Marc Metian

Michel Warnau

François Oberhänsli

Jean-Louis Teyssié

Dr Paco Bustamante

Interspecific comparison of Cd bioaccumulation in European Pectinidae (Chlamys varia and Pecten maximus)

Keywords: Cadmium, Metal, Kinetics, Subcellular Distribution, Scallops, Bivalves

teaching and research institutions in France or abroad, or from public or private research centers.

INTRODUCTION

Bivalves usually concentrate efficiently Cd from the surrounded environment (e.g. [START_REF] Eisler | Cadmium hazards to fish, wildlife and invertebrates: a synoptic review[END_REF]. Among them, Pectinidae can display very high concentrations of this non essential metal that is considered as one of the most toxic ones. High levels of Cd in scallop tissues have been reported even for species from pristine and low-contaminated areas such as the Antarctic Ocean or the sub-polar Atlantic Ocean [START_REF] Mauri | Heavy metals in the Antarctic scallop Adamussium colbecki[END_REF][START_REF] Viarengo | Cu, Zn, Cd content in different tissues of the Antarctic scallop Adamussium colbecki (Smith 1902): role of metallothionein in the homeostasis and in the detoxification of heavy metals[END_REF][START_REF] Bustamante | Interspecific and geographical variations of trace element concentrations in Pectinidae from European waters[END_REF], suggesting that scallops have evolved a natural capacity to accumulate, detoxify and store this metal in their tissues. Investigations carried out in the field and in the laboratory have revealed the involvement of very efficient detoxification mechanisms.

Indeed, the binding of Cd to high-affinity cytosolic proteins, lysosomes, and mineral concretions is well known to result in efficient Cd sequestration in Pectinidae [START_REF] Carmichael | Cadmium accumulation and toxicity in the kidney of the bay scallop Argopecten irradians[END_REF][START_REF] Ballan-Dufrançais | Physiological features of heavy metal storage in bivalve digestive cells and amoebocytes: EPMA and factor analysis of correspondences[END_REF][START_REF] Stone | Cadmium binding components of scallop (Pecten maximus) digestive gland. Partial purification and characterization[END_REF]).

Even though field investigations have shown that Cd levels are influenced by various factors such as geographical origin, season, size and sexual maturity [START_REF] Bryan | The occurence and seasonal variation of trace metals in the scallops Pecten maximus (L.) and Chlamys opercularis (L.)[END_REF][START_REF] Evtushenko | Cadmium bioaccumulation in organs of the scallop Mizuhopecten yessoensis[END_REF][START_REF] Mauri | Heavy metals in the Antarctic scallop Adamussium colbecki[END_REF][START_REF] Bustamante | Interspecific and geographical variations of trace element concentrations in Pectinidae from European waters[END_REF], 2005a), very little is known on the dynamics of Cd bioaccumulation and retention in this family. To the best of our knowledge, no study has described the Cd accumulation in Pectinidae exposed via different pathways and its depuration using environmentally realistic metal levels. For example the earlier study by [START_REF] Eisler | Cadmium uptake by marine organisms[END_REF] exposed Aquipecten irradians to 10 ppm Cd, a concentration with toxic consequences [START_REF] Gould | Uptake and effects of copper and cadmium in the gonad of the scallop Placopecten magellanicus: concurrent metal exposure[END_REF]) and therefore unlikely to produce a typical accumulation pattern for Cd. In natural conditions, scallops are exposed to metal through seawater and food pathways, sediment potentially contributing to either or both. It is therefore necessary to investigate separately these different exposure pathways to understand their relative contribution in the global accumulation of the metal [START_REF] Fowler | Biological transfert and transport processes[END_REF].

Seawater has been often considered as the main source of metal intake for marine organisms (e.g., [START_REF] Janssen | Uptake and cellular distribution of cadmium in Mytilus edulis[END_REF][START_REF] Borchardt | Influence of food quantity on the kinetics of cadmium uptake and loss via food and seawater in Mytilus edulis[END_REF][START_REF] Riisgard | Accumulation of cadmium in the mussel Mytilus edulis: kinetics and importance of uptake via food and seawater[END_REF]; however the role of the particulate phase, mainly food, is now recognized to be of primary importance for a large range of taxa (e.g., [START_REF] Warnau | Biokinetics of selected heavy metals and radionuclides in the common Mediterranean echinoid Paracentrotus lividus: sea water and food exposures[END_REF], 1999[START_REF] Reinfelder | Trace element trophic transfer in aquatic organisms: A critique of the kinetic model approach[END_REF][START_REF] Wang | Delineating metal accumulation pathways for marine invertebrates[END_REF]. In the case of Pectinidae, it has been suggested that food could be the major route of Cd intake on the basis of elevated metal concentrations found in the digestive gland [START_REF] Palmer | Trace metal concentrations in two shellfish species of commercial importance[END_REF][START_REF] Uthe | Cadmium in sea scallop (Plactopecten magellanicus) tissues from clean and contaminated areas[END_REF], Bustamante & Miramand 2005a). However, it appears necessary to confirm this assumption as the contribution of the dissolved phase could also lead to high metal concentrations in the storage and detoxification organs (e.g., [START_REF] Borchardt | Influence of food quantity on the kinetics of cadmium uptake and loss via food and seawater in Mytilus edulis[END_REF].

Therefore, the present work investigated uptake and loss kinetics of Cd in two species of scallops, Chlamys varia and Pecten maximus exposed through seawater, food and/or sediment, depending of their different living habitats -only seawater and food for C. varia and all pathways for P. maximus which is living buried in the bottom sediment and is able to ingest large particles [START_REF] Mikulich | Food of the scallop[END_REF][START_REF] Shumway | Food resources related to habitat in the scallop Placopecten magellanicus (Gmelin, 1791): A qualitative study[END_REF]. The use of highly sensitive radiotracer techniques allowed studying bioaccumulation mechanisms at realistic Cd levels encountered in the field. Three levels of biological organization were considered in this study, the whole individual, the different organs and the subcellular fractions of the digestive gland cells, in order to evaluate the biokinetic parameters of the accumulation, the distribution among the body compartments and the cellular forms of storage in the digestive gland, respectively. Finally, we used a bioaccumulation model to determine the relative contribution of the different exposure pathways of Cd for both species. ; salinity: 36 p.s.u.; temperature: 17 ± 0.5°C; pH: 8.0 ± 0.1; light/dark cycle: 12 h/12 h) prior to experimentations.

MATERIALS AND METHODS

Sampling

During this period, scallops were fed daily an algal mixed diet (Isochrysis galbana, Skeletonema costatum).

Radiotracer and counting

Uptake and loss kinetics of 109 Cd in scallop species were determined using a high specific activity radiotracer purchased from Isotope Product Lab ( 109 Cd as CdCl 2 in 0.1M HCl, T ½ = 426.6 d). The tracer was counted using a high-resolution γ-spectrometer system composed of three Germanium -N or P typedetectors Intertechnique) connected to a multichannel analyser (Intergamma, Intertechnique). The radioactivity was determined by comparison with standards of known activity and of appropriate geometry. Measurements were corrected for counting efficiency and physical radioactive decay. The counting time was adjusted to obtain a propagated counting error less than 5 %.

Seawater exposure

Twenty three Chlamys varia and 23 Pecten maximus (average weight ± SD: 30 ± 7 g and 208 ± 46 g, respectively) were placed in a 70-l glass aquarium (constantly aerated closed circuit aquarium; salinity: 36 p.s.u.; temperature: 17 ± 0.5°C; pH: 8.0 ± 0.1; light/dark cycle: 12 h/12 h) and exposed for 7 d to 109 Cd dissolved in seawater (2 kBq l -1

). No change in pH was detectable after the tracer addition. Spiked seawater was renewed twice a day the first two days and then daily in order to keep radioactivity in seawater constant. Activity of the 109 Cd in seawater was checked before and after each spike renewal, yielding time-integrated activities of 2.1 ± 0.2 kBq l -1 .

Nine scallops of each species were collected at different time intervals and were whole-body radioanalyzed alive (same identified individual each time). At the end of the 7-d exposure period, 5 scallops of each species were sacrificed and dissected. Shell, digestive gland, kidneys, gills, gonad, mantle, intestine, adductor muscle and the rest of soft tissues were separated and radioanalyzed in order to assess the 109 Cd body distribution. The remaining scallops were then placed in non contaminating conditions (constantly aerated open circuit; flux: 50 l h -1 ; salinity: 38 p.s.u.; temperature: 17 ± 0.5 °C; pH: 8.0 ± 0.1; light/dark cycle: 12 h/12 h) for 36 d and nine individuals of each species were regularly radioanalyzed alive in order to follow the loss of 109 Cd from the scallops. Four scallops were collected at the end of the depuration period and dissected into several body compartments as previously described.

Food exposure

The prymnesiophycean Isochrisis galbana was used to study 109 Cd transfer to scallops through their diet.

Phytoplankton cells were exposed to 4.8 kBq l -1 109 Cd during their growing phase (7 d). After that period, phytoplankton medium was filtrated (1 µm-mesh size; Osmonic filters), and then resuspended in a 70-l aquarium (constantly aerated closed-circuit; salinity: 36 p.s.u.; temperature: 17 ± 0.5°C; pH: 8.0 ± 0.1; light/dark cycle: 12 h/12 h) where six C. varia and six P. maximus (average weight ± SD: 17 ± 5 g and 127 ± 14 g, respectively) were placed for one week before the feeding experiment. The radioactivity of the labelled I. galbana was γ-counted before and after the filtration. Scallops were allowed to feed on radiolabelled I. galbana for 2 h (cell concentration -5 10 4 cell ml -1 -was selected to avoid pseudofeces production). After the feeding period, all scallops were γ-counted and flowing seawater conditions (50 l h - 1 ) were restored in the aquarium. Individuals were then whole-body γ-counted alive at different time intervals to follow the loss kinetics of 109 Cd. Four individuals were collected after 16 (P. maximus) and 30 d (C. varia) of depuration, and dissected to determine the 109 Cd tissue distribution among the different body compartments (shell, digestive gland, kidneys, gills, gonad, mantle, intestine, adductor muscle and the rest of soft tissues) and among the subcellular fraction of the digestive gland (see below).

