Sylvaine Jacquart

Robin Siadous

Christel Henocq-Pigasse

Reine Bareille

Christine Roques

Christian Rey

Christe ` Le Combes
email: christele.combes@ensiacet.fr

Á C Rey

Á C Combes

Á R Bareille

Á C Roques

Composition and properties of silver-containing calcium carbonate-calcium phosphate bone cement

The introduction of silver, either in the liquid phase (as silver nitrate solution: Ag(L)) or in the solid phase (as silver phosphate salt: Ag(S)) of calcium carbonate-calcium phosphate (CaCO 3 -CaP) bone cement, its influence on the composition of the set cement (C-Ag(L) and C-Ag(S) cements with a Ca/Ag atomic ratio equal to 10.3) and its biological properties were investigated. The fine characterisation of the chemical setting of silver-doped and reference cements was performed using FTIR spectroscopy. We showed that the formation of apatite was enhanced from the first hours of maturation of C-Ag(L) cement in comparison with the reference cement, whereas a longer period of maturation (about 10 h) was required to observe this increase for C-Ag(S) cement, although in both cases, silver was present in the set cements mainly as silver phosphate. The role of silver nitrate on the setting chemical reaction is discussed and a chemical scheme is proposed. Antibacterial activity tests (S. aureus and S. epidermidis) and in vitro cytotoxicity tests (human bone marrow stromal cells (HBMSC)) showed that silver-loaded CaCO 3 -CaP cements had antibacterial properties (anti-adhesion and anti-biofilm formation) without a toxic effect on HBMSC cells, making C-Ag(S) cement a promising candidate for the prevention of bone implant-associated infections.

Introduction

The first self-setting calcium phosphate cements (CPC) were introduced in the early 1980s as biomaterials for bone repair and regeneration [START_REF] Brown | A new calcium phosphate setting cement[END_REF]. Since then, different CPCs have been developed; their biomimetism and their excellent osteoconductivity make them interesting candidates for dental or orthopaedic applications. On the other hand, their moulding ability allows for the optimal filling of bone. Thus, many studies have been performed in order to improve their physico-chemical properties and their biological behaviour. Nevertheless, some important issues still need to be overcome. Among them, improved resorption capability and better protection against implant-associated infections are major challenges in this field [START_REF] Bohner | Design of ceramic-based cements and putties for bone graft substitution[END_REF][START_REF] Sugawara | Calcium phosphate-based cements: clinical needs and recent progress[END_REF].

Calcium carbonate-calcium phosphate (CaCO 3 -CaP) mixed cements have been presented as a promising resorbable material for bone reconstruction [START_REF] Combes | Calcium carbonate-calcium phosphate mixed cement compositions for bone reconstruction[END_REF]. Vaterite is a metastable polymorph of calcium carbonate whose solubility is higher than phosphocalcium apatite; a high proportion of vaterite (i.e. 50 % w/w in the solid phase) is expected to enhance the resorption of bone cement via faster physicochemical degradation.

Different strategies have been carried out in order to prevent bacterial infection associated with the implantation of CPCs [START_REF] Ginebra | Calcium phosphate cements as drug delivery materials[END_REF]. Many studies were performed on the introduction of antibiotics such as gentamicin, cephalexin or vancomycin [START_REF] Joosten | Evaluation of an in situ setting injectable calcium phosphate as a new carrier material for gentamicin in the treatment of chronic osteomyelitis: studies in vitro and in vivo[END_REF][START_REF] Liu | Gentamicin-loaded strontium-containing hydroxyapatite bioactive bone cement-an efficient bioactive antibiotic drug delivery system[END_REF][START_REF] Hesaraki | Cephalexin-loaded injectable macroporous calcium phosphate bone cement[END_REF][START_REF] Sasaki | In vitro elution of vancomycin from calcium phosphate cement[END_REF][START_REF] Jiang | Comparing the efficacy of three bioceramic matrices for the release of vancomycin hydrochloride[END_REF]. However, if the addition of antibiotics is wellaccepted in the treatment of specific infections, it remains controversial for preventive applications because of the cost and risk of limited efficiency due to the potential resistance of bacteria to the drug [START_REF] Sugawara | Calcium phosphate-based cements: clinical needs and recent progress[END_REF]. The use of Ca(OH) 2 or alkalisubstituted phosphate reactants have also been proposed; the released hydroxyl ions and the formation of highly alkaline products during setting, respectively, provide an antibacterial activity [START_REF] Serraj | Study of a hydraulic calcium phosphate cement for dental applications[END_REF][START_REF] Michaı ¨lesco | Antimicrobial activity and tightness of a DCPD-CaO-based hydraulic calcium phosphate cement for root canal filling[END_REF][START_REF] Gbureck | Antimicrobial potency of alkali ion substituted calcium phosphate cements[END_REF]. Nevertheless, such alkaline systems raise the question of cytocompatibility and they cannot be transposed to most mineral cement, particularly acidic ones.

On the other hand, silver has been widely used in medical devices as a broad-spectrum antimicrobial agent with low toxicity [START_REF] Lansdown | A pharmacological and toxicological profile of silver as an antimicrobial agent in medical devices[END_REF]. In particular, an antibacterial effect was observed on Staphylococcus aureus (S. aureus), which is the most frequent infective agent after prosthesis implantation [START_REF] Feng | A mechanistic study of the antibacterial effect of silver ions on Escherichia coli and Staphylococcus aureus[END_REF][START_REF] Berbari | Risk factors for prosthetic joint infection: case-control study[END_REF]. It must be noted that, since the late 1970s, some cases of silver-resistant bacteria have been identified, but they remain rare and to our knowledge the main bacteria found in usual post-operative infections are not concerned [START_REF] Lansdown | Silver in healthcare: its antimicrobial efficacy and safety in use[END_REF].

Among the developed medical devices, silver was introduced by different methods into apatitic matrices during apatite synthesis, for example by co-precipitation of calcium hydroxide or calcium salt and silver nitrate with a phosphate compound, by direct formation of silver-doped hydroxyapatite (Ag-HA) coatings, or by an additional step of impregnation of the hydroxyapatite (HA) gel or HA coating in a solution of AgNO 3 [START_REF] Kim | Antimicrobial effects of metal ions (Ag ? , Cu 2? , Zn 2? ) in hydroxyapatite[END_REF][START_REF] Singh | In vitro biocompatibility and antimicrobial activity of wet chemically prepared Ca 10-x Ag x (PO 4 ) 6 (OH) 2 (0.0 B x B 0.5) hydroxyapatites[END_REF][START_REF] Chen | In vitro anti-bacterial and biological properties of magnetron co-sputtered silver-containing hydroxyapatite coating[END_REF][START_REF] Ando | Calcium phosphate coating containing silver shows high antibacterial activity and low cytotoxicity and inhibits bacterial adhesion[END_REF][START_REF] Nazari | Ion exchange behaviour of silver-doped apatite micro-and nanoparticles as antibacterial biomaterial[END_REF][START_REF] Shirkhanzadeh | Bioactive delivery systems for the slow release of antibiotics: incorporation of Ag ? ions into micro-porous hydroxyapatite coatings[END_REF][START_REF] Lee | Functionalizing calcium phosphate biomaterials with antibacterial silver particles[END_REF][START_REF] Venkateswarlu | Fabrication of corrosion resistant, bioactive and antibacterial silver substituted hydroxyapatite/titania composite coating on Cp Ti[END_REF][START_REF] Lim | Effect of silver content on the antibacterial and bioactive properties of silversubstituted hydroxyapatite[END_REF].

Although silver has been frequently introduced into PMMA bone cements, only two silver-doped phosphocalcic cements have been proposed recently [START_REF] Spadaro | Silver polymethyl methacrylate antibacterial bone cement[END_REF][START_REF] Alt | An in vitro assessment of the antibacterial properties and cytotoxicity of nanoparticulate silver bone cement[END_REF][START_REF] Ewald | Silver-doped calcium phosphate cements with antimicrobial activity[END_REF]. Those apatitic and brushitic cements were prepared by using silver-doped tricalcium phosphate and showed a significant reduction in the bacterial adherence of S. aureus and S. epidermidis but decreased cytocompatibility in human osteoblast cell lines.

The present study focuses on the association of silver with a CaCO 3 -CaP self-setting paste in order to confer the antibacterial activity of this cement. Two methods of introduction were investigated: the addition of Ag 3 PO 4 , a third powder component, into the solid phase or the use of a solution of AgNO 3 as the liquid phase. The objective of this study was to evaluate the physical-chemical and biological properties of such silver-loaded cements and to determine the best candidate for a dental or orthopaedic application.

Materials and methods

Powders synthesis and characterisation

All syntheses were performed in aqueous media (deionised water). Brushite (B), i.e. dicalcium phosphate dihydrate or DCPD (CaHPO 4 Á2H 2 O), was synthesised by double decomposition between a calcium nitrate solution (Ca(NO 3 ) 2 Á4H 2 O; 0.37 mol in 600 mL) and ammonium dihydrogen phosphate (H 2 PO 4 NH 4 ; 0.37 mol in 1.4 L and 20 mL of ammonium hydroxide solution at 20 % w/w). The pH of the mixture was immediately adjusted to ca. 5.5 by the addition of extra ammonium hydroxide solution. The white precipitate was then allowed to mature in solution, without stirring, for 5 h. It was finally filtered and washed with 2 L of water. Vaterite (V), a polymorph of calcium carbonate CaCO 3 , was also synthesised by double decomposition by adding a solution of calcium chloride (CaCl 2 Á2H 2 O; 0.5 mol in 250 mL) in a solution of sodium carbonate (Na 2 CO 3 Á10H 2 O; 0.5 mol in 500 mL of deionised water) using a peristaltic pump (12 mL/min). The white precipitate was immediately filtered and washed with 1.5 L of water. After filtration and washing, the precipitates were lyophilised and the powders were stored in a freezer.

