N Rizk Ab

N Ait-Mouheb

G Bourrié

B Molle

N Roche

Parameters controlling chemical deposits in micro-irrigation with treated wastewater

Keywords: Calcium carbonate, chemical precipitation, micro-irrigation clogging, PHREEQC, treated wastewater reuse

Micro-irrigation with treated wastewater has the potential to be the most efficient irrigation technique, especially in water scarce areas. Its main disadvantage is the high sensitivity of the drippers to clog. This study focused only on the chemical precipitation mechanisms. In a batch chemical process in parallel with PHREEQC software, two temperatures (22°C and 55°C), four pH (8, 8.5, 9 and 9.5) and CO 2 partial pressure were tested. The aim is to analyze the quantity of precipitates and their crystalline nature and calculate the effects of these factors on the behavior of dissolved chemical elements in treated wastewater to be able to validate and calibrate a geochemical software in order to predict chemical precipitation. The amount of precipitate increases by increasing pH and temperature. Precipitates were analyzed using thermogravimetric analysis (TGA) and X-ray diffraction (XRD). Calcium carbonate (CaCO 3 ) in the form of calcite was found to be the predominant precipitate. Experimental and model results showed that the saturation index (SI) of calcite was found to be the factor that most frequently affected calcite precipitation. Calcite SI is pH, temperature and CO 2 partial pressure dependent. In the case of irrigation, water equilibrium with atmospheric CO 2 minimizes precipitation of calcite.

Introduction

In contexts where water is scarce, using treated wastewater for irrigation can contribute significantly to integrated management of water resources. Drip irrigation is the most efficient and safest irrigation technique for the reuse of treated wastewater. The main benefits of using treated wastewater for irrigation are economic and environmental, in particular for agriculture, where the recycling of water and nutrients increases productivity while preserving groundwater resources. However, clogging is a common problem in drip irrigation. [START_REF] Bucks | Trickle irrigation water quality and preventive maintenance[END_REF] defined three interlinked categories of clogging of irrigation devices: i) physical, i.e. the accumulation of particulate matter due to the presence of suspended solids; ii) chemical, due to precipitation of soluble salts present at a concentration above saturation; iii) biological, due to the formation of biofilm and the growth of algae. The clogging of drippers can result in the dysfunction of the irrigation system as the uniformity of the distribution progressively decreases. [START_REF] Lili | Chemical clogging of emitters and evaluation of their suitability for saline water drip irrigation[END_REF] studied the effect of saline water on dripper clogging. They found that variations in the discharge ratio and in the coefficient of uniformity of all drippers decreased with an increase in operating time. They also underlined the fact that chemical clogging is usually the result of precipitation due to reactions between the cations (Ca 2+ , Fe 2+ and Mg 2+ , etc.) and anions (CO 3 2-, HCO 3 -and SO 4 2-, etc.) in the irrigation water. Several studies on microirrigation systems confirmed the tendency of dripper clogging due to chemical precipitation linked to the quality of the water. [START_REF] Capra | Water quality and distribution uniformity in drip/trickle irrigation systems[END_REF] reported that an increase in the concentration of several water quality parameters, total suspended solids (TSS), total Fe, electrical conductivity (EC), and concentrations of Ca, Mn, and Mg, increased clogging. The solubility of chemical elements is controlled by variations in temperature, pressure, pH, redox potential and the relative concentrations of other substances in solution. In micro-irrigation systems, pH, temperature and partial pressure of gases are the most frequent and are interlinked in some way. Oxygen, carbon dioxide, and hydrogen sulfide gases are important in determining the solubility characteristics of water [START_REF] Haman | Causes and Prevention of Emitter Plugging In Microirrigation Systems[END_REF]). The solubility of carbon dioxide gas (CO 2 ) in water plays a particularly important role in the dissolution and deposition of minerals because it is closely involved in the control of pH. The solubility of CO 2 depends on temperature and pressure, both of which affect its equilibrium [START_REF] Karaca | Elimination of lime causing clogging in emitters by chemical methods in drip irrigation[END_REF]. In micro-irrigation, the system works under pressure, is exposed to sun and to other factors that will raise the pH of the water. Apart from the concentration of CO 2 in the water, the increase in pH can be due to microbial degradation, inputs of fertilizer and high alkalinity (bicarbonate (HCO 3 -) and carbonate (CO 3 2-)). High alkalinity is problematic for drip-irrigation systems due to the hardness of the water, i.e. the concentration of calcium and magnesium. The concentrations of HCO 3 -and CO 3 2depend on pH and CO 2 partial pressure (PCO 2 ). Relatively high concentrations of HCO 3 -and CO 3 2-in the water tend to precipitate calcium and magnesium as carbonates. In the case of high alkalinity, hardness and pH, ions form insoluble minerals that reduce the flow rates through orifices or drippers [START_REF] Bauder | Irrigation Water Quality Criteria[END_REF]. Many researchers have investigated dripper clogging in an experimental context using treated wastewater [START_REF] Karaca | Elimination of lime causing clogging in emitters by chemical methods in drip irrigation[END_REF][START_REF] Tarchitzky | Biological and chemical fouling in drip irrigation systems utilizing treated wastewater[END_REF] especially concerning the development of biofilms and the deposition of particles. However few studies focused on chemical clogging but no studies have focused on the possibility of modeling salt precipitation using treated wastewater under micro-irrigation conditions. Chemical clogging is very difficult to control (Ahmad [START_REF] Aali | The effect of acidification and magnetic field on emitter clogging under saline water application[END_REF]. Preventions and treatments in general are long, expensive and may affect both the soil and the crop [START_REF] Haman | Causes and Prevention of Emitter Plugging In Microirrigation Systems[END_REF]. Alternative measures should be considered. The recommendation generally made to prevent chemical clogging is to decrease the water pH by injecting acid and temperature by irrigating at night (Ahmad [START_REF] Aali | The effect of acidification and magnetic field on emitter clogging under saline water application[END_REF][START_REF] Lili | Chemical clogging of emitters and evaluation of their suitability for saline water drip irrigation[END_REF]. Understanding the parameters that influence the solubility of minerals, ion activities and saturation states are important to prevent precipitation. The objectives of this study were thus to identify which elements precipitate and cause chemical clogging when treated wastewater effluent is used, to evaluate the effect of pH, temperature and CO 2 partial pressure on chemical precipitation, and, for the first time, to use a geochemical model to quantify and qualify chemical precipitation when using treated wastewater effluent. The experiment consisted in changing the pH and temperature of the water to cause precipitation. The precipitate was then characterized by X-ray diffraction (XRD) and thermo gravimetric analysis (TGA). Experimental results validated the model. The model used in this work was PHREEQC [START_REF] Parkhurst | User's guide to PHREEQC (Version 2): a computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations[END_REF]. The overall aim was to identify appropriate measures to avoid or at least to limit chemical precipitation.

Materials and Methods

Sampling and water quality

Treated wastewater was collected from the clarifier outlet of the urban wastewater treatment plant (WWTP) in Mauguio (near the city of Montpellier, southern France). The treatment plant is an activated sludge type and has a capacity of 24000 population equivalent. It meets the demographic and activity trends of the cities of Mauguio and Mudaison (Hérault, France). The full effluent analyzes was carried out one time on one sample and this was before the precipitation experiments. The physico-chemical characteristics of the effluent are listed in Table 1.

Parameters values Parameters values pH

7.8 Sulfates (mg.L -1 ) 109 Conductivity (μS.cm -1 ) 1270 Fluorine (mg.L -1 )) < 0.50 TDS (mg.L -1 ) 1241.7 Aluminium (μg.L -1 ) < 20 Hardness (mg.L -1 ))

223 Br (mg.L -1 ) 0.18 Alkalinity (mg.L -1 ) < 20 B (mg.L -1 ) 0.14 Complete alkalimetric title (mg.L -1 ) 261 Ba (mg.L -1 ) < 0.05 Ammonium (mg.L -1 ) 0.37 Cu (mg.L -1 ) < 0.02 Nitrates (mg.L -1 ) 9.8 Fe (mg.L -1 ) < 0.05 Nitrites (mg.L -1 ) 0.17 Mn (mg.L -1 ) 0.03 Phosphorus (mg Ptot.L -1 ) 0.17 Li (mg.L -1 ) < 0.02 Mg (mg.L -1 ) 7 Pb (mg.L -1 ) < 0.05 Ca (mg.L -1 ) 133 Si (mg.L -1 ) 12 Na (mg.L -1 ) 119 Sr (mg.L -1 ) 0.39 Cl (mg.L -1 ) 171 Zn (mg.L -1 ) 0.03 K (mg.L -1 ) 18.1 COD (mg.L -1 ) < 30 Total TSS (mg.L -1 ) 5 BODn (with ATU) (mg O 2 .L -1 ) < 3.0 Effluents treated at the Mauguio plant fall within in the normal range of water quality recommended to avoid clogging of micro-irrigation drippers [START_REF] Ayers | Water Quality for Agriculture[END_REF], except for hardness and complete alkalimetric title (CAT), whose values are higher than the recommended one [START_REF] Dey | Chemical precipitation : water softening[END_REF]. The acceptable range of hardness is between 60 and 120 mg.L -1 and the recommended range for CAT is between 120 and 200 mg.L -1 . Independently of the work of this study, the quality of the effluent was monitored by the Mauguio station once to twice a month on a sample representing the average of many small samples for 24h. The homogeneity of the water was highlighted over three years regarding the values of pH (7.8 ± 0.2), BODn (3.2 ± 0.8 mg O 2 .L -1 ), TSS (3.7 ± 1.68 mg.L -1 ), total nitrogen (4.2 ± 1.7 mg N.L -1 ) and total phosphorus (0.65 ± 0.54 mg P.L -1 ). So the date of water sampling will have no effect on the results. Calcium and CAT was measured before each precipitation experiments. Results shows that their concentration are also invariable (Ca = 136.6 ± 7.07 mg.L -1 and CAT = 240.3 ± 20.34 mg.L -1 ).The precipitation experiments were done in four replicates to evaluate the variability of the results. Samples were taken in February, March, April and May, 2015. The water was stored in a refrigerator at 6°C to minimize biochemical changes.

