for the calculations. In the case of [HCO3], only theKavalue of HCO3(KaHCO3) and theKavalue of CO2orFigure 1.Schematic of the BF. The five horizontal sections,z,represent the divisions of the BF in the model. Air is humidifiedbefore it enters the channel below the filter and is conducted throughthe filter. At the same time, the BF is irrigated from above at regularintervals to keep the BF moist. Leca pellets are used as the carriermaterial.Figure 2.Structure of the model developed.Nielsen et al.Volume 59February 2009Journal of the Air & Waste Management Association157Downloaded by [University of California, San Diego] at 07:10 08 October 2015
H2CO3*(KaH2CO3*) are used. The principle of the calcula-tions can be exemplified by calculating [HCO3] fromTIC:HCO3TIC1HKaH2CO3*KaHCO3H(5)pH AlgorithmThe individual concentrations of HCO3(eq 5) and otherions are used in the charge balance equation for calculat-ing pH in the aqueous phase. The charge balance equa-tion (eq 6) consists of all charged ions accounted for inthe model as well as the parameter [Z ], which is the totalconcentration of ions such as calcium (Ca2), potassium(K ), sodium (Na ), chloride (Cl ) etc., adjusted so thatthe charge balance is zero at the initial condition beforethe simulations begin:HOHHCO32CO32NH4NO2ZHS2SO42CH3SCH3NH30(6)The concentration of ions and compounds in equi-libria are used to model oxidation kinetics in the BF, masstransfer, and pH.When changes in the concentration of compoundsoccur as a consequence of mass transfer, water move-ment, air movement, and oxidation processes, the chargebalance still needs to be zero. This is used to find pH.Equation 6 is solved to find a [H ] that ensures the chargebalance is always zero.This is done iteratively using the Newton–Raphsonprocedure to find approximations ofxn1in:xn1xnf xnf xn(7)In eq 7,f(xn) is the derivate off(xn) with respect toxnor[H ]. Equation 7 (shortened version), as implemented inthe model of the BF, is:xn1xnNH4NH4TIC/ 1xnKaH2CO3*KaHCO3xnTICKaH2CO3*xn2KaH2CO3*KaHCO3xn2KaH2CO3*xnKaH2CO3*KaHCO32· · ·)(8)The inaccuracy in the calculation of [H ] only usingthe Newton–Raphson procedure twice is less than 1017,when the firstxnis the [H ] from the previous iteration.When the Newton–Raphson procedure has been runthrough twice, in the second round usingx1to replacexnorx0in eq 8, [H ] is assigned the value ofx2and theprocedure stops.TheKLaand the Two-Film TheoryIt is assumed that the mass-transfer rate or flux (F) be-tween air and water can be described from the gradientbetween the concentration of the compound in the airCi,(g), calculated from Henry’s law constant of the gas inquestion (Hi, molatm1), the partial pressure of the gas(pi, atm), and the concentration in the aqueous phasemultiplied by aKLa(the specific surface area, m2m3, notincluded):FKL(HipiCi,aq).