Rotating Equipment: Pumps, Compressors, & Turbines/Expanders Chapters 2 & 9 Topics Fundamentals ▪ Starting relationships Equipment ▪ Pumps • Thermodynamic relationships • Centrifugal pumps • Bernoulli’s equation • Reciprocating pumps ▪ Simplifications • Pumps – constant density compression • Compressors – reversible ideal gas compression ▪ Use of PH & TS diagrams ▪ Multistaging Efficiencies ▪ Adiabatic/isentropic vs. mechanical ▪ Polytropic Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) • 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 Fundamentals Updated: January 4, 2019 Copyright © 2017 John Jechura (jjechura@mines.edu) Review of Thermodynamic Principals 1st Law of Thermodynamics – Energy is conserved ▪ (Change in system’s energy) = (Rate of heat added) – (Rate of work performed) Ê = Q − W ▪ 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 u g Eˆ = Uˆ + + h 2gc gc o Enthalpy, H = U+PV, convenient for systems at constant pressure & flowing systems 2 u g Eˆ = Hˆ + + h 2gc gc Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 4 Review of Thermodynamic Principals 2nd 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 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 5 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 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 6 1st Law for steady state flow Equation 1.19a (ΔH ΔU for flowing systems) 2 u g Hˆ + + z = Q − W 2gc gc For adiabatic, steady-state, ideal (reversible) flow (using WS as positive value) 2 u g Wˆ s = Hˆ + + z 2gc gc P2 2 u g ˆ = V dP + + z 2 g gc c P1 P2 P2 dP Wˆ s Vˆ dP = P1 P1 ▪ The work required is inversely proportional to the mass density Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 7 Thermodynamics of Compression Work depends on path – commonly assume adiabatic or polytropic compression Calculations done with: ▪ PH diagram for ΔH P2 Ws = VdP = H P1 ▪ 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) P2 P dP 1 2 P −P Ws = = dP = 2 1 P1 P1 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 8 Liquid vs. Vapor/Gas Compression Can compress liquids with little temperature change ΔH for gas compression much larger than for liquid pumping GPSA Data Book, 13th ed. Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 9 Mechanical Energy Balance Differential form of Bernoulli’s equation for fluid flow (energy per unit mass) d ( u2 ) 2 + g dz + ( ) dP + d ( wˆ s ) + g d hˆf = 0 ▪ 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 ( u2 ) 2 P + g z + + wˆ s + g hˆf = 0 If density is not constant then you need a pathway for the pressure-density relationship – compressors ( u2 ) 2 dP + g z + + wˆ s + g hˆf = 0 P1 P2 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 10 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 ( u2 ) P Whhp = m ( −wˆ s ) = ( V ) + g z + + g hˆf 2 ( ) 1 = V ( P ) + ( V ) ( g z ) + ( V ) g hˆf + ( V ) ( u2 ) 2 ▪ Just across the pump, in terms of pressure differential or head: Whhp = V ( P ) or Whhp = V gH Brake horsepower – power delivered to the pump itself Wbhp = Whhp pump Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 11 Pump equations for specific U.S. customary units U.S. customary units usually used are gpm, psi, and hp in3 231 gal gal lbf Whhp hp 2 ft lb f / sec min in sec in 60 12 550 min ft hp 1 gal lbf = 2 1714 min in Also use the head equation usually using gpm, ft, specific gravity, and hp lbm ft 8.33719 32.174 2 gal gal sec Whhp hp ft o ft lb f / sec 32.174 lbm ft sec min 60 550 min lb f sec2 hp 1 gal = ft o 39 58 min Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 12 Static Head Terms Fundamentals of Natural Gas Processing, 2nd ed. Kidnay, Parrish, & McCartney Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 13 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 0.485 @ pumping temperature (100oF) ▪ 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, 13th ed. Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 14 Pump Example Pressure drop from Reflux Drum to Pump inlet: P = − g z + ( P )piping gc ( 0.485 )( 62.3665 ) ( −20 ) =− + −0.5 − 0.2 144 = 3.5 psi Pinlet = 203.5 psia Pressure drop from Pump outlet to Depropanizer: P = − g z + ( P )piping gc ( 0.485 )( 62.3665 ) ( 74 ) =− − 3.0 + 2.0 + 1.2 + 13.0 + 1.0 + 9.0 144 = −44.7 psi Poutlet = 264.7 psia Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 15 Pump Example Pump pressure differential: ( P )pump = Poutlet − Pinlet = 264.7 − 203.5 = 61.2 psi Pump differential head: gc ( P )pump gc ( P )pump hpump = = g g ( owater ) =− (144 ) ( 61.2 ) = 291 ft ( 0.485)( 62.3665) Hydraulic power: Whhp = ( 360 gpm)( 61.2 psi) = 12.85 hp 1714 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) OR Whhp = ( 360 gpm )( 0.485 )(291 ft ) = 12.84 hp 3958 16 Gas Compression: PH Diagrams Ref: GPSA Data Book, 13th ed. Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 17 TS Diagram Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 18 Thermodynamics of Ideal Gas Compression Choices of path for calculating work: ▪ Isothermal (ΔT = 0) P2 dP Ws = VdP = RT = RT ln P P1 P1 P1 P2 P2 • 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 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 19 Thermodynamics of Compression Ideal gas isentropic (PV = constant) where = CP/CV ▪ Molar basis ( −1)/ P2 Ws = ( RT1 ) − 1 − 1 P1 ▪ Mass basis P ( −1)/ W RT 2 Wˆ s = s = 1 − 1 M M − 1 P1 Can also determine discharge temperature P T2 = T1 2 P1 ( −1)/ Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 20 Thermodynamics of Compression Calculation of for gas mixture xC = x C i p ,i i V ,i xC = x C −R i i p ,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 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 21 Example Calculation: Ideal Gas Laws For methane: ▪ = 1.3 ▪ M = 16 ▪ T1 = 120oF = 580oR ▪ P1 = 300 psia ▪ P2 = 900 psia ▪ R = 1.986 Btu/lb.mol oR ( −1)/ (1.3)(1.986 )( 580 ) 900 (1.3−1)/1.3 RT1 P2 Ws = − 1 = − 1 = 90 Btu/lb M ( − 1 ) P1 16 1.3 − 1 300 ( )( ) 900 T2 = ( 580 ) 300 (1.3−1)/1.3 = 747°R 287°F Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 22 525 BTU/lb 440 BTU/lb Enthalpy Changes: 𝑊 = ∆𝐻 = 525 − 440 = 85 Outlet temperature: 280°F Compress methane from 300 psia & 120°F to 900 psia 𝐵𝑇𝑈 𝑙𝑏 Example Calculation: Using a Simulator Work Btu/lb Outlet oF HYSYS Peng-Robinson 86.58 281.8 HYSYS Peng-Robinson & Lee-Kesler 87.34 280.5 HYSYS SRK 87.71 281.2 HYSYS BWRS 87.04 281.1 HYSYS Lee-Kesler-Plocker 87.40 280.6 Aspen Plus PENG-ROB 86.61 282.4 Aspen Plus SRK 87.82 281.8 Aspen Plus BWRS 87.10 281.6 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 24 Multi-Stage Gas Compression If customer wants 1,000 psig (with 100 psig & 120oF inlet)… ▪ Then pressure ratio of (1015/115) = 8.8 ▪ Discharge temperature for this ratio is ~500oF For reciprocating compressors the GPSA Engineering Data Book recommends ▪ Pressure ratios of 3:1 to 5:1 AND … ▪ Maximum discharge temperature of 250 to 275oF for high pressure systems To obtain higher pressure ratios higher must use multistage compression with interstage cooling Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 25 Multistaging To minimize work need good interstage cooling and equal pressure ratios The number of stages is calculated using 1/ m P RP = 2 P1 m= ln( P2 / P1 ) ln(RP ) To go from 100 to 1000 psig with a single-stage pressure ratio of 3 takes 2 (1.98) stages & the stage exit temp ~183oF (starting @ 120oF) 1015 ln 115 ln( 8.8 ) m= = = 1.98 m = 2 ln( 3 ) ln( 3 ) P 1/m T2 = T1 2 P1 ( −1)/ 1015 1/2 = (120 + 460 ) 115 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) (1.3−1)/1.3 = ( 580 )2.97 0.2308 = 746°R 286°F 26 Multistaging Work for a single stage of compression P ( −1)/ (1.3)(1.986 )( 580 ) 1015 (1.3−1)/1.3 RT 1 2 Wˆ s = − 1 = − 1 = 204 Btu/lb M ( − 1 ) P1 16 )(1.3 − 1 ) 115 ( Work for two stages of compression (interstage cooling to 120oF) ▪ Intermediate pressure Pint = P2P1 = (1015)(115) = 341.7 psia ▪ Total work – 13% less work 1.3−1 /1.3 1015 (1.3−1)/1.3 1.3)(1.986 )( 580 ) 341.7 ( ) ( Wˆ s = − 1 + − 1 16 1.3 − 1 115 341.7 ( )( ) = 178 Btu/lb Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 27 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 IS = ( H )S=0 ( H ) fluid Wfluid = Total Energy To Device WS =0 IS ▪ Mechanical efficiency relates total work to device to the energy into the fluid mech = Wfluid Wtotal Wtotal = Wfluid Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) mech = WS =0 mechIS { Minimum Energy for Compression Total Energy Into Fluid Energy to Overcome Mechanical Inefficiencies – Goes Into Fluid & Increases Temperature Energy Lost To Environment 28 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 P ( T )S =0 = T1 2 P1 So: ( T )act = ( −1)/ ( T )S =0 IS T2,act = T1 + ( T )act P ( −1)/ − T1 = T1 2 − 1 P1 P2 P = T1 1 ( −1)/ −1 IS P ( −1)/ 2 −1 P = T1 1 + 1 IS Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 29 Example Calculation: 75% isentropic efficiency ΔS =0 Work Btu/lb ΔS =0 Outlet oF =0.75 Work Btu/lb =0.75 Outlet oF Ideal Gas Equations 90 287 120 343 PH diagram 85 280 113 325 HYSYS Peng-Robinson 86.58 281.8 115.4 325.2 HYSYS SRK 87.71 281.2 116.9 325.2 HYSYS BWRS 87.04 281.1 116.1 325.1 HYSYS Lee-Kesler-Plocker 87.40 280.6 116.5 324.8 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 30 Polytropic Compression & Efficiency Definition of polytropic compression (GPSA Data Book 14th 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. Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 31 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 P T2 = T1 2 P1 −1 = Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) ln(T2 / T1 ) 1 where 1− ln( P2 / P1 ) 32 Polytropic Efficiency Actual work is calculated from the polytropic expression divided by its efficiency ( −1) / RT P 1 1 2 Wˆact = = − 1 p p M − 1 P1 Wˆ p Note: Wˆact = Wˆ p Wˆ S =0 = p IS Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 33 Why Use Polytropic Equations? Polytropic equations give consistent P-T pathway between the initial & discharge conditions Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 34 Effect of Internal Pressure Drops Pressure drops at the inlet & outlet give an apparent inefficiency of compression ▪ Assume isenthalpic pressure drops before & after the actual compression Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 35 Effect of Internal Pressure Drops Pressure Reductions Before Compression psia After Compression psia Work Btu/lb Outlet °F Efficiency 0% 300 900 86.58 281.8 100% 1% 297 909 88.36 284.7 98% 5% 285 947 95.76 296.8 90% 10% 270 1000 105.7 313.0 82% 15% 255 1059 116.5 330.2 74% Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 36 Compression vs. Expansion Efficiency Work to compressor is greater than what is needed in the ideal case ▪ Work to the fluid IS = ( H )S=0 ( H ) fluid ▪ Work from the fluid Wfluid = WS =0 IS ▪ Total work to the device mech = Wfluid Wtotal Wtotal = Work from expander is less than what can be obtained in the ideal case IS = ( H ) fluid ( H )S =0 ▪ Total work from the device Wfluid mech W = S =0 mechIS Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) Wfluid = IS (WS =0 ) mech = Wtotal Wfluid Wtotal = mechWfluid = mechISWS =0 37 Equipment: Pumps, Compressors, Turbines/Expanders Updated: January 4, 2019 Copyright © 2017 John Jechura (jjechura@mines.edu) 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% Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 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 39 Pump Classifications Fundamentals of Natural Gas Processing, 2nd ed. Kidnay, Parrish, & McCartney Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 40 Centrifugal Pump Performance Curves Fundamentals of Natural Gas Processing, 2nd ed. Kidnay, Parrish, & McCartney Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 41 Compressor Types Positive displacement – compress by changing volume ▪ Reciprocating ▪ Rotary screw ▪ Diaphragm ▪ Rotary vane Dynamic – compress by converting kinetic energy into pressure ▪ Centrifugal ▪ Axial Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 42 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 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 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 43 Reciprocating Compressors - Principle of Operation Double Acting – Crosshead Single Acting - Trunk Piston Typical applications: ▪ All process services, any gas & up to the highest pressures & power Typical Applications: ▪ Small size standard compressors for air and non-dangerous gases Courtesy of Nuovo Pignone Spa, Italy Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 44 Reciprocating Compressors - Compression Cycle 5 4 Pressure 1 p0 3 2 Volume Suction 1 2 3 4 5 Discharge Courtesy of Nuovo Pignone Spa, Italy Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 45 Reciprocating Compressors - Main Components Pulsation Bottles Crankcase Cast Iron Crankshaft Counterweight Forged Steel for balancing Crosshead Cast Steel Ballast for balancing of inertia forces Slide Body Distance Pieces Pneumatic Valve Unloaders for capacity control Forged Cylinder Main Oil Pump Connecting Rod (die forged steel) Oil Wiper Packing Piston Rod Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) Cast Cylinder Rod Packing Piston Cylinder Valve 46 Reciprocating Compressors https://www.youtube.com/watch?v=E6_jw841vKE Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 47 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, 1997. Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) Courtesy of Ariel Corp 48 Rotary Screw Compressors Oil-free Oil-injected First used in steel mills because handles “dirty” gases Higher throughput and discharge pressures 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 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 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 140oF Oil removal from gas Oil compatibility is critical Widely used in propane refrigeration systems, low pressure systems, e.g., vapor recovery, instrument air 49 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 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 50 Centrifugal compressors Single stage (diffuser) Multi-stage Bett,K.E., et al Thermodynamics for Chemical Engineers Page 226 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 51 Centrifigual Compressor Siemens https://www.energy.siemens.com/br/en/compressionexpansion/product-lines/single-stage/stc-sof.htm Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) https://www.youtube.com/watch?v=s-bbAoxZmBg 52 Centrifugal Compressor Courtesy of Nuovo Pignone Spa, Italy Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 53 Centrifugal vs. Reciprocating Compressors Centrifugal Constant head, variable volume Ideal for variable flow - MW affects capacity ++ Availability > 99% + Smaller footprint - ηIS = 70 – 75% CO & NOx emissions low - Surge control required ++ Lower CAPEX and maint. (maint cost ~1/4 of recip) Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) Reciprocating Constant volume, variable pressure Ideal for constant flow + MW makes no difference - Availability 90 to 95% - Larger footprint + ηIS = 75 – 92% Catalytic converters needed ++ No surge problems ++ Fast startup & shutdown 54 Turbines & Turboexpanders Utilize pressure energy to… ▪ Reduce temperature of gas & (possibly) generate liquids ▪ Perform work & provide shaft power to coupled equipment Similar principles to a centrifugal compressor except in reverse Most common applications: ▪ Turboexpander: NGL recovery ▪ Gas turbine: power to drive pumps, compressors, generators, … Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 55 Turboexpander Cutaway https://www.turbomachinerymag.com/expander-compressors-an-introduction/ Video (LA Turbine. 