Accelerated controlled precipitation

Observing chemical precipitation in irrigation system requires time. In the laboratory, accelerated methods can be used to induce precipitation. Eight beakers were filled with one liter of pre-filtered water. Filtration at 0.45 µm is essential to eliminate all suspended solids and most of the bacteria. The experiments were conducted in an open system, meaning in equilibrium with atmospheric CO 2 . Temperature and pH were the only two parameters modified. Four of the eight beakers were kept at room temperature (22°C) and the others were kept at 55°C in a thermostatic bath. Temperatures as high as 55°C can be encountered in fields in summer when the polyethylene irrigation pipes are black and are fully exposed to the sun (Gamri et al. 2016). Four pHs (8, 8.5, 9 and 9.5) were applied to study the effect of variations in pH on chemical precipitation when treated wastewater is used for irrigation. The pH values were chosen to induce precipitation without being too far from real irrigation conditions. A 0.1 M solution of sodium hydroxide (NaOH) was used to trigger precipitation. The solutions were considered stable when the pH remained unchanged for 2 h [START_REF] Spanos | The transformation of vaterite to calcite: effect of the conditions of the solution in contact with the mineral phase[END_REF]. The precipitate was collected after 24 hours. The water was filtered using a vacuum pump and glass microfiber filter paper with a 0.45 µm pore diameter (Fisherbrand). The filter paper was previously dried in the oven for 24 hours at 105°C to remove all traces of water and then weighed with a precision balance (Denver instrument S-64) (precision 0.1 mg). The same protocol was used for all four different water samples taken in February, March, April and May, 2015.

Modeling precipitation with PHREEQC

PHREEQC is a geochemical model that calculates equilibrium composition in a batch of water containing reactants. The objective was to predict the quality and the quantity of mineral precipitates under different environmental conditions (temperature, pH and CO 2 partial pressure). This helps define the limits of water quality and water supply that can be accepted in irrigation systems.

Two types of water supply are encountered in irrigation in general and in micro-irrigation in particular:

i) Irrigation water is pumped from a water table directly into the distribution system. The water does not come into contact with the atmosphere, so the CO 2 has no opportunity to degas into the atmosphere. ii)

Irrigation water is stored temporarily in a reservoir or pumped from a river. Water is in direct contact with the atmosphere. The partial pressure of CO 2 in water with equilibrium with the atmosphere is 10 -3.5 atm. The saturation index (SI) of CO 2 is -3.5.

When treated wastewater is used for irrigation, the second case applies, but in this study we compared the two situations.

The ionic strength of the effluent produced at the Mauguio WWTP was calculated with PHREEQC to be 1.63 x 10 -2 mol.kgw -1 , which is considered as a dilute solution. Activity and saturation indexes (SI) are two key thermodynamic parameters that show the distribution of elements as solid, liquid or gaseous. They were computed using the phreeqc.dat database: activity coefficients (1) were computed with Debye-Hückel equation, as ionic strength was sufficiently low (I< 0.1 M) [START_REF] Bourrié | Sustainable intensive agriculture: evidence from equeous geochemistry[END_REF].

𝑙𝑛𝛾 𝑖 = - 𝐴 𝑧 𝑖 2 √𝐼 1+𝐵𝑎 𝑖 ̇√𝐼
where γ i is the activity coefficient (dimensionless), A and B are temperature dependent coefficients, 𝑎 𝑖 ̇ is the empirical ion-size parameter and I ionic strength [START_REF] Appelo | Geochemistry, groundwater and pollution[END_REF].

Modeling was conducted in the same way as in laboratory experiments. The concentrations of NaOH added in the experiments were the same as those added in PHREEQC but Na 2 O was used instead of NaOH. Na 2 O thermodynamics is better known than NaOH, so for PHREEQC it is easier and more accurate to use it. Na 2 O reacts with water to give sodium hydroxide according to the following reaction:

𝑁𝑎 2 𝑂 (𝑐𝑟) + 𝐻 2 𝑂 → 2𝑁𝑎𝑂𝐻 (𝑎𝑞)
So that the addition of NaOH is formally equivalent to dissolution of Na 2 O.

(1)

(2)

Results and analysis

Chemical precipitation in the laboratory

pH and temperature were increased to study the potential of treated wastewater to form precipitate. Figure 1 shows the average weight of the precipitate and the corresponding added volumes of NaOH with their standard deviations (SD) at different pH and at 22 and 55°C. The standard deviation (SD) was calculated from the four repetitions in the same conditions using four different water samples collected between February and May, 2015. The difference between the repetitions was negligible. For example, the average weight of the precipitate and the standard deviation was 140.75 ± 16.51 mg and 294.25 ± 6.98 mg respectively at pH 9.5, 22°C and pH 9, 55°C. This underlines the uniformity in the amount of precipitate obtained using the effluent of Mauguio WWTP over time.

At 22°C with a pH below or equal to 9, the weight of the precipitate was 1.3 mg. When the temperature was increased from 22°C to 55°C, precipitation occurred even at pH 8 (53.4 mg).

The variation in the weight of the precipitate as a function of the pH is mainly determined by temperature. The weight increased from 53.5 mg at pH 8 to 101 mg at pH 8.5. At pH 9 and 9.5 the same quantity of precipitate was formed, whose weight was around 293 mg. It can be safely be assumed that at 55°C and from pH 9 on, all compounds precipitate. To better explain the precipitation process, XRD and TGA were used to characterize the precipitate.

Characterization of precipitate by XRD and TGA

Six different samples from the four different precipitation conditions were taken for XRD analysis: pH 8.5 and 9.5 at 22°C and 55°C. For pH = 8.5 at 55°C and for pH = 9.5 at 22°C two samples were taken to evaluate repeatability. Figure 2 shows the result of XRD analysis. In all the samples with a pH of 8.5 at 55°C, a pH of 9.5 at 22°C and a pH of 9.5 at 55°C, XRD signals indicated the presence of calcite (blue strings inside peaks). Vaterite (green peaks) were observed in 60% of the crystallized samples, while aragonite (red peaks) was only observed in one sample (pH = 8.5 at 55°C) (Fig. 2-b). The presence of vaterite and/or aragonite was observed both together and separately but always with calcite. In Figure 2, the most representative peak of calcite was observed for 2θ = 34 (blue arrow). At a pH of 8.5 at 22°C, no peaks were observed, perhaps because the sample was too small or because calcium carbonate was in amorphous form (ACC) and did not crystallize. Calcite is the main precipitate because it is the least soluble phase and the most thermodynamically stable crystal form of calcium carbonate, while vaterite is the most soluble phase and the least thermodynamically stable. Rogriguez-Blanco et al. (2011) showed that the first precipitation is in amorphous form (ACC) and subsequently crystallizes to calcite via vaterite. So the presence of vaterite in our samples is due to our experimental conditions, and particularly to the saturation index. The results of PHREEQC model (table 4) gave the saturation index of calcite at a pH of 8.5 at 55 °C as > 1.72. [START_REF] Spanos | The transformation of vaterite to calcite: effect of the conditions of the solution in contact with the mineral phase[END_REF] pointed out that a very high supersaturation (1.5 -1.9) in which the solid phase is formed affects the transformation of vaterite into calcite. These authors also found a linear dependence of calcite content in the precipitate as a function of time. When the quantity of calcite increases, this results in a decrease in the quantity of vaterite. [START_REF] Sabbides | The precipitation of calcium carbonate in artificial seawater at sustained supersaturation[END_REF] reported that aragonite may also be stabilized depending on the temperature of the supersaturated solutions and on the concentration of foreign ions present in water (Mg 2+ , oxalate anions, etc.). When the concentration of magnesium exceeded 53.3 mM, the aragonite phase was formed, whereas below this concentration, calcite b) a)

Author-produced version of the article published in Journal of Water Supply Research and Technology-Aqua, 2017, N°66 (8), p. 587-597. The original publication is available at http://aqua.iwaponline.com Doi: 10.2166/aqua.2017.065 was the only phase formed. In the XRD results, only crystallized calcium carbonate was found, mostly in the form of calcite. TGA was used to highlight the other forms of precipitation and their percentage mass. One sample was taken randomly (pH 9.5 at 55°C) from the four repetitions and weighed before increasing the temperature. Results of the TGA showed only one notable reduction in mass between 600 and 750°C. This mass loss represented 44% of the initial weight, evidence that only calcium carbonate was present in the sample. The 44% represents the mass of CO 2 which is released from the sample. The remaining 56% corresponds to CaO according to the equation:

CaCO 3 → CaO + CO 2
In theory, the molar mass of CaCO 3 is 100.08 g.mol -1 with 44.01 g.mol -1 for the CO 2 . When the CO 2 was released, 43.97% of mass loss occurred, confirming the results. [START_REF] Lv | Decomposition kinetic characteristics of calcium carbonate containing organic acids by TGA[END_REF], reported that during thermal decomposition of a pure phase of CaCO 3 one mass loss is observed between 600 and 850°C, representing 43.8% of the initial weight. The fact only calcium carbonate was present in our samples is due to the hardness of the water. Its value was 223 mg.L - 1 as shown in table 1, which according to [START_REF] Dey | Chemical precipitation : water softening[END_REF] is considered as very hard water.

Modeling precipitation with PHREEQC

The objective of using PHREEEQC was by modeling, to validate the effect of pH and temperature on calcite precipitation in the treated wastewater from the Mauguio WWTP. Once done, CO 2 partial pressure was added to pH and temperature as a third parameter. This makes it possible to modify the precipitation that can occur under real irrigation conditions. The behavior of calcite precipitation is not the same if the system is open or closed (in equilibrium with the atmosphere or not). Since the precipitate in this study generally consisted of calcite, modeling focused on this mineral. Reproducing the experiments in models will help predict the quality and the quantity of precipitates produced with a given water quality but with different CO 2 partial pressure. The effluent studied here is oversaturated with calcite (value 0.87). Even in such supersaturation conditions, no precipitation of calcite was observed. An increase in pH and temperature will increase the value of supersaturation calculated with PHREEQC software. When a certain threshold is exceeded, precipitation does occur. Tables 3 and4 show the value of SI and pH at 22°C and 55°C respectively. Table (3-a) and table (4-a) show the volume of NaOH that corresponds to the amount of sodium hydroxide added in ml during the laboratory experiments to have a theoretical pH of 8, 8.5, 9 and 9.5. pH and SI were calculated with PHREEQC after adding the volume of NaOH and before precipitation occurs. Table (3-b) and table (4-b) shows the pH and SI after calcite precipitation. The SI was adjusted with PHREEQC to give a weight of calcite similar to the experimental one. Two cases of precipitation were studied with (open system) and without atmospheric equilibrium (closed system). The pH also was calculated with PHREEQC.

