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{"sheet":"Flow","index":0,"n_rows":151,"n_cols":29,"rows_kept":151,"cut":false,"hidden":false,"merged":[]}
["Equivalent hydraulic conductivity calculation (for the deposited restoration materials)"]
[null,null,null,null,null,null,null,null,null,"Key",null,"INPUT CELL (other cells are calculated)"]
["Equivalent hydraulic conductivity perpendicular to the stratification (Domenico & Schwartz, 1998):"]
[]
[null,null,null,"Where:","Kx is the equiavalent hydraulic conductivity for the layered system (m/s)"]
[null,null,null,null,"mi is the thickness if the layer (m)"]
[null,null,null,null,"Ki is the homogeneous conductivity for individual layers (m/s)"]
[]
["Parameter",null,null,"Symbol","Value","Units","Comments"]
["Layer 1: attenuation layer",null,null,"K1",9.9999999999999995E-8,"m/s","K = hydraulic conductivity"]
["Layer 1: attenuation layer",null,null,"m1",1,"m","Attenuation layer thickness"]
["Layer 2: attenuation layer",null,null,"K2",9.9999999999999995E-8,"m/s"]
["Layer 2: attenuation layer",null,null,"m2",528,"m","It is assumed that the bulk K of the deposited waste is similar to the K of the attenuation layer."]
["Layer 3: attenuation layer",null,null,"K3",9.9999999999999995E-8,"m/s"]
["Layer 3: attenuation layer",null,null,"m3",{"$f":"E11","v":1},"m"]
["Equivalent horizontal conductivity",null,null,"Kx",{"$f":"(E11+E13+E15)/((E11/E10)+(E13/E12)+(E15/E14))","v":9.9999999999999995E-8},"m/s","Based on the method in Domenico & Schwartz (1998)."]
[]
[]
["Discharge at the DOWN hydraulic gradient edge of the deposited restoration materials"]
[]
["Based on the modified form of the Dupuit equation for steady unsaturated flow subject to infiltration or evaporation (Fetter, 2001): "]
[]
[null,null,null,null,"Where:","q'x is the flow per unit width at x (m2/s)"]
[null,null,null,null,null,"x is the distance from the origin (the up hydraulic gradient edge of the deposit) (m)"]
[null,null,null,null,null,"K is the hydraulic conductivity (m/s)"]
[null,null,null,null,null,"h1 is the head at the origin (m)"]
[null,null,null,null,null,"h2 is the head at L (m)"]
[null,null,null,null,null,"L is the distance from the origin at the point where h2 is measured (m)"]
[null,null,null,null,null,"ω is the recharge rate (m/s)"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["It is assumed that: "]
[null,"1. the hydraulic gradient is equal to the slope of the water table"]
[null,"2. the streamlines are horizontal and the equipotential lines are vertical"]
[]
["Parameter",null,null,"Symbol","Value","Units","Comments"]
["Distance from origin",null,null,"x",{"$f":"E53","v":530},"m","Origin is assumed as the up hydraulic edge of the deposited restoration material (external to attenuation layer).  "]
["Hydraulic conductivity",null,null,"Kx",{"$f":"E16","v":9.9999999999999995E-8},"m/s","Equivalent horizontal hydraulic conductivity through restoration materials and any attenuation layers."]
["Head at the origin",null,null,"h1",4.8899999999999997,"m","Head at up hydraulic gradient edge of deposited restoration material relative to base of deposited restoration material."]
["Head at L",null,null,"h2",4.71,"m","Head at down hydraulic gradient edge of deposited restoration material."]
["Distance from origin to h2",null,null,"L",{"$f":"E11+E13+E15","v":530},"m","If x = L the flow calculated is that at the down hydraulic gradient boundary."]
["Recharge rate CALCULATED ",null,null,null,{"$f":"(51.8/1000)/(60*60*24*365)","v":1.6425672247590055E-9},"m/s"]
["Recharge rate ADJUSTED ",null,null,null,{"$f":"E128","v":5.8294583430754255E-11},"m/s","See under the heading Location of the water table divide (used to calibrate infiltration) below."]
["Recharge to use?",null,null,null,"ADJUSTED",null,"Specify which recharge rate to use in the calculations."]
["Recharge rate ",null,null,"ω",{"$f":"IF(E56=\"CALCULATED\",E54,IF(E56=\"ADJUSTED\",E55,\"ERROR\"))","v":5.8294583430754255E-11},"m/s","Calculated recharge converted to m/s."]
["Recharge rate",null,null,"ω",{"$f":"(E57*1*1)*(60*60*24*365)","v":1.8383779830722661E-3},"m3/m2/year"]
["Recharge rate ",null,null,"ω",{"$f":"E58*1000","v":1.8383779830722662},"mm/year"]
["Recharge",null,null,"Q",{"$f":"E58*E49","v":0.97434033102830109},"m3/year","Calculated for comparative purposes assuming unit width and a length parallel to flow of L."]
["Discharge per unit width",null,null,"q'x",{"$f":"((E50*(E51^2-E52^2))/(2*E53))-(E57*((E53/2)-E49))","v":1.5611083477074403E-8},"m2/s","Based on the method presented in Fetter (2001).",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"CALCULATED"]
["Width",null,null,"y",1,"m",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"ADJUSTED"]
["Flow",null,null,"Q",{"$f":"E61*E62","v":1.5611083477074403E-8},"m3/s"]
["Flow",null,null,"Q",{"$f":"E63*60*60*24","v":1.3487976124192285E-3},"m3/day"]
["Flow",null,null,"Q",{"$f":"E64*365.25","v":0.49264832793612323},"m3/year","Positive value denotes flow in the x-direction. Negative value denotes flow in the x-direction is reversed."]
["Flow",null,null,"Q",{"$f":"E65*1000","v":492.64832793612322},"l/year"]
[]
["Discharge at the UP hydraulic gradient edge of the deposited restoration materials"]
[]
["Parameter",null,null,"Symbol","Value","Units","Comments"]
["Distance from origin",null,null,"x",0,"m","Origin is assumed as the up hydraulic edge of the deposited restoration material (external to attenuation layer).  X=0 is the up hydraulic gradient edge of the deposit of restoration materials."]
["Hydraulic conductivity",null,null,"Kx",{"$f":"E50","v":9.9999999999999995E-8},"m/s","Average horizontal hydraulic conductivity through restoration materials and any attenuation layers."]
["Head at the origin",null,null,"h1",{"$f":"E51","v":4.8899999999999997},"m","Head at up hydraulic gradient edge of deposited restoration material relative to base of deposited restoration material."]
["Head at L",null,null,"h2",{"$f":"E52","v":4.71},"m","Head at down hydraulic gradient edge of deposited restoration material relative to base of deposited restoration material."]
["Distance from origin to h2",null,null,"L",{"$f":"E53","v":530},"m","If x = 0 the flow calculated is that at the up hydraulic gradient boundary."]
["Recharge rate in use",null,null,"ω",{"$f":"E57","v":5.8294583430754255E-11},"m/s"]
["Recharge rate ",null,null,"ω",{"$f":"(E76*1)*(60*60*24*365)","v":1.8383779830722661E-3},"m3/m2/year"]
["Recharge rate ",null,null,"ω",{"$f":"E77*1000","v":1.8383779830722662},"mm/year"]
["Flow per unit width",null,null,"q'x",{"$f":"((E72*(E73^2-E74^2))/(2*E75))-(E76*((E75/2)-E71))","v":-1.5285045741225349E-8},"m2/s","Based on the method presented in Fetter (2001)."]
["Width",null,null,"y",1,"m"]
["Flow",null,null,"Q",{"$f":"E79*E80","v":-1.5285045741225349E-8},"m3/s"]
["Flow",null,null,"Q",{"$f":"E81*60*60*24","v":-1.3206279520418703E-3},"m3/day"]
["Flow",null,null,"Q",{"$f":"E82*365.25","v":-0.48235935948329312},"m3/year","Positive value denotes flow in the x-direction. Negative value denotes flow in the x-direction is reversed."]
["Flow",null,null,"Q",{"$f":"E83*1000","v":-482.35935948329313},"l/year"]
[]
[]
["Location of the water table divide and maximum elevation of the water table using the CALCULATED infiltration scenario"]
[]
["If the water table is subject to infiltration there may be a water divide. q'x will be zero at the water table divide. Consistent with Fetter (2001):"]
[]
[null,null,null,null,"Where:","d is the distance from the origin to the water table divide (m)"]
[null,null,null,null,null,"K is the hydraulic conductivity (m/s)"]
[null,null,null,null,null,"h1 is the head at the origin (m)"]
[null,null,null,null,null,"h2 is the head at L (m)"]
[null,null,null,null,null,"L is the distance from the origin at the point where h2 is measured (m)"]
[null,null,null,null,null,"ω is the recharge rate (m/s)"]
[]
["The elevation of the water table at the divide may be found with (Fetter, 2001):"]
[]
[null,null,null,null,null,"Where:","hmax is the maximum elevation which is the elevation at the water table divide"]
[]
[]
[]
[]
[]
[]
["Parameter",null,null,"Symbol","Value","Units","Comments"]
["Hydraulic conductivity",null,null,"Kx",{"$f":"E72","v":9.9999999999999995E-8},"m/s"]
["Head at the origin",null,null,"h1",{"$f":"E51","v":4.8899999999999997},"m"]
["Head at L",null,null,"h2",{"$f":"E52","v":4.71},"m"]
["Distance from origin to h2",null,null,"L",{"$f":"E53","v":530},"m"]
["Recharge rate ",null,null,"ω",{"$f":"E54","v":1.6425672247590055E-9},"m/s"]
["Distance from origin to divide",null,null,"d",{"$f":"(E111/2)-((E108/E112)*((E109^2-E110^2)/(2*E111)))","v":264.90075360967438},"m"]
["Elevation at water table divide",null,null,"hmax",{"$f":"((E109^2)-(((E109^2-E110^2)*E113)/E111)+((E112/E108)*(E111-E113)*E113))^0.5","v":34.300744822486777},"m"]
["Maximum possible head at divide",null,null,null,8,"m"]
[]
["Location of the water table divide (used to calibrate infiltration)"]
[]
["For the ADJUSTED infiltration calculation it is recognised that hmax cannot exceed the restored land profile."]
["On this basis the maximum head at the water table divide is restricted by geometry and values of ω are varied iteratively until hmax is no greater than"]
["the maximum possible elevation of the water table divide based on the restored landform."]
[]
["Parameter",null,null,"Symbol","Value","Units","Comments"]
["Hydraulic conductivity",null,null,"Kx",{"$f":"E108","v":9.9999999999999995E-8},"m/s"]
["Head at the origin",null,null,"h1",{"$f":"E51","v":4.8899999999999997},"m"]
["Head at L",null,null,"h2",{"$f":"E52","v":4.71},"m"]
["Distance from origin to h2",null,null,"L",{"$f":"E53","v":530},"m"]
["Recharge rate ",null,null,"ω",5.8294583430754255E-11,"m/s","Vary the recharge rate so that hmax is approximately equal to the maximum possible water level divide elevation."]
["Distance from origin to divide",null,null,"d",{"$f":"(E127/2)-((E124/E128)*((E125^2-E126^2)/(2*E127)))","v":262.20353318729565},"m"]
["Elevation at water table divide",null,null,"hmax",{"$f":"((E125^2)-(((E125^2-E126^2)*E129)/E127)+((E128/E124)*(E127-E129)*E129))^0.5","v":7.999376849654424},"m","If the elevation of water table divide exceeds the restoration profile hmax cannot be maintained. Rainfall which otherwise could have infiltrated will run off."]
["Maximum possible head at divide",null,null,null,{"$f":"E115","v":8},"m","The rate of elevation is varied so that the hmax is similar to the maximum possible recharge mound elevation based on the restoration profile."]
[]
["Flow in the aquifer"]
[]
["Flow in the aquifer is calculated using Darcy's law and assuming unit width."]
[]
[null,null,null,"Where:","Q is the flow in the aquifer (m3/s)"]
[null,null,null,null,"i is the hydraulic gradient (no units)"]
[null,null,null,null,"A is the cross sectional area perpendicular to flow (m2)"]
[]
["Parameter",null,null,"Symbol","Value","Units","Comments"]
["Aquifer hydraulic conductivity",null,null,"Kaq",2.3099999999999999E-5,"m/s"]
["Hydraulic gradient in aquifer",null,null,"i",3.8E-3,"-"]
["Saturated thickness",null,null,"t",{"$f":"E51","v":4.8899999999999997},"m"]
["Cross sectional area ",null,null,"A",{"$f":"E144*1","v":4.8899999999999997},"m2","Assuming unit width"]
["Flow",null,null,"Q",{"$f":"E142*E143*E145","v":4.2924419999999993E-7},"m3/s","Using Darcy's law"]
["Flow",null,null,"Q",{"$f":"E146*(60*60*24*365)","v":13.536645091199999},"m3/year"]
[]
["References"]
["Domenico, P.A. & Schwartz F.W. 1998. Physical and Chemical Hydrogeology. Second Edition. John Wiley & Sons Inc. Page 42."]
["Fetter, C.W. 2001. Applied Hydrogeology, 4th Edition. Pages 140 to 144."]

{"sheet":"WaterBalance","index":1,"n_rows":23,"n_cols":7,"rows_kept":23,"cut":false,"hidden":false,"merged":[]}
["Water balance (unit width perpendicular to groundwater flow in the aquifer)"]
[]
["Recharge",null,null,null,{"$f":"Flow!E60","v":0.97434033102830109},"m3/year","Postive value = INPUT"]
["Flow: down hydraulic gradient edge",null,null,null,{"$f":"Flow!E65","v":0.49264832793612323},"m3/year","Positive value = OUTPUT flow at down hydraulic gradient edge."]
["Flow: up hydraulic gradient edge",null,null,null,{"$f":"-Flow!E83","v":0.48235935948329312},"m3/year","Positive value = OUTPUT flow at up hydraulic gradient edge. Negative value = INPUT flow at up hydraulic gradient edge."]