Silver orthophosphate Ag 3 PO 4 was prepared by double decomposition between silver nitrate (AgNO 3 ; 36 mmol in 200 mL) and disodium hydrogen phosphate (Na 2 HPO 4 ; 12 mmol in 300 mL). The yellow precipitate was filtered and washed with 500 mL of water. As Ag 3 PO 4 is light sensitive, all the glassware was covered by aluminium foil to keep the solution and powder in darkness during synthesis, drying and storage. Commercial silver nitrate salt (AgNO 3 99.9 %; Alfa Aesar Ò ) was purchased and used without further purification.

All the synthesised powders were characterised by transmission Fourier transformed infrared spectroscopy from KBr pellets (FTIR; Perkin-Elmer FTIR 1600 spectrometer), X-ray diffraction (XRD; Inel CPS 120 diffractometer) using a Co anticathode and by scanning electron microscopy (SEM; Leo 435 VP microscope).

Cement preparation

The reference cement (C-REF cement) was obtained by mixing deionised water as the liquid phase with the solid phase composed of an equal mass of vaterite and brushite. These reactive powders were first homogenised with a pestle in a ceramic mortar.

Silver was introduced into the cement either in the solid phase or in the liquid phase by means of silver salts with different solubilities (Ag 3 PO 4 and AgNO 3 ). Silver-loaded cement pastes were prepared by mixing an appropriate amount of silver phosphate salt (Ag 3 PO 4 ) with the solid phase (C-Ag(S) cement), or by using a silver nitrate (AgNO 3 ) solution as the liquid phase (C-Ag(L) cement); the amount of silver salt added in the cement formulation is reported in Table 1. In both types of silver-loaded cements prepared (C-Ag(S) and C-Ag(L)), the silver salt was introduced in the cement formulation in order to reach a Ca/Ag atomic ratio of 10.3 (Table 1). For the three cement compositions (C-REF, C-Ag(S) and C-Ag(L)), the water/ solid weight ratio (W/S) was 0.55 (Table 1). After mixing, the wet paste was placed in a water-saturated oven at 37 °C for setting and hardening.

For the cytotoxicity and microbiological tests, pellets of the cements were prepared under the same conditions using silicon rubber moulds (diameter: 10 mm). After setting and drying, the surface of the pellets was polished with fine sand paper (P1200) before c-ray sterilisation and in vitro tests.

Cement characterisation

The cements were characterised by the FTIR, XRD and SEM techniques. The setting time of the cement paste was evaluated by the Gillmore needle method (standard ISO 9917-1:2007).

The chemical setting reaction was followed by FTIR spectroscopy. For each composition, eight samples of cement (0.9 ± 0.2 g) were formed from the same initial paste immediately at the end of mixing. They were then placed in an oven at 37 °C in a humid atmosphere for various periods of maturation (0, 1, 2, 3, 4, 7, 24 and 48 h) and then lyophilised in order to remove the water and stop the setting reaction. They were then weighed and analysed by FTIR spectroscopy. The 850-450 cm -1 range of wavenumbers contains several vibration bands characteristic of the different phases involved in cement setting and hardening (Table 2). Significant bands at 525, 603, 617 and 745 cm -1 were carefully chosen in order to evaluate the relative ratios between brushite, apatite and vaterite respectively. The silver orthophosphate phase could not be identified in a relevant way by FTIR spectroscopy due to the superimposition of bands, the very low amount of silver phosphate in the cements and the possible precipitation of AgBr within the KBr pellet. Thus, it was not taken into account for the quantification. During the setting reaction, the solid phase lost about 10 % of its weight (because of CO 2 degassing); we also assumed that the silver phase was not involved in this loss. Some binary and ternary standard samples were prepared by mixing known amounts of brushite, vaterite and a synthetic nanocrystalline carbonated apatite left to mature for 48 h. Two domains, i.e. 850-700 and 700-450 cm -1 , of the FTIR spectrum of both cements and standards were decomposed into different bands as reported in Table 2 using OriginPro 8.5 software. The baseline was fixed as a straight line between the two minima of each studied domain. An example of decomposition is shown in Fig. 1 for the C-REF cement after 7 h of maturation. The relative areas of the FTIR bands characteristic of each phase involved in the CaCO 3 -CaP cements were compared to those of the standards. This allowed for an evaluation of the content of the brushite, vaterite and apatite phases in the studied cement.

Indirect cytotoxicity study

Cytotoxicity tests are essential before the in vivo evaluation of a new biomaterial. The indirect cytotoxicity evaluation of silver-doped and reference CaCO 3 -CaP cement compositions was assessed by an extraction method according to NFEN30993-5 ISO 10993-5 [START_REF]Evaluation biologique des dispositifs me ´dicaux. Partie 5: Essais concernant la cytotoxicite ´: Me ´thodes in vitro[END_REF].

Human bone marrow stroma cells, obtained from human bone marrow according to Vilamitjana-Ame ´de ´e et al. [START_REF] Vilamitjana-Ame ´de ´e | Human bone marrow stromal cells express an osteoblastic phenotype in culture[END_REF] with some modifications, were used to test the cytotoxicity of the extracts and cultured in alpha-MEM without ascorbic acid (Invitrogen, France) containing 10 % (v/v) foetal calf serum (FSC, Lonza, France). At passage 2, the cells were seeded at a density of 40,000 cells/cm 2 in 96-well microtitre plates (Nunc, Denmark) and the culture was maintained at 37 °C for 96 h after cell plating. At subconfluency, the medium was replaced by the material extraction vehicle. To obtain extraction vehicles, the hardened cements loaded with silver were sterilised by crays (25 kGy) and then immersed in alpha-MEM medium.

The ratio of the sample surface area to the volume of the vehicle was 5 cm 2 /mL. Extractions were performed in borosilicate glass tubes at 37 °C for 24 h and this step was repeated five times using the same approach. The extraction liquid was supplemented with 10 % (v/v) FCS. Borosilicate tubes containing identical extraction vehicles with either no material or a solution of phenol at a concentration of 64 g/L (known to be cytotoxic) were processed under the same conditions to provide negative and positive controls, respectively. The medium was replaced by each extract solution supplemented with 10 % (v/v) FCS and the plate was incubated for 24 h at 37 °C. At the end of the extract incubation period, tests were performed: cell viability was assessed by the Neutral Red assay and cell metabolic activity using the MTT assay [START_REF] Parish | Automated colorimetric assay for T cell cytotoxicity[END_REF][START_REF] Mosmann | Rapid colorimetric assay for cellular growth and survival: application to proliferation and cytotoxicity assays[END_REF]. The intensity of the colours obtained (red and blue, respectively) is directly proportional to the viability and metabolic activity of the cell population and inversely proportional to the toxicity of the material. Indirect cytotoxicity tests were duplicated for each cement composition. The mean values of absorbance measurements obtained from colorimetric tests and their corresponding standard deviations (±SD) were calculated. The results are expressed as a percentage of the negative control (plastic) tested during the same experiment.

Antibacterial in vitro test

In an attempt to define the effect of silver incorporation, the antibacterial activity was investigated considering the ability of staphylococci to adhere and colonise cement surfaces. S. aureus CIP 4.83 and S. epidermidis CIP 68.21 (Institute Pasteur Collection, Paris, France) were grown in 24-well microplates containing reference and silver-loaded cement pellets and 2 cm 3 of modified biofilm broth (MBB), as previously described by Khalilzadeh et al. [START_REF] Khalilzadeh | Growth inhibition of adherent Pseudomonas aeruginosa by an N-butanoyl-L-homoserine lactone analog[END_REF]. The model was chosen considering that the composition of MBB and the renewal of the medium promotes adherent but not planktonic cell growth with a biofilm structure.

After initial inoculation with 10 2 CFU, the MBB medium was renewed at 2, 4, 6, 20, 24 and 48 h for S. aureus and at 6, 20, 24 and 48 h for S. epidermidis incubation at 37 °C after two gentle rinses with sterilised distilled water (2 cm 3 ). Biofilms were grown for 72 h. After the period of growth (72 h), the wells and cement pellets were rinsed and 2 cm 3 of distilled water were added. Adherent bacteria were removed by scraping with a sterile spatula and CFU numeration was performed on the solution. The entire suspension was directly inoculated in trypcase soy agar (Biome ´rieux, Craponne, France) or tenfold diluted before adding 100 lL in trypcase soy agar (incubation 48 h at 37 °C). Each experiment was performed three times.

Results

Composition and structure

Figure 2 shows the XRD patterns of the cements after setting and hardening. It appears that a biomimetic poorly crystallised apatite was formed during the setting reaction by the consumption of brushite and vaterite. Nevertheless, some vaterite, initially introduced in excess, remained in the final composition. The addition of silver as Ag 3 PO 4 into the solid phase (C-Ag(S) cement) did not affect the final composition: a similar content of apatite and vaterite phases were identified by XRD analysis and silver remained as a distinct crystalline phase (silver orthophosphate) in the cement. Interestingly, similar XRD patterns were obtained for both the C-Ag(S) and C-Ag(L) cements. Thus, it appears that silver orthophosphate, with a very low solubility (1.5310 -5 g/L at 19.5 °C), precipitated when the silver nitrate solution was added to the cement solid phase. An instantaneous yellow coloration, characteristic of silver orthophosphate, appeared at mixing time t 0 and the XRD data (not shown) confirmed the very fast precipitation of Ag 3 PO 4 .

