and species is particularly important, because its material balance can be formulated purely in terms pH

Overview

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Key numbers

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Part 5: Ionic speciation
WASH R&D Centre, School of Engineering, University of KwaZulu-Natal, Durban 4041, South Africa
Water Research Group, Department of Civil Engineering, University of Cape Town, Rondebosch 7700, South Africa
of a plant-wide wastewater treatment model as an example. Received: 3 July 2019
explained in Part 1 (Brouckaert et al., 2021a), the overall model is divided into a kinetically controlled computational efficiency
calculation involves algebraic equations only. Commons Attribution 4.0
Aqueous ionic speciation models such as MINTEQA2 (Allison et al., 2009) and PHREEQC (Parkhurst
to the scope of each biochemical model to reduce the computational burden. Lizzaralde et al. (2014)
model used in the anaerobic digestion model of Brouckaert et al. (2010). Only acid/base and ion-
ISSN (online) 1816-7950 32
(Loewenthal et al., 1994). Additionally, sodium, potassium, of measurable quantities. However, this apparent advantage is
municipal wastewaters. The ionic model therefore has 12 ionic up from pure chemicals. Measurements on wastewater samples
components for the mass balances: H+, Na+, K+, Ca2+, Mg2+, NH4+, very seldom cover all the ions present, and, even when they
Cl−, Ac−, Pr−, CO32−, SO42− and PO43−. Sulphide, NO2−, NO3− and do, measurement errors upset the charge balance. The solution
iron (Fe2+, Fe3+) were not included in this the model, as partial state is very sensitive to the H+ concentration, so the measured
components (HS−, NO2−, NO3−, Fe2+, Fe3+, Al3+), but more than composition measurements.
The concentrations of the 42 ionic species are related to the
The source of information was the minteq.v4.dat database concentrations of the 12 components by a set of 12 stoichiometric
distributed with PHREEQC. PHREEQC automatically includes all balances, together with a set of 30 equilibrium relationships which
(5, 7 and 9). Species were selected that contributed at least 2% to
the inventory of any component in at least one of the model runs. In Eq. 1 the square brackets indicate molal concentrations, italics
So, for example, the species NaHCO3 had to amount to at least indicate species, and Roman typeface indicates a component.
2% of the total Na+, H+ or CO32− in at least one of the simulated (Pr−) is also referred to as a total concentration, as it is the sum of
solutions. The 42 ionic species that were selected in this way were: the concentrations of all species present that include Pr−.
MgHCO3+, H2PO4−, MgPO4−, CaPO4−, MgHPO4, CaHPO4, CaSO4, from more than one component (e.g. HPr, CaPr+). Take HPr, for
MgSO4, CaOH+, MgOH+, NH4SO4−, NaHPO4−, NaCO3−, NaHCO3, example. Its entry in Table 1 corresponds to the formation reaction
MgH2PO4+, CaAc+, NaAc, MgAc+, CaPr+, MgPr+ and NaSO4−, H+ + Pr− → HPr, with the corresponding equilibrium relationship:
where the last 24 in the list are often referred to as ion pairs. Note {HPr } K H Pr {H } {Pr } (2)
to distinguish them from components. In Eq. 2, {…} indicates the activity of the species, and KHPr is an
Table 1 presents the reaction scheme in a form known as a tableau, equilibrium constant, which is a function of temperature only,
matrix contains the stoichiometric coefficients for the formation Table 1.
at 25°C or 298.15°K (obtained from the minteq.v4.dat database).
linear equations. Whether this level of complexity is really required {Pr } Pr (Pr ) (4)
a great deal of investigation to answer fully. If alkalinity and pH Equation 4 can be dimensionally confusing, since {Pr−} and γPr are
to the ion pairs (Solon et al., 2015). As will be discussed in the next {i } i (i )( io)
which is defined so that (iO) = 1 mol/kg for all species i. This
al., 2015) prefer a different formulation of the set of speciation (e.g. KHPr in Eq. 2). By convention (iO) = 1, whatever concentration
equations, in which H+ in the tableau is replaced by the charge units are used, so the form of Eq. 4 remains the same if the units
Table 1. Tableau representation of the Brouckaert et al. (2010) speciation model
CaSO4 1 1 2.36 7 100
NaSO4- 1 1 0.73 1 000
0. 3 I (5) variables. Since this happens only once at the beginning of a

Methods (brief)

model used in the anaerobic digestion model of Brouckaert et al. (2010). Only acid/base and ion-
close to equilibrium. These were represented in the anaerobic digestion model as rate-controlled
anaerobic digestion model. An anaerobic digester typically includes the carbonate, phosphate,
municipal wastewaters. The ionic model therefore has 12 ionic up from pure chemicals. Measurements on wastewater samples
an approximation in the anaerobic digestion model, and dosing of further considerations have to be used to establish an appropriate
the anaerobic digestion model might be expected to encounter
for the anaerobic digestion model is a question that would require
solution obtained at the previous time step provides an excellent A typical set of measurements on a wastewater sample will not
appropriately included in the kinetically limited sub-model. anaerobic digestion model. Proceedings 12th IWA Anaerobic
In setting up an equilibrium speciation sub-model, modellers Digestion Conference (AD12), Guadalajara, Mexico, 1–4 Nov 2010.
KwaZulu-Natal Anaerobic Digestion Model (1994) Modelling struvite precipitation in anaerobic treatment
{i} activity of species i, dimensionless anaerobic digestion. Water Res. 70 235–245. https://doi.org/10.1016/j.
The anaerobic digestion model of Brouckaert et al. (2010) whereas PCO2 is calculated from the gas phase mass balance. The

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Update history

The five most recent substantive edits to this page, classified major (evidence or structure moved), correction (a published value or statement was wrong and has been fixed), or minor (narrative rewritten without changing the underlying evidence). Each description is derived from what the edit did to this page; the linked commit is the authoritative record, routine regeneration passes are excluded, and the full version history lives in git. When DOI minting comes online (see schema docs), each entry below will also link to a version-pinned DataCite DOI.

Commit	Date	Change	Description
3171d06	2026-08-02	major	1 section added
bc84bfc	2026-08-02	major	6 sections added; narrative text revised