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{"sheet":"Introduction","index":0,"n_rows":30,"n_cols":3,"rows_kept":30,"cut":false,"hidden":false,"merged":[]}
["FROM:","Mark Biegert"]
["SUBJECT:","Introduction"]
["DATE:","2016-10-26"]
[]
[]
["Abstract"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Index"]
[null,"Heat Recovery Worksheet","This sheet allows you to select from four scenarios that will illustrate the effect of insulation and ventilation."]
[null,"Scenario List","This sheet contains my list of scenarios"]
[null,"Cross Check","This sheet contains my check computations to verify that my Excel formulas closely match web sources for"]
[null,null,"critical parameters like density and specific humidity."]
[]
["References"]
[null,"These links provided tools I used to cross-check my functions."]
[null,"Link","Psychometric calculator used for cross-check"]
[null,"Link","Second psychometric calculator used for cross-check"]
[null,"Link","Good article on heat recovery ventilators and a worked example "]
[null,"Link","Excellent forum post on modeling heat recovery ventilators"]
[null,"Link","Earlier blog post of mine on a related topic"]

{"sheet":"Heat_Recovery","index":1,"n_rows":114,"n_cols":9,"rows_kept":114,"cut":false,"hidden":false,"merged":[]}
["FROM:","Mark Biegert"]
["SUBJECT:","Garage Insulation Option Evaluation"]
["DATE:","2016-10-26"]
[null,null,"↓"]
["Constants"]
[]
[null,"Constant","Symbol ","Value ","Unit"]
[null,"Universal Gas Constant","R_d",8.3144720000000003,"J/mol K"]
[null,"Molar Mass of Air","MW_air",28.9664,"gm/mol"]
[null,"Molar Mass of H2O","MW_H2O",18.015280000000001,"gm/mol"]
[null,"Air Pressure","p_Air",1,"atm"]
[null,"Epsilon","eps",{"$f":"MW_H2O/MW_air","v":0.62193714096332309},"unitless"]
[]
["Simulation Parameters"]
[]
[null,"Parameters","Symbol","Value","Unit"]
[null,"Room Temperature","T_R",65,"°F"]
[null,"Outside Temperature","T_O",10,"°F"]
[null,"Room Humidity","RH_R",0.3,"unitless"]
[null,"Outside Humidity","RH_O",0.1,"unitless"]
[null,"Recovery Efficiency","e_Rec",0,"unitless"]
[null,"Heating Efficiency","e_Heat",0.8,"unitless"]
[null,"Air Chg. Rate @ 50Pa","ACH50",10,"per hour"]
[null,"House Area","A_House",2500,"ft2"]
[null,"Ceiling Height","h_ceiling",8.2285699999999995,"ft"]
[null,"Natural Gas Cost","k_Rate",1.5,"per therm"]
[null,"Fan Flow Rate","F_fan",100,"cfm"]
[null,"Vent. Air Chg. Rate","ACH_v",0.35,"per hour"]
[]
["Air Characteristics"]
[]
[null,"Parameter","House","Outside","Units"]
[null,"Dry Air Density",{"$f":"CONVERT(p_Air,\"atm\",\"Pa\")*MW_air/(R_d*((T_R-32)*5/9+273.15))*0.001","v":1.2110518391318321},{"$f":"CONVERT(p_Air,\"atm\",\"Pa\")*MW_air/(R_d*((T_O-32)*5/9+273.15))*0.001","v":1.3528702459967599},"gm/cm3"]
