1
2
1
2
1
**0
V
V
T
T
V
V
T
T
dVV
RTdTCPdVdTCWHQ
pp
1)(
*
1
21
*
12
*pC
R
ppP
PTCTTCW
11
1
1
211
P
PVPW
RTPVwhileRCCandC
Cvp
v
p **
*
*
0)()(2
1 22 wf
P
P
oiio hhdP
hhguuo
i
Bernoulli
1st Law
2nd Law 2
1
*
0
T
T
dTT
CS
p
UiO MEK4450 7
November 2013
November 2013 UiO MEK4450
8
Schultz shortcut: Linearization
𝑘 =𝐶𝑝
𝐶𝑣
hp= polytropic efficiency
h𝑝= 𝑉
𝑑𝑃
𝑑𝐻=
𝑉
𝜕𝐻𝜕𝑃 𝑇
+ 𝐶𝑝𝑑𝑇𝑑𝑃
𝑋 =𝑇
𝑉
𝑑𝑉
𝑑𝑇 𝑃 Z-Factor Charts
𝑌 = −𝑃
𝑉
𝑑𝑉
𝑑𝑃 𝑇
November 2013 UiO MEK4450
9
Hi,Si,Vi,CPi,Cvi
V/F,X,Y,n,m,
Top
Feed at P,T
Flash at Pi,Ti
Calculate To,Po,Vo
Flash at Po,To
Ho,So,To,W
Outputs Inputs • Efficiency • Composition
Schultz Algorithm: Wheel by Wheel
Not Rigorous for Multiphase
Dry Gas Compressors
November 2013 UiO MEK4450
10
Compressor Sizing using software
30oC 1 bar ?oC
6 bar
Find Power requirement
Feed rate 1000kg/hr
50oC
21 bar 5 oC 21 bar
U- value For 10” piping 10 km long Seawater at 4oC
75% Adiabatic Efficiency 77.9% Polytropic Efficiency
UiO MEK4450 11
November 2013
Reservoir Fluids
0
20
40
60
80
100
120
140
160
-200 -100 0 100 200 300 400 500
Temperature, oC
Pre
ssu
re, b
ar
Gas Cap
Oil
20vol% Gas
40vol% Gas
60vol% Gas
80vol% Gas
Bubble Point
Bubble Point
Dew Point
Dew Point
99.99vol% Gas
99.9vol% Gas
99vol% Gas
UiO MEK4450 12
November 2013
Basic Evolution
•the molecules have no volume themselves •there are no forces between the molecules
V
RTP
Ideal gas
van der Waals 2v
a
bv
RTP
• The molecules have a volume, which we call b. The free volume for motion is then v-b • There are forces between the molecules which must be proportional to 1/v2
UiO MEK4450
13
November 2013
Corrections to fit vapour pressure
Fits liquids better, but at a cost
SRK PR
) ( b v v
a
b v
RT P
) ( ) ( b v b b v v
a
b v
RT P
c
c
P
RT b 08664 . 0
c
c
P
RT b 0778 . 0
a P
T R a c
2 2
42748 . 0 a P
T R a c
2 2
45724 . 0
( ) [ ] 2
1 1 r T m a ( ) [ ] 2
1 1 r T m a 2
17600 . 0 57400 . 1 48000 . 0 w w a Soave 2
26952 . 0 54226 . 1 3746 . 0 w w a 2
15613 . 0 55171 . 1 48508 . 0 w w a Riazi
UiO MEK4450 14
November 2013
Issues around EOS use
Be consistent with the operator: use theirs Equilibrium Gas Phase Envelope
0.00
100.00
200.00
300.00
400.00
500.00
600.00
700.00
800.00
-100.00 -50.00 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00
Temperature, C
Pre
ssu
re,
bar
Operating Window
Peng-Robinson SRK
Fluid Behaviour based on SRK fit to Reservoir Data
UiO MEK4450 15
November 2013
EOS Comparison: PR-AGA-8
0.6500
0.7000
0.7500
0.8000
0.8500
0.9000
0.9500
1.0000
0.0000 50.0000 100.0000 150.0000 200.0000 250.0000
Pressure, bar
Z F
acto
r
PR @5C
PR @10C
PR @15C
AGA-8 @5C
AGA-8 @10C
AGA-8 @15C
UiO MEK4450 16
November 2013
EOS Comparison: SRK-AGA-8
0.6500
0.7000
0.7500
0.8000
0.8500
0.9000
0.9500
1.0000
0.0000 50.0000 100.0000 150.0000 200.0000 250.0000
Pressure, bar
Z F
acto
r
SRK @5C
SRK @10C
SRK @15C
AGA-8 @5C
AGA-8 @10C
AGA-8 @15C
UiO MEK4450 17
November 2013