["TOTAL",null,null,null,{"$f":"E3-E4-E5","v":-6.6735639111525913E-4},"m3/year","Total flow should be zero if INPUTs balance OUTPUTs."]
[]
["Aquifer flow ",null,null,null,{"$f":"Flow!E147","v":13.536645091199999},"m3/year"]
["Flow across up hydraulic gradient boundary",null,null,null,{"$f":"Flow!E83","v":-0.48235935948329312},"m3/year","Positive value = aquifer flow into deposited restoration materials"]
["Aquifer flow not flowing into deposit",null,null,null,{"$f":"MIN(E8,E8-E9)","v":13.536645091199999},"m3/year","Flow assumed to bypass round deposited restoration materials and be available for dilution down hydraulic gradient."]
["Aquifer flow not flowing into deposit",null,null,null,{"$f":"E10/(60*60*24*365)","v":4.2924419999999993E-7},"m3/s"]
[]
["Flow through restoration materials",null,null,null,{"$f":"Flow!E65+IF(Flow!E83<0,-Flow!E83,0)","v":0.97500768741941635},"m3/year"]
["Flow through restoration materials",null,null,null,{"$f":"E13/(60*60*24*365)","v":3.0917290950641056E-8},"m3/s"]
["Flow through restoration materials",null,null,null,{"$f":"E13*1000","v":975.00768741941636},"l/year"]
["Flow through restoration materials",null,null,null,{"$f":"QsrcLitres/365","v":2.6712539381353873},"l/day"]
[]
["aquifer flow + recharge",null,null,null,{"$f":"E8+E3","v":14.5109854222283},"m3/year"]
["flow out of deposit + flow round",null,null,null,{"$f":"E10+Flow!E65+IF(Flow!E83<0,-Flow!E83,0)","v":14.511652778619416},"m3/year"]
["FLOW CHECK",null,null,null,{"$f":"IF(E18-E19<ABS(0.1),\"OK\",\"ERROR\")","v":"OK"},null,"Is the tolerance within 0.1m3/year?"]
[]
["Notes:"]
["Items in bold are used in the GenericAssessment worksheet"]

{"sheet":"SourceInputs","index":2,"n_rows":13,"n_cols":17,"rows_kept":13,"cut":false,"hidden":false,"merged":[[3,3,4,3],[3,4,4,4],[4,0,5,0],[4,1,5,1],[4,2,5,2]]}
["Source inputs"]
[null,null,null,"Key",null,"INPUT CELL (other cells are calculated)"]
[]
[null,null,null,"Initial concentration","Initial concentration"]
["Parameter","Parameter name","Category"]
[null,null,null,"mg/l","µg/l"]
["P1","Arsenic","Hazardous",0.05,{"$f":"D7*1000","v":50}]
["P2","Mercury","Hazardous",1E-3,{"$f":"D8*1000","v":1}]
["P3","Toluene","Hazardous",0.86950000000000005,869.5]
["P4","Cadmium","Non hazardous",4.0000000000000001E-3,4,null,null,null,null,null,null,null,null,null,null,null,"Non hazardous"]
["P5","Zinc","Non hazardous",0.4,400,null,null,null,null,null,null,null,null,null,null,null,"Hazardous"]
["P6","Copper","Non hazardous",0.2,200]
["P7","Lead","Hazardous",0.05,50]

{"sheet":"GenericAssessment","index":3,"n_rows":17,"n_cols":11,"rows_kept":17,"cut":false,"hidden":false,"merged":[]}
["Calculated concentrations in the aquifer following immediate dilution"]
[]
[null,null,null,"Where:","Caq is the estimated concentration in the aquifer (mg/l)",null,null,null,"Key",null,"INPUT CELL (other cells are calculated)"]
[null,null,null,null,"Csrc is the concentration in the source (mg/l)."]
[null,null,null,null,"Qsrc is the discharge from the imported restoration materials (m3/s)"]
[null,null,null,null,"Cbg is the background concentration in the aquifer (mg/l)"]
[null,null,null,null,"Qaq is the flow in the aquifer not including the flow through the restoration materials (m3/s)"]
[]
[]
[{"$f":"SourceInputsAttenuation!A12","v":"Parameter"},{"$f":"SourceInputsAttenuation!B12","v":"Parameter name"},"Source concentration","Environmental assessment limit (EAL) \n(mg/l)","Assumed background concentrations (mg/l)","Concentration following immediate dilution in groundwater (mg/l)","Ratio of predicted concentrations to EAL"]
[{"$f":"SourceInputsAttenuation!A14","v":"P1"},{"$f":"SourceInputsAttenuation!B14","v":"Arsenic"},{"$f":"SourceInputsAttenuation!E14","v":0.05},0.01,1.8E-3,{"$f":"((C11*Qsrc)+($E11*Qaq))/(Qsrc+Qaq)","v":5.0384574831376884E-3},{"$f":"F11/D11","v":0.50384574831376883}]
[{"$f":"SourceInputsAttenuation!A15","v":"P2"},{"$f":"SourceInputsAttenuation!B15","v":"Mercury"},{"$f":"SourceInputsAttenuation!E15","v":1E-3},1.0000000000000001E-5,0,{"$f":"((C12*Qsrc)+($E12*Qaq))/(Qsrc+Qaq)","v":6.7187914587918846E-5},{"$f":"F12/D12","v":6.718791458791884}]
[{"$f":"SourceInputsAttenuation!A16","v":"P3"},{"$f":"SourceInputsAttenuation!B16","v":"Toluene"},{"$f":"SourceInputsAttenuation!E16","v":0.86950000000000005},4.0000000000000001E-3,0,{"$f":"((C13*Qsrc)+($E13*Qaq))/(Qsrc+Qaq)","v":5.8419891734195435E-2},14.604972933548858]
[{"$f":"SourceInputsAttenuation!A17","v":"P4"},{"$f":"SourceInputsAttenuation!B17","v":"Cadmium"},{"$f":"SourceInputsAttenuation!E17","v":4.0000000000000001E-3},0.03,3.0000000000000001E-3,{"$f":"((C14*Qsrc)+($E14*Qaq))/(Qsrc+Qaq)","v":3.0671879145879192E-3},0.10223959715293064]
[{"$f":"SourceInputsAttenuation!A18","v":"P5"},{"$f":"SourceInputsAttenuation!B18","v":"Zinc"},{"$f":"SourceInputsAttenuation!E18","v":0.4},7.0999999999999994E-2,1.2999999999999999E-2,{"$f":"((C15*Qsrc)+($E15*Qaq))/(Qsrc+Qaq)","v":3.9001722945524599E-2},0.54932004148626201]
[{"$f":"SourceInputsAttenuation!A19","v":"P6"},{"$f":"SourceInputsAttenuation!B19","v":"Copper"},{"$f":"SourceInputsAttenuation!E19","v":0.2},0.23,4.8999999999999998E-3,1.8008362136102969E-2,7.8297226678708559E-2]
[{"$f":"SourceInputsAttenuation!A20","v":"P7"},{"$f":"SourceInputsAttenuation!B20","v":"Lead"},{"$f":"SourceInputsAttenuation!E20","v":0.05},2.0000000000000001E-4,0,3.3593957293959423E-3,16.79697864697971]

{"sheet":"SourceInputsAttenuation","index":4,"n_rows":37,"n_cols":23,"rows_kept":37,"cut":false,"hidden":false,"merged":[[10,6,10,8],[11,0,12,0],[11,1,12,1],[10,4,11,4],[10,5,11,5],[11,3,12,3],[11,2,12,2]]}
["Source inputs (with attenuation and source decline where specified)"]
[]
["Consistent with the LandSim manual (Environment Agency, 1996) the concentration of a species in the source at time t can be calculated based on the kappa constant for the species and the liquid to solid ratio at time t: "]
[]
[null,null,null,null,null,null,null,null,"Key",null,"INPUT CELL (other cells are calculated)"]
[null,null,"Where:","Ct is the concentration of the species in the source at any time t (mg/l)"]
[null,null,null,"C0 is the initial concentration of the species in leachate (mg/l)"]
[null,null,null,"κ (kappa) is a species and waste-specific constant (kg/l)"]
[null,null,null,"LS is the liquid to solid ratio at time t (l/kg) calculated as the aqueous losses from the source to time t divided by the mass of the source."]
[]
[null,null,null,null,"Initial concentration","Initial concentration","Calculation of kappa (κ) constant"]
["Parameter","Parameter name","Source type","Category",null,null,"m (slope)","c (intercept)","κ"]
[null,null,null,null,"mg/l","µg/l","kg/l","kg/l","kg/l",null,null,null,"Graph titles",null,"Stem","Variation in ",null,"Stem2"," concentrations with time"]
["P1",{"$f":"SourceInputs!B7","v":"Arsenic"},"Decline",{"$f":"SourceInputs!C7","v":"Hazardous"},{"$f":"SourceInputs!D7","v":0.05},{"$f":"E14*1000","v":50},4.1500000000000002E-2,-8.6199999999999999E-2,{"$f":"IF(C14=\"DECLINE\",G14*LN(F14)+H14,0)","v":7.6148954725268059E-2},null,null,null,{"$f":"$P$13&LOWER(B14)&$S$13","v":"Variation in arsenic concentrations with time"},null,null,null,null,null,null,null,null,null,"Decline"]
["P2",{"$f":"SourceInputs!B8","v":"Mercury"},"Decline",{"$f":"SourceInputs!C8","v":"Hazardous"},{"$f":"SourceInputs!D8","v":1E-3},{"$f":"E15*1000","v":1},7.6700000000000004E-2,0.1643,{"$f":"IF(C15=\"DECLINE\",G15*LN(F15)+H15,0)","v":0.1643},null,null,null,{"$f":"$P$13&LOWER(B15)&$S$13","v":"Variation in mercury concentrations with time"},null,null,null,null,null,null,null,null,null,"Constant"]
["P3",{"$f":"SourceInputs!B9","v":"Toluene"},"Decline",{"$f":"SourceInputs!C9","v":"Hazardous"},{"$f":"SourceInputs!D9","v":0.86950000000000005},869.5,2.98E-2,0.29189999999999999,0.49358396634707125,null,null,null,"Variation in toluene concentrations with time"]
["P4",{"$f":"SourceInputs!B10","v":"Cadmium"},"Decline",{"$f":"SourceInputs!C10","v":"Non hazardous"},{"$f":"SourceInputs!D10","v":4.0000000000000001E-3},4,8.2299999999999998E-2,0.15890000000000001,0.27299202592016703,null,null,null,"Variation in cadmium concentrations with time",null,null,null,null,null,null,null,null,null,"Non hazardous"]
["P5",{"$f":"SourceInputs!B11","v":"Zinc"},"Decline",{"$f":"SourceInputs!C11","v":"Non hazardous"},{"$f":"SourceInputs!D11","v":0.4},400,4.0300000000000002E-2,5.6099999999999997E-2,0.29755602124845165,null,null,null,"Variation in zinc concentrations with time",null,null,null,null,null,null,null,null,null,"Hazardous"]
["P6",{"$f":"SourceInputs!B12","v":"Copper"},"Decline",{"$f":"SourceInputs!C12","v":"Non hazardous"},{"$f":"SourceInputs!D12","v":0.2},200,6.6400000000000001E-2,-4.8800000000000003E-2,0.30300827313878959,null,null,null,"Variation in copper concentrations with time"]
["P7",{"$f":"SourceInputs!B13","v":"Lead"},"Decline",{"$f":"SourceInputs!C13","v":"Hazardous"},{"$f":"SourceInputs!D13","v":0.05},50,4.4299999999999999E-2,1.7100000000000001E-2,0.19040261914046686,null,null,null,"Variation in lead concentrations with time"]
[]
["Source geometry and physical properties"]
[]
["Parameter","Unit","Value","Comments"]
["Length","m",{"$f":"Flow!E53-2","v":528}]
["Thickness","m",7,"Thickness of the deposited waste used in the calculation of waste mass."]
["Width of source","m",1000000000,"This only changes the transverse dispersion. If set to a high value ngligible transverse dispersion will be assumed to occur.  "]
["Volume","m3",{"$f":"1*C25*C26","v":3696},"Unit width is assumed."]
["Volume","l",{"$f":"C28*1000","v":3696000}]
["Source porosity","Fraction",0.3]
["Source bulk density","kg/l",1.7]
["Source dry density","kg/l",{"$f":"(1.7-(0.3*1))/1","v":1.4}]
["Source mass","kg",{"$f":"C31*C29","v":6283200}]
["Fraction of organic carbon","Fraction",{"$f":"(0.01+0.1)/2","v":5.5E-2}]
[]
["Reference"]
["Environment Agency 1996.  LandSim. Landfill performance assessment: Simulation by Monte Carlo method. R&D Publication 120.  Release 2.  (LandSim version 2)"]

{"sheet":"AttenuationInputs","index":5,"n_rows":34,"n_cols":14,"rows_kept":34,"cut":false,"hidden":false,"merged":[[16,0,17,0],[16,1,17,1]]}
["Calculation input parameters relevant to attenuation in the attenuation layer"]
[]
["Note: See NumericalSoln and AnalyticalSoln worksheets for details on the calculation methods.",null,null,null,null,null,null,null,null,"Key",null,"INPUT CELL (other cells are calculated)"]
[]
["Conservatively it is assumed that discharge from the attenuation layer up hydraulic gradient and down hydraulic gradient emanates from the down hydraulic gradient face which increases the assumed rate of contaminant migration in the attenuation layer."]
[]
["Input parameter",null,null,null,null,"Symbol","Value","Unit","Comment"]
["Distance along the pathway in the direction of flow",null,null,null,null,"x",1,"m","It is assumed that the source is located adjacent to the attenuation layer and that the attenuation layer is 1m thick."]
["Saturated thickness in the outflow region",null,null,null,null,"h",{"$f":"Flow!E52","v":4.71},"m"]
["Specific discharge",null,null,null,null,"q",{"$f":"(WaterBalance!E14)/G9","v":6.5641806689259145E-9},"m/s","Calculated as the flow per unit width divided by the head at the down hydraulic boundary."]
