Characterization Scheme for Property Prediction of Fluid Fractions

Article pubs.acs.org/EF

Characterization Scheme for Property Prediction of Fluid Fractions Originating from Biomass Thanh-Binh Nguyen,†,‡ Jean-Charles de Hemptinne,*,‡ Benoit Creton,‡ and Georgios M. Kontogeorgis§ ‡

IFP Energies nouvelles, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France Chemistry Department, University of Science and Technology, The University of Da Nang, 54 Nguyen Luong Bang, 59000 Da Nang, Vietnam § Center for Energy Resources Engineering (CERE), Department of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark †

ABSTRACT: The composition of industrial fluids is often very difficult to identify from the molecular point of view. In the petroleum industry, the use of the so-called “pseudo-components” is commonly accepted in process modeling, and various approaches exist to determine and/or construct them. We have identified and summarized four such approaches, generally based on experimental information such as boiling temperature and density. Fluids that originate from biomass, however, cannot be treated using only volatility, because of the highly polar character and the high molecular weight of its components, resulting in highly nonideal phase equilibrium behavior. In this work, it is proposed to use a more complete set of experimental descriptors in order to determine the chemical structure of an unknown fluid cut. The definition of such a representative molecule (surrogate) makes it possible to use group contribution or other predictive tools for property calculations or characteristic parameters of an equation of state. In order to achieve this goal, a large database of monofunctional molecules (including alcohols, n-aliphatic acids, aldehydes, ketones, aliphatic ethers, esters, n-alkylbenzenes, and alkanes) has been constructed, which contains a number of descriptors originating from analytical measurements. Using physical insight on the molecular interactions, an algorithm is proposed that uses five descriptors (molecular weight, liquid molar volume, viscosity, refractive index, and dielectric constant) in order to reconstruct a representative molecule.

1. INTRODUCTION Accurate characterization of a fluid plays an important role in both developing predictive thermodynamic models and the design and optimization of refining processes. According to Khan and Pope,1 a fluid characterization has to answer four questions: (1) “How many components should be used?”, (2) “How should pseudo-components be formed?”, (3) “How should fluid characterization parameters be obtained?”, and (4) “Which mixing rules should be used to calculate pseudoproperties?”. The first question concerns the compositional analysis of investigated fluids. It should be noted that the analytical information will determine the approach to generate pseudo-components. The concept of pseudo-components was first introduced by Katz and Brown,2 indicating one or a group of chemical species. In the oil and gas industry, the complexity of petroleum fluids, which usually contain thousands of components belonging to many families, makes it impossible to identify each component individually.3 Therefore, these complex fluids are often characterized using a limited number of pseudo-components by using the analysis information on the true boiling point (TBP) curves and specific gravity. This approach is still a prevailing technique in modeling refining processes. Computeraided molecular design can be used as an alternative tool for characterizing petroleum fluids as discussed by Valdez-Patrinos et al.4 and Gani et al.5 Nowadays, manufacturers are challenged by the treatment of increasingly complex industrial fluids like bio-oils originating from biomass resources. Much research is now focused on the © XXXX American Chemical Society

valorization of the so-called second generation biofuels which are produced from nonedible materials, such as forestry and agricultural residues, and nonfood crops.6,7 The latter is generally called lignocellulosic biomass whose chemical structure is very complex, consisting of three main components, i.e., cellulose, hemicellulose, and lignin.8 Bio-oils produced using some processes including liquefaction, pyrolysis, and gasification,9 contain a very large number of oxygenated compounds spanning a wide range of molecular weights and polarities. These compounds, which are highly polar and hydrogen-bonding, consist of acids, esters, alcohols, ketones, aldehydes, phenols, furans, guaiacols, syringols, and sugars. As a consequence, the characterization of bio-oils for modeling purposes is an important challenge for new refiners. The use of conventional analytical information, i.e., volatility curves, is not appropriate anymore because this information cannot take into account the polarity and hydrogen-bonding effects that exist in biocrudes originating from biomass. In fact, it is often impossible to simply measure the boiling temperature (let alone the full volatility curve) of bio-oils, because the product pyrolyzes at low temperature. In addition, the use of modern equations of state (EoS) serving the phase equilibrium and thermodynamic property calculations increasingly requires a fluid characterization at the molecular level or the knowledge of the chemical structure of Received: April 13, 2015 Revised: September 10, 2015

