This paper discusses the cost optimal area allocation in heat exchanger networks

Atkins, Martin John

Morrison, Andrew S.

Neale, James R.

Walmsley, Michael R.W.

Walmsley, Timothy Gordon

English

Name not available

Cost Optimal Area Allocation in Heat Exchanger Networks

Research Commons@Waikato

Cost Optimal Area Allocation in Heat Exchanger NetworksT. Walmsley,M. Walmsley, A. Morrison, M. Atkins, & J. NealeUniversity of Waikato, NZ (2013)Overview• Context & Motive• Introduction• Cost Derivative Method• Application of Method• SummaryUniversity of Waikato, NZ 2New ZealandUniversity of Waikato, NZ 3University of WaikatoDairyCowsOverall Research Focus / GoalUniversity of Waikato, NZ 4Direct Heat IntegrationMilk Powder FoulingHeat Exchanger Design Heat Recovery Loop0%10%20%30%051015201990 2000 2010 2020Percentage of total exportsValue of exports ($ billions)YearPercentage of total exportsValue of exports ($ billions)NZ Dairy in ContextUniversity of Waikato, NZ 5$12 BillionMilk Powder >85%Percentage of total exportsValue of exports ($ billions)Total dairy exports (left)Milk powder exports (left)Dairy's share of NZ exports(right)FutureGrowth?Milk Spray DryingTref = 0oCStd milkCOW (1)Cond.Vap.COW (2)COW (3)HMER: Split milk & direct condenser integrationCIPTo drainH13853.954PinchStd milkCOWCond. vap.CIP64.3COWHHHHHHH59.348.563.4 58.1Exhaust airMilk conc.FB 1FB 3FB 2Dryer inlet air1520032454965 54557555 15ExhaustAirStd milkCOW (1)Cond.Vap.COW (2)COW (3)HCIPTo drainDryerInlet AirHH13853.954PinchStd milkCOWCond. vap.CIP64.3COWHHHHHHH59.343.563.4 57.6Exhaust airMilk conc.FB 1FB 3FB 2Dryer inlet air1520032454965 54557555 15FB 1,2,348.5Evaporator ZoneDryer ZoneCIPZoneEvaporatorZoneDryer ZoneCIPZoneAB42.848.518.548.518.562.527.562.527.521.642.862.527.562.527.5ExhaustAirDryerInlet AirH1515MER: Split milk & indirect condenser integration43.5Developed Networks Using ΔTcontIs there a better method to size HE’s?Walmsley et al. (2013) I proving E rgy R covery in Milk Powder Production through Soft Data Optimisation. App. Therm. Eng.Introduction• What is optimal area allocation in a HEN?• Can area be better allocated in HEN’s compared to the ΔTmin method?University of Waikato, NZ 7-ΔA +ΔA-ΔQ +ΔQ10 °C 60 °C70 °C20 °C10 °C 60 °C70 °C60 °CChallenges Facing Finding the Design “Optimum”• Fluid property difference, e.g. viscosity• Phase: latent vs senisable heat• Heat Exchanger type: shell & tube or plate• Flow arrangement: counter vs parallel flow• HT film coefficient variations• Construction material: carbon steel or stainless steel• Pressure limitations• Future utility price changesUniversity of Waikato, NZ 8A Brief Review:Minimising HEN Area Pre-SynthesisUniversity of Waikato, NZ 9Find min. area targetusing CC and LMTDSynthesisTargeting “Minimum” HEN Area approaches/constraints:• Minimum approach temperature(s) (ΔTmin or ΔTcont)• Minimum heat flux• Pressure drop