Eric Lichtfouse
email: eric.lichtfouse@dijon.inra.fr

Pierre Albrecht

Françoise Béhar

John M Hayes

A molecular and isotopic study of the organic matter from the Paris Basin, France *

Thirteen Liassic sedimentary rocks of increasing depth and three petroleums from the Paris Basin were studied for 13 C/ 12 C isotopic compositions and biological markers, including steranes, sterenes, methylphenanthrenes, methylanthracene and triaromatic steroids. The isotopic compositions of n-alkanes from mature sedimentary rocks and petroleums fall in a narrow range (2‰) except for the deepest Hettangian rock and the Trias petroleum for which the short-chain n-alkanes are enriched and depleted in 13 C, respectively . Most of the molecular parameters increase over the 2000-2500 m depth range, reflecting the transformation of the organic matter at the onset of petroleum generation. In this zone, carbonate content and carbon isotopic composition of carbonates as well as molecular parameters are distinct for the Toarcian and Hettangian source rocks and suggest a migration of organic matter from these two formations. Two novel molecular parameters were defined for this task, one using methyltriaromatic steroids from organic extracts and the other using 1-methylphenanthrene and 2-methylanthracene from kerogen pyrolysates. The anomalous high maturity of the Dogger petroleum relative to the maturity-depth trend of the source rocks is used to estimate the minimal vertical distance of migration of the organic matter from the source rock to the reservoir.

INTRODUCTION

Molecular fossils have been increasingly used to study the nature and transformation of sedimentary organic matter, and are one of the best tools for the correlation of petroleum to source rocks [START_REF] Welte | Correlation between petroleum and source rock. 9 th World Petr[END_REF][START_REF] Leythaeuser | Source rock/crude oil correlation based on distribution of C 27+ -cyclic hydrocarbons[END_REF][START_REF] Seifert | Steranes and terpanes in kerogen pyrolysis for correlation of oils and source rocks[END_REF][START_REF] Seifert | Paleoreconstruction by biological markers[END_REF][START_REF] Peters | The Biomarker guide. Interpreting molecular fossils in petroleum and ancient sediments[END_REF]. The chemical composition of the organic matter depends on source input, maturation, mineral catalysis, migration and biodegradation, making it necessary to use several and preferably independent parameters to analyse these transformations [START_REF] Tissot | Petroleum formation and occurrence[END_REF]. For example, the use of carbon isotopic compositions in addition to molecular parameters has been found useful to correlate various petroleums [START_REF] Williams | Characterization of oil types in Williston basin[END_REF][START_REF] Koons | Effects of depositional environment and postdepositional history on chemical composition of Lower Tuscaloosa oils[END_REF][START_REF] Seifert | Applications of steranes, terpanes and monoaromatics to the maturation, migration and source of crude oils[END_REF].

The organic matter within Toarcian shales from the Paris Basin, mainly of type-II "marine", undergoes a notable transformation starting below 1500 m depth, the upper limit of the catagenic stage [START_REF] Tissot | Origin and evolution of hydrocarbons in early Toarcian shales, Paris basin, France[END_REF][START_REF] Williams | Characterization of oil types in Williston basin[END_REF][START_REF] Ensminger | Evolution of polycyclic alkanes under the effect of burial (Early Toarcian shales, Paris basin)[END_REF], Mackenzie et al., 1980a, 1980b, 1981). The main source rocks are the Toarcian and Hettangian sedimentary rocks from the Lias formation. An important hydrocarbon depletion has been observed in the Hettangian source rocks : the Transformation Ratio TR, calculated by Rock-Eval pyrolysis, reaches 80% at the maximum subsidence of this formation indicating that it is an important contributing source of petroleum [START_REF] Espitalié | Géochimie organique du bassin de Paris[END_REF][START_REF] Espitalié | Aspects of hydrocarbon migration in the Mesozoic in the Paris Basin as deduced from an organic geochemical survey[END_REF]. However, correlating the pathways of petroleum migration is difficult because the mature source rocks and petroleums are undistinguishable using common molecular parameters, such as n-alkane distributions (I.F.P., unpublished data). In recent communications, we pointed out the possible discrimination between Toarcian and Hettangian source rocks using a novel molecular parameter based on triaromatic steroids [START_REF] Lichtfouse | Short chain 3-methyltriaromatic steroids in main shales from the Paris basin, a novel maturity indicator[END_REF][START_REF] Lichtfouse | Occurrence of 2-methyl-, 3-methyl-and 6methyltriaromatic steroid hydrocarbons in geological samples[END_REF]. In this report we present a comparative study of these source rocks and neighbouring petroleums using several molecular parameters from organic extracts and kerogens together with the carbon isotopic compositions of carbonates and n-alkanes.

EXPERIMENTAL

Geological setting

Thirteen sedimentary rocks of increasing depth from various cores were chosen in the two organic richest formations of the Lias of the Paris Basin, the Toarcian shale and Hettangian marl layers (Table 1). The sedimentary rocks which have experienced enough thermal stress to generate petroleum are located in the central portion of the basin at a burial depth greater than 1500 m [START_REF] Tissot | Origin and evolution of hydrocarbons in early Toarcian shales, Paris basin, France[END_REF]. This depth limit represents the beginning of catagenesis and entrance into the main zone of petroleum generation. The Hettangian sedimentary rock located at the deepest part of this basin (2700m) is the most mature rock. The Dogger, Domerian and Trias petroleums are also located in the center of the basin. For more detailed geological and geochemical information see [START_REF] Espitalié | Géochimie organique du bassin de Paris[END_REF][START_REF] Espitalié | Aspects of hydrocarbon migration in the Mesozoic in the Paris Basin as deduced from an organic geochemical survey[END_REF], [START_REF] Tissot | Origin and evolution of hydrocarbons in early Toarcian shales, Paris basin, France[END_REF].

Organic matter fractionation (scheme)

Detailed extraction and fractionation procedures are described elsewhere [START_REF] Lichtfouse | Nouveaux stéroides aromatiques fossiles[END_REF]. Freeze-dried cuttings were finely grounded and extracted three times with toluenemethanol (3:1 v/v) at 40 °C. Kerogen concentrates, obtained by HF-HCl treatment of the extracted rocks [START_REF] Robinson | Isolation procedures for kerogens and associated soluble organic materials[END_REF], were pyrolysed under argon in open gold tubes at 600 °C [START_REF] Béhar | Analyse quantitative des effluents de pyrolyse en milieu ouvert et fermé[END_REF]. The extracts, petroleums or pyrolysates were fractionated into neutral and acid fractions by column chromatography on KOH impregnated silica gel [START_REF] Carthy | A rapid quantitative method for the separation of free fatty acids from other lipids[END_REF]. The neutral fraction was then fractionated by thin layer chromatography (silica gel, methylene chloride) with friedelin and lupeol as references, to give a fraction enriched in hydrocarbons (R F > ~ 0.7) and an alcohol-ketone fraction (R F ~ 0.2-0.7). The hydrocarbon fraction was fractionated by thin layer chromatography (silica gel, n-hexane) with lup-20(29)ene, 1-ethylnaphthalene, 1-methylphenanthrene and 1,2:5,6-dibenzanthracene as references to give an alkane-alkene fraction and a triaromatic fraction. The alkane-alkene fraction was further fractionated by thin layer chromatography on AgNO 3 impregnated silica gel (n-hexane) to give separate alkane and alkene fractions. n-Alkanes were removed from the alkane fraction by adsorption on 5 Å molecular sieves to give a branched-cyclic alkane fraction [START_REF] O´connor | Determination of normal parafins in C 20 to C 32 parafin waxes by molecular sieve adsorption[END_REF].

Scheme. Fractionnation of sedimentary organic matter. CC: column chromatography. TLC: thin layer chromatography Gas chromatography, mass spectrometry and isotopic analysis.

Gas chromatographic analyses were performed using a Carlo Erba 4160 fitted with an on-column injector and a flame ionization detector (see figure captions for specific conditions). The fractions were eluted on fused-silica capillary columns with hydrogen. The gas chromatographic-mass spectrometric analysis were performed on a home-made gas chromatograph fitted with a Ross injector, coupled with a LKB 9000 S mass spectrometer (B type) or on a Varian 6000 gas chromatograph fitted with an on-column injector, coupled with a Nermag R10 quadrupole mass spectrometer. Conditions: helium carrier gas, electron impact (70 e.V.), source temperature 250 °C. Metastable experiments were performed on a Carlo Erba gas chromatograph coupled with a Kratos MS 80 mass spectrometer (EB type).

The 13 C/ 12 C composition and concentration of carbonates (Table 2) were determined by analysis of the CO 2 evolved by reaction of powdered samples with phosphoric acid (ρ > 1.89 g/cm 3 ) at 50 °C [START_REF] Wachter | Exchange of oxygen isotopes and carbon isotopes in carbon dioxide-phosphoric acid systems[END_REF]. After removal of water and non-condensible gases by cryogenic distillation, the carbon dioxide was quantified, then analysed by mass spectrometry (3-4 replicates). Yields of carbon dioxide are expressed in terms of calcium carbonate equivalents : (moles CO 2 x 100.086 x 100)/sample dry weight. The 13 C/ 12 C compositions of n-alkanes from alkane fractions (3-4 replicates) were measured on a Hewlett-Packard gas chromatograph coupled with a combustion furnace (CuO, 850 °C) coupled with a Finnigan Delta S mass spectrometer [START_REF] Freeman | Evidence from carbon isotope measurements for diverse origins of sedimentary hydrocarbons[END_REF]. Isotopic compositions, expressed in permil, are referred to the Pee Dee Belemnite standard: δ 13 C = [( 13 C/ 12 Csample -13 C/ 12 Cstd)/( 13 C/ 12 Cstd)] x 10 3 . The isotopic compositions of 19, 25, 28 carbon-numbered nalkanes and phytane are not reported due to nearly co-eluting unidentified substances [START_REF] Lichtfouse | Enhanced resolution of organic compounds from sediments by isotopic gas chromatography-combustion-mass spectrometry[END_REF].