(3)

Author-produced version of the article published in Journal of Water Supply Research and Technology-Aqua, 2017, N°66 (8), p. 587-597. The original publication is available at http://aqua.iwaponline.com Doi: 10.2166/aqua.2017.065 In the experiment, the volume of NaOH added to obtain a pH of 8, 8.5, 9 and 9.5 was respectively, 3, 5.5, 9.75 and 19.25 ml (Figure 1). These volumes were added to the software to calculate the corresponding SI after the addition of NaOH (Table 3-a). a). It corresponds to a pH of between 9 and 9.5. The corresponding experimental calcite weight was 1.3 mg and 140.1 mg respectively. For the first two volumes of added NaOH (3 and 5.25 ml), if we compare the pH after adding NaOH (8.4 and 8.7 respectively) and after precipitation in an open system (O) (8.8 in both cases) the pH increases, the same goes for the values of SI.

SI and pH values when

No precipitation occurred to reduce these values and overcome the added NaOH. When precipitation occurred even in very small quantities (1.04 mg of calcite), the pH and SI began to decrease. pH dropped from 9.05 to 8.91 and SI from 1.95 to 1.85 for a volume of 9.75 ml of NaOH.

In the closed system (C), SI and pH before and after precipitation were invariable for the first three measures. When 19.25 ml of NaOH is added, about 143 mg of calcite precipitate reducing both the pH and SI. In an open system, like for experimental precipitation, obtaining calcite precipitation is more difficult than in a closed system. The values of SI are higher in case (O) than in case (C) for the two first volumes of added NaOH. In the case of irrigation with the Mauguio effluent at 22 °C, the water is stored in reservoirs or collected directly from the clarifier. In both cases, water is in balance with the atmosphere. Monitoring the pH is not sufficient to monitor the quality of the water with respect to mineral precipitation. pH is invariable in case (O) even with a high rate of precipitation due to the equilibrium of the carbonic system. Maximum pH was 8.9 and minimum pH was 8.7.

A total analysis of the water is necessary to calculate the SI which is the only indicator of precipitation. In conclusion, calcite precipitates with a particular degree of supersaturation (SI > 1.95). This degree can be achieved by increasing the pH of water. Like in the experiment at 22°C, the experimental volumes were introduced in the software. Tables 3 and4 represent the same thing but at different temperatures. At 55 °C, precipitation begins at pH 8 and the value of SI after adding NaOH is 1.47. After precipitation and in case (O), the pH is the same regardless of the weight of the precipitate. When precipitation is almost compete, the saturation index drops to nearly that of the calcite in the initial state (initial SI = 0.8). The drop in SI is due to the decrease in the concentration of Ca 2+ and HCO 3 -linked to precipitation since the pH is invariable. Conversely in case (C), SI began low and increased with increasing precipitation like the pH. In this case, the value of SI is linked more to pH and temperature than to the weight of calcite. Like at 22 °C in the open system, starting calcite precipitation is more difficult than in a closed system. The temperature of the water reaches 55 °C in the pipes, and it is therefore considered as a closed system. The time the water takes passing through the pipe from the reservoir to the dripper and the pressure applied in the irrigation system influences the partial pressure of the CO 2 as well as precipitation. [START_REF] Sherlock | On the neutralization of acid rock drainage by carbonate and silicate minerals[END_REF] pointed out that the absence or presence of carbon dioxide strongly influences the solubility of calcite. In an open system, there is an increase in the solubility of calcite, which implies a decrease in precipitation. In the opinion of [START_REF] Hills | Effects of chemical clogging on drip-tape irrigation uniformity[END_REF], the value of SI can predict calcium carbonate precipitation. This index measures the solubility of calcium carbonate at a given temperature to ion concentration and pH. In conclusion, precipitation of calcite is greater at higher temperatures and pH. In irrigation, even at low temperatures, water that is equilibrated with the atmosphere in reservoirs before supplying the irrigation system will be subject to less chemical precipitation.

SI and pH values when

Discussion

Calcium carbonate precipitation is reported to be the main precipitate in irrigation waters [START_REF] Hills | Effects of chemical clogging on drip-tape irrigation uniformity[END_REF]). In the present study, the precipitation of calcium carbonate was triggered by heating, by adding a NaOH solution to water (0.1M), and by modifying CO 2 partial pressure. These factors are interlinked and modifying one may entail the modification of the other.

𝑂𝐻 -+ 𝐻 + ↔ 𝐻 2 𝑂 (4) NaOH is added to the water 𝐶𝑂 2 (𝑔) ↔ 𝐶𝑂 2 (𝑎𝑞) + 𝐻 2 𝑂 (5) CO 2 equilibrium 𝐶𝑂 2 (𝑎𝑞) + 𝐻 2 𝑂 ↔ 𝐻 2 𝐶𝑂 3 (6) Carbonic acid 𝐻 2 𝐶𝑂 3 ↔ 𝐻𝐶𝑂 3 -+ 𝐻 + (7) Bicarbonate 𝐻𝐶𝑂 3 -↔ 𝐶𝑂 3 2-+ 𝐻 + (8) Carbonate 𝐶𝑎 2+ + 2𝐻𝐶𝑂 3 -↔ 𝐶𝑎𝐶𝑂 3 + 𝐶𝑂 2 + 𝐻 2 𝑂 (9) Calcium carbonate precipitation
1. Effect of pH on calcite precipitation This situation is observed when fertigation uses high pH fertilizers. As NaOH is added to the water, OH -neutralizes H + in reaction (4). This removes H + from reactions (7) and ( 8) which causes these reactions to shift to the right, generating more free HCO 3 -in solution. As more NaOH is added, this process continues with an accompanying increase in pH until enough free HCO 3 -is present to exceed the solubility of CaCO 3 leading to its precipitation. Figure 1 shows that increases in pH alone do not cause precipitation, especially at 22°C, since precipitation only begins at more than pH 9. This is due to the CO 2 equilibrium, since the experiment was conducted in an open system. The more H + is consumed by adding a base, the more H 2 CO 3 the reaction (7) will consume. Reaction (6) will also shift to the right as well as reaction (5).

Atmospheric CO 2 will dissolve in water to balance the lack of bicarbonate (HCO 3 -), which causes the precipitation to delay. Two ascertainments were observed in the Figure 1, which will be explained below.

Analysis of the high volume of added NaOH:

In Figure 1, for example for pH 9 at 22°C no precipitation is produced. The volume of NaOH added to reach this pH is 10 ml. For the same pH at 55°C, 293 mg of calcium carbonate precipitate. The volume of NaOH added to maintain the pH at 9 is 34 ml. A higher quantity of NaOH volume must be added to maintain the same pH when precipitation occurs. This phenomenon occurs because between pH 8 and 9.5, HCO 3 -is the predominant carbonate ion. For these conditions, the calcite precipitation reaction can be written as in reaction 9. Reaction 9 shows that as CaCO 3 is formed, free HCO 3 -is removed from solution; this troubles the equilibrium of reaction 7. To restore the needed balance, reaction shifts to the right to generate more free HCO 3 -and, at the same time, creates additional H + . The presence of additional H + lowers the pH. It is this sequence which causes the pH to decrease as more NaOH is added.

Stabilization of calcite weight:

In Figure 1, a stabilization of the calcium carbonate weight is observed at 55°C from pH 9 with 293 mg for both pH 9 and 9.5. In Mauguio's water, the calcium concentration is 133 mg.l -1 . Calcium (M = 40:078 g.mol -1 ) is a limiting reagent with respect to the carbonates which are always in excess and forms as long as there is equilibrium with the atmospheric CO 2 (reaction 5 till reaction 8). It is considered that all Ca 2+ is associated with HCO 3 -to form calcium carbonate (M = 100.0869 g.mol -1 ) in solid form. The theoretical weight of calcium carbonate (CaCO 3 ) that can be formed with this initial concentration of calcium is 332.5 mg. For [START_REF] Dey | Chemical precipitation : water softening[END_REF], pH and carbonic acid concentration (H 2 CO 3 ) play an important role in the precipitation of CaCO 3 . Calcium, which is linked to carbonate (carbonate hardness), can be precipitate by the addition of hydroxide ions (OH -) having a pH above 10. The remaining calcium, i.e., non-carbonate hardness, cannot be removed by simple adjustment of pH. Therefore, soda ash (sodium carbonate) must be externally added to precipitate this remaining calcium. This can explain the difference between the experimental mass of calcium 2. Effect of temperature and CO 2 partial pressure on calcite precipitation In the field, scale deposits are mainly determined by thermal effects [START_REF] Hui | Evaluation methods for the scaling power of water[END_REF].

Heating of the water in pipes exposed to sunlight reduces carbon dioxide solubility. The decrease in CO 2 solubility causes the release of CO 2 to the atmosphere through degassing. The release of CO 2 in the atmosphere by heating drives equations (5, 6, 7 and 8) to the left which leads to the consumption of H + and hence to an increase in pH. The rise in pH and the presence of calcium ions and carbonic species (reaction 9) trigger calcium carbonate precipitation [START_REF] Hui | Evaluation methods for the scaling power of water[END_REF]. In figure 1, the increase in pH had more effect on calcite precipitation at 55 °C and began even at pH 8. In this case, as highlighted by PHREEQC, the solubility of calcite is affected.

3. Effect of the calcite saturation index PHREEQC results showed that the calcite saturation index is an important parameter for scale deposits and that it increases with increasing pH and temperature. The saturation index of the water was 0.87 and no precipitation was observed until the index reached 1.95 at 22 °C at a pH of 9, and 1.47 at 55 °C at a pH of 8. [START_REF] Wojtowicz | Calcium Carbonate Precipitation Potential[END_REF] pointed out that a positive saturation index (SI) does not cause calcium carbonate precipitation until a certain degree of supersaturation is reached. A supersaturated solution can be obtained by increasing the temperature and pH with the same water quality or by increasing water alkalinity and calcium content (Larson & Buswell 1942). The modeling and correction that have been done works in the case of water with high content in calcium. For other type of precipitation other correction should be done.

In irrigation systems fed by several qualities of treated wastewater, [START_REF] Ghorbel | Étude du phénomène de colmatage chimique des distributeurs d'eaux utilisés en microirrigation (Study of the phenomenon of chemical clogging of water distributors used in micro-irrigation)[END_REF][START_REF] Tarchitzky | Biological and chemical fouling in drip irrigation systems utilizing treated wastewater[END_REF] found insoluble materials mainly formed of calcium carbonate precipitates. This underlines the precipitation of calcium carbonate when wastewater is used for micro-irrigation.