Sediment exposure

Since P. maximus is living buried into the sediment whereas C. varia is fixed on rocks, Cd exposure through sediment was only assayed for P. maximus. Sediment was collected in Wimereux (North-Atlantic coast of France). Sediment grain size distribution was measured on a Mastersizer micro and the evaluation of the dry/wet weight ratio was calculated after freeze drying in a LABCONCO Freezone18. Aerated sediment (9 kg) was placed in plastic bottle, exposed to 109 Cd (516 kBq) for 6 d with constant agitation, then used to form a homogeneous sediment layer of 4 cm height in a 20-l aquarium. Weakly bound 109 Cd was allowed to leach overnight under flowing seawater (50 l h -1 ) [START_REF] Warnau | Biokinetics of selected heavy metals and radionuclides in the common Mediterranean echinoid Paracentrotus lividus: sea water and food exposures[END_REF]. Ten P. maximus (average weight ± SD: 118 ± 5 g) were then placed for 13 d in the aquarium (constantly aerated open circuit; flux: 50 l h -1

; salinity: 36 p.s.u.; temperature: 17 ± 0.5°C; pH: 8.0 ± 0.1; light/dark cycle: 12 h/12 h). Six individuals as well as sediment aliquots were regularly radioanalyzed during the experiment duration. A ctivity of 109 Cd in sediment was constant all along the exposure period (24.2 ± 1.9 Bq g -1 wet wt). At the end of the uptake period, 4 scallops were collected, dissected (shell, digestive gland, kidneys, gills, gonad, mantle, intestine, adductor muscle and the rest of soft tissues), weighed and γ-counted in order to determine the radiotracer distribution among the body compartments. The remaining individuals were transferred for 49 d to a new 20-l aquarium containing non contaminated sediment with flowing seawater and they were regularly radioanalyzed to follow 109 Cd loss kinetics. Also, 109 Cd activity in sediment was regularly measured in order to ascertain that no contamination of the clean sediment occurred through 109 Cd recycling (for security, the whole sediment layer was renewed anyway after one week). At the end of the loss period, 4 scallops were collected and dissected as described above to determine 109 Cd body distribution and its subcellular distribution in the digestive gland.

Subcellular distribution

For all the experiments, the digestive gland of both scallop species were considered to assess the partitioning of 109 Cd between soluble and insoluble fractions as described by Bustamante & Miramand (2005b). Briefly, part of digestive gland were homogenized individually with a mortar and pestle on ice with 10 ml of 0.02 M Tris-HCl buffer, 0.25 M sucrose, 1 mM phenylmethylsulfonylfluoride (PMSF, as protease inhibitor), at pH 8.6. The homogenates were centrifuged at 80,000 G for 1 h at 5°C in a Sorvall RC28S ultracentrifuge to separate particle-free supernatant (cytosol; soluble fraction) from the pellet (insoluble fraction). Homogenate aliquots, cytosols, and pellets were then radioanalyzed.

Data analysis

Uptake of the radioisotope was expressed in term of concentration factors (CF: ratio between the 109 Cd activity in scallops _ Bq g -1 wet wt _ and time-integrated activity in the seawater _ Bq g -1 ) over time for the seawater exposure and in term of transfer factors (TF: ratio between the 109 Cd activity in scallops _ Bq g -1 wet wt _ and time-integrated activity in the sediment _ Bq g -1 ) over time for the sediment exposure of P. maximus [START_REF] Warnau | Biokinetics of selected heavy metals and radionuclides in the common Mediterranean echinoid Paracentrotus lividus: sea water and food exposures[END_REF][START_REF] Warnau | Biokinetics of radiocobalt in the asteroid Asterias rubens (Echinodermata): sea water and food exposures[END_REF]. Uptake kinetics of 109 Cd in whole-body scallops were fitted using a simple exponential kinetic model (eq. 1) for the sediment exposure (Statistica ® 6) and using a linear model for the seawater exposure (eq. 2): CF t = CF ss (1 -e -k e t ) (eq. 1)

CF t = k u t (eq. 2)
where CF t and CF ss (CF ss = k u /k e ) are the concentration factors at time t (d) and at steady state, respectively; k u and k e are the uptake and loss rate constants (d -1 ), respectively [START_REF] Whicker | Radioecology: nuclear energy and the environment[END_REF][START_REF] Warnau | Biokinetics of selected heavy metals and radionuclides in the common Mediterranean echinoid Paracentrotus lividus: sea water and food exposures[END_REF].

Depuration of Cd (seawater, food and sediment experiments) was expressed in terms of percentage of remaining radioactivity (radioactivity at time t divided by initial radioactivity measured in scallops at the beginning of the decontamination period * 100). The percentages of remaining activity were plotted against time and loss kinetics were described by a double-component exponential model (eq. 3): A t = A 0s e -k es t + A 0l e -k el t (eq. 3)

where A t and A 0 are the remaining activities (%) at time t (d) and 0, respectively; k e is the depuration rate constant (d -1 ); 's' and 'l' are the subscripts for the 'short-lived' and 'long-lived' components. For each exponential component (s and l), a biological half-life can be calculated (T b½s and T b½l ) from the corresponding depuration rate constant (k es and k el , respectively) according to the relation T b½ = ln2/k e [START_REF] Warnau | Biokinetics of selected heavy metals and radionuclides in the common Mediterranean echinoid Paracentrotus lividus: sea water and food exposures[END_REF]. Regarding feeding experiments, the 'long-lived' exponential term describes the fraction of the radiotracer ingested with food that is actually absorbed by the organism [START_REF] Warnau | Biokinetics of selected heavy metals and radionuclides in the common Mediterranean echinoid Paracentrotus lividus: sea water and food exposures[END_REF]. The corresponding A 0l represents the assimilation efficiency (AE) of the considered radiotracer.

The best fitting regression models were selected according to highest determination coefficient and examination of residuals. The level of significance for statistical analysis was always set at α < 0.05.

RESULTS

Seawater exposure

Uptake of 109 Cd in whole-body C. varia and P. maximus displayed linear kinetics (r 2 = 0.85 and 0.66, respectively; see Fig. 1). The values estimated for the kinetic parameters and their associated statistics are presented in Table 1. The concentration factors measured at the end of the uptake period (CF 7d ) of 109 Cd were 37 ± 9 in C. varia and 18 ± 7 in P. maximus (Table 2). Calculated CF 7d for the different organs indicated that 109 Cd was concentrated selectively in each species, according to the following order:

-C. varia: kidneys (928 ± 547) > digestive gland (322 ± 175) ≈ gills (277 ± 102) ≈ foot (265 ± 74) ≈ rest of soft tissues (258 ± 56) > gonad, mantle, intestine and adductor muscle (≤ 53 ± 11) -P. maximus: kidneys (690 ± 402) ≈ digestive gland (659 ± 227) > gills (175 ± 13) > other tissues (≤ 78 ± 33).

In terms of body distribution, 109 Cd was mainly found in the digestive gland and in the gills (~30 and 20 % of total body load, respectively) for both species. At the end of the uptake experiment, the 109 Cd tissue distribution shows a similar pattern (p G-test > 0.40) between C. varia and P. maximus, with the digestive gland and gills accounting for more than 60 % of the total Cd load (Table 2).

After the exposure period, non-contaminating conditions were restored and loss kinetics of 109 Cd were followed for 36 d. The whole-body loss kinetics of 109 Cd in C. varia and P. maximus were best described by a two-component exponential model (Fig. 1 and Table 1). The major part of 109 Cd was efficiently absorbed in C. varia and P. maximus (A 0l > 77 %). The estimated loss rate constant of the long-lived components (k el ) for C. varia was low, i.e. 0.005 ± 0.001 and, consequently, the derived biological halflife reached 145 ± 45 d (Table 1). In the case of P. maximus, the loss rate constant was not significantly different from 0 (p > 0.05), and the related T b½l of 109 Cd may thus be considered as infinite.

After 36 d of depuration, the body distribution of 109 Cd displayed a similar pattern than the one observed at the end of the exposure period (Table 2). However, it is striking to note that the 109 Cd activity in the digestive gland of C. varia and P. maximus remained relatively constant throughout the depuration duration within the two species, i.e. from 680 ± 369 Bq g -1 to 549 ± 255 Bq g -1 for C. varia and from 1,392 ± 479 Bq g -1 to 1,491 ± 316 Bq g -1 for P. maximus, suggesting either a lack of Cd loss from the digestive gland during this period or a redistribution of the radioisotope from the tissues in contact with seawater towards this storage organ.

Dietary exposure

The loss kinetics of 109 Cd ingested with food in both C. varia and P. maximus were best fitted using a double exponential model (Fig. 1 and Table 1). C. varia displayed a higher assimilation efficiency (AE > 86 %) than P. maximus (AE > 80 %). However, in both species, the depuration rate constant, k el , were not significantly different from 0 (p > 0.39), and therefore the derived T b½l were infinite.

At the end of the depuration period, the digestive gland contained the main part of 109 Cd, i.e. 97 % for C. varia and 82 % for P maximus (Table 2).

Sediment exposure

Sediment used in the experiment was mainly (95.8 %) composed of grains which size ranged from 76 to 302 µm and its dry/wet wt ratio was 0.80.

Whole-body uptake kinetics of sediment-bound 109 Cd in P. maximus was best fitted by a single exponential model (Table 1). TF reached steady-state equilibrium within the 2 weeks of exposure (estimated TF ss = 0.034 ± 0.002). Among the different body compartments, the highest TF 13d was found in the digestive gland (3.35 ± 1.68; Table 3). This organ also contained the main fraction of the total 109 Cd body burden (i.e. 78 %; Table 3). The body compartment containing the second highest proportion was the mantle (14 % of total 109 Cd body burden).

The 109 Cd whole-body loss kinetics could not be described accurately by the exponential models; therefore a linear regression (Y = a X + b) was applied in order to estimate the radiotracer retention. The results showed that 92 % of the accumulated 109 Cd were efficiently incorporated in P. maximus tissues, with a biological half-life not significantly different from infinite (Table 1). At the end of the depuration period (31 d) the body distribution of 109 Cd was identical to that at the end of the exposure period (Table 3), with the highest proportion of 109 Cd located in the digestive gland (≈ 80 %), followed by the mantle (≈ 12 -14 %). In addition, the 109 Cd activities were similar in the two latter tissues at the end of exposure and depuration periods, viz. 81 ± 41 and 85 ± 18 Bq g -1 in the digestive gland and 1.4 ± 0.4 and 1.5 ± 1.4 Bq g -1 in the mantle.

Subcellular distribution

Examination of subcellular distributions indicated that, whatever the contamination pathway (i.e., seawater, food or sediment) and the sampling period (i.e., end of uptake or end of loss period), P. maximus stored the major part of the cellular 109 Cd in the soluble fraction (from 70 to 85 %). In contrast, the radiotracer was mainly bound to insoluble compounds in C. varia (Fig. 2).

DISCUSSION

Pectinidae are an important marine resource which are both fished and cultured for human consumption [START_REF] Ansell | Fisheries and aquaculture: three European scallops: Pecten maximus, Chlamys (Aequipecten) opercularis and Chlamys varia[END_REF][START_REF] Waller | Evolutionary relationships among commercial scallops (Mollusca: Bivalvia: Pectinidae)[END_REF]. Hence, the intake of contaminants such as metals by Man through scallop consumption is a matter of concern. Indeed, Pectinidae are well known for their capacity of accumulating high levels of metals, and especially Cd, in their tissues [START_REF] Brooks | The biogeochemistry of trace element uptake by some New Zealand bivalves[END_REF][START_REF] Bryan | The occurence and seasonal variation of trace metals in the scallops Pecten maximus (L.) and Chlamys opercularis (L.)[END_REF][START_REF] Bustamante | Interspecific and geographical variations of trace element concentrations in Pectinidae from European waters[END_REF], 2005b). Interestingly, this high bioaccumulation potential for Cd is not specific to anthropogenic contamination since scallops from the Antarctic Ocean have high Cd levels compare to temperate species living in the coastal waters of industrialised countries [START_REF] Mauri | Heavy metals in the Antarctic scallop Adamussium colbecki[END_REF][START_REF] Viarengo | Cu, Zn, Cd content in different tissues of the Antarctic scallop Adamussium colbecki (Smith 1902): role of metallothionein in the homeostasis and in the detoxification of heavy metals[END_REF].