We followed the chemical setting of the different cements by FTIR spectroscopy. The spectra of the three cement compositions at different maturation times (1, 4 and 48 h) are shown in Fig. 3. We could clearly observe in Fig. 3 that at 1 h and even more at 4 h the decrease in the characteristic band of the brushite phase at 525 cm -1 in favour of an increase in apatite characteristic bands at 603 and 617 cm -1 : this was significantly higher for C-Ag(L) than for the two other types of cement, indicating faster chemical setting for the C-Ag(L) cement. After 48 h, both silver-loaded cements spectra showed that the brushite characteristic band at 525 cm -1 was no longer present, suggesting that this reactive powder was totally consumed, whereas this band was weak but still observable in the reference cement (C-REF) spectrum.

To complete these observations, we performed a semiquantitative study to evaluate the formation of the apatite phase during cement setting and hardening. Figure 4 shows the evolution of the amount of apatite formed, determined as described in the Materials and Methods section, and its evolution during 48 h of maturation for the three types of cement tested. It confirms that during the first 8 h, the addition of Ag 3 PO 4 in the solid phase did not seem to have a significant impact on the formation of apatite, whereas the increase in the amount of apatite was much faster for C-Ag(L) cement. Between 8 and 24 h, C-Ag(S) caught up to C-Ag(L), so that after 48 h, both cements containing silver were totally set, in terms of the chemical setting reaction, whereas for the C-REF cement, it took a longer time for the setting reaction to reach the same level of apatite content.

Complementarily, the physical setting of the cements was measured using a Gillmore needle apparatus (Table 3). For the C-REF cement, the initial and final setting times were 1 h 15 min and 2 h 15 min, respectively. Despite faster chemical reaction rates, no highly significant differences were observed for the silver-containing cements Backscatter SEM images of C-Ag(S) and C-Ag(L) cements are presented in Fig. 5. Particles containing silver, which is the heaviest element in the cement compositions tested, appeared much brighter than the calcium phosphate and calcium carbonate phases. In the C-Ag(S) cement, the silver orthophosphate particles (ca. 2 lm) were homogeneously distributed throughout the cement matrix, in relation to the initial homogenisation of the reactive powders before the addition of the liquid phase, whereas in the C-Ag(L) cement, silver phosphate particles were smaller (a few hundred nanometres) and do not appear homogeneously distributed. In addition, we could see that both cements were microporous. Some macropores ([50 lm in diameter) were also present, in particular in the C-Ag(L) cement.

Biological properties

In vitro cytotoxicity tests

Figure 6 shows the evolution of cell viability based on extracts obtained sequentially every 24 h for the C-Ag(S) cement. The extracts from this cement affected the viability and metabolic activity of cells during the first 24 h only, as evidenced by the results obtained with both the MTT and NR assays. For the following extractions, we found a progressive increase in cell viability, but no significant variation in their metabolic activity, which suggests that with successive extractions, the C-Ag(S) cement remained non-cytotoxic, especially after the fifth extraction of the functionalised cement. Similar results were obtained for the C-Ag(L) cement (data not shown). For both strains of staphylococci tested, which are the main species involved in bone-implant infections, we could observe a dramatically decrease in bacterial numeration (anti-adhesion and anti-biofilm formation effect) since 0 CFU of adherent bacteria were obtained for the C-Ag(S) cement (P \ 0.001) whereas values with the reference cement (control) were similar to those obtained directly in wells with no cement. Log reductions were higher than 6 in all the assays. Similar results were obtained for the C-Ag(L) cement (data not presented).

Antibacterial in vitro tests

Discussion

Composition and setting of silver-loaded cements

In a previous study, it was shown that the setting of the calcium carbonate-calcium phosphate mixed cement and CO 3 2-also present in the self-setting system, thus creating calcium and hydroxyl vacancies to maintain the electroneutrality of the solid. According to the literature, and considering our self-setting system, we can assume that the general chemical formula of the apatite formed is Ca 10-(x?y) (PO 4 ) 6-(x?y) (HPO 4 ) x (CO 3 ) y (OH) 2-(x?y) with 0 B x ? y B 2 [START_REF] Eichert | Nanocrystalline apatite-based biomaterials: synthesis, processing and characterization[END_REF]. Thus, the main chemical reactions involved in the studied cement (dissolution of brushite and vaterite (Eqs. 1, 2), the reaction between hydrogenophosphate and carbonate ions (Eq. 3) and the reprecipitation of apatite (Eq. 4)) are represented by the following equations:

CaHPO 4 Á 2H 2 O ! Ca 2þ þ HPO 2À 4 þ 2H 2 O ð1Þ
CaCO 3 ! Ca 2þ þ CO 2À 3 ð2Þ
2HPO 2À 4 þ CO 2À 3 ! 2PO 3À 4 þ CO 2ðgÞ þ H 2 O ð3Þ
ð10 À x À yÞCa 2þ þ ð6 À x À yÞPO 3À 4 þ xHPO 2À 4 þ yCO 2À 3 þ ð2 À x À yÞ H 2 O ! Ca 10ÀxÀy ðPO 4 Þ 6ÀxÀy ðHPO 4 Þ x ðCO 3 Þ y ðOHÞ 2ÀxÀy þ ð2 À x À yÞH þ ð4Þ
According to these four equations, the global system can be modelled as follows:

ð6 À yÞCaHPO 4 Á 2H 2 O þ ð4 À xÞCaCO 3 ! Ca 10ÀxÀy ðPO 4 Þ 6ÀxÀy ðHPO 4 Þ x ðCO 3 Þ y ðOHÞ 2ÀxÀy þ ð4 À x À yÞCO 2ðgÞ þ ð14 À 2yÞH 2 O ð5Þ
The formation of carbon dioxide (Eqs. 3, 5) can explained the presence of macropores observed within the set cement (Fig. 5).

In the present study, we showed that the introduction of a silver salt into the cement composition did not change the reaction mechanism: brushite dissolved and reacted with some vaterite to form an apatite phase (Fig. 2). Nevertheless, FTIR spectroscopy semi-quantitative analysis revealed a slight change in the setting kinetics, as the setting reaction (chemical setting) rate appeared faster for the cements containing silver (Fig. 2), whereas the setting time (physical setting) was unchanged for C-Ag(S) and slightly longer for C-Ag(L) (Table 3). It shall be recalled that the physical setting time, corresponding to paste hardening, although related to the chemical reactions involved, does not superimpose with the advancement of these chemical reactions. We discuss hereafter the chemical and physical processes leading to the setting of these cements.

As mentioned before, Ag 3 PO 4 , introduced in the C-Ag(S) cement or immediately formed in the C-Ag(L) cement, has a low solubility, much lower, comparatively, than that of brushite and vaterite. Although it may not induce a major change in the dissolution-reprecipitation reactions, it could have an impact on ion equilibrium involved in these processes.

In the case of the C-Ag(L) cement, the precipitation of Ag 3 PO 4 observed immediately after the addition of silver nitrate solution to the cement reactive powders mixture induced, on the one hand, the beginning of the consumption of phosphate ions from the brushite, consistent with the earlier decrease in the phosphate band after 1 and 4 h (Fig. 2) and, on the other hand, an acidification of the medium (Eq. 6). Since Ca(NO 3 ) 2 is highly soluble (1.44 9 10 3 g/L at 25 °C), calcium ions are more readily available to form some apatitic nuclei than in the C-REF cement (Eq. 7). The acidification of the medium can also favour the dissolution of the reactants, particularly acting on vaterite by an acid-base reaction (Eq. 8), which leads to the release of carbon dioxide and the regeneration of Ca(NO 3 ) 2 which was initially involved in the precipitation of apatite. Given Eqs. ( 7) and ( 8), it appears that Ca(NO 3 ) 2 could play the role of a catalyst in the self-setting system, as described in Fig. 7, until the complete dissolution of brushite, the limiting reactant. Its involvement could explain the faster precipitation of apatite observed by FTIR spectroscopy (Fig. 3).

3AgNO 3 þ CaHPO 4 Á 2H 2 O ! Ag 3 PO 4 þ CaðNO 3 Þ 2 þ HNO 3 þ 2H 2 O ð6Þ
ð4 À x À yÞCaðNO 3 Þ 2 þ ð6 À yÞCaHPO 4 Á 2H 2 O þ yCaCO 3 ! Ca 10ÀxÀy ðPO 4 Þ 6ÀxÀy ðHPO 4 Þ x ðCO 3 Þ y ðOHÞ 2ÀxÀy þ 2ð4 À x À yÞHNO 3 þ ð10 þ x À yÞH 2 O ð7Þ
CaCO 3 þ 2HNO 3 ! CaðNO 3 Þ 2 þ CO 2ðgÞ þ H 2 O ð8Þ
In the case of the C-Ag(S) cement, the low solubility of Ag 3 PO 4 introduced directly to the reactive powder mixture (solid phase) made it a ''spectator'' phase at the beginning of the setting process, in agreement with the absence of a significant influence noticed on chemical (Fig. 2) and physical (Table 3) setting. However, during the setting reaction, apatite was formed, hence inducing an acidification of the medium (Eq. ( 4)). This acidification might transiently favour the dissolution of silver phosphate. On the XRD pattern, the relative intensity of Ag 3 PO 4 appeared to decrease during setting (data not shown), and no additional phase was identified. An increased concentration of phosphate ions will favour the formation of apatite. On the other hand, although no shift of the XRD peaks can be clearly observed, some Ag ? ions could probably be incorporated into the cationic lattice of the apatite. This may also accelerate the precipitation process, as observed after about 10 h of maturation (Fig. 4). Vandecandelaere studied the conditions of formation of silver-doped nanocrystalline apatites and showed that neutral and alkaline conditions allowed for obtaining silver-doped nanocrystalline apatites (more Ag incorporated at neutral pH), whereas acidic conditions favoured the precipitation of silver phosphate [START_REF] Vandecandelaere | E ´laboration et caracte ´risation de biomate ´riaux osseux innovants a `base d'apatites phospho-calciques dope ´es[END_REF]. In addition, this study revealed a slight increase in apatite crystal length when silver was incorporated into the nanocrystalline apatite structure. However, no inhibitory or promoter effect of the presence of silver on nanocrystalline apatite crystal growth has been demonstrated.