Conclusion

When wastewater is reused for micro-irrigation, the quality of the water and the environmental conditions affect the precipitation of salts which finally clog the drippers. In this study, three parameters, temperature, pH and CO 2 partial pressure, were varied to evaluate their effect on possible precipitation. The effects of the three parameters were shown to be interlinked in the precipitation of calcium carbonate. Laboratory and modeling experiments with PHREEQC were conducted to validate the model.

1. In the case of the wastewater effluent studied here, calcium carbonate was precipitated as calcite when pH and temperature increased. Calcite was the main and most stable precipitate and was found in all the samples. All dissolved calcium precipitated in combination with the carbonates at pH 9 and 55 °C.

2. PHREEQC also showed calcite to be the most abundant precipitate based on the reuse of effluent from the Mauguio WWTP. The saturation index of calcite was calibrated to obtain the same weight of calcite as in the laboratory experiment. The model provided proof that calcite precipitates at a given degree of supersaturation, which can be achieved by increasing pH and temperature. At a high temperature (55 °C) the value of SI that led

Author-produced version of the article published in Journal of Water Supply Research and Technology-Aqua, 2017, N°66 (8), p. 587-597. The original publication is available at http://aqua.iwaponline.com Doi: 10.2166/aqua.2017.065

to calcite precipitation was 1.47 above a pH of 8, while it was 1.95 at 22°C at pH 9. It was easier to start calcite precipitation at 55°C than at 22 °C.

3. The effect of atmospheric CO 2 was also investigated. In an open system, i.e., in equilibrium with CO 2 , the solubility of calcite increased due to a constant supply of CO 2 .

To minimize calcite precipitation in irrigation, water should be stored in open reservoirs at a low temperature and a low pH.

Practically this study shows that the contribution of CO 2 , high pH and temperature are the main drivers of precipitation. Consequently it can be achieved to privilege acid fertilizers when practicing fertigation, and avoid high temperature period, thus practicing fertigation preferably at night. The next step will be to validate our results by modeling several effluent qualities and comparing them with laboratory precipitation experiments and with water with the same chemical composition but without organic matter such as potable water. In this case, any quality water that would be used for irrigation could be modeled. By varying environmental conditions, the concentrations of elements caused by fertigation among others, the software would show whether or not there will be a risk of precipitation. If yes, preventive measures could be taken depending on the quality and quantity of chemical clogging indicated. Several pressures can be used in micro-irrigation, depending on the type of dripper, the length of the pipes, and the power of the pumps. A degassing phenomenon can be encountered even at the outlet of the drippers, which increases the risk of precipitation. Similarly, evaporation plays a very important role in the precipitation of salts. The evaporation phenomenon is also encountered at the level of the drippers. As perspective, the variations in pressure and evaporation can also be modulated with PHREEQC. This study focuses only on chemical precipitation which is only one aspect of the clogging of micro-irrigation systems but in reality and with the complexity of the wastewater composition, interactions between biofilm developments, chemical precipitation and mineral particles can be found. The emitter's structure and the operating model as the irrigation frequency, the working pressure ets can contribute to the development of biofilm and to the deposition of solid particles which leads to dripper clogging. The link between emitter's structure and the operating model with chemical clogging has not or little been studied and could be a very good approach of research. From the results of this study a perspective can be discussed regarding the interaction between calcium carbonate precipitation and biofilm development in a micro-irrigation system.

Figure 1 :

 1 Figure 1: Changes in the average weight of the precipitate and in added NaOH volume as a function of pH and temperature.

Figure 2 :

 2 Figure 2: XRD pattern of the precipitate. Calcite (blue peaks) are observed in all crystallized samples. Vaterite (green peaks) and aragonite (red peaks) are only observed in some samples (pH 8.5 at 55°C, figure 2-b).

  Author-produced version of the article published in Journal of Water Supply Research and Technology-Aqua, 2017, N°66 (8), p. 587-597. The original publication is available at http://aqua.iwaponline.com Doi: 10.2166/aqua.2017.065

Table 1 :

 1 Physico-chemical characteristics of the effluent from the Mauguio WWTP

	Author-produced version of the article published in Journal of Water Supply Research and Technology-Aqua, 2017, N°66 (8), p. 587-597.
	The original publication is available at http://aqua.iwaponline.com
	Doi: 10.2166/aqua.2017.065

  Author-produced version of the article published in Journal of Water Supply Research and Technology-Aqua, 2017, N°66 (8), p. 587-597. The original publication is available at http://aqua.iwaponline.com Doi: 10.2166/aqua.2017.065

  Author-produced version of the article published in Journal of Water Supply Research and Technology-Aqua, 2017, N°66 (8), p. 587-597. The original publication is available at http://aqua.iwaponline.com Doi: 10.2166/aqua.2017.065

NaOH is added before precipitation occurs (a)

	Volume	NaOH	(ml)	Numerical pH calculation	Numerical	calcite	SI
	(experimental)		after NaOH add		calculation after NaOH add
	3			8.442			1.43
	5.25			8.715			1.68
	9.75			9.05			1.95
	19.25			9.486			2.22
		SI, pH, and weight of calcite after precipitation occurs (b)
				Open system (O)
	Numerical pH calculation	Numerical	calcite	SI	Weight of calcite (mg)
	after calcite precipitation	calculation	after	(experimental)
				precipitation
	8.8			1.78			0.42
	8.8			1.805			0.47
	8.912			1.85			1.04
	8.794			1.4			145.55
				Closed system (C)
	8.43			1.43			0.31
	8.708			1.67			0.81
	9.047			1.94			1.45
	8.194			1.5			143.54

Table 3 :

 3

SI and pH values before (a) and after precipitation (b) in an open and closed system with the corresponding weight of calcite.

   shows SI and pH results after precipitation in an open and closed system. The SI of calcite given by the model for (C) and (O) experiments are calibrated to give a weight of calcite close to that obtained in experimental conditions. For example for pH 8 at 22 °C, the weight of calcite is 0.67 ± 0.31 mg. Precipitation begins when after adding NaOH, the SI of calcite is between 1.95 and 2.22 (table3-

NaOH is added before precipitation occurs (a)

	Volume	NaOH	(ml)	Numerical pH calculation	Numerical	calcite	SI
	(experimental)		after NaOH add	calculation after NaOH add
	1.75			8.088	1.47
	4.75			8.378	1.72
	33.5			8.611	2.35
	39.25			9.249	2.39
		SI, pH,

and weight of calcite after precipitation occurs (b) Open system (O)

	Numerical pH calculation	Numerical	calcite	SI	Weight of calcite (mg)
	after calcite precipitation	calculation	after	(experimental)
		precipitation
	8.863	1.85			57.91
	8.82	1.7			105.61
	8.782	0.85			295.6
	8.855	0.98			294.59
		Closed system (C)
	7.317	0.6			55.63
	7.101	0.25			102.3
	8.938	0.95			295.4
	9.368	1.2			295.8

Table 4 :

 4

SI and pH values before (a) and after precipitation (b) in an open and closed system with the corresponding weight of calcite.

  Author-produced version of the article published in Journal of Water Supply Research and Technology-Aqua, 2017, N°66 (8), p. 587-597. The original publication is available at http://aqua.iwaponline.com Doi: 10.2166/aqua.2017.065

Author-produced version of the article published in Journal of Water Supply Research and Technology-Aqua, 2017, N°66 (8), p. 587-597. The original publication is available at http://aqua.iwaponline.com Doi: 10.2166/aqua.2017.065

Acknowledgments

The authors gratefully acknowledge the financial support of the NGO T.E.R.R.E Liban and Water4crops project and also wish to thank the CEREGE laboratory (Aix-en-Provence) for their help with the DRX tests.

Author-produced version of the article published in Journal of Water Supply Research and Technology-Aqua, 2017, N°66 (8), p. 587-597. The original publication is available at http://aqua.iwaponline.com Doi: 10.2166/aqua.2017.065


S

Fluorescence anisotropy

Conclusions: -Anisotropy measurement of molecule mobility provides information about hydrocolloid viscosity and molecular crowding -Data acquisition is fast (< 5 min) allowing different samples to be compared in a single experiment -This technique is independent of fluorophore concentration.

Arabidopsis thaliana

Camelina sativa

B D C A E G F H
On imbibition, the seeds of certain species form a polysaccharide hydrogel, termed mucilage. In Arabidopsis thaliana and Camelina sativa, this mucilage is composed of 2 layers, the outer being water-soluble while the inner is tightly attached to the seed surface. Determining the macromolecular properties of mucilage polymers in the inner mucilage layer is usually achieved by detaching the polysaccharides from the tegument either by physical or enzymatic methods, which alters or eliminates the structure. In order to characterize these properties, we have developed three non-destructive microscopy techniques. Based on fluorescence excitation or nuclear magnetic resonance, these in situ methods aim at investigating the physicochemical properties of mucilage polysaccharides that could affect accessibility and mobility of molecules within the hydrogel. This work presents results obtained on Arabidopsis and Camelina seeds comparing their inner mucilage properties.

Material: Seeds imbibed in water and then stained with fluorescent probes (FITC-polysucrose) of different sizes (20kD, 40kDa and 400kDa). Conclusions: -FRAP can be to obtain information about molecule mobility; if molecule moves freely or is subject to steric hindrance.

Fluorescence Recovery After Photobleaching

-The physical properties of Camelina and Arabidopsis inner mucilage differ.

Pre-bleach Photobleaching Post-bleach

Three complementary, nondestructive in situ methods have been developed which provide information about hydrocolloid organization and the rheological properties of seed mucilage. Each of them is rapid enough for the analysis of several different seeds in a single experiment.

Figure

  Figure 5. Anisotropy measurement 4 . Fluorescence emission intensity (A) perpendicular and (B) parallel to excitation plane, is analysed with imageJ to obtain (C) the anisotropy and (D) the maximum intensity threshold of the (C) image.

FigureFigure 1 .

 1 Figure 6. Anisotropy values obtained with different fluorophore sizes (pink: 20kDa, green: 40kDa and blue: 400kDa).

Figure 3 .Figure 4 .

 34 Figure 3. Camelina mucilage traps some molecules compared to this of Arabidopsis. Results of FRAP data analysis 3 after normalization and fitting the raw data using a biexponential algorithm shown in (A) for Arabidopsis and (B) for Camelina.

Figure 2 .