Reservoir Fluids
0
20
40
60
80
100
120
140
160
-200 -100 0 100 200 300 400 500
Temperature, oC
Pre
ssu
re, b
ar
Gas Cap
Oil
20vol% Gas
40vol% Gas
60vol% Gas
80vol% Gas
Bubble Point
Bubble Point
Dew Point
Dew Point
99.99vol% Gas
99.9vol% Gas
99vol% Gas
UiO MEK4450 18
November 2013
Process Threats
November 2013 UiO MEK4450
19
Threat Device Mitigation
Sand Pumps/valves Separators and strainers
Droplets (Carry-over) Compressors Scrubbers and internals
Slugging Pumps/compressors Inlet Separator Volume
Deposits All Chemical Treatment
Subsea Transient Effects
November 2013 UiO MEK4450
20
Device Normal Condition Transient Condition
Pump Liquid filled Gas-filled
Gas slugs
Sand-free Sand «slugs»
Discharge flow Blocked discharge
Compressor Gas-filled Liquid-filled
Liquid slugs
Carry-over
Sand-free Fines
Electric Driver Clean dielectric Gas-contaminated
Sour
Water contaminated
Fines
Bearings Clean Lubricant or Gas Sand
Liquids
Facility Complexity
November 2013 UiO MEK4450
21
Suppliers
Compressor: GE
Switchgear: GE
Variable Speed Drive: GE
UPS: GE
Connectors: Tronic/Deutsch
Scrubber: Aker
Pump: Aker
Recycle Cooler: Aker
Compressor
UiO MEK4450 22
November 2013
Building the model: Goliat
November 2013 UiO MEK4450
23 Based on net available data
Reservoir Fluids
0
20
40
60
80
100
120
140
160
-200 -100 0 100 200 300 400 500
Temperature, oC
Pre
ssu
re, b
ar
Gas Cap
Oil
20vol% Gas
40vol% Gas
60vol% Gas
80vol% Gas
Bubble Point
Bubble Point
Dew Point
Dew Point
99.99vol% Gas
99.9vol% Gas
99vol% Gas
UiO MEK4450 24
November 2013
Gas-Lift System Overview
November 2013 UiO MEK4450
25
Compressor Station
Gas in Annulus
Mandrels
Control Valve
Artificial Lift Options
November 2013 UiO MEK4450
26
Water-Filled
Co
mp
ress
or/
Pu
mp
Oil-Filled Two-Phase
Co
mp
ress
or/
Pu
mp
Co
mp
ress
or
Liq
uid
Aft
er
Op
era
tio
n o
r fr
om
Ho
ldu
p
Liq
uid
Ho
ldu
p p
lus
Co
nd
en
sati
on
Condensation
Gas Lift
Example Case
November 2013 UiO MEK4450
27
Gas-Lift Point at 1050 m TVD (seabed) Two Tubing Sizes (3.5” and 5.125”) Initial GOR = 110 Sm3/Sm3
PI=250 Sm3/bar/day (all phases) 25% water-cut Simple fluid model (fixed phase split)
Approach
November 2013 UiO MEK4450
28
1. Start-up dynamics • Oil-Filled • Water-Filled
2. Operating Case • 3.5 and 5.125” tubing
Depth02550751001251501752002252502753003253503754004254504755005255505756006256506757007257507758008258508759009259509751000102510501075 Gaslift?11001125115011751200122512501275130013251350137514001425145014751500152515501575
Two-Phase
Gas-Lift Water / Mud Filled
November 2013 UiO MEK4450
29
Annulus Pressure 120 bar - Need Valve Cv at tree - Gaslift Valve Cv / Orifice - What else?
0
200
400
600
800
1000
1200
1400
0,0 50,0 100,0 150,0
De
pth
, m
Pressure, bar
Seawater
Gas
Oil Filled
November 2013 UiO MEK4450
30
Annulus Pressure 115 bar - Need Valve Cv at tree - Gaslift Valve Cv / Orifice - Is this Interesting?