The setting and hardening of cements is a complex phenomenon, and is not always correlated with the chemical reaction rate involved in the setting process: while during the first 12 h of cement maturation, apatite was formed more rapidly in the C-Ag(L) cement than in the C-Ag(S) or C-REF cements (Fig. 4), hardening took slightly longer (higher initial setting time, Table 3). The more acidic initial medium and/or the presence of silver might lead to smaller crystallites of apatite or to a greater disorder of the structure, which could explain the slight delay in the physical entanglement of particles and thus of hardening.

The backscatter mode SEM images showed two major differences in C-Ag(S) and C-Ag(L) cement microstructure: the size of the silver-rich particles (2 lm and a few hundred nanometres respectively) and their distribution. These two key parameters could have an impact on the antibacterial activity of the cement. Homogeneity of the distribution of silver is of course necessary in order to control the local concentration of the antibacterial agent in the material. It would be necessary to optimise the mixing time and processing of the paste of the C-Ag(L) cement in order to better homogenise the distribution of the silver phosphate formed in situ. The size of the particles can be discussed in terms of solubility: smaller particles will probably have a higher rate of solubilisation and thus faster kinetics of Ag ? release. Our objective was to obtain a preventive effect of silver and to avoid any bacterial growth on the material. For this application, it would be better to maintain a sufficient concentration of silver on the surface of the materials, avoiding rapid release. Considering these two aspects, and given that there were no major differences in the physico-chemical properties between the two silver-loaded cements, C-Ag(S) appears to be better candidate as bone substitute, as it did not introduce any other counter ions such as nitrate in the cement composition.

Biological properties of silver-loaded cements

The preliminary study on the in vitro biological properties showed that silver-loaded CaCO 3 -CaP cements had antibacterial properties (anti-adhesion and anti-biofilm formation) without cytotoxic effects on human bone marrow stromal cells after several washings of the cements, even if a high dose of Ag was incorporated within cement (Ag/Ca atomic ratio equal to 9.7 %).

The significant decrease in cell viability and metabolic activity observed for cells in contact with the first extract (first 24 h) suggests that a burst release of Ag should occur during the equilibration of the C-Ag(S) cement with the medium (alpha-MEM) at a high dose, such that cell viability and metabolic activity were affected. However, for the following extracts, cell viability as well metabolic activity were restored, suggesting that with the equilibration of the cements in alpha-MEM, HBMS cells are able to grow and to proliferate in contact with the extracts. Successive washings of CaP cements or ceramics are needed for equilibrating the materials before cell seeding or metabolic activity test. Considering the dynamic renewal of biological fluids in vivo and the homogeneous distribution of silver within the C-Ag(S) cement observed by microscopy (Fig. 4), we can expect good cytocompatibility of this cement even in the early period after implantation.

The introduction of silver as an antibacterial agent in hydroxyapatite and brushite bone cements has been reported by Ewald et al. [START_REF] Ewald | Silver-doped calcium phosphate cements with antimicrobial activity[END_REF], who used silver-doped TCP (a-or b-TCP, respectively) as reactive powders to prepare both cements. They showed that silver-doped brushite cement (Ag/Ca = 0.6 %) was the most efficient cement with regards to two strains of staphylococci, but this cement was also cytotoxic to osteoblasts in which activity began to recover only after 7 days of culture. This behaviour may be related to the high solubility of brushite under biological conditions, which should in turn contribute to the release of a high amount of silver into the cell culture medium. In addition, the probable hydrolysis of brushite into apatite in vivo may generate locally an acidic pH favouring Ag ? release. However, the possibility of precipitating a poor soluble silver phosphate after brushite hydrolysis was not considered by the authors although it may explain the recovery of cell activity after 7 days.

The dose of silver incorporated in the CaCO 3 -CaP cements was high, but this can be optimised with regards to the antibacterial properties and cytocompatibility of the biomaterial. In addition, the route of introduction proposed in the present study (silver salt added as a separate ingredient within the solid or liquid phase) has the advantage of allowing the dose of antibacterial agent to be adapted during surgery and then delivered locally depending on the application and the patient. Biological activity (antibacterial and cytotoxicity) of silver associated or not to hydroxyapatite has been earlier described and explored [START_REF] Feng | A mechanistic study of the antibacterial effect of silver ions on Escherichia coli and Staphylococcus aureus[END_REF][START_REF] Chen | In vitro anti-bacterial and biological properties of magnetron co-sputtered silver-containing hydroxyapatite coating[END_REF][START_REF] Ando | Calcium phosphate coating containing silver shows high antibacterial activity and low cytotoxicity and inhibits bacterial adhesion[END_REF]. The presented assays had to be considered as preliminary results to check the maintenance of known efficiency when silver is incorporated in calcium carbonate-calcium phosphate bone cement. Antimicrobial assays were performed in conditions allowing biofilm formation but not planktonic growth, because such adherent bacteria are significantly more resistant to immune system and antibiotics treatments. In addition, these conditions are more representative of the pathologic situation since biofilm formation is required to induce chronic bones infections [START_REF] Palmer | Molecular techniques to detect biofilm bacteria in long bone nonunion: a case report[END_REF]. Pellets including the tested silver amount displayed some strong anti-adhesive and/or anti-biofilm formation exerted by silver associated with a CaCO 3 -CaP cement on S. aureus and S. epidermidis, two major bone pathogens [START_REF] Ciampolini | Pathophysiology of chronic bacterial osteomyelitis. Why do antibiotics fail so often?[END_REF][START_REF] Carek | Diagnosis and management of osteomyelitis[END_REF]. Our protocol allowed us to get a detection limit as low as we were able to assess no CFU from the cement surface after 72 h of incubation, whereas more than 10 6 CFU were detected for control cement pellets. The observed effects for such components can be expected to be reproducible in long term in vivo conditions, because of the total adhesion and biofilm formation inhibition, even after 3 days of contact with an initial inoculum of 10 2 CFU/cm 2 , which can be considered as an in vivo worth case. A thorough study focusing on the release properties (Ag release) and on the effect of Ag dose on the biological properties of these cements is in progress and will be presented in another paper.

Local delivery of the antibacterial agent presents an alternative to the use of high and daily doses delivered systemically and the toxicity or side effects associated with this mode of drug administration.

Conclusion

This study contributes to understanding the complex chemical reactions involved in silver-doped CaCO 3 -CaP cement paste setting, and we proposed a chemical scheme involving calcium nitrate as a catalytic agent in apatite precipitation during C-Ag(L) cement setting. In vitro biological tests revealed the antibacterial properties of these cements and their non-cytotoxicity after washing, making silver-doped CaCO 3 -CaP cement a promising bone substitute material to reduce implant-associated infections. Interestingly, we can take advantage of the two routes of introduction of silver as a separate ingredient in the cement formulation to adapt the dose of antibacterial agent up to the final step, i.e. during surgery.

Fig. 1

 1 Fig. 1 Example of decomposition of the 850-450 cm -1 domain for the cement C-REF after 7 h of maturation. The grey curve corresponds to the experimental FTIR spectrum and the black curve to the sum of the fitted bands. The circled bands are those used for the evaluation of the relative composition between brushite (B), vaterite (V) and apatite (Ap)

Fig. 2 Fig. 3 Fig. 4

 234 Fig. 2 XRD patterns of the three types of hardened cements: C-REF, C-Ag(S) and C-Ag(L)

Finala 15 Fig. 5

 155 Fig. 5 SEM images (backscattered electrons) of C-Ag(S) and C-Ag(L) cements showing the distribution of silver (bright dots) into both types of cement

Fig. 6 3

 63 Fig. 6 Indirect cytotoxicity evaluation. Cell viability (neutral red (NR) assay) and cell metabolic activity (MTT assay) of cells incubated for 24 h at 37 °C in five different extracts obtained by successive extractions. Five extractions of C-Ag(S) cement in the vehicle medium were performed every 24 h and are designated in the figure as 24 (1) to 24 (5). Results are expressed as % of the negative control material (plastic)

Fig. 7

 7 Fig. 7 Schematic representation of the catalytic role of Ca(NO 3 ) 2 in apatite precipitation within the C-Ag(L) cement

Table 1

 1 Composition (weight in g) of the different prepared and studied cements: C-REF, C-Ag(S) and C-Ag(L) cements

	Cements	Solid phase (S) (g)		Liquid phase (L) (g)	Weight ratio	Atomic ratios
		Brushite (B)	Vaterite (V)	Ag 3 PO 4	Water (W)	AgNO 3	W/S	Ca/Ag	Ca/P	Ca/C
	C-REF	0.50	0.50	-	0.55	-	0.55	-	2.72	1.58
	C-Ag(S)	0.45	0.45	0.10	0.55	-	0.55	10.3	2.50	1.58
	C-Ag(L)	0.50	0.50	-	0.55	0.13	0.55	10.3	2.72	1.58

Table 2

 2 Assignments of the characteristic absorption bands used to decompose the FTIR spectra in the 850-450 cm -1 domain

	Position (cm -1 ) Phases Attribution
	787	B	P-O-H
	745	V	m 2 CO 3	2-
	743	Ap-B	Water libration
	664	B	Water libration
	615	Ap	Non-apatitic PO 4 3-
	601	Ap	Apatitic PO 4	3-
	577	Ap-B	Apatitic and brushitic PO 4
	560	Ap-	Apatitic and silver orthophosphate PO 4 3-
		Ag
	533	Ap-B	Non-apatitic and brushitic HPO 4	2-
	524	B	HPO 4	2-

B brushite, V vaterite, Ap carbonated apatite, Ag Ag 3

PO 4

Table 4

 4 presents the CFU enumeration per cement pellet after 72 h of incubation with S. aureus CIP 4.83 and S. epidermidis CIP 68.21.