[null,"Sat Vapor Pressure",{"$f":"6.1094*EXP(17.625*CONVERT(T_R,\"F\",\"C\")/(243.04+CONVERT(T_R,\"F\",\"C\")))*100","v":2103.2882565532968},{"$f":"6.1094*EXP(17.625*CONVERT(T_O,\"F\",\"C\")/(243.04+CONVERT(T_O,\"F\",\"C\")))*100","v":240.26028729248935},"Pa"]
[null,"Moist Air Density",{"$f":"C33*(1-0.378*RH_R*C34/CONVERT(p_Air,\"atm\",\"Pa\"))","v":1.2082010967481749},{"$f":"D33*(1-0.378*RH_O*D34/CONVERT(p_Air,\"atm\",\"Pa\"))","v":1.3527489871803555},"gm/cm3"]
[null,"Dew Temperature",{"$f":"-(5354475*(T_R-32)*5/9+73835552*LN(RH_R)+303800*(T_R-32)*5/9*LN(RH_R))/\n  (303800*LN(RH_R)+1250*(T_R-32)*5/9*LN(RH_R)-5354475)","v":0.4460204762527179},{"$f":"-(5354475*(T_O-32)*5/9+73835552*LN(RH_O)+303800*(T_O-32)*5/9*LN(RH_O))/\n  (303800*LN(RH_O)+1250*(T_O-32)*5/9*LN(RH_O)-5354475)","v":-37.699481994834031},"°C"]
[null,"Vapor Pressure @ Dew",{"$f":"6.1094*EXP(17.625*C36/(243.04+C36))*100","v":630.98647696598891},{"$f":"6.1094*EXP(17.625*D36/(243.04+D36))*100","v":24.026028729248932},"Pa"]
[null,"Specific Humidity",{"$f":"eps*C37/(CONVERT(p_Air,\"atm\",\"Pa\")-(1-eps)*C37)","v":3.882161608960091E-3},{"$f":"eps*D37/(CONVERT(p_Air,\"atm\",\"Pa\")-(1-eps)*D37)","v":1.4748600329068706E-4},"unitless"]
[null,"Moist Air Enthalpy",{"$f":"1.006*(T_R-32)*5/9+C38*(2501+1.755*(T_R-32)*5/9)","v":28.277528067110815},{"$f":"1.006*(T_O-32)*5/9+D38*(2501+1.755*(T_O-32)*5/9)","v":-11.929856636096135},"kJ/kg"]
[]
["House Parameters"]
[]
[null,"Parameter","Symbol","Value","Unit"]
[null,"House Volume","V_house",{"$f":"A_House*D25","v":20571.424999999999},"ft3"]
[]
["Air Flow Rates"]
[]
[null,"Ventilation Parameter","Value","Unit"]
[null,"Daily On-Time",1,"hour"]
[null,"Fan Air Changes/Hour",{"$f":"60*F_fan*(C49/24)/V_house","v":1.2152779887635398E-2},"per hour"]
[null,"Nat. Air Changes/Hour",{"$f":"ACH50_/20","v":0.5},"per hour"]
[null,"Vent. Air Chg./Hour",{"$f":"ACH_v","v":0.35},"per hour"]
[null,"Act. Air Chg./Hour",{"$f":"C50+C51+C52*(1-e_Rec)","v":0.86215277988763539},"per hour"]
[]
["Heat Losses"]
[null,"Wall R-value",18,"ft2*Δ°F*hr/BTU"]
[null,"Ceiling R-value",38,"ft2*Δ°F*hr/BTU"]
[]
[null,"Outside Facing Surfaces","Areas","R Values","Heat Flow\n(BTU/hour)"]
[null,"Wall 1",{"$f":"10*60","v":600},{"$f":"Wall_R_value","v":18},{"$f":"(C60-C65)/D60*(T_R-T_O)","v":1805.8333333333335}]
[null,"Wall 2",{"$f":"10*60","v":600},{"$f":"Wall_R_value","v":18},1778.3333333333335]
[null,"Wall 3",{"$f":"10*30","v":300},{"$f":"Wall_R_value","v":18},867.77777777777783]
[null,"Wall 4",{"$f":"10*30","v":300},{"$f":"Wall_R_value","v":18},889.16666666666674]
[null,"Ceiling",{"$f":"30*60","v":1800},{"$f":"Ceiling_R_value","v":38},2605.2631578947371]