["Effective porosity",null,null,null,null,"n",{"$f":"SourceInputsAttenuation!C30","v":0.3},"-"]
["Mean groundwater velocity",null,null,null,null,"νw",{"$f":"G10/G11","v":2.1880602229753049E-8},"m/s"]
["Tortuosity",null,null,null,null,"τ",5,"-"]
["Dispersivity in the x direction (longitudinal)",null,null,null,null,"αL",{"$f":"G8*0.1","v":0.1},"m"]
["Dispersivity (transverse)",null,null,null,null,"αT",0.03,"m"]
[]
["Parameter","Parameter name","Free water diffusion coefficient","Coefficient of molecular diffusion","Longitudinal dispersion coefficient","Transverse dispersion coefficient","Organic carbon partition coefficient ","Distribution coefficient ","Retardation factor","Retarded velocity","Degradation half life","Degradation half life","Decay constant","Comments"]
[null,null,"Dw","Dm","DL","DT","Koc","Kd","Rf ","ν = vw/Rf","t½","t½","γ"]
["Units",null,"m2/s","m2/s","m2/s","m2/s","l/kg","l/kg","-","m/s","years","s","1/s"]
["P1",{"$f":"SourceInputsAttenuation!B14","v":"Arsenic"},5.9400000000000002E-10,{"$f":"IF(C20=\"\",0.000000000001,C20/τ)","v":1.1879999999999999E-10},{"$f":"(α*νw)+D20","v":2.3068602229753052E-9},{"$f":"(αT*νw)+D20","v":7.7521806689259141E-10},null,25,{"$f":"1+((SourceInputsAttenuation!$C$31/n)*H20)","v":142.66666666666669},{"$f":"νw/$I20","v":1.5336870721789519E-10},null,null,{"$f":"IF(L20=\"\",0,(LN(2)/L20))","v":0}]
["P2",{"$f":"SourceInputsAttenuation!B15","v":"Mercury"},5.9400000000000002E-10,{"$f":"IF(C21=\"\",0.000000000001,C21/τ)","v":1.1879999999999999E-10},{"$f":"(α*νw)+D21","v":2.3068602229753052E-9},{"$f":"(αT*νw)+D21","v":7.7521806689259141E-10},null,3835.4,{"$f":"1+((SourceInputsAttenuation!$C$31/n)*H21)","v":21734.933333333334},{"$f":"νw/$I21","v":1.0067020631803049E-12},null,null,{"$f":"IF(L21=\"\",0,(LN(2)/L21))","v":0}]
["P3",{"$f":"SourceInputsAttenuation!B16","v":"Toluene"},{"$f":"((0.413+0.847+0.6)/3)*0.000000001","v":6.2000000000000003E-10},1.2400000000000001E-10,2.3120602229753051E-9,7.8041806689259146E-10,{"$f":"(131+242)/2","v":186.5},{"$f":"G22*SourceInputsAttenuation!$C$34","v":10.2575},{"$f":"1+((SourceInputsAttenuation!$C$31/n)*H22)","v":59.12583333333334},3.700683947471305E-10,0.82199999999999995,{"$f":"K22*(60*60*24*365.25)","v":25940347.199999999},{"$f":"IF(L22=\"\",0,(LN(2)/L22))","v":2.6720813534829839E-8}]
["P4",{"$f":"SourceInputsAttenuation!B17","v":"Cadmium"},5.9400000000000002E-10,1.1879999999999999E-10,2.3068602229753052E-9,7.7521806689259141E-10,null,222.2,{"$f":"1+((SourceInputsAttenuation!$C$31/n)*H23)","v":1260.1333333333334},1.7363719894524162E-11,null,null,0]
["P5",{"$f":"SourceInputsAttenuation!B18","v":"Zinc"},5.9400000000000002E-10,1.1879999999999999E-10,2.3068602229753052E-9,7.7521806689259141E-10,null,25,{"$f":"1+((SourceInputsAttenuation!$C$31/n)*H24)","v":142.66666666666669},1.5336870721789519E-10,null,null,0]
["P6",{"$f":"SourceInputsAttenuation!B19","v":"Copper"},5.9400000000000002E-10,1.1879999999999999E-10,2.3068602229753052E-9,7.7521806689259141E-10,null,126.8,{"$f":"1+((SourceInputsAttenuation!$C$31/n)*H25)","v":719.5333333333333},3.0409435138172494E-11,null,null,0]
["P7",{"$f":"SourceInputsAttenuation!B20","v":"Lead"},5.9400000000000002E-10,{"$f":"IF(C26=\"\",0.000000000001,C26/τ)","v":1.1879999999999999E-10},2.3068602229753052E-9,7.7521806689259141E-10,null,434.5,{"$f":"1+((SourceInputsAttenuation!$C$31/n)*H26)","v":2463.166666666667},8.8831188428525795E-12,null,null,0]
[]
[null,"Rf = 1 + (ρ/η).Kd",null,null,"Equation 6.31 in the LandSim manual",null,null,"Rf ","retardation factor for specific contaminant (-)"]
[null,null,null,null,null,null,null,"ρ","bulk density of material (kg/l)"]
[null,null,null,null,null,null,null,"Kd","distribution coefficient for specific contaminant (l/kg)"]
[null,null,null,null,null,null,null,"η","effective porosity of material (-)"]
[]
["Reference"]
["Environment Agency 1996.  LandSim. Landfill performance assessment: Simulation by Monte Carlo method. R&D Publication 120.  Release 2.  (LandSim version 2)"]

{"sheet":"WithAttenuation","index":6,"n_rows":35,"n_cols":11,"rows_kept":35,"cut":false,"hidden":false,"merged":[[14,7,14,9],[14,5,14,6]]}
["Calculated concentrations in the aquifer following immediate dilution and taking into account attenuation in the attenuation layer"]
[]
[null,null,null,"Where:","Caq is the estimated concentration in the aquifer (mg/l)"]
[null,null,null,null,"Csrc is the concentration in the source (mg/l)."]
[null,null,null,null,"Qsrc is the discharge from the imported restoration materials (m3/s)"]
[null,null,null,null,"Cbg is the background concentration in the aquifer (mg/l)"]
[null,null,null,null,"Qaq is the flow in the aquifer not including the flow through the restoration materials (m3/s)"]
[]
[]
["Where attenuation is taken into account in the attenuation layer it is assumed that that Qsrc is the concentration at the outer edge of the attenuation layer. "]
["For the calculation of attenuation in the attenuation layer it is assumed that the calculated flow from both the up hydraulic gradient and down hydraulic gradient edges of the attenuation layer flow through the down hydraulic gradient boundary.  "]
["Breakthrough may therefore occur sooner than would otherwise be the case."]
[]
[]
[null,null,null,null,null,"Maximum concentration predicted at the edge of the imported materials \n[DOWN hydraulcic gradient]\n(mg/l)",null,"Concentration predicted in the aquifer following immediate dilution\n(mg/l)"]
[{"$f":"SourceInputsAttenuation!A12","v":"Parameter"},{"$f":"SourceInputsAttenuation!B12","v":"Parameter name"},"Source concentration","Environmental assessment limit (EAL) \n(mg/l)","Assumed background concentrations (mg/l)","With attenuation (and source decline for inorganics)\n(numeric)","With attenuation (and source decline for inorganics)\n(analytical)","Immediate dilution in groundwater only","With attenuation (and source decline for inorganics)\n(numeric)","With attenuation (and source decline for inorganics)\n(analytical)","Ratio of predicted concentrations to EAL"]
[{"$f":"SourceInputsAttenuation!A14","v":"P1"},{"$f":"SourceInputsAttenuation!B14","v":"Arsenic"},{"$f":"SourceInputsAttenuation!E14","v":0.05},{"$f":"GenericAssessment!D11","v":0.01},{"$f":"GenericAssessment!E11","v":1.8E-3},{"$f":"MAX('P1'!D4:D1903)","v":4.9648061826188659E-2},{"$f":"IFERROR(MAX(P1an!J4:J1903),\"NOT SOLVED\")","v":4.9659930607949189E-2},{"$f":"((C17*Qsrc)+($E17*Qaq))/(Qsrc+Qaq)","v":5.0384574831376884E-3},{"$f":"MAX('P1'!G4:G1903)","v":5.0148114911754233E-3},{"$f":"IFERROR(MAX(P1an!K4:K1903),\"NOT SOLVED\")","v":5.0156089298706123E-3},{"$f":"I17/D17","v":0.50148114911754227}]
[{"$f":"SourceInputsAttenuation!A15","v":"P2"},{"$f":"SourceInputsAttenuation!B15","v":"Mercury"},{"$f":"SourceInputsAttenuation!E15","v":1E-3},{"$f":"GenericAssessment!D12","v":1.0000000000000001E-5},{"$f":"GenericAssessment!E12","v":0},{"$f":"MAX('P2'!D5:D1904)","v":6.2429565466118279E-6},{"$f":"IFERROR(MAX(P2an!J4:J1903),\"NOT SOLVED\")","v":6.3564679340685173E-6},{"$f":"((C18*Qsrc)+($E18*Qaq))/(Qsrc+Qaq)","v":6.7187914587918846E-5},{"$f":"MAX('P2'!G5:G1904)","v":4.1945123122984428E-7},{"$f":"IFERROR(MAX(P2an!K4:K1903),\"NOT SOLVED\")","v":4.2707782463504048E-7},{"$f":"I18/D18","v":4.1945123122984422E-2}]
[{"$f":"SourceInputsAttenuation!A16","v":"P3"},{"$f":"SourceInputsAttenuation!B16","v":"Toluene"},{"$f":"SourceInputsAttenuation!E16","v":0.86950000000000005},{"$f":"GenericAssessment!D13","v":4.0000000000000001E-3},{"$f":"GenericAssessment!E13","v":0},{"$f":"MAX('P3'!D6:D1905)","v":2.9006950436289741E-10},{"$f":"IFERROR(MAX(P3an!J4:J1903),\"NOT SOLVED\")","v":2.8613203022930364E-10},5.8419891734195435E-2,{"$f":"MAX('P3'!G6:G1905)","v":1.9489165083694304E-11},{"$f":"IFERROR(MAX(P3an!K4:K1903),\"NOT SOLVED\")","v":1.9224614407914264E-11},4.8722912709235757E-9]
[{"$f":"SourceInputsAttenuation!A17","v":"P4"},{"$f":"SourceInputsAttenuation!B17","v":"Cadmium"},{"$f":"SourceInputsAttenuation!E17","v":4.0000000000000001E-3},{"$f":"GenericAssessment!D14","v":0.03},{"$f":"GenericAssessment!E14","v":3.0000000000000001E-3},{"$f":"MAX('P4'!D7:D1906)","v":3.5617936481685208E-3},{"$f":"IFERROR(MAX(P4an!J4:J1903),\"NOT SOLVED\")","v":3.560126584290519E-3},{"$f":"((C20*Qsrc)+($E20*Qaq))/(Qsrc+Qaq)","v":3.0671879145879192E-3},{"$f":"MAX('P4'!G7:G1906)","v":3.0377457436491818E-3},{"$f":"IFERROR(MAX(P4an!K4:K1903),\"NOTSOLVED\")","v":3.0376337371037345E-3},0.10125819145497274]
[{"$f":"SourceInputsAttenuation!A18","v":"P5"},{"$f":"SourceInputsAttenuation!B18","v":"Zinc"},{"$f":"SourceInputsAttenuation!E18","v":0.4},{"$f":"GenericAssessment!D15","v":7.0999999999999994E-2},{"$f":"GenericAssessment!E15","v":1.2999999999999999E-2},{"$f":"MAX('P5'!D8:D1907)","v":0.39138804356970552},{"$f":"IFERROR(MAX(P5an!J4:J1903),\"NOT SOLVED\")","v":0.39140284958853255},{"$f":"((C21*Qsrc)+($E21*Qaq))/(Qsrc+Qaq)","v":3.9001722945524599E-2},{"$f":"MAX('P5'!G8:G1907)","v":3.8423103552451085E-2},{"$f":"IFERROR(MAX(P5an!K4:K1903),\"NOT SOLVED\")","v":3.8424098337979426E-2},0.54117047256973361]
[{"$f":"SourceInputsAttenuation!A19","v":"P6"},{"$f":"SourceInputsAttenuation!B19","v":"Copper"},{"$f":"SourceInputsAttenuation!E19","v":0.2},{"$f":"GenericAssessment!D16","v":0.23},{"$f":"GenericAssessment!E16","v":4.8999999999999998E-3},{"$f":"MAX('P6'!D9:D1908)","v":0.18435084826078502},{"$f":"IFERROR(MAX(P6an!J4:J1903),\"NOT SOLVED\")","v":0.18428129692678688},1.8008362136102969E-2,{"$f":"MAX('P6'!G9:G1908)","v":1.6956928265675211E-2},{"$f":"IFERROR(MAX(P6an!K4:K1903),\"NOT SOLVED\")","v":1.6952255256587067E-2},7.3725775068153088E-2]
[{"$f":"SourceInputsAttenuation!A20","v":"P7"},{"$f":"SourceInputsAttenuation!B20","v":"Lead"},{"$f":"SourceInputsAttenuation!E20","v":0.05},{"$f":"GenericAssessment!D17","v":2.0000000000000001E-4},{"$f":"GenericAssessment!E17","v":0},{"$f":"MAX('P7'!D10:D1909)","v":4.3172487428060569E-2},{"$f":"IFERROR(MAX(P7an!J4:J1903),\"NOT SOLVED\")","v":4.31507580039781E-2},3.3593957293959423E-3,{"$f":"MAX('P7'!G10:G1909)","v":2.9006693978645337E-3},{"$f":"IFERROR(MAX(P7an!K4:K1903),\"NOT SOLVED\")","v":2.8992094431752359E-3},14.503346989322667]
[]
["Notes:","For the analytical solution to the advection dispersion equation a value of \"NOT SOLVED\" denotes that the value of µ is negative number which is the case for certain combinations of inputs. This means that √µ becomes an imaginary number. "]
[null,"The LandSim manual provides an alternative solution to advection dispersion equation when µ is negative but the solution is not implemented here and the numerical results should be used instead."]
