Product data table1 gas properties

Name fraction Mw Pseudo Tc Pseudo Pc Pseudo k Pseudo Name Mw Tc Pc Cp Cv k

mol Mw Tc Pc k g/mol K atm Kj/kg /k Kj/kg /k

g/mol g/mol K K atm atm Methane CH4 16.04 190.70 45.50 2.22 1.70 1.30

methane 0.85 16.04 13.63 190.70 162.10 45.50 38.68 1.30 1.11 Ethane C2H6 30.07 305.46 48.16 1.75 1.47 1.19

ethane 0.10 30.07 3.01 305.46 30.55 48.16 4.82 1.19 0.12 Propane C3H8 44.10 370.00 42.00 1.67 1.48 1.13

propane 0.05 44.10 2.21 370.00 18.50 42.00 2.10 1.13 0.06 Butane C4H10 58.12 425.20 37.50 1.67 1.53 1.09

0.00 0.00 0.00 0.00 0.00 Nitrogen N2 28.01 126.20 33.50 1.04 0.74 1.40

0.00 0.00 0.00 0.00 0.00 Oxygen O2 32.00 154.80 50.10 0.92 0.66 1.39

0.00 0.00 0.00 0.00 0.00 Water H2O 18.00 647.00 218.30 1.97 1.51 1.31

0.00 0.00 0.00 0.00 0.00

Mw Tc Pc k

gas g/mol K Atm

mixture 1.00 18.85 211.14 45.59 1.28 table 2

Equipment design polytropic efficiency Ep Published by Ankur , Feb 21th 2011

ref Inlet gas Centrifugal compressor Metric Units:

Mass Flowrate 136078 kg/h Qv1 acfm 1000 2000 3000 4000 5000 7000 10000 40000 100000 Ep = 0.0992 +0.2463*log10Q1-0.02167*(log10Q1)2

Inlet adiabatic Outlet Compression ratio Qv1 m3/h 1699 3398 5097 6796 8495 11893 16990 67960 169901 Breizh March 1st 2011

T1 288.70 K compression T2 375.72 K P2/P1 table Ep 0.653 0.693 0.710 0.716 0.720 0.725 0.730 0.749 0.760 Ep=0.1746721+0.2152712*log10(Qv)-1.9708661821e-2*(log10Qv)^2

T1 15.55 C T2 102.57 C correlation Ep 0.664 0.689 0.702 0.710 0.716 0.725 0.733 0.755 0.761 where:

T1 519.66 R T2 676.30 R axial compressor

P1 2.07 Bar P2 6.90 bar 3.33 Qv1 acfm 100000 200000 400000 600000 Ep = polytropic efficiency

2.04 atm 6.81 atm Qv1 m3/h 169901 339802 679604 1019406 Q1 = inlet volume flow, m3/h

P1/Pc 0.04 P2/Pc 0.15 Ep 0.817 0.827 0.83 0.831

T1/Tc 1.37 T2/Tc 1.78 Ep 0.745197

z1 0.964 zaverage 0.939 z2 0.914

R01 4.07 kg/m3 R02 12.52 kg/m3 table 3

Q1v(T1,P1) 33434 m3/h Q2v(T2,P2) 10869 m3/h nominal inlet nominal polytropic Efficiency nominal Impeller

Ep 0.745 correlation or interpolation from table 2 volumique flowrate head HP max polytropic rotation speed diameter

P adiab 2650.27 Kw Ea = 0.711 frame m3/h kg-Nm/kg ft-lbf/lbm % RPM mm

P shaft 3728.94 Kw

P motor 3840.81 Kw a 1700-12000 30 10000 76 11000 406

b 10000-31000 30 10000 76 7700 584

adiabatic & polytropic exponants c 22000-53000 30 10000 77 5900 762

k/(k-1) 4.57 (n-1)/n 0.294 n/(n-1) 3.41 n 1.42 d 39000-75000 30 10000 77 4900 914

(k-1)/k 0.219 e 56000-110000 30 10000 78 4000 1120

f 82000-170000 30 10000 78 3300 1370

Inlet Polytropic Outlet Compression ratio

T1 288.70 K compression T2 411.14 K P2/P1 table 4 maximum polytropic head /stage

T1 15.55 C T2 137.99 C

T1 519.66 R T2 740.05 R teta 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

