Battaglia-Brunet Fabienne

Casiot Corinne

Fernandez-Rojo Lidia

Hery Marina

Pape Le

Tris Pierre

Morin Hafida

Touzé Guillaume

Joulian Catherine F Solène

Battaglia-Brunet

H Tris

S Touzé

C Joulian

C Casiot

L Fernandez-Rojo

M Hery

P Le Pape

G Morin

Laboratory-scale Bio-treatment of Real Arsenic-rich Acid Mine Drainage

Keywords: arsenic, acid mine drainage, bioreactors, sulfate-reduction, bio-oxidation

Acid mine drainage (AMD) still represents a huge environmental problem. Technical and scientific breakthroughs are still needed to decrease environmental damages, treatment cost and waste production associated with AMD. The feasibility of combining continuously fed anaerobic sulfate-reducing bioreactor with downstream iron oxidation step was tested, at laboratory scale, with two types of real arsenic rich AMD waters from the site of Carnoulès (France), that differed in acidity (pH 3.3 and 4.0), arsenic (As, 18 and 174 mg/L) and metals concentrations. Iron remained in solution while up to 99% of As was precipitated as amorphous orpiment in the anaerobic sulfate-reducing bioreactor. Zinc (Zn) precipitation was also observed, up to 99%, however the efficiency of Zn precipitation was less stable than that of As.

The anaerobic bioreactor presented a stable bacterial community including a

Desulfosporosinus-related sulfate-reducer. When the effluents from the anaerobic process step were treated in a laboratory aerobic bioreactor, iron was oxidized efficiently. The feasibility of efficient orpiment bio-precipitation coupled with downstream iron oxidation was shown, thus opening the perspective of low-cost combination of treatment steps for the removal of arsenic, zinc and iron in As-rich AMDs.

Introduction

Acid mine drainage (AMD) causes extensive damage to the aquatic environment all around the world [START_REF] Simate | Acid mine drainage: Challenges and opportunities[END_REF]. This phenomenon affects many abandoned and remote sites, where the application of the classical active lime treatment is technically and economically problematic. Passive or semi-passive technologies have been developed, the global remediation strategy generally involving several biological or physic-chemical treatment steps (Johnson and Hallberg, 2005;[START_REF] Nairn | A large, multi-cell, ecologically engineered passive treatment system for ferruginous lead-zinc mine waters[END_REF][START_REF] Mattes | The long term operation of a biologically based treatment system that removes As, S and Zn from industrial (smelter operation) landfill seepage[END_REF]. Oxidation steps can be efficient to remove iron (Fe), manganese (Mn), or co-precipitate Fe and arsenic (As) [START_REF] Casiot | Bacterial immobilization and oxidation of arsenic in acid mine drainage (Carnoulès creek, France)[END_REF][START_REF] Battaglia-Brunet | A simple biogeochemical process removing arsenic from a mine drainage water[END_REF]Wang et al., 2006;De Sa et al., 2010;[START_REF] Nairn | A large, multi-cell, ecologically engineered passive treatment system for ferruginous lead-zinc mine waters[END_REF][START_REF] Fernandez-Rojo | Biological attenuation of arsenic and iron in a continuous flow bioreactor treating acid mine drainage (AMD)[END_REF], 2019). However, such aerobic processes are unsuitable for the removal of divalent metal cations due to their poor sorption onto positively charged surface of Fe-oxyhydroxides in acid conditions [START_REF] Lee | Removal of trace metals by coprecipitation with Fe, Al and Mn from natural waters contaminated with acid mine drainage in the Ducktown Mining District, Tennessee[END_REF]. On a complementary way, biological reduction of sulfate efficiently removes metals such as zinc (Zn), copper (Cu), and lead (Pb) as metallic sulfide precipitates and induces an increase of alkalinity and pH (Kaksonen andPuhakka, 2007, Touzé et al., 2008). This treatment is also efficient to remove As [START_REF] Mattes | The long term operation of a biologically based treatment system that removes As, S and Zn from industrial (smelter operation) landfill seepage[END_REF], provided that low pH and/or low dissolved sulfide concentrations maintain sulfide amounts sufficiently low (< 1 mg.L -1 ) to avoid the formation of soluble thioarsenic species (Smieja and Wilkin, 2003). Sulfate reduction needs a costly supply in electron donor, such as hydrogen or organic molecules. To limit such costs, passive anaerobic bioreactors are generally filled with raw organic materials, such as agricultural, wood or food processing wastes which degradation provides electron donors for sulfate reduction [START_REF] Parvis | Design, construction and performance of a full-scale compost wetland for mine-spoil drainage treatment at quaking houses[END_REF][START_REF] Gibert | Chemical characterisation of natural organic substrates for biological mitigation of acid mine drainage[END_REF][START_REF] Mattes | The long term operation of a biologically based treatment system that removes As, S and Zn from industrial (smelter operation) landfill seepage[END_REF]. However, in these systems, the sulfate-reducing activity cannot be regulated, all metals being precipitated as a bulk without selectivity. It would be interesting to regulate the activity of sulfate-reducing bacteria so as to remove only metals that cannot be eliminated, or only partially removed, in the aerobic steps. In this respect, iron sulfide (FeS) precipitation should be avoided since Fe can be efficiently treated in an oxidizing process [START_REF] Fernandez-Rojo | Biological attenuation of arsenic and iron in a continuous flow bioreactor treating acid mine drainage (AMD)[END_REF]. Allocate the sulfate-reducing activity to the precipitation of a selection of metals will thus save organic substrate costs. Considering that FeS precipitates at pH higher than 5 [START_REF] Kontopoulos | Effluent treatment in the mining industry[END_REF], the sulfate-reducing bioreactor should be able to perform efficiently at lower pH. Sulfate reduction by acidophilic or acido-tolerant sulfatereducing bacteria (SRB) has been reported as a promising way to remediate acid mine water while selectively precipitating metals as sulfides [START_REF] Kimura | Sulfidogenesis in low pH (3.8-4.2) media by a mixed population of acidophilic bacteria[END_REF][START_REF] Johnson | Sulfidogenesis at low pH by acidophilic bacteria and its potential for the selective recovery of transition metals from mine waters[END_REF][START_REF] Nancucheo | Selective removal of transition metals from acidic mine waters by novel consortia of acidophilic sulfidogenic bacteria[END_REF][START_REF] Nancucheo | Removal of sulfate from extremely acidic mine waters using low pH sulfidogenic bioreactors[END_REF]Sanchez-Andrea et al., 2015;Gonzales et al., 2019). The feasibility of As sulfide biosynthesis was demonstrated in batch laboratory bioreactors [START_REF] Serrano | Removal of Arsenic using acid/metal-tolerant sulfate reducing bacteria: a new approach for bioremediation of high-arsenic acid mine waters[END_REF][START_REF] Pape | Complete removal of arsenic and zinc from a heavily contaminated Acid Mine Drainage via an indigenous SRB consortium[END_REF] or continuously fed with acidic (pH 2.5 to 4, [START_REF] Battaglia-Brunet | Precipitation of arsenic sulphide from acidic water in a fixed-film bioreactor[END_REF][START_REF] Altun | Arsenic removal in a sulfidogenic fixed-bed column bioreactor[END_REF] or mild acidic synthetic (pH 6-7, [START_REF] Rodriguez-Freire | Biomineralization of arsenate to arsenic sulfides is greatly enhanced at midly acidic conditions[END_REF], 2015) solutions. Growth of SRB inducing precipitation of the orpiment and realgar, together with ZnS nanoparticles, has been proven in the real arsenic-rich acid mine water from Carnoulès site (France) in batch experiments (Le [START_REF] Pape | Complete removal of arsenic and zinc from a heavily contaminated Acid Mine Drainage via an indigenous SRB consortium[END_REF].

Here, the two steps of a semi-passive process configuration including complementary anaerobic and aerobic reactions were separately tested with the Carnoulès AMD in continuous laboratoryscale bioreactors. These two complementary processes should allow removal of toxic metals and high As contents from the AMD. Three main issues were addressed: (i) the feasibility of orpiment precipitation from real arsenic-rich acidic mine water in an anaerobic SRB bioreator, (ii) the separation of Fe, remaining in solution, from Zn and As, precipitated as sulfides, and (iii) the aerobic bio-oxidation of remaining Fe present in the effluent from the anaerobic bioreactor, and subsequent As removal.

Materials and Methods

Mine waters

AMD water was collected in July 2014 at the Carnoulès mine (Gard, France) from two different springs: S1 and SSR, filtrated at 0.45 µm in a glovebox and stored at 5°C under nitrogen. NaOH solution (1 M) was added to the water in a glovebox when pH adjustment was needed.

Characteristics of the water samples are given in Table 1. Among all metals and metalloids present in these mine waters, As is particularly toxic, Zn is the most concentrated divalent metal, and Fe is present at high level, close to 1 g.L -1 (le [START_REF] Pape | Complete removal of arsenic and zinc from a heavily contaminated Acid Mine Drainage via an indigenous SRB consortium[END_REF].

Sulfate-reducing bioreactor

Experimental device

The sulfate-reducing bioreactor consisted of a 320 mm high and 35 mm internal diameter glass column, equipped with a water jacket for temperature regulation. The bioreactor filling method was conceived to: (1) test the passive distribution of nutrients to the bacteria, and (2) try to establish different levels of SRB activities in the bottom and the top zones based on the stimulation of SRB growth by yeast extract, thus testing the possibility to precipitate As in the top layer (lower sulfate-reduction activity) and Zn in the bottom layer. The bioreactor (Fig. 1) was filled in two distinct layers. For the top half of the bioreactor, pozzolana was mixed with hot liquid agar (25 g.L -1 ) prepared with deionized water acidified at pH 4.5 with H2SO4, containing 5 g.L -1 glycerol and 0.5 g.L -1 K2HPO4. After solidification of the agar, pozzolana grains were separated using a spatula and mixed with a carrier biomaterial named "biocompounds", provided by Vertum GmbH (Walter et al., 2009) and composed of polyhydroxybutyrate and polycaprolactone. The proportions of components were 160 g of pozzolana / 100 g of biocompounds / 200 mL of agar with nutrients. The bottom filling material had same composition except for the nutritive agar, supplemented with 1 g.L -1 yeast extract.

Sampling ports equipped with septa allowed liquid sampling from the middle, bottom and top levels.

The bioreactor was inoculated with a sulfate-reducing microbial consortium, enriched from sediments of the Carnoulès site. A basal medium (SM1) prepared at pH 3.5 and 4.5 was supplemented with 327 mg.L -1 Zn and 75 mg.L -1 As(V) (using respectively 16 g.L -1 ZnSO4 and 10 g.L -1 As(V) anaerobic stock solutions). Active cultures precipitating yellow-white precipitates were sub-cultured in 40 mL basal medium supplemented with As and major metals present in Carnoulès water: 2 mL of Fe(II) solution (final concentration 1 g.L -1 ), 2 mL of metals solution, 0.5 mL of As(III) solution (final concentration 100 mg.L -1 ) and 0.2 mL of As(V) solution (final concentration 40 mg.L -1 ). Concentrated Fe(II) and metals solutions were prepared under N2 atmosphere, with oxygen-free ultrapure water acidified at pH 4.5 with H2SO4. Fe(II) solution contained, per litre, 99.2 g of FeSO4.7H2O. Metals solution contained, per litre: Al2(SO4)3.18H2O, 13.6 g ; MnSO4.H2O, 368 mg; NiSO4.6 H2O, 44 mg ; ZnSO4.7H2O, 1.77 g; CuSO4.5 H2O, 32 mg. Concentrated As(III) and As(V) solutions (10 g.L -1 As) were prepared as described in [START_REF] Battaglia-Brunet | An arsenic(III)-oxidizing bacterial population: selection, characterization and performance in reactors[END_REF]. Two sulfate-reducing cultures were obtained after five sub-cultures at pH 3.5 and 4.5; they were mixed to obtain the sulfatereducing microbial consortium used to inoculate the bioreactor. A pellet of this inoculum was stored at -20°C for DNA extraction and bacterial taxonomic identification.