feasibility• Number of exchanger shells and unitse.g. Pinch Design MethodA Brief Review:Minimising HEN Area During-SynthesisUniversity of Waikato, NZ 10Synthesis Computer Programming e.g. Transhipment models• Numerous studies in this spaceA Brief Review:Minimising HEN Area Post-SynthesisUniversity of Waikato, NZ 11Synthesis Min. Area• Very few non-programming based studies in this space• Ait-Ait & Wade (1980) derived the conditions for optimal area allocation in a multi-stage HEA1 A2 A3 A4HEN Structure Complete DesignComposite CurvesajC(i)H(i)j+dTa1-dQC(i)-dQH(i)+dQ1-dTj1a+dA1Hot streamCold stream-dTjn+dTam-dAC(i)-dAH(i)What is the Cost Optimum HE Size in a HEN?University of Waikato, NZ 12+ Δ Capital Cost on HE1- Σ Δ Hot/cold Utility Savings- Σ Δ Capital Savings UtilitiesΔ Total Cost    1)(1)()(111 dAdCCdAdQPdACCddATCd iutiutiutTCAopt 01dATCdACost Derivative MethodUniversity of Waikato, NZ 131 nn knAdAdCCkAFCC    1)(1)()(111 dAdCCdAdQPdACCddATCd iutiutiutCost Derivative MethodUniversity of Waikato, NZ 14    1)(1)()(111 dAdCCdAdQPdACCddATCd iutiutiutPut$/kW/yTsupplyChilledWaterLP SteamHot WaterCoolingTower WaterHP/MP SteamCost Derivative MethodUniversity of Waikato, NZ 15    1)(1)()(111 dAdCCdAdQPdACCddATCd iutiutiut111)(1)(dAdQdQdQdAdQ iutiut  NTUddTUUNTUCdTCddAdQ maxminmaxmin11 ε-NTU method definitionsAssume Cmin, ΔTs, and U are constant with area1)()(1dQdQ iutiut Define:Chain Rule:Where Θ is called the heat duty flow-on factorε-NTU Relationship for Counter-flowSlope = 1  tArrangemen*,,or      CNTUfNTUddDiminishingReturnsCounterflow HE’s   CNTUdd 11Cost Derivative MethodUniversity of Waikato, NZ 17    1)(1)()(111 dAdCCdAdQPdACCddATCd iutiutiut )()(1)(11)()(1)(iutiutiutiutiutiutdQdAdQdQdAdQdAdCCdAdCC1 nknAdAdCC NTUddTUdAdQ max11 )(11)( iutiutdQdQputCCdNTUdTUdAdQminmax when,1uutCCdNTUdCNTUTUdAdQminmax when,*Chain Rule:Cost Derivative Method• If d(TC)/dA = 0, then cost “optimum” sizing is achieved for one HE• Let’s look at the Utility-Capital Trade-offUniversity of Waikato, NZ 18    )()()(1)()(11max,111iutiutiutniutiutndAdQknAPTUknANTUdd    1)(1)()(111 dAdCCdAdQPdACCddATCd iutiutiutUtility-Capital Cost Trade-offUniversity of Waikato, NZ 19    )()()(1)()(11max,111iutiutiutniutiutndAdQknAPTUknANTUdd050010001500200025003000350040002000 2005 2010 2015 2020Cost indexCoalNGCapitalNZ Data )Capital(UtilityRatio Base)(IIkPiiutCost Derivative Method• If d(TC)/dA = 0 and all HE’s fulfil the criteria below, then cost “optimum” sizing is achieved.