 2 Figure 2. FRAP acquisition sequence. A Leica SP5 confocal microscope was used to achieve pre-bleach, bleach and post-bleach.

Perspectives


Marilys Pradel
email: marilys.pradel@irstea.fr

Lynda Aissani
email: lynda.aissani@irstea.fr

Jean-Pierre Canler
email: jean-pierre.canler@irstea.fr

Jean-Christophe Roux
email: jean-christophe.roux@irstea.fr

Jonathan Villot
email: jonathan.villot@mines-stetienne.fr

Jean-Christophe Baudez
email: jean-christophe.baudez@list.lu

Valérie Laforest
email: valerie.laforest@mines-stetienne.fr

Constructing an allocation factor based on product-and process-related parameters to assess environmental burdens of producing value-added sludgebased products

Keywords: Allocation factor, product-related parameter, process-related parameter, sludge, wastewater treatment, mathematical modelling

Sludge is slowly moving away from providing basic by-products and towards providing value-added products (e.g. fertilisers); therefore, it is no longer perceived as waste but as a product. Consequently, wastewater treatment plants become multifunctional systems that produce two coproducts that are given a second life: sludge and "clean" water. An allocation factor in Life Cycle Assessment can partition environmental burdens of wastewater treatment between these two products, but doing so remains highly challenging. To address this challenge, we followed a four-step procedure to develop an allocation factor using a mesoscopic approach and process-and product-related parameters in a mathematical model. The first two steps consisted of determining and mathematically representing process-and product-related parameters and their associations to define a global allocation factor. The third step consisted of constructing a corrective inventory matrix to adjust the global allocation factor, since inventory flows can be specific to certain processes. The last step consisted of mathematical modelling of the final corrected allocation factor. Based on the parameters chosen, the global allocation factor equalled 45% for sludge and 55% for water. A sensitivity analysis was performed to assess the robustness of the sludge allocation factor, which varied from 39-49%. The allocation factor developed reflects technological performances of the system and considers environmental impacts of sludge production to assess environmental impacts of value-added sludge-based products.

Introduction

Reuse and recovery of matter or energy from municipal and industrial waste streams has gained increasing interest in the context of circular economy [START_REF] Cec | regions on the implementation of the Circular Economy Action Plan[END_REF][START_REF] Meem | Économie circulaire -Les avancées de la loi de transition énergétique pour la croissance verte -Plan de réduction et de valorisation des déchets 2025 -Contribution à la stratégie nationale de transition vers l'économie circulaire[END_REF] and the European Waste Framework Directive [START_REF] Cec | Council directive of 19 November 2008 on waste and repealing certain Directives[END_REF].

The total amount of waste produced by domestic sources in France in 2015 was estimated at 33 million tons, which represents 14% of the total volume produced in Europe (Eurostat, 2017). Within this waste, wastewater sludge has potential utility, as it is a valuable source of organic matter and macronutrients such as nitrogen (N), phosphorus (P) and potassium. Two main approaches are used to manage wastewater sludge in a more sustainable manner [START_REF] Cieślik | Review of sewage sludge management: standards, regulations and analytical methods[END_REF][START_REF] Wang | Technological options for the management of biosolids[END_REF][START_REF] Yoshida | Life cycle assessment of sewage sludge management: A review[END_REF]: "sludge-to-energy", which recovers energy, and "resource recovery", which recovers matter or nutrients. Depending on the technology used, both approaches provide sludge-based valueadded products. Research on sludge-to-energy approaches has increased over the past 10 years [START_REF] Mills | Environmental & economic life cycle assessment of current & future sewage sludge to energy technologies[END_REF][START_REF] Rulkens | Sewage sludge as a biomass resource for the production of energy: Overview and assessment of the various options[END_REF][START_REF] Tyagi | Sludge: A waste or renewable source for energy and resources recovery?[END_REF]. The most common include:

-anaerobic digestion to produce biogas, which is converted into heat or electricity using a cogeneration system [START_REF] Bond | A critical review of experimental and predicted methane generation from anaerobic codigestion[END_REF][START_REF] Cao | Sewage sludge-to-energy approaches based on anaerobic digestion and pyrolysis: Brief overview and energy efficiency assessment[END_REF], or purified into biomethane, which is injected into the natural gas network.

-biohydrogen production [START_REF] Angenent | Production of bioenergy and biochemicals from industrial and agricultural wastewater[END_REF][START_REF] De Gioannis | A review of dark fermentative hydrogen production from biodegradable municipal waste fractions[END_REF][START_REF] Kalinci | Biomass-based hydrogen production: A review and analysis[END_REF][START_REF] Mudhoo | Biohydrogen production and bioprocess enhancement: A review[END_REF].

-thermal conversion of sludge via pyrolysis or gasification to produce bio-oil or biodiesel [START_REF] Bridle | Energy and nutrient recovery from sewage sludge via pyrolysis[END_REF][START_REF] Fonts | Sewage sludge pyrolysis for liquid production: A review[END_REF]. It also provides value-added products such as ceramsite [START_REF] Xu | Ceramsite Made with Water and Wastewater Sludge and its Characteristics Affected by SiO2 and Al2O3[END_REF] and adsorbents [START_REF] Hadi | A critical review on preparation, characterization and utilization of sludge-derived activated carbons for wastewater treatment[END_REF][START_REF] Smith | Sewage sludge-based adsorbents: A review of their production, properties and use in water treatment applications[END_REF].

-biofuel production [START_REF] Kargbo | Biodiesel Production from Municipal Sewage Sludges[END_REF][START_REF] Manara | Towards sewage sludge based biofuels via thermochemical conversion -A review[END_REF][START_REF] Siddiquee | Lipid extraction and biodiesel production from municipal sewage sludges: A review[END_REF]. Among nutrient recovery processes, P recovery is documented most frequently [START_REF] Egle | Overview and description of technologies for recovering phosphorus from municipal wastewater[END_REF][START_REF] Mehta | Technologies to Recover Nutrients from Waste Streams: A Critical Review[END_REF]. P can be recovered either via anaerobic stripping of sludge liquor by precipitating or crystallising phosphate as struvite or calcium phosphate or via anaerobic digestion of sludge after separating sludge particles and further treatment of the sludge liquor [START_REF] Rahman | Production of slow release crystal fertilizer from wastewaters through struvite crystallization -A review[END_REF]. Thermal conversion can also recover P from sludge by producing biochar, which is a byproduct of pyrolysis [START_REF] Bridle | Energy and nutrient recovery from sewage sludge via pyrolysis[END_REF].

While some of these technologies exist only at laboratory or pilot scales, others are fully functional at the industrial scale, and there is growing willingness to increase the sustainability of sludge management via recovery processes and potentially marketable value-added products. Life Cycle Assessment (LCA) is often performed to assess environmental impacts of these ambitious sludge management systems [START_REF] Johansson | Sewage sludge handling with phosphorus utilization: life cycle assessment of four alternatives[END_REF][START_REF] Lederer | Comparative goal-oriented assessment of conventional and alternative sewage sludge treatment options[END_REF][START_REF] Mills | Environmental & economic life cycle assessment of current & future sewage sludge to energy technologies[END_REF][START_REF] Remy | Life Cycle Assessment of selected processes for P recovery from sewage sludge, sludge liquor, or ash[END_REF]. In these LCA studies, sludge is modelled mainly as waste, even when added-value products are produced. Thus, sludge is considered to have no environmental burden, which creates a distortion in comparative LCA.

Reflecting on consequences for LCA of the paradigm shift in which sludge is considered a product instead of waste, [START_REF] Pradel | From waste to added value product: towards a paradigm shift in life cycle assessment applied to wastewater sludge -a review[END_REF] highlighted that system boundaries among scenarios become unequal when "product" sludge or "waste-to-product" sludge (after matter or nutrient recovery) is compared to fossil-based products such as chemical fertilizers. In LCA studies that compare sludge-based products to fossil or non-waste alternatives, the functional unit (i.e. the value to which LCA results are related to) focuses on a value-added product. In the paradigm shift, upstream processes of sludge production must be considered. Although sludge is a natural result of cleaning wastewater in wastewater treatment plants (WWTPs), it is not considered in the functional unit. To address this issue, environmental burdens must be allocated to sludge when treatments are oriented to produce value-added products. Doing so is challenging, however, because allocation factors must separate the environmental burdens of wastewater treatment between sludge and clean water for each process in the WWTP. This article describes development of an allocation factor that partitions environmental burdens between sludge and treated water. Following a section on the allocation procedure in LCA and the mathematical calculations, the method for constructing this allocation factor based on process-and product-related parameters is described. Following this is a discussion on the limits and robustness of the allocation factor developed and choosing and determining the process-and product-related parameters. Several perspectives are provided on the possible use of this allocation method within the LCA allocation procedure.

Allocation procedure in LCA

LCA guidelines describe general principles for allocation [START_REF] Heijungs | The computational structure of life cycle assessment[END_REF]ISO, 2006a, b;[START_REF] Handbook | ILCD Handbook: General guide for Life Cycle Assessment -Detailed guidance[END_REF], which are based on three main methodological points: definition of allocation factors (section 2.1.), the unit process considered (section 2.2), and how allocation is quantified through mathematical modelling (section 2.3).

Constructing allocation factors based on relevant causal relationships

Standards such as ISO 14044 and the ILCD Handbook state "where allocation cannot be avoided, the inputs and outputs of the system should be partitioned between its different products or functions in a way that reflects the underlying physical relationships between them; i.e. they should reflect the way in which the inputs and outputs are changed by quantitative changes in the products or functions delivered by the system". Therefore, allocation should be based on causal relationships. [START_REF] Ekvall | Open-loop recycling: Criteria for allocation procedures[END_REF] developed two categories of causal relationships: cause-oriented (between a system and its causes) and effect-oriented (between a system and its effects). We considered only the former because they help establish a relation between process functioning and product creation, which is appropriate for sludge production from wastewater treatment.

In practice, burdens are partitioned by identifying the relevant fractions of matter/energy ("input") and emissions/waste ("output") that should be allocated to each of the coproducts [START_REF] Weidema | In Search of a Consistent Solution to Allocation of Joint Production[END_REF]. These fractions are called "allocation factors" or "partitioning coefficients" [START_REF] Chen | LCA allocation procedure used as an incitative method for waste recycling: An application to mineral additions in concrete[END_REF][START_REF] Suh | Generalized make and use framework for allocation in life cycle assessment[END_REF], the former of which we use hereafter.