[]
[]
[]
[]
[]
[null,"Information used for plotting EALs on the graph"]
[null,"Year",{"$f":"B17","v":"Arsenic"},null,{"$f":"B18","v":"Mercury"},{"$f":"B19","v":"Toluene"},null,{"$f":"B20","v":"Cadmium"},{"$f":"B21","v":"Zinc"},{"$f":"B22","v":"Copper"},{"$f":"B23","v":"Lead"}]
[null,1,{"$f":"$D$17","v":0.01},null,{"$f":"$D$18","v":1.0000000000000001E-5},{"$f":"$D$19","v":4.0000000000000001E-3},null,{"$f":"$D$20","v":0.03},{"$f":"$D$21","v":7.0999999999999994E-2},{"$f":"$D$22","v":0.23},{"$f":"$D$23","v":2.0000000000000001E-4}]
[null,10000,{"$f":"$D$17","v":0.01},null,{"$f":"$D$18","v":1.0000000000000001E-5},{"$f":"$D$19","v":4.0000000000000001E-3},null,{"$f":"$D$20","v":0.03},{"$f":"$D$21","v":7.0999999999999994E-2},{"$f":"$D$22","v":0.23},{"$f":"$D$23","v":2.0000000000000001E-4}]

{"sheet":"SrcDecline","index":14,"n_rows":1903,"n_cols":24,"rows_kept":1125,"cut":true,"hidden":false,"merged":[],"bounds":{"rows_first":500,"rows_last":125,"rows_between":500,"halvings":2}}
["P1",{"$f":"SourceInputsAttenuation!B14","v":"Arsenic"},{"$f":"SourceInputsAttenuation!C14","v":"Decline"},"P2",{"$f":"SourceInputsAttenuation!B15","v":"Mercury"},{"$f":"SourceInputsAttenuation!C15","v":"Decline"},"P3",{"$f":"SourceInputsAttenuation!B16","v":"Toluene"},{"$f":"SourceInputsAttenuation!C16","v":"Decline"},"P4",{"$f":"SourceInputsAttenuation!B17","v":"Cadmium"},{"$f":"SourceInputsAttenuation!C17","v":"Decline"},"P5",{"$f":"SourceInputsAttenuation!B18","v":"Zinc"},{"$f":"SourceInputsAttenuation!C18","v":"Decline"},"P6",{"$f":"SourceInputsAttenuation!B19","v":"Copper"},{"$f":"SourceInputsAttenuation!C19","v":"Decline"},"P7",{"$f":"SourceInputsAttenuation!B20","v":"Lead"},{"$f":"SourceInputsAttenuation!C20","v":"Decline"},null,null,"References"]
["Years of leaching","Liquid to solid ratio at time t\nLS (l/kg)","Source concentration Ct (mg/l)","Years of leaching","Liquid to solid ratio at time t\nLS (l/kg)","Source concentration Ct (mg/l)","Years of leaching","Liquid to solid ratio at time t\nLS (l/kg)","Source concentration Ct (mg/l)","Years of leaching","Liquid to solid ratio at time t\nLS (l/kg)","Source concentration Ct (mg/l)","Years of leaching","Liquid to solid ratio at time t\nLS (l/kg)","Source concentration Ct (mg/l)","Years of leaching","Liquid to solid ratio at time t\nLS (l/kg)","Source concentration Ct (mg/l)","Years of leaching","Liquid to solid ratio at time t\nLS (l/kg)","Source concentration Ct (mg/l)",null,null,"Golder Associates. 2003.  Addendum to LandSim 2 manual relevant to LandSim 2.5."]
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{"sheet":"NumericalSoln-->","index":15,"n_rows":62,"n_cols":9,"rows_kept":62,"cut":false,"hidden":false,"merged":[]}
["Numerical solution to the advection dispersion equation for a declining source (adapted from Environment Agency, 1996)"]
[]
["LandSim uses a Laplace Transformation approach to solve the advection dispersion equation:"]
[]
[null,null,null,null,null,null,"Where:","x is the distance along the pathway in the direction of flow (m)"]
[null,null,null,null,null,null,null,"t is the time (s)"]
[null,null,null,null,null,null,null,"c(x,t) is the concentration at a distance x and a time t (m,s)"]
[null,null,null,null,null,null,null,"ν is the mean true veloicty of groundwater (m/s)"]
[null,null,null,null,null,null,null,"R is the retardation factor for the species (-)"]
[null,null,null,null,null,null,null,"γ is the rate of decay of the species (first order decay only) (1/s)"]
[null,null,null,null,null,null,null,"DL is the longitudinal coefficient of hydrodynamic dispersion (m2/s)"]
[]
["The Laplace Transform of the above equation is:"]
[]
[]
[]
[]
[]
["and the Laplace Transformed boundary condition for a constant or declining source is:"]
[]
[null,null,null,null,null,null,"Where:","C0 is the initial concentration"]
[null,null,null,null,null,null,null,"λ is the rate of decline of the source. For a constant source λ = 0."]
[]
["Compared with LandSim which calculates Laplace Transform concentrations for multiple pathways including the unsaturated zone, "]
["vertical pathway and saturated pathway a slightly simplified approach is taken whereby only concentrations at the edge of a single saturated"]
["pathway comprising the perimeter attenuation layer are calculated. "]
[]
["If csat(x,t) is the concentration at the end of the saturated pathway (the perimeter attenuation layer) the concentration is given by:"]
[]
[null,null,null,null,null,null,"Where:",null,"is a \"transfer function\" for the saturated pathway"]
[]
["The Laplace Transform of the transfer function for the saturated pathway includes the effects of transverse dispersion (in the 'y' direction) as well as "]
["longitudinal dispersion in the 'x' direction. This is accomplished using a factor from the Domenico (1987) solution 'fy'."]
["LandSim includes also a dilution factor 'fz' which is omitted from this calculation as dilution external to the attenuation is calculated separately."]
[]
[null,null,null,null,"(the factor fz is omitted)"]
[]
[]
[null,"Where:"]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Where:",null,"x and y","are the coordinates of the observation point in the aquifer (flow along the 'x' axis)"]
[null,null,null,null,"is the groundwater velocity in the saturated zone"]
[null,null,null,null,"is the logitudinal dispersion coefficient for the saturated pathway"]
[null,null,null,null,"is the transverse dispersion coefficient (perpendicular to the flow direction)"]
[null,null,null,null,"is the decay constant for each species (=0 if there is no decay)"]
[null,null,null,null,"is the retardation coefficient along the saturated pathway for each species (=1 if unretarded)"]
[null,null,null,"Y","is half the distance in the 'y' direction over which contamination enters the saturated zone."]
[]
["Once the Laplace Transformed concentrations have been calculated a numerical \"inversion\" algorithm is used to determine the concentrations in real time."]
["For the purpose of this spreadsheet a numerical inversion algorithm has been implemented in Visual Basic for Applications."]
["As both an analytical approach and numerical apporach to solving the advection dispersion equation are used in this spreadsheet it is possible to compare the results."]
[]
["Reference"]
["Domenico, P.A. 1987. An analytical model for multidimensional transport of a decaying contaminant species. J. Hydrolo., v.91, p. 49-58."]
["Environment Agency. 1996.  LandSim. Landfill performance assessment: Simulation by Monte Carlo method. R&D Publication 120.  Release 2.  (LandSim version 2)"]

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["P1",{"$f":"SourceInputsAttenuation!B14","v":"Arsenic"},{"$f":"SourceInputsAttenuation!C14","v":"Decline"}]
["Time (years)","Time (s)","Declining source coefficient (λ)","C (at edge of attenuation layer) NUMERICAL","C (at edge of attenuation layer) ANALYTICAL","Numerical:Analytical","C (following immediate dilution)","Time (years)"]
[0,{"$f":"A3*(60*60*24*365.25)","v":0},null,null,null,null,null,0,null,"Additional parameters for NumericalSolution function"]
[{"$f":"IF(A3<1000,A3+1,A3+10)","v":1},{"$f":"A4*(60*60*24*365.25)","v":31557600},{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B4)/B4)","v":3.7444422348967719E-13},{"$f":"Inversion(B4,C4,$P$5,$N$5,$J$5,$K$5,$L$5,$O$5,$M$5)","v":-1.6537330530810492E-19},{"$f":"P1an!J4","v":2.4214253854139592E-214},{"$f":"D4/E4","v":-6.829585016506021E+194},{"$f":"((D4*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.679061753741746E-3},{"$f":"IF(H3<1000,H3+1,H3+10)","v":1},null,"vw","R","gamma","fy","c0","DL","x"]
[{"$f":"IF(A4<1000,A4+1,A4+10)","v":2},63115200,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B5)/B5)","v":3.7444422348967719E-13},{"$f":"Inversion(B5,C5,$P$5,$N$5,$J$5,$K$5,$L$5,$O$5,$M$5)","v":-6.7038398330375039E-15},{"$f":"P1an!J5","v":8.259123315829938E-108},{"$f":"D5/E5","v":-8.1168903486263688E+92},{"$f":"((D5*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790617537412954E-3},{"$f":"IF(H4<1000,H4+1,H4+10)","v":2},null,{"$f":"νw","v":2.1880602229753049E-8},{"$f":"AttenuationInputs!I20","v":142.66666666666669},{"$f":"AttenuationInputs!M20","v":0},{"$f":"L17","v":1},{"$f":"SourceInputsAttenuation!E14","v":0.05},{"$f":"AttenuationInputs!$E$20","v":2.3068602229753052E-9},{"$f":"x","v":1}]
[3,94672800,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B6)/B6)","v":3.7444422348967714E-13},-4.8064159849133452E-13,{"$f":"P1an!J6","v":2.8985988252274214E-72},-1.6581859976901902E+59,{"$f":"((D6*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790617537094528E-3},3]
[4,126230400,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B7)/B7)","v":3.7444422348967719E-13},-6.7381367752447186E-13,{"$f":"P1an!J7","v":1.7807268515502241E-54},{"$f":"D7/E7","v":-3.7839249570358235E+41},{"$f":"((D7*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790617536964739E-3},4]
[5,157788000,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B8)/B8)","v":3.7444422348967714E-13},3.4324790797854465E-11,{"$f":"P1an!J8","v":8.5604643205995702E-44},4.0096879692911767E+32,{"$f":"((D8*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.679061756047957E-3},5,null,"Calculation of fy (transverse dispersion term)"]
[6,189345600,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B9)/B9)","v":3.7444422348967714E-13},1.7171137239964232E-10,{"$f":"P1an!J9","v":1.1462936913374239E-36},1.4979701423576728E+26,{"$f":"((D9*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.679061765278675E-3},6,null,null,"y",0]
[7,220903200,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B10)/B10)","v":3.7444422348967724E-13},2.5776196632056755E-10,{"$f":"P1an!J10","v":1.4241797502259457E-31},1.8098977062387924E+21,{"$f":"((D10*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790617710602351E-3},7,null,null,"Y",{"$f":"SourceInputsAttenuation!C27/2","v":500000000}]
[8,252460800,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B11)/B11)","v":3.7444422348967719E-13},{"$f":"Inversion(B11,C11,$P$5,$N$5,$J$5,$K$5,$L$5,$O$5,$M$5)","v":-3.3092636468095758E-10},{"$f":"P1an!J11","v":9.4810406781576008E-28},-3.4904012746548486E+17,{"$f":"((D11*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790617315074936E-3},8,null,null,"(y+Y)",{"$f":"L9+L10","v":500000000}]
[9,284018400,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B12)/B12)","v":3.7444422348967714E-13},-2.3082054406910041E-9,{"$f":"P1an!J12","v":8.9619091442774691E-25},-2575573355555478,{"$f":"((D12*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.679061598658236E-3},9,null,null,"(y-Y)",{"$f":"L9-L10","v":-500000000}]
[10,315576000,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B13)/B13)","v":3.7444422348967714E-13},-5.5235753968042951E-9,{"$f":"P1an!J13","v":2.1588599783997503E-22},-25585612091890.426,{"$f":"((D13*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790613826242341E-3},10,null,null,"Dt",{"$f":"AttenuationInputs!F20","v":7.7521806689259141E-10}]
[11,347133600,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B14)/B14)","v":3.7444422348967719E-13},-8.2580951672615189E-9,{"$f":"P1an!J14","v":1.9232522105018765E-20},-429381810776.99384,{"$f":"((D14*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790611988975533E-3},11,null,null,"DT*x",{"$f":"L13*P5","v":7.7521806689259141E-10}]
[12,378691200,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B15)/B15)","v":3.7444422348967714E-13},-7.4830217112368584E-9,{"$f":"P1an!J15","v":8.1222863905189369E-19},-9212949841.2807922,{"$f":"((D15*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790612509731224E-3},12,null,null,"(DT*x)/v",{"$f":"L14/J5","v":3.5429466645961728E-2}]
[13,410248800,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B16)/B16)","v":3.7444422348967714E-13},-7.0439872545208683E-11,{"$f":"P1an!J16","v":1.9312401235829003E-17},-3647390.6939405501,{"$f":"((D16*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790617490090379E-3},13,null,null,"2*((DT*x)/v)^(1/2)",{"$f":"2*(L15)^(1/2)","v":0.37645433532348505}]
[14,441806400,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B17)/B17)","v":3.7444422348967724E-13},1.5650086454675701E-8,{"$f":"P1an!J17","v":2.9233121630706766E-16},53535461.085471943,{"$f":"((D17*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790628052384179E-3},14,null,null,"fy",{"$f":"0.5*(ERF(L11/L16)-ERF(L12/L16))","v":1}]
[15,473364000,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B18)/B18)","v":3.7444422348967719E-13},3.8711863051870487E-8,{"$f":"P1an!J18","v":3.0827810778011226E-15},12557447.990916947,{"$f":"((D18*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790643547110943E-3},15]
[16,504921600,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B19)/B19)","v":3.7444422348967719E-13},6.5167100466302764E-8,{"$f":"P1an!J19","v":2.4233124842986325E-14},2689174.4621686195,{"$f":"((D19*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790661321833262E-3},16]
[17,536479200,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B20)/B20)","v":3.7444422348967714E-13},8.8650815248939881E-8,{"$f":"P1an!J20","v":1.4953502149167168E-13},592843.16385962651,{"$f":"((D20*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790677100051493E-3},17]
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[20,631152000,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B23)/B23)","v":3.7444422348967714E-13},6.9027248619468519E-8,{"$f":"P1an!J23","v":1.1811119780614889E-11},5844.2594691792165,{"$f":"((D23*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790663915386304E-3},20]