Table 3

 3 Setting time of the cements measured by the Gillmore needle apparatus Initial setting time a

Acknowledgments The authors thank the Agence Nationale de la Recherche (ANR-TecSan 2009 program) for supporting this research (BIOSINJECT-ANR-09-TECS-004 project).


Hassiba Benyounes

Weifeng Shen

Vincent Gerbaud

Entropy Flow and Energy Efficiency Analysis of Extractive Distillation with a Heavy Entrainer

The minimization of the entropy production is equivalent to minimizing the work or energy consumption required by a separation process. Sources of entropy creation during the extractive distillation of a minimum-and maximumboiling azeotropic mixture with a heavy entrainer are evaluated at each column stage in accordance with the second law of thermodynamics, and the distribution of entropy flow in different sections of the column is analyzed. Results show that mixing on feed trays and heat exchange in the reboiler and condenser are the main sources of entropy production. The temperature of the main feed and entrainer feed does not significantly affect the irreversibility of the process at the reference temperature of all flows. Although optimal values can be proposed to achieve a minimum isothermal work, the energy loss of the real process steadily increases with increases in the entrainer/feed flow rate ratio and reflux. The influence of the feed tray shows that product purity tends to vary inversely with energy loss.

INTRODUCTION

Distillation is a widely used separation technique that requires significant input of energy. The thermodynamic efficiency of the distillation process is often expressed in terms of total energy consumption. Alternatively, the second law of thermodynamics shows where energy losses occur and where modifications could be made to increase the overall utilization of energy in the column and improve performance. 1 A common way of reducing dissipated energy is to increase the process reversibility. The irreversibility in a distillation column comes from the driving forces that make the separation possible. Distillation can be regarded as a reversible process when it is performed at minimum driving force and equilibrium state. 2 Reducing the irreversibility of distillation processes has received extensive attention. For example, Nakaiwa et al. 3 conducted a parameter analysis and optimization of the internally heatintegrated distillation column (HIDiC), an energy efficient column. Rivero 4,5 studied the optimization of adiabatic and diabatic binary distillation, where heat is added to or withdrawn from each tray by heat exchangers.

Extractive distillation is defined as distillation in the presence of an entrainer fed at a location different from that of the main feed. The entrainer is added to the azeotropic mixture to alter the relative volatility of the key component without additional azeotrope formation, and for many years only heavy boiling entrainers were considered. 6,7 Generally, the entrainer is fed in the upper part of the column, above the feed stream, and it remains at a high concentration in the liquid phase in stages below its introduction into the column.

Reversible distillation columns have second law efficiencies better than those of irreversible distillation columns. 8 The first and the second laws may be used simultaneously to determine the departure from the reversible limitation in terms of the entropy generation of the system. Indeed, entropy is an alternative for energy optimization. Once the minimum entropy generation design is determined for the system, it provides a target for other, more realistic, designs. 9,10 It is well-known that mixing processes occur spontaneously in nature and they are highly irreversible; the reverse process of spontaneous mixture separation into its pure components is impossible. During a mixing process, some recoverable work is lost. In contrast, during a separation process, the potential work must be replenished. The lost work is proportional to the entropy generation. The entropy production approach leads to showing the location of energy losses as well as their causes, [11][12][13] and it serves to explain the effect of operational conditions and equipment design on energy efficiency; meanwhile, the entropy production approach helps to define the optimum conditions for minimizing the energy losses. 14,15 New process opportunities have arisen since the publication of new insights into the design and synthesis of feasible extractive distillation processes with a heavy entrainer. 16, [START_REF] Rodriguez-Donis | Thermodynamic insights on the feasibility of homogeneous batch extractive distillation, 2. Low-relative-volatility binary mixtures with a heavy entrainer[END_REF] Shen et al. [START_REF] Shen | Extension of thermodynamic insights on batch extractive distillation to continuous operation. 1. Azeotropic mixtures with a heavy entrainer[END_REF][START_REF] Shen | Extension of thermodynamic insights on batch extractive distillation to continuous operation. 2. Azeotropic mixtures with a light entrainer[END_REF] proposed an extension of thermodynamic insights derived from batch extractive distillation to continuous operation for azeotropic mixtures with a heavy or light entrainer. However, in those processes, many questions remain to be answered, such as how does the reflux ratio, the entrainer/feed flow rate ratio, and the temperature of the main feed and entrainer feed affect the entropy production and thus process efficiency. In the present work, we focus on the sensitivity analysis of the aforementioned operating parameters on the entropy generation and on the energy efficiency of the extractive distillation column with a heavy entrainer. The entrainer recovery column is not considered here.

CALCULATION AND ASSESSMENT APPROACH

2.1. Calculation of Entropy Production. Unlike azeotropic distillation, in which the entrainer is added along with the main feed, the entrainer is fed to a tray above the main feed in extractive distillation, as shown in Figure 1a. We assume that the distillation process takes place under adiabatic conditions through the exchange of mass and heat between the downward flowing liquid and the upward flowing vapor. All of the heat is supplied by the reboiler Q B and provided at temperature T B , which corresponds to the maximum temperature of the distillation process. The cooling Q C is provided at T C , which is the minimum temperature.

The entropy balance is used to quantify the total entropy production in a column section as well as in the reboiler and condenser. Figure 1b shows mixing takes place at the jth stage of the column and temperature T j . The liquid stream L j-1 descending from the (j-1)th stage must be preheated to T j , and similarly the vapor stream V j+1 in state a rising from the (j +1)th stage must be precooled to T j . Stages are numbered from the top down.

The steady-state entropy balance for a separation process is a summation of the physical contribution due to energy exchange and the chemical contribution related to inflows and outflows. The entropy flows are calculated from eqs 1 and 2:

∑ ∑ γ = + - ⎛ ⎝ ⎜ ⎜ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎞ ⎠ ⎟ ⎟ S L x S C T T R x x ln ln j j i j i p i j ij ij ij L 0 L L 0 (1) ∑ ∑ = + + - ⎛ ⎝ ⎜ ⎜ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎞ ⎠ ⎟ ⎟ S V y S C T T R P P R y y P P ln ln ln j j ij i P i j i T ij ij T i V 0 V V 0 0 0 (2)
Each stage of the distillation column is represented by the combination of two processes: the mixing of liquid and vapor flows (L j-1 and V j+1) and the separation into two liquid and vapor streams at equilibrium (V j and L j ). The flow mixing entropy S mix and the flow separation entropy S sep are given by eqs 3 and 4, respectively:

= = + - + S S S S j j j J in, mix, 1 L 1 V (3) = = + S S S S j j j j out, sep, L V (4)
The entropy production on jth stage comes from the difference between the entropy flows into and out of this stage and is given by by eq 5:

Δ = - S S S j j j out, in, (5)
The entropy production in a column section without reboiler and condenser ΔS section_flow is given by

∑ ∑ ∑ ∑ Δ = - = - _ S S S S S j j jj j j j j j section flow out, in, sep, mix, (6)
The entropy production of the entire extractive distillation column is obtained from

Δ = Δ + Δ + Δ -- S S S S S S column C B section flow F FE (7)
with the entropy production in the condenser

Δ = - + S V S S Q T ( ) C 1 C L 1 V C C (8)
and the entropy production in the reboiler

Δ = + - - S V S WS L S Q T n n B B B V B L L B B (9)
The overall entropy production of the extractive distillation process combined with the entropy production related to the heating and cooling of the inflows and outflows with respect to the ambient temperature are found from

∑ ∑ Δ = Δ + Δ + Δ S S S S total column coolers heaters (10)
where the entropy production contributed by the heater is and the entropy production contributed by the cooler is

Δ = - - ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ S S S Q T ( )
Δ = - + ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ S S S Q T ( ) cooler flow,out flow,in cooler cooler cooler (12)
A useful measure for the process inefficiency can be evaluated by the irreversibility process using the well-known Gouy-Stodola relation: 20

= Δ Δ ≥ T S S LW
w h e r e 0 0 total total (13) The lost work LW is always positive, and it is proportional to the energy inefficiency.

