F Espitalier

B Biscans

Sere Peyrigain

C Lagu6rie

Ternary diagram: alpha-(3-benzoylphenyl)-propionic acid (ketoprofen) in acetone-water mixtures at different temperatures. Experimental data and predicted results

Keywords: Multicomponent, Phase equilibria, Experimental data, Polar interactions, UNIQUAC model

Experimental data are determined for a ternary system, ketoprofen-acetone-water, at various temperatures and atmospheric pressure. Specific procedures are applied. The diagram exhibits five regions: one homogeneous, three two-phase (two liquid-solid and one liquid-liquid equilibria) and one three-phase zones.

The variation of the solubility of ketoprofen in acetone-water mixtures is interpreted by analysing the molecular forces induced in the solution according to the acetone mass ratio in the mixture.

The validity of semi-empirical models is tested for liquid-solid and liquid-liquid equilibria by comparing the calculated values with the experimental ones. The agreement depends on the precision of the estimated parameters used for calculations.

Introduction

Liquid-solid equilibria (LSE) and liquid-liquid equilibria (LLE) data are needed in design of crystallization processes. For specific industrial problems, these data are rarely found in literature and must be most of time determined experimentally.

This study deals with a crystallization process in which a pharmaceutical drug, ketoprofen called "Ke" in this work, dissolved in acetone is precipitated out by adding water, acting as an anti solvent, to the solution. The aims of this article are to present experimental equilibria data for the system acetone-water-drug and to examine the validity of the semi-empirical models UNIQUAC for predictions of LLE and LSE, at several temperatures.

Experimental

Materials

The pharmaceutical drug is a well-known antiinflammatory agent under generic name of ketoprofen. It is racemic a-(3-benzoylphenyl)-propionic acid (+). It is made up of three groups: a phenyl group (-C6H5), a benzoyl group (-C6H4-CO) and an acetic chain (-CH-COOH). It is provided by Rhrne-Poulenc Rorer Company.

Bidistilled water is used and synthesis grade acetone, with a minimum purity of 99.7%, is purchased from Soci&6 de Distribution de Service et de Recherche.

Procedure and techniques

Preliminary experiments were carried out, with binary systems (ketoprofen-acetone on the one hand and ketoprofen-water on the other hand), and with the ternary system (ketoprofen-acetonewater), in order to roughly position the different zones of the ternary diagram. These preliminary experiments allowed to set up the experimental techniques. Then, more precise measurements were achieved.

The solubility of ketoprofen in acetone was determined according to an usual procedure (Mullin, 1972) consisting in dissolving periodically small amounts of ketoprofen in acetone contained in a 25 ml stirred vessel maintained at a constant temperature ( T + 0.1 °C). When ketoprofen does not seem to dissolve any more, the suspension is still stirred for a few days more, during which the evolution of the concentration of ketoprofen in acetone is measured. The equilibrium is considered reached when the concentration remains constant. As the experiments proceed, loss of acetone due to evaporation is avoided by condensing the vapor. Sampling of the solution for the measurement of the concentration of ketoprofen in acetone requires stopping the stirring of the suspension for one hour and taking 1-3 ml from the solution with a syringe. The sample is then filtered through a 0.45 /xm porosity membrane and weighed at room temperature. The concentration of ketoprofen is obtained by weighing the dry solid after complete evaporation of the solvent.

The solubility of ketoprofen in water is determined according to the same experimental procedure as that described above. The concentrations of ketoprofen in water are measured by using a high performance liquid chromatograph (HPLC). The maximum relative deviation between all the data has been evaluated to 12% at 30 °C. This maximum can be explained by the difference between the solution temperature (30 °C) and the room temperature (about 20-25 °C) which can induce crystallization of the drug during sampling. However it can be noted that absolute deviations are only a few hundreds of ppm concentrations.

According to the number of the existing phases of the ternary system ketoprofen-acetone-water, three experimental procedures have been used. The first one is the dissolution procedure previously described for liquid-solid equilibria. The second one is a settling procedure for liquid-liquid equilibria. An acetone-water-ketoprofen mixture of about 100 ml, is stirred continuously for one hour in a reactor at a constant temperature controlled by less than + 0.1 °C. After one hour agitation, this mixture is poured into a thermostated settling flask. After twenty four hours settling, the liquid aqueous and organic phases are separated and stored. The concentrations of ketoprofen and water are determined respectively by weighing the dry extract and by measuring out with a Karl Fisher titrator. The third procedure used is a specific procedure for liquid-liquid-solid equilibria. An acetonewater-ketoprofen mixture, of about 100 ml is also continuously stirred for one hour in a particular reactor at constant temperature. The system is allowed to separate and settle in this reactor whose a schematic representation is shown in Fig. 1. The reactor is a small double jacketed glass vessel with facilities for sampling a few ml of the solution with syringes at various levels. So, syringes permit to take simultaneously samples of the two liquid phases without disturbing the equilibrium.

Results

The nature of the observed phases depends on the mass ratio of acetone in acetone-water mixtures ( R a ) .

For weight fractions of acetone in the acetone-water mixtures, R a, ranging approximately between 0 and 0.35, and between 0.70 and 1, a liquid-solid equilibrium is found. A liquid-liquid equilibrium is reached for values of R a between 0.35 and 0.70 and a liquid-liquid-solid equilibria are obtained in the same range of R a (0.35 < R a < 0.70).

Binary systems

Solubilities of ketoprofen in acetone and in pure water, at atmospheric pressure, are presented in Table 1. The range of temperatures corresponds to that used in the crystallization process studied. The upper limit is fixed by the boiling point of acetone (56 °C). Deviations on the concentration of the 1. The results show a high solubility of ketoprofen in acetone, and a very low solubility (a few hundreds of ppm) of ketoprofen in pure water. In both cases, the solubilities obtained increase with increasing temperature.