[null,"Wall 1 Windows",{"$f":"3*3","v":9},2.8,176.78571428571431]
[null,"Wall 2 Windows",{"$f":"6*3","v":18},2.8,{"$f":"(C66-C71)/D66*(T_R-T_O)","v":353.57142857142861}]
[null,"Wall 3 Windows",{"$f":"4*4","v":16},2.8,{"$f":"(C67-C72)/D67*(T_R-T_O)","v":314.28571428571428}]
[null,"Wall 4 Windows",{"$f":"3*3","v":9},2.8,{"$f":"(C68-C73)/D68*(T_R-T_O)","v":176.78571428571431}]
[null,"Ceiling Windows",0,2.8,{"$f":"(C69-C74)/D69*(T_R-T_O)","v":0}]
[null,"Ventilation Heat Losses",null,null,{"$f":"C53*V_house*(C39-D39)*D35*0.06243","v":60223.360697415636}]
[null,null,null,null,{"$f":"SUM(Table18[Heat Flow\n(BTU/hour)])","v":69191.16353785005},"BTU/hr lost"]
[]
["Heat Replacement Cost"]
[]
[null,"Monthly Heat Loss",{"$f":"E71*365/12*24","v":50509549.382630534},"BTU"]
[null,"Replacement Heat",{"$f":"C75/e_Heat","v":63136936.728288166},"BTU"]
[null,"Replacement Cost",{"$f":"C76*k_Rate/10^5","v":947.0540509243225}]
[]
["Graphical View","Select Building Type→","Leaky Building, No Ventilator"]
[]
["Jan Cost","Wall R Value "]
[{"$f":"C77","v":947.0540509243225},8,12,18,24,32,40,50]
[18,1080.7773239506382,1024.3163864506382,986.67576145063845,967.85544895063845,953.74021457563845,945.27107395063842,938.4957614506385]
[28,1054.667874545876,998.20693704587609,960.56631204587654,941.7459995458762,927.6307651708762,919.16162454587618,912.38631204587625]
[38,1042.3002406173048,985.83930311730489,948.19867811730523,929.37836561730501,915.26313124230501,906.79399061730498,900.01867811730506,"Blue box indicates my selection"]
[48,1035.0857874923047,978.62484999230469,940.98422499230514,922.16391249230514,908.04867811730514,899.57953749230523,892.80422499230508]
[58,1030.3590768242016,973.89813932420168,936.25751432420168,917.43720182420168,903.32196744920168,894.85282682420166,888.07751432420162]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Title","Maximum Monthly Heating Bill Versus Ceiling And Wall Insulation"]
["X Axis","Wall R Value"]
["Y Axis","Monthly Bill ($)"]
[null,{"$f":"\"ACH50 = \"&ACH50_&\" per hour\"&CHAR(10)&\"Recovery Efficiency = \"&e_Rec*100&\"%\"","v":"ACH50 = 10 per hour\nRecovery Efficiency = 0%"}]
[null,{"$f":"C79","v":"Leaky Building, No Ventilator"}]

{"sheet":"ScenarioList","index":2,"n_rows":9,"n_cols":2,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
["FROM:","Mark Biegert"]
["SUBJECT:","Scenario List"]
["DATE:","2016-10-26"]
[]
[null,"Scenarios"]
[null,"Leaky Building, No Ventilator"]
[null,"Medium Tight Building, No Ventilator"]
[null,"Tight Building, Ventilator  with No Heat Recovery"]
[null,"Tight Building, Ventilator  with Heat Recovery"]