In accordance with the first law of thermodynamics, the steady-state energy balance for the distillation column can be written as

- = + - - Q Q H H H H D W F F E B C (16)
The isothermal minimum reversible molar work of separation at T 0 = 298.15 K for a nonideal mixture is given by 20

∑ ∑ ∑ γ γ γ γ = + - - W R T F x x F x x D x x W x x [ ( ln ) ( ln ) ln ln ] T i i i i i i i i i i i i min , 0 F F F E E E E D D D W W W 0 (17)
The second law efficiency measures the fraction of the part of total exergy input which is not lost by the irreversible processes:

η = + W W LW min min (18)
For an energy-demanding process, the rational efficiency in accordance with the second law of thermodynamics can be defined according to Gomez-Munos et al. [START_REF] Gomez-Munos | Synthesis of distillation trains by thermodynamic analysis[END_REF] 2.2. Distillation Column Feasibility Assessment. A sensitivity analysis was carried out to assess the parameter influence on the entropy balance of the extractive distillation column. The parameters studied are reflux ratio R, entrainer/feed flow rate ratio F E /F, physical state q of the main and entrainer feed (q = 1 means at boiling temperature; q = 0 means at saturated vapor temperature), and the entrainer feed tray N FE and main feed tray N F . The reference temperature T 0 is set at 298.15 K.

Δ = Δ Δ × S S S % ( / ) 100 B B c o l u m n (19)
Δ = Δ Δ × S S S % ( / ) 100 C C c o l u m n (20)
Δ = Δ - - Δ × _ _ S S
On the basis of Figure 1a, the entropy balance of the column section alone, without reboiler and condenser, is analyzed first; the entropy balance of the column with external flows at a boiling temperature and at the reference temperature T 0 are studied subsequently.

We consider two azeotropic systems belonging to different Serafimov's class 1.0-1a, corresponding to the separation of a minimum-boiling azeotropic mixture acetone (A)-methanol (B) using a heavy entrainer water (E), and class 1.0-2, corresponding to the separation of the maximum-boiling azeotropic mixture acetone (A)-chloroform (B) using a heavy entrainer benzene (E). For the latter we investigated two subcases: case I when acetone can be obtained as distillate product and case II when chloroform is expected to be the distillate product.

The thermodynamic properties are computed using the modified (Dortmund) UNIFAC thermodynamic model. [START_REF] Gmehling | Equilibrium Data Collection[END_REF] Table 1 lists the specifications of the columns to be studied. The number of trays N and main feed composition x F are considered to be constant, and operating pressure is set at 1 atm.

We assume (i) there is no significant pressure gradient in the system, (ii) heat is supplied by the reboiler and lost in the condenser, and (iii) the column is adiabatic.

On the basis of a MESH equilibrium distillation column model, simulation using ProSimPlus 3.1 software 24 was carried out. Considering R, F E /F, and composition as constants, those simulations provide the exact composition profiles, flow profiles, and temperature profile required for entropy calculations.

Many studies have been carried out for the class 1.0-1a system of acetone-methanol-water. The reflux ratio R and the values of F E /F are taken from Knapp et al. [START_REF] Knapp | Thermal integration of homogeneous azeotropic distillation sequences[END_REF][START_REF] Knapp | Minimum entrainer flows for extractive distillation: A bifurcation theoretic approach[END_REF] They proposed a minimum reflux ratio for the feasibility of continuous process at target product purity; the optimal operational parameters R = 2.76 and F E /F = 0.55 are suggested on the basis of their flowsheet simulation. [START_REF] Knapp | Thermal integration of homogeneous azeotropic distillation sequences[END_REF] For the class 1.0-2 corresponding system of acetone-chloroform-benzene, the operating parameters are set to make the process feasible; further optimization is out of our present objective. Depending on the expected distillate, either A or B, the overall column feed x F + x E composition point is located in a different region of Figure 2; each of them are able to obtain either A or B (Table 1). For case II, the entrainer feed is not pure because that would lead to an unfeasible process under given values of x D , R, and F E . [16][START_REF] Rodriguez-Donis | Thermodynamic insights on the feasibility of homogeneous batch extractive distillation, 2. Low-relative-volatility binary mixtures with a heavy entrainer[END_REF][START_REF] Shen | Extension of thermodynamic insights on batch extractive distillation to continuous operation. 1. Azeotropic mixtures with a heavy entrainer[END_REF] The feasibility of extractive distillation processes with a heavy entrainer for 1.0-1a and 1.0-2 classes has been studied in the literature 16,[START_REF] Shen | Extension of thermodynamic insights on batch extractive distillation to continuous operation. 1. Azeotropic mixtures with a heavy entrainer[END_REF][START_REF] Shen | Extension of thermodynamic insights on batch extractive distillation to continuous operation. 2. Azeotropic mixtures with a light entrainer[END_REF][START_REF] Knapp | Minimum entrainer flows for extractive distillation: A bifurcation theoretic approach[END_REF][START_REF] Laroche | Homogeneous azeotropic distillation: Comparing entrainers[END_REF][START_REF] Laroche | The curious behaviour of homogeneous azeotropic distillation -Implications for entrainer selection[END_REF][START_REF] Bruggemann | Shortcut methods for nonideal multicomponent distillation: 3. Extractive Distillation Columns[END_REF] . According to the aforementioned works, feasibility is assessed by looking at the volatility order regions, univolatility curves, and topological characters of the residue curve map. Figure 2 displays the residue curve map of both systems.

In application of the general criterion for extractive distillation for 1.0-1a class, 16 the product A (acetone) is recovered in the distillate because it is located in the region where acetone is the most volatile and there exists a residue curve going from the entrainer vertex E to A in the direction of decreasing temperatures. For the 1.0-1a class, a minimum F E /F is required to set at the point of stable extractive node near the E-A edge to make the separation feasible. For class 1.0-2, the feasibility criterion allows both A and B to be recovered depending on the location of the univolatility line α AB = 1; there is no entrainer flow Figure 3. Entropy production without considering reboiler and condenser for the system of acetone-methanol-water at boiling liquid (q = 1) and saturated vapor feed states (q = 0) as a function of (a) reflux ratio at F E /F = 0.55 and (b) as a function of F E /F at R = 2.76. rate limit to recover product A (acetone), but there exists a maximum entrainer flow rate to recover B (chloroform) because of the intersection of the univolatility line with the B-E edge.

For the class 1.0-1a system of acetone-methanol-water, at the fixed F E /F = 0.55, the reflux ratio is varied in the range of 2-10. At the fixed R = 2.76, the F E /F is varied in the range of 0.11-1.20. The entrainer feed temperature ranges from 298.15 to 373.15 K (boiling liquid). The main feed temperature ranges from 308.15 K to a temperature slightly above its saturated vapor feed temperature 330.3 K. The position of the entrainer feed tray is varied by keeping N F = 45. Then, the position of the feed tray is varied by keeping N FE =10

For the two cases of class 1.0-2 corresponding to acetonechloroform-benzene, the reflux ratio R is varied in the range of 2-10 at fixed F E /F. The F E /F is varied in the range of 0.2-1.2 at the fixed reflux ratio. The entrainer feed temperature ranges from 298.15 to 353.28 K (boiling liquid temperature). The total number of trays is first fixed at 30; feed tray is considered to be 20, and the entrainer feed tray is correspondingly varied. The total number of trays is varied by setting the entrainer and feed trays as 10 and 20, respectively.

RESULTS AND DISCUSSION

3.1. Column Section without Reboiler and Condenser. Figures 345illustrate the evolution of the entropy production, ΔS section_flow , in the column section excluding the reboiler and condenser for two thermal feed states (q = 0 and q = 1). In view of the fact that the entropy of mixing S mix is almost indistinguishable from entropy of separation S sep , their difference ΔS section_flow is shown on the right axis.

The analysis of the results shows that at a fixed F E /F rate, the entropy of mixing S mix and entropy of separtion S sep increase significantly. The entropy production is the difference between S sep and S mix in the column section; ΔS section_flow increases with the increase in reflux ratio as shown in Figures 3a,4a, and 5a. At a fixed R, the entropy of mixing S mix and entropy of separtion S sep increase slightly. The entropy production in the column section ΔS section_flow increases with the increase in F E /F (Figures 3b, 4b, and5b), and the extent of increase is more significant than that of the reflux ratio.

3.2. Extractive Column and Extractive Distillation Process. The entropy production of the column section with condenser and reboiler ΔS column and the total entropy production of the whole process, namely the whole column and the inflow We note that both ΔS column and ΔS total increase significantly with the increase in R; however, only a slight increase is observed because of the increase in F E /F. In addition, the R increase leads to an increase of the entropy production in the column section that is greater than that of the F E /F increase because of the augmentation of internal flows in the column section. At fixed reflux ratio, the internal liquid flowrate remains constant at the rectifying section of the column and varies moderately along the extractive and stripping sections with F E /F. For class 1.0-1a, within the range of F E /F from 0.1 to 1.1, the internal liquid flowrate varies from 1.441 to 2.464 kmol/h at the entrainer feed stage and from 2.399 to 3.418 kmol/h at the main feed stage. On the other hand, at fixed solvent rate, the internal liquid flowrate varies at the top of the column along with the reflux ratio. Within the range of reflux ratio from 2 to 10, the internal liquid flowrate varies from 1 to 5 kmol/h at the top of the column, from 1.513 to 5.423 kmol/h at the entrainer feed stage, and from 2.478 to 6.255 kmol/h at the main feed stage. For class 1.0-2, we notice the same behavior of internal flowrates along the extractive distillation column. Therefore, in order to make separation of azeotropic mixtures possible by extractive distillation with less entropy production, we recommend increasing the entrainer feed ratio and reducing the reflux ratio as low as possible.

The feed state significantly affects the extractive column entropy separation ΔS column . This happens because a boiling liquid feed has to be vaporized in the reboiler, whereas a saturated vapor feed does not, as ΔS B values show in Table 2.