Several field studies assumed that food would be the main intake pathway of Cd in scallops as high metal levels are always found in the digestive gland [START_REF] Palmer | Trace metal concentrations in two shellfish species of commercial importance[END_REF][START_REF] Uthe | Cadmium in sea scallop (Plactopecten magellanicus) tissues from clean and contaminated areas[END_REF], Bustamante & Miramand 2005a). However, the contribution of the dissolved phase is difficult to ascertain in the field as this route can lead to a significant uptake of Cd and to its redistribution towards storage tissues such as the digestive gland. Therefore, there is a need to assess the relative importance of dissolved and particulate Cd pathways in order to better understand their respective contributions, as well as to evaluate the retention mechanisms leading to the high Cd levels measured in scallop tissues.

The experimental exposure of Chlamys varia and Pecten maximus to 109 Cd via seawater confirmed their ability to concentrate Cd from the dissolved phase, as previously shown using elevated exposure levels of stable Cd [START_REF] Eisler | Cadmium uptake by marine organisms[END_REF][START_REF] Carmichael | Cadmium accumulation and toxicity in the kidney of the bay scallop Argopecten irradians[END_REF]. Indeed, after only 7 days of exposure to the dissolved radiotracer, both scallop species exhibited high whole-body concentration factors (CFs), with 37 ± 9 for C. varia and 18 ± 7 for P. maximus whole bodies. This difference in CF between the two species exposed to the same contamination conditions is related (1) to a higher Cd uptake rate (uptake rate constant: 5.4 vs 2.7) and (2) secondarily, to a higher assimilated fraction (87.8 vs 77.1) in C. varia compared to P. maximus (Table 1). However in the specimens collected from the field, C. varia displayed typically lower Cd concentrations than P. maximus [START_REF] Palmer | Trace metal concentrations in two shellfish species of commercial importance[END_REF][START_REF] Uthe | Cadmium in sea scallop (Plactopecten magellanicus) tissues from clean and contaminated areas[END_REF], Bustamante & Miramand 2005a). This would suggest that C. varia has far more limited capacities of Cd storage than P. maximus.

Considering the tissues separately, the organs involved in respiration (i.e. gills), excretion (i.e. kidneys) and digestion (i.e. digestive gland) displayed higher CFs compared to other body compartments in P. maximus, whereas the foot and the compartment "rest of the soft tissues" also showed elevated CFs in C. varia (see Table 2). However, in terms of distribution among tissues and organs, Cd was mainly located in the digestive gland, the gills, the kidney and the mantle in both species, the digestive gland containing more than 30 % of the whole body burden of 109 Cd (Table 2). These results strongly suggest the occurrence of efficient redistribution mechanisms towards the tissues involved in the storage, excretion and detoxification processes, i.e. the kidneys and the digestive gland (e.g., [START_REF] Carmichael | Cadmium accumulation and toxicity in the kidney of the bay scallop Argopecten irradians[END_REF][START_REF] Ballan-Dufrançais | Physiological features of heavy metal storage in bivalve digestive cells and amoebocytes: EPMA and factor analysis of correspondences[END_REF][START_REF] Stone | Cadmium binding components of scallop (Pecten maximus) digestive gland. Partial purification and characterization[END_REF]. It is also striking to note the difference between both species concerning the Cd CF in the foot that reached elevated values in C. varia (Table 2). In the latter species, the foot is well developed and contains a byssal gland which main role is to produce the byssus to stick to rocky substrates whereas P. maximus does not produce byssus as it lives buried in the sediment.

Byssus is known to play a role in the elimination of metals from bivalves [START_REF] Szefer | A comparative assessment of heavy metal accumulation in soft parts and byssus of mussels from subarctic, temperate, subtropical and tropical marine environments[END_REF], it is therefore likely that some metals are transferred from the soft tissues and concentrated in the byssus rather than merely adsorbed onto its surface from seawater. However, in the case of Cd, previous studies on mussels suggested that this metal is derived mainly from seawater [START_REF] Coombs | Mytilus byssal threads as an environmental marker for metals[END_REF][START_REF] Nicholson | Accumulation of metals in the soft tissues, byssus and shell of the mytilid mussel Perna viridis (Bivalvia: Mytilidae) from polluted and uncontaminated locations in Hong Kong coastal waters[END_REF]. The present study was not designed to address this specific issue and our results do allow supporting internal transfer or waterborne origin of Cd in the byssus. However, further specificallydesigned studies using sensitive radiotracer techniques could bring most interesting information on the origin of byssal Cd.

It is noteworthy that the Cd distribution pattern among the tissues was similar after 7 d of seawater exposure and after 36 d of depuration for both species (Table 2). Similarly, the subcellular distribution of Cd was identical at both times for P. maximus, with more than 80 % in the soluble fraction of the digestive gland cells (Fig. 2). Taking into account the relatively long biological half-life of Cd in P. maximus, this result indicate that the metal is mainly bound to soluble compounds involved in the storage of this metal. The implication of metallothionein-like proteins in Cd detoxification and storage in the digestive gland is well documented in Pectinidae (e.g., [START_REF] Stone | Cadmium binding components of scallop (Pecten maximus) digestive gland. Partial purification and characterization[END_REF][START_REF] Evtushenko | Cadmium bioaccumulation in organs of the scallop Mizuhopecten yessoensis[END_REF], Bustamante & Miramand 2005b). However, in C. varia, Cd was mainly bound to insoluble compounds (from 59 to 80 %; see Fig. 2), suggesting a time-limited role of the soluble metalloproteins when the metal enters through the dissolved route (as well as via the food as similar results were found for the dietary exposure; see Fig. 2). Such a predominant interaction of Cd with the insoluble cellular fraction in the digestive gland is not a common observation among Pectinidae but has already been shown in some species (e.g., Adamussium colbecki; [START_REF] Viarengo | Cu, Zn, Cd content in different tissues of the Antarctic scallop Adamussium colbecki (Smith 1902): role of metallothionein in the homeostasis and in the detoxification of heavy metals[END_REF] and would be due to the fact that, among insoluble cellular components (i.e., organelles, membranes and granules), the lysosomal system can play a major role in Cd detoxification (by trapping) and excretion [START_REF] Ballan-Dufrançais | Physiological features of heavy metal storage in bivalve digestive cells and amoebocytes: EPMA and factor analysis of correspondences[END_REF][START_REF] Marigómez | Cellular and subcellular distribution of metals in molluscs[END_REF].

After exposure to sediment-bound Cd, P. maximus exhibited very low transfer factors (viz., TF ss = 0.034 ± 0.009), indicating that direct contamination due to burying into sediment would represent a minor Cd uptake pathway in this species. However, at the end of the exposure period, 80 % of the incorporated metal was found in the digestive gland, which displayed a TF higher than 3 (Table 3). As this organ is not in direct contact with the sediment, it is suggested that either (1) the radiotracer was progressively translocated from the tissues in direct contact with sediment and pore water to the digestive gland and/or (2) P. maximus was able to ingest sediment grains. Although sediment grains were never observed in the valves or in the digestive system in the many dissections carried out during this study, this latter hypothesis would be plausible as scallops were reported to be able to ingest particles of a wide size range (particles up to 950 µm have been found in scallop stomachs; [START_REF] Mikulich | Food of the scallop[END_REF][START_REF] Shumway | Food resources related to habitat in the scallop Placopecten magellanicus (Gmelin, 1791): A qualitative study[END_REF]. Nevertheless, the assimilated Cd in the digestive gland was efficiently retained and was mainly bound to cytosolic compounds in the same proportions as in the food experiment, supporting the hypothesis of ingestion of sediment particles.

In the case of dietary exposure, Cd was assimilated to a similar extent in both species, with approx. 80 % of the radiotracer being incorporated in the scallop tissues. Such a high assimilation efficiency (AE) is striking as in other bivalve species, lower values were generally reported, e.g. for the tropical clam Gafrarium tumidum (AE = 42 %), the tropical oysters Isognomon isognomon and Malleus regula (AEs = 58 and 51 %, respectively) and the blue mussel Mytilus edulis (AE ranging from 8 to 40 %) (e.g., [START_REF] Wang | Modeling metal bioavailability for marine mussels[END_REF][START_REF] Hédouin | Caractérisation d'espèces bioindicatrices pour la surveillance des activités minières et la gestion de l'environnement en milieu récifal et lagonaire : application au lagon de la Nouvelle-Calédonie[END_REF]. These results suggest that food would be an important source of Cd for Pectinidae. However, inter-specific differences in Cd concentrations in scallops from the field (where C. varia showed the lowest concentrations) are difficult to explain in regards to the results obtained in our experiments. Indeed, lower depuration rates resulted in calculated biological half-life exceeding 3 years (Table 1), meaning that virtually all the assimilated Cd is readily stored in C. varia tissues. In contrast, the biological half-life following food exposure was approx. 4 months for P. maximus, indicating a faster turnover of the metal compared to C. varia. It is therefore likely that although living in the same areas, C. varia and P. maximus do not share the same food in the marine environment. Indeed, different storage mechanisms in prey can determine Cd bioavailability to higher trophic levels (e.g., [START_REF] Wallace | Bioavailability of biologically sequestered cadmium and the implications of metal detoxification[END_REF][START_REF] Wallace | Subcellular compartmentalization of Cd and Zn in two bivalves. II. Significance of trophically available metal (TAM)[END_REF]. Moreover, the dissolved and sediment pathways should also have a strong importance in P. maximus (see above). The use of a bioaccumulation model is therefore a mandatory step to further explore the importance of each exposure pathways [START_REF] Thomann | Steady-state model of biota sediment accumulation factor for metals in two marine bivalves[END_REF][START_REF] Wang | Delineating metal accumulation pathways for marine invertebrates[END_REF]. When applying such a model, food appears to be the major route of Cd accumulation in C. varia, with 99.6 % of the metal being accumulated from phytoplankton. In P. maximus, it was not possible to determine accurate data for the model because the kinetic parameters of the post sedimentexposure loss phase were not significant. Therefore, we only considered food and seawater pathways. In such conditions, results indicated that food accounted for 84.0 % of the accumulated Cd in P. maximus.

Owing to the high assimilation efficiency of sediment-bound Cd (A 0l = 92 %), it appears necessary to better delineate the sediment contribution to Cd accumulation in order to consider the three different pathways (seawater, food and sediment) on the global Cd bioaccumulation by P. maximus.