• Let’s look at the Heat Duty Flow-on FactorUniversity of Waikato, NZ 20    )()()(1)()(11max,111iutiutiutniutiutndAdQknAPTUknANTUddThe Heat Duty Flow on Effect in HENs+dA, +dQHeat Duty Flow-on: OriginUniversity of Waikato, NZ 22y nx+dQ1+dT’n,y-dT’n,xHot streamColdstream+dA1xxCdQdT 1,1' yyCdQdT 1,1' 1Heat Duty Flow-on Factor: PropagationUniversity of Waikato, NZ 23w nv-dQn-dTn,v-dT’n,wdTn,w=0-dT’n,vHot streamColdstream vnvnvnCCdTdT min,, 1' wnvnwnCCdTdTmin,,'Flow-on Effect on Downstream Exchanger “n”P UtUTu1Tp1+dTp1Utility streamProcessstreamTu2TptCpCu + dCuHeat Duty Flow-on Factor: TerminationUniversity of Waikato, NZ 24±dQutppCdQdT 1,1' Flow-on Effect on Downstream Utility UseHeat Duty Flow-on Factor: PathwaysUniversity of Waikato, NZ 25a 1 23Ci j+dA1+dQ1-dQ2-dQ3+dT2,a±dQc,j±dTc,j4b+dQ4-dT3,i+dT4,j-dT4,bHot streamsCold streamsExample: Gundersen (2000)University of Waikato, NZ 26Stream CodeTs(°C)Tt(°C)C (kW/°C)Q (kW)h (kW/m2 °C)φ($/y/kW)Reactor outlet H1 270 160 18 1980 0.5Product H2 220 60 22 3520 0.5Feed C1 50 210 20 3200 0.5Recycle C2 160 210 50 2500 0.5Steam HU 250 249 2.5 200Cooling water CU 15 20 1 20Stream data for a  simple distillation separation process*Data from A Process Integration Primer (2000)Application AlgorithmUniversity of Waikato, NZ 27StreamdataCostdataΔTcontPinchtargetsNetwork designusing ΔTcontHEselectionAdjustsoft data?YesNoRelaxnetwork?YesNoPinch Design MethodAdd UE’s to  allstreamsHEN design(CDM)Limiting Tt?Use dTC/dA < 0for streamCost Derivative MethodFind θ for RE’sto UE’sCalculatesolutionInputdTC/dA = 0Eliminatesmall UE(s)?Use dTC/dA > 0for streamNoNo YesYesHEN design(ΔTcont)Network structuresAction!Example: HEN from PDMUniversity of Waikato, NZ 28Qr = 5.0 MW for ΔTmin(opt) = 12.5 °CCan HE sizing be improved to achieve lower Total Annual Cost?H1H2C1C2754 10001044 2200702276226(a) PDMH1H2C1C21318(+33)662(-33)1150 184033 (-33)531(b) CDM698 (+33)H2H2H1C2C1C2A AB BC C DDStreamdataCostdataΔTcontPinchtargetsNetwork designusing ΔTcontHEselectionAdjustsoft data?YesNoRelaxnetwork?YesNoPinch Design MethodAdd UE’s to  allstreamsHEN design(CDM)Limiting Tt?Use dTC/dA < 0for streamCost Derivative MethodFind θ for RE’sto UE’sCalculatesolutionInputdTC/dA = 0Eliminatesmall UE(s)?Use dTC/dA > 0for streamNoNo YesYesHEN design(ΔTcont)Network structuresApplication AlgorithmUniversity of Waikato, NZ 29H1H2C1C2H2C2C1A BC DH1Example: Flow-on effects for AUniversity of Waikato, NZ 30Two HX’s in series1min,)( 1HBBHutACC 1)( 2 HutA1min,)(11HBBCutACC 0)( 2 CutAH1H2C1C2H2C2C1A BC DH1Example: Flow-on effects for BUniversity of Waikato, NZ 311)( 1 CutB0)( 2 CutB1)( 1 HutB0)( 2 HutBH1H2C1C2H2C2C1A BC DH1Example: Flow-on effects for CUniversity of Waikato, NZ 321min,1min,)(11CBBCDDHutCCCCC 2min,)(12HDDCutCCC 2min,)(12CAACutCCC 1min,1min,1min,1min,)(11HBBHAACBBCDDCutCCCCCCCCCH1H2C1C2H2C2C1A BC DH1Example: Flow-on effects for DUniversity of Waikato, NZ 331min,)(11CBBHutDCC 0)( 2 HutD1)( 2 CutD1min,)( 1HBBCutDCC StreamdataCostdataΔTcontPinchtargetsNetwork designusing ΔTcontHEselectionAdjustsoft data?YesNoRelaxnetwork?YesNoPinch Design MethodAdd UE’s to  allstreamsHEN design(CDM)Limiting Tt?Use dTC/dA < 0for streamCost Derivative MethodFind θ for RE’sto UE’sCalculatesolutionInputdTC/dA = 0Eliminatesmall UE(s)?Use dTC/dA > 0for streamNoNo YesYesHEN design(ΔTcont)Network