{"sheet":"Cross_Check","index":3,"n_rows":73,"n_cols":14,"rows_kept":73,"cut":false,"hidden":false,"merged":[]}
["FROM:","Mark Biegert"]
["SUBJECT:","Verify Calculation of Key Parameters"]
["DATE:","2016-10-26"]
[]
[]
["Constants"]
[]
[null,"Constant","Symbol ","Value ","Unit"]
[null,"Universal Gas Constant","R_d",8.3144720000000003,"J/mol K"]
[null,"Molar Mass of Air","MW_air",28.9664,"gm/mol"]
[null,"Molar Mass of H2O","MW_H2O",18.015280000000001,"gm/mol"]
[null,"Air Pressure","p_Air",{"$f":"OFFSET(A49,B45,0)","v":1},"atm"]
[null,"Epsilon","eps",{"$f":"MW_H2O/MW_air","v":0.62193714096332309},"unitless"]
[]
["Simulation Parameters"]
[]
[null,"Parameters","Symbol","Value","Unit"]
[null,"Room Temperature","T_R",{"$f":"OFFSET(A49,B45,2)","v":53},"°F"]
[null,"Outside Temperature","T_O",10,"°F"]
[null,"Room Humidity","RH_R",{"$f":"OFFSET(A49,B45,1)","v":0.49},"unitless"]
[null,"Outside Humidity","RH_O",0.1,"unitless"]
[null,"Recovery Efficiency","e_Rec",0.7,"unitless"]
[null,"Heating Efficiency","e_Heat",0.8,"unitless"]
[null,"Air Chg. Rate @ 50Pa","ACH50",1,"per hour"]
[null,"House Area","A_House",2500,"ft2"]
[null,"Ceiling Height","h_ceiling",8.2285699999999995,"ft"]
[null,"Natural Gas Cost","k_Rate",1.5,"per therm"]
[null,"Fan Flow Rate","F_fan",100,"cfm"]
[null,"Vent. Air Chg. Rate","ACH_v",0.35,"per hour"]
[]
["Air Characteristics"]
[]
[null,"Parameter","House","Outside","Units"]
[null,"Dry Air Density",{"$f":"CONVERT(p_Air,\"atm\",\"Pa\")*MW_air/(R_d*((T_R-32)*5/9+273.15))*0.001","v":1.2393987719923112},{"$f":"CONVERT(p_Air,\"atm\",\"Pa\")*MW_air/(R_d*((T_O-32)*5/9+273.15))*0.001","v":1.3528702459967599},"gm/cm3"]
[null,"Sat Vapor Pressure",{"$f":"6.1094*EXP(17.625*CONVERT(T_R,\"F\",\"C\")/(243.04+CONVERT(T_R,\"F\",\"C\")))*100","v":1369.6355532555099},{"$f":"6.1094*EXP(17.625*CONVERT(T_O,\"F\",\"C\")/(243.04+CONVERT(T_O,\"F\",\"C\")))*100","v":240.26028729248935},"Pa"]
[null,"Vapor Pressure @ Dew",{"$f":"6.1094*EXP(17.625*C38/(243.04+C38))*100","v":671.12142109519982},{"$f":"6.1094*EXP(17.625*D38/(243.04+D38))*100","v":24.026028729248932},"Pa"]
[null,"Moist Air Density",{"$f":"C34*(1-0.378*RH_R*C35/CONVERT(p_Air,\"atm\",\"Pa\"))","v":1.2362957321637233},{"$f":"D34*(1-0.378*RH_O*D35/CONVERT(p_Air,\"atm\",\"Pa\"))","v":1.3527489871803555},"gm/cm3"]
[null,"Dew Point Temperature",{"$f":"-(5354475*(T_R-32)*5/9+73835552*LN(RH_R)+303800*(T_R-32)*5/9*LN(RH_R))/\n  (303800*LN(RH_R)+1250*(T_R-32)*5/9*LN(RH_R)-5354475)","v":1.3024850686967713},{"$f":"-(5354475*(T_O-32)*5/9+73835552*LN(RH_O)+303800*(T_O-32)*5/9*LN(RH_O))/\n  (303800*LN(RH_O)+1250*(T_O-32)*5/9*LN(RH_O)-5354475)","v":-37.699481994834031},"°C"]