P1 2.07 Bar P2 6.90 bar 3.33 HP/stage 12000 12000 12000 12000 10700 9200 8000 7000 6400

2.04 atm 6.81 atm teta 1.9 2 2.1 2.2 2.3 2.4 2.5

P1/Pc 0.02 P2/Pc 0.15 HP/stage 5800 5100 4800 4200 3900 3500 3200

T1/Tc 1.37 T2/Tc 1.95

z1 0.964 zaverage 0.945 z2 0.926

R01 4.07 kg/m3 R02 11.77 kg/m3

Q1v(T1,P1) 33434 m3/h Q2v(T2,P2) 11561 m3/h

table 4 table 5 mechanical losses % Gas power (shaft)

Hp 65053.64 ft-lbf/lbm teta 0.88 HP/stage 9950 ft-lbf/lbm

KW %

P Polytro 2778.80 Kw N 7 stages 0-2500 3

P shaft 3728.94 Kw rotation speed 5688 RPM 2500-5000 2.5

P motor 3840.81 Kw 5000-7500 2

>7500 1.5

data filled manualy

data calculated

From Z& density

ref : Pipe line rules of thumbs E.W.Mcallister

Rules of Thumbs for Chemical engineers C Branam

Perry 7th edition

Calculation

Cp-Cv =R/Mw Mayer's relation

P*V=Z*R*T Real gas

P*V^k =cte adiabatic transformation

P*V^n =cte Polytropic transformation

H ≈ N^2 Affinity law

Power

P adiab= 2.78e-4*(k/(k-1))*Qv1*P1*((P2/P1)^(k-1)/k -1) P Kw Qv1 m3/h P1 Kpa

Ea= ((p2/p1)^(k-1)/k -1)/ ( (p2/p1)(k-1)/(k*Ep)-1)

Pshaft= Pad/Ea

Pmotor= Pshaft *( 1+% loss)

P poly = 2.78e-4*(n/(n-1))*Qv1*P1*((P2/P1)^(n-1)/n -1) P Kw Qv1 m3/h P1 Kpa

teta = (26.1* Mw/ (k1*T1*z1))^.5 T1 : Rankine

HP/stage table 4 HP ft-lbf/lbm

n stage= Hpmax/Hpstage tables 3 & 4

speed= Nominal speed *( HP max/ HP nominal/Number of stages) ^.5

Symbol Value Units Symbol Value

Physical data Reduced conditions

Reduced temp. Tr 1.4405

Compound Reduced press. Pr 0.1732

Molec. weight MW 18.85 g/mol

Critical temp. Tc -62.01oC Equation constants

Critical temp. Tc 211.14oK

Critical temp. Tc -79.62oF A 0.0001 b^2*(Pr/Tr)^2

Critical temp. Tc 380.05oR B 0.0104 b*(Pr/Tr)

Critical press. Pc 45.59 atm C -0.0297 a*Pr/Tr^2.5

Critical press. Pc 670.19 psia A+B+C -0.0192

Critical press. Pc 46.20 bars D 0.0003 a*b*Pr^2/Tr^3.5

Operation conditions

Operation temp. T 31.00oC Predicted Z N&R 0.9807

Operation temp. T 304.15oK Halley 0.9807

Operation temp. T 87.80oF

Operation temp. T 547.47oR density 6.08 kg/m3

Operation press. P 7.90 atm

Operation press. P 116.06 psia

Operation press. P 8.00 bars

Note - Cells in pink are input cells. All other cells are calculated cells.

Working equations Redlich & Kwong P= R*T/(V-b) -a/( T^0.5 *V *(V+b)) a=0.42748

Where: Real fluid P*V=Z*R*T b=0.08664

after eliminating V from equations above , get a cubic equation of the compressibility factor Z

Z^3-Z^2-Z*( A+B+C) -D = 0 F(Z)

3*Z^2-2Z-(A+B+C) F'(Z)

6*Z-2 F"(Z)

