Introducton to geochemcal modelng Prof. Dr. Broder J. Merkel Char of Hydrogeology Technsche Unverstät Bergakademe Freberg Germany What determnes the dstrbuton of aquatc speces? Interactons of aquatc speces among themselves (complexaton, redox reactons) of aquatc speces wth gases of aquatc speces wth mneral phases (dssoluton / precptaton, sorpton) Transport processes Decay processes (bologcal degradaton, radoactve decay) 1
What determnes the dstrbuton of aquatc speces? Defnton of chemcal reactons thermodynamcal approach mass acton law (MAL) Gbbs free energy knetc approach 2
mass acton law aa + bb cc + dd K c d {} C {} D a { A} { B} b mass acton law aa + bb cc + dd cc + dd aa + bb K c d {} C {} D a { A} { B} b a b K* { A} { B} 1 c d {} C {} D K 3
Gbbs free energy G H S 0 * T G Gbbs free energy H enthalpy S 0 entropy T temperature Gbbs free energy G 0 G + R T ln c d {} C {} D a { A} { B} b R general gas constant (8.315 J/Kmol) G 0 standard Gbbs free energy at 25 C and 100 kpa 4
actvty / concentraton Ionc strenght ( I mol/l ) a f c f onspecfc correcton, < 1 (.e. a < c) I 0.5 m z 2 wth m molalty of a speces z valence of a speces Relatonshp onc strength and actvtycoeffcent f 0.66 5
Ion dssocaton theory Debye-Hückel-equaton 2 log(f ) A z I I < 0.005 mol/kg z valence, A temp.dependng parameter extended Debye-Hückel-equaton A z I log(f ) I < 1 + B a I 2 0.1 mol/kg B temp.dependng param., a on spec. param. (dependng on on radus) Güntelberg-equaton 2 I log(f ) 0.5z I < 0.1 mol/kg 1 + 1,4 I Ion dssocaton theory Daves-equaton 2 I log(f ) A z ( 1+ I - 0.3I) I < 0.5mol/kg WATQ-Debye-Hückel-equaton 2 A z I log(f ) + b I I < 1mol/kg 1 + B a I A, B temp.dependng param., a on spec. param. (dependng on on radus) Ion dssocaton theory ends at 1 mol/kg at the latest! 6
Specfc Ion Interacton (SIP) model at onc strengths > 1 mol/l (e.g. Ptzer equaton) Ionc strenght mol/l Actvty coeffcent Specff Ion Interacton (SIP) theory onc strenghts > 1 mol/kg e.g. salne waters For comparson: 1 kg water ~ 55.3 mol water Ptzer-equaton Debye-Hückel-equaton + Vral equaton 7
Comparson on dssocaton vs specfc on nteracton (SIP Ptzer) theory 1 actvty coeffcent 0.8 0.6 0.4 0.2 0 Ptzer DebyeHückel DebyeHückelx ext.debyehückel ext.debyehückelx Güntelberg Güntelbergx Daves Davesx WATQ WATQx Na + 0.001 0.01 0.1 1 10 onc strength [mol/kg] What determnes the dstrbuton of aquatc speces? Interactons of aquatc speces among themselves (complexaton, redox reactons) of aquatc speces wth gases of aquatc speces wth mneral phases (dssoluton / precptaton, sorpton) Transport processes Decay processes (bologcal degradaton, radoactve decay) 8
Dssoluton / Precptaton AB A + K { A} { B} { AB} B snce {AB} sold phase 1 Ion actvty product IAP {A} {B} Dependency of the on actvty product temperature partal pressure ph H complex formaton / complex destructon 9
Saturaton Index SI SI log(iap) - log (K) log (IAP/K) IAP > K IAP/K > 1 IAP < K IAP/K < 1 Defnes whether a water s over- or under saturated wth respect to a certan mneral Saturaton Index SI SI > 0? Water s super saturated wth respect to a certan mneral. Wll the mneral precptate? Not necessarly, depends on knetcs and boundary condtons SI < 0? Water s under saturated wth respect to certan mneral Wll the mneral dssolve? yes, but dssoluton mght be very slowly 10