As expected, the feed state does not significantly affect the total entropy ΔS total . This can be explained by the fact that the entropy production is computed with respect to the reference temperature T 0 for the whole process with heater and cooler. In the case of saturated vapor feed, if an ideal mixture is fed, the extra heat that is needed to vaporize the feed would be equivalent to the extra heat that was provided in the reboiler for the case of boiling the liquid feed; while those two heats are not equal to those for a nonideal mixtures, the difference remains small compared to the latent heat of vaporization of the feed. Accordingly, regardless of the thermal feed state when distillate and bottom products are cooled to room temperature, the entropy production varies very slightly, but the value is larger than that when the products are withdrawn to their bubble points. Therefore, we recommend extractive distillation process with vapor main feed state and recovered products at boiling temperature. Heat flow and energy efficiency of the extractive distillation process as a function of reflux ratio and entrainer/feed ratio are analyzed. One of the means of reducing energy consumption in the distillation process is to decrease the heat supplied to the reboiler. The minimum power input for separating a mixture into the required products is usually quite small in relation to the actual heat input; therefore, the efficiency of the separation process is low. In this section, we compute the minimum work and the lost work for both mixtures in different thermal feed states. Results for the system of acetone-methanol-water are presented in Table 3 and illustrated in Figure 9. For a system of acetone-chloroform-benzene, the main results are indicated in Table 3 and displayed in Figures 1011.

We can see that at a fixed entrainer/feed ratio, the minimum isothermal work for the system acetone-methanol-water shows a minimum reflux ratio close to 3.5. However, the energy loss steadily increases along with the reflux ratio. This can be observed for both thermal feed states (Figure 9a). At a fixed reflux ratio, for investigated thermal states of feed, both the minimum isothermal separation work and the enthalpy separation increase steadily with the entrainer/feed ratio. For LW, this increase is smaller than that of the case in Figure 9a. These results indicate that a reversible separation should be run at a reflux ratio of 3.5. Although not exactly the same as the optimal design result reported in the literature, this value of reflux ratio is within the range of the literature recommendation. [START_REF] Knapp | Minimum entrainer flows for extractive distillation: A bifurcation theoretic approach[END_REF][START_REF] Luyben | Comparison of extractive distillation and pressureswing distillation for acetone-methanol separation[END_REF][START_REF] Gil | Extractive distillation of acetone/methanol mixture using water as entrainer[END_REF] For the mixtures of class 1.0-2, Figure 10 suggests that an irreversible separation in lower degree should be run at a reflux greater than 6, and the entrainer flow rate should be set as low as possible (subcase I) or as high as possible (subcase II).

Considering the fact that the enthalpy of separation represents the difference between the heat supplied to the reboiler and that recovered from the condenser (Q B -Q C ), Figure 12 shows a maximum at a reflux ratio of 3.5 and a steady increase with the entrainer flow rate for class 1.0-1a. The enthalpy difference is more influenced by reflux ratio than by the value of F E /F. The amount of heat loss varies slightly when the feed is introduced to the column at the saturated vapor state (q = 0).

Figure 13 displays that (Q B -Q C ) is slightly influenced by the reflux ratio, whereas the increase in F E /F has an appreciable effect on this enthalpy difference.

The entropy production of system 1.0-2 at different operating conditions for distillate purity of 99% acetone for case I and chloroform for case II are given in Table 4.

3.3. Effect of Phase in the Main Feed. Concerning the thermal state of the main feed (the entrainer being fed as boiling liquid), ΔS section_flow is more important for a saturated vapor feed state than for a boiling liquid feed state. This is because, for a saturated vapor feed, the entropy inside the column section already incorporates the entropy contribution of the preheating of the feed to its saturated vapor state that is effectively noticed in the S F value (Table 2). In parallel, the reboiler entropy ΔS B is lower as no extra heat is required in the reboiler to vaporize the saturated vapor feed (Table 2). The entropy production and irreversibility of the column as a function of thermal feed state for the systems of classes 1.0-1a and 1.0-2 for given operational parameters are presented in Table 5.

The entropy production percentage generated in the reboiler, condenser, and tray column are computed from the entropy balance eqs 19-21 and reported in Table 6.

As shown in Table 6, for a distillation process, the reboiler percentage dominates, followed by the condenser and the column section. This can be explained by the fact that the change Table 3. Heat Flow of the Column for System 1.0-1a at R = 2.76 and F E /F = 0.55 and for System 1.0-2 case I at R = 5 and F E /F = 0.9 and case II at R = 5 and F E /F = 1.1 (in Kilojoules per Hour). in temperature in the reboiler and condenser is greater than that in the column. The fact that the reflux ratio R should be as low as possible is also validated by entropy production analysis. Indeed, R increases the internal flows inside the column and thus the energy required in both the energy exchanges inside the column and vaporization in the reboiler. Those in turn sharply increase the entropy. Similarly, F E /F should be kept as low as possible, but above the minimum value for feasibility (1.0-1a). However, it is important to keep it less than R. It impacts moderately the total entropy production ΔS total . Finally, the main feed state has no influence on ΔS total and there is no incentive to promote either a boiling liquid or a saturated vapor state to reduce the process irreversibility.

case thermal feed state Q C Q B Q loss W min,T0
It was expected that the liquid and vapor entropy flow profiles would have the same tendency as those of liquid and vapor flows in the extractive distillation column. The entropy of mixing and the entropy of separation vary moderately along the extractive and rectifying sections, while they change significantly in the stripping section irrespective of the thermal feed state. Furthermore, the lower values of the entropy flows are obtained in the case of a saturated vapor feed state. This can be explained by the decrease in the energy supplied to the reboiler and increase of the temperature in the stripping section for each investigated thermal feed state.

Figures 141516show the entropy production on each tray ΔS column,j and the temperature profile. The temperature profiles for class 1.0-1a are similar to those published by Luyben et al. [START_REF] Luyben | Comparison of extractive distillation and pressureswing distillation for acetone-methanol separation[END_REF] The entropy production profiles show that the entropy is mostly generated at the entrainer feed tray, at the main feed tray, and at the reboiler (Figures 14a-16a), and it results from the mixing of entrainer and feed flows with the internal column's flows. For both systems of classes 1.0-1a and 1.0-2, the temperature profiles increase from the top to the bottom of the column. We note that the thermal feed state has less effect on temperature profile for both investigated systems.

3.4. Effect of Entrainer and Feed Temperatures on the Entropy Production of the Extractive Distillation Process. In this section, we investigate the influence of the entrainer and feed temperatures on the entropy production of the extractive process.

Figures 17a and18a show that the entropy production of the column ΔS column is reduced with the increase of the entrainer feed temperature, whereas the total entropy production, ΔS total, does not change. In Figure 18a, ΔS total decreases as the entrainer temperature increases. This quantity is lower in the case of the saturated vapor feed state compared to that in the case of saturated liquid feed state for the same reason as mentioned before. These trends are not significant and there is no true recommendation for setting the entrainer feed temperature.

Figure 17b shows that the entropy production in the column for class 1.0-1a decreases steadily as the feed temperature increases in a liquid, and it drops significantly when the feed vaporizes. There is a very steep decrease during vaporization because the bubble and dew temperature difference of the equimolar feed is only 0.89 K. The steady decrease would mean that it is advantageous to introduce the feed at a saturated vapor state. However, when considering the process as a whole with the preheater and postcooler, ΔS total remains constant and again there is no true recommendation for setting the main feed temperature.

3.5. Influence of the Feed Trays Position on the Entropy Production of the Column. Finally, the effect of the entrainer and main feed tray positions on the entropy production is evaluated at a fixed total number of trays. That affects the extractive section length and could affect process feasibility or at least the product purity. However, for the case of class 1.0-1a, the process feasibility is rather dominated by the entrainer flow rate that should be above a minimum value. 16 The results are displayed in Figure 19.

The column entropy production, ΔS column, changes moderately and reaches a minimum value at N FE = 20, while the mole fraction of acetone in the distillate reaches a maximum of 0.956. The longer the extractive section, the closer the ending point of the extractive section to the water-acetone edge in the triangle graph; thus, the rectifying section composition is able to reach a point with higher acetone purity.

The column entropy production decreases as a function of the main feed tray position and the mole fraction of acetone in the distillate and increases when the number of stages in the extractive section increases near to stages 20 at the purity of 0.956 (Tables 7 and8).

For system 1.0-2 case II (Table 8), we notice a behavior oppostite that in Figure 19a for the system of class1.0-1a as there is a minimum in distillate composition corresponding to a maximum in ΔS column increase as the entrainer feed tray is changed. This may be related to the length of the column sections as this minimum appears when the three sections of the column have the same lengths (Figure 20).

For system of class 1.0-2, we observe that in both case I and case II, the entropy production ΔS column as a function of entrainer feed tray decreases and the total entropy product ΔS total increases as the total tray column number increases. This is due to the increase of the stripping section and the increase of the mole fraction of product in the distillate. For all three cases, the higher the product purity, the smaller the heat loss.

CONCLUSIONS

The entropy production of the extractive distillation column was analyzed for the separation of a minimum-and maximum-boiling azeotropic mixture by using a heavy entrainer (Serafimov's classes 1.0-1a and 1.0-2) by varying the reflux ratio, entrainer/ feed ratio, and the temperatures of entrainer and main feed. Most of the entropy is generated in the reboiler and condenser because of the temperature changes at the feeding points of the entrainer and main feed because of the irreversibility of mixing.

Increasing the reflux ratio increases the entropy production of the process because of the rise of the internal flows. The F E /F ratio has a similar but smaller effect on the entropy generation of the column.