Identification of organic compounds

Methylphenanthrenes, 2-methylanthracene, 9-methylanthracene and triaromatic steroids were identified by co-injection of pure standards (see also [START_REF] Radke | Class separation of aromatic compounds in rock extracts and fossil fuels by liquid chromatography[END_REF], 1990[START_REF] Ludwig | C 26 -C 29 Triaromatic steroid derivatives in sediments and petroleums[END_REF][START_REF] Lichtfouse | Nouveaux stéroides aromatiques fossiles[END_REF], Lichtfouse et al., 1990). Other compounds were identified by their gas chromatographic and mass spectroscopic properties and by comparison with literature data: steranes [START_REF] Seifert | Steranes and terpanes in kerogen pyrolysis for correlation of oils and source rocks[END_REF]Moldowan, 1979, Moldowan et al.,1980), diasteranes [START_REF] Ensminger | Rearranged steranes in sediments and crude oils[END_REF][START_REF] Sieskind | Structural elucidation of diacholestanes[END_REF], diasterenes (Rubinstein and[START_REF] Rubinstein | Rearranged sterenes in a shale: occurrence and simulated formation[END_REF]Albrecht, 1985), spirosterenes [START_REF] Peakman | Naturally occurring spiro steroid hydrocarbons[END_REF] and de-A-diasterenes [START_REF] Peakman | De-A-steroids in immature marine shales[END_REF]. The configuration of steroids at position 24 was not determined because 24R and 24S isomers nearly co-elute in routine gas chromatography [START_REF] Maxwell | Configuration at C-24 in steranes and sterols[END_REF]. The names "pristane" or "phytane" refer to mixtures of their stereoisomers. The names of steroids follow the IUPAC-IUB rules (1972), but, for convenience, abbreviations are sometimes used in figures.

RESULTS AND DISCUSSION

Carbonate content and 13 C/ 12 C composition

The carbonate content of the samples ranges from 9 to 65 % (Fig. 1).The rocks located in the basin center below 1500 m depth can be clearly divided into two facies which correspond with their geological age: carbonate-poor rocks from the Toarcian formation (shales, 9-15% CaCO 3 ), and carbonate-rich rocks from the Hettangian formation (marls, 35-65% CaCO 3 ). In this zone, carbonate in the marls is enriched by about 1.5‰ in 13 C relative to the shales. The 13 C content of the carbonates is inversely correlated with the abundance of carbonate (Fig. 2), presumably indicating dilution of diagenetically derived carbonate by increasing quantities of primary marine carbonate.

Alkane distributions

In immature sedimentary rocks, located in the Eastern part of the basin, distributions of n-alkanes from extracts display modes at C 17 and C 29 , with an odd-carbon predominance.

These modes likely reflect both marine and terrigenous plant sources for the n-alkanes [START_REF] Winters | Hydrocarbons of blue-green algae: geochemical significance[END_REF][START_REF] Gelpi | Olefins of high molecular weight in two microscopic algae[END_REF][START_REF] Gelpi | Hydrocarbons of geochemical significance in microscopic algae[END_REF][START_REF] Huc | Mise en évidence de provinces géochimiques dans les schistes bitumineux du Toarcien de l'Est du bassin de Paris[END_REF][START_REF] Rieley | The biogeochemistry of Ellesmere Lake, U.K. I: source correlation of leaf wax inputs to the sedimentary lipid record[END_REF]. Contributions from bacteria are confirmed by identification of C 31 -C 35 hopanes, mainly 17α,21β isomers, in all the samples studied (see also [START_REF] Ensminger | Evolution of polycyclic alkanes under the effect of burial (Early Toarcian shales, Paris basin)[END_REF][START_REF] Ourisson | The hopanoids, paleochemistry and biochemistry of a group of natural products[END_REF][START_REF] Tissot | Discussion during a seminar at the French Petroleum Institute[END_REF]. Pristane, phytane and polycyclic alkanes are major components in some samples.

In mature sedimentary organic matter and petroleums, distributions of n-alkanes from extracts favor low molecular-weight members, maximizing at C 12 -C 16 , without any notable odd-even predominance. The pristane/phytane ratio is always greater than 1, suggesting less reducing paleoconditions [START_REF] Tissot | Petroleum formation and occurrence[END_REF]. The alkane distributions are very similar for all mature sediments and petroleums located in the center of the basin, making it difficult to postulate a genetic relationship (Tissot, 1987, I.F.P., unpublished results).

Isotopic compositions of n-alkanes

The carbon isotopic compositions of n-alkanes from most rocks and petroleums examined in this investigation fall in a narrow range, about 2 ‰ (Fig. 3). This is in agreement with the relative homogeneity of the organic matter in the Paris Basin and also confirms that the Lias formations are probably the major source-rocks of the petroleums [START_REF] Espitalié | Géochimie organique du bassin de Paris[END_REF]. Shorter-chain (C 13 -C 18 ) alkanes in the Hettangian rock from 2700 m depth are enriched in 13 C relative to most other n-alkanes from mature rocks, with the enrichment being most pronounced at the shortest chain lengths. This sedimentary rock is derived from the middle and deepest part of a basin noted for homogeneity of organic matter input [START_REF] Espitalié | Géochimie organique du bassin de Paris[END_REF][START_REF] Palacas | Characteristics of carbonate source rocks of petroleum. In Petroleum Systems of the United States[END_REF][START_REF] Tissot | Origin and evolution of hydrocarbons in early Toarcian shales, Paris basin, France[END_REF]. Admixture of materials from some distinct source is thus an unlikely cause for the enrichment and effects of thermal maturation must be considered. It is possible either that the noted enrichment in 13 C indicates breakdown of some isotopically distinct source, present in all samples but yielding alkanes only at the greatest depth, or the prior generation and expulsion of isotopically depleted products of thermolytic cleavage. Normal kinetic isotope effects are presumably associated with such cleavage reactions and it is expected that their products will be depleted in 13 C [START_REF] Welte | 13 C/ 12 C Isotope ratios of individual n-parafins and the implication to their origin[END_REF][START_REF] Sackett | Carbon and hydrogen isotope effects during the thermocatalytic production of hydrocarbons in laboratory simulation experiments[END_REF][START_REF] Waples | Mathematical models for petroleum-forming processes: carbon isotope fractionation[END_REF]. According to the latter view, the shorter-chain n-alkanes extracted from the 2700 m depth sample represent a residue, with the isotopically depleted cleavage products having been lost by migration. Indeed, the highest migration ratio (88%) was recorded at 2700 m depth, indicating that large amounts of hydrocarbons have been expelled [START_REF] Espitalié | Aspects of hydrocarbon migration in the Mesozoic in the Paris Basin as deduced from an organic geochemical survey[END_REF].

In the same line of thought, the depletion in 13 C of short-chain n-alkanes from the Trias petroleum might be due to the preferential expulsion of 13 C-depleted n-alkanes from the source-rock. However, the Trias petroleum could have a quite distinct unknown source, differing significantly either in maturity or initial inputs, thus giving a different isotopic curve.

In the shallowest sedimentary rock from the Toarcian at 810 m depth, the isotopic composition of most n-alkanes (ca. -28.5‰) are enriched in 13 C to about 3‰ compared to other sedimentary rocks (ca. -31.5‰). Accordingly, it is possible that the extractable alkanes initially present in all sediments had isotopic compositions near those of the 810 m depth sample and that alkanes released later by catagenetic breakdown of kerogen are lighter.

Steranes

In mature sediments, C 26 -C 30 steranes are usually present as a complex mixture of isomers and are poorly resolved by single ion monitoring (SIM, m/z = 217) gas chromatography-mass spectrometry. Therefore, cholestane and diacholestane isomers (C 27 )

were selectively analysed by gas chromatography-mass spectrometry with metastable reaction monitoring (Fig. 4 and 5; [START_REF] Steen | Gas chromatographic/mass spectrometric analysis (GC/MS) of C 27-30steranes[END_REF]. In the sediment extracts from the Paris Basin, the major steranes and diasteranes are C 27 -C 29 members. The minor presence of C 21 -C 22 , C 26 and C 30 steranes in each sample probably reflects the contribution of marine organisms to the organic matter [START_REF] Mackenzie | Chemical fossils: the geological fate of steroids[END_REF][START_REF] Moldowan | C 30 -steranes, novel markers for marine petroleums and sedimentary rocks[END_REF][START_REF] Moldowan | Sedimentary 24-n-Propylcholestanes, molecular fossils diagnostic of marine algae[END_REF], 1991). Three changes in the composition of the sterane mixture were observed with increasing depth, allowing the maturity of the organic matter to be followed closely (Fig. 5,6). The molecular parameters measure the relative concentration increase of 20S-versus 20R-steranes ("SR"), diasteranes versus non-rearranged steranes ("DIA") and ββ-versus αα-steranes ("BA"): The rapid increase of BA between 2000 and 2500 m, previously observed in the Toarcian shales for steranes and porphyrins (Mackenzie et al. 1980a,b), reflects the rapid transformation of the organic matter within a relatively short depth interval (ca. 2000-2500 m). It is of interest to note that these trends also coincide with changes in organic matter fluorescence observed by [START_REF] Alpern | Réflectance et fluorescence des organoclastes du Toarcien du bassin de Paris en fonction de la profondeur et de la température[END_REF] in the Toarcian shales.

Depth is used as a proxy for maturation because sedimentary rocks from the center of the basin (below 1500 m depth) have experienced a rather regular subsidence as shown by burial-history curves [START_REF] Tissot | Origin and evolution of hydrocarbons in early Toarcian shales, Paris basin, France[END_REF]. Sedimentary rocks located in eastern area, above 1500 m depth, have been slightly uplifted. In the catagenetic zone, the SR and BA parameters indicate that Hettangian sedimentary rocks are in the same maturity range as the Toarcian shales although DIA values suggest the Hettangian rock is slightly more mature. Petroleums are often in the most mature range, close to the most mature Toarcian or Hettangian rocks which appear therefore to be the dominant sources. A comparison of the 372→217 fragmentograms also shows that the Dogger petroleum is most likely derived from deep Hettangian sediments (Fig. 5).

Sterenes

The extracts which contain substantial amounts of alkenes, mainly steroid derivatives, are restricted to the diagenetic zone, above 1500 m depth. Monitoring ion currents at m/z = 257, the major diasterenes are C 27 -C 29 members with lower amounts of C 21 -C 24 and C 30 members, and 20S-20R isomeric doublets occur in the C 23 -C 30 range. Diasterenes and diasteranes, absent in living organisms, are probably derived from sterols via sterenes under acidic conditions possibly by mineral catalysis (Rubinstein et al., 1975;[START_REF] Dastillung | Δ 2 -sterenes as diagenetic intermediates in sediments[END_REF][START_REF] Sieskind | Efficient synthesis of rearranged Cholest-13(17)-enes catalysed by montmorillonite-clay[END_REF]. The presence of C 27 -C 29 spirosterenes and spirodiasterenes (20R and 20S), detected by monitoring ion currents at m/z = 206, 220 and 234, provides additional evidence for molecular rearrangements under acidic conditions [START_REF] Peakman | Naturally occurring spiro steroid hydrocarbons[END_REF](Peakman et al., , 1988;;Peakman and Maxwell, 1988). Traces of C 23 -C 25 de-Adiasterenes, as doublets, were also detected by monitoring the ion current at m/z = 203 [START_REF] Peakman | De-A-steroids in immature marine shales[END_REF].