[21,662709600,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B24)/B24)","v":3.7444422348967714E-13},1.5559755845000108E-8,{"$f":"P1an!J24","v":3.8412428018662706E-11},405.07087543230512,{"$f":"((D24*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790627991692926E-3},21]
[22,694267200,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B25)/B25)","v":3.7444422348967719E-13},-6.2583947447062249E-8,{"$f":"P1an!J25","v":1.1223326924683951E-10},-557.62384778633373,{"$f":"((D25*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790575488568305E-3},22]
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[25,788940000,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B28)/B28)","v":3.7444422348967719E-13},-3.8588692696974011E-7,{"$f":"P1an!J28","v":1.6732551622895497E-9},-230.62049092484079,{"$f":"((D28*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790358268038562E-3},25]
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[28,883612800,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B31)/B31)","v":3.7444422348967724E-13},-6.2851511664086119E-7,{"$f":"P1an!J31","v":1.3973505209779905E-8},-44.979059098283393,{"$f":"((D31*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790195251217719E-3},28]
[29,915170400,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B32)/B32)","v":3.7444422348967714E-13},-6.3809928340246063E-7,{"$f":"P1an!J32","v":2.5708497027975471E-8},-24.820559626962783,{"$f":"((D32*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790188811815941E-3},29]
[30,946728000,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B33)/B33)","v":3.7444422348967719E-13},-5.9509243296994706E-7,{"$f":"P1an!J33","v":4.5408439511894491E-8},-13.105326661006835,{"$f":"((D33*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790217707221876E-3},30]
[31,978285600,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B34)/B34)","v":3.7444422348967719E-13},-4.912046380377828E-7,{"$f":"P1an!J34","v":7.7302298971196789E-8},-6.3543341475627786,{"$f":"((D34*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790287507264805E-3},31]
[32,1009843200,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B35)/B35)","v":3.7444422348967719E-13},-3.1925943782970359E-7,{"$f":"P1an!J35","v":1.2727368913103892E-7},-2.5084480540278773,{"$f":"((D35*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790403033659057E-3},32]
[33,1041400800,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B36)/B36)","v":3.7444422348967724E-13},-7.2759145436507888E-8,{"$f":"P1an!J36","v":2.0327734362477476E-7},-0.35793042224524746,{"$f":"((D36*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790568652064969E-3},33]
[34,1072958400,{"$f":"IF(SourceInputsAttenuation!$I$14=0,0,(SourceInputsAttenuation!$I$14*SrcDecline!B37)/B37)","v":3.7444422348967714E-13},2.5475493902086083E-7,{"$f":"P1an!J37","v":3.1579336113782604E-7},0.8067140426985564,{"$f":"((D37*Qsrc)+(WithAttenuation!$E$17*Qaq))/(Qsrc+Qaq)","v":1.6790788701948299E-3},34]
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{"sheet":"P2","index":17,"n_rows":1903,"n_cols":16,"rows_kept":1125,"cut":true,"hidden":false,"merged":[[0,3,0,7]],"bounds":{"rows_first":500,"rows_last":125,"rows_between":500,"halvings":2}}
["P2",{"$f":"SourceInputsAttenuation!B15","v":"Mercury"},{"$f":"SourceInputsAttenuation!C15","v":"Decline"}]
["Time (years)","Time (s)","Declining source coefficient (λ)","C (at edge of attenuation layer) NUMERICAL","C (at edge of attenuation layer) ANALYTICAL","Numerical:Analytical","C (following immediate dilution)","Time (years)"]
[0,{"$f":"A3*(60*60*24*365.25)","v":0},null,null,null,null,null,0,null,"Additional parameters for NumericalSolution function"]
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[9980,314944848000,{"$f":"IF(SourceInputsAttenuation!$I$15=0,0,(SourceInputsAttenuation!$I$15*SrcDecline!E1901)/B1901)","v":8.0790584902066608E-13},6.152486801225303E-6,{"$f":"P2an!J1901","v":6.2647190463860532E-6},0.9820850313749514,{"$f":"((D1901*Qsrc)+(WithAttenuation!$E$18*Qaq))/(Qsrc+Qaq)","v":4.1337275770402366E-7},9980]
[9990,315260424000,{"$f":"IF(SourceInputsAttenuation!$I$15=0,0,(SourceInputsAttenuation!$I$15*SrcDecline!E1902)/B1902)","v":8.0790584902066608E-13},6.1976019480317041E-6,{"$f":"P2an!J1902","v":6.3104753085266611E-6},0.98211333457838845,{"$f":"((D1902*Qsrc)+(WithAttenuation!$E$18*Qaq))/(Qsrc+Qaq)","v":4.1640395033427359E-7},9990]
[10000,315576000000,{"$f":"IF(SourceInputsAttenuation!$I$15=0,0,(SourceInputsAttenuation!$I$15*SrcDecline!E1903)/B1903)","v":8.0790584902066618E-13},6.2429565466118279E-6,{"$f":"P2an!J1903","v":6.3564679340685173E-6},0.98214238022844313,{"$f":"((D1903*Qsrc)+(WithAttenuation!$E$18*Qaq))/(Qsrc+Qaq)","v":4.1945123122984428E-7},10000]

{"sheet":"P3","index":18,"n_rows":1903,"n_cols":16,"rows_kept":1125,"cut":true,"hidden":false,"merged":[[0,3,0,7]],"bounds":{"rows_first":500,"rows_last":125,"rows_between":500,"halvings":2}}
["P3",{"$f":"SourceInputsAttenuation!B16","v":"Toluene"},{"$f":"SourceInputsAttenuation!C16","v":"Decline"}]
["Time (years)","Time (s)","Declining source coefficient (λ)","C (at edge of attenuation layer) NUMERICAL","C (at edge of attenuation layer) ANALYTICAL","Numerical:Analytical","C (following immediate dilution)","Time (years)"]
[0,{"$f":"A3*(60*60*24*365.25)","v":0},null,null,null,null,null,0,null,"Additional parameters for NumericalSolution function"]
[{"$f":"IF(A3<1000,A3+1,A3+10)","v":1},{"$f":"A4*(60*60*24*365.25)","v":31557600},{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H4)/B4)","v":2.4270807875509345E-12},{"$f":"Inversion(B4,C4,$P$5,$N$5,$J$5,$K$5,$L$5,$O$5,$M$5)","v":5.8203838888546195E-18},{"$f":"P3an!J4","v":1.706173594159565E-88},{"$f":"D4/E4","v":3.411366761728399E+70},{"$f":"((D4*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":3.9105945559326307E-19},{"$f":"IF(H3<1000,H3+1,H3+10)","v":1},null,"vw","R","gamma","fy","c0","DL","x"]
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[3,94672800,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H6)/B6)","v":2.4270807875509345E-12},{"$f":"Inversion(B6,C6,$P$5,$N$5,$J$5,$K$5,$L$5,$O$5,$M$5)","v":5.4935951586568811E-14},{"$f":"P3an!J6","v":2.409957885736493E-30},2.2795399003323312E+16,{"$f":"((D6*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":3.6910320230044304E-15},3]
[4,126230400,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H7)/B7)","v":2.4270807875509345E-12},-1.9198767951858064E-13,{"$f":"P3an!J7","v":2.5706249417229546E-23},-7468521619.1009722,{"$f":"((D7*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":-1.2899251813427132E-14},4]
[5,157788000,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H8)/B8)","v":2.4270807875509341E-12},-2.5350418514672823E-13,{"$f":"P3an!J8","v":3.1275319965996842E-19},-810556.6479330766,{"$f":"((D8*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":-1.7032417539318343E-14},5,null,"Calculation of fy (transverse dispersion term)"]
[6,189345600,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H9)/B9)","v":2.4270807875509345E-12},1.2278038821533177E-12,{"$f":"P3an!J9","v":1.2861039550251651E-16},9546.6923754953641,{"$f":"((D9*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":8.2493582364832287E-14},6,null,null,"y",0]
[7,220903200,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H10)/B10)","v":2.4270807875509345E-12},1.3801010804112057E-12,{"$f":"P3an!J10","v":7.6522811571205571E-15},180.35159086215774,{"$f":"((D10*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":9.2726113513362593E-14},7,null,null,"Y",{"$f":"SourceInputsAttenuation!C27/2","v":500000000}]
[8,252460800,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H11)/B11)","v":2.4270807875509345E-12},-1.4506042651921865E-12,{"$f":"P3an!J11","v":1.3647057428963762E-13},-10.629428891487654,{"$f":"((D11*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":-9.7463075470603395E-14},8,null,null,"(y+Y)",{"$f":"L9+L10","v":500000000}]
[9,284018400,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H12)/B12)","v":2.4270807875509341E-12},-3.3865393539834529E-12,{"$f":"P3an!J12","v":1.0944127720085205E-12},-3.0943894667533058,{"$f":"((D12*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":-2.2753451686406609E-13},9,null,null,"(y-Y)",{"$f":"L9-L10","v":-500000000}]
[10,315576000,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H13)/B13)","v":2.4270807875509341E-12},1.5215821928592322E-12,{"$f":"P3an!J13","v":5.0388438788124263E-12},0.3019704974899608,{"$f":"((D13*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.0223193441232436E-13},10,null,null,"Dt",{"$f":"AttenuationInputs!F22","v":7.8041806689259146E-10}]
[11,347133600,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H14)/B14)","v":2.4270807875509345E-12},1.6790044369680639E-11,{"$f":"P3an!J14","v":1.5575129236355912E-11},1.0780035346665913,{"$f":"((D14*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.1280880670374704E-12},11,null,null,"DT*x",{"$f":"L13*P5","v":7.8041806689259146E-10}]
[12,378691200,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H15)/B15)","v":2.4270807875509345E-12},4.2142515517560079E-11,{"$f":"P3an!J15","v":3.5908934514872414E-11},1.1735941510630425,{"$f":"((D15*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":2.8314677331138709E-12},12,null,null,"(DT*x)/v",{"$f":"L14/J5","v":3.5667120068175538E-2}]
[13,410248800,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H16)/B16)","v":2.4270807875509345E-12},7.4621439316702002E-11,{"$f":"P3an!J16","v":6.6484581698588007E-11},1.1223871371411036,{"$f":"((D16*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":5.0136588912381431E-12},13,null,null,"2*((DT*x)/v)^(1/2)",{"$f":"2*(L15)^(1/2)","v":0.37771481341443591}]
[14,441806400,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H17)/B17)","v":2.4270807875509345E-12},1.103301013314352E-10,{"$f":"P3an!J17","v":1.043066145353968E-10},1.0577478889796994,{"$f":"((D17*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":7.4128494247328994E-12},14,null,null,"fy",{"$f":"0.5*(ERF(L11/L16)-ERF(L12/L16))","v":1}]
[15,473364000,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H18)/B18)","v":2.4270807875509345E-12},1.4573127119787837E-10,{"$f":"P3an!J18","v":1.4436221469361752E-10},1.0094834822752368,{"$f":"((D18*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":9.7913802020318895E-12},15]
[16,504921600,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H19)/B19)","v":2.4270807875509345E-12},1.7826560524051492E-10,{"$f":"P3an!J19","v":1.8178391874063952E-10},0.98064562847748726,{"$f":"((D19*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.1977294258863375E-11},16]
[17,536479200,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H20)/B20)","v":2.4270807875509341E-12},2.0645378571187192E-10,{"$f":"P3an!J20","v":2.1333629712634611E-10},0.96773867594412166,{"$f":"((D20*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.3871199320761749E-11},17]
[18,568036800,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H21)/B21)","v":2.4270807875509341E-12},2.2972325908206191E-10,{"$f":"P3an!J21","v":2.3777382414438126E-10},0.96614192040991498,{"$f":"((D21*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.5434626710063926E-11},18]
[19,599594400,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H22)/B22)","v":2.4270807875509345E-12},2.4814287785519402E-10,{"$f":"P3an!J22","v":2.5540220096296525E-10},0.97157689683017312,{"$f":"((D22*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.6672202482935155E-11},19]
[20,631152000,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H23)/B23)","v":2.4270807875509341E-12},2.6216890552636797E-10,{"$f":"P3an!J23","v":2.6737677818939711E-10},0.9805223449160565,{"$f":"((D23*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.7614582032113778E-11},20]
[21,662709600,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H24)/B24)","v":2.4270807875509341E-12},2.7244534655349076E-10,{"$f":"P3an!J24","v":2.7510345689683397E-10},0.99033777920013555,{"$f":"((D24*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.8305034674111889E-11},21]
[22,694267200,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H25)/B25)","v":2.4270807875509345E-12},2.7966635838995218E-10,{"$f":"P3an!J25","v":2.7987232428729865E-10},0.99926407193754874,{"$f":"((D25*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.8790199400618407E-11},22]
[23,725824800,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H26)/B26)","v":2.4270807875509341E-12},2.8449220586885916E-10,{"$f":"P3an!J26","v":2.8270268784262467E-10},1.0063300354159728,{"$f":"((D26*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.9114438028845535E-11},23]
[24,757382400,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H27)/B27)","v":2.4270807875509345E-12},2.8750519364871808E-10,{"$f":"P3an!J27","v":2.843240978516926E-10},1.0111882735971427,{"$f":"((D27*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.9316874394453136E-11},24]
[25,788940000,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H28)/B28)","v":2.4270807875509345E-12},2.8919258206168494E-10,{"$f":"P3an!J28","v":2.85222192297719E-10},1.0139203395499519,{"$f":"((D28*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.9430246503020199E-11},25]
[26,820497600,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H29)/B29)","v":2.4270807875509345E-12},2.8994593415069371E-10,{"$f":"P3an!J29","v":2.8570251100851884E-10},1.0148525930948096,{"$f":"((D29*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.948086265883115E-11},26]
[27,852055200,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H30)/B30)","v":2.4270807875509345E-12},2.9006950436289741E-10,{"$f":"P3an!J30","v":2.8594872350688335E-10},1.0144109083806239,{"$f":"((D30*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.9489165083694304E-11},27]