Autoprotolyss of water H 2 O H + + OH K w + { H }{ OH } { H O} 2 + K W {H } {OH } 10 14 SATP Standard Ambent Temperature and Pressure ph-value neutral: {H + } {OH - }.e. K W {H + } {OH - } {H + } 2 10-14 resp. {H + } 10-7 snce ph -log {H + } -log 10-7 7 ph < 7 acd ph > 7 alkalne 11
What determnes the dstrbuton of aquatc speces? Interactons of aquatc speces among themselves (complexaton, redox reactons) of aquatc speces wth gases of aquatc speces wth mneral phases (dssoluton / precptaton, sorpton) Transport processes Decay processes (bologcal degradaton, radoactve decay) Henry-Law c K H p xample Ntrogen N 2 : p(n 2 ) 0.78 bar, Henry constant 6.40. 10-6 mol/(kg. kpa) at 25 C c 6.40. 10-6 mol/kg/kpa 0.78 10 2 kpa 0.5 mmol/kg c 0.5 mmol/kg 2 14 mg/mmol 14 mg/kg temperature [ C] 0 10 25 35 50 Henry-const. N 2 [ 10-6 mol/kg/kpa] 10.5 8.3 6.4 5.6 4.85 conc. mg/l 22.9 18.1 14.0 12.2 10.6 12
Henry-Law xample Carbon-Doxde CO 2 Henry constant 3.34 10-2 mol/kg/bar at 25 C (log K H -1.468) 3 Vol% CO 2 n sol gas (0.03 bar) c 10 1.468 0.03 bar c 1 mmol/kg 44 mg/kg CO 2 rght? CO 2(g) CO 2(aq) CO 2(aq) + H 2 O HCO 3- + H + Ca 2+ + HCO - 3 CaHCO + 3 CO 2-3 + H + HCO - 3 CaCO 3(s) Ca 2+ + CO 2-3 etc. open closed systems open system closed system CO 2 CO 2 CO 2 Wasser Calct Wasser Calct 13
What determnes the dstrbuton of aquatc speces? Interactons of aquatc speces among themselves (complexaton, redox reactons) of aquatc speces wth gases of aquatc speces wth mneral phases (dssoluton / precptaton, sorpton) Transport processes Decay processes (bologcal degradaton, radoactve decay) Redox potental - H -value [oxdzed speces] + n[e ] [reduced speces] H 0 + R T [ox] ln n F [red] 0 normal redox potental (V) R general gas constant (8.315 J/K mol) T absolute temperature (K) n number of transfered electrons (e) F FARADAY-constant (96484 C/mol J/V mol) [ox] actvty of oxdzed partners [red] actvty of reduced partners 14
15 Redox potental at standard condtons 25 C [ox] [red] log n 0.0591 0 H [red] [ox] ln F n T R 0 H + [ox] [red] log F n T R 2.303 0 H NRNST-potental Redox potental of ph-dependng reactons [ox] [red] log F n T R 2.303 ph F n T R m 2.303 0 H [ox] [red] log F n T R 2.303 0 H
Redox potental n dependency of temperature H M 0.198 (T 25 C) Potental varatons at ph-varatons of 1 ph-unt -59.1 mv be 25 C -58.2 mv be 20 C -56.4 mv be 10 C -54.2 mv be 0 p - concept [oxdzed speces] + n[e ] [reduced speces] log K log [red] [ox] [e - ] n [red] 1 log K log + log n [ox] [e ] log K - log[e ] - [red] log [ox] - n log[e 1 1 [red] logk - log n n [ox] ] - n p - [red] log[e ] logk - log [ox] 1 n log K 1 n log [red] [ox] 16
Transformaton pe - H - p - log[e ] F 2.303R T H at standard condtons (25 C) approxmately: p 16.9 H H n Volt measured whth H 2 - probe! at ph 7... 8: Ranges of H n natural groundwater -400 mv to +800 mv 400... 800 oxdzed condtons 0... 400 partly reduced condtons -400... 0 reduced condtons 17
pe-ph-dagram ron (predomnance-dagram) Vald for: The system Fe-H + -OH - Certan onc strenght Certan temeperature Certan ron concentraton 18