Methylphenanthrenes, methylanthracenes

The parameters based on alkyl phenanthrenes have previously been found to be very useful indicators of maturity for sedimentary rocks containing type-III organic matter, such as coals [START_REF] Radke | The methylphenanthrene index (MPI): a maturity parameter based on aromatic hydrocarbons[END_REF][START_REF] Garrigues | Relation of the methylated hydrocarbon distribution pattern to the maturity of organic matter in ancient sediments from the Mahakam delta[END_REF]. In the extracts and petroleums from the Paris Basin, which contain type-II organic matter, the methyphenanthrene indexes MPI 1 and MPI 3 do not show significant variations with increasing depth (Fig. 7, [START_REF] Lichtfouse | Nouveaux stéroides aromatiques fossiles[END_REF], Lichtfouse et al., 1989). However, methylphenanthrenes also occur in triaromatic fractions from kerogen pyrolysates, with notable amounts of methylanthracenes (Fig. 8,9). The absence of alkyl anthracenes in the extracts and petroleums from the Paris Basin suggests that these substances are formed during pyrolysis of the kerogen from unknown precursors. The concentration of methylphenanthrenes (i.e. 2-MP) relative to methylanthracenes (i.e. 2-MA) increases with depth (Fig. 9, 10), allowing definition of a novel maturity parameter, the "MethylPhenanthrene-Anthracene" parameter: MPA= 2-MP/2-MA In kerogen pyrolysates, the MPI 3 and MPA give low values for immature samples, above 1500 m (Fig. 7, 10). A dramatic increase is observed below 2000 m suggesting the notable transformation of the organic matter at this stage. The mature rocks can be clearly separated into two classes with MPA and MPI 3; the pyrolysates from Hettangian rocks give significantly higher values than Toarcian rocks, suggesting the higher thermal maturity of the Hettangian rocks. Alternatively, the higher carbonate content of Hettangian rocks in the center of the basin suggests that a facies effect is also possible. Indeed, Toarcian and Hettangian rocks of about the same depth, for example at 2243 m and 2253 m, should have experienced approximately the same thermal history. Therefore the apparent higher maturities of the Hettangian rocks can not be explained solely by a greater amount of thermal stress. These kerogen parameters might be particulary useful to measure the thermal evolution of marine organic matter (type-II), where classical parameters are usually inadequate : in the Paris Basin, for example, the measurement of maturity by means of vitrinite reflectance is unfeasible because organic particles determined as vitrinite are generally not vitrinite [START_REF] Alpern | Réflectance et fluorescence des organoclastes du Toarcien du bassin de Paris en fonction de la profondeur et de la température[END_REF][START_REF] Durand | Reflectance of vitrinite as control of thermal history of sediments[END_REF]. Moreover, parameters based on the kerogen composition represent the evolution of the bulk organic matter because the mass of kerogen constitutes more than 80% of the total organic matter [START_REF] Tissot | Petroleum formation and occurrence[END_REF]. We note that values as high as 4.7 for MPI 3 and 50 for MPA were recorded for a Paleozoic sediment of type-III organic matter, located at 3150 m in the eastern part of the basin.

Aromatic steroids

In a previous study of Toarcian shales from the Paris Basin, changes in the composition of mono-and triaromatic steroid mixtures were related to the transformation of the organic matter with increasing depth [START_REF] Mackenzie | Molecular parameters of maturation in the Toarcian shales, Paris Basin, France. III. Changes in aromatic steroid hydrocarbons[END_REF]. For example, the relative concentration of short-chain versus long-chain triaromatic steroids increases with depth, presumably as a result of maturation (Fig. 11,12). The Dogger and the Domerian petroleums show similar fragmentograms, whereas the Trias petroleum has a much higher relative concentration of short-chain triaromatic steroids (Fig. 13). This clear difference probably reflects the higher maturity or a different input for the Trias petroleum, as proposed earlier in the isotopic section. Triaromatic steroids methylated at position 2, 3 or 6, first detected as substances of possible geochemical interest by [START_REF] Riolo | Distribution of aromatic steroids in geological samples: their evaluation as geochemical parameters[END_REF], were identified later in the Paris basin sedimentary rocks by comparison with synthetic substances and proposed as maturity parameters (Fig. 14, [START_REF] Lichtfouse | Short chain 3-methyltriaromatic steroids in main shales from the Paris basin, a novel maturity indicator[END_REF][START_REF] Lichtfouse | Occurrence of 2-methyl-, 3-methyl-and 6methyltriaromatic steroid hydrocarbons in geological samples[END_REF]. Though their mode of formation remains unknown, we also predicted a common precursor for 3-methyltriaromatic steroids, 3methylsteranes and 3-carboxysteranes based on their structural comparison [START_REF] Lichtfouse | Nouveaux stéroides aromatiques fossiles[END_REF][START_REF] Lichtfouse | 3-Methyltriaromatic steroids in sediments. Molecular fossils with unknown precursors. inPolycyclic Aromatic Compounds[END_REF]. This hypothesis is supported by the identification of 3β-alkylsteranes in various sediments [START_REF] Summons | Fossil steranes with unprecedented methylation in ring-A[END_REF], 1991[START_REF] Dahl | A new class of natural products revealed by 3β-alkyl steranes in petroleum[END_REF]. The relative concentration of triaromatic steroids methylated at postion 2, 3 or 6 versus 4-methyl homologs increases with depth (Fig. 15). This trend is similar to that observed in type-III organic matter for methylphenanthrenes [START_REF] Radke | The methylphenanthrene index (MPI): a maturity parameter based on aromatic hydrocarbons[END_REF], which are structurally similar to triaromatic steroids. Accordingly, methylphenanthrenes could eventually derive from methyltriaromatic steroids after degradation of the D ring. The evolution of the organic matter in the Paris basin was also followed using the SL parameter, an index based on the relative abundance of short-chain-length triaromatic steroids [START_REF] Mackenzie | Molecular parameters of maturation in the Toarcian shales, Paris Basin, France. III. Changes in aromatic steroid hydrocarbons[END_REF], and a novel parameter based on MethylTriaromatic Steroids (Fig. 16). Expressions for these parameters are: As seen earlier for kerogen parameters, Hettangian rocks give significantly higher values for SL and MTS than Toarcian rocks in the catagenetic zone (Fig. 16). This distinction could result from a difference in thermal maturity or reflect a facies effect between the Hettangian marls and the Toarcian shales. Furthermore, the only presence of 3-methyl homologues (C 29 ) among methyltriaromatic steroids in the immature evaporite sedimentary rocks from the Mulhouse Basin, France, suggests a strong facies dependance of the MTS parameter [START_REF] Fache-Dany | Etude des marqueurs moléculaires en série évaporitique: le bassin potassique du sud de l'Alsace[END_REF]. In a series of sedimentary rocks of increasing depth from the Kimmeridge formation, the MTS values also suggest an influence from both maturity and facies (R. Houghton, pers. commun.). In the Monterey formation, the MTS values show a drastic increase in the zone of petroleum generation (E. Idiz, pers. commun.). Like most of the molecular parameters, SL and MTS show an increase below 2000 m for petroleums and Hettangian rocks, suggesting a rapid transformation of the organic matter in a relatively short depth interval. The SL and MTS values of the petroleums are intermediate between those of Toarcian and Hettangian sedimentary rocks. An exclusive generation from Toarcian rocks is therefore unlikely because petroleums are usually subjected to lower thermal stress than their source-rocks, after expulsion. On the other hand, the Transformation Ratio of the organic matter in Hettangian rocks (TR = 80%) is higher than in Toarcian rocks (TR = 40%), based on Rock-Eval pyrolysis in the center of the basin [START_REF] Espitalié | Géochimie organique du bassin de Paris[END_REF]. An important contribution of organic matter from the Hettangian sediments is also likely because Hettangian source-rocks are generally more mature than Toarcian source-rocks, according to Rock-Eval Pyrolysis parameters (i.e. Tmax parameter, [START_REF] Espitalié | Géochimie organique du bassin de Paris[END_REF]. Moreover, carbonate-rich sediments have also been widely recognized as excellent source beds for petroleum generation [START_REF] Jones | Comparison of carbonate and shale source rocks[END_REF][START_REF] Palacas | Characteristics of carbonate source rocks of petroleum. In Petroleum Systems of the United States[END_REF] and a zone of oil production has been found recently within the Hettangian formation below Paris.

Migration of the organic matter

The minimal distance of vertical upward migration of a petroleum can be estimated by the following difference:

-(depth of the source-rock having the same maturity as the petroleum, calculated by regression of the maturity-depth plots of mature source-rocks) minus (depth of the petroleum reservoir).

This concept is based on the following observation: the Dogger petroleum displays an anomalous high maturity for its depth (1858 m) relative to the general trend of the mature source-rocks, suggesting that the organic matter has migrated from source rocks located deeper (see calculations in Fig. 6, 16). By linear regression of the maturity-depth points of Toarcian and Hettangian rocks in the zone of petroleum generation, it is possible to estimate the theorical depth of the source-rock and, therefore, the minimal distance of vertical migration. Using sterane and triaromatic steroid parameters, the calculated source-rock depth ranges from 2300 to 2560 m, thus giving a minimal distance of vertical migration from 440 m to 700 m. In the zone of petroleum generation, the maturity-depth points of Domerian and Trias petroleums are close to the general trend of mature source-rocks (Fig. 6,16). According to the previous concept, these petroleums should have experienced a low vertical distance of upward migration.

The true migration distance should be corrected by the following points: 1) the calculation should take into account the horizontal migration. 2) Usually, the maturity of a source-rock will increase faster than the maturity of the petroleum generated by this source-rock due to higher thermal stress and higher mineral catalysis inside the source-rock. Few exceptions are possible, like petroleums occurring in pools located deeper than their sourcerocks and, therefore, probably subjected to higher thermal stress. 3) Various maturity parameters should be used to avoid possible source or facies effects. 4) Other regressions than linear might better follow the maturity-depth trend. 5) Anomalous high maturities might also be detected in basins which have locally high geothermal gradients.