Ternary s y s t e m

Tables 2 -5 report all the experimental data with their absolute deviation, in ternary mixtures at several temperatures (10.1 + 0.1 °C, 20.2 + 0.2 °C, 30.2 + 0.2 °C and 48.9 + 0.1 °C). Table 2 shows that the solubility of the drug at 20.2 °C slightly increases with the weight fraction of acetone for R a < 0.24. The increase becomes more abrupt as Ra increases, up to a liquid-liquid phase splitting (R a = 0.24). The solubility reaches a maximum for a value of R a in the interval contained between 0.90 and 0.95 kg acetone k g -1 acetone-water mixture. All these results are plotted in the ternary diagram illustrated in Fig. 2 at 20.2 °C. So, in acetone-water mixtures, depending on the acetone mass ratio, two phases (liquid-liquid or liquid-solid phases) are in equilibrium. These liquid-liquid and liquid-solid zones surround a three-phase area (liquid-liquid-solid). The different one-phase, two-phase and three-phase regions are indicated in Fig. 2 by the regions I, II, III.

The same trends have been observed for the other temperatures (Tables 345). The curves corresponding to 10.1, 20.2, 30.2 and 48.9 °C have been gathered on the same ternary diagram in Fig. 3. In the liquid-solid regions, the solubility of ketoprofen increases with temperature. However the influence of the temperature in these solid-liquid regions is much more important for high values of R a on the right side of the phase diagram than for small ones on the left side.

! 56
A comparison between the liquid-liquid regions obtained respectively at 10.1 °C and 20.1 °C shows that this region is reduced as the temperature decreases. But this tendency is reversed when comparing the experimental points at 20.2 0(2 and 30.2 0(2. This last observation is probably due to the increase of experimental errors at 30.2 °C.

Discussion

Several observations can be drawn from the experimental data with binary and ternary systems. First, let us deal with the difference of the solubility of ketoprofen according to the nature of the pure solvent used in the case of binary solutions.

The structure of the crystals has been modeled by using a molecular simulation software [START_REF] Cavalier-Frontin | Prediction of the best linear precursor in the synthesis of cyclotetrapeptides by molecular mechanic calculations[END_REF]. It has enabled us to build an elementary lattice of a crystal and a combination of elementary lattices. The atomic coordinates of ketoprofen crystal used have been given by [START_REF] Briard | Ketoprofene[END_REF], from a crystallographic study. This representation shows that the crystal exhibits more numerous hydrophobic faces (-C6H 5) than hydrophilic ones (-COOH). So water keeps its maximally hydrogen-bonded and voluminous structure in front of the hydrophobic faces and the drug is weakly soluble in water. On the contrary, acetone exhibits charges all along its ,o 0,0 0,2 0,4 0,6 0,8 1 Fig. 5. Enthalpy of mixing data of acetone-water mixtures vs. acetone mass ratio, R a at 20 °C [START_REF] Timmermans | The physico-chemical constants of binary systems in concentrated solutions[END_REF].

H I Ell.-C-C -H a tO I N .
structure so that hydrogen bonds are created with the ketoprofen molecules. Fig. 4 gives a schematic representation of the interactions occuring.

We have calculated the solubility of ketoprofen in acetone versus temperature, in the case of an ideal solution. The experimental solubility is 40% higher than the calculated one. This difference may be explained by the strong polar solvent-drug interactions which cannot be neglected when calculating activities of the components of the system [START_REF] Bustamante | Prediccion de la solubilidad seghn Martin: Aplicacibn al ketoprofeno en mezclas polares[END_REF].

In the case of the ternary system, it can also be referred to interactions between acetone and water. Mixtures of both species exhibit changes of structure with acetone mass ratio, R a. For example, these changes of structure affect the enthalpy of mixtures. Indeed, the study of the enthalpy of acetone-water mixture, AHmi x, presents a particular behaviour versus acetone mass ratio as given in Fig. 5 [START_REF] Timmermans | The physico-chemical constants of binary systems in concentrated solutions[END_REF]. It shows that AHmi x is negative for R a < 0.85 and becomes positive for R a >__ 0.85. It can be assumed that the enthalpy of mixing, AH,~ x, is the result of two additional thermal effects [START_REF] Franks | The structural properties of alcohol-water mixtures[END_REF]: the endothermic destruction of water-water hydrogen bonds and the exothermic formation of rather strong and well-organized acetone-water hydrogen bonds. It may be inferred that intercomponent attractions are dominant factors in the formation of acetone-water mixtures and in the formation of ketoprofen-acetone water mixtures.

Fig. 5 brings to the fore three particular points marked C1, C2, C3. Point C2 corresponds to R c2 = 0.85 for which the enthalpy is equal to zero. Points C 1 and C3 are respectively the minimum for R cl = 0.45 and the maximum for Ra c3 = 0.92 of the enthalpy curve. These particular ratios, Ra c~,

C2 C3
R a , R a , can be compared to particular ratios, Ra Tl, R~, R T3, appearing in the ternary diagram of Fig. 2. c~ In the acetone-water mixture, for an acetone mass ratio less than R a , the enthalpy of the mixture is negative and its absolute value increases as the acetone mass ratio increases: the number of hydrogen bonds between water molecules and acetone molecules increases. In the presence of ketoprofen, whose molecule has a ketone functional group in the acetic chain, the number of hydrogen bonds between water molecules, acetone molecules and ketoprofen molecules also increases. Thus, the solubility of ketoprofen in the mixture increases. In fact, the ternary diagram shows that the maximum solubility of ketoprofen is observed with an acetone mass ratio, R~ t, equal to approximately 0.24.