[28,883612800,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H31)/B31)","v":2.4270807875509345E-12},2.8979268311154248E-10,{"$f":"P3an!J31","v":2.8606715049801391E-10},1.0130232800482082,{"$f":"((D31*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.9470566041102148E-11},28]
[29,915170400,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H32)/B32)","v":2.4270807875509345E-12},2.8928332607807378E-10,{"$f":"P3an!J32","v":2.861174091619879E-10},1.0110650971059698,{"$f":"((D32*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.9436343404242695E-11},29]
[30,946728000,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H33)/B33)","v":2.4270807875509345E-12},2.8866044890228697E-10,{"$f":"P3an!J33","v":2.8613203022930364E-10},1.0088365453911508,{"$f":"((D33*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.9394493585757168E-11},30]
[31,978285600,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H34)/B34)","v":2.4270807875509341E-12},2.8800546492854585E-10,{"$f":"P3an!J34","v":2.8612835092756675E-10},1.0065603914987589,{"$f":"((D34*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.9350486578472992E-11},31]
[32,1009843200,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H35)/B35)","v":2.4270807875509345E-12},2.8737140472801739E-10,{"$f":"P3an!J35","v":2.8611542290935273E-10},1.0043897732107319,{"$f":"((D35*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.9307885395876291E-11},32]
[33,1041400800,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H36)/B36)","v":2.4270807875509345E-12},2.8679053103774381E-10,{"$f":"P3an!J36","v":2.860978871908666E-10},1.0024210030129133,{"$f":"((D36*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.926885770398782E-11},33]
[34,1072958400,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H37)/B37)","v":2.4270807875509341E-12},2.8628029940087759E-10,{"$f":"P3an!J37","v":2.8607808549561298E-10},1.0007068486385957,{"$f":"((D37*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.9234576304349997E-11},34]
[35,1104516000,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H38)/B38)","v":2.4270807875509345E-12},2.8584777810088512E-10,{"$f":"P3an!J38","v":2.8605718264098141E-10},0.99926796265640672,{"$f":"((D38*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.9205516100188646E-11},35]
[36,1136073600,{"$f":"IF(SourceInputsAttenuation!$I$16=0,0,(SourceInputsAttenuation!$I$16*SrcDecline!H39)/B39)","v":2.4270807875509341E-12},2.8549328806141056E-10,{"$f":"P3an!J39","v":2.8603575067326899E-10},0.9981035146460483,{"$f":"((D39*Qsrc)+(WithAttenuation!$E$19*Qaq))/(Qsrc+Qaq)","v":1.9181698653694165E-11},36]
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{"sheet":"P4","index":19,"n_rows":1903,"n_cols":16,"rows_kept":1125,"cut":true,"hidden":false,"merged":[[0,3,0,7]],"bounds":{"rows_first":500,"rows_last":125,"rows_between":500,"halvings":2}}
["P4",{"$f":"SourceInputsAttenuation!B17","v":"Cadmium"},{"$f":"SourceInputsAttenuation!C17","v":"Decline"}]
["Time (years)","Time (s)","Declining source coefficient (λ)","C (at edge of attenuation layer) NUMERICAL","C (at edge of attenuation layer) ANALYTICAL","Numerical:Analytical","C (following immediate dilution)","Time (years)"]
[0,{"$f":"A3*(60*60*24*365.25)","v":0},null,null,null,null,null,0,null,"Additional parameters for NumericalSolution function"]
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[9830,310211208000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1886)/B1886)","v":1.3423728209184676E-12},2.8513174045559273E-3,{"$f":"P4an!J1886","v":2.851418809272544E-3},0.99996443710187821,{"$f":"((D1886*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9900103264765936E-3},9830]
[9840,310526784000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1887)/B1887)","v":1.3423728209184678E-12},2.8501137115065915E-3,{"$f":"P4an!J1887","v":2.8502114621860031E-3},0.99996570406066065,{"$f":"((D1887*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9899294528508047E-3},9840]
[9850,310842360000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1888)/B1888)","v":1.3423728209184678E-12},2.8489098100389276E-3,{"$f":"P4an!J1888","v":2.8490046220193909E-3},0.99996672101556783,{"$f":"((D1888*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9898485652218231E-3},9850]
[9860,311157936000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1889)/B1889)","v":1.3423728209184678E-12},2.847706881991941E-3,{"$f":"P4an!J1889","v":2.8477982886200895E-3},0.99996790270276037,{"$f":"((D1889*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9897677429949468E-3},9860]
[9870,311473512000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1890)/B1890)","v":1.3423728209184676E-12},2.8465040921145288E-3,{"$f":"P4an!J1890","v":2.8465924618346758E-3},0.99996895596354873,{"$f":"((D1890*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9896869300513958E-3},9870]
[9880,311789088000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1891)/B1891)","v":1.3423728209184678E-12},2.8453026396427438E-3,{"$f":"P4an!J1891","v":2.8453871415089265E-3},0.9999703021550389,{"$f":"((D1891*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9896062069653404E-3},9880]
[9890,312104664000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1892)/B1892)","v":1.3423728209184678E-12},2.844100724660314E-3,{"$f":"P4an!J1892","v":2.8441823274878396E-3},0.99997130886204555,{"$f":"((D1892*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.989525452804159E-3},9890]
[9900,312420240000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1893)/B1893)","v":1.3423728209184678E-12},2.84289936498191E-3,{"$f":"P4an!J1893","v":2.8429780196156398E-3},0.99997233371725458,{"$f":"((D1893*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9894447359526972E-3},9900]
[9910,312735816000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1894)/B1894)","v":1.3423728209184678E-12},2.8416990850440443E-3,{"$f":"P4an!J1894","v":2.8417742177357943E-3},0.99997356134372639,{"$f":"((D1894*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9893640916467501E-3},9910]
[9920,313051392000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1895)/B1895)","v":1.3423728209184678E-12},2.8404990496092289E-3,{"$f":"P4an!J1895","v":2.840570921691021E-3},0.9999746980153732,{"$f":"((D1895*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9892834637684535E-3},9920]
[9930,313366968000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1896)/B1896)","v":1.3423728209184678E-12},2.8392993126841594E-3,{"$f":"P4an!J1896","v":2.8393681313233065E-3},0.99997576269227373,{"$f":"((D1896*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9892028559464034E-3},9930]
[9940,313682544000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1897)/B1897)","v":1.3423728209184676E-12},2.8381003398927091E-3,{"$f":"P4an!J1897","v":2.8381658464739098E-3},0.99997691939627764,{"$f":"((D1897*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9891222994648985E-3},9940]
[9950,313998120000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1898)/B1898)","v":1.3423728209184678E-12},2.8369018637564424E-3,{"$f":"P4an!J1898","v":2.8369640669833806E-3},0.99997807401663552,{"$f":"((D1898*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9890417763526194E-3},9950]
[9960,314313696000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1899)/B1899)","v":1.3423728209184678E-12},2.835703375566889E-3,{"$f":"P4an!J1899","v":2.8357627926915673E-3},0.99997904721620889,{"$f":"((D1899*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9889612524305049E-3},9960]
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[9980,314944848000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1901)/B1901)","v":1.3423728209184676E-12},2.8333081007458566E-3,{"$f":"P4an!J1901","v":2.8333617590600452E-3},0.99998106196146075,{"$f":"((D1901*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9888003189104148E-3},9980]
[9990,315260424000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1902)/B1902)","v":1.3423728209184676E-12},2.8321118851050058E-3,{"$f":"P4an!J1902","v":2.8321619993966285E-3},0.99998230528775067,{"$f":"((D1902*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9887199476761085E-3},9990]
[10000,315576000000,{"$f":"IF(SourceInputsAttenuation!$I$17=0,0,(SourceInputsAttenuation!$I$17*SrcDecline!K1903)/B1903)","v":1.3423728209184678E-12},2.830916253667369E-3,{"$f":"P4an!J1903","v":2.830962744284534E-3},0.99998357780678715,{"$f":"((D1903*Qsrc)+(WithAttenuation!$E$20*Qaq))/(Qsrc+Qaq)","v":2.9886396156931982E-3},10000]

{"sheet":"P5","index":20,"n_rows":1903,"n_cols":16,"rows_kept":1125,"cut":true,"hidden":false,"merged":[[0,3,0,7]],"bounds":{"rows_first":500,"rows_last":125,"rows_between":500,"halvings":2}}
["P5",{"$f":"SourceInputsAttenuation!B18","v":"Zinc"},{"$f":"SourceInputsAttenuation!C18","v":"Decline"}]
["Time (years)","Time (s)","Declining source coefficient (λ)","C (at edge of attenuation layer) NUMERICAL","C (at edge of attenuation layer) ANALYTICAL","Numerical:Analytical","C (following immediate dilution)","Time (years)"]
[0,{"$f":"A3*(60*60*24*365.25)","v":0},null,null,null,null,null,0,null,"Additional parameters for NumericalSolution function"]
[{"$f":"IF(A3<1000,A3+1,A3+10)","v":1},{"$f":"A4*(60*60*24*365.25)","v":31557600},{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N4)/B4)","v":1.4631603772242344E-12},{"$f":"Inversion(B4,C4,$P$5,$N$5,$J$5,$K$5,$L$5,$O$5,$M$5)","v":-1.3229208477359642E-18},{"$f":"P5an!J4","v":1.937140173171612E-213},{"$f":"D4/E4","v":-6.8292468766986136E+194},{"$f":"((D4*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":1.2126557110357055E-2},{"$f":"IF(H3<1000,H3+1,H3+10)","v":1},null,"vw","R","gamma","fy","c0","DL","x"]
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[3,94672800,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N6)/B6)","v":1.4631603772242344E-12},-3.8443983709119118E-12,{"$f":"P5an!J6","v":2.3188776182704042E-71},-1.6578703164936135E+59,{"$f":"((D6*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":1.2126557110098758E-2},3]
[4,126230400,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N7)/B7)","v":1.4631603772242344E-12},-5.3818072558496707E-12,{"$f":"P5an!J7","v":1.4245799139490737E-53},-3.7778205372352746E+41,{"$f":"((D7*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":1.2126557109995462E-2},4]
[5,157788000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N8)/B8)","v":1.4631603772242344E-12},2.7460302229684339E-10,{"$f":"P5an!J8","v":6.8483597390724226E-43},4.0097633996960133E+32,{"$f":"((D8*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":1.2126557128807058E-2},5,null,"Calculation of fy (transverse dispersion term)"]
[6,189345600,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N9)/B9)","v":1.4631603772242344E-12},1.3734757111309453E-9,{"$f":"P5an!J9","v":9.1703270406323555E-36},1.4977390719494285E+26,{"$f":"((D9*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":1.2126557202638022E-2},6,null,null,"y",0]
[7,220903200,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N10)/B10)","v":1.4631603772242344E-12},2.0610519543430426E-9,{"$f":"P5an!J10","v":1.1393400141278853E-30},1.8089875970174605E+21,{"$f":"((D10*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":1.2126557248834838E-2},7,null,null,"Y",{"$f":"SourceInputsAttenuation!C27/2","v":500000000}]
[8,252460800,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N11)/B11)","v":1.4631603772242344E-12},-2.6498135427064725E-9,{"$f":"P5an!J11","v":7.5847997685218118E-27},-3.4935840412078406E+17,{"$f":"((D11*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":1.2126556932321609E-2},8,null,null,"(y+Y)",{"$f":"L9+L10","v":500000000}]
[9,284018400,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N12)/B12)","v":1.4631603772242342E-12},-1.8468409423895139E-8,{"$f":"P5an!J12","v":7.1694882780873002E-24},-2575973166779791.5,{"$f":"((D12*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":1.212655586950314E-2},9,null,null,"(y-Y)",{"$f":"L9-L10","v":-500000000}]
[10,315576000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N13)/B13)","v":1.4631603772242344E-12},-4.4187612876013373E-8,{"$f":"P5an!J13","v":1.7270764228592404E-21},-25585209948532.043,{"$f":"((D13*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":1.2126554141483495E-2},10,null,null,"Dt",{"$f":"AttenuationInputs!F24","v":7.7521806689259141E-10}]
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[9770,308317752000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1880)/B1880)","v":1.4631603772242344E-12},0.25721109100251072,{"$f":"P5an!J1880","v":0.2572108028224927},1.0000011204040222,{"$f":"((D1880*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9408033923699166E-2},9770]
[9780,308633328000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1881)/B1881)","v":1.4631603772242344E-12},0.25709241730191124,{"$f":"P5an!J1881","v":0.25709206615860303},1.0000013658270885,{"$f":"((D1881*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9400060485239455E-2},9780]
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[9810,309580056000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1884)/B1884)","v":1.4631603772242346E-12},0.25673650289497901,{"$f":"P5an!J1884","v":0.256736184941391},1.0000012384447798,{"$f":"((D1884*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9376147338465886E-2},9810]
[9820,309895632000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1885)/B1885)","v":1.4631603772242346E-12},0.25661795558979411,{"$f":"P5an!J1885","v":0.25661766737616754},1.0000011231246451,{"$f":"((D1885*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9368182392250492E-2},9820]