Allocation factors are defined/supported by quantitative, measurable criteria that are usually based on relative amounts of each product, measured in units (i.e. partitioning criteria) such as mass, energy content or monetary value [START_REF] Suh | Generalized make and use framework for allocation in life cycle assessment[END_REF]. Choosing appropriate criteria is controversial because no consensus exists on which ones are the most suitable (Curran, 2007a,b;[START_REF] Handbook | ILCD Handbook: General guide for Life Cycle Assessment -Detailed guidance[END_REF]. As illustrated by [START_REF] Hanes | Allocation games: addressing the ill-posed nature of allocation in life-cycle inventories[END_REF], "mass allocation works well in manufacturing processes but cannot be applied to energetic outputs 1 , such as electricity; energetic allocation is not intuitive for products not commonly quantified according to energy content; and economic allocation is problematic for products that are typically treated as waste and products with volatile prices." Allocation factors should be designed in accordance with unique characteristics of each system and following "relevant physical relationships" [START_REF] Pelletier | Rationales for and limitations of preferred solutions for multi-functionality problems in LCA: is increased consistency possible?[END_REF]. A relevant physical relationship is, for example, a physical property that represents the primary function defined for the coproduct considered and that is a reasonable common denominator for allocation among coproducts. In this way, the model directly quantifies environmental consequences of the function based on physical relationships between inputs and outputs [START_REF] Marvuglia | Toward a solution of allocation in life cycle inventories: the use of leastsquares techniques[END_REF][START_REF] Pelletier | Rationales for and limitations of preferred solutions for multi-functionality problems in LCA: is increased consistency possible?[END_REF]. Food production systems illustrate allocation factors that are based on physical relationships between system characteristics [START_REF] Mackenzie | The need for co-product allocation in the life cycle assessment of agricultural systems-is "biophysical" allocation progress?[END_REF]. For example, allocation factors can be based on biophysical criteria such as metabolic energy flow or biological processes in livestock systems [START_REF] Idf | A common carbon footprint approach for dairy In[END_REF], or on the energy required to produce biomass (van der [START_REF] Van Der Werf | Construction cost of plant compounds provides a physical relationship for co-product allocation in life cycle assessment[END_REF]. Food and Agriculture Organization guidelines (FAO, 2014) provide allocation factors for agricultural products and manure that consider the latter a coproduct instead of waste.

Industrial systems provide other examples. In the chemical industry, allocation factors are usually based on molar relationships (i.e. stoichiometry and molecular weights), enthalpy or exergy [START_REF] Alvarez-Gaitan | Understanding the impacts of allocation approaches during process based life cycle assessment of water treatment chemicals[END_REF]. According to Azapagic and Clift (1999a,b;2000), the performance of an industrial system is based on product-and process-related parameters. These authors used linear programming to model physical relationships based on these parameters in a boron production system to model infinitesimal variations in outputs to determine "marginal allocation coefficients".

1 "energetic outputs" refers to energy products.

For wastewater treatment, it is not relevant to base allocation factors on energy or economics. Because treated water has no energy content, energetic allocation would result in no allocation, while economic allocation would function only when both sludge and treated water had a market value [START_REF] Pradel | From waste to added value product: towards a paradigm shift in life cycle assessment applied to wastewater sludge -a review[END_REF].

Treated water is usually measured by its volume (cubic meter or litre) and described by chemical parameters (e.g. chemical oxygen demand (COD), biochemical oxygen demand), while sludge is usually measured by its mass and dryness (kg or ton produced on a raw-or dry-matter basis). As treated water can also be measured by its mass (e.g. ton released per day or year), mass allocation would favour treated water over sludge because nearly all of the mass released is water. Indeed, a WWTP releasing 40 000 tons of water and producing 10 tons of sludge per year will have a 100:0 mass allocation factor so that all the burdens will be allocated to clean water. Therefore, mass allocation is not appropriate for water treatment when both sludge and water are produced because it does not reflect the function of the system.

Traditional allocation factors for wastewater treatment have several disadvantages because they do not reflect system function or the potential to increase the efficiency of sludge production. The novelty of the present study is the development of an allocation factor that is based on process-and product-related parameters that circumvent these disadvantages. Because these parameters reflect process performance, any technological improvement in the latter will be mirrored in environmental impacts of each coproduct. Process-related parameters are operational or technical parameters that influence the functioning of the process to which they are related (e.g. temperature, pressure, reagent use efficiency). In contrast, product-related parameters are intrinsic parameters that directly influence product creation and composition within a process. Product-related parameters are specific to a process and are based on physical, chemical, biological or technical characteristics. Parameters based on a product's stoichiometric characteristics or specific macroelement capture rate can be used as product-related parameters. Indeed, from the moment the macro-element capture rate increases the concentration of an expected element in a product, it becomes a product-related parameter.

2.2. Using a macroscopic to microscopic approach to determine an allocation factor [START_REF] Kim | Allocation Procedure in Multi-Output Process: An Illustration of ISO 14041[END_REF] highlighted that the definition of the unit process strongly influences the resulting allocation factors. The unit process can be defined from the largest process (i.e. the entire manufacturing system)  a "macroscopic" approach  to the smallest one (i.e. an operational engineering unit)  a "microscopic" approach. In the macroscopic approach, the process is not subdivided; thus, a single allocation factor is applied to all sub-processes regardless of their function. It is not feasible, however, to use either approach to determine an allocation factor for sludge production. The macroscopic approach requires mass, energy or economic allocation, none of which, as mentioned, is appropriate. The microscopic approach, in contrast, models each operational engineering unit, making it is difficult and time consuming to determine an allocation factor for each unit based on causal relationships.

An intermediate approach is "quasi-microscopic" [START_REF] Kim | Allocation Procedure in Multi-Output Process: An Illustration of ISO 14041[END_REF] (i.e. mesoscopic), in which the unit process refers to each sub-process, which can be combined or joint, physically separated or fully separated. This approach divides a process into sub-processes to identify underlying physical relationships (i.e. process-and product-related parameters) more easily. A sub-process includes all steps involved in manufacturing one product within a process. This approach is useful for identifying key issues related to a product or function and the sub-process concerned. Using the mesoscopic approach to determine an allocation factor is more suitable for sludge production because wastewater treatment is easily subdivided into sub-processes, each of which produces sludge. These sub-processes can be removal of carbon (C), N and P.

Mathematical modelling used in the allocation procedure

Mathematical modelling that considers a system's characteristics is often used to quantify allocation factors. Given system complexity and the mathematical structure of LCA, mathematical modelling takes the form of a matrix to address allocation in the Life Cycle Inventory (LCI) [START_REF] Heijungs | A special view on the nature of the allocation problem[END_REF][START_REF] Heijungs | The computational structure of life cycle assessment[END_REF]. Matrices have been used to perform allocation when connecting LCA and Input-Output analysis [START_REF] Majeau-Bettez | Unified theory of allocations and constructs in life cycle assessment and input-output analysis[END_REF][START_REF] Suh | Generalized make and use framework for allocation in life cycle assessment[END_REF] and to address the multifunctional problem caused by non-common products [START_REF] Jung | Comparative LCA of multi-product processes with non-common products: a systematic approach applied to chlorine electrolysis technologies[END_REF]. Other authors have highlighted the ill-posed problem of allocation using the matrix notation (Cruze et al., 2014a;[START_REF] Hanes | Allocation games: addressing the ill-posed nature of allocation in life-cycle inventories[END_REF] or have improved the matrix-based approach by using regression with rectangular coefficient matrices (Cruze et al., 2014b;[START_REF] Marvuglia | Toward a solution of allocation in life cycle inventories: the use of leastsquares techniques[END_REF]. Others have developed the matrix-based approach to improve uncertainty analysis of multifunctional systems using sensitivity coefficients [START_REF] Jung | Sensitivity coefficient-based uncertainty analysis for multi-functionality in LCA[END_REF][START_REF] Wang | Application of robust optimization in matrix-based LCI for decision making under uncertainty[END_REF] or to assess uncertainty propagation in fuzzy LCI models [START_REF] Heijungs | Rigorous proof of fuzzy error propagation with matrix-based LCI[END_REF].

As summarised by [START_REF] Heijungs | Sensitivity coefficients for matrix-based LCA[END_REF], the "inventory problem" refers to scaling all unit processes in the system in a way that exactly produces the reference flow (or functional unit). Scaling is performed in the LCI. The following generic formula is commonly used [START_REF] Hanes | Allocation games: addressing the ill-posed nature of allocation in life-cycle inventories[END_REF][START_REF] Heijungs | The computational structure of life cycle assessment[END_REF][START_REF] Jung | Comparative LCA of multi-product processes with non-common products: a systematic approach applied to chlorine electrolysis technologies[END_REF]:

g B • A • f (Eq. 1)
where vector g refers to LCI results (i.e. environmental flows, as rows in a single column), B is the intervention matrix (with environmental flows as rows and processes as columns), A -1 is the technology matrix (with processes as rows and economic flows as columns), and vector f is the functional unit defined in the goal and scope (with economic flows as rows in a single column).

Multifunctional processes have more products than processes, which makes matrix A is rectangular; consequently, matrix A -1 does not exist, and Eq. 1 cannot be applied. One solution is to expand matrix A using partitioning allocation so that it will represent monofunctional processes and become square. An allocation factor (C) [START_REF] Jung | Sensitivity coefficient-based uncertainty analysis for multi-functionality in LCA[END_REF] can be used to convert matrices A and B into their allocated forms * and * .

When allocation factor C is used to partition economic and environmental flows, Eq. 1 becomes:

g * B * • A * • f (Eq. 2)
Allocated inventory results * are then converted into environmental impacts (h * ) by multiplying them by a matrix of characterisation factors (Q):

h * Q • g * (Eq. 3)
Jung et al. ( 2014) argued that allocation factor C is a potential source of uncertainty, and [START_REF] Hanes | Allocation games: addressing the ill-posed nature of allocation in life-cycle inventories[END_REF] argued that it can be calculated from common partitioning criteria or other criteria. The purpose of mentioning these articles was to explore a theoretical allocation procedure. The purpose of the present study was to determine a value for allocation factor C for wastewater treatment. Therefore, we developed a mathematical model, based on process-and product-related parameters and a mesoscopic approach, to allocate environmental burdens between sludge and treated water.

Constructing an allocation factor for wastewater treatment

It was first necessary to identify sub-processes involved in wastewater treatment and the related process-and productrelated parameters used to construct the allocation factor.