[null,"Specific Humidity",{"$f":"eps*C36/(CONVERT(p_Air,\"atm\",\"Pa\")-(1-eps)*C36)","v":4.1297128422351313E-3},{"$f":"eps*D36/(CONVERT(p_Air,\"atm\",\"Pa\")-(1-eps)*D36)","v":1.4748600329068706E-4},"unitless"]
[null,"Moist Air Enthalpy",{"$f":"1.006*(T_R-32)*5/9+C39*(2501+1.755*(T_R-32)*5/9)","v":22.149634355541494},{"$f":"1.006*(T_O-32)*5/9+D39*(2501+1.755*(T_O-32)*5/9)","v":-11.929856636096135},"kJ/kg"]
[]
[null,null,{"$f":"OFFSET(C37,B46,0)","v":1.2362957321637233}]
["Test Cases"]
[]
["Parameter Select",0]
["Output Select",0,null,null,null,"My Values",null,null,null,null,"Web Calculator Values"]
[null,null,null,null,null,"Moist Density","Dewpoint","Humidity Ratio","Enthalpy",null,"Moist Density","Dewpoint","Humi.Ratio","Enthalpy"]
["Pressure \n(atm)","Rel. Humidity\n(%)","Temperature\n(°F)","Temperature\n(°C)",{"$f":"C42","v":1.2362957321637233},0,1,2,3]
[1,0.49,53,{"$f":"CONVERT(C49,\"F\",\"C\")","v":11.666666666666666},0,1.2362957321637233,1.3024850686967713,4.1297128422351313E-3,22.149634355541494,null,1.24,1.31,4.1999999999999997E-3,22.22]
[1,0.22,49,{"$f":"CONVERT(C50,\"F\",\"C\")","v":9.4444444444444446},1,1.247933998174374,-11.242616227158415,1.5965949500135045E-3,13.520658642391361,null,1.25,-9.99,1.6000000000000001E-3,13.53]
[1,0.26,51,10.555555555555555,2,1.2427172431738822,-8.1747499366012111,2.0330281883945939E-3,15.741154235253779,null,1.24,-7.26,2E-3,15.75]
[1,0.41000000000000003,90,32.222222222222221,3,1.147468726284834,17.305969535168007,1.219125507201624E-2,63.595299964990694,null,1.1499999999999999,17.32,1.24E-2,64.05]
[1,0.57000000000000006,80,26.666666666666664,4,1.1686534714500445,17.44733141910806,1.2301415592907119E-2,58.168213314275427,null,1.17,17.47,1.2500000000000001E-2,58.65]
[1,0.21,75,23.888888888888889,5,1.1856472015252226,0.23060584568779441,3.8220135694080636E-3,33.751316078209229,null,1.19,0.24,3.8E-3,33.83]
[1,0.37,86,30,6,1.1576352031265953,13.727438049100808,9.6783607474746035E-3,54.895145922788522,null,1.1599999999999999,13.76,9.7999999999999997E-3,55.2]
[1,0.3,69,20.555555555555554,7,1.1986404768034411,2.373369536022722,4.4589167725679422E-3,31.991495159651706,null,1.2,2.38,4.4999999999999997E-3,32.07]
[1,0.6,83,28.333333333333332,8,1.1607984312668282,19.826494696414265,1.4292737889124005E-2,64.960177185569165,null,1.1599999999999999,19.84,1.4500000000000001E-2,65.59]
[1,0.7,87,30.555555555555554,9,1.1490390677148405,24.461574493784472,1.9009707374485253E-2,79.301562590433278,null,1.1499999999999999,24.46,1.9400000000000001E-2,80.39]
[]
[]
[null,null,null,null,null,"Web Calculator 2",null,null,null,null,"Errors"]
[]
[null,null,null,null,null,null,null,null,null,null,"%","ABS","%","%"]