The effect of mixing in the column section on the entropy production is more significant with increase in the reflux ratio than with increase in F E /F. Therefore, to reduce the entropy production and hence the energy consummation, we recommend maintaining the reflux as low as possible and increasing the solvent rate as much as possible to achieve the required purity.

Increasing the temperature of the main feed or the entrainer feed, both kept as liquids, reduces the entropy production of the whole column (sections with reboiler and condenser) and its irreversibility because it lowers the reboiler heat and entropy. When considering the whole process with inflows and outflows at the reference temperature, the feed temperature effect is negligible. The same can be said when the main feed vaporizes. Therefore, determination of an optimum value for setting the main feed temperature cannot be made here. That decision should be taken at the plant flowsheet level, where pinch analysis for energy integration could rule out the transfer of heat to the reboiler in favor of a preheating of the feed.

Computing the minimum isothermal work in order to find the less irreversible design, an optimal reflux R = 3.5 is found for class 1.0-1a, whereas R should be higher than 6 for the two subcases of class 1.0-2. However, the real irreversible separation has no such optimum as the energy loss always steadily increases with either the reflux or the entrainer flow rate for the systems of class 1.0-1a and two subcases of class 1.0-2.

Finally, the entropy generation is sensitive to feed tray positions of both the entrainer and main feed. No recommendation is clear, but they evidently affect the product purity through the length of each column section. It is noticed that for all three cases, the higher the product purity, the smaller the energy loss.

This work shows how entropy generation is sensitive to many design and operating parameters of the extractive distillation process. This work should help engineers to operate the process at an optimal set of parameters, reducing the energy loss.

The analysis of entropy generation carried out in this study is the starting point to define new operational strategies and design features that allow a more efficient use of energy. Future work is in progress to consider the process with the regeneration column and to investigate separations of azeotropic mixtures with light or intermediate boiling entrainers. Table 7. Entropy Production as a Function of Entrainer Feed Tray for System 1.0-2 (Case I) at R = 5 and F E /F = 0.9

Figure 1 .

 1 Figure 1. (a) Configuration of extractive distillation column; (b) schematic diagram of equilibrium stage in an adiabatic column.

Figure 2 .

 2 Figure 2. Residue curve map and univolatility line α AB = 1: (a) minimum-boiling azeotropic mixture acetone (A)-methanol (B) with heavy entrainer water (E) (class 1.0-1a); (b) maximum-boiling azeotropic mixture acetone (A)-chloroform (B) with heavy entrainer benzene (E) (class 1.0-2).

Figure 4 .

 4 Figure 4. Entropy production in the column section without reboiler and condenser for the system of acetone-chloroform-benzene (case I) as a function of (a) reflux ratio at F E /F = 1 and (b) as a function of F E /F at R = 8.

Figure 5 .

 5 Figure 5. Entropy production in the column section without reboiler and condenser for the system of acetone-chloroform-benzene (case II) as a function of (a) reflux ratio at F E /F = 1.2 and (b) as a function of F E /F at R = 10.

Figure 6 .

 6 Figure 6. Entropy production in the extractive distillation process as function of (a) the reflux ratio at F E /F = 0.55 and (b) as a function of F E /F at R = 2.76.

Figure 7 .

 7 Figure 7. Entropy production in the extractive distillation (case I) as function of (a) the reflux ratio at F E /F = 1 and (b) as a function of F E /F at R = 8.

Figure 8 .

 8 Figure 8. Entropy production in the extractive distillation (case II) as function of (a) the reflux ratio at F E /F = 1.2 and (b) as a function of F E /F at R = 10.

Figure 9 .

 9 Figure 9. Minimum work and lost work for system 1.0-1a as a function of (a) reflux ratio and (b) F E /F.

Figure 10 .

 10 Figure 10. Minimum work and lost work for system 1.0-2 case I as a function of (a) reflux ratio and (b) F E /F.

Figure 11 .

 11 Figure 11. Minimum work and lost work for system 1.0-2 case II as a function of (a) reflux ratio and (b) F E /F.

Figure 12 .

 12 Figure 12. Enthalpy of separation (Q B -Q C ) for system 1.0-1a as a function of (a) reflux ratio and (b) entrainer/feed flow ratio for the system acetonechloroform-benzene 1.0-2.

Figure 13 .

 13 Figure 13. Enthalpy of separation (Q B -Q C ) as a function of reflux ratio and entrainer/feed flow ratio for system 1.0-2 for (a, b) case I and (c, d) case II.

Figure 14 .

 14 Figure 14. (a) Entropy production profile and (b) temperature profile of the column operating at R = 2.76 and F E /F = 0.55 of class 1.0-1a system.

Figure 15 .

 15 Figure 15. (a) Entropy production profile and (b) temperature profile of the column operating at R = 5 and F E /F = 0.9 of class 1.0-2 case I system.

Figure 16 .

 16 Figure 16. (a) Entropy production profile and (b) temperature profile of the column operating at R = 5 and F E /F = 1.1 of class 1.0-2 case II system.

Figure 17 .

 17 Figure 17. Entropy production of the column and the extractive distillation process for system of class1.0-1a at R = 2.76 and F E /F = 0.55 as a function of (a) entrainer feed temperature for boiling main feed and for saturated vapor main feed and (b) feed temperature at T FE = 298.15 K.

Figure 18 .

 18 Figure 18. Evolution of entropy production as a function of entrainer feed temperature for system of class1.0-2 for (a) case I at R = 5 and F E /F = 0.9 and (b) case II at R = 5 and F E /F = 1.1.

Figure 19 .

 19 Figure 19. Entropy production and mole fraction of acetone separated in distillate for system 1.0-1a: (a) the entrainer feed stage position; (b) the main feed stage position.

  and De Nevers et al.:[START_REF] De Nevers | Lost work: A measure of thermodynamic efficiency[END_REF]

Table 1 .

 1 Column Specifications for Separation of the Azeotropic Mixtures of Acetone (A)-Methanol (B)-Water (E) and Acetone (A)-Chloroform (B)-Benzene (E).

	class 1.0-2

Table 2

 2

		. Entropy Production in the Column Section, Reboiler,
	and Condenser As Function of Thermal Feed State of System
	1.0-1a for R = 2.76 and F E /F = 0.55 and of System 1.0-2 for Case I at R = 5 and F E /F = 0.9 and for Case II at R = 5 and F E /F
	= 1.1 (in Kilojoules per Hour-Kelvin)
	case	thermal feed state ΔS section_flow	ΔS C	ΔS B	S FE	S F
	1.0-1a	q = 1	223.54	19.45	28.61	38.53	179.32
		q = 0	321.09	19.50	12.42	38.53	277.68
	1.0-2	q = 1	401.82	51.95	68.89	155.93	217.49
	case I	q = 0	486.91	51.96	56.65	155.93	308.11
	1.0-2	q = 1	435.18	57.82	80.62	202.37	218.94
	case II	q = 0	522.19	57.71	66.34	202.37	307.92

Table 4 .

 4 Entropy Production in Extractive Distillation Process of System 1.0-2 at Different Operating Conditions (in Kilojoules per Hour-Kelvin)

	case	R	F E /F	x D	ΔS C	ΔS B	ΔS section_flow	ΔS column	ΔS total
	1.0-2 case I	5	0.9	0.9856	51.95	68.89	401.82	149.23	153.71
		6	0.8	0.9860	60.58	80.28	387.61	172.36	176.75
		8	0.7	0.9863	68.87	91.17	392.24	219.27	223.59
	1.0-2 case II	5	1.1	0.99	57.82	80.62	435.18	152.31	157.32
		6	1.0	0.99	67.26	93.42	417.44	175.20	180.11

Table 5 .

 5 Entropy Production and Irreversibility of System 1.0-1a at R = 2.76 and F E /F=0.55 and of System 1.0-2 for Case I at R = 5 and F E /F = 0.9 and for Case II at R = 5 and F E /F = 1.1

	entropy production (kJ/(h K))	irreversibility (kW)

Table 6 .

 6 Entropy Production Percentage Generated in the Reboiler, Condenser, and Trayed Column

			entropy production (%)	temperature (K)
		thermal	column
	system	feed state	section condenser reboiler	T B	T C
	1.0-1a	q = 1	10.59	36.17	53.23	344.11	329.15
		q = 0	13.26	33.75	52.98	343.86	329.11
	1.0-2	q = 1	19.02	34.81	46.16	351.11	329.45
	case I	q = 0	17.39	39.52	43.09	351.08	329.47
	1.0-2	q = 1	9.10	37.96	52.93	347.01	334.39
	case II	q = 0	8.76	42.45	48.79	347.01	334.41

Table 8 .

 8 Entropy Production as a Function of Entrainer Feed Tray for System 1.0-2 (Case II) at R = 5 and F E /F =1.1

	5	0.9277	152.43	154.25	45990.3
	10	0.9856	149.23	153.71	45829.7
	15	0.9878	149.08	153.57	45785.4
	N FE	x D	ΔS column (kJ/(h K)) ΔS total (kJ/(h K)) Q loss (kJ/h)
	5	0.9903	152.31	157.32	46903.5
	10	0.9673	153.60	158.63	47295.8
	15	0.9926	152.11	157.12	46845.6

N FE

x D ΔS column (kJ/(h K)) ΔS total (kJ/(h K)) Q loss (kJ/h)

■ AUTHOR INFORMATION

Corresponding Author *E-mail: bhassba@yahoo.fr

Notes

The authors declare no competing financial interest.

■ NOMENCLATURE