For R a between Rct and Ra c2, i.e. between C1 and C2, the number of hydrogen bonds between water molecules and acetone molecules is important but decreases as the absolute value of Anraix decreases. In fact, in the ternary system, two liquid phases are in equilibrium for R a between 0.24 and 0.67. Moreover liquid-liquid phase splitting occurs for Ra T1 = 0.24, at 20.0 °C. For an acetone mass ratio equal to R c2 (point C2 in the Fig. 5), AHmi x is equal to zero. In the ternary mixture, the ratio corresponding to the change of two liquid phases in one liquid phase is 0.67. It can be compared with the point where AHm~ x is equal to zero.

As the acetone mass ratio increases between Ra c2 and R C3, the positive enthalpy of binary mixture increases: the number of hydrogen-bonded water molecules decreases; thus in the ternary mixture, the solubility of ketoprofen increases. On the ternary diagram the maximum solubility is obtained for R T3 equal to 0.90-0.95.

For an acetone mass ratio above 0.92, the number of hydrogen-bonded water molecules increases, and this increase explains the observed decrease of the solubility of ketoprofen in the ternary mixture.

The previous comparisons between the particular ratios appearing in the enthalpy diagram and those obtained in phase diagram, have shown the influence of ketoprofen. Indeed, the presence of ketoprofen in the mixture moves back the positions of the particular ratios obtained in the enthalpy diagram.

All this development has been made for a temperature of 20 °C. The behaviour of the ternary system at 10.1 or at 30.2 °C is similar to the one at 20.2 °C as shown in Fig. 3. But the particular ratios, RaT l, R~, R T3 a r e function of temperature.

Representation model for LSE

In the case of solute solid, the condition of equality of partial fugacities at equilibrium leads to the reduced relation [START_REF] Walas | Phase equilibria in chemical engineering[END_REF]:

, L=exp( m(1 1))

Xsgs ~ T m T (1)
with xL: mol fraction of the solute, S, in the solution TsL: activity coefficient of the solute, S, in the solution AHm: melting enthalpy of the pure solid (J mol -l)

Tm: melting temperature of the solid (K)

The required input data on ketoprofen are the melting enthalpy, A H m, the melting temperature, Tin, and the activity coefficient, ca~ ')tKe.

A H m and T m have been obtained for pure solid component by differential scanning calorimetry (DSC). They are respectively equal to 28,226 + 254 J mol -I and 94.21 + 0.5 °C.

The LSE is calculated to find the optimal value of parameters by minimizing the difference between computed and experimental activity coefficients, T~ ale -T~ xp.

Using the same model for liquid phase activity coefficients, calculated either from measurements of vapor-liquid equilibria (VLE) or liquid-liquid equilibria (LLE), or liquid-solid equilibria [START_REF] Walas | Phase equilibria in chemical engineering[END_REF], we have considered reasonable to choose the UNIQUAC model [START_REF] Abrams | Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems[END_REF] to estimate 3t~ ~ac in the liquid phase.

The UNIQUAC model has a combinatorial contribution to the activity coefficients, essentially due to the differences in size and shape of the molecules, and a residual contribution essentially due to energetic interactions:

In ~/i = In Ti c + In T 3 (2)
The combinatorial term can be written as follows:

Z 0i (~i In TiC = In q~i + - * qi * i n --+ l i ---* ~x j l j (3) X i 2 $i Xi j
where z is the coordination number, equal to 10;

Z qi)-i) (4) 0 i and thi are the molecular surface area and molecular volume of each component i with r i X i

4'i = (5)

Exjq J qi xi

0 i = ~ (6)
E xj qj J x~ is the mol fraction of the component i.

Pure components parameters r i and qi are, respectively, determined from measurements of molecular van der Waals volumes and molecular surface areas. They are calculated as the sum of the group-volume and group-area parameters, R k and Qk: r i = Eu(ki)Rk and qi = EU(ki)Qk ( 7)

where u °), always an integer, is the number of groups of type k in the molecule i. Group parameters R k and Qk are obtained from van der Waals group volumes V k and surface areas A k [START_REF] Bondi | Van der Waals Volumes and Radii[END_REF]. The expression of R k and Qk can be given as follows:

Vk e k = 15.17 The normalization factors appearing in Eqs. ( 8) and ( 9), 15.17 and 2.5* 10 9 are those derived by [START_REF] Abrams | Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems[END_REF]. However, since data for the benzoyl group are not available, this group has been decomposed into two independent groups, C6H 4 and C = O, The van der Waals group volumes, Vk, and surface areas, A k of > C = O group are given by [START_REF] Bondi | Van der Waals Volumes and Radii[END_REF]. The other volume and surface factors of others groups have been found in [START_REF] Walas | Phase equilibria in chemical engineering[END_REF].

The expression of the residual term, in UNIQUAC equation, is:

with

~' ij = exp( uiJ'e'-T ) --nil (10)
(11) The uij are the interaction parameters between the two components i and j. They can be found in tables. These factors, r i and qi, are reported in Table 6. The calculated values of ketoprofen volume and surface factors are high compared with the values obtained for the other components.

Representation of the ternary system

The validity of the semi-empirical models which represent LLE and LSE have been tested. The parameters, uij and uji of the tested semi-empirical UNIQUAC model are not available in tables and have been evaluated for each particular binary system. The parameters of the system acetone-water are deduced from VLE data using the PROREG regression tool designed by PROSIM A., 1993). For the systems, ketoprofen-acetone and ketoprofen-water, these parameters were computed from the experimental mutual solubility data, by minimization of the

(~/~C --~/~(xeP ) ( ' ysCo~lvCent --'~seo~Pen t )
differences and

,~exp ,~exp Ke tsolvent

The parameters, aij and aji, obtained are given in Table 7.

Table 9 Relative deviations between the calculated and the experimental concentrations of ketoprofen function of R a at 20.2 °C w~ -woxp~ ) The calculated and experimental solubilities in the binary liquid-solid zones are shown at 20.2 °C in Fig. 6. It is important to note that the form of the calculated curve is very similar to the experimental one. Moreover this curve seems able to describe all regions, even the liquid-liquid region. This continuity can be explained by that of the thermodynamic equations used.

