In the case of HCO 3 only the K a value of HCO 3 K a HCO 3 and the K a value of

In the case of hco 3 only the k a value of hco 3 k a

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for the calculations. In the case of [HCO 3 ], only the K a value of HCO 3 ( K a HCO 3 ) and the K a value of CO 2 or Figure 1. Schematic of the BF. The five horizontal sections, z , represent the divisions of the BF in the model. Air is humidified before it enters the channel below the filter and is conducted through the filter. At the same time, the BF is irrigated from above at regular intervals to keep the BF moist. Leca pellets are used as the carrier material. Figure 2. Structure of the model developed. Nielsen et al. Volume 59 February 2009 Journal of the Air & Waste Management Association 157 Downloaded by [University of California, San Diego] at 07:10 08 October 2015
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H 2 CO 3 * ( K a H 2 CO 3* ) are used. The principle of the calcula- tions can be exemplified by calculating [HCO 3 ] from TIC: HCO 3 TIC 1 H K a H 2 CO 3 * K a HCO 3 H (5) pH Algorithm The individual concentrations of HCO 3 (eq 5) and other ions 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 in the model as well as the parameter [Z ], which is the total concentration of ions such as calcium (Ca 2 ), potassium (K ), sodium (Na ), chloride (Cl ) etc., adjusted so that the charge balance is zero at the initial condition before the simulations begin: H OH HCO 3 2 CO 3 2 NH 4 NO 2 Z HS 2 SO 4 2 CH 3 S CH 3 NH 3 0 (6) The concentration of ions and compounds in equi- libria are used to model oxidation kinetics in the BF, mass transfer, and pH. When changes in the concentration of compounds occur as a consequence of mass transfer, water move- ment, air movement, and oxidation processes, the charge balance still needs to be zero. This is used to find pH. Equation 6 is solved to find a [H ] that ensures the charge balance is always zero. This is done iteratively using the Newton–Raphson procedure to find approximations of x n 1 in: x n 1 x n f x n f x n (7) In eq 7, f ( x n ) is the derivate of f ( x n ) with respect to x n or [H ]. Equation 7 (shortened version), as implemented in the model of the BF, is: x n 1 x n NH 4 NH 4 TIC/ 1 x n K a H 2 CO 3 * K a HCO 3 x n TIC K a H 2 CO 3 * x n 2 K a H 2 CO 3 * K a HCO 3 x n 2 K a H 2 CO 3 * x n K a H 2 CO 3 * K a HCO 3 2 · · ·) (8) The inaccuracy in the calculation of [H ] only using the Newton–Raphson procedure twice is less than 10 17 , when the first x n is the [H ] from the previous iteration. When the Newton–Raphson procedure has been run through twice, in the second round using x 1 to replace x n or x 0 in eq 8, [H ] is assigned the value of x 2 and the procedure stops. The K L a and the Two-Film Theory It is assumed that the mass-transfer rate or flux ( F ) be- tween air and water can be described from the gradient between the concentration of the compound in the air C i,(g) , calculated from Henry’s law constant of the gas in question ( H i , mol atm 1 ), the partial pressure of the gas ( p i , atm), and the concentration in the aqueous phase multiplied by a K L a (the specific surface area, m 2 m 3 , not included): F K L ( H i p i C i,aq ).
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