0
200
400
600
800
1000
1200
1400
0,0 50,0 100,0 150,0D
ep
th,
m
Pressure, bar
OIl
Gas
In Operation
November 2013 UiO MEK4450
31
Annulus Pressure 105 bar + - Need Valve Cv at tree - Gaslift Valve Cv / Orifice - Annulus Pressure Drop
0
200
400
600
800
1000
1200
1400
0,0 50,0 100,0 150,0D
ep
th,
m
Pressure, bar
OIl
Gas
Operation
November 2013 UiO MEK4450
32
Depth02550751001251501752002252502753003253503754004254504755005255505756006256506757007257507758008258508759009259509751000102510501075 Gaslift?11001125115011751200122512501275130013251350137514001425145014751500152515501575
Two-Phase
Operation
November 2013 UiO MEK4450
33
How about the Compressor
November 2013 UiO MEK4450
34
T C 60 S1,ideal 136.5731 H1, ideal 10516.77 10516.77222 136.5731
1 2 3 4 5 6 P bar 35 Ss,ideal 136.8359 T2, ideal 149.8785 147.7694442 420.9194 136.5731
3 Z 0.954991 H2, Ideal 14082.59 13971.6931
Choke Sizing Calculator 4 mw 19.63837 dH, Ideal 3565.818 3454.920886 175.927
V1.2 5 v/f (volume) - 1.0000 H2, real 14974.04 dh, real 4318.651107 14835.42
6 P bar 110.1 T2, Real 184.58 164.157489
Inlet Pipe ID, in5.13 7 R kj/kmol/K 8.3145 H2, calc 15919.51 14835.42333 4318.651 219.9088
Choke Outlet Pipe ID, in5.13 8 Error -945.469 2.24052E-07
Choke Body ID, in5.13 9 polytropic adiabatic
Valve Style Modifier, Fd 1.00 10 Z 1.001245 0.727242 Z 0.994604
Liquid Pressure Recovery Factor, F11.00 11 efficiency η 0.8 efficiency η 0.8
12
13
14
15 v1/R v2,i/R
16 9.090152349 3.998329106
Tref , C 15.00 17 0.754729488 0.223460311 0.941596
Pref , bar 1.00 Feed 18 v1/R v2,i/R
Component mol% 19 9.090152349 4.16253813
Water 0.00 20 n 1.448968 1.384 k=Cp/Cv 1.32958 0.754729488 0.345024383 1.464132
H2S 0.00 21 1.464132 1.395373 -0.081
CO2 0.95 22 (n-1)/n 0.277 (k-1)/k 0.248
N2 8.85 23
Methane 78.96 24
Ethane 7.75 25
Propane 2.51 26
i-Butane 0.30
n-Butane 0.49
i-Pentane 0.08
n-Pentane 0.07 T C 184.58 T C 169.45
Benzene 0.00
Toluene 0.00
e-Benzene 0.00
o-Xylene 0.00
m-Xylene 0.00 Density
p-Xylene 0.00 mw kg/m3
Hexane 0.02 84.40 670 head kj/kg 181.7094 head kj/kg 178.5325
Heptane 0.01 92.60 734
Octane 0.00 105.20 760
Nonane 0.00 117.70 781
Decane 0.00 171.50 800
Total Head kj/kg 227.1367 Total Head kj/kg 223.1657
pk
k
n
n
h
111
gasideal
1
1
2
1
2k
k
P
P
T
T
gasreal
1
1
2
1
2n
n
P
P
T
T
11
1
1
211n
n
pP
P
MW
RTZ
n
nH
11
1
1
211k
k
aP
P
MW
RTZ
k
kH
11
1
1
1
211n
n
p
totalP
P
MW
RTZ
n
nH
h
2
1
1
2
ln
ln
P
P
n
i
P
P
k
,2
1
1
2
ln
ln
Note: 1st Iteration Result
Schultz Approximation?
