Rotating Equipment: Pumps, Compressors, & Turbines/Expanders. Chapters 2 & 9

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1 Rotating Equipment: Pumps, Compressors, & Turbines/Expanders Chapters 2 & 9

2 Topics Fundamentals Starting relationships Thermodynamic relationships Bernoulli s equation Simplifications Pumps constant density compression Compressors reversible ideal gas compression Use of PH & TS diagrams Multistaging Efficiencies Adiabatic/isentropic vs. mechanical Polytropic Equipment Pumps Centrifugal pumps Reciprocating pumps Gear pumps Compressors Centrifugal compressors Reciprocating compressors Screw compressors Axial compressors Turbines & expanders Expanders for NGL recovery Gas turbines for power production o What is heat rate? 2

3 Fundamentals

4 Review of Thermodynamic Principals 1 st Law of Thermodynamics Energy is conserved (Change in system s energy) = (Rate of heat added) (Rate of work performed) Ê QW Major energy contributions Kinetic energy related to velocity of system Potential energy related to positon in a field (e.g., gravity) Internal energy related to system s temperature o Internal energy, U, convenient for systems at constant volume & batch systems 2 ˆ ˆ u g E U h g g 2 c c o Enthalpy, H = U+PV, convenient for systems at constant pressure & flowing systems 2 ˆ ˆ u g E H h g g 2 c c 4

5 Review of Thermodynamic Principals 2 nd Law of Thermodynamics In a cyclic process entropy will either stay the same (reversible process) or will increase Relationship between work & heat All work can be converted to heat, but Not all heat can be converted to work 5

6 Common Paths for Heat and Work Isothermal constant temperature ΔT = 0 Isobaric constant pressure ΔP = 0 Isochoric constant volume ΔV = 0 Isenthalpic constant enthalpy ΔH = 0 Adiabatic no heat transferred Q = 0 Isentropic (ideal reversible) no increase in entropy ΔS = 0 6

7 1 st Law for steady state flow Equation 1.19a (ΔH ΔU for flowing systems) 2 ˆ u g H z QW g g 2 c c For adiabatic, steady-state, ideal (reversible) flow (using WS as positive value) 2 ˆ ˆ u g Ws H z 2g g Wˆ s P 2 2 ˆ u g VdP z 2g g P P P Vˆ dp c P P 1 1 c dp c c The work required is inversely proportional to the mass density 7

8 Thermodynamics of Compression Work depends on path commonly assume adiabatic or polytropic compression Calculations done with: PH diagram for ΔH s P 2 W VdP H P 1 Evaluate integral using equation of state Simplest gas EOS is the ideal gas law Simplest liquid EOS is to assume incompressible (i.e., constant density with respect to pressure) W s P P 2 2 dp 1 P2 P1 dp P P 1 1 8

9 Liquid vs. Vapor Compression Can compress liquids with little temperature change ΔH for gas compression much larger than for liquid pumping GPSA Data Book, 13th ed. 9

10 Mechanical Energy Balance Differential form of Bernoulli s equation for fluid flow (energy per unit mass) d u 2 2 dp gdz dwˆ ˆ s gd hf0 Frictional loss term is positive Work term for energy out of fluid negative for pump or compressor If density is constant then the integral is straight forward pumps u 2 2 P g z wˆ ˆ s ghf 0 If density is not constant then you need a pathway for the pressure-density relationship compressors 2 P2 u dp g z wˆ ˆ s ghf 0 2 P 1 10

11 Pump equations Pumping requirement expressed in terms of power, i.e., energy per unit time Hydraulic horsepower power delivered to the fluid Over entire system 2 u P Whhp m wˆ ˆ s V gz ghf 2 ˆ 1 2 V P V gz V ghf V u 2 Just across the pump, in terms of pressure differential or head: W V P or W VgH hhp Brake horsepower power delivered to the pump itself W bhp W hhp pump hhp 11

12 Pump equations for specific U.S. customary units U.S. customary units usually used are gpm, psi, and hp W hp 3 in 231 gal lb gal min in sec in ftlb f / sec min ft hp 1 gal lbf min in f hhp 2 Also use the head equation usually using gpm, ft, specific gravity, and hp W hhp lbm ft gal gal 2 sec lb ft hp ft o min sec ftlb f / sec m min hp lbf sec 1 gal 3958 min ft o 12