CONCLUSION

In the zone of petroleum generation of the Paris Basin, Hettangian source-rocks are distinguished from Toarcian source rocks by higher carbonate content, 13 C-enriched carbonates and higher values of molecular maturity parameters. The intermediate maturity of the petroleums show the possible migration of the organic matter from the Toarcian and Hettangian formations. Excluding the deepest Hettangian source-rock and the Trias petroleum, the isotopic compositions of n-alkanes from mature sediments and petroleums fall in a narrow range.

The MPI 3 parameter and the novel MPA parameter based on the relative concentration of 1-methylphenanthrene and 2-methylanthracene in the kerogen pyrolysates, show dramatic increases in the oil window, suggesting the possible use of these parameters to follow the evolution of type-II "marine" organic matter. Similar increases were also observed with parameters based on sterane abundances and a novel MTS parameter based on the relative concentration of methyltriaromatic steroids in the organic extracts. Such trends indicate a rapid transformation of the organic matter within a relative short depth interval (2000-2500 m).

The minimal vertical distance of migration of a petroleum can be estimated by the following difference: (depth of the source-rock having the same maturity as the petroleum, calculated by regression of the maturity-depth plots of mature source-rocks) minus (depth of the petroleum). Accordingly, the anomalous high values of molecular parameters observed for the Dogger petroleum, relative to its depth, suggest an upward migration from the source-rocks currently located at about 2300-2560 m, which is in good agreement with the study of [START_REF] Espitalié | Aspects of hydrocarbon migration in the Mesozoic in the Paris Basin as deduced from an organic geochemical survey[END_REF].

  from various cores of the Paris Basin. The steranes parameters SR, DIA, BA, were measured by gas chromatography-mass spectrometry monitoring the highly specific 372→217 transition. Other parameters were measured by gas chromatography-mass spectrometry using reconstructed ion currents: m/z = 192 (MPI3, MPA), m/z = 231 (SL) and m/z = 245 (MTS). SR = 100 x ααS/(ααS + ααR) (C 27 ). DIA = βαS x 100/(βαS + ααS) (C 27 ). BA = 100 x ββR/(ββR + ααR) (C 27 ). MPI3 = (2-MP + 3-MP)/(1-MP + 4-MP + 9-MP). MPA = 2-MP/2-MA. SL = 100 x C 20 /(C 20 + C 26 S). MTS = 100 x (2-C 21 + 3-C 21 )/(2-C 21 + 3-C 21 + 4-C 21 ). *: parameters from kerogen pyrolysates. n.d.: not determined.

Figure 1 .

 1 Figure 1. Carbonate isotopic compositions and carbonate contents of the sedimentary rocks from the Paris Basin versus depth. Note the higher carbonate content and isotopic enrichment of Hettangian rocks in the zone of petroleum generation (below 1500 m depth). Carbonate content is expressed in terms of calcium carbonate equivalents : (moles CO 2 x 100.086 x 100)/sample dry weight.

Figure 2 .

 2 Figure 2. Isotopic compositions of carbonate versus carbonate content in the sedimentary rocks from the Paris Basin. Isotopic compositions increase with increasing carbonate contents in sediments containing more than 15% carbonate. Carbonate content is expressed in terms of calcium carbonate equivalents : (moles CO 2 x 100.086 x 100)/sample dry weight.

Figure 3 .

 3 Figure 3. Carbon isotopic compositions of n-alkanes in petroleums and rock organic extracts from the Paris Basin. The isotopic compositions of n-alkanes from most rocks and petroleums fall in a narrow range (2‰). By comparison, short-chain n-alkanes from the most mature rock (Hettangian, 2700 m) and the Trias petroleum are enriched and depleted in 13 C respectively. n-Alkanes from the shallowest sediment (Toarcian, 810 m) are enriched in 13 C.

Figure 4 .

 4 Figure 4. Molecular structures of C 27 steranes occurring in petroleums and rock organic extracts from the Paris Basin. α and β refer to the stereochemistry of the hydrogen atom of cholestane stereoisomers at position 14 and 17, respectively (ααR, ααS, ββR, ββS). α and β refer to the stereochemistry of the hydrogen atom of diacholestane stereoisomers at position 13 and 17, respectively (βαR, βαS). R and S refer to the configuration at position 20.

Figure 5 .

 5 Figure 5. Metastable reaction fragmentograms for C 27 steranes in petroleums and rock organic extracts from the Paris Basin, for the 372→217 transition. Diacholestane isomers (shaded) elute earlier than cholestane isomers. Note the increase of (20S)-5α-cholestane ("ααS") versus 5α-cholestane ("ααR"), (20S)-13β,17α-diacholestane ("βαS") versus (20S)-5α-cholestane ("ααS"), (20R)-5α,14β,17β-cholestane ("ββR") versus (20R)-5α-cholestane ("ααR") with increasing depth. Note also the similar fingerprints of the Hettangian sediment and the Dogger petroleum. Conditions: gas chromatography-mass spectrometry; fused-silica capillary column (30 m x 0.25 mm), DB 17 phase (0.1 µm), on column injector, Helium carrier gas (1.4 b.), temperature: 150-300 °C at 3 °/min. E.I. (70 e.V., Kratos), 4 kV acceleration voltage after the source.

  SR = 100 x ααS/(ααS + ααR) : (20S)-5α-cholestane ("ααS") versus 5α-cholestane ("ααR") DIA = 100 x βαS/(βαS + ααS) : (20S)-13β,17α-diacholestane ("βαS") versus (20S)-5α-cholestane ("ααS") BA = 100 x ββR/(ββR + ααR) : (20R)-5α,14β,17β-cholestane ("ββR") versus (20R)-5α-cholestane ("ααR") Molecular structures are shown in figure 4.

Figure 6 .

 6 Figure 6. Steranes parameters versus depth in petroleums and rock organic extracts from the Paris Basin. Note the rapid increase of BA values (2000-2500 m) in the oil zone. A linear regression for Toarcian and Hettangian rocks below 1500 m gives Depth = 1607 + 14.4 x BA (r = 0.76). The point on this line having the same BA value as the Dogger petroleum (BA = 66%, Depth = 1858 m) has a depth of 2559 m, suggesting a minimum distance of vertical migration of about 700 m. Similar regressions using SR and DIA give distances of about 470 m and 480 m, respectively.

Figure 7 .

 7 Figure 7. Methyphenanthrenes parameter versus depth in the petroleums, organic extracts and kerogen pyrolysates from the Paris Basin. Note the increase of MPI3 for kerogen pyrolysates below 2000 m. MPI3 = (2-MP + 3-MP)/(1-MP + 4-MP + 9-MP), calculated with relative intensities on the m/z = 192 ion current.

Figure 8 .

 8 Figure 8. Molecular structures of 2-methylphenanthrene and 2-methylanthracene.

Figure 9 .

 9 Figure 9. Mass fragmentograms showing the methylphenanthrenes (MP) and methylanthracenes (MA) in kerogen pyrolysates from the Paris Basin sedimentary rocks. Note the increase of 3-methyl-and 2methylphenanthrenes versus 9-methyl, 4-methyl and 1-methyl homologues, with increasing depth. Note also the increase of methylphenanthrenes versus methylanthracenes, with increasing depth. 1-Methylanthracene possibly coelutes with 9-methyl-or 1-methylphenanthrene (Dr. M. Radke, personnal communication). Conditions: gas chromatography-mass spectrometry: fused-silica capillary column (60 m x 0.32 mm), DB 1 phase (0.25 µm), on column injector, Helium carrier gas (1.4 b.); temperature: 60 °C (4 min.), 60-110 °C at 10 °/min., 110-325 °C at 3 °/min. , E.I. (70 e.V., Nermag).

Figure 10 .

 10 Figure 10. MethylPhenanthrene-Anthracene parameter versus depth in kerogen pyrolysate of Paris Basin sedimentary rocks. Hettangian rocks give higher MPA values than Toarcian rocks in the oil zone. MPA= 2-MP/2-MA, calculated with relative intensities on the m/z = 192 ion current.

Figure 11 .

 11 Figure 11. Molecular structures of triaromatic steroids, including methyltriaromatic steroids. R and S refer to the stereochemistry at position 20. 3-and 4-indicate the position of the methyl group on the aromatic nucleus.

Figure 12 .

 12 Figure 12. Mass fragmentograms showing the triaromatic steroids in organic extracts of Paris Basin sedimentary rocks. Note the increase of short chain versus long chain triaromatic steroids with increasing depth (see also Mackenzie et al., 1981). Two unidentified compounds coelute with C 27 R, as seen by GC-MS on a more polar phase (DB 17). Conditions: gas chromatography-mass spectrometry: fused-silica capillary column (25 m x 0.3 mm), SE 30 phase (0.1 µm), Ross injector, Helium carrier gas (1 b.); temperature: 150-300 °C at 2 °/min. , E.I. (70 e.V., LKB 9000S).

Figure 13 .

 13 Figure 13. Mass fragmentograms showing the triaromatic steroids in petroleums from the Paris Basin. Note the highest concentration of short chain versus long chain triaromatic steroids in the Trias petroleum, also seen for methyltriaromatic steroids on m/z = 245 fragmentograms. Conditions: see Fig.12.

Figure 14 .

 14 Figure 14. Mass fragmentograms showing the methyltriaromatic steroids in an organic extract of a Paris Basin sedimentary rock (depth 2243 m). Numbers refer to the position of the methyl group on the steroid. Unidentified compounds coelute with 3-C 27 R and 3-C 29 R, as seen by GC-MS on a more polar phase (DB 17). 2-C 21 elutes before 3-C 21 on a DB 17 phase. Conditions: see Fig.12.

  SL = 100 x C 20 /(C 20 + C 26 S) MTS = 100 x (2-C 21 + 3-C 21 )/(2-C 21 + 3-C 21 + 4-C 21 ) Molecular structures are shown in Figure 11.

Figure 15 .

 15 Figure 15. Mass fragmentograms showing the methyltriaromatic steroids from organic extracts of Paris Basin sedimentary rocks. Note the increase of 2-methyl-and 3-methyltriaromatic steroids (2 + 3, C 21 ) versus the 4 methyl homolog (4) with increasing depth. Conditions: see Fig.12.

Figure 16 .

