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Stanford CEE 373 - Ion Activity, Ion Association and Solubility

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Ion Activity, IonAssociation and SolubilityCEE 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")EQUILIBRIUM THERMODYNAMICSOBJECTIVES1. Build a modeling framework for equilibriumchemistry2. Examine and understand computer code.3. Produce model results and interpret critically.EQUILIBRIUM THERMODYNAMICS1. Ion activity• Review of general expressions• Activity coefficient calculations• Implementation in computer code2. Ion pairing• Calculation of ion pairing• Implementation in computer code• Calculation of CaSO40 formation3. Solubility• Saturation Index (SI)• Interpretation of SI results• Model calculations (Wateq4f, Visual Minteq)Equilibrium State and Ion ActivityA QUICK REVIEW OF RELEVANT EXPRESSIONS€ Activity, ai= miγi€ Ionic Strength, I =12mizi2i∑€ Generalized chemical reaction : aA + bB ⇔ cC + dD€ Keq=aCaDaAaB=mCγCmDγDmAγAmBγB€ Mean activity coefficient, γ±=γ+γ−Equilibrium State and Ion ActivityA QUICK REVIEW OF RELEVANT EXPRESSIONSEquilibrium State and Ion ActivityA QUICK REVIEW OF ACTIVITY COEFFICIENT FORMULAE€ logγi= −Azi2I1+ Bå I€ logγi=−Azi2I1+ I+ 0.3Azi2I€ logγi=−Azi2I1+ BåiI+˙ B IExtended Debye-Hückel EquationLow ionic strength (I<10-1 M)Davies EquationLow ionic strength (I<0.5 M)B-dot EquationDesigned for NaCl solutions€ logγi= −0.5zi2IDebye-Hückel Limiting LawVery low ionic strength (I<10-2.3 M)Equilibrium State and Ion ActivityIMPLEMENTATION IN CODE€ logγi=−Azi2I1+ I+ 0.3Azi2IDavies EquationLow ionic strength (I< 10-5 M)C********************** ENTRY IONCOR(XMU) NC=NN(1)+NN(2)+NN(3)+NN(4)+NN(5)+NN(6) NX=NNNCC The A-factor in ACTCOF calculation is obtainedC using a regression fit of Helgeson/C Kirkham data 25-225 deg and Harned/OwenC data below 25 TO 0.C DT=TEMP-25. AFACTR=0.50886+0.0008*DT+0.00001*DT*DT ET=-AFACTR XIS=SQRT (XMU) GF(1)=ET*(XIS/(1.0+XIS)-0.3*XMU) DO 2100 IZ=1,5 GF(IZ)=GF(1)*IZ*IZ ACTCOF(IZ)=10.**GF(IZ) 2100 CONTINUEFromHYDRAQL.FOREquilibrium State and Ion ActivityIMPLEMENTATION IN CODEC CALCULATE ACTIVITY COEFFICIENTS AMU=-A*MUHALF BMU=B*MUHALF CMU=-A*(MUHALF/(1.0D0+MUHALF)-0.3D0*MU) ZCHRG=0.1D0*MU LG(1)=AMU/(1.0D0+DHA(1)*BMU) IF (IOPT(6).EQ.1) LG(1)=CMU LG(2)=0.0D0 LG(3)=0.0D0 DO 70 I=4,LASTS IF (SFLAG(I).EQ.0) GO TO 70 IF (DABS(ZSP(I)).LT.1.0D-40) GO TO 40 IF (GFLAG(I).EQ.1) GO TO 50 IF (DHA(I).LE.0.0D0) GOTO 60 IF (IOPT(6).EQ.1) GO TO 60C EXTENDED DEBYE-HUCKEL WITH ION SIZE PARAMETER LG(I)=AMU*ZSP(I)*ZSP(I)/(1.0D0+DHA(I)*BMU) GO TO 65C GAMMA FOR UNCHARGED SPECIES 40 LG(I)=ZCHRG GO TO 65C WATEQ DEBYE-HUCKEL 50 LG(I)=AMU*ZSP(I)*ZSP(I)/(1.0D0+ADHSP(I,1)*BMU)+ADHSP(I,2)*MU GO TO 65C DAVIES GAMMA 60 LG(I)=CMU*ZSP(I)*ZSP(I) 65 CONTINUE IF(LG(I).LT.-1.0D1) LG(I)=-1.0D1 IF(LG(I).GT.1.0D1) LG(I)=1.0D1 70 CONTINUE RETURNFromphreeqe.fRevision 1.14(1993)Generalized Steps forComputational Solution1. Compose a balanced chemical reaction. If more thanone reaction occurs simultaneously, write a reactionfor each.2. Invoke Law of Mass Action and write equilibriumconstant expression(s), and relate to numeric valuesof Keq.3. Produce other pertinent expressions such as massbalance and charge balance. Need to have as manyrelations as unknowns.4. Solve algebraically. Typically, successiveapproximations are needed to converge on a value.Application to Ion Pairing€ CaSO40⇔ Ca2++ SO42−CaSO40 in 0.01M CaSO4 SolutionCa2+SO42-Private Sub Command1_Click()pKCaSO4 = -2.274IPFC = 10 ^ pKCaSO4tolerance = 0.01maxIterations = 30loops = 0oldIS = 0conc = Val(Text1.Text)CaTot = concSO4Tot = concCa = CaTot * 0.5SO4 = SO4Tot * 0.5electron = 2 * (CaTot - SO4Tot)IonStrength = (2 * (Ca + SO4)) + (0.5 * electron)DooldIS = IonStrengthloops = loops + 1RootIS = Sqr(IonStrength)Gamma2 = 10 ^ (-1 * (2 * (RootIS / (1 + RootIS) - 0.3 * IonStrength)))IPCaSO4 = Gamma2 * Gamma2 * Ca * SO4 / IPFCCa = CaTot - IPCaSO4SO4 = SO4Tot - IPCaSO4IonStrength = (2 * (Ca + SO4)) + (0.5 * electron)ChangeIS = Abs(IonStrength - oldIS)Loop While (ChangeIS > tolerance) Or (loops < maxIterations)ActCa = Ca * Gamma2Text2.Text = "{Ca2+} = " & ActCaEnd SubSolubility CalculationsSolubility Product, KspIon Activity Product, IAPSaturation Index, SISolubility ReactionRelationship to equilibriumconstantProduct of free ion speciesactivitiesSI = log (IAP/Ksp)Solid phase, dissociated speciesSolubility CalculationsIf IAP>Ksp, then SI is +ve. Mineral precipitates.If IAP=Ksp, then SI is zero. Mineral equilibrium with solution.How do you interpret saturation indices?• Possibility vs Reality• Ideal Equilibrium vs Local Equilibrium• Supersaturation - why would it occur?If IAP<Ksp, then SI is -ve. Mineral dissolves.€ SI = logIAPKspSolubility CalculationsVadose Cave ("Ceiling Leaks") Water ExampleSolubility Calculations• What do the modeling results tell you about thechemistry in the cave?• What would you need to know to make a soundinterpretation of the results?Vadose Cave ("Ceiling Leaks") Water ExampleT (°C) = 12 pH = 7.56 DO (ppm) = 6.8Concentrations (mg/l)Ca = 92Mg = 24.9Na = 1.6Sr = 0.02Cl = 6.0SO4 = 0.4HCO3 = 366.0SiO2 = 8.0Numeric Types: Visual


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Stanford CEE 373 - Ion Activity, Ion Association and Solubility

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