13 Static Head Terms Fundamentals of Natural Gas Processing, 2 nd ed. Kidnay, Parrish, & McCartney 13

14 Pump Example Liquid propane (at its bubble point) is to be pumped from a reflux drum to a depropanizer. Pressures, elevations, & piping system losses as shown are shown in the diagram. Max flow rate 360 gpm. Propane specific gravity pumping temperature (100 o F) Pump nozzles elevations are zero & velocity head at nozzles negligible What is the pressure differential across the pump? What is the differential head? What is the hydraulic power? GPSA Data Book, 13 th ed. 14

15 Pump Example Pressure drop from Reflux Drum to Pump inlet: P g P zp g inlet c piping psi psia Pressure drop from Pump outlet to Depropanizer: P g P zp g outlet c piping psi psia 15

16 Pump Example Pump pressure differential: P Poutlet Pinlet pump psi Pump differential head: h pump gc g P pump ft Hydraulic power: W hhp 360 gpm61.2 psi 360 gpm ft hp OR Whhp hp

17 PH Diagrams Ref: GPSA Data Book, 13 th ed. 17

18 TS Diagram 18

19 19

20 20

21 21

22 Thermodynamics of Compression Assume ideal gas: PV = RT Choices of path for calculating work: Isothermal (ΔT = 0) P2 P2 dp P2 s ln P P P P 1 W VdP RT RT 1 1 Minimum work required but unrealistic Adiabatic & Isentropic (ΔS = 0) Maximum ideal work but more realistic Polytropic reversible but non-adiabatic Reversible work & reversible heat proportionately added or removed along path More closely follows actual pressure-temperature path during compression 22

23 Thermodynamics of Compression Ideal gas isentropic (PV = constant) where = C P /C V Molar basis Mass basis W s RT 1 1/ P P1 1/ ˆ RT1 P 2 s W M P Polytropic (PV = constant) where is empirical constant usually greater than 1/ ˆ RT 1 P 2 p W M P 23

24 Thermodynamics of Compression Calculation of for gas mixture xc i p, i xc i p, i xc xc R i V, i i p, i Use the ideal gas heat capacities, not the real gas heat capacities Heat capacities are functions of temperature. Use the average value over the temperature range 24

25 Example Compression Calculation Want to compress sales gas (assume pure methane) from initial conditions of 40 o F & 100 psig to 400 psig. Compute work of compression on mass basis Using PH diagram Assuming ideal gas and adiabatic compression Using a process simulator 25

26 Example Calculation PH Diagram H 2 = 462 Btu/lb H 1 = 370 Btu/lb W S = (H 2 H 1 ) = 92 Btu/lb 26

27 Example Calculation Ideal Gas Compression For methane: = 1.3 M = 16 T 1 = 40 o F = 500 o R P 1 = 100 psig = psia P 2 = 400 psig = psia R = Btu/lb.mol o R 1/ /1.3 RT P W s M 1 P Btu/lb 27

28 Example Calculation Using a Simulator Work Btu/lb Outlet o F HYSYS Peng-Robinson HYSYS Peng-Robinson & Lee Kesler HYSYS SRK HYSYS BWRS Aspen Plus PENG-ROB Aspen Plus SRK Aspen Plus BWRS Aspen Plus BWR-LS

29 Discharge temperature For ideal gas compression P 2 2 T1 P1 T 1/ For the example problem: T / R 213 F

30 Thermodynamics of Compression If customer wants 1,000 psig (when the inlet pressure 100 psig) Then pressure ratio of (1015/115) = 8.8 Discharge temperature for this ratio is ~360 o F For reciprocating compressors the GPSA Engineering Data Book recommends Maximum discharge temperature of 250 to 275 o F for high pressure systems AND Pressure ratios of 3:1 to 5:1 To obtain pressure ratios higher than 5:1 must use multistage compression with interstage cooling 30

31 Multistaging To minimize work need good interstage cooling and equal pressure ratios in stages. The number of stages is calculated using R P P P1 1/ m 2 m P ln / P ln 2 1 R P To go from 100 to 1000 psig with a single-stage pressure ratio of 3 takes 2 (1.98) stages & the stage exit temp ~183 o F 40 o F) ln ln 8.8 m 1.98 ln 3 ln 3 1/ m 1/ 1/2 1.3 P 1 / T1 P T R 183 F 31

32 Multistaging Work for a single stage of compression Work for two stages of compression (interstage cooling to 40 o F) Intermediate pressure Total work 1/ /1.3 RT P W s M 1 P Btu/lb Pint PP psia W s / / Btu/lb 32