2:54 minutes): https://www.youtube.com/watch?v=f5Gz_--_NBM Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 56 Turboexpanders GPSA Engineering Data Book, 14th ed. Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) Methane Expansion – Isentropic vs. Isenthalpic Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 58 Gas Turbine Engine https://aceclearwater.com/product/case-study-ge-power-ducts/ Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 59 Gas Turbine Coupled to Centrifugal Compressor Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 60 Industrial Gas Turbines Ref: GPSA Data Book, 13th ed. Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 61 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 Btu(LHV ) Heat rate, hp hr ▪ Example: Dresser-Rand VECTRA 30G heat rate is 6816 Btu/hp·hr Thermal efficiency = 2544 = 0.3732 6816 Includes effects of adiabatic & mechanical efficiencies Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 62 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 P1 Compressor Combustion chamber shaft P3 shaft Turbine P4 Atmospheric air Load 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 Cp are constant Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 63 Gas Turbine Engine P2 = P3 T Temperature Patm = P1 = P4 3 2 4 1 Entropy S wS = -∆h = -CP∆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: wnet = wt – wc = CP(T3 – T4) – (T2 -T1) Since (T3 – T4) > (T2 – T1) (see T – S diagram) Since wnet is positive work flows to the load Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 64 GT - Principle of Operation Theoretical Cycle Temperature °F Fuel Gas Combustion Chamber ~650 - 950°F 3 2 1 Air ~1800 2300°F 3 Exhaust Gas (~950°F) Real Cycle 4 4 2 Centrifugal Compressor Axial Compressor 1 H.P./L.P. Turbine Simple Cycle Gas Turbine A B Entropy Ideal Cycle Efficiency P T −T id = 1 − 4 1 = 1 − 1 T3 − T2 P2 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) ( −1)/ 65 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 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 66 Summary Updated: January 4, 2019 Copyright © 2017 John Jechura (jjechura@mines.edu) 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 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 68 Supplemental Slides Updated: January 4, 2019 Copyright © 2017 John Jechura (jjechura@mines.edu) Reciprocating Compressors Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 70 Propane Refrigeration Compressors Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 71 Propane Compressors with Air-cooled Heat Exchangers Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 72 Reciprocating Compressor at Gas Well Courtesy of Nuovo Pignone Spa, Italy Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 73 2 stage 2,000 HP Reciprocating Compressor Courtesy of Ariel Corp Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 74 Oil-Injected Rotary Screw Compressor Courtesy of Ariel Corp Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 75 Two-stage screw compressor Courtesy of MYCOM / Mayekawa Mfg Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 76 Centrifugal Compressors – Issues Surge • When gas flow reaches sonic Axial Centrifugal Stonewall Line Stonewall Surg e Lin e pressures can cause backflow; this can become cyclic as the compressor tries to adjust. The resulting pressure oscillations are called SURGE Pressure Head • Changes in the suction or outlet Reciprocating velocity flow cannot be increased. Inlet Volume Flow Rate Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 77 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 Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 78 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 EXHAUST COMBUSTION COMPRESSION MECHANICAL ENERGY Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 79 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 EXHAUST COMBUSTION EXPANSION COMPRESSION TURBINE MECHANICAL ENERGY Updated: January 4, 2019 Copyright © 2019 John Jechura (jjechura@mines.edu) 80