Modelling a wastewater treatment plant

A WWTP generally consists of two processes that treat wastewater and sludge, respectively. For the former, the most common one is the aerobic activated sludge process. In its most complete form, wastewater is progressively cleaned in three sub-processes, according to a mesoscopic approach, to remove organic C, N and P before being released into the environment.

Organic C is removed by bacteria, whose growth and decay degrade soluble organic matter. The bacteria grow by using oxygen to consume the organic matter. Autolysis of bacteria causes them to decay, which also uses oxygen. During their growth, bacteria also consume ammonium (NH 4 + ) and P. The remaining N is removed by nitrification, oxidation of ammonia (NH 4 + ) to nitrite (NO 2 -) and nitrate (NO 3 -), and denitrification, reduction of NO 2 -and NO 3 -into nitrogen gas (N 2 ) [START_REF] Degrémont | Memento technique de l'eau[END_REF]. P that is not assimilated within bacteria (i.e. "normal" biological P removal (NBPR)) can be removed by two processes: chemical precipitation and enhanced biological P removal (EBPR). When NBPR is unable to decrease P concentrations below legal thresholds, chemical precipitation is required. It consists of adding chemical salts to produce chemical sludge such as iron (III) phosphate or aluminium phosphate when ferric chloride or aluminium sulphate is respectively used. EBPR is similar to NBPR but includes an anaerobic phase before the aerobic phase. Sludge from EBPR has higher P concentration (6%) than that from NBPR (1.5%). Together, the three sub-processes of C, N and P removal produce biological sewage sludge (Fig. 1). Afterwards, the environmental impacts of sludge treatment are fully allocated to the sludge-based product.

Determining which parameters to use to construct the allocation factor

This section presents how process-and product-related parameters are determined. After a brief description, a wastewater treatment case study is used to explain and illustrate the calculation of the process-and product-related parameters.

Process-related parameters

Description

A process-related parameter can be specific to only one sub-process or can contribute to several sub-processes. In the latter case, its contributions among sub-processes can be weighted by a ratio that equals the proportion of each processrelated parameter used by each sub-process in the entire process. The ratio is calculated by dividing the value of a characteristic (e.g. mass, volume) involved in each sub-process by the total value of the characteristic involved in the entire system.

The process-related parameter is noted j and ranges from 1 to n. The sub-process is noted k and ranges from 1 to p. The relation between the sub-process and the process-related parameter is noted β , . β , is calculated according to Eq. 4 and refers to the ratio used to partition each process-related parameter j between each sub-process k using it. where Q , is the value of the process-related parameter used by each sub-process k, and ∑ Q , is the total value of process-related parameters used by all sub-processes k. 10

When a process-related parameter contributes to only one sub-process, β , equals 1. When it contributes to several subprocesses, β , ranges from 0 to 1 (exclusive), and the sum of β , equals 1.

Wastewater treatment process-related parameters

According to expert opinion, oxygen demand (OD) and the shift between aerobic and anaerobic periods are the processrelated parameters that most influence these processes of wastewater treatment.

OD equals the amount of oxygen required during C and N removal. In contrast, P removal does not require oxygen because the bacteria have already assimilated oxygen. Values for calculating each process-related parameter are provided in Table 1 and detailed in Supplementary Information. Values come from literature and are related to standard oxygen requirement for C and N removal. OD of C removal equals that used for direct oxidation of organic matter (via bacterial growth) and indirect oxidation from bacterial autolysis (decay) [START_REF] Degrémont | Memento technique de l'eau[END_REF]. OD of N removal equals that used to oxidise NH 4 + during nitrification. The OD ratio ( , Eq. 5) for C and N equals the OD for the removal of each nutrient (OD ) divided by the total OD (OD ).

(Eq. 5)

To optimise C and P removal and nitrification (which require oxygen) and denitrification (which requires a lack of oxygen), wastewater is subjected to alternating aerobic and anaerobic periods (AAP). AAP is most effective when the aerobic period lasts 16 h, leaving 8 h in the 24 h cycle for complete denitrification (J.-P. Canler, Irstea, pers. comm.).

AAP ratios for the four C, N and P removal processes ( , Eq. 6) are calculated to partition the 24 h cycle. They equal the proportion of the complete cycle under an aerobic condition (% ) divided by the number of sub-processes under that condition ( ) plus the proportion of the complete cycle under an anaerobic condition (% ) divided by the number of sub-processes under that condition ( ).

% % (Eq. 6)

Product-related parameters

Description

As a sub-process can produce two or more coproducts simultaneously, product-related parameters, like process-related parameters, can be integrated into the allocation factor via ratios, in this case based on physical, chemical or stoichiometric properties. The sub-process is noted k and ranges from 1 to p. Coproducts of the sub-process are noted r and range from 1 to q. The relation between sub-processes and products is based on the product-related parameter and is codified with a  symbol. The ratio (α , ) is calculated according to Eq. 7.:

α , , ∑ , (Eq. 7)
where Q , is the value of product-related parameters used to generate each product r, and ∑ Q , is the total value of product-related parameters used by the sub-process k.

When a product-related parameter contributes to only one product, α , equals 1. When it contributes to several coproducts, α , ranges from 0 and 1 (exclusive), and the sum of α , equals 1.

Wastewater treatment product-related parameters

Sludge production resulting from C and N removal is based on stoichiometric equations, while that from P removal is based on chemical precipitation and bacterial assimilation. Values and equations used to calculate each product-related parameter were determined according to expert opinion (Table 2 and Supplementary Information).

Carbon removal

Average compositions of organic matter in wastewater and sludge were assumed to be C 18 H 19 NO 9 and C 5 H 7 NO 2 , respectively [START_REF] Deronzier | Traitement de l'azote dans les stations d'épuration biologique des petites collectivités[END_REF][START_REF] Hahn | Chemical Water and Wastewater Treatment V, 8th Gothenburg Symposium[END_REF]. Bacteria degrade organic matter via growth (Eq. 8) and decay (endogenous respiration) (Eq. 9):

C

Nitrogen removal

Nitrification and denitrification produce sludge according to the following stoichiometric equations (Eq. 11 and 12, respectively) [START_REF] Deronzier | Traitement de l'azote dans les stations d'épuration biologique des petites collectivités[END_REF][START_REF] Qasim | Wastewater Treatment Plants: Planning, Design, and Operation[END_REF]: These two equations are used to calculate the product-related parameter for sludge production from N removal ( , Eq. 13). As N removal requires an organic substrate, the corresponding ratio is based on the N and C contents of sludge compared to total N and C output. It is the sum of the number of N moles from biomass produced from nitrification (n , ) and the number of C and N moles from biomass produced from denitrification (n , , ,

NH 4 + +
). This sum is then divided by the total number of C and N moles produced from denitrification, assuming a 0.98 correction factor (i.e.

amount of NO 3 --N produced from nitrification, n , , ).

Phosphorus removal

Sludge produced from phosphorus removal is the results from two operations of the phosphorus assimilation within the bacteria (both NBPR and EBPR can be considered) and an additional chemical precipitation. Additional chemical precipitation is required when phosphorus removal is not sufficient to meet the required phosphorus concentrations to be released within the natural media. P assimilation ( ) depends on the COD:P ratio of incoming wastewater and the food-to-mass (F:M) ratio. ranges from 20-60% at a F:M ratio of 0.1, depending on the COD:P ratio and whether NBPR or EBPR is performed [START_REF] Stricker | Phosphore des eaux usées -Etat des lieux et perspectives[END_REF]. We assumed a value of 30%, which corresponds to NBPR (J.-P. Canler, Irstea, pers. comm.). Chemical precipitation of P (RE ) uses chemical salts. We assumed only an iron-based reactant because it is commonly used in water treatment. RE (Eq. 14) is a function of P concentration of incoming wastewater and the molar Fe:P ratio (range = 0.25-4.00) [START_REF] Canler | Les clarifloculateurs plus particulièrement utilisés en traitement tertiaire, Dossier technique[END_REF]. The product-related parameter for sludge production from P removal ( , Eq. 15) equals RE plus RE , assuming a molar Fe:P ratio of 1.8 because chemical precipitation of P required 70% efficiency:

1 • (Eq. 15)

Constructing the allocation factor C

Combining these independent process-and product-related parameters (β , and α , , respectively; Fig. 2a) for coproducts r yields the allocation factor C , which we applied to the wastewater treatment case study (Fig. 2b). C was developed in a four-step procedure: mathematically representing process-and product-related parameters (step 1), constructing a global allocation factor C , (step 2), determining a corrective inventory matrix I (step 3) and finalising C (step 4).

Step 1. Mathematical representation of process-and product-related parameters

Equations

The process-related parameter influences each sub-process k (β , ), and the product-related parameter influences the creation of each coproduct r (α , ). Process-related parameters are expressed as the sum of their contribution ratios to each sub-process k (Eq. 16).

δ ∑ β , (Eq. 16)

As ratios must range from 0 to 1, δ is scaled down by dividing it by the total number of process-related parameters n, which makes δ′ a single-row matrix (Eq. 17): δ′ ∑ , (Eq. 17) with ∑ ′ 1

Product-related parameters are represented in matrix P, with terms α , :

P α , … α , … α , ⋮ ⋱ ⋮ ⋱ ⋮ α , … α , … α , ⋮ ⋱ ⋮ ⋱ ⋮ α , … α , … α , with 1  r  q and 1  k  p

Application to wastewater treatment parameters

For wastewater treatment, the contribution ratio of each process-related parameter of each sub-process was then calculated using the process-related parameter calculated in the previous section ( The global allocation factor C was constructed by multiplying δ′ by matrix P (Eq. 18). The result is a matrix composed of δ α , terms that allocates each environmental burden to the product and sub-process from which it originated.

C δ′ • P δ′ α , (Eq. 18)

with 1  k  p, 1  r  q and ∑ ∑ δ′ α , 1

C took the following form for wastewater treatment: C 0.191 0.232 0.170 0.296 0.085 0.026

3.3.3.
Step 3. Determining a corrective inventory matrix I Economic and environmental flows are used or created by one or more sub-processes, while others are used or generated by the entire process (i.e. all sub-processes). A corrective inventory matrix I, with terms  , , is created to adjust C by specifying whether inputs/outputs i (range = 1-m, in rows) are used or created by sub-processes k (range = 1-p, in columns). Matrix I contains only ones and zeros, the formers indicate inputs/outputs i are used or created by sub-process k, the latter they are not.