CONCLUSION

The present work on the bioaccumulation of Cd in two Pectinidae has confirmed the high Cd bioaccumulation potential of C. varia and P. maximus. The organs accumulating Cd to the highest extent in both species are the digestive gland and the kidneys whatever the exposure pathway was. Comparison of results from laboratory experiments clearly showed that C. varia showed higher bioconcentration and bioaccumulation capacities than P. maximus. Since field data have reported higher Cd levels in P. maximus than in C. varia, it is suggested that Cd should be bioaccumulated by other uptake pathways than food and seawater. The high assimilation efficiency of Cd ingested through sediment pathway in P. maximus indicated that the particulate pathway could play an important role in the global Cd bioaccumulation process and studies on sediment as well as on suspended particulate matter should be further investigated to better simulate the different exposure routes of Cd to which Pectinidae are exposed in the field. Nevertheless, differences between field and laboratory observations could be related to different detoxification mechanisms in the two species.

Table 1. Chlamys varia and Pecten maximus. Whole-body uptake and loss kinetic parameters of 109 Cd following different exposure experiments: 1) 7-d exposure via seawater (n = 9) followed by 36 d of depuration (n = 9); 2) 2-hr feeding on radiolabelled Isochrysis galbana followed by a depuration period of 16 d (P. maximus, n = 6) or 30 d (C. varia, n = 6);

3) 13-d exposure of P. maximus via the sediments (n = 8) followed by 31 d of depuration (n = 8).

Uptake parameters: CF ss / TF ss concentration and transfer factors at steady state; k u : uptake rate constant (d -1 ) Depuration parameters: A 0s and A 0l : activity (%) lost according to the short-and the long-lived exponential component, respectively; T b½ : biological half-life (d). ASE: asymptotic standard error; r²: determination coefficient of the uptake or loss kinetics

  In spring 2004 and 2005, one hundred variegated scallops Chlamys varia and seventy king scallops Pecten maximus were collected on the Atlantic coast (Pertuis Breton, Charente-Maritime) by SCUBA diving. They were carefully transported to IAEA-MEL premises in Monaco and were acclimatized to laboratory conditions for 4 weeks (constantly aerated open circuit aquarium; flux: 50 l h -1

Figure 1 .

 1 Chlamys varia and Pecten maximus. Uptake and loss kinetics of 109 Cd in scallops exposed for 7 d via seawater (uptake kinetics A1; Concentration Factors -CF-; mean ± SD; n = 9), then maintained for 36 d in non contaminated conditions (loss kinetics A2; Remaining activity -%-; mean ± SD; n = 9) and after a 2-hr feeding on radiolabelled phytoplankton Isochrysis galbana (loss kinetics B; Remaining activity -%-; mean ± SD; n = 6 C. varia and n = 9 P. maximus).

Figure 2 .

 2 Figure 2. Chlamys varia and Pecten maximus. Subcellular distribution of 109 Cd in the digestive gland cells following different exposure experiments: (1) 7-d exposure via seawater followed by 36 d of depuration; (2) 2-hr feeding on radiolabelled Isochrysis galbana followed by a depuration period of 16 d (P. maximus) or 30 d (C. varia); (3) 13-d exposure of P. maximus via the sediments followed by 31 d of depuration.

  Probability of the model adjustment: a p < 0.05, b p < 0.01, c p < 0.001, d p < 0.0001; NC: not calculated Caption to figures.

			a. Uptake					b. Loss
	Experiment	Species	CF ss / TF ss ± ASE	k u ± ASE	r²	A 0s ± ASE	T b½s ± ASE	A 0l ± ASE	T b½l ± ASE	r²
	1) Seawater	C. varia	-	5.4 ± 0.2 d	0.85	12.2 ± 3.8 b	0.8	87.8 ± 2.4 d	145 ± 45 b	0.31
		P. maximus	-	2.7 ± 0.1 d	0.66	23.4 ± 5.7	c	1.1	77.1 ± 4.8	d	913	0.49
	2) Feeding	C. varia	-	-	-	14.5 ± 4.1 c	0.4	85.8 ± 2.1	989	0.21
		P. maximus	-	-	-	20.5 ± 6.1 b	0.02	79.5 ± 3.7 d	138	0.37
	3) Sediment	P. maximus	0.034 ± 0.002 d 0.014 ± 0.002 d 0.62	NC		NC	92 d		NC	-

Acknowledgements:

The IAEA is grateful for the support provided to its Marine Environment Laboratories by the Government of the Principality of Monaco. This work was supported by the IAEA, the GIP Seine-Aval, the Conseil Général de la Charente-Maritime and the CRELA (Université de la Rochelle). We thank IFREMER and the Aquarium of La Rochelle for providing the scallops. We are grateful to L. Hédouin for her help in the modelling approach. MW is an Honorary Senior Research Associate of the National Fund for Scientific Research (NFSR, Belgium).


Yang Deng
email: yang.deng@ls2n.fr

Vincent Léchappé
email: vincent.lechappe@insa-lyon.fr

Emmanuel Moulay
email: emmanuel.moulay@univ-poitiers.fr

Franck Plestan
email: franck.plestan@ec-nantes.fr

Prediction-based control with delay estimation of LTI systems with input-output delays

Keywords: Time-delay systems, Delay estimation, Lyapunov-Razumikhin theorem

The aim of this article is to propose a predictionbased controller combined with a new time-delay estimation method for LTI systems with unknown input and output delays. The global asymptotic stability of the time-delay system is ensured. The proposed control scheme includes a delay estimator which estimates the unknown round-trip delay (the sum of input and output delays), a Luenberger observer and a prediction-based controller. Among the main results of this article, the delay estimator is firstly introduced; secondly, a Lyapunov-Razumikhin analysis is given to prove the stability of the closed-loop system; finally, several examples are given to illustrate the performances of the proposed method.

I. INTRODUCTION

Time-delay system (TDS) is a wide research domain in the control community since time-delays are very common in real systems. For example, time-delays can arise from communication protocol, remote control and sensor measurement [START_REF] Chiasson | Applications of time delay systems[END_REF]. Input and output delays are important to consider because they can degrade performances or even destabilize systems [START_REF] Fridman | Introduction to time-delay systems: Analysis and control, ser. Systems & Control: Foundations & Applications[END_REF]. This article deals with the system with unknown constant input and output delays which appear for instance in networked control systems [START_REF] Garca-Rivera | Analysis of networked control systems with drops and variable delays[END_REF]. In real systems, it is very difficult to directly measure the unknown input and output delays or separately estimate them, then a round-trip delay estimation is proposed in this article.

A vast literature is available on the control of input-delay systems. Finite spectrum assignment (FSA) [START_REF] Manitius | Finite spectrum assignment problem for systems with delays[END_REF] and reduction method [START_REF] Artstein | Linear systems with delayed controls: A reduction[END_REF] are standard methods to deal with known inputdelays. Prediction-based control is also an efficient way to stabilize the TDS with known input-delays, it is used in [START_REF] Karafyllis | Predictor feedback for delay systems: Implementations and approximations[END_REF] for linear systems and in [START_REF] Cacace | Stabilization of strict-feedback nonlinear systems with input delay using closed-loop predictors[END_REF] for nonlinear systems. For the systems with unknown input-delays, the works in [START_REF] Krstic | Delay compensation for nonlinear, adaptive, and PDE systems[END_REF], [START_REF] Bekiaris-Liberis | Delay-adaptive feedback for linear feedforward systems[END_REF], [START_REF] Bresch-Pietri | Adaptive control scheme for uncertain time-delay systems[END_REF] present a backstepping partial differential equation (PDE) transformation method. The new system is a combination of an ordinary differential equation (ODE) and a PDE transport equation. Therefore, the adaptive controller design and Lyapunov-Krasovskii analysis are proposed to stabilize the ODE-PDE system. Besides, a large number of works without PDE transformation have been done to deal with the unknown input-delay. Several approaches among them are based on the time-delay estimation (TDE) algorithm. A modified Smith predictor with transfer function based TDE algorithm is provided in [START_REF] Herrera | On-line delay estimation for stable, unstable and integrating systems under step response[END_REF]. The authors of [START_REF] Cacace | State feedback stabilization of linear systems with unknown input time delay[END_REF] propose a memory-free controller combined with a piecewise-constant input delay identifier for LTI systems with an input-delay. The exponential stability of the closed-loop system is obtained but the delay identifiability of the closed-loop system must be ensured. The works in [START_REF] Léchappé | Delay estimation and predictive control of uncertain systems with input delay: Application to a DC motor[END_REF] provide an open-loop TDE algorithm and a robust predictive controller with an application to a DC motor, the TDS is stabilized in practice.

However, the systems with input and output delays are not as widely studied as input-delay systems. The works in [START_REF] Jankovic | Recursive predictor design for state and output feedback controllers for linear time delay systems[END_REF] present an advanced reduction method which stabilizes the linear systems with known constant input, output and state delays. A predictor-based controller for nonlinear systems with zero-order-hold input and sampled measurement is proposed in [START_REF] Karafyllis | Stabilization of nonlinear delay systems using approximate predictors and high-gain observers[END_REF], this work is extended to output feedback controller in [START_REF] Karafyllis | Global stabilisation of nonlinear delay systems with a compact absorbing set[END_REF]. In [START_REF] Zhou | Observer based output feedback control of linear systems with input and output delays[END_REF], a truncated predictor feedback approach is proposed to stabilize the systems with known input and output time-varying delays, but this technique only deals with the systems with particular poles. An adaptive controller for hyper-minimum-phase systems with uncertain input and output delays is proposed in [START_REF] Selivanov | Passification-based adaptive control: Uncertain input and output delays[END_REF], but the drawback is that the controller only ensures the local stability and it cannot deal with arbitrarily long delays.

In this article, a real-time round-trip delay estimation method is combined with a Luenberger observer and a prediction-based controller. It is shown that if the initial condition of the delay estimator is close enough to the round-trip delay value, then the asymptotic stability of the TDS can be obtained. The stability condition is obtained by using Lyapunov-Razumikhin1 method. Thus, one obtains the stabilization of the system and the convergence of the state estimation.

The article is organized as follows. The problem statement is presented in Section II. Then, the main results are provided in Section III and illustrated by simulation results in Section IV. Finally, a conclusion is given in Section V.