 16 Figure 16. Aromatic steroid parameters versus depth in organic extracts of Paris Basin sedimentary rocks and petroleums. Hettangian rocks give higher SL and MTS values than Toarcian rocks in the oil zone. Note the rapid increase of SL and MTS below 2000 m. Note also the anomalous high maturity of the Dogger petroleum for its depth, relative to the general trend: linear regressions for Toarcian and Hettangian rocks below 1500 m give Depth = 1911 + 6.6 x SL (r = 0.57 ) and Depth = 1624 + 17.2 x MTS (r = 0.80). The calculated depths for the SL (61%) and MTS (39%) values of the Dogger petroleum are 2311 m and 2296 m, respectively, suggesting a minimum distance of upward migration of about 450 and 440 m.

Table 1 .

 1 Geological characteristics and molecular parameters of organic-rich sedimentary rocks and petroleums

	DEPTH NATURE	GEOLOGICAL	SR DIA BA MPI3	MPI3*	MPA* SL MTS
	(m)		AGE	(%) (%) (%)				(%) (%)
	810	Rock	Toarcian	25	47	19	0.95	0.76	0.97	50	19
	1030	Rock	Toarcian	22	66	14	n.d.	0.63	0.76	32	27
	1075	Rock	Hettangian	18	71	8	0.92	0.74	0.85	43	29
	1325	Rock	Hettangian	31	58	13	0.72	0.72	0.94	30	25
	2030	Rock	Toarcian	39	75	26	0.90	0.81	1.28	29	26
	2105	Rock	Toarcian	49	77	48	0.74	0.86	1.71	45	34
	2110	Rock	Toarcian	45	76	33	0.64	0.79	1.46	38	33
	2243	Rock	Hettangian	44	87	46	0.79	0.87	3.12	79	43
	2253	Rock	Toarcian	53	82	56	0.76	0.86	1.74	52	31
	2298	Rock	Toarcian	51	72	49	0.73	0.84	1.64	47	34
	2326	Rock	Hettangian	37	88	47	0.77	1.02	2.71	77	48
	2371	Rock	Toarcian	48	85	50	0.73	0.90	2.03	64	34
	2700	Rock	Hettangian	50	84	59	0.76	1.14	5.44	63	55
	1858	Petroleum	Dogger	54	85	66	0.77			61	39
	2200	Petroleum	Trias	43	90	61	0.69			74	37
	2435	Petroleum	Domerian	56	89	65	0.73			63	39

ACKNOWLEDGEMENTS

This research was supported by the Institut Français du Pétrole, the Centre National de la Recherche Scientifique, Indiana University (DOE Grant DE-FG02-88ER13978) and the Institut National de la Recherche Agronomique. We thank B. Tissot, B. Durand, A. Huc, G. Bessereau, F. Marquis, C. Leblond, M. Da Sylva, C. St Paul (Institut Français du Pétrole), J.-M. Trendel, G. Teller, P. Wehrung, P. Blanc, D. Durrenberger (Université Louis Pasteur), J. Oudin (Total), K. Freeman, J. Collister, S. Studley, R. Droppo and D. Merritt (Indiana University) and E. Idiz (Shell) for helpful discussions or assistance. Helpful and critical comments have been provided by Dr. Jean Espitalié, Dr. Torren Peakman and two anonymous reviewers.


Lucas Garnier
email: lucas.garnier@univ-rennes1.fr

Hervé Lhermite

Véronique Vié

Qingyue Li

Mathieu Berges

Vincent Cazin

Hervé Cormerais

Jacques Weiss

Etienne Gaviot

Bruno Bêche
email: bruno.beche@univ-rennes1.fr

Photonic micro-resonators for steam evaporation dynamic sensing

Keywords: Integrated photonics, micro-resonators, dynamic sensor, steam condensation detection

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INTRODUCTION AND BACKGROUND

The accurate knowledge of humidity conditions in a gaseous environment is an important piece of information in numerous cases. Indeed, many industrial sectors need precise monitoring of the humidity in the air [START_REF] Asch | Les capteurs en instrumentation industrielle[END_REF]. For example, in food industry, the conservation of edible products needs to be ensured with a wellcontrolled atmosphere in order to avoid the development of moisture. Various technical solutions may be considered to monitor humidity: capacitive hygrometers [START_REF] Neis | [END_REF], resistive hygrometers [3], psychrometers [4,5] and dew-point hygrometers… Technical solutions to monitor humidity via photonic structures are already investigated by several research teams [6]. In this paper, the interest is focused on the possibility to measure humidity with integrated photonic micro-resonators by studying the influence of water condensation and evaporation on the mode propagating in such photonic structures. Photonic micro-resonator sensors have known a large expansion in the past few years [START_REF] Chremmos | Photonic Microresonator Research and Applications[END_REF]. Indeed, specific properties of these devices foster significant advantages compared to many other sensing techniques. The integration of such sensors on relevant chips allows designing lab-on-chip sensors [8], which facilitate both miniaturization and transportability [9]. This kind of structures also provides very precise measurements, with low limit of detection, and high sensitivity [10]. As miniaturizable and most accurate, photonic micro-resonator sensors come up as very efficient in following small-scale phenomena, or in detecting sparsely concentrated chemical species [11]. These characteristics are most interesting for both environmental monitoring [12] and biology together with biomedical or biophysics [13] fundamental research (among other fields). However, with a large majority of scientific works using integrated micro-resonator sensors focusing on static phenomena [9,[11][12][13], most often the transduced signal of the photonic structure is monitored against concentration values of given species or versus temperature. Then, noteworthy variations of the signal versus time, so as to measure dynamic reactions are rarely investigated with. In this paper, integrated micro-resonators are used to perform a dynamic tracking of water condensation and evaporation mechanisms on the acting surface of the sensor.

The transduced signal of a micro-resonator coupled to an access waveguide depends on two phenomena. The first one is the coupling which is an optic tunnel effect between the access waveguide and the resonator. The opto-geometric parameters of the structure determine the quality of the coupling. The second phenomenon is the resonance caused by the excitation of stationary modes in the resonator. This phenomenon is driven, for a given geometry, by the refractive index of the surrounding medium. The transfer function associated to a micro-resonator coupled to an access waveguide is [14]:

T(Φ) = (1 -γ) [1 - (1-a 2 )(1-τ 2 ) (1-aτ) 2 +4aτ.sin 2 ( Φ 2 ) ] (1)
With Φ=βP the phase delay inside the resonator for a single-trip (with β the propagation constant of the mode and P the opto-geometrical perimeter),γ the intensity-insertion-loss coefficient, τ the internal amplitude transmission coefficient which corresponds to the quantity of energy that is not coupled from the access waveguide to the resonator and vice-versa. Finally, 𝑎 = √1 -𝛾𝑒 -𝜌𝐿 𝑚𝑐 is the total amplitude loss factor, related to ρ the amplitude attenuation coefficient in the resonator and L mc the mean circumference of the resonator excluding the coupling part. These different parameters (β, τ, γ, ρ and a) are suddenly perturbed by the condensation of water, and continuously vary during its evaporation. The measurable spectral characteristics that can be related to these parameters are the quality factor Q, the finesse F, the full width at half maximum FWHM, and the free spectral range FSR. Each one of these quantities strongly depends on several of the above parameters, except the FSR that only depend on the effective refractive index n eff g = 𝛽 𝑘

with k the wavenumber associated to the mode. As the refractive index of water is superior to the index of air, the effective index of the mode is correlated to the presence or not of condensed water on the sensor. The relevant parameter to track is so the free spectral range i.e. the distance between two consecutive resonances in the spectral domain. The free spectral range (FSR) is given by [START_REF] Rabus | Integrated Ring Resonators[END_REF]:

FSR = λ 0 2 P.n eff g (2)
With λ 0 the central wavelength, P the opto-geometrical perimeter of the resonator, and n eff g the effective group refractive index associated to the mode, which depends on the optical index of both the waveguide itself and its close environment. By tracking the FSR, we are so able to track any change in the refractive index above the resonator.

Water condensation on a surface depends on the relative humidity (RH) of its surrounding environment. The quantity RH is defined as the ratio between the partial pressure of water vapor p H2O and the saturation vapor pressure (in equilibrium) noted p e : 𝑅𝐻 % = 100.

𝑝 𝐻2𝑂 𝑝 𝑒

. The saturation vapor pressure depends on the temperature of the air; the greater the temperature, the higher the equilibrium vapor pressure. The condensation occurs when the RH value reaches 100%. As the RH increases when temperature decreases (because p e decreases), the condensation occurs when the air is cooled down (until 𝑝 𝑒 = 𝑝 𝐻2𝑂 ): for example, during the night, in humid regions, dew appears when the temperature becomes sufficiently low (reaching the so-called dew point t d ) or when the air is in contact with a cold surface (with a temperature t < t d ).

In the second section, the fabrication of the structures is detailed. The experimental setup is presented in the third section, with relevant results exposed and discussed in section 4.

STRUCTURE FABRICATION

Materials

In the literature, two types of materials are mainly used for the fabrication of integrated photonic structures:

semi-conductors and polymers [START_REF] Rabus | Integrated Ring Resonators[END_REF]. In this study, the chosen material is the polymer DUV210 [16], for the following reasons: first, refractive indices of polymers are smaller than the ones of semi-conductors; for an upper cladding composed of air or water, which is often the case for sensing applications, the evanescent wave of the propagating mode is then larger for polymer resonators than for semi-conductors structures. This difference implies better sensing properties for polymer-based-on resonators. Secondly, polymers are quite less expensive than semi-conductors, reducing then the fabrication cost and facilitating industrial large-scale production. Eventually, among other polymers, we have selected the DUV210 as a chemically amplified positive resin due to its specific absorption band at 248 nm [17] allowing performing deep-UV photolithography most suited to design sub-micronic gaps. An advantageous substrate for such structures is a SiO 2 /Si wafer, with a SiO 2 layer 1 μm in thickness obtained by thermal oxidation. This layer stands as the lower cladding for the waveguides.