Operating conditions

The bioreactor first worked in passive down-flow condition for 199 days, during which the microbial activity was exclusively supported by the nutrients present in the solid filling materials [START_REF] Battaglia-Brunet | Development of a passive bioremediation process based on sulfate-reduction to treat arsenic-containing acidic mine water[END_REF]. During this phase, the feed solution was a synthetic mine water prepared adding the following components to 1 L deionized water whose pH was adjusted with concentrated H2SO4: 2.3 g Na2SO4, 50 mL of Fe(II) solution, 50 mL of metals solution, 10 mL of As(III) solution and 2.5 mL of As(V) solution. The pH dropped from 4.5 to 3.0 in 60 days. The present experiment started at Day 200, after this passive phase, using real spring S1 mine water (pH 3.3) amended with 250 mg.L -1 of glycerol as feed. The bioreactor was down-flow fed during 26 days. Down-flow configuration consumes less energy than upflow however it increases the phenomena of preferential flow paths and clogging. Then, downflow was changed to up-flow feeding (day 226). At last, from day 315, the column was up-flow fed with the spring SSR (pH 4.0) mine water complemented with 50 mg.L -1 glycerol. The temperature was maintained constant at 25°C.

Monitoring of the bioreactor

The outlet solution was collected and maintained under N2 atmosphere. Once a day, the outlet bottle was weighted to measure flow-rate. pH was measured and 5 mL of bioreactor outlet were filtrated at 0.45 µm, acidified with nitric acid and stored at 5°C until As, Fe and Zn analyzes.

The remaining effluent was stored at 5°C under N2 atmosphere until treatment in the aerobic bioreactor. Feed was sampled once a week to check pH and chemical composition. Total As was analyzed by oven AAS (Varian SpectrAA 220Z), Zn and Fe by flame AAS (VARIAN SpectrAA 300). Total organic carbon was quantified by hot oxidation with sodium persulfate (method NF EN 1484) and acetate was analyzed by ionic chromatography. Punctually (on days 201, 219, 288, 309 and 367), 5 mL of slurry were collected from top, middle and bottom septa with a sterile syringe, filtrated on a sterile 0.22 µm cellulose acetate filter and the filters were stored at -20°C for biomolecular analyzes. At the end of the experiment, the column was opened in a glovebox under N2 atmosphere. Samples of the filling material were stored at -20 °C for biomolecular analyzes, and other samples were stored under N2 for mineralogical analyzes.

After the bioreactor dismantling, "biocompound" particles were recovered, rinsed with deionized water and dried at 40°C for 24 h then weighted to estimate the amount of consumed material.

2.2.4

Composition of the inoculated sulfate-reducing consortium and evolution of the bacterial community structure in the column Microbial DNA was extracted from the -20°C stored samples, i.e. pellet of the inoculum, frozen filters and filling materials (sampled at the end of the experiment), with the FastDNA Spin Kit for soil applying a mechanical lysis at speed 5 during 30 s. Bacteria composing the inoculum were identified by cloning and sequencing of the 16S rRNA gene. Briefly, about 1400 bp of the gene were amplified from the extracted microbial DNA with primers 8F (5'-AGAGTTTGATCMTGGCTCAG-3') and 1406R (5'-GACGGGCGGTGTGTRCA-3'), and the purified PCR product was cloned into a PCR®4-TOPO vector, according to the manufacturer instructions (Invitrogen). 32 plasmids carrying correct-length insert were sequenced by the GATC company with primers T7 end T3 targeting the vector. Consensus sequences were manually verified and aligned with ClustalW, and distances on unambiguous nucleotide sequences were determined by DNADist, using applications implemented in the BioEdit software [START_REF] Hall | BioEdit: a user-friendly biological sequence alignment editor and analysis program for Windows 95/98/NT[END_REF]. Operating taxon units (OTU) were built with retrieved sequences sharing more than 98% identities. Distances between most related Genbank 16S rRNA gene

Results

Anaerobic bioreactor

Evolution of physic-chemical parameters

During the down-flow feeding phase with spring S1, As removal efficiency averaged 64 ± 4 % (157 mg.L -1 As in the feed, 46 to 71 mg .L -1 in the outlet) for a measured residence time of 298 ± 26 h (Fig. 2A and 2B) whereas within the same time, Zn removal (Fig. 2C) varied from 2 to 25% (24 mg.L -1 Zn in the feed, 16 to 23 mg .L -1 in the outlet) and Fe removal (Fig. 2D) from 10 to 30% (1270 mg.L -1 Fe in the feed, 84 to 1146 mg .L -1 in the outlet).

Substantial increase of Zn (Fig. 2C) concentration in the effluent after 208 days occurred concomitantly to effluent pH decrease (Fig. 2E), consequence of clogging of the filling material that resulted in disconnections of feeding pipe. The change (day 226) from down-flow to upflow configuration improved the efficiency of the bioreactor for As removal, that was higher than 85% from day 245 to day 290 (Fig. 2B). As removal declined slightly with the decrease of residence time from 300 h to 250 h after day 245 (event 1 on Fig. 2) but recovered at day 260.

The decrease of the mine water pH from 3.1 to 2.9 after day 270 (event 2 on Fig. 2) also induced transient rise of As concentration in the outlet. A delay of 4-5 days was still observed between the source of disturbance and the rise of As concentration in the outlet because of the high residence time. After day 290, a new decrease in residence time from 250 h to 70 h (event 3 on Fig. 2) induced a worsening of As removal that stabilized around 65%. Zn concentration followed the same evolution as As but with variations of higher amplitude. The events that affected As removal by 15% affected Zn removal by 90%. After day 290, the decrease of residence time resulted in a very low level of Zn removal (less than 10%). During all the upflow feeding period, Fe was not removed (Fig. 2D). The pH always increased: while fed with real mine water at pH close to 3, the pH in the outlet ranged from 4.3 to 4.8 (Fig. 2E).

Changing fed water from S1 to SSR corresponded to a decrease in Fe, Zn and As concentrations and higher pH of the feed (event 4 on Fig. 2). After a transient period during which parameters were influenced by the change of feed water quality, from day 312 to day 330, complete removal of As and Zn was obtained. When the residence time in the bioreactor was progressively decreased from 70 to 30 h (Fig. 1A), As and Zn were always almost entirely removed from SSR water (Fig. 2B and2C) and Fe was not precipitated (Fig. 2D).

Most of both As and Zn was precipitated in the bottom half of the column (Fig. SM2), so the separation of As and Zn inside the column using different filling compositions was not achieved. Acetate was always found in the outlet during the monitoring, however acetate concentration in the outlet was 50% to 99% lower than the theoretical concentration that would result from the incomplete oxidation of glycerol (Table SM3), except at the end of experiment with spring SSR water, when the bioreactor was in a phase of degraded efficiency. At the end of experiment, the visual appearance of the biocompounds and their weight did not differ significantly from those of fresh biocompounds, suggesting they have not been biodegraded in the bioreactor.

Composition of the inoculum and evolution of the bacterial community in the column

The 32 sequences of the 16S rRNA gene retrieved from the sulfate-reducing consortium enriched from the Carnoulès site were classified into three OTU. The dominant OTU (90.6 % of the sequences) shared 99.1 % identity on the 16S rRNA gene sequence with the acidophilic sulfate-reducing bacterium Desulfosporosinus sp. PFB [START_REF] Sen | Acidophilic sulphate-reducing bacteria: candidates for bioremediation of acid mine drainage[END_REF]. Another

Desulfosporosinus-related OTU represented 6.3 % of the sequences and showed more than 3 % differences on the 16S rRNA gene with the dominant OTU; it shared 97.7 % and 97.8 % 16S

rRNA gene identities with Desulfosporosinus sp. OK and Desulfosporosinus sp. OL isolated from an AMD (sequences available in Genbank under numbers MT359229 and MT359230).

The closest described Desulfosporosinus species most related (96-97 % identity) to these two OTU were D. lacus, D. meridiei, D. orientis, D. fructosivorans and D. auripigmenti. The third OTU grouping 3.1 % of the sequences was related (99.7 % 16S rRNA gene identity) to the Propionibacteraceae strain H7p isolated from Carnoulès acid mine drainage [START_REF] Delavat | Novel and unexpected bacterial diversity in an arsenic-rich ecosystem revealed by culture-dependent approaches[END_REF]; except for its tolerance to low pH, no data is currently available on its metabolism. present, only as a small fraction of the total community.

Characterization of the precipitates

In the samples from the column, i.e. black pouzzolana and yellow precipitate, analyzed using XRD (Fig. SM4-A), no As-bearing phase was observed. The composition is in line with usual mineral compounds used in pouzzolana, e.g. feldspars. In the yellow precipitate recovered around the pouzzolana grains, only gypsum was observed as crystalline material. However, very low amplitude reflexions as well as large bumps above the background suggest the presence of amorphous or nanocrystalline materials.

Both XANES and EXAFS spectra obtained at the As K-edge for the different samples collected in the column were compared to reference materials representative for specific As local molecular environments. Realgar (AsS) and amorphous orpiment (am_As2S3) were used as references for sulfur bound As, and As(III)-sorbed ferrihydrite and As(V)-sorbed ferrihydrite were used as proxies of oxygen bound As. Linear combination fitting analysis performed on As K-edge XANES spectra shows that the samples mainly contained amorphous orpiment (89 to 100 %) and a minor amount of oxygen bound As(III) (0 to 13 %) (Fig. SM4-B and Table SM4-C). Even considering the low quality of EXAFS signal for some of the samples (Fig. SM4-D), both EXAFS oscillations and Fast Fourier Transform confirm the major occurrence of amorphous orpiment in the samples recovered from the column experiment (Fig. 4). As both XANES and EXAFS spectra of thiol-bound As(III) are difficult to differ from the one of amorphous orpiment, the presence of such As species cannot be excluded in the samples. In addition, the presence of minor amount of oxygen bound As(V) and realgar (< 5%) cannot be discarded considering the standard uncertainty of XAS-LCF analysis.

In Fig. 4, the image of yellow precipitate was taken in backscattering electron mode, thus the brightest spots indicate the presence of the heaviest elements. In this particular case, the brightness of particles is related to the As content. Both encrusted and non-encrusted bacteria are observed, as well as submicrometric aggregates of spherical particles connected or not with bacteria. All the particles probed using EDXS (1 to 6, Fig. 4) showed a major signal of As and S, which is consistent with arsenic sulfides as the main products of the sulfate-reducing activity of the biofilm. Only traces of Fe and Zn were detected in the EDXS spectra, confirming that As was the main element to precipitate as biogenic sulfide in the bioreactor. In addition to the large occurrence of aggregates of spherical nanoparticles in the biofilm, nanospheres can be observed on the surface of bacterial cells (Fig. 4A). This observation would be consistent with those of Newmann (1997) who observed the extracellular precipitation of orpiment nanoparticles on sulfate-reducing bacteria mineralizing arsenic.