A

DOI: 10.1021/acs.energyfuels.5b00782 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels an investigated fluid. Such information is required as an input to group contribution (GC) approaches, which is the recommended way to parametrize many such EoS. Examples are predictive Soave−Redlich−Kwong (PSRK),10 group contribution association (GCA)11 or the GC versions of the statistical associating fluid theory (SAFT).12−19 The characterization procedure requires two steps: (1) separating the fluid into fractions and (2) characterizing each fraction. The objective of this work is focused on the second step only: once physical fractions of a biomass fluid are obtained (through preparative chromatographic techniques, for example), what experimental descriptors are significant in order to determine its average chemical structure? The definition of a representative (surrogate) molecule will make it possible to use group contribution or other predictive tools for property calculations or characteristic parameters of an EoS.20−22 In order to achieve this goal, a large database of monofunctional molecules has been used, which contains a number of descriptors that originate from analytical measurements (extracted from the DIPPR database23). Using physical insight on the molecular interactions, an algorithm is proposed that uses five descriptors (molecular weight, density, dynamic viscosity, refractive index, and dielectric constant) in order to distinguish among the following chemical families: alcohols, aliphatic acids, aldehydes, ketones, aliphatic ethers, esters, alkylbenzenes, and hydrocarbons. A method is then proposed to reconstruct a pseudo-molecule that is representative of the original cut. The report is organized as follows. As a starting point, a review of some approaches used to characterize fluids is briefly presented. The construction of the database used in this work is introduced in section 3. Section 4 will present some physical observations on molecular interactions. Based on these observations, we will present the construction of the characterization scheme in section 5. The application of this scheme in some examples is shown in section 6. Finally, some conclusions and perspectives are provided at the end.

the representation will be. An adequate temperature interval lies between 10 and 15 K.25 Each pseudo-component defined from the TBP curve is characterized by an average boiling temperature and specific gravity. This latter property is either measured or evaluated using a “constant Watson factor method”.26 Using these two properties, the pseudo-components can then be attributed to some physical properties (e.g., critical temperature and pressure or acentric factor) using adequate correlations, for example, those of Lee and Kesler,27 but many others can be found in the literature.3,26 Recently, an approach was proposed by Xu et al. in order to estimate the binary-interaction parameters, kij, for pseudo-components within cubic equations of state.28 Although satisfying the simulation purposes for refiners, and furthermore being still a prevailing technique in modeling of refining processes today, this approach has some inevitable limitations as discussed by Eckert and Vaněk.29 The most important limitation is that the input information almost exclusively refers to the fluid volatility. As a result, it is incapable of taking into account the wealth of complexity that exists in crudes originating from biomass. In addition, this technique does not provide molecular information in a detailed way. 2.2. Lumping Approach. Another approach used to characterize fluids is the lumping technique. It requires a detailed analysis of all of the components present in the investigated fluid. The development of modern analytical instruments (such as chromatography, spectroscopy, and spectrometry, etc.) allows identification of the composition and structural information for a large number of components in fluids, particularly for petroleum fluids.30,31 Recently, the development of the two-dimensional gas chromatography, known as GC-2D or GCxGC, makes it possible to extend this type of analysis to oxygenated bio-oils.32 This approach is based on the lumping of components having one or a few similar properties (e.g., critical temperature and pressure, acentric factor, and molecular weight, etc.) into a hypothetical group. The most frequently used lumping method is that of Montel and Gouel,33 known as the dynamic cloud method. In this lumping technique, a number of molecular properties are used as criteria together with a corresponding weight factor. The algorithm will then identify a number of pseudo-components by minimizing the distances between the barycenters (centers of lumps) of these groups and the species they contain in a multidimensional space for all properties considered. Finally, properties or EoS parameters need to be determined for each pseudo-component that we call also a lump. For this purpose, an averaging rule based on the properties of the initial components is often used. Examples of averaging rules for calculating critical properties, molecular weight, and acentric factor for a lump can be found in the literature.33,34 Consequently, the well-defined lumps can be used as pure components in the chosen EoS. Such a lumping procedure has for example been applied to describe gasoline35 and diesel36 surrogates; using this latter information as inputs of molecular simulations, authors mimicked gasoline and diesel behavior in extreme conditions (for instance, temperature and pressure in an engine under working conditions). The difficulty for this approach is to identify the criteria used for the lumping. Most often, when this method is used for hydrocarbon fluids, the critical parameters and acentric factor are used as criteria. For the polar fluids that originate from