November 2013 UiO MEK4450
35
Bubbles: Compressors and Pumps WIP
v2013 Gas
Gas Rate Oil Rate MEG Aqueous Rate Inlet T Inlet P Discharge PDischarge T Gas RateCompressibilityGas DensityGas Mol Wt Gas Cp/Cv Enthalpy
Sm3/d Sm3/d wt% Sm3/d oC bar baroC m3/d Z Tf c,Pf c Tf c,Pf c Tf c,Pf c Change
1 1000.0 0.00 0.00 0.00 60.00 35.00 41.22 72.948 31.5 0.95 26.11 19.64 1.33 25.36408
2 1000.0 0.00 0.00 0.00 72.95 41.22 48.55 86.141 27.8 0.96 29.55 19.64 1.33 26.212
Inlet Pipe ID, in5.13 3 1000.0 0.00 0.00 0.00 86.14 48.55 57.18 99.565 24.6 0.96 33.45 19.64 1.33 27.07727
Choke Outlet Pipe ID, in5.13 4 1000.0 0.00 0.00 0.00 99.57 57.18 67.34 113.210 21.7 0.96 37.85 19.64 1.33 27.96542
Choke Body ID, in5.13 5 1000.0 0.00 0.00 0.00 113.21 67.34 79.31 127.063 19.2 0.97 42.81 19.64 1.32 28.88544
Valve Style Modifier, Fd 1.00 6 1000.0 0.00 0.00 0.00 127.06 79.31 93.40 141.110 17.0 0.97 48.40 19.64 1.32 29.85079
Liquid Pressure Recovery Factor, F11.00 7 1000.0 0.00 0.00 0.00 141.11 93.40 110.01 155.342 15.0 0.98 54.67 19.64 1.32 30.88048
196.2355
Tref , C 15.00
Pref , bar 1.00 Feed
Component mol%
Water 0.00
H2S 0.00
CO2 0.95
N2 8.85
Methane 78.96
Ethane 7.75
Propane 2.51
i-Butane 0.30
n-Butane 0.49
i-Pentane 0.08
n-Pentane 0.07
Benzene 0.00
Toluene 0.00
e-Benzene 0.00
o-Xylene 0.00
m-Xylene 0.00 Density
p-Xylene 0.00 mw kg/m3
Hexane 0.02 84.40 670
Heptane 0.01 92.60 734
Octane 0.00 105.20 760
Nonane 0.00 117.70 781
Decane 0.00 171.50 800
PhasePhase
Solution Strategy
November 2013 UiO MEK4450
36
Optimum: Really?
November 2013 UiO MEK4450
37
The ESP Overview
November 2013 UiO MEK4450
38
Speed Controller
Cable
Motor Pump
ESP Performance
November 2013 UiO MEK4450
39
Rotating EQPT = Vendor Sizing
But We Can Estimate
November 2013 UiO MEK4450
40
Need to consider Operating Points
Seabed Booster System Level
November 2013 UiO MEK4450
41
Power • Variable Speed Drive • Switch Gear • Transformers Process • Slug-catcher • Mixers • Recycle Coolers • Barrier Fluid • Lubricants
Seabed booster
November 2013 UiO MEK4450
42
Barrier Fluid and Lubricants
November 2013 UiO MEK4450
43
Problem: Protecting the motor and bearings Solution: Applying a pressurized fluid Helps Control Bearings
Mo
tor
Pu
mp
Ba
rrie
r F
luid
Flo
w
Compressors and Pumps: Bearings
November 2013 UiO MEK4450
44
How to provide a stiff support for a shaft
1- Support it in a liquid lubricant 2- Support it by magnetism 3- Use rollers
Bearings
November 2013 UiO MEK4450
45
Journal bearing: 1. Simplest and stiffest 2. Lubricant functions as coolant
Magnetic 1. Complex control
Film
Lubrication Models
November 2013 UiO MEK4450
46
Film
Flow Laminar Heat transfer Simple
Finally: Compressor Maps
November 2013 UiO MEK4450
47
Rate
He
ad
UiO MEK4450 48 November 2013
Enthalpy-Entropy Diagram
-1.0E+05
0.0E+00
1.0E+05
2.0E+05
3.0E+05
4.0E+05
5.0E+05
6.0E+05
-2000 -1000 0 1000 2000
Entropy, J/kg/C
En
tha
lpy
, J
/kg
5oC
25oC
65oC
125oC
165oC
185oC
1 bar 26 bar
6 bar
36 bar
16 bar
135oC
155oC
175oC
195oC
215oC
115oC
95oC
75oC
55oC
35oC
15oC 45oC
85oC
145oC
105oC
205oC
225oC
11 bar
21 bar
31 bar
41 bar
UiO MEK4450 49
November 2013
Reference Fluids
DEMO2000 Application
Luciano E. Patruno
November 2011
Treated use entropy-enthalpy balance.
Pressure-Enthalpy Diagram for Water and Steam Based on the IAPWS-97 Formulation for General and Scientific Use
0.01
0.1
1
10
100
1000
0 500 1000 1500 2000 2500 3000 3500 4000
Enthalpy, kJ/kg
Pre
ssu
re,
ba
r
Copyright © 1998 ChemicaLogic Corporation. Drawn with SteamTab Duo V3.0.
Hi
deal hideal/
h
UiO MEK4450 50
November 2013