DAILY LOADS

In order to compare the measured and modelled daily loads, the ratio modelled over measured daily loads is used. Given the data available and the analytical uncertainties of the 15 molecules, the results of the model for one molecule are considered satisfactory whenever the ratio modelled over measured daily loads is between 0.5 and 2 (i.e. whenever the model over or under estimates less than two times the measured daily loads).

Also, the model is considered reliable if it has satisfactory results for every molecule. Results are shown in table 38 and figure 74.

Travel time estimation

Table 38: Comparison of the measured and modelled daily loads for the urban catchment. For clarity purposes, ratios considering glucuro and sulfo-conjugates are only shown when such metabolites are actually excreted.

Molecule

Ratios of modelled over measured daily loads,

parent compound Ratios of the

Figure 74: Comparison of the measured and modelled daily loads for the urban catchment. The modelled daily loads include the parent molecule and the glucuro-conjugates.

Looking at the ratios modelled over measured daily loads, only six out of the nine modelled molecules have ratios between 0.5 and 2 if only the parent molecules loads are taken into account for the modelled loads. Six molecules have glucuro-conjugates, if they are taken into account, then eight out of the nine molecules have satisfactory ratios. Two molecules have glucuro and sulfo-conjugates, if they are taken into account, then seven out of the nine molecules have satisfactory ratios. No molecule has sulfo-conjugates without glucuro-conjugates.

These results indicate that the model has better performance when metabolites are taken into account.

Glucuro-conjugates are essential, the only molecule out of the 0.5 to 2 ratio interval is Ketoprofen (ratio of 2.19), but the range of the molecule excreted as glucuro-conjugates is wide (from 66 to 95 %, appendix 4). Also, with Diclofenac, they are the only two molecules that are not sold only as oral forms (Diclofenac: 53 % dermal forms; Ketoprofen: 17 % dermal forms). Their fractions directly discharged into the sewer are not well known and approximated by the model (from 25 to 75 %, appendix 4) which over-estimates their daily loads.

Approximations for both the fraction directly discharged into the sewer and the fraction excreted as glucuro-conjugates could explain the small over-estimation of the Ketoprofen daily loads. However, sulfo-glucuro-conjugates lead to overestimations. Ratios for Paracetamol and Sulfamethoxazole increase respectively from 1.96 and 1.17 without sulfo-conjugates to 3.07 and 1.44 with them.

Thus, with the current results, it seems reasonable and realistic to assume that glucuro-conjugates are rapidly and totally transformed back to their parent molecule when discharged into the sewer network while sulfo-conjugates are not.

As seen in section 6.3.1, the dispersion of the measured daily loads is quite important (coefficients of variation mostly between 24 and 34 %). The ratios between the coefficients of variation of the modelled over the measured daily loads indicate that the model is underestimating the dispersion of the daily loads (table 38).

This seems to be mainly the result of the temporal scale used for the pharmaceutical sales. Indeed, daily sales derived from monthly data are understandably unable to represent daily sales and so daily consumption and loads in wastewater. This is, however, mitigated in the case of low consumption pharmaceuticals. The dispersion of Sulfamethoxazole that is the less sold pharmaceutical of the nine molecules (section 6.1.1) is even

overestimated (135 %). Conversely, the dispersion of the most consumed pharmaceutical, Paracetamol, is hugely underestimated.

It appears that the model, in its current state, is able to predict reliably the daily loads of pharmaceuticals at the WWTP with an acceptable accuracy considering the available data and the analytical uncertainties. Daily loads are either over or underestimated depending on the molecule. The variability of the daily loads is under-estimated. The difference between modelled and measured loads can be the result of many factors (non-exhaustive list):

 Uncertainties in estimating the number of people associated to a specific pharmaceutical sales record,

 Discrepancies between quantities of pharmaceuticals bought and consumed by a set of population (in both space and temporal scales),

 Un-exclusive and incomplete representation of the population discharging in the catchment by the population associated to the pharmaceutical sales records,

 Specificity of the population sample regarding pharmaceuticals consumption in comparison to consumption trends on a larger scale (only a few patients per day on the whole catchment for some molecules),

 Incomplete or badly defined human metabolism of pharmaceuticals,

 Rapid and daily evolution of the definition of the population discharging in the catchment (workers or visitors entering the catchment, inhabitants leaving momentarily the catchment),

 Unknown physico-chemical processes in the sewer systems (transformation of either parent molecule to transformation products or metabolites to parent molecule, absorption and transformation by biofilm, unknown transformation rates and influencing factors).

Weighting these different factors is not possible without further data. Each and every one of them should be considered for further studies.

A proportional model based on Heberer and Feldmann (2005) is used as a comparison. The details of the proportional model are given in appendix 21. The relative error (Re) of each model is calculated and then compared (table 39):

𝑅𝑒 =|𝜑_{𝑚𝑒𝑎𝑠}− 𝜑_𝑚𝑜𝑑| 𝜑𝑚𝑒𝑎𝑠

With:

𝑅𝑒: relative error

𝜑𝑚𝑒𝑎𝑠 and 𝜑𝑚𝑜𝑑: respectively the measured and modelled daily loads (mg/day)

Table 39: Comparison between the classic proportional model and the new stochastic model for the urban

Classic proportional model New stochastic model Average modelled

Relative errors for the new stochastic model are smaller than for the classic proportional model for five of the nine modelled molecules. Also, the average, minimum and maximum relative errors of all the molecules of the new stochastic model are smaller compared to the classic proportional model. This indicates that the new stochastic model gives better results than the classic proportional one. Also, it provides data on the variability of the daily loads. Apart from the stochastic nature of the new model, the main difference impacting the daily loads between the two models is the consideration of the dynamics of population during the course of the day (people leaving or entering the catchment to go to work).