33 Compression Efficiency Compression efficiencies account for actual power required compared to ideal Isentropic (also known as adiabatic) efficiency relates actual energy to fluid to energy for reversible compression H W IS W H S0 S0 fluid fluid IS Mechanical efficiency relates total work to device to the energy into the fluid W W W mech W W fluid fluid S0 total total mech mechis 33

34 Compressor Efficiency Discharge Temperature GPSA Engineering Data Book suggests the isentropic temperature change should be divided by the isentropic efficiency to get the actual discharge temperature 1/ 1/ P 2 P 2 T T 0 1 T1 T1 1 S P1 P1 So: act 1/ P 2 T P S0 1 T 1 IS IS 1/ P 2 T P1 T2, act T1 T T1 1 act IS

35 Polytropic Compression & Efficiency Definition of polytropic compression (GPSA Data Book 14 th ed.): A reversible compression process between the compressor inlet and discharge conditions, which follows a path such that, between any two points on the path, the ratio of the reversible work input to the enthalpy rise is constant. In other words, the compression process is described as an infinite number of isentropic compression steps, each followed by an isobaric heat addition. The result is an ideal, reversible process that has the same suction pressure, discharge pressure, suction temperature and discharge temperature as the actual process. 35

36 Polytropic Efficiency Polytropic path with 100% efficiency is adiabatic & is the same as the isentropic path Polytropic efficiency, p, is related to the isentropic path P 1/ 1/ In general P > IS Polytropic coefficient from discharge temperature 1 P ln 2 1 T2 / T1 2 T 1 where P1 1 ln P2 / P1 T 36

37 Polytropic Efficiency Actual work is calculated from the polytropic expression divided by its efficiency 1/ ˆ Wp RT 1 P 2 act 1 p p M 1 P1 W ˆ 1 Note: Wˆ Wˆ ˆ p S0 act p IS W 37

38 Compressor efficiency example Compress methane from 40 o F & 100 psig to % isentropic efficiency & 10% mechanical losses Actual work required is: 1/ / RT P Btu/lb ˆ 1 2 fluid 1 1 IS M 1 P W Discharge temperature: T 2, act 1 1/ 1.31 /1.3 P P T R 256 F IS

39 Compressor efficiency example Using polytropic pathway: ln T / T ln 716 / ln P2 / P 1 ln414.7 / / 1.31/1.3 P / / / / RT P Btu/lb ˆ 1 2 fluid 1 1 p M 1 P W 39

40 Compressor efficiency example Can use either expression for the power to the fluid to determine the total power to the compressor Wfluid 116 Wtotal 129 Btu/lb 10.1 mech 40

41 Why Use Polytropic Equations? Polytropic equations give consistent P-T pathway between the initial & discharge conditions 41

42 Compression vs. Expansion Efficiency Work to compressor is greater than what is needed in the ideal case Work to the fluid H W IS W H S0 S0 fluid fluid IS Total work to the device W fluid mech Wtotal W total Wfluid W S 0 mech mech IS Work from expander is less than what can be obtained in the ideal case Work from the fluid H W fluid IS fluid IS S 0 H S 0 Total work from the device W total mech Wfluid W W W W total mech fluid mech IS S 0 42

43 Equipment: Pumps, Compressors, Turbines/Expanders

44 Pump & Compressor Drivers Internal combustion engines Industry mainstay from beginning Emissions constraints Availability is 90 to 95% Electric motors Good in remote areas Availability is > 99.9% Gas turbines Availability is > 99% Lower emissions than IC engine Steam turbines Uncommon in gas plants on compressors Used in combined cycle and Claus units 44

45 Pump Classifications Fundamentals of Natural Gas Processing, 2 nd ed. Kidnay, Parrish, & McCartney 45

46 Centrifugal Pump Performance Curves Fundamentals of Natural Gas Processing, 2 nd ed. Kidnay, Parrish, & McCartney 46

47 Compressor Types Positive displacement compress by changing volume Reciprocating Rotary screw Diaphragm Rotary vane Dynamic compress by converting kinetic energy into pressure Centrifugal Axial 47