Coupling with aerobic step

The aerobic step was tested as a preliminary evaluation of the feasibility of biological oxidation of Fe(II) and increase of As removal in the sulfate-reduction bioreactor effluent, that contained also organic substances, potentially inhibitors of Fe(II) and As(III) bio-oxidation. This treatment induced a decrease of pH and Fe concentration: 7% (S1) and 9% (SSR) removal were obtained within 300 minutes (Fig. 5). Concerning As, for spring S1, nearly 90% removal was obtained in the anaerobic bioreactor, and the aerobic step improved the overall removal, decreasing both As(III) and As(V) concentrations by 33% and 44%, respectively. These results represent a gain of 6% removal for As(III) and 4% for As(V) considering the initial composition of the mine water. Conversely, with spring SSR, the aerobic step did not induce any As removal.

Surprisingly, a release of As(III) was observed in these conditions. The aerobic step had no effect on Zn concentration.

Discussion

Up to now, laboratory continuous experiments dedicated to the biological precipitation of arsenic sulfide were fed with synthetic solutions [START_REF] Battaglia-Brunet | Precipitation of arsenic sulphide from acidic water in a fixed-film bioreactor[END_REF][START_REF] Altun | Arsenic removal in a sulfidogenic fixed-bed column bioreactor[END_REF][START_REF] Rodriguez-Freire | Biomineralization of arsenate to arsenic sulfides is greatly enhanced at midly acidic conditions[END_REF], 2015). Here, a real As-rich acidic mine water, of complex composition, was used to confirm the feasibility of continuous anaerobic precipitation of orpiment at low pH, in accordance with batch experiment data (Le [START_REF] Pape | Complete removal of arsenic and zinc from a heavily contaminated Acid Mine Drainage via an indigenous SRB consortium[END_REF]. The present experiment with real mine water and glycerol supply started on day 200, after the bioreactor was fed with synthetic mine water during 199 days under entirely passive conditions [START_REF] Battaglia-Brunet | Development of a passive bioremediation process based on sulfate-reduction to treat arsenic-containing acidic mine water[END_REF]. During this previous experimental phase, a progressive decrease of the bioreactor efficiency had been observed, linked to the exhausting of substrates initially placed into the column. Semi-passive sulfate-reducing bioreactors are increasingly seen as a viable option for highly contaminated AMD [START_REF] Lounate | Performance of a Semipassive Sulfate-reducing Bioreactor for Acid Mine Drainage Treatment and Prediction of Environmental Behavior of Post-treatment Residues[END_REF]. One of the objectives of the present study was to evaluate the precipitation of As and Zn in the sulfate-reducing bioreactor working in semi-passive condition, while Fe remained in solution, knowing that: (1) As is toxic and cannot be valorized, thus should be precipitated in the smallest volume of waste as possible,

(2) Zn must be removed during the sulfate-reducing step because the oxidation step will not remove it, (3) Fe can be efficiently removed downstream by passive microbial or chemical oxidation step, co-precipitating the residual As. Furthermore, as Fe is the most concentrated metal in Carnoulès AMD, avoiding its precipitation in the anaerobic bioreactor will save organic substrates and prevent rapid clogging.

The theoretical mass balance comparing our process configuration with a classical lime treatment directly applied to the spring S1 AMD (Fig. 6) suggests that the amount of Ascontaminated solid waste could be drastically decreased applying a sulfate-reduction step followed by aerobic oxidation. Moreover, the classical lime application could not remove Zn from water unless reaching pH 9.5 [START_REF] Murdock | Treatment of acid mine drainage by the high density sludge process[END_REF], thus implying a supplementary final step of acid addition.

The direct feeding of sulfate-reducing bacteria with the acid mine waters S1 et SSR was possible, in spite of the low pH, because iron, although present in high concentration, is mainly under the Fe(II) form in Carnoulès water [START_REF] Casiot | Bacterial immobilization and oxidation of arsenic in acid mine drainage (Carnoulès creek, France)[END_REF]. The sulfate reduction induced an increase of one unit pH along the experiment. However, the pH in the outlet remained acidic, contrary to previous studies [START_REF] Battaglia-Brunet | Precipitation of arsenic sulphide from acidic water in a fixed-film bioreactor[END_REF][START_REF] Altun | Arsenic removal in a sulfidogenic fixed-bed column bioreactor[END_REF][START_REF] Rodriguez-Freire | Biomineralization of arsenate to arsenic sulfides is greatly enhanced at midly acidic conditions[END_REF], 2015), where the electron donor was not limiting, supporting an extended sulfatereduction activity and resulting in a pH value higher than pH 5-6 in the outlet. Here, the moderate pH increase, linked to the limited substrate supply, allowed separating Fe, that remained in solution, from Zn and As that were precipitated together during periods of efficient microbial activity. However, the anaerobic bioreactor was more efficient to remove As than Zn:

the weakening of bacterial activity always affected Zn precipitation more than As removal during the experiment with spring S1. Precipitation of amorphous orpiment is favored at low pH [START_REF] Eary | The solubility of amorphous As2S3 from 25 to 90°C[END_REF]: the more acid the medium is, the more orpiment precipitation is efficient.

With spring S1 water, le [START_REF] Pape | Complete removal of arsenic and zinc from a heavily contaminated Acid Mine Drainage via an indigenous SRB consortium[END_REF] already showed that As precipitation was more rapid than that of Zn. With spring SSR, the feed pH (pH 4) was already higher than the value necessary for ZnS precipitation, that could explain the efficient removal of both Zn and As from this mine water. [START_REF] Mattes | The long term operation of a biologically based treatment system that removes As, S and Zn from industrial (smelter operation) landfill seepage[END_REF] already reported efficient removal of both As and Zn from a smelter landfill seepage (pH 5.9), through a real scale anaerobic passive bioreactor filled with a mixture of limestone, quartz sand and organic waste.

Here, considering that production of sulfide was mainly coupled to incomplete degradation of glycerol (reaction 1), and consumption of sulfide occurred according to reactions (2) and (3), the total amount of glycerol necessary to precipitate all As (2 mM) and Zn (0.3 mM) present in S1 should be 4.4 mM, i.e. 405 mg L -1 . Yet, the bioreactor feed contained only 250 mg L -1 glycerol, a limiting concentration that should not have been sufficient for the precipitation of both As and Zn, whereas the complete removal of these two elements was observed during some periods of the experiment.

C3H8O3 + 0.75 SO4 2-+ 1.5 H + C2H4O2 + CO2 + 0.75 H2S + 2 H2O (1) 2 H3AsO3 + 3 H2S As2S3 + 6 H2O (2)

Zn 2+ + S 2- ZnS (3)
This result may be explained by the complete oxidation of glycerol, according to reaction (4), that would produce 2.3 times more H2S than reaction (1). As a fact, acetate concentration in the bioreactor outlet was lower than the theoretical concentration corresponding to the incomplete oxidation of all the glycerol supplied with the feed water. [START_REF] Nancucheo | Removal of sulfate from extremely acidic mine waters using low pH sulfidogenic bioreactors[END_REF] already observed a decrease of acetate concentration in a sulfate-reducing bioreactor fed with glycerol, when the working pH was decreased from 4.5 to 3.0. The switch from incomplete to complete oxidation of glycerol was accompanied by a change in the bacterial community structure. The solid filling material, initially loaded with agar, yeast extract and glycerol, could also slowly release organic molecules that played the role of complementary electron donors.

4 C3H8O3 + 7 SO4 2-+ 14 H + 12 CO2 + 7 H2S + 16 H2O (4)

Initially, the bioreactor was inoculated with a sulfate-reducing consortium mainly composed SRB affiliated to the Desulfosporosinus genus. Two distinct OTU were retrieved; they showed less than 97 % sequence identity on their 16S rRNA genes, and 96-97 % identities with described Desulfosporosinus species (D. lacus D. meridiei, D. orientis, D. fructosivorans and D. auripigmenti). If we consider a cut-off value at the species level of 98.7% or above on the 16S rRNA gene [START_REF] Rossi-Tamisier | Cautionary tale of using 16S rRNA gene sequence similarity values in identification of human-associated bacterial species[END_REF], the two-retrieved OTU may represent new acidophilic species of the Desulfosporosinus genus. The OTU sequences had higher identity

values with yet undescribed acidophilic isolates of the genus: 99 % between the dominant OTU and Desulfosporosinus sp. PFB [START_REF] Sen | Acidophilic sulphate-reducing bacteria: candidates for bioremediation of acid mine drainage[END_REF] and 98 % between the second SRB OTU and Desulfosporosinus sp. OK and OL (MT359229 and MT359230 Genbank accession numbers). The Desulfosporosinus genus comprises several members known to reduce sulfate, in acidic conditions, and often isolated from mining sites (e.g. [START_REF] Sen | Acidophilic sulphate-reducing bacteria: candidates for bioremediation of acid mine drainage[END_REF][START_REF] Karnachuk | Bacteria of the sulfur cycle in the sediments of gold mine tailings, Kuznetsk Basin, Russia[END_REF][START_REF] Alazard | Desulfosporosinus acidiphilus sp. nov.: a moderately acidophilic sulfate-reducing bacterium isolated from acid mining drainage sediments[END_REF][START_REF] Sánchez-Andrea | Desulfosporosinus acididurans sp. nov.: an acidophilic sulfate-reducing bacterium isolated from acidic sediments[END_REF]. All these Desulfosporosinus strains are incomplete oxidizers using glycerol to reduce sulfate and produce Desulfosporosinus-related sulfate reducers in diverse SRB reactors treating AMD from laboratory to real scale [START_REF] Habe | Design, application, and microbiome of sulfate-reducing bioreactors for treatment of mining-influenced water[END_REF].

In the present study, mineralogical observations of the precipitates formed in the bioreactor were globally in line with those obtained from batch experiments, with AMD from the same site, in comparable conditions (Le [START_REF] Pape | Complete removal of arsenic and zinc from a heavily contaminated Acid Mine Drainage via an indigenous SRB consortium[END_REF]. However, if the major occurrence of amorphous orpiment is strongly suspected from SEM-EDXS and confirmed by XANES and EXAFS spectroscopy, no realgar was detected in the form of nanowires in the biofilm observed by SEM-EDXS. Thus, the processes occurring within the continuous column experiment would be representative of the early stages of As reduction and precipitation processes identified in the batch experiment system, before reduction of orpiment into realgar (Le [START_REF] Pape | Complete removal of arsenic and zinc from a heavily contaminated Acid Mine Drainage via an indigenous SRB consortium[END_REF].