II. PROBLEM STATEMENT

In this article, the following notations are used. Let x denote the euclidean norm of a vector x ∈ R n . The matrix I n represents the identity matrix of size n × n. The matrix norm of a matrix A reads as A . The maximum and minimum eigenvalues of the matrix A are respectively defined as λ (A)

and λ (A). Let C = C ([σ -h, σ + r], R n ) for any t ∈ [σ , σ + r]
, then x t (θ ) can be defined as x t (θ ) = x(t + θ ) ∈ C with -h ≤ θ ≤ 0. The other notations of the Lyapunov stability are given in [START_REF] Hale | Introduction to functional differential equations[END_REF]. Consider a LTI system with input and output delays

ẋ(t) = Ax(t) + Bu(t -h i ) y(t) = Cx(t -h o ) (1)
where

x(t) ∈ R n , A ∈ R n×n , B ∈ R n×p , C ∈ R m×n , u(t) ∈ R p
and h i , h o are unknown constant time-delays. Therefore, the round-trip delay reads as

h io = h i + h o (2)
which is bounded in [h min , h max ]. The boundedness h max > h min > 0 are assumed to be known. The initial condition of system (1) is defined as

x(θ ) = x 0 (θ ) ∈ C and u(θ ) = u 0 (θ ) ∈ C for all θ ∈ [-2h max , 0].
A Luenberger observer presented in [6, p.61] is proposed to estimate the output-delayed state x(th o ):

ẋ(t) = A x(t) + Bu(t -h io ) + L[y(t) -C x(t)] (3)
with initial condition x(θ

) = x0 (θ ) ∈ C for all θ ∈ [-2h max , 0]
. The estimation error is defined as

e(t) = x(t) -x(t -h o ). (4)
An approximated prediction2 z(t) based on ĥ(t) and x(t) used in [START_REF] Bresch-Pietri | Adaptive control scheme for uncertain time-delay systems[END_REF] is proposed in this article z(t) = e A ĥ x(t) + t t-ĥ e A(t-s) Bu(s)ds [START_REF] Artstein | Linear systems with delayed controls: A reduction[END_REF] with initial condition z(θ

) = z 0 (θ ) ∈ C for all θ ∈ [-2h max , 0].
The problem to solve is to design the dynamics of ḣ(t) and a controller u(z(t)), in order to obtain the asymptotic stability of the closed-loop system.

In the sequel the following assumptions are made.

Assumption 1. The pair (A, B) is stabilizable and the pair (A,C) is observable.

Assumption 1 ensures that the controller and observer can be designed. It follows that there exists feedback matrices K, L with appropriate dimensions such that A + BK, A -LC are Hurwitz, and for all positive constants c u , c l , there exists symmetric positive definite matrices P ∈ R n×n , Q ∈ R n×n that are the solutions of the following Lyapunov equations

(A + BK) T P + P(A + BK) = -c u I n (6) (A -LC) T Q + Q(A -LC) = -c l I n . (7)
Assumption 2. The delayed input value u(th io ) is known.

In practical application, it is possible to save the delayed input value u(th i ) and send it to the controller along with the system's output. Therefore, as a result of the transport delay h o , one obtains u(th ih o ). The structure of the closed-loop system is shown in Figure 1. The information sent from the controller to the system and from the system to the controller are subject to the unknown input and output delays. The blue dashed rectangle represents the control scheme that includes the observer, the predictorbased controller and the delay estimator. The violet dashed rectangle represents the communication delays introduced by the communication channels.

Cx(t) u(t -hi) y(t) u(t -hi -ho) u(t -hi -ho) u(t) u(t) u(t) ĥ(t) x(t) z(t) Control architecture Delays (Communication lag) u(t -hi -ho) u(t -hi) u(t) y(t) x(t) ĥ(t)

III. DELAY ESTIMATION AND STABILIZATION OF THE INPUT-OUTPUT DELAY SYSTEM

The main result of this paper is given by Theorem 1.

Theorem 1. Consider that the system (1) satisfies Assumptions 1 and 2, the observer (3) and the predictor [START_REF] Artstein | Linear systems with delayed controls: A reduction[END_REF] . The control law satisfies

u(t) = Kz(t), t > 0 u(θ ) = u 0 (θ ) = Kz 0 (θ ), θ ∈ [-2h max , 0] ( 8
)
where K is the linear feedback matrix referred in Assumption 1. Suppose that the control input u(t) given in (8) is continuously differentiable at t = 0. Define the delay estimator

ḣ(t) = min{γ u(t -h io ) -u(t -ĥ(t)) , δ }, t > 0 ĥ(θ ) = ĥ0 , θ ∈ [-2h max , 0] (9
) where γ, δ are positive constants and the initial condition ĥ0 satisfies h min ≤ ĥ0 ≤ h io . If ĥ0 is sufficiently close to h io , then there exists a constant δ * > 0, such that for all δ < δ * , the z-system is uniformly globally asymptotically stable, then one gets

lim t→+∞ x(t) = 0; (10) lim t→+∞ e(t) = 0. ( 11
)
Proof: The proof is divided into 3 parts. The first part studies the properties of delay estimator [START_REF] Bekiaris-Liberis | Delay-adaptive feedback for linear feedforward systems[END_REF]; the second part proves the stability of the closed-loop z-system; the last part demonstrates the convergence of x(t) to zero by using the stability of the z-system and the convergence of e(t).

Step 1. In this step, the properties of the delay estimator ĥ(t) are studied. The delay estimation satisfies the following inequalities ĥ0 ≤ ĥ(t) ≤ h io [START_REF] Cacace | State feedback stabilization of linear systems with unknown input time delay[END_REF] for all t ≥ 0. Inequalities [START_REF] Cacace | State feedback stabilization of linear systems with unknown input time delay[END_REF] are hereafter proven by contradiction. Assume that there exists t 0 > 0 such that ĥ(t 0 ) > h io . From equation ( 9), it follows that ḣ(t) ≥ 0 for all t ≥ -2h max . Therefore, ĥ(t) is continuous, monotonically increasing with initial condition ĥ0 ≤ h io for all θ ∈ [-2h max , 0]. The intermediate value theorem given in [20, p.105] implies that there exists t 1 ∈ (0,t 0 ) such that ĥ(t 1 ) = h io and ḣ(t 1 ) > 0. However, if ĥ(t 1 ) = h io , then one has

ḣ(t 1 ) ≤ γ u(t -h io ) -u(t -ĥ(t 1 )) = 0. ( 13
)
Therefore, inequality (13) contradicts the fact ḣ(t 1 ) > 0 and the existence of t 0 . Then, inequalities [START_REF] Cacace | State feedback stabilization of linear systems with unknown input time delay[END_REF] are proven by contradiction. This step ensures that if the initial condition of the delay estimator satisfies

h io -ĥ0 ≤ D (14)
with D > 0, then the delay estimator ĥ(t) satisfies

0 ≤ h io -ĥ(t) ≤ h io -ĥ0 ≤ D (15)
for all t ≥ 0 due to the monotonicity and the boundedness of ĥ(t).

Step 2. Differentiating equation ( 5) for all t > 0 and substituting ẋ(t) by equation ( 3), one obtains ż(t) =(A + BK)z(t) + ḣ(t)Az(t) + ḣ(t)e A ĥ(t) Bu(t -ĥ(t))

ḣ(t)A t t-ĥ(t) e A(t-s) Bu(s)dse A ĥ(t) LCe(t) + e A ĥ(t) B[u(th io )u(t -ĥ(t))].

(16

)
Developing system (1) at th o yields that

ẋ(t -h o ) = Ax(t -h o ) + -h o -h i ). (17)
Noticing that h o is constant, it implies that

d dt x(t -h o ) = ẋ(t -h o ). (18)
Differentiating the estimation error e(t) by using equations ( 3), ( 17) and [START_REF] Selivanov | Passification-based adaptive control: Uncertain input and output delays[END_REF], it leads to

ė(t) = ẋ(t) - d dt x(t -h o ) = A x(t) + Bu(t -h io ) -LCe(t) -Ax(t -h o ) -Bu(t -h o -h i ) = (A -LC)e(t). (19)
Define V 1 (z(t)) = z(t) T Pz(t), V 2 (e(t)) = e(t) T Qe(t). From equation ( 9), it yields that | ḣ(t)| is upper bounded by δ for all t ≥ -2h max . Differentiating V 1 (z(t)) along the trajectories of ( 16), it leads to

V1 (z(t)) ≤ -c u z(t) 2 + 2 δ PA z(t) 2
+ 2 δ e A h max B P z(t) u(t -ĥ(t))

+ 2 δ e A h max PA B z(t) v(t) + 2e A h max P LC z(t) e(t)

+ 2e A h max P B z(t) w(t) (20)
where v(t) = t t-ĥ(t) u(s) ds and w(t) = t-ĥ(t) t-h io u(s) ds. Differentiating V 2 (e(t)) along the trajectories of ( 19), one obtains V2 (e(t)) = -c l e(t) 2 .

(

) 21
The following Lyapunov-Razumikhin candidate function is defined by

V (z(t), e(t)) = V 1 (z(t)) + αV 2 (e(t)) ( 22
)
where α is a positive constant. Defining c 1 = 2 PA , c 2 = 2e A h max B P , c 3 = 2e A h max PA B and c 4 = 2e A h max P LC , the time-derivative of V (z(t), e(t)) satisfies and therefore one has

V (z(t), e(t)) ≤ -(c u -δ c 1 ) z(t) 2 + δ c 2 z(t) u(t -ĥ(t)) + δ c 3 z(t
z(t -s) ≤ c 5 ( z(t) + √ α e(t) ), s ∈ [0, 2h max ] e(t -s) ≤ c * 5 ( z(t) / √ α + e(t) ), s ∈ [0, 2h max ] (25)
where c 5 = κ max( λ (P), λ (Q))/λ (P) and c * 5 = κ max( λ (P), λ (Q))/λ (Q). Thus, one can simplify the second and third terms of inequality (23) as follows:

δ c 2 z(t) u(t -ĥ(t)) ≤ δ c 2 c 5 K z(t) ( z(t) + √ α e(t) ) ≤ δ c 6 z(t) ( z(t) + √ α e(t) ) (26) δ c 3 z(t) v(t) ≤ δ c 3 c 5 K h max z(t) ( z(t) + √ α e(t) ) ≤ δ c 7 z(t) ( z(t) + √ α e(t) ) (27)
where c 6 = c 2 c 5 K and c 7 = c 3 c 5 K h max . To simplify the term c 2 z(t) w(t) of inequality (23), one uses

w(t) ≤ D(t) K sup s∈[t-h io ,t-ĥ(t)] ż(s) (28)
with D(t) = h io -ĥ(t). For all s 1 ∈ [ ĥ(t), h io ], one can develop the expression of ż(ts 1 ) by using equation ( 16):

ż(t -s 1 ) =(A + BK)z(t -s 1 ) + ḣ(t -s 1 )Az(t -s 1 ) -ḣ(t -s 1 )A t-s 1 t-s 1 -ĥ(t-s 1 )
e A(t-s 1 -s) Bu(s)ds + ḣ(ts 1 )e A ĥ(t-s 1 ) Bu(ts 1 -ĥ(ts 1 ))

+ e A ĥ(t-s 1 ) B[u(t -s 1 -h io ) -u(t -s 1 -ĥ(t -s 1 ))]
e A ĥ(t-s 1 ) LCe(ts 1 ).