However, when comparing with experimental data, the UNIQUAC model gives underestimated concentrations of ketoprofen when the mass ratio of acetone is higher than 0.75. The relative deviations between the calculated and the experimental concentrations of solute vvKe ~ rvK¢ ~v~x~" * 100 as a function of R a are reported in Tables 891011, for the different tempera-

" K e tures. For acetone-water mixtures with a high mass ratio of acetone, the deviation increases as R a decreases. So the concentrations of ketoprofen are underestimated (until 80% at 10.1 °C). For acetone-water mixtures with R~ less than 0.075, there is a good agreement between experimental and content (hundreds of ppm), the activity coefficients of ketoprofen are very high (about 10000). It is well known that these semi-empirical models do not give good predictions for high activity coefficients. So, in order to take into account the overestimation of the interaction parameters, these ketoprof e n -w a t e r parameters have been re-calculated from experimental data obtained in the ternary system, at each temperature, and in the range of high R a value (R a > 0.70). Indeed, the highest absolute deviations are obtained in this range.

Tables 1 2 -1 5 report the absolute and relative deviations between calculated and experimental data, as a function of R a, after adjustment of the interactions parameters ketoprofen-water and water-ketoprofen respectively at 10.1, 20.2, 30.2 and 48.9 °C. The absolute deviations are considerably reduced for high values of R a and the agreement is quite good. The same adjusted parameters have been used to calculate the concentrations in the smallest range of R a. The results remain reasonably good, for the range of considered concentrations. For 48.9 °C, only few experimental points are available Table 15 Relative deviations between the calculated and the experimental concentrations of ketoprofen as a function of R a at 48.9 °C (after adjustment of the interaction parameters between ketoprofen and water) because this temperature is very close to the upper limit of stability of the system. So, in that case, the predicted values must to be regarded with less confidence.

LLE evaluation method

As LLE data on the binary mixtures of ketoprofen-acetone and ketoprofen-water mixtures, is not available, the parameters of the UNIQUAC model were evaluated from smoothing experimental LLE data at 20.2°C. These parameters are presented in Table 16. They have also been used to calculate the LLE at the other temperatures (10.1 and 30.2 °C) by using PROPHY software (ProSim S.A., 1993).

LLSE evaluation method

Figs. 6-9 present predicted and experimental curves for both LLE and LSE respectively at 20.2, 10.1, 30.2 and 48.9 °C. They show that liquid-liquid equilibria slightly depend on the temperature. The superposition of LLE and LSE predicted curves should allow us to obtain the complete ternary diagram. In the range of high Ra, the intersection point, T2, between the LLE and the LSE predicted curves, is in good agreement with the experimental point. But for small Ra, the intersection between LLE and LSE curves creates a point T1 that does not correspond to the experimental point. The level of agreement between the calculated and experimental intersection points (T1 and T2) depends on the results of prediction of LSE previously discussed. Since T2 corresponds to the experimental point, TI can be deduced by the following procedure: by creating the first intersection point T2 (in the Fig. 6, for example at 20.2 °C), LLE allows to join the corresponding point T1, by the tie-line. To avoid the discontinuity between LLE and LSE at small R a values, the tie-line has been extended up to the calculated LSE curve.

Conclusion

Experimental and calculated equilibrium data have been determined for the organic system ketoprofen-acetone-water at four temperatures (10.1, 20.2, 30.2 and 48.9 °C).

The experimental diagram exhibits five regions: one homogeneous, three two-phase (two liquidsolid and one liquid-liquid equilibria) and one three-phase zones. Specific experimental procedures have been applied to determine the liquid-liquid and the liquid-liquid-solid equilibria.

The behaviour of the mixtures has been explained by ketoprofen-water, ketoprofen-acetone and acetone-water interactions (hydrogen bonding).

We applied the UNIQUAC model to calculate the LSE and LLE for this system. For LSE, since the interaction parameters, ketoprofen-water and ketoprofen-acetone did not exist, they have been evaluated for each binary system from experimental data. To obtain a better agreement between experimental and calculated data, the interaction parameters ketoprofen-water have been recalculated from experimental data in the ternary system, at each temperature. After adjustment of these last parameters, the results of the semi-empirical model UNIQUAC are in agreement with experimental LSE data. For LLE, we have evaluated the missing parameters from smoothing experimental data at 20.2 °C (PROSIM). The obtained parameters have been used to calculate the LLE at the other temperatures. Finally prediction of the temary diagram can be carried out by the presented methods.

List of symbols

  Fig. i. Schematical representation of the reactor used to establish liquid-liquid-solid equilibrium.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Five different zones in the ternary diagram studied: one L area, two LSE area, one LLE area and one LLSE area. Experimental data at 20.2 °C.

Fig. 4 .

 4 Fig. 4. Schematic representation of molecular interactions between the two components: ketoprofen-acetone.

Fig. 6 .

 6 Fig.6. Predicted LLE and LSE data (after adjustment of the interaction parameters between ketoprofen and water) and experimental data at 20.2 °C.

  c a l c u l a t e d d a t a ( r e l a t i v e e r r o r is l o w e r than 10.%). H o w e v e r for R a h i g h e r than 0.075, the k e t o p r o f e n c o n c e n t r a t i o n s a r e u n d e r e s t i m a t e d too. A c c o r d i n g to the p r i n c i p l e o f the m e t h o d , the c a l c u l a t e d c o n c e n t r a t i o n s d i r e c t l y d e p e n d on the e s t i m a t e d U N I Q U A C p a r a m e t e r s . A n a n a l y s i s o f the v a l u e s o f these p a r a m e t e r s can e x p l a i n the r e p o r t e d e r r o r on the p r e d i c t e d values. In b i n a r y m i x t u r e s k e t o p r o f e n -w a t e r , with a l o w k e t o p r o f e n

Fig. 7 .Fig. 8 .Fig. 9 .