Geometrical characteristics

Beyond the choice of the material, the shape and the geometrical characteristics of the structure are determinant factors with a view to sensing properties. The structure hinges on a mono-mode access waveguide laterally coupled from either side to four identical mono-mode racetrack shaped micro-resonators as depicted in fig. 1. The mono-mode nature of these structures has first been confirmed in a theoretical way by a FDTD simulation of the propagation of the optical power inside the overall structure, then in an experimental way by imaging both the cross-sectional output by the means of a CCD camera and the top of the chip under injection. The presence of multiple resonators leads to a greater extinction ratio and quality factor, and allow more precise measurements [18]. The resonators are characterized by four quantities: the coupling length L C , the radius of curvature R associated to the bent part of the resonator, the gap g between the access waveguide and the resonator and the width w, made equal for each resonator and its access waveguide as shown in fig. 2. The study has been performed on structures with L C -R-w set values equal to 5-5-3 and 10-10-3 in micrometers (g=0.4 μm for each) in order to estimate the impact of the size of a resonator on its sensing properties. Using lateral coupling allows to fabricate the chip by way of a single deep-UV insolation, reducing then the fabrication costs and allowing to eradicate any misalignment hazard in case of necessary multiple insolation.

Fabrication process

The structures have been fabricated in a class 100 cleanroom. The wafer supporting the photonic circuits is a silicon wafer on which has been performed a thermal oxidation to obtain a SiO 2 layer of 1 μm. The UV210 is spread on the wafer by spin coating, with the relevant speed and acceleration values in order to get a 800 nm thick layer. This thickness is necessary to make all the structures mono-mode. The sample is then exposed to deep-UV via a mercury lamp to reproduce structures shape previously designed on a photolithography mask.

Then, development is ensured with tetramethylammonium hydroxide (TMAH). Each one of these steps are followed by a softbake to consolidate the structure. A quality control is then performed on these structures to verify their geometrical characteristics such as the width of the guides as well as the gap separating the access waveguide and the resonators.

EXPERIMENTAL SETUP

So as to carry out the measurements, the resonators are placed on an injection bench as depicted in fig. 3. The laser source used in this bench is a Gaussian broadband laser diode with a λ 0 = 790 nm central wavelength and FWHM = 40 nm. The light is then TE-polarized before being injected in the access waveguide in order to excite only the TE 00 mode. The latter operation is performed by way of microscope objectives focusing the light within the guide, and defocusing it after proceeding through the photonic structure. Any resulting ray of light is then split by a beamsplitter prior respective analysis with a CCD camera (PulNix CCD camera) and an optical spectrum analyzer (OSA Ando AQ-6315E). A top-view imaging camera is placed above the chip to link the spectral results to a visual of the process. The width of the optical spectrum produced by the laser allows us to visualize several resonances together with each spectrum acquired by the OSA. The OSA is remotely controlled by a MATLAB software [19] which allow defining every parameter of the acquisition (span, resolution…). A program has also been implemented for both the acquisition of the spectra and the data treatment in real time. The FSR is extracted from each spectrum by computing its Fast Fourier Transform (FFT) and extracting its maximum value by a Lagrange polynomial interpolation. Finally, the photonic circuit is thermally controlled so as to quantify the influence of temperature on the behavior of this circuit, while a top-view imaging camera allows correlating the steam behavior with the modifications in the transduced optical signal.

RESULTS -DISCUSSION

Once the setup is ready, the spectra are continuously acquired. A few seconds after the beginning of the acquisition, the water condenses on the sensor. The water condensation is obtained by blowing a hot flow of humid air; its contact with a cooler surface (the chip) leads to the condensation of part of the water contained in this air stream. The RH of the room we perform the experiments in is approximately 50%. After whole evaporation of the water, acquisition is carried out further a short amount of time to ensure the resonator being reset back to its initial state. Fig. 4 shows photos extracted from a movie of the surface of the chip at different times, corresponding to different phases in the condensation/evaporation process. Fig. 4-a) and 4-d) correspond to initial and final state, i.e. before the water condenses and after it evaporates. Fig. 4-b) and 4-c)

show the condensed water before and after coalescence respectively. When water condenses on a surface, small drops appear, the coalescence phenomenon is the fusion of several of these small drops into bigger ones in order to decrease the surface energy and reach a more stable configuration. This coalescence phenomenon occurs to rapidly to be investigated with our setup; the present study focuses on evaporation dynamics. Fig. 5 represents spectra at different times during this process, for two different mono-mode resonant structures.

This graphs yield that, considering mono-mode resonators, the greater the perimeter of the resonator, the smaller the free spectral range as predicted in equation ( 2).

For each spectrum, the free spectral range (FSR) and the maximum intensity are extracted by means of an automatized data treatment program. Evolution of these characteristics over time is depicted in fig. 6.

A strong correlation comes up between the FSR and the maximum intensity, owing to the fact that as water condenses on the sensor, the upper cladding of the photonic structure changes from air to condensed water.

This upper cladding change yields two major effects on the intensity. Firstly, as the cladding index changes the acceptance cone of the access waveguide is also modified, leading to a lower coupling strength between the laser ray and the access waveguide, with then a diminished amount of optical power in the structure.

Secondly, as the cladding index is increased, the evanescent wave of the propagating mode enlarges itself and is partly absorbed by the condensed water. Intensity variations are also confirmed by the photos on fig. 4.

Such effects being difficult to quantify and decorrelate, the present study is focused on the FSR dynamics.

The graphs representing the evolution of the FSR can be sliced in four zones (A, B, C and D) as shown in fig. 6-a). Zones A and D correspond to the bare sensor, i.e. a resonator with air as upper cladding. In zone B, as the water has just condensed, the amount of water is sufficient to form a semi-infinite cladding; hence, as long as the amount of water is sufficient, the FSR does not vary. This value of the FSR corresponds to the test value of these structures when the upper cladding is entirely composed of water. This situation is equivalent to the spontaneous condensation of water in case of relative humidity of 100%. Finally, in zone C the water is progressively evaporating, yielding the FSR to decrease until reaching again its initial value when the water is entirely evaporated. Fig. 7 shows the schematic representation of this process accomplished in four steps.

The principal interest of this study relies in the zone C, considering particularly the slope of the linear regression of the dynamics of the FSR 𝑑𝐹𝑆𝑅 𝑑𝑡 , quantity closely related to the evaporation kinetics. Then, table 1 summarizes the results for both geometrical configurations as regard different temperatures.

In order to get rid of the influence of the size of the resonator on the slope, the above values are normalized by the initial value of the FSR, i.e. the value before the condensation of water, with air as upper cladding. These values are presented on table 2. These results show that the higher the temperature, the steeper the slope due to the evaporation speed increased with temperature. The differences between the 5-5-3 and the 10-10-3 structures are due to the value of the radius of curvature R. Indeed, the smaller the radius of curvature, the larger the evanescent wave, leading then to increased variations of the FSR. We have thus proved that fixed geometrical parameters (L C -R-w) implies a temporal sensibility to FSR variations.

The possibilities to design humidity sensors from this optical integrated device are of two kinds. In one hand, the difference between zone A and B allows designing a dew-point sensor, which can detect the presence or not of condensed water on the surface of such a sensor. In the other hand, zone C yields further information.

As we have seen previously the slope

𝑑𝐹𝑆𝑅 𝑑𝑡

in the zone C is related to evaporation dynamic process, which is physically representative of the ability of the surrounding air (considered as a reservoir of gas at fixed relative humidity) to exchange mass of water with the liquid medium. No exact quantitative analytical link between these two quantities is presented in the literature, but the present study clearly highlights their interdependency. The evaporation speed, as for it, is directly correlated to the relative humidity for given conditions of temperature and pressure. By performing a proper calibration in controlled conditions of humidity, temperature and pressure, it is thus possible to design a relative humidity sensor by an adequate monitoring of water evaporation conditions.

CONCLUSION

This work presents a quantitative study about the behavior of integrated photonic micro-resonators subject to sudden water condensation. By dynamically tracking the free spectral range of the resonant structure against time, we have pointed out four steps during the condensation/evaporation process, among which one is correlated to the evaporation dynamics. These measurements have been realized on two different geometrical structures characterized by their values of coupling length and radius of curvature, and for three different temperatures. By performing a proper calibration of such a device, the design of a humidity sensor is possible.

Moreover, the UV-210 material and the single deep-UV photolithography used for the fabrication of this labon-chip sensor allow a low-cost production of such devices. In this study the interest is focused on the analysis of the temporal variations of the free spectral range, but to achieve a complete description of the

Fig. 1 .

 1 Figure caption

Fig. 2 .

 2 Fig. 2. Optical top-view imaging and schematic sectional view of the photonic device.

Fig. 3 .

 3 Fig. 3. Schematic representation of the experimental setup; the acquisition and treatment of data is made in real time.

Fig. 4 .

 4 Fig. 4. Top-view imaging of the chip under injection during the condensation/evaporation process at a) t = 0 s, b) t = 25 s, c) t = 30 s, d) t > 50 s.

Fig. 5 .

 5 Fig. 5. Examples of spectra acquired at different times during the process for values L C -R-w of: a) 5-5-3 b) 10-10-3 in micrometers.

Fig. 6 .

 6 Fig. 6. Evolution of the free spectral range (black) and of the maximum intensity (red) for a 5-5-3 structure, at T= a) 20 °C and b) 28 °C.

Fig. 7 .

 7 Fig. 7. Schematic representation of the succession of the different upper cladding for each zone.

Fig. 1 Fig. 2 Fig. 3

 123 Fig.1

Fig. 4 Fig. 5 Fig. 6 Fig. 7

 4567 Fig. 4

Table captions Table 1 :

 captions1 Numerical values of 𝑑𝐹𝑆𝑅 𝑑𝑡 (μm/s) for different sensing configurations.

Table 2 :

 2 Normalized values of 𝑑𝐹𝑆𝑅 𝑑𝑡 (μm/s) with respect to nominal FSR values.

	Table 1:
	T(°C)
	Resonators
	Lc-R-w (μm)

phenomenon of condensation/evaporation process, wider investigations should be undertaken on the other characteristics of the structures, such as the Q factor and the finesse. These investigations would give more information on the dynamics of the coupling conditions between the access waveguide and the resonators.


Haiqing Zhang
email: haizhang@univ-lyon2.fr

Abdelaziz Bouras
email: abdelaziz.bouras@qu.edu.qa

Aicha Sekhari
email: aicha.sekhari@univ-lyon2.fr

Yacine Ouzrout
email: yacine.ouzrout@univ-lyon2.fr

Suiran

Suiran Yu

A PLM components monitoring

Keywords: PLM components monitoring framework, PLM maturity model, Fuzzy AHP methodology, PLM components maturity assessment, PLM benefits

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INTRODUCTION

PLM is an improving important business and strategic approach for enterprises. It supplies sets of solutions for collaboration, data management, and requirements management from a product's beginning of life to end-of-life. However, PLM is rather a concept than a system. Enterprises cannot adopt and implement PLM well at the right time. PLM maturity models have been developed and used to assess the PLM implementation situation and determine the relative position of the enterprise by comparing PLM maturity levels with other enterprises. The paper gives an overview of PLM maturity models and studies the benefits and restrictions of these maturity models in section 1.1. Then it defines the maturity dimensions based on PLM functionalities in section 1.2. In section 1.3, multi-criteria decision making methodologies are studied to aid selecting the optimal PLM components among various PLM functionalities, in the right context, at the right time.

