Kinetics and Rates ofReactionsCEE 373RoadmapSANDBOXModeling concepts,scales and approachesSANDBOXProgramminglanguages, softwareengineering &numerical methodsDESIGNIMPLEMENTATIONExamination ofEquilibrium-basedCodeIMPLEMENTATIONExamination ofReaction Rate-basedCodeIMPLEMENTATIONExamination ofExisting Models forComplex SystemsProject ProposalIMPLEMENTATIONVisualization, InterfaceDesign and UsabilityREADINESSInternal Testing andCode FreezeRELEASEFinal Presentations("Rollout")KINETICS AND RATE LIMITED REACTIONSOBJECTIVES1. Build a modeling framework for reaction rate-limited chemistry.2. Examine and understand computer code.3. Produce model results and interpret critically.KINETICS AND RATE LIMITED REACTIONS1. Rate-Limited Reactions2. Kinetics of Nitrification in a Batch Reactor• Derivation of expressions used in model• Temperature effect on rate constant• Implementation in computer code3. Kinetics of Nitrification in a Column Reactor• Expressions used in model4. Michaelis-Menten Kinetics• Substrate-limited reaction ratesRate-Limited ReactionsSIMPLE IRREVERSIBLE REACTION EXAMPLESFirstA ➞ BZeroA ➞ B € −d[ A]dt= k0 € −d[ A]dt= k1[A] € t1/2=[A]02k0 € [A] = [A]0− k0t € t1/ 2=1k1ln 2 € ln[A][A]0= k1tReaction MechanismsThe Added Complexity of RealityA0A1A2A0A1A2A0A1A0A1A2A0A11A21A12A13A22A23A0A11A21A12A13A22A23CONSECUTIVE IRREVERSIBLE PARALLEL IRREVERSIBLEREVERSIBLE CONSECUTIVE REVERSIBLEPARALLEL CONSECUTIVE PARALLEL CONSECUTIVENitrification KineticsNitrification in a Batch ReactorDERIVATION € NH4+k1,nitrosomonas →     NO2−k2,nitrobacter →    NO3−Pair of irreversible, first order kinetic reactions € d[NH4+]dt= −k1[NH4+] € [NH4+] = [NH4+]0e−k1t € d[NO2−]dt= k1[NH4+] − k2[NO2−] € [NO2−] =k1[NH4+]0k2− k1e−k1t− e−k2t{ } € [NO3−] = [NH4+]0− [NH4+] − [NO2−]First order rate law for step 1Integrated form for step 1First order rate lawexpression for consecutivefirst order stepsIntegrated formfor consecutivestepsMass balance expressionNitrification in a Batch ReactorRELATING TO COMPUTER CODETC = TC + (TB / 10)S = S + 1DA = Exp(-K1 * TC)DB = Exp(-K2 * TC)N1(S) = CA * DAJ = K1 * CA / (K2 - K1)N2(S) = J * (DA - DB)N3(S) = CA - N1(S) - N2(S)K1 = LA * Exp(A * (TA - 20))K2 = LB * Exp(B * (TA - 20)) € [NH4+] = [NH4+]0e−k1t € [NO2−] =k1[NH4+]0k2− k1e−k1t− e−k2t{ } € [NO3−] = [NH4+]0− [NH4+] − [NO2−]Temperature Effect Adjustments € ′ k i= kiea(T −20)20°C Reference StateConstant € where a =EaRT1T2Nitrification in a ColumnNUMERICAL SOLUTIONS (STEADY STATE) € v =QθAVelocity in porous media € x = vtSimple Transport € [NH4+] = [NH4+]0e−′ K 1x € [NO2−] =′ K 1[NH4+]0′ K 2−′ K 1e−′ K 1x− e−′ K 2x{ } € [NO3−] = [NH4+]0− [NH4+] − [NO2−] € where Ki=kiv € ′ K i=′ K iea(T −20)Temperature Effect Adjustmentswhere Q = application rate, v = porewater velocity, θ = volumetric watercontent, A = cross-sectional areawhere x = distance, v = velocity, t = timeReaction MechanismsThe Added Complexity of RealityA0A1A2A0A1A2A0A1A0A1A2A0A11A21A12A13A22A23A0A11A21A12A13A22A23CONSECUTIVE IRREVERSIBLE PARALLEL IRREVERSIBLEREVERSIBLE CONSECUTIVE REVERSIBLEPARALLEL CONSECUTIVE PARALLEL CONSECUTIVEBiologically Controlled ReactionsGrowth, Decay, and BiodegradationMichaelis-Menten KineticsE + S ES P + Ek1k-1kp € µ=µmax[S]Km+ [S]Examples• Biodegradation of pesticides• Algal growthNumeric Types: Visual