 789 Fig. 7. Predicted LEE and LSE data (after adjustment of the interaction parameters between ketoprofen and water) and experimental data at 10.1 °C.

  constant defined in Eq. (4) (-) number of experimental data (-) UNIQUAC group surface parameters of pure component i (-)

Table 3

 3 Solubility of ketoprofen in acetone-water mixture at 10.1 °C

	(a)
	Experimental liquid-solid equilibrium at 10.15 4-0.15 °C
	W ~	R a
	(kg ketoprofen/	(kg acetone/
	kg solution)	kg acetone-
		water mixture)
	105 X 10 -6 -t-3 X 10 -6	0.023
	199 × 10 -6 4-6 × 10 -6	0.072
	623X 10 -6 +31×10 -6	0.151
	2 182X l0 -6	0.219
	0.410	0.727
	0.427	0.773
	0.444	0.811
	0.447	0.888
	0.423	0.906
	0.447	0.960
	0.416	0,967
	(b)
	Experimcntal liquid-liquid-solid equilibrium at I O. I + O. l °C
	w~:~	r p	W~o °r~	R °r~
	(kg ketoprofen/	(kg acetone/	(kg ketoprofen/	(kg acetone/
	kg solution)	kg acetone-	kg solution)	kg acetone-
		water mixture)		water mixture)
	0.073	0.462	0.269	0.606
	(c)
	Binodal compositions of the experimental liquid-liquid equilibrium at 10.0 + 0.1 °C
	w ~q	Rp	w~o °~	R °rg
	(kg ketoprofen/	(kg acetone/	(kg ketoprofen/	(kg acetone/
	kg solution)	kg acetone-	kg solution)	kg acetone-
		water mixture)		water mixture)
	0.089 + 0.00001	0.474	0.304:1:0.00006	0.657

Table 4

 4 Solubility of ketoprofen in acetone-water mixture at 30.2 °C

	(a)
	Experimental liquid-solid equilibrium at 30.15 5:0.15 °C
	Wi~e	Ra
	(kg ketoprofen/	(kg acetone/
	kg solution)	kg acetone-
		water mixture)
	261X 10 -6 5:27X 10 -6	0.017
	261X 10 -6 5:17.10 -6	0.026
	0.550	0.669
	0.577	0.730
	0.596	0.747
	0.589	0.796
	0.576	0.896
	0.602	0.902
	0.589	0.934
	(b)
	Wi~eaq	Raaq	w,, Ke°rg	-' aR°rg
	(kg ketoprofen/	(kg acetone/	(kg ketoprofen/	(kg acetone/
	kg solution)	kg acetone-	kg solution)	kg acetone-
		water mixture)		water mixture)
	0.038	0.342	0.452	0.646
	(c)
	Binodal compositions of the experimental liquid-liquid equilibrium at 30.4 5: 0.1 °(2
	WK~Ie	ga aq	Wl~e °rg	-' aR°rg
	(kg ketoprofen/	(kg acetone/	(kg ketoprofen/	(kg acetone/
	kg solution)	kg acetone-	kg solution)	kg acetone-
		water mixture)		water mixture)
	0.058 + 0.0007	0.367	0.359 + 0.004	0.624
	Table 5
	Solubility of ketoprofen in acetone-water mixture at 48.9 °(2: experimental liquid-solid equilibrium
	WZ		R a (kg acetone/
	(kg ketoprofen/kg solution)		kg acetone-water mixture)
	0.703		0.852
	0.710		0.924
	0.701		0.950
	0.695		0.967

Experimental liquid-liquid-solid equilibrium at 30.0 + 0.1 °C

Table 8

 8 Relative deviations between the calculated and the experimental concentrations of ketoprofen

				163
			(l,I/cal _ IMexp~ ) k"Ke "Ke ]
			w'exp -Ke	as a
	function of R a at 10.1 °C
	Ra (kg acetone/	Absolute deviations	Relative deviations
	kg acetone-water)	(kg ketoprofen/kg solution)	on concentration (%)
	0	2X10 -6	2
	0.023	1 × 10 -6	1
	0.072	37 X 10 -6	19
	0.151	291 X 10 -6	47
	0.219	1 563× 10 -6	72
	0.727	0.327	80
	0.775	0.292	68
	0.811	0.257	58
	0.888	0.147	33
	0.906	0.102	24
	0.960	0.088	20
	0.967	0.055	13
	1	0.001	0.2
	Company (ProSim S.

  Table 12Relative deviations between the calculated and the experimental concentrations of ketoprofen as a function of R a at 10.1 °C (after adjustment of the interaction parameters between ketoprofen and water)

	Ra(kg acetone/	Absolute deviations	Relative deviations
	kg acetone-water)	(kg ketoprofen/kg solution)	on concentration (%)
		AAD = 2 650× 10 -6	ARD --820
	0	1 001 × 10 -6	1 164
	0.023	1 228× 10 -6	1 170
	0.072	1 865 × 10 -6	937
	0.151	3 566 × 10 -6	572
	0.219	5 589× 10 -6	256
		AAD = 0.013	ARD = 2.9
	0.727	0.011	3
	0.775	0.015	3
	0.811	0.005	1
	0.888	0.002	0.3
	0.906	0.017	4
	0.960	0.037	8
	0.967	0.013	3
	1	0.001	0.2
	Table 11 Relative deviations between the calculated and the experimental concentrations of ketoprofen	(c. ) (w~ -~' ~ "'Ke ] "Ke U/exp	as a
	function of R a at 48.9 °C
	R a (kg acetone/	Absolute deviations	Relative deviations
	kg acetone water)	(kg ketoprofen/kg solution)	on concentration (%)
	0.852	0.007	1.0
	0.924	0.002	0.2
	0.950	0.003	0.4
	0.967	0.005	1
	1	0.011	2