Taking norm of equation ( 29), by using the Razumikhin condition (25) and the triangle inequality, it leads to

ż(t -s 1 ) ≤ A + BK c 5 ( z(t) + √ α e(t) ) + δ A c 5 ( z(t) + √ α e(t) ) + δ A e A h max BK h max c 5 ( z(t) + √ α e(t) ) + δ e A h max BK c 5 ( z(t) + √ α e(t) ) + 2e A h max BK c 5 ( z(t) + √ α e(t) ) + e A h max LC c * 5 ( z(t) / √ α + e(t) ) (30)
for all s 1 ∈ [ ĥ(t), h io ]. Inequality (30) is equivalent to sup s∈[t-h io ,t-ĥ(t)] ż(s) ≤(c 8 ( δ ) + c 9 / √ α) z(t)

+ (c 8 ( δ ) √ α + c 9 ) e(t) (31)
with parameters c 8 ( δ ) and c 9 defined by

c 8 ( δ ) = A + BK c 5 + δ A c 5 + e A h max BK (2 + δ + δ A h max )c 5 , c 9 =e A h max LC c * 5 . ( 32
)
Substituting inequality (31) into inequality (28), and using inequality (15) one maximizes c 2 z(t) w(t) as:

c 2 z(t) w(t) ≤D(t)(c 10 ( δ ) + c 11 / √ α) z(t) 2 + D(t)(c 10 ( δ ) √ α + c 11 ) z(t) e(t) ≤ D(c 10 ( δ ) + c 11 / √ α) z(t) 2 + D(c 10 ( δ ) √ α + c 11 ) z(t) e(t) (33) with c 10 ( δ ) = c 2 c 8 ( δ ) K , c 11 = c 2 c 9 K and D = h io -ĥ0 .
Therefore, inequality (23) can be simplified as 2 (34) with c 12 = c 1 + c 6 + c 7 and c 13 = c 6 + c 7 . Finally, one obtains the following inequality by completing the squares:

V (z(t), e(t)) ≤ -(c u -δ c 12 -Dc 10 ( δ ) - Dc 11 √ α ) z(t) 2 + ( δ c 13 √ α + c 4 + Dc 10 ( δ ) √ α + Dc 11 ) z(t) e(t) -αc l e(t)
V (z(t), e(t)) ≤ -(c u -δ c 12 -Dc 10 ( δ ) - Dc 11 √ α - δ c 13 √ α 2 - Dc 10 ( δ ) √ α 2 - Dc 11 2 - c 2 4 2αc l ) z(t) 2 -α( c l 2 - Dc 10 ( δ ) 2 √ α - Dc 11 2α - δ c 13 2 √ α ) e(t) 2 . (35)
Choosing α sufficiently large so that

c 2 4 2αc l
can be ignored by comparing with c u , then there exists sufficiently small constants δ * and D * such that

c u -δ * c 12 -D * c 10 ( δ * ) - D * c 11 √ α - δ * c 13 √ α 2 - D * c 10 ( δ * ) √ α 2 - D * c 11 2 ≥ 0, c l 2 - D * c 10 ( δ * ) 2 √ α - D * c 11 2α - δ * c 13 2 √ α ≥ 0. (36)
If the initial condition of the delay estimator is sufficiently close to h io such that h io -ĥ0 = D < D * is ensured. Then, for all δ < δ * , there exists two constants c 14 , c 15 > 0 such that V (z(t), e(t)) ≤ -c 14 z(t) 2c 15 e(t) 2 (37) which implies that there exists a nondecreasing continuous function w(s) : R + → R + such that V (z(t), e(t)) ≤ -w(z(t), e(t)).

The Lyapunov-Razumikhin theorem referred in [19, Subsection 5.4, Theorem 4.2] ensures that the closed-loop z-system is uniformly globally asymptotically stable. Therefore, the convergence results lim t→∞ z(t) = 0 and lim t→∞ e(t) = 0 are also ensured.

Step 3. As proven in Step 2, one obtains lim t→∞ z(t) = 0 and lim t→∞ e(t) = 0. Reminding that equation (5) equals to x(t) = e -A ĥ(t) z(t) -t t-ĥ(t) e A(t-ĥ(t)-s) Bu(s)ds.

(39)

Reminding the definition of e(t), equation (39) can be developed as

x(th o ) = e -A ĥ(t) z(t)e(t) -t t-ĥ(t)

e A(t-ĥ(t)-s) Bu(s)ds.

(40) As known that 0 < ĥ(t) ≤ h max , by using the mean value theorem referred in [20, p. 101], one bounds the integral term of equation (40) as follows: t t-ĥ(t) e A(t-ĥ(t)-s) Bu(s)ds ≤ e A h max B t t-ĥ(t) u(s) ds

≤ e A h max B t t-h io u(s) ds ≤ e A h max B K h max sup s∈[t-h io ,t] z(s) (41)
for all t ≥ h io . Taking the norm of equation ( 40) and using the triangle inequality, it leads to x(th o ) ≤ e A h max z(t) + e(t)

+ e A h max B K h max sup s∈[t-h io ,t] z(s) . (42)
Noticing that the limit of the right-hand side of inequality (42) is zero as t tends towards infinity because of the convergences lim t→∞ z(t) = 0 and lim t→∞ e(t) = 0, then one obtains lim t→∞ x(t) = 0. Remark 1. Delay estimator (9) is the key point of the stabilization of system (1). It is not necessary for the delay estimator to converge to the nominal round-trip delay since the system can be stabilized with delay mismatch [START_REF] Cacace | State feedback stabilization of linear systems with unknown input time delay[END_REF], [START_REF] Bresch-Pietri | Prediction-based control for linear systems with input-and state-delay-robustness to delay mismatch[END_REF]. However, in applications, the unknown round-trip delay can be estimated by delay estimator (9) as it will be shown in simulations.

Remark 2. In theory, it is necessary to set δ sufficiently small to ensure that the stability condition (36) always holds. Indeed, Theorem 1 presents only a sufficient condition for the stability of the closed-loop system. Although condition (36) is not satisfied with larger δ , the convergence lim t→∞ z(t) = 0 ultimately holds with higher convergence speed of the TDE algorithm in applications.

Remark 3. Delay estimator (9) is always increasing, if the initial condition ĥ0 is not carefully chosen such that ĥ0 ≥ h io , then the delay estimation and the system will diverge. In practice, it is possible to set ĥ0 = h min in order to avoid the divergence.

Remark 4. Theorem 1 also shows that the predictor-based controller is robust with respect to the slight delay mismatch.

If one uses a constant estimation h that is sufficiently close to h instead of ĥ(t) to calculate the control law given in [START_REF] Artstein | Linear systems with delayed controls: A reduction[END_REF] and [START_REF] Krstic | Delay compensation for nonlinear, adaptive, and PDE systems[END_REF]. Then the same proof as Theorem 1 can be given to guarantee that the closed-loop system is asymptotically stable. This result is very similar to the one given in [START_REF] Bresch-Pietri | Prediction-based control for linear systems with input-and state-delay-robustness to delay mismatch[END_REF].

Remark 5. The proposed TDE method is robust with respect to the model uncertainties and the external disturbances. The reason is that the control input u(t) is memorized and the delayed input value u(th io ) is measured, then the delay estimator will not be influenced by the model uncertainties and the external disturbances.

IV. SIMULATIONS

Two simulations of a second-order system are made to evaluate the results provided in Theorem 1. Moreover, the delay estimator converges to the round-trip delay in simulations.

A. Simulation results with ĥ0 close to h io

Consider the second-order system Fig. 2. Evolution of x(t) , e(t) and ĥ(t) versus time for system (43) with ĥ0 = 0.7s.

ẋ(t) = Ax(t) + Bu(t -h i ) y(t) = Cx(t -h o ) (43
The simulation results are presented in Figure 2. The unknown round-trip delay is well estimated and one gets lim t→∞ e(t) = 0, lim t→∞ x(t) = 0. Figure 2 also verifies the discussions in Remark 2, i.e. the fact that the theoretical stability condition (36) can only be satisfied with sufficiently small δ because of the conservatism. Indeed, the convergence of system (43) holds when δ * = 0.1 whereas the theoretical bound is around 10 -4 in order that condition (36) can be ensured.

B. Simulation results with ĥ0 far from h io

Another simulation is done for the same system (43), except ĥ0 that has been redefined as ĥ0 = 0.2s. The simulation Fig. 3. Evolution of x(t) , e(t) and ĥ(t) versus time for system (43) with ĥ0 = 0.2s. results are presented in Figure 3. The unknown round-trip delay is also well estimated, and one has the convergences lim t→∞ e(t) = 0, lim t→∞ x(t) = 0. Since the initial condition of ĥ(t) is far from h io , there exists a transient for the delay estimator to be sufficiently close to the round-trip delay. As the delay estimation ĥ(t) gets sufficiently close to h io after t = 6s, the convergences of x(t) and e(t) to zero ultimately hold. This simulation shows that the constraints on the initial condition of ĥ(t) can be relaxed in practice.

V. CONCLUSION In this article, a new round-trip delay estimation method for constant input and output delays is proposed. The stability of the closed-loop system is guaranteed by Lyapunov-Razumikhin theorem. The practical implementation of this approach is discussed, and the theoretical results are illustrated by simulations. The extension of this method to nonlinear systems and to time-varying delays will be considered for future works.

Fig. 1 .

 1 Fig. 1. Closed-loop scheme of the prediction-based controller with TDE algorithm.

T

  for all θ ∈ [-2h max , 0] and z(θ ) = x(θ ) = 0 0 T for all θ ∈ [-2h max , 0]. The unknown time-delays are set to h i = 0.5s, h o = 0.3s, the initial condition of the delay estimator is set to ĥ0 = 0.7s, the gain γ = 5 and the derivative of delay estimator (9) is bounded by δ = 0.1. The parameters of the controller are defined as K = -7.7 -3.35 and L = 4.5 2.5T .

The details of the Lyapunov-Razumikhin theorem are presented in [2, Subsection 3.1.3] and [19, Subsection 5.4].

The predictor-based controller contains infinite dimensional term which may cause implementation issues. To well implement this controller, a trapezoid discretization method and a periodic reset of the update law when convergence is achieved are proposed in[START_REF] Bresch-Pietri | Adaptive control scheme for uncertain time-delay systems[END_REF].

VI. ACKNOWLEDGEMENTS

This work is a part of the Ph.D. thesis of Yang Deng, who is supported by China Scholarship Council (CSC).


Tony Merle

Jean-Stéphane Pic

Marie-Hélène Manero

Hubert Debellefontaine

Comparison of Activated Carbon and Hydrophobic Zeolite Efficiencies in 2,4-Dichlorophenol Advanced Ozonation

Keywords: Ozone, Zeolite, Activated Carbon, 2, 4-dichlorophenol, Adsorption

This study aims at comparing the removal of 2,4-dichlorophenol (2,4-DCP) by 3 methods; adsorption using hydrophobic zeolite (faujasite) or activated carbon (S-23 and L-27), conventional ozonation and hybrid adsorption/ozonation treatment. On the one hand, the three materials correctly adsorb 2,4-DCP; however the adsorption kinetics using zeolite is very low. On the other hand, ozonation totally removes 2,4-DCP after 1 h experiment and the simultaneous combination of adsorbent and ozone does not change the 2,4-DCP degradation. But, though ozonation and hybrid process appear to be equivalent for 2,4-DCP removal, activated carbons are able to decompose ozone and to improve chemical oxygen demand (COD) removal, whereas the zeolite does not show this catalytic effect. Similar results were also observed in a former study with nitrobenzene. Adsorbent degradation is evaluated by Brunauer, Emmet and Teller (BET) and differential thermogravimetric (DTG) analysis, which evidence that Faujasite and S-23 activated carbon are resistant to ozone exposure whereas the pore volume and the surface area of L-27 activated carbon decrease during ozonation.