structuresApplication AlgorithmUniversity of Waikato, NZ 34Excel ModelIterativelysolveModelling CDM in Excel• Set-up method in a Excel Spreadsheet• Located the cost optimal area allocationUniversity of Waikato, NZ 35Initial Comparison of CDM to PDMUniversity of Waikato, NZ 36H1H2C1C2754 10001044 2200702276226(a) PDMH1H2C1C21318 6621150 184033531(b) CDM698H2H2H1C2C1C2A AB BC C DDTC = $386 k /y TC = $363 k /yInitial Comparison of CDM to PDMUniversity of Waikato, NZ 37H1H2C1C2754 10001044 2200702276226(a) PDMH1H2C1C21318 6621150 184033531(b) CDM698H2H2H1C2C1C2A AB BC C DDTC = $386 k /y TC = $363 k /y12°CEMAT’s17°C8°C24°C47°C13°C13°C13°CHRAT’sH1H2C1C2754 10001044 2200702276226(a) PDMH1H2C1C21318 6621150 184033531(b) CDM698H2H2H1C2C1C2A AB BC C DDUtility Exchanger Reduction• Does this produce minimum total cost?University of Waikato, NZ 38+33 kW -33 kW+33 kWTCTarget dTC/dQut*Utility Exchanger ReductionUniversity of Waikato, NZ 39H1H2C1C21318 6621150 184033531(b) CDM698H2H1C2A BC DH1H2C1C21323 6571178 1845 498(c) CDM*698H1C2A BC D+5 +28-5 +5-33TC = $363 k /yNew Conditions for Heat Exchangers A & COptimalDesignTarget Temperature ConstraintsUniversity of Waikato, NZ 40H1H2C1C21318 6621150 184033531(b) CDM698H2H1C2A BC DH1H2C1C21323 6571178 1845 498(c) CDM*698H1C2A BC D+5 +28-5 +5-33TC = $363 k /y1 2TsTtA2,optA1,optTCTCA1A2,actYX X+1A2TCTarget dTC/dQut*Optimal DesignHE “A” HE “B”Optimise Duty/Area AllocationUniversity of Waikato, NZ 41H1H2C1C21318 6621150 184033531(b) CDM698H2H1C2A BC DH1H2C1C21323 6571178 1845 498(c) CDM*698H1C2A BC D+5 +28-5 +5-33TC = $358 k /yTC = $363 k /y+5 +28-5 +5-33Compared to Programming HEN Solutions (Escobar & Trierweiler, 2013)University of Waikato, NZ 42Super structureHyper structure SynHeat ModelTC = $376 k /yTC = $361 k /y TC = $367 k /yH1H2C1C21318 6621150 184033531(b) CDM698H2H1C2A BC DH1H2C1C21323 6571178 1845 498(c) CDM*698H1C2A BC D+5 +28-5 +5-33CDMTC = $358 k /ySummary• Optimising area/duty allocation is valuable and can give 5-10% improvement beyond Pinch• The new method accounts for different phases, HE types & arrangement, temp profiles, etc.• In the example, the new method:– Saved 7% of total cost compared to the PDM– Similar total cost to the Hyper-structure network solution, but required no splits compared to 4 splitsUniversity of Waikato, NZ 43Future Work• Understand how the cost derivative could inform synthesis • Application to dairy and indirect heat exchange systems• Inclusion of film coefficient correlations assuming some HE selection• Application to retro-fit analysis and design University of Waikato, NZ 44Acknowledgements• Todd Energy Foundation • Claude McCarthy Trust• School of Engineering, University of Waikato• Energy Research Centre, University of WaikatoUniversity of Waikato, NZ 45

Cost Optimal Area Allocation in Heat Exchanger Networks

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