PLM maturity models

The success of PLM motivates a significant number of companies to adopt and implement PLM.

PLM maturity models can make the implementation of PLM more accessible and better planned.

Evaluation of PLM maturity is essential and advantageous. The objective of this section is to review the important works, and analyze the strengths and weaknesses of these models.

Several important maturity models are worth analyzing. CMMI [START_REF] Dayan | KM your way to CMMI[END_REF][START_REF] Paulk | Capability maturity model, version 1.1[END_REF][10][11][START_REF] Curtis | People Capability Maturity Model (P-CMM) Version 2.0, Second Edition[END_REF] for instance aims to improve the usability of maturity models by integrating several maturity models into one framework. The detail maturity levels and key process areas of CMMI are shown in Table 1. PDM (Product Data Management) maturity models [START_REF] Stark | Product Lifecycle Management-21Century Paradigm for Product Realization[END_REF] define the activities that a company needs to carry out at each stage and define a generic five-step process per stage, which related to the as-is situation and to-be situation of the studied company. CPI (Collaborative Product Innovation) maturity model [START_REF] Sharma | Collaborative Product Innovation: Integrating Elements of CPI via PLM Framework[END_REF] proposes three unique stages of CPI based on collaborative maturity of People, Processes and Data. Batenburg [START_REF] Batenburg | PLM roadmap: stepwise PLM implementation based on the concepts of maturity and alignment[END_REF] developed a PLM framework which supported by a PLM maturity and alignment model to assess and guide PLM implementations. Sä ä ksvuori Model [START_REF] Saaksvuori | Product lifecycle management[END_REF] determines the maturity of a large international corporation for a corporate-wide PLM development program and develops business and PLM related issues. This model is a one-dimensional maturity model, which mixes different organizational aspects into one general dimension. Bensiek & Kuehn model [START_REF] Bensiek | Maturity Model for Improving Virtual Engineering in Small and Medium-Sized Enterprises[END_REF] focuses on virtual engineering and aims to evaluate performance and improvement in SMEs. This model proposes a step by step improvement strategy to SMEs based on specialized SMEs' requirements. Other PLM maturity models include PLMIG [START_REF] Plmig | PLM Maturity Reference Manual[END_REF], PCMA model [START_REF] Zhang | PLM Components Selection Based on a Maturity Assessment and AHP Methodology[END_REF], and BPMM [START_REF] Van Looy | Towards a Decision Tool for Choosing a Business Process Maturity Model[END_REF]. Next, we discuss and compare five important works according to several aspects (aim area, target users, etc.) in Table 2.

Maturity dimensions based on TIFOS framework

To better handle PLM functionalities which have been adopted in a company, our previous work proposed TIFOS framework [START_REF] Zhang | PLM Components Selection Based on a Maturity Assessment and AHP Methodology[END_REF][START_REF] Zhang | Sustainability consideration within Product Lifecycle Management through Maturity Models Analysis[END_REF]. In figure 1

Decision Methodology of fuzzy analytic hierarchy process

The research questions as follows: 1). which PLM component is the relative weak one; and 2). which PLM component should be improved in the first time.

To solve these issues, we need to define the objective, the corresponding criteria, and the alternatives, and then calculate the relative weights of each alternative to achieve the objective. It is a typical multi-criteria decision making issue. Therefore, we study multi-criteria decision making methodologies.

The obtained data about PLM components has the feature of uncertainty and fuzzy, which can be solved by triangular fuzzy numbers. A number of methods have been developed to handle fuzzy triangular numbers. Van Laarhoven & Pedrycz [START_REF] Van Laarhoven | A fuzzy extension of Saaty's priority theory[END_REF] suggest a fuzzy logarithmic least squares method to obtain the fuzzy weights from a triangular fuzzy comparison matrix. Buckley [START_REF] Buckley | Fuzzy hierarchical analysis[END_REF] utilizes the geometric mean method to calculate fuzzy weights. Chang [START_REF] Chang | Applications of the extent analysis method on fuzzy AHP[END_REF] proposes an extent analysis method, which derives crisp weights for fuzzy comparison matrices. Xu [START_REF] Xu | Fuzzy least-squares priority method in the analytic hierarchy process[END_REF] provides forward a fuzzy least squares priority method (LSM). Csutora & Buckley [START_REF] Csutora | Fuzzy hierarchical analysis: the Lambda-Max method[END_REF] propose a Lambda-Max method, which is the direct fuzzification of the well-known λ-max method. Mikhailov [START_REF] Mikhailov | Evaluation of services using a fuzzy analytic hierarchy process[END_REF] develops a fuzzy preference programming method, which also derives crisp weights from fuzzy comparison matrices. Srdjevic [START_REF] Srdjevic | Combining different prioritization methods in the analytic hierarchy process synthesis[END_REF] proposs a multi-criteria approach for combining prioritization methods within the AHP, including additive normalization, eigenvector, weighted least-squares, logarithmic least-squares, logarithmic goal programming and fuzzy preference programming (FPP). Wang et al. [START_REF] Wang | A modified fuzzy logarithmic least squares method for fuzzy analytic hierarchy process[END_REF] presents a modified fuzzy logarithmic least square method. Yu & Cheng [START_REF] Yu | An integrated approach for deriving priorities in analytic network process[END_REF] develop a multiple objective programming approach for the ANP to obtain all local priorities for crisp or interval judgments at one time, even in an inconsistent situation. Huo et al. [START_REF] Huo | New Parametric Prioritization Methods for an Analytical Hierarchy Process Based on a Pairwise Comparison Matrix[END_REF] propose a new parametric prioritization method to determine a priority vectors in AHP.

FPP method [START_REF] Mikhailov | Evaluation of services using a fuzzy analytic hierarchy process[END_REF], as a reasonable and effective means, is adopted in this study. This method can obtain more precise weights of alternatives and can acquire the consistency ratios of fuzzy pairwise comparison matrices without additional study, and the local weights can be easily solved by Matlab. Besides FPP method solves the various shortcomings of different fuzzy AHP methodologies [START_REF] Rezaei | An Improved Fuzzy Preference Programming to Evaluate Entrepreneurship Orientation[END_REF].

Fig. 1. TIFOS Framework and Categorized PLM functionalities

The structure of this paper is structured as follows:

PLM components maturity model will be proposed in section 2, and the maturity situation of PLM components in a swimming industry will be studied as well. In section 3, FAHP methodology will be adopted to rank PLM components' weights and help a company to make decisions of investment. In section The issue is how to make the industries understand KPIs which are proposed and get the accuracy value of these KPIs. The solution is to categorize these KPIs by considering their contribution to return on investment. The categories are cost, time, quality, defects, safety, integrity, and ownership. We give an example in Table 5. The component of product data management is selected, and takes the 'cost' category as an example. Four KPIs are proposed based on 'cost' category, and then the detail content is explained for each KPI, and specific questions are proposed based on the contents. These specific questions can help the companies obtain the exact value of each KPI. Table 6 gives an example of calculations in the final maturity level of the product data management based on the information proposed in Table 3, Table 4, and Table 5. The data is gotten from a swimming industry, which is located in Chengdu (south of China). This company focuses on three categories:

Adopt fuzzy triangular numbers to express linguistic terms

We can get the As-Is situation by using the maturity model PCMA, then the issue is how to help company to improve to the expected To-Be situation by proposing specific strategies.

Define the maturity level of PCMA from level 1 to level 5 is: very low, low, middle, high, and very high.

Then define the value range for each level. The Linguistic terms (very low, etc.) can better explain the uncertainty of each level. The membership function of triangular fuzzy numbers is used to express linguistic terms and has the feature of piece-wise continuous and strictly monotone. The definition and membership function from 'very low' to 'very high' is shown in Table 7.

FPP Methodology calculation steps

FPP is an approach which can guarantee the preservation of the preference intensities and provide a well interpretive consistency index. The steps of this methodology as follows:

Step 1. Develop the fundamental objective hierarchy. Group the related criteria, and structure the hierarchy in Figure 4. The objective is to find the optimal PLM component to invest based on several criteria (cost, time, urgent, and expected income). The alternatives are PLM components. It is not necessary for a company to own all fifteen components. This study just focuses on the specific situation of a company.

Step 2. Construct the fuzzy pairwise comparisons matrix based on Table 7 and Figure 3. In our work, we start from comparing the alternatives with their importance to each of the criteria. Then we compare the criteria with respect to their importance to the goal.

Where ij a  is a triangular fuzzy number to show the decision-maker's preference of i over j, and ij ji aa   . The value of each variable follows Table 7. Take 'Product data management' and 'configuration management' as an example, the first level comparison from 'criteria' to 'objective' for these two PLM components is:

A 1/ 1 / 1 / 1 / 1 / 1 / goal Goal Cost Time Urgent Income Cost equal VH L M Time VH equal VL M Urgent L VL equal M Income M M M equal                   (2)
The value of A goal can be defined by Table 6, 1 0.9 0.3 0.5 0.9 1 0.1 0.5

0.3 0. A 1/ 1 / 1 1 1 0.5 0.5 0.5 0.5 1 / 1/ 1/ 1/ goal                 (3)
On the basis of fuzzy triangular numbers definition, the exactly value of A goal is:

            (1,1,1) (1,1.1,1.42) (1,
               (4)
Step 3. Derive a crisp priority vector w=(w 1 ,w 2 , …, w n ) T by using FPP. The problem is to derive a crisp priority vector w=(w 1 ,w 2 , …, w n ) T , and the priority ratios w i /w j are approximately within the scopes of the initial fuzzy judgments, or equivalently: ( ) ( )

i j i j wi l u wj     (5)
Where the symbol '  ' denotes the statement "fuzzy less or equal to". α means decision maker's preference (α-cut), and ( ), ( )

i j i j l u 
 is the lower and upper bound of fuzzy triangular numbers.

For instance, the priority ratios w i /w j can be the ratios between 'product data management'/'configuration management'.