When the outlet water from the anaerobic reactor was treated in aerobic condition, partial oxidation of iron and a decrease of pH were observed. The iron removal rate with S1 and SSR waters were 1.1 x 10 -7 and 0.9 x 10 -7 mol.L -1 .s -1 respectively, that is of the same range but lower than the iron removal rates previously reported during direct aerobic treatment of this AMD in the same reactor (1.3 -2.4 x 10 -7 mol.L -1 .s -1 , [START_REF] Fernandez-Rojo | Biological attenuation of arsenic and iron in a continuous flow bioreactor treating acid mine drainage (AMD)[END_REF]. The hydraulic residence time was only 300 min, so largely lower than that applied in the anaerobic step. The conditions of this aerobic step remain to be optimized. Gonzales et al. ( 2019) observed the complete oxidation of the ferrous iron present in the outlet of a SRB bioreactor, corresponding to nearly 1 mM, in 1 h aeration. Here, some As was removed from S1 water previously treated anaerobically, however with SSR water, some release of As(III) occurred. This phenomenon may be linked to the sharp shift from S1 to SSR water compositions, inducing a decrease of As concentration in the feed (17 to 3 mg L -1 respectively), and might be linked to the sorptiondesorption equilibrium of As(III) associated with the iron precipitates, or to the solubility of As(III)-shwermannite accumulated in the reactor during the previous step. A decrease of As(III)-oxidation activity might also have occurred. The activity of As(III)-oxidizing bacteria may be influenced by the residual organic molecules from the anaerobic reactor. As(III)oxidizing bacteria can grow heterotrophically or autotrophically [START_REF] Santini | A new chemolithoautotrophic arsenite-oxidizing bacterium isolated from a gold mine: Phylogenetic, physiological, and preliminary biochemical studies[END_REF][START_REF] Battaglia-Brunet | A simple biogeochemical process removing arsenic from a mine drainage water[END_REF][START_REF] Garcia-Dominguez | Novel autotrophic arsenite-oxidizing bacteria isolated from soil and sediments[END_REF]. In particular, strains of Thiomonas, the main As(III)-oxidizing genus found in Carnoulès AMD [START_REF] Hovasse | Spatio-temporal detection of the Thiomonas Population and the Thiomonas arsenite oxidase involved in natural arsenite attenuation processes in the Carnoulès acid mine drainage[END_REF], are facultative chemolithoautotrophs that grow optimally in mixotrophic media containing reduced inorganic sulfur compounds and organic supplements [START_REF] Bryan | Carbon and arsenic metabolism in Thiomonas strains: differences revealed diverse adaptation processes[END_REF][START_REF] Slyemi | Characteristics of a phylogenetically ambiguous, arsenic-oxidizing Thiomonas sp., Thiomonas arsenitoxydans strain 3AsT sp[END_REF]. Tardy et al. ( 2018) observed a stimulation of As(III)-oxidation by yeast extract, in the AMD of Carnoulès mine. However, the effect of organic substrates might depend on the nature of the supplied molecules: how the bacterial communities of the biofilms inside the aerobic channel are impacted by the anaerobic effluent would require further analyzes.

Conclusions

The feasibility of arsenic precipitation as orpiment in a sulfate-reducing bioreactor fed with two types of real As-rich mine drainage waters was demonstrated at laboratory scale. Limitation of sulfate-reduction by low supply of carbon and energy source allowed the removal of most arsenic while iron remained in the water. Precipitation of zinc in the sulfate-reducing reactor was efficient with the low-concentrated AMD, whereas optimization is still needed in order to stabilize this process with the most concentrated AMD. The separation of arsenic from iron in such type of mine water may be beneficial in terms of most hazardous waste mass, as the main part of the arsenic would be concentrated as As2S3. The net consumption of glycerol for a given

As and Zn removal could be lower than initially expected because this substrate can be entirely ), E: pH. Numbered vertical lines show specific events: (1) and (3) decrease of residence time;

(2) decrease in feed pH, (4) change from spring S1 to spring SSR.

The pH value increased from 4.0 in the feed to 4.5-5.0 in the outlet, except during the last days of experiment, probably because of the decrease of residence time from 40 to 30 h (Fig. 2E). SM4C).

  //www.ncbi.nlm.nih.gov/blast/Blast.cgi), and defined OTU sequences were determined by DNADist on 1372 aligned and unambiguous nucleotides. In addition, about 1.9 kb of the dsrAB gene encoding the dissimilatory bisulfite reductase involved in reduction of sulfate, were amplified with primers DSR1F (5'-ACSCAYTGGAARCACG-3') and DSR42R (5'-GTGTARCAGTTDCCRCA-3'), cloned and sequenced as described. Consensus dsrAB gene sequences sharing more than 98% identities by DNADist were grouped in OTU and compared to Genbank reference sequences by Blastn. Most related reference and OTU dsrAB gene sequences were translated into amino acids sequences, aligned and distances were calculated by ProtDist (implemented in BioEdit software) on 552 unambiguous amino acids. Sequences reported in this study are available under GenBank accession numbers MZ476566-MZ476597 (16S rRNA gene sequences) and MZ497397 to MZ497410 (dsrAB gene sequences).The evolution of the structure of the bacterial community in the bioreactor was monitored by 16S rRNA gene CE-SSCP genetic fingerprints. About 200 bp of the V3 region of the bacterial 16S rRNA gene were amplified from DNAs (column samples and clones representing each OTU from the inoculum) with the reverse primer w34 (5′-TTACCGCGGCTGCTGGCAC-3′), 5′ end-labelled with the fluorescent dye FAM, and the forward primer w49 (5′-ACGGTCCAGACTCCTACGGG-3′). Diluted PCR products (100 to 200 fold, to avoid saturation of the fluorescent signal) were heat-denaturated (95°C, 10 min) in HiDi Formamide (Applied BioSystems) and submitted to a non-denaturating electrophoresis using the polymer CAP and an ABI 310 genetic analyzer (Life Technologies), as already described[START_REF] Battaglia-Brunet | Precipitation of arsenic sulphide from acidic water in a fixed-film bioreactor[END_REF]. Internal DNA standard (Genescan 600-LYZ, Life Technologies) was used to calibrate the runs. DNA fragments of 200 bp from columns' samples and inoculum clones were run concomitantly in the same CE-SSCP capillary electrophoresis. Matching migration pattern was used to assign a clone to a signal of the community patterns and determine if OTU maintained or not in the column. Fingerprint profiles were aligned and compared with BioNumerics version 7.6 software (Applied Maths).2.2.5 Characterization of the precipitatesBlack pouzzolana and yellow precipitate samples were analyzed using XRD. XRD measurements were performed using a specifically designed anoxic cell with CoKa radiation using a Panalytical X'Pert Pro diffractometer. Samples were grinded and suspended in ethanol within an anaerobic chamber before being deposited on a Si single-crystal low-background sample holder. Data were collected between 5 and 80°2 with a 0.033°2 step, counting 2 hour per sample. The yellow precipitate around pozzolana grains was observed using electron microscopy associated with microanalysis (SEM-EDXS analysis) on a GEMINI ZEISS Ultra55 Field Emission Gun Scanning Electron Microscope operating at 15 kV. Observations and microanalysis were performed using backscattering electron signal and a Bruker QUANTAX Energy dispersive X-ray spectrometer, respectively. For synchrotron based X-ray absorption spectroscopy, the set of As-sulfide references considered in this study is detailed in LePape et al. (2017). Briefly, experimental XAS spectra obtained on the column samples were compared to the ones of amorphous orpiment (am_As2S3), crystalline orpiment (As2S3), and realgar (AsS), minerals that are representative of an S-bound local molecular environment. As(V)-and As(III)-sorbed ferrihydrites were used as reference compounds for O-bound local molecular environment. As K-edge XANES and EXAFS spectra were collected at 15 K (He crysostat) in both transmission and fluorescence mode on the SAMBA beamline (SOLEIL, France) using a Si(220) double-crystal monochromator. Samples were always kept under inert atmosphere to avoid oxidation. The incident energy was calibrated by measuring the LIII-edge of an Au foil recorded in double transmission. Scans were averaged, normalized and background substracted using the Athena software. Linear combination fitting of XANES spectra were performed over the -20 to 60 eV energy range.2.3 Aerobic stepEffluents from the anaerobic bioreactor were treated in an aerobic bioreactor whose design was described inFernandez-Rojo et al. (2017b). Briefly, it was composed of 4 rectangular polyvinyl chloride channels (1 m length × 0.06 m width × 0.06 m depth) equipped with a double envelope for temperature regulation (20 ± 0.8 °C). One channel was used for the present experiment. A canvas was placed on the bottom of the channel to provide a rough surface for the adhesion of the biogenic precipitate. A peristaltic pump (Gilson, Minipuls 3) supplied the channel inlet with AMD at a flow rate that determined the water residence time, here 300 min. A second peristaltic pump was necessary to pump the fluid out of the channel and to maintain the water level at specific height (4 mm). A valve was positioned at the end of outlet tube for sample collection. Prior to the treatment, a "conditioning" step was required to allow the development of an active Fe-oxidizing biofilm. During this step, the aerobic bioreactor was fed with 0.5 mL.min -1 of water S1, corresponding to a residence time (RT) of 324 ± 30 min. Inlet and outlet water was collected at regular time intervals for dissolved Fe(II) and total dissolved Fe determination until steady-state was reached with respect to Fe(II) oxidation. After steady-state achievement (19 days), the channel was successively fed with (1) the anaerobically-treated spring S1 water and (2) the anaerobically-treated spring SSR water. Efficiency of the aerobic step was assessed by monitoring the inlet and outlet water chemistry. Analyzes included measurement of pH, the determination of total concentrations of dissolved Fe(II) using spectrophotometry, and total dissolved Fe, Zn and As using ICP-MS, after 0.2 µm filtration. Arsenic redox speciation was determined using HPLC-ICP-MS. Details of these analytical procedures are reported in[START_REF] Fernandez-Rojo | Biological attenuation of arsenic and iron in a continuous flow bioreactor treating acid mine drainage (AMD)[END_REF].

  Sixteen dissimilatory bisulfite reductase (DsrAB) sequences retrieved from the inoculum formed two related OTU sharing 97.4 % identity on their DsrAB aminoacids sequences. The closely related (85.6 % identity) DsrAB sequence to both OTU belonged to the acidophilic Desulfosporosinus sp. DB isolated from an AMD[START_REF] Karnachuk | Bacteria of the sulfur cycle in the sediments of gold mine tailings, Kuznetsk Basin, Russia[END_REF], and the closest described species were Desulfosporosinus adidiphilus, D. acididurans and D. meridiei with respectively 76.5 %, 75.7 % and 72.3 % identities. These results are in line with those obtained from 16S rRNA gene sequence analyzes, and confirm that sulfate-reducing strains belonging to the Desulfosporosinus genus are present in the sulfate-reducing inoculum enriched from Carnoulès site.The evolution of fingerprints of the bacterial community sampled during time and location in the column are presented in Fig.3. Fingerprints were quite similar at the top, middle and bottom of the column, showing a homogeneous distribution of the bacteria in the bioreactor. At days 288 and 309, the structure of the community has evolved and only two of the peaks detected at day 219 remained largely dominant. Changes in operating conditions, i.e. upflow fed and pH decrease from 3.1 to 2.9, may have favored the corresponding bacteria. The change from spring S1 to SSR site water from day 309 to the end of the monitoring (day 367) did not affect much the structure of the community at the top and bottom location, while more peaks were detected at the middle location. The signal corresponding to the Desulfosporosinus OTU initially dominant in the sulfate-reducing inoculum, which was also present during the previous stage of feeding with synthetic mine water[START_REF] Battaglia-Brunet | Development of a passive bioremediation process based on sulfate-reduction to treat arsenic-containing acidic mine water[END_REF], was one of the dominant throughout the monitoring. Its presence regardless of the condition applied to the column emphasizes its ability to maintain itself under the different conditions applied to the column, in particular a pH of 3 of the feed water. It was also found on the filling material sampled at the end of the monitoring (data not shown), confirming its presence in the biofilm attached on the solid support. No signal corresponding to the Propionibacteraceae bacterium found in the inoculum was evidenced, indicating that its proportion amongst other bacteria represented, if

  acetate. Based on community fingerprints, one of the SRB OTU was among the dominant microorganism in the bioreactor, all along the experiment. Desulfosporosimus-like 16S sequences were already detected in bioreactors treating As-containing acid solutions (Battaglia-Brunet et al., 2012) and Gonzales et al. (2019) observed a SRB affiliated to Desulfosporosinus acididurans becoming dominant in their bioreactor treating a synthetic AMD in continuous mode. Moreover, analysis of microbial communities revealed the widespread presence of

  and not incompletely degraded. Downstream oxidation and precipitation of iron, besides additional As removal, was proven to occur in an aerobic laboratory bioreactor, although not optimized in the present study. Whereas the two treatment steps studied here allowed the removal of 70 to 95% of As, in two different AMD streams, a down-stream lime drain would be necessary in order to increase the final pH of the treated water, and remove the residual As and Fe by co-precipitation. Results support the feasibility of applying simple combination of low-cost treatment options, including semi-passive SRB bioreactor, for the remediation of Asrich AMDs.

