Adaptation de la mesure potentiométrique à l'estimation en continu de la teneur en cuivre de solutions aqueuses présentant de fortes variations physico-chimiques Adaptation of potentiometric measurements to continuous estimation of copper in aqueous solutions with fluctuating physicochemical parameters

Résumé

La mesure en continu, sans prélèvement et sous conditions physico-chimiques variables, de la teneur en cuivre d'une solution aqueuse, constitue le cadre de ce travail. La méthode d'estimation proposée est basée sur la potentiométrie sélective à l'aide d'une électrode spécifique au cuivre. Le comportement de l'électrode est modélisé par une loi non linéaire s'inspirant de la relation de Nernst généralisée. Le modèle intègre les paramètres température, conductivité et pH de la solution. Il rend possible une estimation de la concentration totale de cuivre même en présence de complexations hydroxyles. La phase de modélisation est présentée en détail. Les performances de l'estimateur sont évaluées puis discutées.

Mots-clés:

• Contrôle de la qualité de l'eau,
• pollution par le cuivre,
• électrode sélective

Abstract

Ion Selective electrodes (ISEs) offer an attractive solution for continuously evaluating the content of certain ionic species in aqueous media. Manufacturers propose a wide range of electrodes specific to heavy metals (Cu²⁺, Pb²⁺ …). Because they eliminate the need for sampling, are of reasonable size and have few electronic parts, ISEs seem highly appropriate for continuous monitoring in urban purification systems. Measurements obtained by these sensors in controlled media in the laboratory are usually precise, reliable and reproducible. However, it is not so with complex and uncontrolled media. This work falls within the general scope of the continuous measurement of heavy metals in wastewater. More particularly, it is devoted to the description of the behaviour of a copper-selective electrode (ISE_Cu) in a medium presenting wide physicochemical variations.

Experimental set-up

In order to study ISE behaviour, we developed an experimental platform that allowed us to reproduce in a reactor the physicochemical variations observed in wastewater, particularly with regards to salinity and acidity. The reactor was fitted with a measuring set consisting of five electrodes that measured the following parameters: pH (ref. integrated Ag/Agcl), redox (red), ISE^Cu (E^Cu), temperature (T) and conductivity (s). A computer system carried out the acquisition of the five signals with a 10-second sampling period. The species concentration in the reactor was determined by calculating the weight of the solutions extracted from or injected into the reactor. Controlling the temperature of the system was undertaken using a cryostat. Sequential tests allowed the pH, redox potential and conductivity of the medium to be varied and were carried out by successive injections of different chemical products. The response times of the conductivity probe and of the pH and redox electrodes are shown here; the short response time of the sensors (20 to 30 s) and the strong correlation between the measured pH and redox are noted.

ISE modelling

The model used to explain the ISE response is based on a generalization of Nernst's Law that takes into account the temperature and the activity of the free ions (Cu2+). Taking into consideration chemical equilibria and mass equations allowed us to link the activity of the free copper ions to the total injected copper concentration |Cu²⁺|_tot and to the pH. Redox, strongly correlated to pH, was ignored in the mathematical model. Since hydroxyl complexation is the major complexation reaction (compared to other copper-binding ligands), the potential measured with the ISE took the following form:

E_Cu=b₀+b₁T.log[(ϒ₂|Cu²⁺|_tot) / (1+b₂ϒ₂10^pH+b₃ϒ₂10^2pH) + b₄]

The activity coefficient ϒ2 of the Cu2+ ions was calculated from the ionic strength (I) of the solution, using the Debye-Hückel approximation. Ionic strength was derived from conductivity corrected to 25 °C. In wastewater, the ranges of the physicochemical parameters were as follows: T from 5 to 35°C; pH from 4 to 9; Omega from 500 to 2000 mS/cm; redox from 400 to -400 mV/ENH; and copper concentrations 10^-3 mol/dm³.

In order to identify the bi coefficients of the model, we established an experimental plan comprising 108 measurement points that covered, with a minimal number of experiments, the ranges of variations of the parameters of influence. A dispersion diagram of measured and modelled values gave a linear adjustment coefficient close to 0.99 and a standard deviation of 8.8 mV, which corresponds to a 0.34 decadal standard error in the concentration estimate. With a temperature of 25 °C, the model has a sensitivity of -26.4 mV/decade, very close to the theoretical slope of an electrode sensitive to divalent ions.

ISE measurement of the copper concentration with large pH variations

pH is the parameter which exerts the greatest influence on ISE response, which is why tests simulating copper pollution with large variations of pH were carried out. These tests enabled us to evaluate the performances of the model in terms of the estimation of copper content. Four solutions of total copper concentration equal to 10^-6, 10^-5, 10^-4, 10^-3 mol/dm³ respectively, were used. Their temperature was 25 °C and their conductivity was fixed at approximately 500 mS/cm. We varied the pH of each solution between 4 and 10. For the four tests, we show the estimate of the copper concentration obtained with our model starting from the potential measured by the ISE.

In the case of strong copper pollution (10^-3 mol/dm³), the model yields an overestimated concentration below pH 7 with a decadal error of less than 0.5. Above pH 7, the concentration is underestimated while maintaining a decadal error of less than 0.5. At pH 7, a 0.04-decade minimal error is found. For pollution equal to or less than 10^-4 mol/dm³, the model gives good results in an acid or neutral medium with a decadal error usually less than 0.3. In an alkaline medium, concentration is overestimated. In this case the error increases in a roughly linear manner with the pH and the co-logarithm of copper concentration. From the results of these tests, we defined a valid domain of ISE copper concentration measurement using our model.

In conclusion, the suggested method, although not very accurate, could be used as an indicator of the copper concentration level in wastewater. The ISE-response correction model is currently being tested under operational conditions at a water treatment plant in Nancy-Maxéville (France).

Keywords:

• Water quality control,
• copper pollution,
• ISE