Step 4. Propose Membership function to measure the ratio in equation 5. Each crisp priority vector w satisfies the double-side inequality with some degree, which can be measured by a membership function, linear with respect to the unknown ratio w i /w j.

, ()

,

i ij j i ij i j i j j i ij i j ij j i ij i j i j j w l w w m m l w w w w u w w m m u w                                 (6)
The membership function takes the following values:

( ) [0,1],

i i i j ij ij j j w w if l u w w        (7)
( ) ( ,0),

i i i i j ij ij j j j w w w if l or u w w w         (8)
It takes the maximum value of 1 when

i ij j w m w  (9)
For example, this membership function can mean the function of ratio 'product data management/configuration management'.

Step 5. Propose two assumptions to obtain the optimal crisp priority vector. For example, it means find the optimal value of 'product data management/configuration management'. The solution to the prioritization problem by the FPP method is based on two main assumptions. The first one requires the existence of non-empty fuzzy feasible area P on the (n-1) dimensional simplex Q n-1 :

1 1 { | 1, 0} n n i i i i Q w w w       (10)
The membership function of the fuzzy feasible area P is given by:

( ) = { ( ) | = 1, 2,..., -1, = 2,3,..., , > } min p i j ij μ w μ w i n j n j i (11)
The second assumption of the FPP method specifies a selection rule, which determines a priority vector, having the highest degree of membership in the aggregated membership function. It can easily be proved that µ p (w) is a convex set, so there is always a priority vector w * ∈Q n-1 that has a maximum degree of membership. Next, we build fuzzy comparison pairwise matrix for obtaining local weights and global weights. Table 8 gives the data of fuzzy comparison matrix based on 'cost' criterion. Table 9 shows the comparison from criteria to global goal. Apply FPP steps in section 3.2 to obtain the final weights of three components in Table 10. 'Product data management' is the optimal component for investment based on the final weights. In this framework, we adopted PCMA model to evaluate the as-is maturity situation of PLM components. Next, various KPIs will be studied to help propose strategies which PLM component should be selected to invest. Then, the FPP methodology is used to determine the relative considerable PLM component. After that, a detailed report will be generated for PLM components' current maturity level, and the obtained the weights of all PLM components to determine of the optimal selection. On the basis of optimal selection, the maturity situation of a company will achieve to a higher level after improving a specific PLM component. Then, the PLM components that should be used in a specific company is determined, the suitable PLM models should be invested in this company based on cost, quality, time, etc. Finally, the feedback loop in Figure 5 indicates that is required to re-assess the PLM maturity with a certain frequency, say every six months or once in a year. By doing so we can measure whether the PLM components are on track in reaching the new maturity level, and the adopted PLM model is the optimal option in terms of cost, time, quality, etc. 8 REFERENCES

Table 3 .No effort has been made to consider about recycling 3 

 33 cost, time, and quality. KPIs are proposed based on these three categories. Questions are made to help the company to get the values of these KPIs. Maturity level is gotten based on KPIs. The final maturity level is the average score of all KPIs, and product data management is level 2 for this company. The maturity level of all PLM components for this swimming industry is shown in Figure 2. PCMA Maturity Level and Corresponding Content Maturity Levels Our Work (Items for PLM components Maturity Levels) 1 ad-hoc  The activity is done with expediency  Nobody is responsible for PLM  Documentation is at the lowest point to satisfy operational needs  PLM software system and processes have deficiencies 2 Managed  The activity is defined and managed, but it is repetitious  Documentation and record is carefully studied  Mutual actions are finished in processes and departments  PLM systems are involved and used in the proper places. Defined The activity is formalized and supported by standards  Documentation and record is studied and shared  Personal actions and mutual actions are carried out efficiently  PLM systems cooperate with other enterprise systems  The products run efficiently and are effective  Progressively eliminates errors and failures 5 optimized  The activity runs optimally  PLM system helps company make improved decisions  Best practices and innovative ideas are considered

  Figure 3 is used to describe the function. The aim to set a range of each level is to help questionnaire responders when they do not know the exact value of the corresponding KPIs.

Step 6 . 3 . 3

 633 Transform the problem into a bilinear program based on the rule of Bellman and Zadeh[START_REF] Bellman | Decision-making in a fuzzy environment[END_REF].The equation is in the following: ..., -1, = 2,..., , > , = 1,..., Implementation in real-word cases Data was selected in a swimming industry from January to July. The reason we selection this company is because the security and sustainability become the first issue to be considered in China. Take three widely used PLM components as the alternatives, which are: product data management (C1), new product development (C2), and configuration management (C3). The goal is to help the manager to make the decision of which component should be first invested in. The criteria are cost to invest, time to invest, urgent to invest, and the expected income after invest. This company is a small and middle enterprise. They need to update the product data management to afford the increasing information, at the same time, new security software should be invested to protect customers' safety and configuration management should be updated to configure new requirements. Four pair-wise comparison matrixes are established based on four criteria. The aim of these matrixes is to find the optimal components to balance the cost, time, urgent need, and expected income. The weights which are obtained from these matrixes are called local weights. After that, build a global matrix to determine the relative weights of cost, time, urgent, and income to obtain the global weights. The final weights are gotten by combining local weights and global weights.

Fig. 5 .

 5 Fig.5. PLM components monitoring framework

  This work has been funded by Hubert CurienPartnership with Cai Yuanpei China project 2012-2014.

Table 1

 1 CMMI Maturity Levels and Key Process Areas

	CMMI Maturity Levels	Focus	Key Process Areas
	1: Initial 2. Repeatable	Basic project management	Requirements management; Project planning; Project monitoring and control; Supplier agreement management; Process and product quality assurance; Configuration management
			Requirements development; Technical solution; Product
	3.Defined	Process standardization	integration; Verification; Validation; Organizational process focus; Organizational process definition; Organizational training;
			Risk management; Decision analysis and resolution
	4. Quantitative	Quantitative management	Organizational process performance; Quantitative project management;
	5.Optimizing	Continuous process improvement	Organizational innovation and deployment; Causal analysis and resolution

Table 2

 2 Comparison of Some PLM Maturity Models

	Maturity Models	CMMI [7,9-12]	Batenburg model [3]	PLMIG model [6]	Sä ä ksvuori & Immonen model[4]	Bensiek& Kuehn model [5]
	Aim area	Process Improvement	PLM	PLM	PLM	Virtual engineering

CMMI: separates organizational functions, sets process improvement goals and priorities, provides guidance for quality processes, and provides a point of reference for appraising current processes Batenburg model: Balance between dimensions, easier to understand and apply, provides benchmark data to other maturity models.

PLMIG model: Advices to next steps, identifies gaps among levels, coordinates between different dimensions.

Table 3 .

 3 We give an example in Table4for how to evaluate

		indicators of PLM components. This maturity model
		follows the principle structure of CMMI by using the
		same maturity levels and structured questionnaires.
		CMMI defined process maturity is developed
		incrementally from one level to the next level and it
		does not allow for skipping levels. This limitation of
		CMMI will result in misleading interpretations for
	4, five different PLM models which contain different	small and middle enterprises (SMEs). PCMA model
	PLM components will be discussed. Section 5	concerns the limitation and provides clearly gap
	proposes a PLM components monitoring framework	among each level. Our previous work gives detailed
	by combining a PLM maturity model and FAHP	information of fifteen components in each maturity
	methodology. Section 6 concludes our work.	level in which the maturity is assessed separately, and
	2 THE PROPOSED PLM COMPONENTS	the items of maturity level descriptions are outlined in
	MATURITY ASSESSMENT MODEL
	PLM Components Maturity Assessment model	the PLM components maturity level by using PCMA
	(PCMA) [14] considered viewpoints of different	model. Two PLM components (C1 and C2) are
	maturity models and analyzed key performance	selected in Technoware, several KPIs (C1_K1 to

Table 4 .

 4 PLM components and corresponding key performance indicators

	TIFOS Framework	PLM Components	KPIs	Levels 1 2	3	4	5
			C1_K1: %of new products	■
		C1: Techniques &Practices	C1_K2: Produce products accuracy		■
	TechnoWare		C1_K3: Running cycle time			■
		C2: PLM software &	C1_K4: Installation Planning costs		■
		Applications …	C1_K5: % of Waste…		■

Table 5 .

 5 Product Data Management component and its' corresponding key performance indicators

		Product Data Management
		KPIs	Description	Questions	Value
				How much you pay for
				information storage (including
			Measure of all data	hardware and software)?
		1. Average Data storage cost	storage/ number of documents (categories)	How many documents you have to manage?
				How much memory you need to
				manage information? (GB)
	Cost	2. Average Document using frequency per day	Number of document using frequency/ number frequency of all documents using	How many documents you used more than 30 minutes per day?
		3. Average Document finding time-to-cost	How many time it takes for users to find it in seconds/minutes	How long you spend to find the documents you use every day?
		4. Average using cost per document	Average cost for printing and creating the .pdf per document	How much you spend to use these documents (including printing, creating the .pdf, ...)

Table 6 .

 6 Product Data Management component and its' maturity level

	Product Data Management
	Categories KPIs

Table 7 .

 7 Definition and membership function of fuzzy scale

	Fuzzy numbers	Definition	Membership function
	̂	Very Low (VL) (0, 0.1, 0.3)
	̂	Low (L)	(0.1, 0.3, 0.5)
	̂	Middle (M)	(0.3, 0.5, 0.7)
	̂	High (H)	(0.5, 0.7, 0.9)
	̂	Very High (VH)	(0.7, 0.9, 1)
	Fig.3. Structure of Fuzzy triangular numbers
	3.2

Table 8 .

 8 Fuzzy comparison pairwise matrix for getting local weight

	Cost	C1	C2	C3
	C1	Equal	H	VH
	C2	1/H	Equal	H
	C3	1/VH	1/H	Equal

Table 9 .

 9 Fuzzy

		comparison pairwise matrix for getting
			global weight
		Cost	time	urgent	income
	cost	Equal	VH	L	M
	time	1/VH	Equal	VL	M
	urgent	1/L	1/VL	Equal	M
	income 1/M	1/M	1/M	Equal

Table 10 .

 10 Local weights and global weights

		C1	C2	C3	Global Weight
	Cost	0.6286	0.2854 0.1014	0.1857
	time	0.5058	0.3230 0.1676	0.1296
	urgent	0.3378	0.4305 0.2317	0.3823
	income	0.2485	0.4251 0.3264	0.2845
	Final weight	0.3821	0.3804 0.2220

Fig.4. FAHP hierarchy towards of PLM components selection ......