[9830,310211208000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1886)/B1886)","v":1.4631603772242344E-12},0.25649946057136336,{"$f":"P5an!J1886","v":0.25649920452241087},1.0000009982446261,{"$f":"((D1886*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9360220959073074E-2},9830]
[9840,310526784000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1887)/B1887)","v":1.4631603772242346E-12},0.25638106082356837,{"$f":"P5an!J1887","v":0.25638079635486449},1.0000010315464638,{"$f":"((D1887*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9352265926930993E-2},9840]
[9850,310842360000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1888)/B1888)","v":1.4631603772242344E-12},0.25626283726025495,{"$f":"P5an!J1888","v":0.25626244284828348},1.0000015390939347,{"$f":"((D1888*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.934432273225681E-2},9850]
[9860,311157936000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1889)/B1889)","v":1.4631603772242346E-12},0.25614433854278607,{"$f":"P5an!J1889","v":0.25614414397743462},1.0000007595932057,{"$f":"((D1889*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9336361050548734E-2},9860]
[9870,311473512000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1890)/B1890)","v":1.4631603772242344E-12},0.25602617408680345,{"$f":"P5an!J1890","v":0.25602589971709638},1.0000010716482488,{"$f":"((D1890*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9328421827172844E-2},9870]
[9880,311789088000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1891)/B1891)","v":1.4631603772242346E-12},0.25590799855923557,{"$f":"P5an!J1891","v":0.25590771004205876},1.0000011274266678,{"$f":"((D1891*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9320481859920235E-2},9880]
[9890,312104664000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1892)/B1892)","v":1.4631603772242346E-12},0.25578986700043305,{"$f":"P5an!J1892","v":0.25578957492712345},1.0000011418499353,{"$f":"((D1892*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9312544846837273E-2},9890]
[9900,312420240000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1893)/B1893)","v":1.4631603772242344E-12},0.25567168385801226,{"$f":"P5an!J1893","v":0.25567149434710373},1.0000007412281491,{"$f":"((D1893*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9304604367958571E-2},9900]
[9910,312735816000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1894)/B1894)","v":1.4631603772242346E-12},0.25555381540166999,{"$f":"P5an!J1894","v":0.25555346827682468},1.0000013583257064,{"$f":"((D1894*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9296685032181236E-2},9910]
[9920,313051392000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1895)/B1895)","v":1.4631603772242344E-12},0.25543579885825385,{"$f":"P5an!J1895","v":0.25543549669112275},1.0000011829488658,{"$f":"((D1895*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.928875574674223E-2},9920]
[9930,313366968000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1896)/B1896)","v":1.4631603772242346E-12},0.25531792445624257,{"$f":"P5an!J1896","v":0.25531757956484624},1.0000013508329388,{"$f":"((D1896*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9280836011487794E-2},9930]
[9940,313682544000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1897)/B1897)","v":1.4631603772242344E-12},0.25520002870779207,{"$f":"P5an!J1897","v":0.25519971687285486},1.0000012219250907,{"$f":"((D1897*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9272914842010625E-2},9940]
[9950,313998120000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1898)/B1898)","v":1.4631603772242344E-12},0.25508212312088224,{"$f":"P5an!J1898","v":0.25508190859002011},1.000000841027352,{"$f":"((D1898*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9264993011507888E-2},9950]
[9960,314313696000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1899)/B1899)","v":1.4631603772242346E-12},0.25496446445407156,{"$f":"P5an!J1899","v":0.25496415469122485},1.0000012149270436,{"$f":"((D1899*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9257087771051682E-2},9960]
[9970,314629272000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1900)/B1900)","v":1.4631603772242344E-12},0.25484672330308028,{"$f":"P5an!J1900","v":0.25484645515136389},1.000001052208932,{"$f":"((D1900*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9249176988655399E-2},9970]
[9980,314944848000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1901)/B1901)","v":1.4631603772242344E-12},0.25472902922033941,{"$f":"P5an!J1901","v":0.25472880994534325},1.0000008608174169,{"$f":"((D1901*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9241269368676701E-2},9980]
[9990,315260424000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1902)/B1902)","v":1.4631603772242344E-12},0.2546115030781651,{"$f":"P5an!J1902","v":0.25461121904808082},1.0000011155442614,{"$f":"((D1902*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9233373032274447E-2},9990]
[10000,315576000000,{"$f":"IF(SourceInputsAttenuation!$I$18=0,0,(SourceInputsAttenuation!$I$18*SrcDecline!N1903)/B1903)","v":1.4631603772242346E-12},0.25449394194783581,{"$f":"P5an!J1903","v":0.25449368243450582},1.0000010197240556,{"$f":"((D1903*Qsrc)+(WithAttenuation!$E$21*Qaq))/(Qsrc+Qaq)","v":2.9225474345091023E-2},10000]

{"sheet":"P6","index":21,"n_rows":1903,"n_cols":16,"rows_kept":1125,"cut":true,"hidden":false,"merged":[[0,3,0,7]],"bounds":{"rows_first":500,"rows_last":125,"rows_between":500,"halvings":2}}
["P6",{"$f":"SourceInputsAttenuation!B19","v":"Copper"},{"$f":"SourceInputsAttenuation!C19","v":"Decline"}]
["Time (years)","Time (s)","Declining source coefficient (λ)","C (at edge of attenuation layer) NUMERICAL","C (at edge of attenuation layer) ANALYTICAL","Numerical:Analytical","C (following immediate dilution)","Time (years)"]
[0,{"$f":"A3*(60*60*24*365.25)","v":0},null,null,null,null,null,0,null,"Additional parameters for NumericalSolution function"]
[{"$f":"IF(A3<1000,A3+1,A3+10)","v":1},{"$f":"A4*(60*60*24*365.25)","v":31557600},{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q4)/B4)","v":1.48997051838393E-12},{"$f":"Inversion(B4,C4,$P$5,$N$5,$J$5,$K$5,$L$5,$O$5,$M$5)","v":-8.9849982982549496E-39},{"$f":"P6an!J4","v":0},{"$f":"D4/E4","v":{"$error":"#DIV/0!"}},{"$f":"((D4*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":4.570779218519198E-3},{"$f":"IF(H3<1000,H3+1,H3+10)","v":1},null,"vw","R","gamma","fy","c0","DL","x"]
[{"$f":"IF(A4<1000,A4+1,A4+10)","v":2},63115200,{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q5)/B5)","v":1.48997051838393E-12},{"$f":"Inversion(B5,C5,$P$5,$N$5,$J$5,$K$5,$L$5,$O$5,$M$5)","v":-2.8688023206598944E-28},{"$f":"P6an!J5","v":0},{"$f":"D5/E5","v":{"$error":"#DIV/0!"}},{"$f":"((D5*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":4.570779218519198E-3},{"$f":"IF(H4<1000,H4+1,H4+10)","v":2},null,{"$f":"νw","v":2.1880602229753049E-8},{"$f":"AttenuationInputs!I25","v":719.5333333333333},{"$f":"AttenuationInputs!M25","v":0},{"$f":"L17","v":1},{"$f":"SourceInputsAttenuation!E19","v":0.2},{"$f":"AttenuationInputs!$E$25","v":2.3068602229753052E-9},{"$f":"x","v":1}]
[3,94672800,{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q6)/B6)","v":1.4899705183839298E-12},-1.2686886915466605E-23,{"$f":"P6an!J6","v":0},{"$error":"#DIV/0!"},{"$f":"((D6*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":4.570779218519198E-3},3]
[4,126230400,{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q7)/B7)","v":1.48997051838393E-12},-7.380735270413261E-21,{"$f":"P6an!J7","v":2.6999038869633291E-269},-2.7337029684840439E+248,{"$f":"((D7*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":4.570779218519198E-3},4]
[5,157788000,{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q8)/B8)","v":1.48997051838393E-12},-5.6436428562253969E-19,{"$f":"P6an!J8","v":1.3643985646434901E-215},-4.1363594205334343E+196,{"$f":"((D8*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":4.570779218519198E-3},5,null,"Calculation of fy (transverse dispersion term)"]
[6,189345600,{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q9)/B9)","v":1.4899705183839298E-12},-1.3771805916387658E-17,{"$f":"P6an!J9","v":8.7956366875779441E-180},-1.5657542944943992E+162,{"$f":"((D9*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":4.5707792185191972E-3},6,null,null,"y",0]
[7,220903200,{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q10)/B10)","v":1.48997051838393E-12},-1.6375720780695875E-16,{"$f":"P6an!J10","v":3.3670256600735028E-154},-4.8635568700531941E+137,{"$f":"((D10*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":4.5707792185191868E-3},7,null,null,"Y",{"$f":"SourceInputsAttenuation!C27/2","v":500000000}]
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[9930,313366968000,{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q1896)/B1896)","v":1.4899705183839302E-12},0.13172741314737221,{"$f":"P6an!J1896","v":0.13171790570660966},1.0000721803213584,{"$f":"((D1896*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":1.3421269401952339E-2},9930]
[9940,313682544000,{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q1897)/B1897)","v":1.48997051838393E-12},0.13166543402050507,{"$f":"P6an!J1897","v":0.1316559866465021},1.0000717580282037,{"$f":"((D1897*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":1.3417105153670157E-2},9940]
[9950,313998120000,{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q1898)/B1898)","v":1.48997051838393E-12},0.13160351226119743,{"$f":"P6an!J1898","v":0.13159409669380881},1.0000715500742448,{"$f":"((D1898*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":1.3412944759794661E-2},9950]
[9960,314313696000,{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q1899)/B1899)","v":1.4899705183839302E-12},0.13154161774024298,{"$f":"P6an!J1899","v":0.13153223583484713},1.0000713278029245,{"$f":"((D1899*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":1.3408786196007312E-2},9960]
[9970,314629272000,{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q1900)/B1900)","v":1.4899705183839302E-12},0.13147972305773781,{"$f":"P6an!J1900","v":0.13147040405594096},1.0000708828870175,{"$f":"((D1900*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":1.3404627621365709E-2},9970]
[9980,314944848000,{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q1901)/B1901)","v":1.48997051838393E-12},0.13141785846268347,{"$f":"P6an!J1901","v":0.13140860134342033},1.0000704453069929,{"$f":"((D1901*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":1.3400471068237184E-2},9980]
[9990,315260424000,{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q1902)/B1902)","v":1.48997051838393E-12},0.13135601696976285,{"$f":"P6an!J1902","v":0.1313468276836221},1.0000699619952975,{"$f":"((D1902*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":1.3396316067292842E-2},9990]
[10000,315576000000,{"$f":"IF(SourceInputsAttenuation!$I$19=0,0,(SourceInputsAttenuation!$I$19*SrcDecline!Q1903)/B1903)","v":1.4899705183839302E-12},0.13129426067801117,{"$f":"P6an!J1903","v":0.13128508306288916},1.0000699060008029,{"$f":"((D1903*Qsrc)+(WithAttenuation!$E$22*Qaq))/(Qsrc+Qaq)","v":1.3392166790837363E-2},10000]

{"sheet":"P7","index":22,"n_rows":1903,"n_cols":16,"rows_kept":1125,"cut":true,"hidden":false,"merged":[[0,3,0,7]],"bounds":{"rows_first":500,"rows_last":125,"rows_between":500,"halvings":2}}
["P7",{"$f":"SourceInputsAttenuation!B20","v":"Lead"},{"$f":"SourceInputsAttenuation!C20","v":"Decline"}]
["Time (years)","Time (s)","Declining source coefficient (λ)","C (at edge of attenuation layer) NUMERICAL","C (at edge of attenuation layer) ANALYTICAL","Numerical:Analytical","C (following immediate dilution)","Time (years)"]
[0,{"$f":"A3*(60*60*24*365.25)","v":0},null,null,null,null,null,0,null,"Additional parameters for NumericalSolution function"]
[{"$f":"IF(A3<1000,A3+1,A3+10)","v":1},{"$f":"A4*(60*60*24*365.25)","v":31557600},{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T4)/B4)","v":9.3625921894362392E-13},{"$f":"Inversion(B4,C4,$P$5,$N$5,$J$5,$K$5,$L$5,$O$5,$M$5)","v":-6.549018712931006E-70},{"$f":"P7an!J4","v":0},{"$f":"D4/E4","v":{"$error":"#DIV/0!"}},{"$f":"((D4*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-4.4001490991909062E-71},{"$f":"IF(H3<1000,H3+1,H3+10)","v":1},null,"vw","R","gamma","fy","c0","DL","x"]
[{"$f":"IF(A4<1000,A4+1,A4+10)","v":2},63115200,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T5)/B5)","v":9.3625921894362392E-13},{"$f":"Inversion(B5,C5,$P$5,$N$5,$J$5,$K$5,$L$5,$O$5,$M$5)","v":-1.9188307449716044E-50},{"$f":"P7an!J5","v":0},{"$f":"D5/E5","v":{"$error":"#DIV/0!"}},{"$f":"((D5*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-1.2892223620182484E-51},{"$f":"IF(H4<1000,H4+1,H4+10)","v":2},null,{"$f":"νw","v":2.1880602229753049E-8},{"$f":"AttenuationInputs!I26","v":2463.166666666667},{"$f":"AttenuationInputs!M26","v":0},{"$f":"L17","v":1},{"$f":"SourceInputsAttenuation!E20","v":0.05},{"$f":"AttenuationInputs!$E$26","v":2.3068602229753052E-9},{"$f":"x","v":1}]
[3,94672800,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T6)/B6)","v":9.3625921894362392E-13},-7.9963798795336902E-42,{"$f":"P7an!J6","v":0},{"$error":"#DIV/0!"},{"$f":"((D6*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-5.3726008835866237E-43},3]
[4,126230400,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T7)/B7)","v":9.3625921894362392E-13},-1.0935800142821872E-36,{"$f":"P7an!J7","v":0},{"$error":"#DIV/0!"},{"$f":"((D7*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-7.3475360594646658E-38},4]
[5,157788000,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T8)/B8)","v":9.3625921894362392E-13},-3.4842225721475333E-33,{"$f":"P7an!J8","v":0},{"$error":"#DIV/0!"},{"$f":"((D8*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-2.3409764858274738E-34},5,null,"Calculation of fy (transverse dispersion term)"]