48 Reciprocating Compressors Workhorse of industry since 1920 s Capable of high volumes and discharge pressures High efficiency up to 85% Performance independent of gas MW Good for intermittent service Drawbacks Availability ~90 to 95% vs 99+% for others, spare compressor needed in critical service Pulsed flow Pressure ratio limited, typically 3:1 to 4:1 Emissions control can be problem (IC drivers) Relatively large footprint Throughput adjusted by variable speed drive, valve unloading or recycle unless electrically driven 48

Reciprocating Compressors - Principle of Operation Double Acting Crosshead Typical applications: All process services, any gas & up to the highest pressures &

49 Reciprocating Compressors - Principle of Operation Double Acting Crosshead Typical applications: All process services, any gas & up to the highest pressures & power Single Acting - Trunk Piston Typical Applications: Small size standard compressors for air and non-dangerous gases Courtesy of Nuovo Pignone Spa, Italy 49

Reciprocating Compressors - Compression Cycle 1 5 4 Pressure p 0 2 3

50 Reciprocating Compressors - Compression Cycle Pressure p Suction Volume Courtesy of Nuovo Pignone Spa, Italy Discharge 50

51 Reciprocating Compressors - Main Components 51

52 Reciprocating Compressors 52

53 Rotary Screw Compressor Left rotor turns clockwise, right rotor counterclockwise. Gas becomes trapped in the central cavity The Process Technology Handbook, Charles E. Thomas, UHAI Publishing, Berne, NY, Courtesy of Ariel Corp 53

54 Rotary Screw Compressors Oil-free First used in steel mills because handles dirty gases Max pressure ratio of 8:1 if liquid injected with gas High availability (> 99%) Leads to low maintenance cost Volumetric efficiency of ~100% Small footprint (~ ¼ of recip) Relatively quiet and vibration-free Relatively low efficiency 70 85% adiabatic efficiencies Relatively low throughput and discharge pressure Oil-injected Higher throughput and discharge pressures Has two exit ports Axial, like oil-free Radial, which permits 70 to 90% turndown without significant efficiency decrease Pressure ratios to 23:1 Tight tolerances can limit quick restarts Requires oil system to filter & cool oil to 140 o F Oil removal from gas Oil compatibility is critical Widely used in propane refrigeration systems, low pressure systems, e.g., vapor recovery, instrument air 54

55 Dynamic Compressors Centrifugal High volumes, high discharge pressures Axial Very high volumes, low discharge pressures Use together in gas processing Centrifugal for compressing natural gas Axial for compressing air for gas turbine driving centrifugal compressor 55

56 Centrifugal compressors Single stage (diffuser) Multi-stage Bett,K.E., et al Thermodynamics for Chemical Engineers Page

Centrifigual Compressor Siemens https://www.

57 Centrifigual Compressor Siemens

58 Centrifugal Compressor Courtesy of Nuovo Pignone Spa, Italy 58

59 Centrifugal Compressors vs. Reciprocating Compressors Centrifugal Constant head, variable volume Ideal for variable flow - MW affects capacity ++ Availability > 99% + Smaller footprint - η IS = 70 75% CO & NOx emissions low - Surge control required ++ Lower CAPEX and maint. (maint cost ~1/4 of recip) Reciprocating Constant volume, variable pressure Ideal for constant flow + MW makes no difference - Availability 90 to 95% - Larger footprint + η IS = 75 92% Catalytic converters needed ++ No surge problems ++ Fast startup & shutdown 59

60 Gas Turbine Centrifugal Compressor Axial Compressor Centrifugal Compressor Exhaust Gas Low Pressure Gas Air Fuel Gas High Pressure Gas Combustion Turbine 60

61 Industrial Gas Turbines Ref: GPSA Data Book, 13 th ed. 61

62 What is heat rate? Heat rate is the amount of fuel gas needed (expressed heating value) to produce a given amount of power Normally LHV, but you need to make sure of the basis Essentially the reciprocal of the thermal efficiency Thermal efficiency 2544 BtuLHV Heat rate, hp hr Example: Dresser-Rand VECTRA 30G heat rate is 6816 Btu/hp hr 2544 Thermal efficiency Includes effects of adiabatic & mechanical efficiencies 62

63 Gas Turbine Courtesy of Nuovo Pignone Spa, Italy 63

64 Gas Turbine Engine Gas Turbine Engine From: F.W.Schmuidt, R.E. Henderson, and C.H. Wolgemuth, Introduction to Thermal Sciences, second edition Wiley, 1993 Fuel P2 Combustion chamber P3 P1 shaft shaft Compressor Turbine Load Atmospheric air P4 Combustion products Assumptions To apply basic thermodynamics to the process above, it is necessary to make a number of assumptions, some rather extreme. 1) All gases are ideal, and compression processes are reversible and adiabatic (isentropic) 2) the combustion process is constant pressure, resulting only in a change of temperature 3) negligible potential and kinetic energy changes in overall process 4) Values of C p are constant 64