Iteration results 2 Methods proposed

Newton Raphson's method Zn+1=Zn-F(Zn)/F'(Zn)

initialization : Z=1

Iteration Zn F(Zn) F'(Zn) Zn+1 Δ

Number

1 1 0.01889098 1.01920059 0.981464905 -0.01854

2 0.9814649 0.00068073 0.94609086 0.980745384 -0.00072

3 0.98074538 1.0063E-06 0.94329435 0.980744317 -1.1E-06

4 0.98074432 2.2101E-12 0.94329021 0.980744317 -2.3E-12

5 0.98074432 -2.987E-17 0.94329021 0.980744317 0

6 0.98074432 -2.987E-17 0.94329021 0.980744317 0

7 0.98074432 -2.987E-17 0.94329021 0.980744317 0

8 0.98074432 -2.987E-17 0.94329021 0.980744317 0

9 0.98074432 -2.987E-17 0.94329021 0.980744317 0

10 0.98074432 -2.987E-17 0.94329021 0.980744317 0

11 0.98074432 -2.987E-17 0.94329021 0.980744317 0

12 0.98074432 -2.987E-17 0.94329021 0.980744317 0

13 0.98074432 -2.987E-17 0.94329021 0.980744317 0

14 0.98074432 -2.987E-17 0.94329021 0.980744317 0

15 0.98074432 -2.987E-17 0.94329021 0.980744317 0

Halley's method Zn+1=Zn-(2*F(Zn)*F'(Zn))/(2F'(Zn)^2-F(Zn)*F"(Zn))

initialization : Z=1

Iteration Zn F(Zn) F'(Zn) F"(Z) Zn+1 Δ

Number

1 1 0.01889098 1.01920059 4 0.980765 -0.0192347

2 0.9807653 1.9797E-05 0.94337173 3.884591821 0.980744 -2.099E-05

3 0.98074432 2.7622E-14 0.94329021 3.884465904 0.980744 -2.931E-14

4 0.98074432 -2.987E-17 0.94329021 3.884465904 0.980744 0

5 0.98074432 -2.987E-17 0.94329021 3.884465904 0.980744 0

6 0.98074432 -2.987E-17 0.94329021 3.884465904 0.980744 0

7 0.98074432 -2.987E-17 0.94329021 3.884465904 0.980744 0

8 0.98074432 -2.987E-17 0.94329021 3.884465904 0.980744 0

9 0.98074432 -2.987E-17 0.94329021 3.884465904 0.980744 0

10 0.98074432 -2.987E-17 0.94329021 3.884465904 0.980744 0

11 0.98074432 -2.987E-17 0.94329021 3.884465904 0.980744 0

12 0.98074432 -2.987E-17 0.94329021 3.884465904 0.980744 0

13 0.98074432 -2.987E-17 0.94329021 3.884465904 0.980744 0

14 0.98074432 -2.987E-17 0.94329021 3.884465904 0.980744 0

15 0.98074432 -2.987E-17 0.94329021 3.884465904 0.980744 0

INPUT DATA CALCULATIONS

Qv Ep log 10 Qv mod1

ACFM QV ACFM

1000 0.6527 3 0.666864

2000 0.6934 3.30103 0.690389

3000 0.7097 3.477121 0.702624

4000 0.7167 3.60206 0.710622

5000 0.7213 3.69897 0.716435

10000 0.7306 4 0.732317

20000 0.74 4.30103 0.744906

40000 0.7493 4.60206 0.754204

60000 0.7539 4.778151 0.758116

80000 0.7586 4.90309 0.760209

100000 0.7609 5 0.761442

200000 0.7702 5.30103 0.763095

with QV (ACFM)

model 1 Ep = 0.252531+0.192604 *log10 Qv -1.8164379 E-02*(log10Qv)^2

Qv Ep log 10 Qv mod2

m3/h QV m3/h

1699.01 0.6527 3.230196 0.664397

3398.02 0.6934 3.531226 0.689085

5097.03 0.7097 3.707317 0.701871

6796.04 0.7167 3.832256 0.710201

8495.05 0.7213 3.929166 0.716239

16990.1 0.7306 4.230196 0.732634

33980.2 0.74 4.531226 0.745456

67960.4 0.7493 4.832256 0.754707

101940.6 0.7539 5.008347 0.758462

135920.8 0.7586 5.133286 0.760385

169901 0.7609 5.230196 0.761453

339802 0.7702 5.531226 0.76241

with QV (m3/h)

model 2 Ep=0.1746721+0.2152712*log10(Qv)-1.9708661821e-2*(log10Qv)^2