Table 13

 13 Relative deviations between the calculated and the experimental concentrations of ketoprofen as a function of R a at 20.2 °C (after adjustment of the interaction parameters between ketoprofen and water)

	R a (kg acetone/	Absolute deviations	Relative deviations
	kg acetone water)	(kg ketoprofen/kg solution)	on concentration (%)
	0	AAD = 2 197× 10 -6	ARD = 481
	0.016	916× 10 -6	738.5
	0.024	1048 × 10 -6	691.8
	0.072	1111 × 10 -6	628.0
	0.163	1644× 10 -6	487.9
		3099× 10 -6	219.8
		AAD = 0.009	ARD = 1.7
	0.755	0.007	1.5
	0.786	0.003	0.5
	0.868	0.011	2.1
	0.910	0.007	1.5
	0.941	0.014	2.6
	0.961	0.003	0.6
	1	0.015	3.5

Table 14

 14 Relative deviations between the calculated and the experimental concentrations of ketoprofen as a function of R a at 30.2 °C (after adjustment of the interaction parameters between ketoprofen and water)

	R a (kg acetone/	Absolute deviations	Relative deviations
	kg acetone water)	(kg ketoprofen/kg solution)	on concentration (%)
		AAD = 904.3 × 10 -6	ARD = 376
	0	813 X 10 -6	361
	0.017	949 × 10 -6	363
	0.026	1 051 × 10 -6	403
		AAD --0.010	ARD --1.8
	0.669	0.005	1
	0.730	0.001	0.2
	0.747	0.012	2
	0.796	0.004	1
	0.896	0.011	2
	0.902	0.017	3
	0.934	0.014	2
	1.0	0.019	4

Acknowledgements

The authors wish to acknowledge Rhrne-Poulenc-Rorer Company and the French Ministry of University Education and Research (MESR) for their financial supports to this project.


Keywords: induction machine, bearing fault, signal processing, current, voltage, phase modulation, high-resolution algorithm

In this paper, we propose to perform early fault diagnosis using high-resolution spectral analysis of the stator current to detect bearing faults in electrical induction machine. While most research works focus on mechanical vibration analysis, the originality of our work relies on the use of highresolution methods to detect modulations in the stator current. We present the results obtained for real data to detect inner and outer raceway bearing defects made articially as well as bearing defects obtained through on-site ageing. The obtained results show that the proposed method yields better detection than classical spectum analysis.

I. INTRODUCTION

owadays, induction motors are widely used in different industry applications due to their simple construction, high reliability and the availability of power converters based on efficient control strategies. In order to sustain and increase the productivity, reliability and safety of industrial installations, a permanent condition monitoring of critical motors is necessary. This is the main reason why research on condition monitoring of electric motors has been widely studied for decades. These researches and developments conducted in universities and in industries has yielded means for predictive condition monitoring and fault detection algorithms. Many different devices and systems are being developed and are used in many kinds of applications such as transportation, power generation and so on. A general review of monitoring and fault diagnosis techniques can be found in [START_REF] Nandi | Condition monitoring and fault diagnosis of electrical machine[END_REF], [START_REF] Benbouzid | What stator current processing-based technique to use for induction motor faults diagnosis?[END_REF]. Moreover, according to an IEEE motor reliability study [START_REF]Reporton large motor reliability survey of industrial and commercial installations[END_REF], bearing faults have been shown to be the most frequent faults in induction machines (41%) followed by stator (37%) and rotor faults (10%).

The aim of this research work is the early detection of bearing faults in electrical induction machines using signal processing tools. Our approach is mainly based on processing electrical quantities, i.e. currents and voltages, instead of analysing Mounir Djeddi and Pierre Granjon are with the Gipsa-lab, int the Institut National Polytechnique de Grenoble (INPG), 961 rue de la Houille Blanche 38402, Saint Martin d'Hères, Grenoble, France.

(e-mail: mounir_djeddi@ieee.org, granjon@lis.inpg.fr).

Benoit Leprettre is with Schneider Electric -Electropole research center 38050 Grenoble, France. (e-mail: leprettre@schneider-electric.fr).

vibration signals, acoustic noise, magnetic flux or temperature which necessitate additional sensors on the motor.

Firstly, a short overview of bearing fault types is given in section II, followed by the characteristic vibration frequencies and the existing fault model developed by R. R. Schoen [START_REF] Schoen | Motor bearing damage detection using stator current monitoring[END_REF]. In the sections III, the theoretical background for a new fault model is presented and new expressions for the frequency content of the stator current in case of bearing faults are obtained. The general algorithm applied to stator current in order to early detect bearing faults is developed and exposed in section IV. Finally, experimental results with different fault types are given in section V, validating different aspects of the theoretical approach. In section VI, we give some conclusions.

II. BEARING FAULT TYPES AND CHARACTERISTIC FREQUENCIES

A. Bearing Fault Types

The different faults occurring in a rolling-element bearing can be classified according to the damaged element as : 1-outer raceway defect 2-inner raceway defect 3-ball defect The fault is assumed to be modelled as a small hole created from a missing piece of material on the corresponding element.

The definition of these fault types is somehow artificial regarding real bearing damages. Nevertheless, this is useful for distinguishing the different bearing fault effects on the machine. In a realistic case, one can imagine that a combination of these three effects is more likely to be found. In the following analysis, we will only focus on the outer and inner raceway defects which were artificialy produced (see Fig. 1). We will also present some results based on real defects obtained by in-situ bearing ageing.