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .

 2 Figure 2. Evolution of parameters in the bioreactor fed with springs S1 then SSR mine water.

Figure 3 .

 3 Figure 3. Evolution of 16S rRNA gene CE-SSCP fingerprints at the bottom (B), mid (M) and

Figure 4 .

 4 Figure 4. Analysis of As mineralogy and speciation in yellow deposits that precipitated at the

Figure 5 .

 5 Figure 5. Evolution of S1 (A) and SSR (B) water parameters before treatment, after the

Figure 6 .

 6 Figure 6. Theoretical mass balance for the treatment of spring S1 AMD by a SRB bioreactor

Figure

  Figure SM4-B -X-ray Absorption Near Edge Structure (XANES) experimental spectra and linear combination fits for samples 1, 2, and 3.

Figure

  Figure SM4-D -Extended X-Ray Absorption Fine Structure (EXAFS) presented for the experimental spectra of samples 1, 2, and 3 and for the amorphous orpiment reference mineral.

Table 1 .

 1 Characteristics of the two water samples treated in this studyWater sampleAs mg.L -1 Zn mg.L -1 Fe mg.L -1 SO4 mg.L -1 pH

	Spring S1	174	26.0	1345	3700	3.29
	Spring SSR	18	4.4	307	1500	4.02

Funding This research was financially supported by the French ANR (Agence Nationale de la Recherche) in the frame of IngECOST-DMA project (ANR-13-ECOT-0009).

Availability of data and material

All data are available on request to the corresponding author (e.mail: f.battaglia@brgm.fr)

Declarations

Conflict of Interest The authors declare they have no conflict of interest.

Authors contribution F. Battaglia-Brunet: Conceptualization, Writing, Supervision; L.

Laboratory-scale bio-treatment of real arsenic-rich acid mine drainage

Battaglia-Brunet Fabienne, Casiot Corinne, Fernandez-Rojo Lidia, Hery Marina, Le Pape Pierre, Tris Hafida, Morin Guillaume, Touzé Solène, Joulian Catherine

Supplementary Material SM1. Composition of the basal medium used to enrich sulfate-reducing bacteria

The basal enrichment medium contained the following ingredients, per litre: K2HPO4, 0.5 g ; NH4Cl, 2 g ; Na2SO4, 1.4 g ; MgSO4, 7 H2O, 2 g ; glycerol, 0.5 g ; yeast extract, 1 g ; trace elements solution, 1 ml. The pH of this basal solution was adjusted to 4.

The trace metals solution composition was the following, per litre: EDTA, 3 g ; FeSO4, 7 H2O, 1.1 g ; MnSO4, 65 mg ; ZnSO4, 89 mg ; NiCl2, 24 mg ; Na2MoO4, 2 H2O, 18 mg ; H3BO3, 0.3 g ; CuCl2, 2 mg and CoSO4, 7 H2O, 130 mg.

The basal medium was heated to ebullition, then distributed in 50 mL penicillin flasks equipped with rubber stoppers, flushed with N2, and sterilized by autoclaving 30 min at 120°C.

Supplementary Material SM2. Profiles of As and Zn concentrations

Supplementary Material SM3. Acetate and total organic carbon in the anaerobic bioreactor outlet.


Emna Farjallah

Jean-Marc Armani

Valentin Gherman

Luigi Dilillo

Improvement of the Tolerated Raw Bit Error Rate in NAND Flash-based SSDs with Selective

Keywords: NAND flash, SSD, reliability, adaptability, data retention, bit error rate

A recent large-scale study revealed that the uncorrectable bit error rates in data center solid-sate drives (SSDs) may fall far below the JEDEC standard recommendations. Here, a technique is proposed to improve the tolerated raw bit error rate (RBER) based on the observation that (a) a small SSD ratio may have a much higher RBER than the rest and (b) the RBER is dominated by the retention error rate. Instead of employing stronger but costly error-correcting codes an approach is used to estimate the remaining retention time, i.e., the reliable data storage time, of flash memory pages. This estimation can be performed each time a memory page is read based on the number of detected retention errors and the elapsed time since data was programmed. The fact that the estimated remaining retention time is smaller than a maximum time interval before the next read and check operation is an indication that data needs to be refreshed. It is estimated that the tolerated RBER can be increased by up to 35× over a storage period of 3 years if the stored data are checked on a monthly basis and refreshed only if necessary. The proposed technique has the ability to adapt the average time between refresh operations to the actual RBER. Maximum refresh time reductions of about 12x are reported as compared to systematic refresh schemes.

I. INTRODUCTION

Solid-state drives (SSDs) based on NAND flash memories provide an attractive storage solution as they are faster and less power hungry than traditional hard-disc drives [START_REF] Micheloni | Inside NAND flash memories[END_REF]. Unfortunately, the continuous technology scaling and emergence of flash memories with multilevel cells (MLC) brought not only cost per gigabit reductions but also reliability degradations. For instance, the cumulative number of program/erase (P/E) cycles that can be sustained by a flash memory cell, i.e., the cycling endurance, is decreased by an order of magnitude each time the cell storage capacity is enhanced with an additional bit [START_REF] Chang | Hybrid solid-state disks: combining heterogeneous NAND flash in large SSDs[END_REF] [START_REF] Micheloni | Inside NAND flash memories[END_REF] [START_REF] Sundby | Beyond capacity: storage architecture choices for the modern datacenter[END_REF]. What is more, a recent large-scale study revealed that the uncorrectable bit error rate (UBER) of data center SSDs can significantly exceed the JEDEC standard recommendations [START_REF] Meza | A large-scale study of flash memory failures in the field[END_REF]. The reported UBER values are between 10 -11 and 10 -9 while client and enterprise class SSDs are required to provide an UBER below 10 -15 and 10 -16 , respectively [START_REF] Standard | Solid-state drive (SSD) requirements and endurance test method[END_REF].

An efficient approach to improve UBER is to use stronger error-correcting codes (ECCs). Unfortunately, powerful ECCs come with important storage and latency overheads. For instance, the storage overhead of a BCH code increases almost linearly with the number of correctable errors [START_REF] Fujiwara | Code design for dependable systems: theory and practical applications[END_REF].

The need for strong ECCs may be reduced by containing the raw bit error rate (RBER). Besides technological fixes or solutions based on improved read and write algorithms [START_REF] Bertozzi | Performance and reliability analysis of cross-layer optimizations of NAND flash controllers[END_REF][4] [START_REF] Micheloni | Inside NAND flash memories[END_REF], the RBER can be tempered if the stored data are periodically refreshed [START_REF] Cai | Flash correct-and-refresh: retention-aware error management for increased flash memory lifetime[END_REF][13] [START_REF]TN-12-30: NOR flash cycling endurance and data retention introduction[END_REF] [START_REF] Pan | Quasi-nonvolatile SSD: trading flash memory nonvolatility to improve storage system performance for enterprise applications[END_REF]. A refresh operation can be executed in-place by injecting only the missing amount of charge into the floating gate of the flash memory cells or by relocating the data to a different physical location [START_REF] Cai | Flash correct-and-refresh: retention-aware error management for increased flash memory lifetime[END_REF] [START_REF] Cai | Error analysis and retention-aware error management for nand flash memory[END_REF]. Relocation operations may result in significant P/E cycle overhead especially in the case of read-intensive applications for which the data relocation frequency may become larger than the functional update rate [START_REF] Cai | Flash correct-and-refresh: retention-aware error management for increased flash memory lifetime[END_REF]. A way to reduce this overhead is to adapt the relocation rate to the number of P/E cycles endured by each flash memory block [START_REF] Cai | Flash correct-and-refresh: retention-aware error management for increased flash memory lifetime[END_REF] [START_REF] Cai | Error analysis and retention-aware error management for nand flash memory[END_REF].

Existent refresh schemes are based on worst-case scenarios, oblivious to intra-and inter-device variations, which may lead to unnecessary overheads with respect to response latency, dissipated power and P/E cycles. For example, the large-scale study reported in [START_REF] Meza | A large-scale study of flash memory failures in the field[END_REF] unveiled that only a small number of SSDs may contribute to the overall UBER degradation.

This work proposes an approach to avoid the utilization of strong ECCs or worst-case refresh frequencies for dealing with a whole population of NAND flash memories or SSDs that may contain some error-prone units. The idea is to exploit the fact that the retention error rate dominates the RBER in NAND flash memories [START_REF] Cai | Error analysis and retention-aware error management for nand flash memory[END_REF] and take advantage of flash read operations to estimate the remaining reliable retention time for each memory page. Such an estimation can be done based on the detected number of retention errors and the retention age, i.e., the elapsed time since data was programmed. A valid memory page needs to be refreshed only when its estimated remaining retention time is smaller than the time left to the next read and check operation. Such a technique is effective when a maximum time interval is imposed between consecutive read and check operations of any memory page. For example, the tolerated RBER can be increased by up to 35× over a storage period of 3 years if one makes sure that the stored data are checked at least once in a month. The resulting data refresh frequency is not necessarily correlated with the data check frequency since it depends on the actual RBER. It is shown that the refresh probability is negligible at RBERs that can be managed by the available ECC alone and starts to increase only at larger RBERs. Compared to systematic refresh schemes able to ensure the same protection level, flash refresh time reductions of about 12× have been simulated.

The solution proposed here is orthogonal to other techniques used to reduce the number of retention errors based on the utilization of read reference voltages which are aware of (a) the data retention age [START_REF] Cai | Data retention in MLC NAND flash memory: characterization, optimization, and recovery[END_REF] or (b) the number of bits vulnerable to retention errors [START_REF] Lee | A 32Gb MLC NAND-flash memory with Vth-enduranceenhancing schemes in 32nm CMOS[END_REF].

Types of storage errors that may affect NAND flash memories are analyzed in Section II. The proposed refresh scheme based on the estimation of the remaining retention time of flash memory pages is presented in Section III. A method to reduce the number of check operations is proposed in Section IV. Simulation results concerning the improvement of the tolerated RBER and the reduction of the refresh frequency are reported in Section V. Concluding remarks are drawn in Section VI.

II. TYPICAL STORAGE ERRORS IN NAND FLASH MEMORIES

A flash memory cell consists of a MOS transistor with a supplementary floating gate or a charge trap layer embedded in the dielectric between channel and control gate. Data are programmed via the injection/erasure of electric charge into/from the floating gate or the charge trap layer. The threshold voltage distribution created by the injected charge into the floating gate of an MLC flash memory is illustrated in Fig. 1 [START_REF] Micheloni | Inside NAND flash memories[END_REF]. In a NAND flash memory, between 32 and 64 memory cells are connected together to form a string. Thousands of strings are assembled in a storage array called block and few thousands of blocks may be contained in a flash memory chip. In a block, memory cells on the same string are accessed with the help of different word lines. The bits stored in memory cells accessed by the same word line are logically grouped into one or several pages.

A NAND flash memory can be affected by different types of storage errors like retention errors, write errors, also called program-interference or over-programming errors, readdisturb errors and erase errors. Retention errors affect the ability of a memory to keep the stored information over a required period of time. As shown in Fig. 2, retention errors appear due to a drift to the left of the threshold voltage distribution and the resulting crossing of the reference values used during read operations. For retention ages larger than one month, the retention error rate largely dominates the other error rates [START_REF] Cai | Error analysis and retention-aware error management for nand flash memory[END_REF].

