Subsea Boosting Day 2 November 2015 John Friedemann thermodynamic design and test evaluation of centrifugal compressors is frequently based upon a polytropic analysis employing perfect-gas

Subsea Boosting Day 2

November 2015 John Friedemann

Multiphase

November 2015 UiO MEK4450

2

Do I even have design tools for this?

Process Mixture @ Pi,Ti

Output Fluid @ Po,To

F

Work

Heat

An Example: Flow Modeling


3

Single Phase

Bubbly

Plug

Slug

Stratified / wavy

Annular

Mist

Inc

rea

sing

Ga

s Ra

te

Challenges: Uncertainty


4

Ref: Darby, Chemical Engineering Fluid Mechanics 2001

Early Horizontal Flow Map

Early Vertical Flow Map

Spreadsheet


5

Pref 1 bar Methane

Tref 288.15 K Tc 190.6

zref 1 Pc 45.4

rhoc 192.66

Qref 4 MSm3/d acentric factor 0.001

46.30 Sm3/s mw 16.043

Wellbore Diameter 0.1524 m R 0.083145

FlowLine Diameter 0.1524 m

Absolute Roughness 0.00000381 m

L Inlet Elevation Outlet Elevation Diameter Segmentation Inlet P Outlet P Z t Qa density viscosity theta Pressure Loss

m m m - bar bar - K m3/s kg/m3 Pa-s rad bar

Well 4000 -5000 -1000 0.15240 80 500.0 414.4 1.288 400 0.166 187.242 2.30E-06 1.5708 85.59

500 -1000 -500 0.15240 10 414.4 404.1 1.175 400 0.182 170.074 2.16E-06 1.5708 10.31

Jumper 5000 -500 -500 0.15240 100 404.1 383.5 1.162 400 0.185 167.684 2.14E-06 0.0000 20.61

Booster 150.0 cooler 333

Seabed 5000 -500 -500 0.15240 100 554.1 538.3 1.479 333 0.143 217.135 2.38E-06 0.0000 15.77

Seabed to shore 50000 -500 0 0.15240 1000 538.3 373.6 1.607 278 0.133 232.448 2.35E-06 0.0100 164.76


6

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.


7

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


8

Question: Compressible fluid? 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

ss

ure

, b

ar

Copyright © 1998 ChemicaLogic Corporation. Drawn with SteamTab Duo V3.0.

DHideal

Dhideal/h


10

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

• Ie: Simple log-log relationships • Utilize Corresponding States Models


11

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

D2

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 D2

1

*

0

T

T

dTT

CS

p

UiO MEK4450 12

November 2015


13

Schultz shortcut: Linearization

𝑘 =𝐶𝑝

𝐶𝑣

hp= polytropic efficiency

h𝑝= 𝑉𝑑𝑃

𝑑𝐻=

𝑉

𝜕𝐻𝜕𝑃 𝑇+ 𝐶𝑝𝑑𝑇𝑑𝑃

𝑋 =𝑇

𝑉

𝑑𝑉

𝑑𝑇 𝑃 Z-Factor Charts

𝑌 = −𝑃

𝑉

𝑑𝑉

𝑑𝑃 𝑇


14

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


15

Compressor Sizing

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 16

November 2015

Key Inputs

Fluid Behaviours

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 2015

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 19

November 2015

Corrections to fit vapor 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 20

November 2015

How to Calculate Parameters

Methods are based on one of two options

• Know mw and spgr

– Functions for each

Tc = k mwm spgrn (Riazi Daubert) Pc = l mwo spgrp (Riazi Daubert) Or Polynomials (Pedersen)

• Similar if you know Tb and mw – Twu, etc polynomials

UiO MEK4450 21

November 2015

Mixtures and mixing rules

For b we say that the volume taken up by the molecules is just the sum of the component molecule volumes:

For a we say that this term is still proportional to the number of binary collisions, just as for a single component. For a mixture we then get the expression.