Bearing Fault Diagnosis in Induction Machine Based on Current Analysis Using High-Resolution Technique

Mounir Djeddi, Member IEEE, Pierre Granjon, and Benoit Leprettre N

B. Characteristic Frequencies of bearing faults

A characteristic frequency c f can be associated with each type of bearing fault. This frequency correspond to the periodicity of occurence of the abnormal physical phenomenon related to the existence of the fault. For exemple if one considers a hole on the outer raceway, then, as the rolling elements move over the defect, they are regularly in contact with the hole which produces an effect on the machine at a given frequency. The characteristic frequencies are functions of the bearing geometry and the mechanical rotor frequency r f . A detailed calculation of these frequencies can be found in [START_REF] Li | Neural Network based motor rolling bearing fault diagnosis[END_REF]. The frequencies of the two fault types considered here, are given by Outer raceway : In this section, we establish a model for the stator current in the case of bearing faults in the induction machine as it has been derived in [START_REF] Blödt | Models for Bearing Damage Detection in Induction Motors Using Stator Current Monitoring[END_REF]. This enables to identify the frequencies of the spectral components and their amplitudes.

1 cos (1) b b O r c N D f f E D β   = -     Inner raceway 1 cos (2) b b I r c N D f f E D β   = +    
Here, we suppose that the faults provoke small variations in the mechanical torque as well as small eccentricities in the rotor.

In order to establish the mathematical model of the faults, we first suppose that all magnetic and electrical quantities are purely sinusoidal.

In the presence of mechanical torque variations only, one can write the stator current phasor as follows:

( ) Hence, torque variations due to bearing fault induce phase and therefore frequency modulations in the stator current as descibed by equation [START_REF]Reporton large motor reliability survey of industrial and commercial installations[END_REF]. The goal of this work is to detect these modulations in order to check the existance of a fault. These different models have been used to generate current signals in order to validate the proposed approach described below.

( ) 0 0 0 2 d d 2 (3) t v s t t s p j t u u v J j t S S R I t I e I e πυ ε πυ Γ   Γ   - +     - Φ   ∫∫ = +

IV. THEORETICAL STUDY II : SUBSPACE ESTIMATION TECHNIQUE

The goal of the proposed approach is to detect frequency modulations induced by the bearing fault. Because of the well known limitations of the Fourier analysis, we consider here a different approach based on subspace techniques which are known to be very powerful techniques [START_REF] Bracale | On Some Spectrum Estimation Methods for Analysis of Non-stationary Signals in Power Systems, Part I: Theoretical Aspects[END_REF]. The method utilized is called the Root-MUSIC estimator.

The fault detection scheme is mainly based on three steps : -signal filtering using a lowpass FIR digital filter in order to eliminate the different harmonics and to verify the purely sinusoidal assumption, -a sliding window Root-MUSIC algorithm in order to precisely estimate the instantaneous frequency of the stator current, -computation of the power spectral density (PSD) of the previously estimated instantaneous frequency. This method is illustrated by Fig. 3 :

The sliding window Root-MUSIC algorithm :

Because the bearing defect induces frequency modulations in the stator current, our objective is to determine the existance of these modulations and their characteristics compared to the carateristics of the healthy machine signal. The main idea of the proposed estimation approach is to apply a sliding window to the stator signal and compute for each block of data the frequency content using a high-resolution algorithm known as the Root-MUSIC algorithm. Hence, as the window moves, we obtain a temporal evolution of the frequency on which we apply the fourier transform as illustrated in Fig. 4.

The application of the algorithm to each block considers that the signal is made of a sum of p sinusoidal components. This can be written as follows : 1 ;

(

) i P j i i i i i x A n A A e φ = = + = ∑ s where [ ] i i M j j i e e s 7

+ > p M

) correspond to the noise subspace and the p largest (all greater than n σ ) correspond to the signal subspace. The algorithm performs eigenspace analysis of the signal correlation matrix in order to estimate the signal frequency content. The correlation matrix can be written as :

(9) The MUSIC method uses only the noise subspace to estimate frequencies of sinusoidal components. The MUSIC pseudospectrum is given by : By substituting, the resulting equations can be solved for i P ( power of the component) using the following expression :

H H x s s s n n n E E E E = Γ + Γ R
{ } * 2 1 1 E ( 1 5
)

P M T T x i i i i n i i i n i i R AA P σ σ = = = + = +

∑ ∑ s s I s s I

In the estimation process, a window is passed through the analyzed signal and then each frequency and power values are computed for this sliding window [START_REF] Flandrin | Signaux non stationnaires analyse temps-fréquence et segmentation[END_REF]. Since the estimation of the correlation matrix is important, performance study has been conducted for different lengths of windows and SNR, where the noise is assumed white Gaussian.

In order to chose the right correlation matrix estimator, we have computed the bias and variance of the frequency estimator based on different methods, the results are shown in Table I. According to the above tables, we conclude that the value of the sliding window is very important for the frequency modulation estimation. In our case we showed that its length must not be below Ns/50 which corresponds to almost one fundamental period of the signal.The performance of the tested estimators showed that the SNR must be greater than 15dB using the modified covariance technique for the estimation of the correlation matrix.

V. EXPERIMENTAL RESULTS

In this section, we present experimental results obtained from the analysis of electrical current of a test machine equipped with faulty bearing carrying artificial inner and outer raceway defects. We also conducted tests with industrially used bearings called "real defect" in the following which were replaced due to an unknown fault type problem. In that case, the vibration signal analysis showed a small peak at 33 Hz compared to the healthy machine vibration signal. In our experiemental analysis, we consider both 50Hz and 33Hz power supplies in order to asses the performance of our method for different power supply frequencies. The stator current is filtered using a lowpass FIR digital filter of order 30 with passband frequency pass f =160Hz and stopband frequency stop f =210Hz. This filter is obtained by leastsquares design method in Matlab, the sampling frequency is s f =16026Hz and the sliding window length is r N =20. In the following, we present the obtained results using the Root-MUSIC technique. Fig. 5 compares the power spectral densities of the filtered stator current of healthy machine and of a machine with an outer raceway defect. One can observe that the detection of defect from these spectra is very difficult. We observe in Fig. 7 that the detection of the inner raceway defect is still possible using the spectrum of the instantaneous frequency, even though the peak is very small. In Fig. 8, we can observe again that the real defect appears clearly in the spectrum of the estimated frequency. Moreover, according to the frequency value which is very close to the one observe in Fig. 6, one may suppose that this real defect is an outer raceway defect.