The remaining error types are characterised by a drift to the right of the threshold voltage distribution. Write errors are induced by parasitic capacitance-coupling affecting memory cells on a certain word line subsequent to a program operation on a neighbour word line. Once a memory block is fully programmed, the number of write errors does not increase with the retention age. In NAND flash memories, the write errors have the second largest occurrence rate [START_REF] Cai | Error analysis and retention-aware error management for nand flash memory[END_REF].

Erase errors are the consequence of an erase operation that fails to reset all cells in a memory block to the erased state [START_REF] Cai | Error analysis and retention-aware error management for nand flash memory[END_REF]. Upon the occurrence of an erase error an entire block may be marked as bad and discarded [START_REF] Micheloni | Inside NAND flash memories[END_REF].

A read-disturb error occurs when the content of a memory cell is corrupted due to repeated read operations of cells on the same string. In the following, read-disturb errors will be neglected due to their very small occurrence rate [START_REF] Cai | Error analysis and retention-aware error management for nand flash memory[END_REF].

Retention errors will be considered as the only storage errors whose rate may increase with the retention age once a memory bloc has been programmed. It will be assumed that the retention RBER (𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 ), i.e., the probability that a vulnerable bit is affected by a retention error, is given by the following expression:

𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 (𝑡 𝐴𝐺𝐸 ) = 1 -𝑒 -𝜆𝑡 𝐴𝐺𝐸 (1)
where 𝑡 𝐴𝐺𝐸 is the retention age. The parameter 𝜆 is called failure rate and may vary from one SSD or flash memory to another [12][15], between the pages of the same memory block [START_REF] Cai | Error analysis and retention-aware error management for nand flash memory[END_REF] and with the number of P/E cycles endured by a memory block [2][3]. This law is in agreement with reported results [START_REF] Mielke | Bit error rate in NAND flash memories[END_REF] and our own experience. The law also has the properties of a cumulative distribution function, i.e., 𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 (0) = 0 and 𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 (∞) = 1.

Retention errors can be easily distinguished from other error types. Typically, each read operation is followed by an error correction step during which the erroneous bits are identified with the help of an ECC. The error-correcting process allows to infer the polarity of each error, i.e., the difference between the corrected and the initial values of the erroneous bit. The error polarity allows to identify the error type if one assumes that errors can only result from threshold voltage transitions between neighbouring states. V th "11" "10" "00" "01"

V REF1 V REF2 V REF3
Erased state Table I gives the retention error fingerprints for the MLC considered in Fig. 2. For flash memories with 1 bit per cell (SLC), the retention error fingerprint is given by the first line in Table I.

Programmed states

Bits in the same cell

Read value

Corrected value

Value of the other bit

First bit 1 0 -Second bit 1 0 1

Second bit 0 1 0

III. SELECTIVE REFRESH BASED ON A LINEAR APPROXIMATION OF THE RETENTION RBER

Here, an approach is proposed to deal with retention RBER variations in NAND flash memories beyond the error protection provided by an ECC. The main idea is to take advantage of read operations of any valid flash memory page to estimate its left retention time 𝑡 𝐿𝐸𝐹𝑇 i.e. the storage time before the UBER target is exceeded [START_REF] Standard | Solid-state drive (SSD) requirements and endurance test method[END_REF]. Assuming a maximum time period 𝑇 𝐶𝐻𝐸𝐶𝐾 between two consecutive read operations of any page, the read data has to be relocated or refreshed if 𝑡 𝐿𝐸𝐹𝑇 is smaller than 𝑇 𝐶𝐻𝐸𝐶𝐾 .

The proposed 𝑡 𝐿𝐸𝐹𝑇 estimation is based on the observation that (1) can be approximated by the linear relation (2) since, in concrete situations, the product 𝜆𝑡 𝐴𝐺𝐸 is much smaller than 1. For instance, if one considers an RBER equal to 10 -3 , which is already a very large value, 𝜆𝑡 𝐴𝐺𝐸 is equal to 10 -3 with a difference of about 510 -7 between ( 1) and ( 2). Smaller and more realistic RBER values correspond to smaller 𝜆𝑡 𝐴𝐺𝐸 values and the relative error induced by (2) becomes much smaller.

𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 (𝑡 𝐴𝐺𝐸 ) ≅ 𝜆𝑡 𝐴𝐺𝐸 (2)
Taking into account that RBER represents the number of retention errors divided by the number of vulnerable bits and neglecting the statistical variations that may affect the number of retention errors, one obtains:

𝑀-𝑛 ¬𝑅𝐸𝑇 𝑛 𝑅𝐸𝑇 = 𝑡 𝐴𝐺𝐸 +𝑡 𝐿𝐸𝐹𝑇 𝑡 𝐴𝐺𝐸 (3)
where:

• 𝑛 𝑅𝐸𝑇 represents the number of retention errors at the retention age 𝑡 𝐴𝐺𝐸 .

• 𝑛 𝑅𝐸𝑇 stands for the number of non-retention errors that may appear during the programming of the block where the considered memory page is stored,

• M is an a priori known parameter and refers to the maximum number of errors that can be corrected with the available ECC,

• 𝑀 -𝑛 𝑅𝐸𝑇 stands for the maximum number of retention errors that can be corrected in the considered memory page.

Based on (3), 𝑡 𝐿𝐸𝐹𝑇 can be estimated as follows:

𝑡 𝐿𝐸𝐹𝑇 = 𝛼 𝐷𝐴𝑀𝑃 𝑡 𝐴𝐺𝐸 ( 𝑀-𝑛 ¬𝑅𝐸𝑇 𝑛 𝑅𝐸𝑇 -1) (4)
where the damp factor 𝛼 𝐷𝐴𝑀𝑃 is used to take into account statistical variations that may affect the number of retention errors. Here, 𝛼 𝐷𝐴𝑀𝑃 values between 0.005 and 0.1 are used. In the absence of retention errors, i.e., 𝑛 𝑅𝐸𝑇 = 0, 𝑡 𝐿𝐸𝐹𝑇 is considered to be equal to the target retention time.

Neither the parameter 𝜆 nor the number of bits vulnerable to retention errors in the considered page does come out in the final expression and they do not need to be estimated in order to get 𝑡 𝐿𝐸𝐹𝑇 .

V th "11" "10" "00" "01"

V REF1 V REF2 V REF3

Erased state

Programmed states (a)

V th "11" "10" "00" "01"

V REF1 V REF2 V REF3 Erased state Programmed states (b)
V th "11" "10" "00" "01"

V REF1 V REF2 V REF3 Erased state Programmed states (c)
The variables 𝑛 𝑅𝐸𝑇 and 𝑛 𝑅𝐸𝑇 can be calculated with the help of the ECC decoder. For example, the decoding scheme of a BCH ECC is usually concluded by the execution of a socalled Chien algorithm that checks each bit position for a potential error [START_REF] Fujiwara | Code design for dependable systems: theory and practical applications[END_REF]. When an error location is found, a simple verification of the conditions in Table I allows to identify a retention or non-retention error. Two specially devoted counters can be used to keep track of 𝑛 𝑅𝐸𝑇 and 𝑛 𝑅𝐸𝑇 .

The retention age 𝑡 𝐴𝐺𝐸 can be calculated as the difference between a timestamp associated to the page being accessed and the current state of the timer used to provide timestamps [START_REF] Carlo | FLARES: an aging aware algorithm to autonomously adapt the error correction capability in NAND flash memories[END_REF]. A single timestamp may be used to characterize the programing time of all pages in a flash memory block [START_REF] Seif | Refresh frequency reduction of data stored in SSDs based on A-timer and timestamps[END_REF]. The resulting storage overhead of the timestamp table is significantly smaller than in the case of other metadata structures such as the remapping table of the flash translation layer [START_REF] Seif | Refresh frequency reduction of data stored in SSDs based on A-timer and timestamps[END_REF].

The necessary check operations that should follow a page read operation are formalized in Algorithm 1 described below. A maximum time interval 𝑇 𝐶𝐻𝐸𝐶𝐾 between consecutive check operations can be imposed via periodic scrubbing [START_REF] Mukherjee | Cache scrubbing in microprocessors: myth or necessity?[END_REF]. As it will be shown later, the tolerated RBER can be significantly improved when 𝑇 𝐶𝐻𝐸𝐶𝐾 is equal to one or a few months. The remaining retention time 𝑡 𝐿𝐸𝐹𝑇 can be computed online or off-line for all possible 𝑛 𝑅𝐸𝑇 and 𝑛 𝑅𝐸𝑇 combinations. In the latter case, the storage overhead can be reduced by observing that 𝑡 𝐿𝐸𝐹𝑇 decreases with 𝑛 𝑅𝐸𝑇 and one only needs to store the largest 𝑛 𝑅𝐸𝑇 value with 𝑡 𝐿𝐸𝐹𝑇 larger than 𝑇 𝐶𝐻𝐸𝐶𝐾 . In such a case, the line 3 in Algorithm 1 may be implemented as the comparison between the maximum tolerated 𝑛 𝑅𝐸𝑇 and the measured 𝑛 𝑅𝐸𝑇 . The cost of storing the maximum tolerated 𝑛 𝑅𝐸𝑇 does not depend on the storage capacity of the protected SSD or flash memory system. This cost increases proportionally with 1/𝑇 𝐶𝐻𝐸𝐶𝐾 and with the maximum number of errors that can be corrected by the available ECC. For example, this cost amounts to a few hundred bits with an ECC able to correct up to 10 errors per page and 𝑇 𝐶𝐻𝐸𝐶𝐾 equal to 1 month. Refresh operations have a negative impact on the average response time of a flash memory system or SSD. It has been reported that this impact can be reduced by increasing the refresh interruption granularity [START_REF] Pan | Quasi-nonvolatile SSD: trading flash memory nonvolatility to improve storage system performance for enterprise applications[END_REF]. The performance overhead of the proposed refresh scheme is expected to be lower since not all check operations have to be followed by a refresh operation. Furthermore, a method to decrease the number of check operations is proposed in the following section.

IV. REDUCTION OF THE NUMBER OF CHECK OPERATIONS

Check operations as described in Algorithm 1 can be imposed periodically via warnings triggered by a conventional or temperature aware timer [START_REF] Seif | Refresh frequency reduction of data stored in SSDs based on A-timer and timestamps[END_REF]. Since such checks can also be associated to functional read operations, frequently accessed pages may be skipped during the periodical checks triggered by the timer.

This can be achieved with the help of one flag bit per flash memory page that indicates whether the page has already been checked. The page flag is set to 0 each time a page is read, programmed or refreshed as illustrated in Fig. 3. After the first subsequent warning, the page does not need to be checked, only its flag is set to 1. After a second warning, the page has to be checked and its flag set to 0 only if the page is still valid and if no functional read operation occurred between the first and second warnings. Otherwise, only the page flag will be set to 1. Invalid pages can be neglected and the warnings need to be triggered with a period 𝑇 𝑊𝐴𝑅𝑁𝐼𝑁𝐺 which is equal to 𝑇 𝐶𝐻𝐸𝐶𝐾 /2.

In order to improve performance with the proposed method, the page flags have to be kept in the RAM memory of the SSD controller and not in the relatively slower flash memory. This method has no storage overhead since the page flags do not need to be stored but only initialized to 1 at system start-up.

V. SIMULATION RESULTS

In order to assess the effectiveness of the proposed approach, we first evaluated the increase of the tolerated 𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 with respect to the case when the stored data is not refreshed. We considered data characterized by a small functional update frequency and, implicitly, very large retention

Periodic warnings

Time

Program or refresh T CHECK =2T WARNING

Functional read and check

Read and check T WARNING

Read and check

F PAGE =0 F PAGE =1 F PAGE =0 F PAGE =1 F PAGE =0 F PAGE =1
age 𝑡 𝐴𝐺𝐸 . Such data may contain user files, executable files and operating system files.

