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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
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