[6,189345600,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T9)/B9)","v":9.3625921894362392E-13},-1.3392343818175754E-30,{"$f":"P7an!J9","v":0},{"$error":"#DIV/0!"},{"$f":"((D9*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-8.9980365258763546E-32},6,null,null,"y",0]
[7,220903200,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T10)/B10)","v":9.3625921894362392E-13},-1.3638248388979971E-28,{"$f":"P7an!J10","v":0},{"$error":"#DIV/0!"},{"$f":"((D10*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-9.163254678876081E-30},7,null,null,"Y",{"$f":"SourceInputsAttenuation!C27/2","v":500000000}]
[8,252460800,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T11)/B11)","v":9.3625921894362392E-13},-5.6559470662611937E-27,{"$f":"P7an!J11","v":0},{"$error":"#DIV/0!"},{"$f":"((D11*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-3.8001128840174726E-28},8,null,null,"(y+Y)",{"$f":"L9+L10","v":500000000}]
[9,284018400,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T12)/B12)","v":9.3625921894362392E-13},-1.23556694865923E-25,{"$f":"P7an!J12","v":0},{"$error":"#DIV/0!"},{"$f":"((D12*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-8.3015166614171846E-27},9,null,null,"(y-Y)",{"$f":"L9-L10","v":-500000000}]
[10,315576000,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T13)/B13)","v":9.3625921894362392E-13},-1.6764186608719972E-24,{"$f":"P7an!J13","v":0},{"$error":"#DIV/0!"},{"$f":"((D13*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-1.1263507380026103E-25},10,null,null,"Dt",{"$f":"AttenuationInputs!F26","v":7.7521806689259141E-10}]
[11,347133600,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T14)/B14)","v":9.3625921894362412E-13},-1.5785240218832533E-23,{"$f":"P7an!J14","v":0},{"$error":"#DIV/0!"},{"$f":"((D14*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-1.0605773715727015E-24},11,null,null,"DT*x",{"$f":"L13*P5","v":7.7521806689259141E-10}]
[12,378691200,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T15)/B15)","v":9.3625921894362392E-13},-1.1150270174979336E-22,{"$f":"P7an!J15","v":4.4520622784604882E-308},-2.5045180138034976E+285,{"$f":"((D15*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-7.4916340014873063E-24},12,null,null,"(DT*x)/v",{"$f":"L14/J5","v":3.5429466645961728E-2}]
[13,410248800,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T16)/B16)","v":9.3625921894362392E-13},-6.2517207978695108E-22,{"$f":"P7an!J16","v":3.2659346599608904E-284},-1.9142210266828716E+262,{"$f":"((D16*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-4.2004008299477256E-23},13,null,null,"2*((DT*x)/v)^(1/2)",{"$f":"2*(L15)^(1/2)","v":0.37645433532348505}]
[14,441806400,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T17)/B17)","v":9.3625921894362392E-13},-2.901731647542955E-21,{"$f":"P7an!J17","v":5.1814167839179146E-264},-5.6002668161136008E+242,{"$f":"((D17*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-1.9496129809217709E-22},14,null,null,"fy",{"$f":"0.5*(ERF(L11/L16)-ERF(L12/L16))","v":1}]
[15,473364000,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T18)/B18)","v":9.3625921894362392E-13},-1.1512776965621008E-20,{"$f":"P7an!J18","v":1.6691317880406858E-246},-6.8974643273287057E+225,{"$f":"((D18*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-7.735194754359038E-22},15]
[16,504921600,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T19)/B19)","v":9.3625921894362392E-13},-4.0030356479515809E-20,{"$f":"P7an!J19","v":3.4905496969426505E-231},-1.146820986808414E+211,{"$f":"((D19*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-2.6895561720696521E-21},16]
[17,536479200,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T20)/B20)","v":9.3625921894362392E-13},-1.2440551989210408E-19,{"$f":"P7an!J20","v":1.1525472079862351E-217},-1.0793963061128673E+198,{"$f":"((D20*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-8.3585474447763278E-21},17]
[18,568036800,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T21)/B21)","v":9.3625921894362392E-13},-3.5106919786342862E-19,{"$f":"P7an!J21","v":1.1995378282017554E-205},-2.9267038488458639E+186,{"$f":"((D21*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-2.3587607280497225E-20},18]
[19,599594400,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T22)/B22)","v":9.3625921894362392E-13},-9.1122269777103833E-19,{"$f":"P7an!J22","v":6.7918296972846863E-195},-1.3416453862724754E+176,{"$f":"((D22*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-6.1223152788413512E-20},19]
[20,631152000,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T23)/B23)","v":9.3625921894362392E-13},-2.1984549346074376E-18,{"$f":"P7an!J23","v":3.2374481104178096E-185},-6.790703231761498E+166,{"$f":"((D23*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-1.4770960237179323E-19},20]
[21,662709600,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T24)/B24)","v":9.3625921894362392E-13},-4.9736617163483206E-18,{"$f":"P7an!J24","v":1.8499989609341531E-176},-2.6884673026177702E+158,{"$f":"((D24*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-3.3416995858721281E-19},21]
[22,694267200,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T25)/B25)","v":9.3625921894362412E-13},-1.0628883395748066E-17,{"$f":"P7an!J25","v":1.6923645245790068E-168},-6.2804929088147307E+150,{"$f":"((D25*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-7.1413250975846982E-19},22]
[23,725824800,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T26)/B26)","v":9.3625921894362392E-13},-2.1589544041921893E-17,{"$f":"P7an!J26","v":3.1472380844239401E-161},-6.8598382018733008E+143,{"$f":"((D26*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-1.4505564410807604E-18},23]
[24,757382400,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T27)/B27)","v":9.3625921894362392E-13},-4.1901904909635302E-17,{"$f":"P7an!J27","v":1.4519327196765148E-154},-2.8859398470592281E+137,{"$f":"((D27*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-2.8153016081396741E-18},24]
[25,788940000,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T28)/B28)","v":9.3625921894362392E-13},-7.8058431546894413E-17,{"$f":"P7an!J28","v":1.964170164298084E-148},-3.9741175670891724E+131,{"$f":"((D28*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-5.2445832316396514E-18},25]
[26,820497600,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T29)/B29)","v":9.3625921894362392E-13},-1.4011722511219441E-16,{"$f":"P7an!J29","v":8.9761197177583901E-143},-1.5609999589798914E+126,{"$f":"((D29*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-9.4141841531343157E-18},26]
[27,852055200,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T30)/B30)","v":9.3625921894362412E-13},-2.431716704166015E-16,{"$f":"P7an!J30","v":1.5632625692895276E-137},-1.5555395184004072E+121,{"$f":"((D30*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-1.6338197422152172E-17},27]
[28,883612800,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T31)/B31)","v":9.3625921894362392E-13},-4.0922203934055483E-16,{"$f":"P7an!J31","v":1.1505014765963989E-132},-3.5569014700544515E+116,{"$f":"((D31*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-2.7494775426707163E-17},28]
[29,915170400,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T32)/B32)","v":9.3625921894362392E-13},-6.6949110942620886E-16,{"$f":"P7an!J32","v":3.9114992273070316E-128},-1.7115971920749593E+112,{"$f":"((D32*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-4.4981711477499146E-17},29]
[30,946728000,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T33)/B33)","v":9.3625921894362392E-13},-1.0672102490727238E-15,{"$f":"P7an!J33","v":6.6363783858876705E-124},-1.6081214587494856E+108,{"$f":"((D33*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-7.1703631062049759E-17},30]
[31,978285600,{"$f":"IF(SourceInputsAttenuation!$I$20=0,0,(SourceInputsAttenuation!$I$20*SrcDecline!T34)/B34)","v":9.3625921894362392E-13},-1.6608804641860673E-15,{"$f":"P7an!J34","v":6.0097423697889117E-120},-2.7636466956309888E+104,{"$f":"((D34*Qsrc)+(WithAttenuation!$E$23*Qaq))/(Qsrc+Qaq)","v":-1.115910947684765E-16},31]
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{"sheet":"AnalyticalSoln-->","index":23,"n_rows":26,"n_cols":13,"rows_kept":26,"cut":false,"hidden":false,"merged":[]}
["Analytical solution to the advection dispersion equation for a declining source (Environment Agency, 1996)"]
[]
[]
[]
[]
[]
[]
[]
["Where:","x","the distance along the pathway in the direction of flow (m)"]
[null,"ν","the mean true velocity of groundwater (i.e. ν = q/n where q is the specific discharge and n is the effective porosity) (m/s)"]
[null,"cd","the concentration in the declining source "]
[null,"λ","the coefficient describing the declining source term which for inorganic substances is -(Κ*LS)"]
[null,"t","time (s)"]
[null,"DL or D","the longitudinal coefficient of hydrodynamic dispersion (m2/s)",null,null,null,null,null,"DL = αν + Dm",null,"where:","α","is the dispersivity of the medium"]
[null,null,null,null,null,null,null,null,null,null,null,"Dm","is the coefficient of molecular diffusion for the chemical species in the porous medium (m2/s)"]
[null,null,null,null,null,null,null,null,null,null,null,null,"this is calculated by dividing the free water diffusion coefficient by the tortuosity"]
[]
[]
[]
[null,"γ","is the decay constant for each species (equal to zero for a non-decaying species)"]
[]
["Notes:","For the analytical solution to the advection dispersion equation a value of \"NOT SOLVED\" denotes that the value of µ is negative number which happens for certain combinations of inputs. This means that √µ becomes an imaginary number. "]
[null,"The LandSim manual provides an alternative solution to advection dispersion equation when µ is negative but the solution is not implemented here and the numerical results should be used instead."]
[]
["Reference"]
["Environment Agency. 1996.  LandSim. Landfill performance assessment: Simulation by Monte Carlo method. R&D Publication 120.  Release 2.  (LandSim version 2)"]

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["P1",{"$f":"SourceInputsAttenuation!B14","v":"Arsenic"},{"$f":"SourceInputsAttenuation!C14","v":"Decline"}]
["Time (years)","Time (s)","Declining source coefficient (λ)","µ","EXP argument 1","ERFC argument 1","EXP argument 2","ERFC argument 2","C/Cd","C (at edge of attenuation layer)","C (following immediate dilution)","Time (years)"]
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{"sheet":"P2an","index":25,"n_rows":1903,"n_cols":12,"rows_kept":1125,"cut":true,"hidden":false,"merged":[],"bounds":{"rows_first":500,"rows_last":125,"rows_between":500,"halvings":2}}
["P2",{"$f":"SourceInputsAttenuation!B15","v":"Mercury"},{"$f":"SourceInputsAttenuation!C15","v":"Decline"}]
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{"sheet":"P3an","index":26,"n_rows":1903,"n_cols":12,"rows_kept":1125,"cut":true,"hidden":false,"merged":[],"bounds":{"rows_first":500,"rows_last":125,"rows_between":500,"halvings":2}}
["P3",{"$f":"SourceInputsAttenuation!B16","v":"Toluene"},{"$f":"SourceInputsAttenuation!C16","v":"Decline"}]
["Time (years)","Time (s)","Declining source coefficient (λ)","µ","EXP argument 1","ERFC argument 1","EXP argument 2","ERFC argument 2","C/Cd","C (at edge of attenuation layer)","C (following immediate dilution)","Time (years)"]
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{"sheet":"P4an","index":27,"n_rows":1903,"n_cols":12,"rows_kept":1125,"cut":true,"hidden":false,"merged":[],"bounds":{"rows_first":500,"rows_last":125,"rows_between":500,"halvings":2}}
["P4",{"$f":"SourceInputsAttenuation!B17","v":"Cadmium"},{"$f":"SourceInputsAttenuation!C17","v":"Decline"}]
["Time (years)","Time (s)","Declining source coefficient (λ)","µ","EXP argument 1","ERFC argument 1","EXP argument 2","ERFC argument 2","C/Cd","C (at edge of attenuation layer)","C (following immediate dilution)","Time (years)"]
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{"sheet":"P5an","index":28,"n_rows":1903,"n_cols":12,"rows_kept":1125,"cut":true,"hidden":false,"merged":[],"bounds":{"rows_first":500,"rows_last":125,"rows_between":500,"halvings":2}}
["P5",{"$f":"SourceInputsAttenuation!B18","v":"Zinc"},{"$f":"SourceInputsAttenuation!C18","v":"Decline"}]
["Time (years)","Time (s)","Declining source coefficient (λ)","µ","EXP argument 1","ERFC argument 1","EXP argument 2","ERFC argument 2","C/Cd","C (at edge of attenuation layer)","C (following immediate dilution)","Time (years)"]
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{"sheet":"P6an","index":29,"n_rows":1903,"n_cols":12,"rows_kept":1125,"cut":true,"hidden":false,"merged":[],"bounds":{"rows_first":500,"rows_last":125,"rows_between":500,"halvings":2}}
["P6",{"$f":"SourceInputsAttenuation!B19","v":"Copper"},{"$f":"SourceInputsAttenuation!C19","v":"Decline"}]
["Time (years)","Time (s)","Declining source coefficient (λ)","µ","EXP argument 1","ERFC argument 1","EXP argument 2","ERFC argument 2","C/Cd","C (at edge of attenuation layer)","C (following immediate dilution)","Time (years)"]
[0,{"$f":"A3*(60*60*24*365.25)","v":0},null,null,null,null,null,null,null,null,null,0]
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{"sheet":"P7an","index":30,"n_rows":1903,"n_cols":12,"rows_kept":1125,"cut":true,"hidden":false,"merged":[],"bounds":{"rows_first":500,"rows_last":125,"rows_between":500,"halvings":2}}
["P7",{"$f":"SourceInputsAttenuation!B20","v":"Lead"},{"$f":"SourceInputsAttenuation!C20","v":"Decline"}]
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