The obtained results are reported in Table II for different numbers of correctable errors per page. The tolerated 𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 values are compliant with the requirement to keep UBER below 10 -16 [START_REF] Standard | Solid-state drive (SSD) requirements and endurance test method[END_REF]. UBER calculation details are given in Annex I and Annex II. It should be noted that UBER is a bitlevel observable that only depends on 𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 , page size, ECC strength, refresh frequency and numbers of non-retention errors and bits vulnerable to retention errors in a page. The impact of the page size is not investigated since it affects UBER only as a scaling factor. Only 2KB pages have been considered in the most unfavourable case when all bits are vulnerable to retention errors.

As illustrated in Table II, the tolerated 𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 is increased by the reduction of 𝑇 𝐶𝐻𝐸𝐶𝐾 , i.e., the maximum time interval between two successive check operations of flash memory pages. When 𝑇 𝐶𝐻𝐸𝐶𝐾 is equal to 1 month, the obtained improvement factors are between 32× and 35×. Better results should be expected for lower 𝑇 𝐶𝐻𝐸𝐶𝐾 values. Moreover, the maximum tolerated 𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 values and resulting improvement factors are pessimistic as check operations triggered by functional read operations are not taken into account.

A 𝑇 𝐶𝐻𝐸𝐶𝐾 equal to 1 month may have a larger impact on the tolerated 𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 than a multiplication by four of the number of correctable errors. This can be observed by comparing the 1 month column for 10 correctable errors with the no check column for 40 correctable errors. A 𝑇 𝐶𝐻𝐸𝐶𝐾 value equal to 6 months may provide a larger improvement of the tolerated 𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 than a duplication of the number of correctable errors. This can be verified by comparing the 6 months column for 20 correctable errors with the no check column for 40 correctable errors. For BCH codes, the increase of the number of errors from 20 to 40 may augment the storage overhead by 75%. This overhead may become 230% when the number of correctable errors is changed from 10 to 40.

The results reported here can only be expected for systems with downtimes much shorter than the imposed check period 𝑇 𝐶𝐻𝐸𝐶𝐾 . This is true for enterprise class SSDs with limited outage periods, i.e., maximum few hours per year [START_REF] Sundby | Beyond capacity: storage architecture choices for the modern datacenter[END_REF]. When longer outage periods are expected, one has to consider the maximum downtime 𝑇 𝑃𝑂𝑊𝐸𝑅-𝑂𝐹𝐹 and modify the if condition in Algorithm 1 such that a data refresh operation is initiated if 𝑡 𝐿𝐸𝐹𝑇 < 𝑇 𝐶𝐻𝐸𝐶𝐾 + 𝑇 𝑃𝑂𝑊𝐸𝑅-𝑂𝐹𝐹 . In such a case, the benefit brought by the proposed approach can be calculated by considering an imposed check period equal to 𝑇 𝐶𝐻𝐸𝐶𝐾 + 𝑇 𝑃𝑂𝑊𝐸𝑅-𝑂𝐹𝐹 . For instance, both 𝑇 𝐶𝐻𝐸𝐶𝐾 and 𝑇 𝑃𝑂𝑊𝐸𝑅-𝑂𝐹𝐹 are 1 month, the improvements obtained with our approach are given by the 2 months column in Table II. The case when 𝑇 𝑃𝑂𝑊𝐸𝑅-𝑂𝐹𝐹 is equal to 3 months corresponds to a JEDEC requirement for enterprise class SSDs [START_REF] Standard | Solid-state drive (SSD) requirements and endurance test method[END_REF]. In Table II, the 4 months column gives worst-case improvement factors larger than 8× for JEDEC compliant enterprise class SSDs in which data are checked every month.

The reported improvements of the tolerated 𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 require a number of refresh operations that may be greatly reduced as compared to a conventional scheme with systematic refresh operations [2][3]. As illustrated in Fig. 4, when the check period is 1 month, the average time between refresh operations may be significantly improved as compared to the case when the data are systematically refreshed, not to speak of the difficulty to infer an ideal refresh period at run-time for a scheme with systematic refresh operations.

A larger average time between refresh operations enables a reduction of the time during which the flash chips are accessed for refresh operations. Compared to a systematic refresh scheme with fixed refresh frequency, the reduction of the time spent for refresh-triggered read and write operations can be expressed as follows: where:

• 𝑇 𝑅𝐸𝐹𝑅𝐸𝑆𝐻 and 𝑇 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 represent the overall times spent for refresh-triggered read and write operations with the proposed and systematic refresh schemes, Fig. 4 Average time between refresh operations with the proposed scheme and an ideal systematic refresh scheme with the refresh frequency adapted to the actual RBER. We considered flash memory pages with 2KB bits and up to 40 correctable errors. Each colored curve stops at the maximum retention RBER that can be tolerated.

• 𝜏 𝑊𝑅 and 𝜏 𝑅𝐷 stand for the latencies of page write and read operations,

• 𝑓 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 and 𝐷 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 represent the fixed refresh frequency and the amount of data that needs to be systematically refreshed with a conventional refresh scheme,

• 𝑓 𝐶𝐻𝐸𝐶𝐾 and 𝑓 𝑅𝐸𝐹𝑅𝐸𝑆𝐻 are the check frequency and the average refresh frequency of the proposed refresh scheme,

• 𝐷 𝐶𝐻𝐸𝐶𝐾 and 𝐷 𝑅𝐸𝐹𝑅𝐸𝑆𝐻 represent the amounts of data that are checked and refreshed with the proposed scheme.

With the method proposed in Section IV to reduce the amount of checked data, 𝐷 𝐶𝐻𝐸𝐶𝐾 will include all data with a retention age larger than 𝑇 𝑊𝐴𝑅𝑁𝐼𝑁𝐺 in Fig. 3. The same is true for 𝐷 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 when the method illustrated in Fig. 3 is adapted to implement a systematic refresh scheme [START_REF] Gherman | Improvement of the Tolerated Raw Bit Error Rate in NAND Flashbased SSDs with the Help of Embedded Statistics[END_REF]. In our experiments, 𝛼 𝐷𝐴𝑀𝑃 in ( 4) is selected such that the maximum tolerable UBER is reached at an 𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 for which the average retention time is equal to 𝑇 𝐶𝐻𝐸𝐶𝐾 = 1/𝑓 𝐶𝐻𝐸𝐶𝐾 . Since the average retention time can be expressed as1/𝑓 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 , 𝑓 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 and 𝑓 𝐶𝐻𝐸𝐶𝐾 are equal. As a consequence, 𝐷 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 and 𝐷 𝐶𝐻𝐸𝐶𝐾 will be equal as well. Since 𝐷 𝑅𝐸𝐹𝑅𝐸𝑆𝐻 is smaller or equal to 𝐷 𝐶𝐻𝐸𝐶𝐾 , a lower bound for the reduction of the time spent for refresh-triggered read and write operations can be defined as follows: Maximum reductions of about 12× are obtained for retention RBER values that actually do not require refresh operations. For flash memory and SSD populations where only a small number of units are error-prone [START_REF] Meza | A large-scale study of flash memory failures in the field[END_REF], the average reduction of the time spent for refresh-triggered read and write operations is expected to approach the maximum reduction values near the vertical dashed lines in figures 5 to 8. Even better results Fig. 5 Reduction of the overall time spent for refresh-triggered read and write operations compared to a systematic scheme with fixed refresh frequency. Each curve stops at the maximum tolerated retention RBER. The considered parameters are the same as those used in Fig. 4. can be obtained for larger 𝜏 𝑊𝑅 /𝜏 𝑅𝐷 ratios.

When up to 10 errors per page can be corrected, the reductions of the time spent for refresh operations are smaller and the curve shapes are different as illustrated in Fig. 8. This is due to the fact that in this case refresh operations are avoided only in the absence of retention errors. This is also the reason for the slightly smaller improvement factors reported in Table II.

Here, the impact of ECC encoding and decoding on refresh latency is not explicitly considered as these steps can be performed in parallel to flash chip operations. For BCH codes and other linear block ECCs the encoding latency is relatively small. Moreover, during triggered check operations the ECC decoding process does not need to be completed if the number of detected errors does not require a refresh operation. For example in the case of a BCH, the number of errors is calculated before the relatively long error correction step [START_REF] Fujiwara | Code design for dependable systems: theory and practical applications[END_REF]. This means that the ECC decoding latency is relatively small when the number of errors and the refresh probability are low. Particularly, the absence of errors can be rapidly detected by checking whether the generated syndrome is an all-zero vector.

The discussed refresh schemes may also trigger erase operations when data refresh is based on data relocations. One can estimate that the number of erase operations is proportional to the amount of data that needs to be refreshed and, implicitly, relocated. In this case, the reduction of the number of refresh-triggered erase operations can be expressed as shown below: where 𝐸 𝑅𝐸𝐹𝑅𝐸𝑆𝐻 and 𝐸 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 represent the numbers of refresh-triggered erase operations with the proposed and systematic refresh schemes.

As long as 𝑓 𝑅𝐸𝐹𝑅𝐸𝑆𝐻 is smaller than 𝑓 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 , 𝐷 𝑅𝐸𝐹𝑅𝐸𝑆𝐻 is also smaller or equal to 𝐷 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 and a lower bound for the reduction of the number of refresh-triggered erase operations can be defined as follows:

𝐸 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 𝐸 𝑅𝐸𝐹𝑅𝐸𝑆𝐻 ≥ 𝑓 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 𝑓 𝑅𝐸𝐹𝑅𝐸𝑆𝐻 (6)
Estimations of the lower bound used in [START_REF] Carlo | FLARES: an aging aware algorithm to autonomously adapt the error correction capability in NAND flash memories[END_REF] are illustrated in figures 9 to 12. As with the read and write operations, maximum reductions of the number of refresh-triggered erase operations, i.e. larger than 30×, are obtained for retention RBER values that actually do not require refresh operations. At such RBER values, one could expect that the reduction would become very high or reach infinity. This is not the case as retention errors may still occur and trigger refresh operations even with the proposed method. The reductions could be improved by increasing the value of 𝛼 𝐷𝐴𝑀𝑃 in (4) at the cost of a smaller tolerated retention RBER.

The number of refresh-triggered erase operations and, implicitly, the time required for the execution of such operations Fig. 9 Reduction of the number of refresh-triggered erase operations compared to a systematic scheme with fixed refresh frequency.

Each curve stops at the maximum tolerated RBER. The considered parameters are the same as those used in Fig. 5. is reduced to a larger extent than the time spent for refreshtriggered read and write operations. This means that the figures reported for the reduction of the read and write operations can be used as a lower bound for the reduction of the time spent for all three types of refresh-triggered operations.

VI. CONCLUSIONS

An approach was proposed to improve the tolerated raw bit error rate (RBER) in NAND flash-based SSDs via an estimation of the remaining retention time. This estimation can be performed each time a flash memory page is read and relies on the number of detected retention errors and the calculated retention age, i.e., the elapsed time since data was programmed. The checked data should be refreshed if the estimated remaining retention time is smaller than a maximum time period to the next read operation. Improvement factors of the tolerated retention error rate between 32× and 35× have been simulated for data checked on a monthly basis over a storage period of 3 years. Such an improvement may be larger than what can be obtained by using an ECC able to correct 4 more errors. Even for a check period of 6 months the tolerated RBER improvement can be larger than when the ECC strength is doubled. The proposed method has the ability to adapt the average time between refresh operations to the actual retention RBER. This enabled maximum refresh time reductions of about 12× as compared to systematic refresh schemes.