65 Gas Turbine Engine P 2 = P 3 Temperature T P atm = P 1 = P 4 1 Entropy S w S = - h = -C P T (9.1 and 1.18) Note the equations apply to both the compressor and the turbine,since thermodynamically the turbine is a compressor running backwards Neglecting the differences in mass flow rates between the compressor and the turbine, the net work is: w net = w t w c = C P (T 3 T 4 ) (T 2 -T 1 ) Since (T 3 T 4 ) > (T 2 T 1 ) (see T S diagram) Since w net is positive work flows to the load 65

66 GT - Principle of Operation Theoretical Cycle Fuel Gas Combustion Chamber Exhaust Gas (~950 F) Temperature F 3 Real Cycle 1 Air ~ F 2 Axial Compressor 3 ~ F 4 Centrifugal Compressor H.P./L.P. Turbine Simple Cycle Gas Turbine A B Entropy Ideal Cycle Efficiency T T P id T3 T2 P2 1/ 66

67 Modeling Gas Turbine with Aspen Plus Basics to tune model Combine heat rate & power output to determine the fuel required Determine the air rate from the exhaust rate Adjust adiabatic efficiencies to match the exhaust temperature Adjust the mechanical efficiencies to match the power output 67

68 Turboexpanders GPSA Engineering Data Book, 14 th ed.

69 Summary

70 Summary Work expression for pump developed assuming density is not a function of pressure Work of compression is much greater than that for pumping a great portion of the energy goes to increase the temperature of the compressed gas Need to limit the compression ratio on a gas Interstage cooling will result in decreased compression power required Practical outlet temperature limitation usually means that the maximum compression ratio is about 3 There are thermodynamic/adiabatic & mechanical efficiencies Heat lost to the universe that does affect the pressure or temperature of the fluid is the mechanical efficiency 70

71 Supplemental Slides

72 Reciprocating Compressors 72

73 Propane Refrigeration Compressors 73

74 Propane Compressors with Air-cooled Heat Exchangers 74

75 Reciprocating Compressor at Gas Well Courtesy of Nuovo Pignone Spa, Italy 75

76 2 stage 2,000 HP Reciprocating Compressor Courtesy of Ariel Corp 76

77 Oil-Injected Rotary Screw Compressor Courtesy of Ariel Corp 77

78 Two-stage screw compressor Courtesy of MYCOM / Mayekawa Mfg 78

79 Centrifugal Compressors Issues Surge Changes in the suction or outlet pressures can cause backflow; this can become cyclic as the compressor tries to adjust. The resulting pressure oscillations are called SURGE Surge Line Axial Centrifugal Reciprocating Stonewall Line Stonewall When gas flow reaches sonic velocity flow cannot be increased. 79

80 Air & Hot Gas Paths Gas Turbine has 3 main sections: A compressor that takes in clean outside air and then compresses it through a series of rotating and stationary compressor blades FRESH AIR EXHAUST COMPRESSION MECHANICAL ENERGY 80

81 Air & Hot Gas Paths Gas Turbine has 3 main sections: A combustion section where fuel is added to the pressurized air and ignited. The hot pressurized combustion gas expands and moves at high velocity into the turbine section. FRESH AIR COMPRESSION COMBUSTION EXHAUST MECHANICAL ENERGY 81

Air & Hot Gas Paths Gas Turbine has 3 main sections: A turbine that converts the energy from the hot/high velocity gas flowing from the combustion chamber into

82 Air & Hot Gas Paths Gas Turbine has 3 main sections: A turbine that converts the energy from the hot/high velocity gas flowing from the combustion chamber into useful rotational power through expansion over a series of turbine rotor blades FRESH AIR COMBUSTION EXPANSION COMPRESSION TURBINE EXHAUST MECHANICAL ENERGY 82

Introduction to Chemical Engineering Thermodynamics. Chapter 7. KFUPM Housam Binous CHE 303

Introduction to Chemical Engineering Thermodynamics Chapter 7 1 Thermodynamics of flow is based on mass, energy and entropy balances Fluid mechanics encompasses the above balances and conservation of momentum