Activity corrections for ionization constants in defined media S.A. Smith and S. Chen Department of Biological Systems Engineering, Washington State University, Pullman, WA 99164, USA (E-mail: simon_smith@wsu.edu; chens@wsu.edu) Abstract Correcting ionization constants for activity effects can have a larger impact on some ionic species than correcting for temperature effects. Computer trials compared two pH calculation methods, and showed that an interpolation algorithm found a precise charge balance quickly but was unstable under certain conditions, while a slower pH search method was stable under all test conditions. The optimal calculation strategy was a hybrid of these two approaches. The hybrid calculation method is stable, quick, includes activity and temperature corrections, does not need kinetic rate constants, allows all known ionic species to be included, and allows for easy addition of new chemical species. Keywords Activity correction; ADM1; ASM; ionization constant; pH; pK a ; proton balance; volatile fatty acid Introduction Accurate physico-chemical parameters are important in the Anaerobic Digestion Model 1 (ADM1) because the biological inhibition factors are expressed in terms of chemical species concentration, and physico-chemical parameters are used to link crucial perform- ance measures such as gas flow and carbonate alkalinity (Batstone et al., 2002a). In model- ling acid-base reactions, the ADM1 Task group recommends the charge balance method (Batstone et al., 2002b). The group provides equations for both algebraic and differential equation pH calculations, and suggests a number of simplifications (Batstone et al., 2002b). These simplifications include the assumption that volatile fatty acid ionization constants do not change, as they do not vary appreciably over the anaerobic digestion temperature ranges, and the exclusion of low concentration species such as the carbonate and sulphide ions. One challenge in calculating pH is that the solution method must simultaneously be precise and yet function over a large dynamic range. This difficulty is addressed by a number of researchers: Henze et al. (2000) recommends deriving stoichiometric coeffi- cients based on the bicarbonate rather than the proton system to avoid this problem in the Activated Sludge Model 3C. A broader approach was used by Loewenthal et al. (1991) who proposed using alkalinity as the reference species because this varies monotonically with pH. These difficulties posed by reference species selection and the simultaneous solution of multiple weak acid/base equilibrium state equations prompted Musvoto et al. (2000) to develop a kinetic-based approach. This paper discusses an alternative approach that does not require kinetic rate constants. One of the key insights of ADM1 is the need to correct for the effects of temperature on physico-chemical parameters, and Batstone et al. (2002b) recommend the van’t Hoff equation to compensate for these changes. The van’t Hoff equation was recommended because of its fundamental basis in chemistry and because it is effective in the tempera- ture range of 0–60 8C for seven of the parameters listed in ADM1 (Batstone et al., 2002b). An alternative to the van’t Hoff equation is to fit a polynomial to the reported Water Science & Technology Vol 54 No 4 pp 21–29 Q IWA Publishing 2006 21 doi: 10.2166/wst.2006.522 Downloaded from http://iwaponline.com/wst/article-pdf/54/4/21/431761/21.pdf by guest on 02 November 2023