ANNEX I

In the absence of refresh operations, the uncorrectable bit error rate (UBER) of a flash memory page can be computed with the expression below based on the assumption that only retention errors may accumulate in time [START_REF] Mielke | Bit error rate in NAND flash memories[END_REF]. where:

• 𝑡 𝐴𝐺𝐸 represents the storage period,

• N is the total number of bits in a flash memory page,

• M is the maximum number of errors that can be corrected with the available ECC,

• 𝑁 𝑉𝑈𝐿 is the actual number of bits vulnerable to retention errors in the considered flash memory page,

• 𝑛 𝑅𝐸𝑇 and 𝑛 𝑅𝐸𝑇 are the numbers of bits affected by retention and non-retention errors in the considered flash memory page,

• 𝑀 -𝑛 𝑅𝐸𝑇 represents the maximum number of retention errors that can be corrected with the available ECC in the considered flash memory page,

• 𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 (𝑡 𝐴𝐺𝐸 ) is calculated according to (1).

ANNEX II

For flash memories with pages that are periodically checked and may be refreshed according to Algorithm 1, UBER can be obtained by adding the probabilities of the uncorrectable errors that may occur in a flash memory page between consecutive check operations as follows:

𝑈𝐵𝐸𝑅 = 1 𝑁 ∑ 𝑈𝐵𝐸𝑅(𝑖) ⌈ 𝑇 𝑀𝐴𝑋 𝑇 𝐶𝐻𝐸𝐶𝐾 ⌉ 𝑖=1
where:

• N is the total number of bits in a flash memory page,

• 𝑇 𝑀𝐴𝑋 is the maximum required retention time,

• 𝑇 𝐶𝐻𝐸𝐶𝐾 is the time interval between consecutive triggered check operations,

• 𝑈𝐵𝐸𝑅(𝑖) represents the contribution to UBER of the uncorrectable errors that may occur during the time interval between the (i-1) th and i th triggered check operations,

•  stands for the ceiling function.

UBER(i) can be calculated with the relation below that takes into account the occurrence probabilities of all retention error numbers which do not impose a page refresh according to Algorithm 1 during the (i-1) th check operation and (b) the probability that during the i th triggered check operation the errors cannot be corrected anymore:

where:

• 𝑃((𝑖 -1) * 𝑇 𝐶𝐻𝐸𝐶𝐾 , 𝑁 𝑉𝑈𝐿 , 𝑛 𝑅𝐸𝑇 ) is the occurrence probability of 𝑛 𝑅𝐸𝑇 retention errors that do not impose a page refresh according to Algorithm 1 during the (i-1) th check operation,

• 𝑛 𝑖-1 is the maximum number of retention errors for which the if condition in Algorithm 1 is false and no refresh operation needs to executed during the (i-1) th check operation,

• 𝑃(𝑇 𝐶𝐻𝐸𝐶𝐾 , 𝑁 𝑉𝑈𝐿 -𝑛 𝑅𝐸𝑇 , 𝑛′ 𝑅𝐸𝑇 ) is the occurrence probability of 𝑛′ retention errors that can still be handled by the available ECC during the i th check operation,

• M is the maximum number of errors that can be corrected by the available ECC,

• 𝑁 𝑉𝑈𝐿 is the actual number of bits vulnerable to retention errors in the considered flash memory page,

• 𝑛 𝑅𝐸𝑇 is the number of non-retention errors in the considered flash memory page,

• 𝑛 𝑅𝐸𝑇 and 𝑛′ 𝑅𝐸𝑇 are numbers of retention errors that can be tolerated in the considered flash memory page.

The probability to have 𝑛 𝑅𝐸𝑇 retention errors in a flash memory page with 𝑁 𝑉𝑈𝐿 vulnerable bits after a storage period 𝑖 * 𝑇 𝐶𝐻𝐸𝐶𝐾 can be calculated recursively as follows: where:

• each term represents the probability of a possible repartition of 𝑛 𝑅𝐸𝑇 retention errors over the time period before the (i-1) th check operation and the time interval between the (i-1) th and i th check operations,

• as in [START_REF] Fujiwara | Code design for dependable systems: theory and practical applications[END_REF], 𝑛 𝑖-1 indicates that not all error occurrence scenarios are possible due to a refresh operation that may be triggered during the execution of the (i-1) th check operation,

• for 𝑖 = 1, one can use the expression below:

𝑃(𝑇 𝐶𝐻𝐸𝐶𝐾 , 𝑁 𝑉𝑈𝐿 , 𝑛 𝑅𝐸𝑇 ) = ( 𝑁 𝑉𝑈𝐿 𝑛 𝑅𝐸𝑇 ) (𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 (𝑇 𝐶𝐻𝐸𝐶𝐾 ))

𝑛 𝑅𝐸𝑇 × (1 -𝑅𝐵𝐸𝑅 𝑅𝐸𝑇 (𝑇 𝐶𝐻𝐸𝐶𝐾 ))

𝑁 𝑉𝑈𝐿 -𝑛 𝑅𝐸𝑇

Fig. 1

 1 Fig. 1 Threshold voltage distribution and example of logical state encoding for a 2-bit MLC flash memory.

Fig. 2

 2 Fig. 2 Threshold voltage distribution of the logical states in a 2-bit MLC flash memory affected by (a) retention errors, (b) erase errors and (c) write and read-disturb errors.

Algorithm 1 :

 1 Optimization of flash page refresh based on linear approximation of RBERRET Require: Read data from a flash memory page that has been decoded and corrected with the help of an ECC with known error correction strength Require: nRET, the number of already existing retention errors Require: nRET, the number of already existing non-retention errors Require: TCHECK, the maximum time interval between consecutive check operations 1 Calculate the retention age tAGE of the accessed page 2 Get the remaining retention time tLEFT as a function of tAGE, nRET and nRET such that the UBER target is still preserved 3 if tLEFT < TCHECK then 4 Refresh the considered page 5 end

Fig. 3

 3 Fig. 3 Management of page flags 𝐹 𝑃𝐴𝐺𝐸 used to reduce the number of page read and checks as decribed in Algorithm 1.

  +𝜏 𝑅𝐷 ) 𝐷 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 𝑓 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 𝜏 𝑅𝐷 𝐷 𝐶𝐻𝐸𝐶𝐾 𝑓 𝐶𝐻𝐸𝐶𝐾 +𝜏 𝑊𝑅 𝐷 𝑅𝐸𝐹𝑅𝐸𝑆𝐻 𝑓 𝑅𝐸𝐹𝑅𝐸𝑆𝐻

  +𝜏 𝑅𝐷 ) 𝑓 𝑆𝑌𝑆_𝑅𝐸𝐹𝑅𝐸𝑆𝐻 𝜏 𝑊𝑅 𝑓 𝑅𝐸𝐹𝑅𝐸𝑆𝐻 +𝜏 𝑅𝐷 𝑓 𝐶𝐻𝐸𝐶𝐾

Figures 5

 5 Figures 5 to 8 illustrate estimations of the lower bound used in (5) for MLC NAND flash chips with average write and read latencies equal to 975𝜇𝑠 and 50𝜇𝑠 [10], respectively.Maximum reductions of about 12× are obtained for retention RBER values that actually do not require refresh operations. For flash memory and SSD populations where only a small number of units are error-prone[START_REF] Meza | A large-scale study of flash memory failures in the field[END_REF], the average reduction of the time spent for refresh-triggered read and write operations is expected to approach the maximum reduction values near the vertical dashed lines in figures 5 to 8. Even better results

Fig. 6

 6 Fig. 6 Similar to Fig. 5 but for an ECC able to correct up to 30 errors per flash memory page.

Fig. 7

 7 Fig. 7 Similar to Fig. 5 but for an ECC able to correct up to 20 errors per flash memory page.

Fig. 8

 8 Fig. 8 Similar to Fig. 5 but for an ECC able to correct up to 10 errors per flash memory page.

Fig. 10

 10 Fig. 10 Similar to Fig. 9 but for an ECC able to correct up to 30 errors per flash memory page.

Fig. 11

 11 Fig. 11 Similar to Fig. 9 but for an ECC able to correct up to 20 errors per flash memory page.

Fig. 12

 12 Fig. 12 Similar to Fig. 9 but for an ECC able to correct up to 10 errors per flash memory page.

  𝑈𝐵𝐸𝑅(𝑖) = ∑ 𝑃((𝑖 -1) * 𝑇 𝐶𝐻𝐸𝐶𝐾 , 𝑁 𝑉𝑈𝐿 , 𝑛 𝑅𝐸𝑇 ) 𝐶𝐻𝐸𝐶𝐾 , 𝑁 𝑉𝑈𝐿 -𝑛 𝑅𝐸𝑇 , 𝑛 ′ 𝑅𝐸𝑇 ) 𝑀-𝑛 𝑅𝐸𝑇 -𝑛 𝑅𝐸𝑇 𝑛 ′ 𝑅𝐸𝑇 =0 ]

TABLE I .

 I RETENTION ERROR FINGERPRINTS FOR THE MLC FLASH MEMORY CELL CONSIDERED IN FIG. 2.

TABLE II .

 II IMPROVEMENT OF THE MAXIMUM RETENTION RBERTHAT CAN BE TOLERATED IN A 2KB FLASH MEMORY PAGE. THE REPORTED RBER FIGURES CORRESPOND TO A TARGET RETENTION TIME OF 36 MONTHS. IT IS CONSIDERED THAT ALL BITS IN A PAGE ARE VULNERABLE TO RETENTION ERRORS AND THAT THERE ARE 0 NON-RETENTION ERRORS.

	Number of
	correctable
	errors
	per page

Maximum tolerated RBERRET with UBER ≤ 10 -16 Improvement factor with respect to no refresh

			check period (𝑻 𝑪𝑯𝑬𝑪𝑲 )			check period (𝑻 𝑪𝑯𝑬𝑪𝑲 )
		no check	6 months 4 months	3 months	2 months	1 month	6 months 4 months 3 months	2 months	1 month
	10	2.6410 -5 1.4410 -4 2.1410 -4 2.8510 -4 4.2610 -4	8.5210 -4	5.5	8.1	10.8	16.1	32.3
	20	1.6510 -4 9.6210 -4 1.4210 -3 1.8910 -3 2.8310 -3	5.6510 -3	5.8	8.6	11.5	17.2	34.2
	30	3.8410 -4 2.2110 -3 3.3210 -3 4.4210 -3 6.6310 -3	1.3210 -2	5.8	8.6	11.5	17.3	34.4
	40	6.5610 -4 3.8910 -3 5.8210 -3 7.7610 -3 1.1610 -2	2.3110 -2	5.9	8.9	11.8	17.7	35.2

  𝑃(𝑖 * 𝑇 𝐶𝐻𝐸𝐶𝐾 , 𝑁 𝑉𝑈𝐿 , 𝑛 𝑅𝐸𝑇 ) = ∑ 𝑃((𝑖 -1) * 𝑇 𝐶𝐻𝐸𝐶𝐾 , 𝑁 𝑉𝑈𝐿 , 𝑛′ 𝑅𝐸𝑇 ) min(𝑛 𝑅𝐸𝑇 ,𝑛 𝑖-1 ) 𝑛′ 𝑅𝐸𝑇 =0 × 𝑃(𝑇 𝐶𝐻𝐸𝐶𝐾 , 𝑁 𝑉𝑈𝐿 -𝑛′ 𝑅𝐸𝑇 , 𝑛 𝑅𝐸𝑇 -𝑛′ 𝑅𝐸𝑇 )