LCI data (Table 3) came from a French WWTP that can treat up to 140 000 population equivalents and are provided for the annual production of 3 120 000 kg dry matter of sludge, which yields 25 317 kg of P. Matrix I had five rows for flows of electricity, infrastructure, reactants, and CO 2 and N 2 O emissions and three columns for C, N and P removal subprocesses. Because the first two flows were used within all sub-processes and the other three were specific to P, C, and N removal, respectively, matrix I took the form: I =

1 1 1 1 1 1 0 0 1 1 0 0 0 1 0 3.3.4.
Step 4. Finalising allocation factor C

Allocation factor C was finalised by multiplying the global allocation factor (C ) by matrix I (Eq. 19):

C , I • C (Eq. 19)
As the sum of allocation factors of each input/output i must equal 1, C was scaled down by dividing each element in a row by the sum of each row in matrix C , (Eq. 20):

C , ∑ , (Eq. 20)
The corrected allocation factor C results in a matrix in which rows represent allocation factors for each input/output i and columns represent allocation factors for each coproduct.

For wastewater treatment, the first and second columns in matrix C represented corrected allocation factors for sludge 1 and2). Supplementary Information provides detailed explanation of how each one's range of variation was determined.

A complete factorial experimental design was performed using R software [START_REF] Isoz | R -statistical software, one software to Rule them all -Cookbook[END_REF]

Benefits of the method for LCA allocation

The allocation factor developed in this study can be used as-is in LCA of sludge production when assessing environmental impacts of sludge-based products. However, in practice, using it requires more mathematical modelling. LCI flows (Table 3) can be represented as a square matrix (I') that contains zeros except for diagonal elements, each of which represents a flow (i.e. electricity, infrastructure resources, reactants, and CO 2 and N 2 O emissions, respectively). This matrix must be multiplied by allocation factor C (Eq. 20) so that the resulting matrix has a shape that can replace B * • A * in Eq. 2. In the wastewater treatment case study: and Eq. 2 can be transformed as follows:

I' = 3
g * I′ • C • f (Eq. 21)
The allocated inventory flow g * for sludge production is calculated by considering that the vector f represents the scaled functional unit (i.e. if 25 317 kg of P are produced and the functional unit is set to 1 kg of P, f equals 3.95E-05): This simplified mathematical modelling is one way to assess environmental impacts of sludge production using a technology-oriented allocation factor.

Discussion

The importance of modelling the system and determining the process-and product-related parameters and their values are key issues in determining the developed allocation factor, and are therefore discussed below.

Importance of system modelling in constructing C

Allocation factors depend strongly on how the system is modelled. The allocation factor for sludge production was based on a mesoscopic approach to consider the sub-processes that produce sludge. This approach allows for accurate description of system functioning because the process-and product-related parameters focus on operational process functioning and product creation, respectively. This approach is technologically oriented, and performances of wastewater treatment and mechanisms involved in sludge production are reflected in the allocation factor. Dividing the system into sub-processes, however, required a wastewater treatment expert to adequately identify and model the sub-processes as individual unit processes.

The WWTP was modelled as an aerobic activated sludge process, for which the allocation factor calculated is valid. Other biological processes are available to treat wastewater, however, such as attached growth systems, or extensive processes such as reed bed filters. Validating the allocation factor for sludge production requires in-depth analysis of such systems to identify whether the process-and product-related parameters are also valid for these systems and the allocation factor developed.

4.2. Determining the process-and product-related parameters used to construct C

Two critical steps are necessary to construct allocation factor C : (i) identifying the process-and product-related parameters and (ii) determining their values and how to calculate α , and β , ratios.

Identifying parameters

From a mathematical viewpoint, there is no limit to the number of process-and product-related parameters that can be used to construct the allocation factor. Identifying these parameters is extremely important because they must be relevant and reflect the process performances. This requires selecting the parameters that influence process functioning and product creation the most. Because the process functioning is well known, the parameters can be identified with a qualitative or quantitative mechanistic approach. In the present study, the most relevant process-and product-related parameters were identified with a qualitative method that required the help of experts in corresponding technical and scientific domains. This approach ensures that appropriate parameters are used, but remains subjective because they are based on expert opinion. A quantitative method, based on process modelling, is more appropriate when the allocation factor is used to optimise processes to reduce their environmental impacts. Examples include (i) activated sludge models [START_REF] Henze | Activated Sludge Models ASM1, ASM2, ASM2d and ASM3[END_REF], (ii) a data-driven approach that identifies useful patterns and models using algorithms based on statistics and artificial intelligence [START_REF] Wei | Modelling and optimization of wastewater treatment process with a data-driven approach[END_REF], and (iii) empirical modelling based on artificial neural networks and multivariate polynomial regression [START_REF] Raduly | Empirical modelling of wastewater treatment processes -An approach to model reduction and integration[END_REF].

Determining parameter values

Once parameters are identified, the second key issue is to determine their values. In the present study, standard values from legislation for P removal and those used to calculate WWTP capacity for C and N removal were considered under the supervision of technical experts. This enables using the allocation factor for wastewater treatment systems similar to the system modelled. The allocation factor can be used as-is in LCA studies without further calculations. These standard values, however, do not consider characteristics that may be specific to certain wastewater treatment processes. This might be restrictive if the allocation factor is used with the aim of decreasing environmental impacts of sludge-based products. In this context, parameter values should come from measurements and model predictions in priority, then on expert opinion and literature data.

Robustness of C

Determining the allocation factor comes with uncertainties. Uncertainties occur when real process operations are simplified and processes are subdivided. Identifying parameters and determining their values is also a source of uncertainty in calculating the allocation factor. Further uncertainty occurs in assuming that relationships between processand product-related parameters are linear. Linear modelling is common in LCA because process models are developed for an average operating status without considering time dependencies and substance-specific wastewater composition. It may thus oversimplify modelling of processes technologies [START_REF] Köhler | Input-dependent life-cycle inventory model of industrial wastewater-treatment processes in the chemical sector[END_REF].

To decrease the uncertainty in determining product-and process-related parameters, uncertainty analysis is recommended for the chosen parameters and the calculated ratios to highlight the robustness of the allocation factor and the most influent parameters. Determination of α , and β , requires more caution if the allocation factor varies greatly when the processor product-related parameters vary. If the allocation factor varies little, it can be argued that determination of these process-and product-related parameters is relevant and the allocation factor is robust.

Conclusion

This study used a modelling approach to allocate environmental burdens of wastewater treatment between sludge and treated water based on the technological efficiency of the treatment processes. The approach considers possible links between processes and products according to their respective related parameters to calculate an allocation factor following a matrix-based approach. Technical and scientific expert opinions were used to determine these parameters to base allocation factor calculation on realistic data not founded on arbitrary choices. Two process-related parameters and three product-related parameters were identified and combined to calculate the allocation factor for sludge production. The allocation factor was approximately 45% and ranged from 39-49% depending on the values of each parameter in the calculation. Finally, determining these parameters requires careful consideration to avoid uncertainty. Specific models, experimental results, and expert opinion can provide relevant values for each process-and product-related parameter.

  to assess the robustness of C in response to variation in these 11 variables and the relative influence of these 11 variables on it. The complete factorial design resulted in 3 11 possible combinations, which yielded many values for C (box plot representation, Fig 3a). Minimum and maximum values of C , which had a median value of 0.437, varied by no more than 10%, mainly because the nature of the parameters caused them to have small ranges of variation. Statistical analysis of the influence of parameters on C indicated that the stoichiometric parameters used for N or P removal had little influence. Only the number of moles of oxygen used for bacterial decay ( , ) had an influence (Fig. 3b), decreasing C as , increased. However, the range of variation in , varied C by only 3%. Thus, the C calculated seemed relevant within the range of values used.

  Author-produced version of the article published in Journal of CleanerProduction, 171, 2017Production, 171, , 1546Production, 171, -1557. The original publication is available at http://www.sciencedirect.com/ doi: 10.1016/j.clepro.2017.10.112

  the moles of O 2 for growth, refers to the biomass molar mass (i.e. sludge), and 1.74 refers to the moles of sludge in Eq. 8.

	where	,	is moles of O 2 for decay,
			18 H 19 NO 9 + 8.8 O 2 + 0.74 NH 3 => 9.3 CO 2 + 1.74 C 5 H 7 NO 2 + 4.52 H 2 O	(Eq. 8)
			0.87 C 5 H 7 NO 2 + 4.35 O 2 => 4.35 CO 2 + 0.87 NH 3 + 1.74 H 2 O	(Eq. 9)
	The product-related parameter for C removal ( ) is based on the C contents of sludge and wastewater, and the amount
	of sludge produced per gram of COD eliminated ( ,	). After calculating	,	,	is calculated as m ,
	times the proportions of C in sludge (% ,	) and wastewater (% ,	) per g of COD eliminated (m ,	):
					,	,	• % , • % ,	(Eq. 10)
			with	,	,	. •	,	•	expressed in g/g COD

, refers to

  , is the number of N atoms in the biomass, and , is the number of N atoms in N 2 .

			,		, ,	, ,	,	(Eq. 13)
		with , ,	,	,	•	,		,		•	,
		and , ,	, ,	,		,	•	,	•	,	,
	where ,	is moles of NO 3 -from nitrification, ,		is moles of biomass from nitrification,	,	is moles of N 2
	from denitrification,

, is moles of CO 2 from denitrification, , is moles of sludge from denitrification, , is the number of C atoms in the biomass,

Table 1

 1

	):

  Cequals the sum of global allocation factors C for sludge (i.e. first column of matrix C g ) and is equivalent to the value calculated when inputs/outputs of all sub-processes are used (i.e. C 0.45). The sensitivity analysis focused on 11 variables used to calculate process-and product-related parameters (Tables

	(C	) and treated water (C	), respectively:
			0.446 0.554		0.45 0.55		0.45		0.55
		C ,	0.446 0.554 0.085 0.026 0.191 0.232	, thus, C	0.45 0.55 0.77 0.23 0.45 0.55	leading to C	0.45 0.77 0.45	and C	0.55 0.23 0.55
			0.170 0.296		0.37 0.63		0.36		0.63
	Thus, based on the LCI, the C	matrix indicated the percentages of environmental burdens that should be allocated
	to sludge production: 45% of electricity and infrastructure resources, 77% of reactant resources, 45% of CO 2 emissions
	and 36% of N 2 O emissions.
	3.4. Robustness of allocation factor C	for sludge production
	Sensitivity analysis was performed for allocation factor C	to assess the latter's relevance for sludge production.