One simple, common and wholly empirical improvement of the mixing rule

is to include a binary interaction parameter per pair:

SRK: determined from binary interaction data PR: (strict) predicted from critical volume

Not exchangeable

𝑎 = 𝑥𝑖𝑥𝑖 𝑎𝑖𝑎𝑗

𝑁

𝑖=1

𝑁

𝑗=1

𝑎 = 𝑥𝑖𝑥𝑖 𝑎𝑖𝑎𝑗

𝑁

𝑖=1

𝑁

𝑗=1

(1 − 𝑘𝑖𝑗)

𝑏 = 𝑥𝑖𝑏𝑖

𝑁

𝑖=1

UiO MEK4450 22

November 2015

Calculation procedure for Flash

n

)-AA(- y + RT G =

n

)-AA(- x + RT G V

i

V

tot

*

i

*iL

i

L

tot

*

i*i

lnln

Minimize free-energy in system

UiO MEK4450 23

November 2015

They are not interchangeable

Peng Robinson Phase Envelope

0.00

50.00

100.00

150.00

200.00

250.00

-100.00 0.00 100.00 200.00 300.00 400.00 500.00 600.00

Temperature, C

Pre

ss

ure

, b

ar

UiO MEK4450 24

November 2015

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

ss

ure

, b

ar

Operating Window

Peng-Robinson SRK

Fluid Behaviour based on SRK fit to Reservoir Data

UiO MEK4450 25

November 2015

How can these errors affect us?


26

250 bar 4oC

3 bar ?oC

Methane

Flow

Slippage Effect of Slip

Q, Flow Rate

h, head

Twin Screw Performance

UiO MEK4450 27

November 2015

Axial Compressors

Surge Control


29

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 30

November 2015

Process Threats


31

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


32

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


33

Suppliers

Compressor: GE

Switchgear: GE

Variable Speed Drive: GE

UPS: GE

Connectors: Tronic/Deutsch

Scrubber: Aker

Pump: Aker

Recycle Cooler: Aker

Compressor

UiO MEK4450 34

November 2015

Gas-Lift System Overview


35

Compressor Station

Gas in Annulus

Mandrels

Control Valve

Artificial Lift Options


36

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


37

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


38

1. Start-up dynamics • Oil-Filled • Water-Filled

2. Operating Case • 3.5 and 5.125” tubing

Depth0

255075

100125150175200225250275300325350375400425450475500525550575600625650675700725750775800825850875900925950975

1000102510501075 Gaslift?11001125115011751200122512501275130013251350137514001425145014751500152515501575

Two-Phase

Gas-Lift Water / Mud Filled


39

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


40

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


41

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


42

Depth0

255075

100125150175200225250275300325350375400425450475500525550575600625650675700725750775800825850875900925950975

1000102510501075 Gaslift?11001125115011751200122512501275130013251350137514001425145014751500152515501575

Two-Phase

Operation


43

How about the Compressor


44

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

Solution Strategy


45

Schultz Approximation?


46

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

Optimum: Really?


47

The ESP Overview


48

Speed Controller

Cable

Motor Pump

ESP Performance


49

Rotating EQPT = Vendor Sizing

But We Can Estimate


50

Need to consider Operating Points

Seabed Booster System Level


51

Power • Variable Speed Drive • Switch Gear • Transformers Process • Slugcatcher • Mixers • Recycle Coolers • Barrier Fluid • Lubricants

Barrier Fluid and Lubricants


52

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

Seabed booster


53

Compressors and Pumps: Bearings


54

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


55

Journal bearing: 1. Simplest and stiffest 2. Lubricant functions as coolant

Magnetic 1. Complex control

Film

Lubrication Models


56

Film

Flow Laminar Heat transfer Simple

Finally: Compressor Maps


57

Rate

He

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Documents

Subsea Boosting Day 2 November 2015 John Friedemann thermodynamic design and test evaluation of centrifugal compressors is frequently based upon a polytropic analysis employing perfect-gas