INTRODUCTION

Nowadays, industrial wastewater is mainly purified by biological treatment. Yet some effluents cannot undergo biological treatment for they contain many bio-recalcitrant organics or toxic compounds. In these cases, expensive shock treatments are often required such as incineration or advanced oxidation processes (AOPs). Indeed, radicals (especially HO•) involved in these AOPs increase the oxidation efficiency [START_REF] Hoigné | The Role of Hydroxyl Radical Reaction in Ozonation Process in Aqueous Solution[END_REF]. [START_REF] Jans | Activated Carbon and Carbon Black Catalyzed Transformation of Aqueous Ozone into OH-radicals[END_REF] have shown that the decomposition of ozone into hydroxyl radicals is increased by activated France. E-mail: debelle@insa-toulouse.fr carbon. Zeolites were also proven to improve refractory compounds removal [START_REF] Fujita | Decomposition of Thrichloroethene on Ozone-Adsorbed High Silica Zeolites[END_REF][START_REF] Sano | Degradation of Aqueous Phenol by Simultaneous Use of Ozone with Silica-Gel and Zeolite[END_REF]. Even though activated carbon is a cheaper adsorbent, its properties can be affected whereas zeolites are supposed to be stronger facing ozonation. Thus, this study compares activated carbon and zeolite media in terms of resistance to ozone treatment and efficiency to remove bio-recalcitrant compounds.

MATERIAL AND METHODS

2,4-DCP Reagent and Organic Molecular Analyses

Analytical grade 2,4-dichlorophenol (2,4-DCP) was purchased from Acros chemicals. The kinetic diameter is 6.3 Å and was calculated by the method of [START_REF] Reid | The Properties of Gases and Liquids, 3 rd Ed[END_REF]. The chemical oxygen demand (COD) of the solutions was measured by Hanna Instrument test tube (COD MR Reagent, Woonsocket, RI, USA) and total organic carbon (TOC) concentration was determined using a Shimadzu TOC-VCSH analyzer. COD and TOC samples were filtered using a 0.45 µm filter before analyses.

The 2,4-DCP residual concentration was determined by high pressure liquid chromatography using HP 1050 series chromatograph with a C-18 column (EQUISORB ODS2 5 µm) and a diode array detector (Agilent Technologies model HP 1200, Santa Clara, CA, USA).

Adsorbents and Characterization

Three adsorbents were used in this study: 2 granular activated carbon (supplied by PICA Corporation, France) called S-23 and L-27 and 1 hydrophobic zeolite called faujasite (FAU supplied by TOSOH Corp., Japan). First, their physical properties were characterized through the measurement of the nitrogen adsorption isotherms at 77 K using a Micrometrics ASAP 2010 device. The Brunauer, Emmet and Teller (BET) surface area and the external surface area were determined using the BET method whereas mesoporous and microporous volumes were calculated with the t-plot method. The corresponding results are reported in Table 1. Second, 2,4-DCP adsorption isotherms were determined for the 3 materials at 25 • C adding increasing quantities (between 10 and 900 mg) in 100 mL deionized water loaded with 233 ± 3 mg.L -1 2,4-DCP. They exhibit classical shapes as shown in Figure 1. The isotherms onto faujasite and S-23 activated carbon could be described through the Langmuir's model (Equation 1), whereas L-27 activated carbon behavior was better described through the Freundlich's model (Equation 2). The parameters for both models are given in Table 2. Adsorption of 2,4-DCP is favored onto the three materials and, for 2,4-DCP equilibrium concentrations below 100 mg.L -1 , the adsorption capacity is relatively low for faujasite, intermediate for L-27 activated carbon and higher for S-23 activated carbon.

= Q Max × K × C Eq 1 + K × C Eq [1]
Freundlich model:

Q Eq = F × C Eq 1 / n [2]
with:

Q Eq , Q Max equilibrium [resp. maximum] adsorbed quantity; C Eq equilibrium concentration in the liquid phase; K Langmuir constant; F Freundlich constant; n Freundlich coefficient At last, differential thermogravimetric (DTG) analyses were carried out using a thermo balance system (TA instruments STD 2960 and STD Q600, New Castle, DE, USA) by heating about 10 mg adsorbent from 303 K up to 1173 K at a rate of 10 K.min -1 under flowing argon (100 mL.min -1 ).

Experimental Setup

All the experiments described in this study were carried on using the device presented in Figure 2. It consists in a 2 L liquid capacity semi-batch reactor. Mixing was ensured by a 6-blades Rushton turbine and allowed to prevent any limitation of the process by the external mass transfer resistance. The gas was fed through a pipe located below the stirrer and collected through another pipe located at the top of the reactor. Ozone was produced from pure oxygen using an ozone generator (Trailigaz model Labo-Lox-sp, Paris, France), the nominal capacity is 16 g O 3 .h -1 for a concentration equal to 50 mg.L -1 and the gas flow rate and ozone concentrations could be varied according to the values required.

A set of valves and a flowmeter ensured a constant 0.5 L.min -1 input flow into the reactor. The excess gas flow, as well as the off-gas flow, was driven to an ozone destructor before atmospheric release. A UV absorbance analyzer (Trailigaz model UVOZON TLG 200) allowed the measurement of ozone concentration either in the inlet or in the outlet gas flow. Moreover, a polarographic probe (Orbisphere model 410 -probe 31330.15xx, Loveland, CO, USA) mounted on a circulation loop allowed to measure continuously the dissolved ozone concentration. At last, when solid materials were used, they were inserted into a stainless steel grid basket in order to avoid both attrition and floatation. A series of blank tests [START_REF]Couplage des procédés d'adsorption et d'ozonation pour l'élimination de molécules bio-récalcitrantes[END_REF] allowed verifying that the reactor itself and its various accessories were inert with respect to ozone decomposition.

Determination of Ozone Transfer and Selfdecomposition Parameters in the Presence of Materials

Ozonation of the adsorbents was carried out into this batch reactor (Figure 2) with 2 g adsorbent into 2 L deionized water. A 0.5 L.min -1 gas input flow was used with a 63 ± 4 mg.L -1 ozone concentration in order to enhance the possible effect of ozone onto the materials. The experiments were run during two 7.5 h cycles.

The volumic ozone transfer coefficient, k L .a, and the selfdecomposition kinetic constant, k C -pseudo first order -were measured through mass balances established simultaneously in both the gas and the liquid phases during ozone dissolution into water, according to the method proposed by Lopez-Lopez et al., 2009. As shown in Figure 3 (S-23 and FAU), an experiment of ozone dissolution in water starts by an unsteady state period -about 10 min -during which ozone accumulates into the liquid, then followed by a steady state period. During the unsteady state period, the mass balance for ozone in the liquid phase provides, after integration, the expression of the volumic ozone transfer coefficient, k L .a. Once the steady state has been reached, the rate of ozone self-decomposition equals the rate of dissolution, which is obtained from the gas phase balance, thus providing an expression for the rate constant, k C .

Adsorption, Ozonation and Simultaneous Process Experiments in the Presence of 2,4-DCP

All experiments were carried out into the batch reactor during 4 h at 25 • C with a 240 ± 10 mg.L -1 concentration 2,4-DCP solution (equivalent to a COD load of 280 ± 10 mg O 2 .L -1 ). For adsorption experiments, 2 g material was mixed with 2 L 2,4-DCP solution. Ozonation experiments were conducted with an ozonated oxygen gas flow (flow rate: 0.5 L.min -1 ; ozone concentration: 39 ± 3 mg.L -1 ). At last, the simultaneous process experiments consisted in ozonation experiments in the presence of 2 g.L -1 adsorbent.

Sequential Adsorption/Ozonation Experiments

Sequential adsorption/ozonation experiments were also carried on into the batch reactor, under the conditions described below. After a 4 h adsorption period, ozone process was turned on during 2.5 h (flow rate: 0.5 L.min -1 ; ozone concentration: 39 ± 3 mg.L -1 )). This duration was chosen because it corresponds to the time required for the total oxidation of a 240 mg.L -1 2,4-DCP solution by ozone under these experimental conditions. The experiment was repeated twice with the same material but a fresh 2,4-DCP solution was loaded before beginning the second run.

RESULTS AND DISCUSSION

Ozone Decomposition in the Presence of Adsorbent Materials

The evolution of ozone concentrations either in the liquid phase or in the outlet gas phase are reported in Figure 3. The results for ozone decomposition in water were determined from these curves and are reported in Table 3.

The values of the volumic ozone transfer coefficient, k L .a, are much lower than the values usually observed in bubble columns. However, these results are consistent with the results published by [START_REF] Bouafi | A Comparative Study of Gas Hold-up, Bubble Size, Interfacial Area and Mass Transfer Coefficients in Stirred Gas-Liquid Reactors and Bubble Columns[END_REF]; the very low superficial velocity of the gas -about 1.0 10 -3 m.s -1 -provides a limited gas hold-up and interfacial area despite the mechanical stirring.

First, the results show that ozone transfer kinetics is not modified in the presence of the solid materials. This result was anticipated since this parameter only depends on physico-chemical conditions which are similar with or without material (same liquid phase composition, gas velocity and gas-liquid interfacial area . . .). The volumic ozone transfer coefficient for the L-27 experiment could not be calculated because the ozone concentration profile was modified in relation with the catalytic effect of the activated carbon and, thus, did not follow the evolution expected (see Figure 3). Ozone self-decomposition kinetics is not changed in the presence of Faujasite whereas it is increased about 1.3 times with S-23 and about 24 times with L-27. This result is not surprising since activated carbons are known for their ability to decompose ozone into hydroxyl radicals. The difference between the two activated carbons can be linked to a difference in their active surface (as shown in Table 1) but also in the chemical composition of the material itself. As already mentioned for L-27 activated carbon, an unexpected decrease in ozone concentration was observed after about 10 minutes. Among the various hypotheses which can help explaining this behavior, the more likely is a change in the L-27 structure leading to higher ozone decomposition, since similar behaviors were observed by [START_REF] Reungoat | Etude d'un procédé hybride couplant adsorption et oxydation par l'ozone. Application au traitement d'effluents aqueux industriels[END_REF], during ozonation of nitrobenzene in solutions buffered at pH 2.2. Moreover, the change in L-27 activated carbon structure is confirmed by BET and DTG measurements (see Table 4 and Figure 4).

Evolution of the Material Structure after Exposure to Dissolved Ozone

Table 4 reports the main physical characteristics of the materials before ozonation (V), after 15 h exposure to ozone (O) and after sequential adsorption/ozonation process (SP). Figure 4 reports the DTG analyses for the three materials after the same treatment conditions. The results for adsorption and oxidation kinetics during the SP treatment will be discussed later.