[null,null,null,null,0,1.2316659999999999,{"$f":"CONVERT(34.38,\"F\",\"C\")","v":1.3222222222222235},{"$f":"29.2/7000","v":4.1714285714285716E-3},17.25,null,{"$f":"(F49-K49)/K49","v":-2.9873127711908406E-3},{"$f":"(G49-L49)","v":-7.5149313032287779E-3},{"$f":"(H49-M49)/M49","v":-1.6735037563063927E-2},{"$f":"(I49-N49)/N49","v":-3.1667706777004962E-3}]
[null,null,null,null,1,1.2470000000000001,{"$f":"CONVERT(14.03,\"F\",\"C\")","v":-9.9833333333333325},{"$f":"11.26/7000","v":1.6085714285714286E-3},13.51,null,{"$f":"(F50-K50)/K50","v":-1.6528014605007967E-3},{"$f":"(G50-L50)","v":-1.2526162271584145},{"$f":"(H50-M50)/M50","v":-2.1281562415597331E-3},{"$f":"(I50-N50)/N50","v":-6.9041815289273801E-4}]
[null,null,null,null,2,1.2410000000000001,{"$f":"CONVERT(18.98,\"F\",\"C\")","v":-7.2333333333333325},{"$f":"14.34/7000","v":2.0485714285714287E-3},14.47,null,2.1913251402275987E-3,-0.91474993660121129,1.6514094197296905E-2,-5.6163585690292112E-4]
[null,null,null,null,3,1.1339999999999999,{"$f":"CONVERT(63.15,\"F\",\"C\")","v":17.305555555555554},{"$f":"86.99/7000","v":1.2427142857142857E-2},35.298000000000002,null,-2.201107578405154E-3,-1.4030464831993328E-2,-1.6834268385787061E-2,-7.099141842455939E-3]
[null,null,null,null,4,1.15445,{"$f":"CONVERT(63.42,\"F\",\"C\")","v":17.455555555555556},{"$f":"87.79/7000","v":1.2541428571428573E-2},32.96,null,-1.1508791025260068E-3,-2.2668580891938461E-2,-1.5886752567430551E-2,-8.2146067472220266E-3]
[null,null,null,null,5,1.181,{"$f":"CONVERT(32.47,\"F\",\"C\")","v":0.26111111111111046},{"$f":"27.04/7000","v":3.8628571428571427E-3},22.24,null,-3.657813844350689E-3,-9.3941543122055826E-3,5.7930445810693816E-3,-2.3258623053730352E-3]
[null,null,null,null,6,1.1466000000000001,{"$f":"CONVERT(56.72,\"F\",\"C\")","v":13.733333333333333},{"$f":"68.88/7000","v":9.8399999999999998E-3},31.47,null,-2.0386179943143352E-3,-3.2561950899191672E-2,-1.2412168625040429E-2,-5.5227187900630526E-3]
[null,null,null,null,7,1.1930000000000001,{"$f":"CONVERT(36.32,\"F\",\"C\")","v":2.4},{"$f":"31.56/7000","v":4.5085714285714286E-3},14.696,null,-1.1329359971323782E-3,-6.6304639772778451E-3,-9.1296060960127743E-3,-2.4479214327500667E-3]
[null,null,null,null,8,1.2010000000000001,{"$f":"CONVERT(67.57,\"F\",\"C\")","v":19.761111111111106},{"$f":"101.76/7000","v":1.4537142857142858E-2},35.892000000000003,null,6.8830281623131519E-4,-1.3505303585734652E-2,-1.4293938681103145E-2,-9.6024213207933865E-3]
[null,null,null,null,9,1.127,{"$f":"CONVERT(76.03,\"F\",\"C\")","v":24.461111111111112},{"$f":"136.6/7000","v":1.9514285714285713E-2},42.35,null,{"$f":"(F58-K58)/K58","v":-8.3559329144292701E-4},1.5744937844708318E-3,{"$f":"(H58-M58)/M58","v":-2.0118176572925157E-2},{"$f":"(I58-N58)/N58","v":-1.3539462738732711E-2}]