B. Power supply of fundamental frequency

= s f Hz

In order to assess the performance of the proposed approach, we considered a different power supply fundamental frequency. When the latter is at 33 Hz, the frequency of the real defect wich was at 33Hz with a fundamental frquency of 50Hz is moved to a new value which is equal to 33 2 /50=20 Hz. Fig. 9 shows the is the spectrum of the stator current which does not exhibit clearly the defect. In Fig. 10, we observe a very small peak in around 23 Hz, which approaches the theoretical value computed above.

VI. CONCLUSION

In this paper, we have investigated the detection of rollingelement bearing faults in induction motors by monitoring the stator current. An experimental study has been conducted on a test rig with several types of faulty bearings, by measuring electrical quantities such as stator current which exhibits frequency modulation due to torque oscillations induced by the defect. Indeed, the Fourier analysis showed that the spectrum of the stator current does not always yield to detectable defect frequencies because of their small magnitudes. The proposed approach takes advantage of poweful signal processing tool known as high-resolution techniques. The proposed algorithm relies on the estimation of the instantaneous frequency content based on sliding window high-resolution Root-MUSIC algorithm. The application of this approach lead to an effective method to detect artificially as well as real outer raceway and inner raceway defects. The detection of inner raceway defect was still possible even though much more difficult. This can be explained by the fact that inner raceway defects do not contribute energically enough in the phase modulation of the stator current.

Fig. 1 .

 1 Fig. 1. Artificial bearing defects; (a): outer race defect, (b): inner race defect

N

  Fig. 2.

Fig. 2 .

 2 Fig. 2. Geometrical characteristics of the rolling-element bearings

IΓ

  is the amplitude of the stator current at the fundamental frequency, R I Φ is the amplitude of the stator current induced by the rotor magnetic field, is the constant load torque, J is the total inertia of the mechanical system.Depending on the machine condition, the torque variations Equation (4) corresponds to torque variations due to a simple mechanical defect such as mechanical unbalance or a mechanical coupling problem.

  corresponds to torque variations due to a simple mechanical defect and a localized bearing fault.

  corresponds torque variations due to a simple mechanical defect plus localized and distributed bearing faults. Indeed, noise which modelizes torque variations induced by a distributed bearing fault.

Fig. 3 .

 3 Fig. 3. Defect detection scheme

MFig. 4 .

 4 Fig. 4. The sliding window root-MUSIC algorithm The eigenvectors and eigenvalues of the correlation matrix are then computed. It can be observed that the p Msmallest eigenvalues of the correlation matrix (matrix of dimension 1 + > p M

  is the transpose conjugate, and the set of eigenvectors can be divided into signal and noise matrices:

∑=

  The root-MUSIC algorithm converts the pseudo-power spectrum of the MUSIC algorithm into a polynomial with roots that contain information about the estimated frequencies. This polynomial has p double roots lying on the unit circle. These roots correspond also to the frequencies of the signal components. That is, if k z is a root of P(z)=0, the frequency component k f associated with this root is directly proportional to its phase k φ , i.e : This method of finding the frequencies from the root of the is therefore called Root-MUSIC. On the other hand, the power of each estimated frequency component can be itself estimated from the eigenvalues and eigenvectors of the correlation matrix, using the following relation:

Fig. 5 .Fig. 6 .

 56 Fig. 5. Stator current power spectral density

Fig. 7 .

 7 Fig. 7. : Spectrum of the instantaneous frequency estimated by the Root-MUSIC algorithm on a sliding window, for a healthy motor and a motor with inner raceway bearing defect.

Fig. 8 .

 8 Fig.8. Spectrum of instantaneous frequency estimated by the Root-MUSIC algorithm on a sliding window, for a healthy motor and a motor with a real bearing defect.

Fig. 9 .

 9 Fig. 9. Spectrum of stator current.

Fig. 10 .

 10 Fig.10. Spectrum of the instantaneous frequency estimated by the Root-MUSIC algorithm on a gliding window, for a healthy motor and a motor with a real bearing defect.

TABLE I

 I By setting the SNR =25 dB, we obtain the following results in TableIIfor different lengths of the sliding window Nr in function of the signal length Ns.

	: ESTIMATION METHOD OF x R VERSUS THE SNR
					SNR
	Estimation Method of x R	5 dB	Bias	25 dB	5 dB Variance 25 dB
	Autocorrelation -9 .10 3		-1.3573 6 .10 4	0.034
	Covariance	-9 .10 3 -1.4326 1.8 .10 4	0.011
	Modified	-9 .10 3	-1.300 3.10 3	0.0016
	Covariance

TABLE II :

 II BIAS AND VARIANCE VERSUS WINDOW LENGTH

	Length of	Bias	Variance
	window Nr
	Ns/2	0	0
	Ns/4	0	0
	Ns/10	0	0
	Ns/50	0.0200	0.4490
	Ns/100	-0.1700	1.2860
	Ns/500	0.0280	23.1215
	Ns/1000	0.4790	90.9625

t t ε ε πυ ϕ

ε ε πυ ϕ ε πυ ϕ Γ Γ Γ

ε ε πυ ϕ ε πυ ϕ Γ Γ Γ Γ

VIII. BIOGRAPHIES