The comparison of the first two columns (V and O) for each material in Table 4 leads to the following remarks. Both S-23 activated carbon and faujasite structures were not changed after exposure to ozone whereas L-27 activated carbon was degraded after exposure ozone. Its total surface area was decreased by about 26% and its porous volume was reduced by about 47% (89% for mesoporous volume and 18% for microporous volume). The material also became very friable. Moreover, the DTG curves for virgin (V) and ozonated (O) materials (Figure 4) were quite similar except for very high temperatures, where ozonated S-23 seems to decompose whereas virgin S-23 does not. The peak close to 100 • C corresponds to water desorption.

The ageing of the materials after the Sequential Process is more difficult to interpret. As shown by the results in Table 4, for each material, SP surface area was different from the two other values (V and O), probably indicating that the material regeneration by ozone was not complete. This was confirmed by DTG curves where a peak around 210 • C appeared which corresponds to 2,4-DCP desorption. As can be seen for this temperature, there was an approximately 10% mass loss for FAU and S-23 due to 2,4-DCP desorption. A second desorption peak appeared for S-23 around 600 • C probably indicating a slight degradation of the material. On the other hand the mass loss for L-27 activated carbon was continuous between 200 and 800 • C and was quite 100% for the latter temperature. Here again, it is confirmed that L-27 activated carbon is strongly degraded by ozone and that this material is not suited for a combined adsorption/oxidation process.

Removal of 2,4-DCP by Adsorption, Ozonation and Simultaneous Adsorption/Ozonation Process

Figure 5 shows 2,4-DCP removal by adsorption (A), single ozonation (O) and simultaneous adsorption/ozonation process (AO). In a first approach, the evolution of the concentrations can be modeled by a pseudo-first-order kinetics law as described by Equation 3. The values of the corresponding kinetic constants are reported in Table 5.

C = C 0 × e -k×t [3] with:
C,C 0 current [resp. initial] concentration in the liquid phase (either 2,4-DCP or COD); t time; k 1 st -order kinetic constant (either adsorption k Ads or ozonation k Ozo )

The 2,4-DCP adsorption onto Faujasite was about 10 times slower than 2,4-DCP adsorption onto S-23, as proven by the corresponding kinetic constants in Table 5. This is easily explained by a higher granular diameter which induced slower diffusion phenomena. Above this, pore diameter and BET surface are lower for the zeolite than for activated carbons.

Ozonation -single or combined -is a more efficient process than adsorption. However, the addition of either S-23 activated carbon or faujasite during ozonation does not improve 2,4-DCP removal since the kinetic constants remain in the same order of magnitude. In the case of this molecule, single ozonation is efficient enough for a fairly quick removal; thus the catalytic material considered during this study did not exhibit any dramatic increase in the reactivity.

Yet, the interest of the combined S-23 ozonation process is proven when the COD abatement is followed (Figure 5, right side). The radical process induced by S-23 activated carbon allowed a faster oxidation of 2,4-DCP degradation byproducts and a better efficiency at the end of the reaction period. Comparable conclusions were observed by Reungoat el al. (2007aReungoat el al. ( , 2007b)), during additional experiments with nitrobenzene and it was established that ozone consumption was lower during the combined process than during classical ozonation.

Removal of 2,4-DCP by Sequential Adsorption/Ozonation Process (SP)

Figure 6 shows the evolution of 2,4-DCP and of COD concentrations during two successive cycles of the sequential adsorption/ozonation process. The kinetics of the two adsorption steps were once again modeled through pseudofirst-order laws and the corresponding constants are given in Table 6.

The values for the first adsorption step are consistent with the adsorption kinetics constants given in Table 5. As regards the second adsorption step (i.e., after exposure to ozone during 2.5 h), the kinetics seemed to be quite slowed down for the two activated carbons, whereas it was not changed for faujasite. Two phenomena can explain this behavior: first, the surface regeneration during the ozonation steps are not complete as discussed in the following paragraph. Indeed, DTG measurements after the two cycles as well as BET surface determinations (Table 4) showed that an amount of molecules remained adsorbed onto the solids surface. This amount was low for Faujasite, higher for S-23 and far higher for L-27 activated carbon. This result is consistent with the decrease in the adsorption kinetics. Secondly, the porous volume of the two activated carbons was also decreased after the two SP cycles, which can also explain the decrease in the adsorption kinetics.

As regards the ozonation of adsorbed pollutants, it allowed a total removal of 2,4-DCP for each material. A little difference could be found in terms of duration: for S-23 experiments, ozonation time to reach zero DCP in water was lower than for AO experiments (30 min versus 45 min); on A concentration effect must account for this result. At last, after the second cycle, a slight difference between the materials could be noticed in terms of COD but not for DCP removal. The residual COD value for FAU experiments was 26% whereas this COD value was 17% after ozonation of S-23 or of L-27. But these were not significant differences according to experimental and measurement standard deviations.

CONCLUSIONS

This work investigated a hybrid process coupling adsorption and oxidation by ozone for pollutants removal in water. An aqueous solution of 2,4-dichlorophenol was used as a model pollutant accounting for industrial wastewater. Two granular activated carbons (microporous S-23 and micro/mesoporous L-27) and a de-aluminized zeolite (FAU) were chosen for adsorbents. All materials exhibited good adsorption capacities towards 2,4-DCP. The adsorption kinetics was faster for the activated carbons than for zeolite, due to both lower particle diameters and higher pore diameters and surface areas.

As expected, the two activated carbons showed good ability to decompose ozone whereas the zeolite did not exhibit such a catalytic effect. On the other hand, the short term stability of Faujasite towards ozone could be proved. S-23 activated carbon also seemed to hold its adsorption capacities after 15 hours exposure to ozone, whereas L-27 activated carbon seemed to be degraded by ozone: decrease of surface area, dramatic loss of either meso and micro-porosities and increased mechanical fragility. Hence, despite its good catalytic properties, this material was withdrawn of the rest of the study.

The simultaneous combination of adsorbent and ozone did not improve 2,4-DCP removal kinetics compared to classical ozonation. It appeared that 2,4-DCP ozonation was fast enough not to need any catalysis. Yet, the combined process with S-23 activated carbon seemed to enhance COD removal; this is probably related to HO • radicals production which improves the further oxidation of 2,4-DCP decomposition products. These results were comparable to results obtained with nitrobenzene (9, 10 and 11). Ozone consumption was not determined in this work but it is expected to be improved in the Combined Process compared to classical ozonation.

The solids regeneration by ozone was also investigated in a 4 hours adsorption and 2.5 hours ozonation Sequential Process. Two successive cycles were performed with both S-23 and FAU. For the durations used in this work, it was evidenced that 2,4-DCP was completely removed through the ozonation stage but that incomplete COD oxidation was achieved. Moreover, DTG analyses showed the persistence of residual molecules onto the solid surfaces. Thus, the duration of the two phases should still be optimized in order to reduce ozone consumption along with improving the oxidation efficiency. At last, the materials submitted to two cycles seemed to keep correct adsorption capacities. A long-term investigation is underway to better characterize the materials ageing.

  Address correspondence to Hubert Debellefontaine, Université de Toulouse, LISBP (UMR INSA/CNRS 5504 & UMR INSA/INRA 792), INSA, 135 Avenue de Rangueil, Toulouse, Cedex 4, 31077,

  FIGURE 1. 2,4-DCP adsorption isotherms onto the three materials.

FIGURE 2 .

 2 FIGURE 2. Sketch diagram of the batch reactor.

FAUFIGURE 3 .

 3 FIGURE 3. Evolution of outlet ozone gas concentration (bold lines), input ozone gas concentration (dashed lines) and dissolved ozone concentration (plain lines) during ozonation of the materials.

FIGURE 4 .

 4 FIGURE 4. DTG of Virgin (plain lines), Ozonated (dashed lines) and Sequential Process (bold lines) adsorbents.

FIGURE 5 .

 5 FIGURE 5. DCP and COD removal by adsorption, ozonation and simultaneous adsorption/ozonation process.

FIGURE 6 .

 6 FIGURE 6. The 2,4-DCP and COD removal by the sequential adsorption/ozonation process.

TABLE 1 .

 1 Main Characteristics of the Adsorbents

		Activated carbon	Zeolite
		S-23	L-27	FAU
	Specific area	1374	2337	614
	(m 2 .g -1 )
	Microporous volume	0.56	0.85	0.21
	(cm 3 .g -1 )
	Mesoporous volume	0.05	0.53	0.26
	(cm 3 .g -1 )
	Mean pore diameter	17	25	7.48
	(Å)
	Granular diameter	1.46	1.79	3.0
	(mm)
	Si/Al ratio	-	-	95
	Binding amount (%)	-	-	25

TABLE 2 .

 2 Langmuir and Freundlich Parameters

	S-23		L-27		FAU
	(Langmuir)		(Freundlich)	(Langmuir)
	Q Max				Q Max
	(mg/g)	K	F	1/n	(mg/g)	K
	354	0.83	70.9	0.34	192	0.14
	Langmuir model: Q Eq

TABLE 4 .

 4 Characteristics of Virgin (V), Ozonated (O) and Sequential Process (SP) Media

				Activated carbon				Zeolite
			S-23			L-27			FAU
		V	O	SP	V	O	SP	V	O	SP
	Total surface area	1374	1426	704	2337	1716	1745	614	617	556
	Microporous area	1373	1424	695	2313	1708	1722	515	533	477
	External area	1	2	9	24	8	23	99	84	78
	Total porous volume	0.58	0.59	0.31	1.36	0.72	1.07	0.45	0.49	0.44
	Mesoporous volume	0.05	0.04	0.08	0.53	0.06	0.46	0.26	0.29	0.24
	Microporous volume	0.56	0.58	0.29	0.85	0.70	0.57	0.21	0.21	0.20
	Areas are in m 2 .g -1 .
	Volumes are in cm 3 .g -1 .

TABLE 5 .

 5 Adsorption and Ozonation Pseudo-first-order Constant with 2,4-DCP

	Without adsorbent	S-23		FAU
	k Ozo	k Ads	k Ozo	k Ads	k Ozo
	77	9.0	110	0.88	59

All constants are in 10 -3 min -1 .

TABLE 6 .

 6 Evolution of the First-Order Constants During the Two 2,4-DCP Adsorption Steps in the Sequential Process

	S-23		L-27		FAU
	k Ads 1	k Ads 2	k Ads 1	k Ads 2	k Ads 1	k Ads 2
	7.3	2.4	8.0	1.5	1.2	0.9
	All constants are in 10 -3 min -1 .
	the contrary, this time was higher for SP experiments on FAU
	(1 h) than for AO experiments on FAU (45 min) and, at last,
	L-27 behaved like S-23. However, considering global pol-
	lution, the efficiency was not total for the 3 materials: a
	residual value of COD still remained after ozonation. This
	value seemed to be weaker than for AO experiments, as well

ACKNOWLEDGMENTS

The authors thank the PICA Company for supplying the activated carbons, the LACCO Laboratory (Université de Poitiers -CNRS) for analyses of the solids and the French National Agency for Research (ANR) for financial support (PRECODD program).