Modeling Acid Rain Formation and Atmospheric Deposition (2)

Modeling S(IV) oxidation in cloud SO 2 H 2 SO 3 HSO 3 - SO 3 2- SO 4 2- Chemical Equilibrium O 3, H 2 O 2, O 2 (Fe 3+,Mn 2+ ) H2O2H2O2 O3O3 Chemical Reaction Kinetics Partitioning (gas phase) (aqueous phase)

Modeling S(IV) oxidation in cloud Chemical equilibrium is usually fast so concentration of aqueous phase species quickly adjusted to obey equilibrium relationships Phase partitioning is usually fast too. However, subsequent diffusion process in the cloud/fog droplet can be slow and led to non-uniform distribution of these species. We will ignore this diffusion limitation in our simple analysis.

Modeling S(IV) oxidation in cloud Approach for numerical modeling Phase & Chemical Equilibrium Calculation of Reaction Rates Update Species Concentrations for Time step Δt Calculate S(IV) species concentrations Calculate d[S(IV)]/dt due to different pathways Update S(IV) and S(VI) concentrations General Approach Acid rain formation

Review of Chemical Kinetics Modeling To solve an ODE system in MATLAB: (1) Define a function for the ODE system: (2) Use the ODE solver ode15s for stiff system:

For the S(IV) oxidation problem The structure of the ODE function we defined should be function dc=s4tos6oxidation(t,c) Species: c(1) – total of S(IV) species; c(2) – total of S(VI) species s1=chem_speciation(c); % call a function to do speciation dc=s4rates(s1); % call a function to calculate the rates % dc(1) is dc1/dt, dc(2) is dc2/dt end

Modeling S(IV) oxidation in cloud Equilibrium partitioning K H,SO2 =1.25 M atm -1 K a1 =1.29x10 -2 K a2 =6.25x10 -8 K w =1x In this example, we will consider this as a closed system. SO 2 concentration is not a constant but decreases as some SO 2 partitions into the aqueous phase. The total S(IV) concentration is: C S(VI),TOT = C SO2,gas + C H2SO3 + C HSO3 + C SO3 Note that consistent units are needed for the gas, aqueous and total concentration.

Modeling S(IV) oxidation in cloud Unit conversion issue – Gas phase concentration is in atm – Aqueous phase concentration is in mol/L of water Liquid water content (LWC) – Mass of liquid water in a specific volume of air – Typical LWC ranges from g/m3 of air mol/L mol/m3m3/gg/L

Example Total SO2 concentration is 20 µg m -3. The LWC is 1 g/m3. What is the total concentration in mol/L? Water density is 1000 g/L.

Modified Henry’s Law Equation From We can get Define

Review Chemical Equilibrium Modeling using the Tableau Method Define the system, find all species Choose components Express concentrations of all species as a function of components Find the Tableau matrix A; vector logK; Solve using iterative N-R method

Modeling S(IV) oxidation in cloud Solve the problem using the Tableau method Components SpeciesSO2(g)H+logK H2SO3(aq)10log(KH') HSO3-1log(Ka1KH’) SO32-1-2log(Ka1Ka2KH’) OH-0log(Kw) SO2(g)100 H+010

Example

Add another partitioning species in the calculation Add H2O2, for example Components SpeciesSO2(g)H2O2(g)H+logK H2SO3(aq)100log(KH') HSO3-10log(KH'Ka1) SO log(KH'Ka1Ka2) OH-00log(Kw) H2O2(aq)010log(KH_H2O2') SO2(g)1000 H2O2(g)0100 H+0010

Calculating Reaction Rates Aqueous oxidation of S(IV) into S(VI) – due to H2O2

MATLAB function for reaction rates

Speciation function

Putting these together Create the function dc=s4tos6oxidation(t,c) Solve the following system for 10 hours – Initial SO2 = 10 ppb, H2O2=0.1 ppb; cloud forms with LWC=0.1; Temperature=298K

MATLAB function

Script to solve the example problem Convert ppb to atm [S(VI)]=0 initially Y is total concentration in mol/L This returns concentration in mol/L or atm.

Script to solve the example problem % plot concentrations subplot(2,2,1); plot(T,-log10(spec(:,8)),'-o'); xlabel('Time (s)'); ylabel('pH'); subplot(2,2,2); semilogy(T,spec(:,2),'-o',T,Y(:,2),'-*'); legend('[HSO_3^-]','[SO_4^{2-}]') xlabel('Time (s)'); ylabel('Conc (mol/L)'); subplot(2,2,3); plot(T,spec(:,6)*1e9,'-o'); xlabel('Time (s)'); ylabel('SO_2 (ppb)'); subplot(2,2,4); plot(T,spec(:,7)*1e9,'-o'); xlabel('Time (s)'); ylabel('H_2O_2 (ppb)'); S(VI), assume entirely in SO 4 2-

Results