2. REVIEW OF SOME CHARACTERIZATION APPROACHES An EoS is traditionally used for performing phase equilibrium and thermodynamic property calculations. Yet, such equation of state requires characteristic parameters for each component. In this section, we propose a short literature review of how a fluid characterization may help in estimating the equation of state parameters. Even though many examples exist for petroleum fluids that are adequately described using cubic EoS, emphasis has been placed in this section on the molecularbased equations of state that can be used for oxygenated fluids on which this work is focused. As mentioned in section 1, a procedure for characterizing fluids is indispensable. The fluid is often characterized using a limited number of pseudocomponents. The advantages of this approach for simulation purposes lie in the facts that (1) no molecular information is required and (2) the number of compounds being simultaneously modeled is reduced. 2.1. Use of the True Boiling Point Curve. Traditionally, pseudo-components are identified from the analysis of distillation curves or TBP curves24 which represent the cumulative liquid volume percentage as a function of the temperature. The curve is cut into temperature intervals, each of which gives rise to a pseudo-component. It should be noted that the smaller the temperature intervals, the more accurate B


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using selected solvents. On the basis of some selected properties (solubility and polarity), the oil is separated into several fractions. This step will facilitate the analytical operations that are performed on the fractionated fractions. The second step consists of identifying the chemical composition of the separated fractions. The recent developments of modern analytical instruments may provide a lot of detailed information regarding the chemical composition of oil fractions even when only small amounts are available.44 In order to use an EoS for phase equilibrium calculations, each fraction is considered as a pseudo-component for which it is necessary to have characteristic parameters. At this point in time, we are only aware of examples stemming from the petroleum industry. For instance, Szewczyk used the SARA characterization, combined with the group contribution in order to determine some characteristic parameters of each fraction, to describe asphaltene fluids.50 The disadvantage of this technique lies in the fact that the chemical nature of fluids that is identified on the basis of the solubility characteristics varies with the origin and processing conditions of the considered fluid. This operation has also other limitations such as being time-consuming and expensive and lacking reproducibility.44 Nevertheless, it is the only way that we know for identifying fractions according to their chemical affinity rather than their volatility. This is why, in this work, we will assume that such a fractionation method is available and propose a way to characterize the fractions based on a number of simple measurements. We shall thus propose a representative molecule whose structure can be used as input in any predictive model for further use. 2.5. Conclusion. The four main approaches identified here are summarized as shown in Table 1. The use of one or another method depends on the available input data (boiling point curve, density, chromatographic analysis, and spectroscopic and spectrometric techniques, etc.). The treatment describes how these data are used to select the pseudo-components. In the next step called “characterization”, the pseudo-components must be given parameters for use in a predictive model (for example an EoS). It appears that the characterization is often based either on the corresponding states principle, which works well for hydrocarbon mixtures but is quickly limited for oxygenated fluids, or on group contribution concepts. In this work, we will focus on how to reconstruct a representative molecule by using descriptors that can be obtained using analytical measurements.

biomass, these criteria are no longer adequate because they do not take into account polarity or hydrogen-bonding, and other descriptors, such as those proposed later, could be used instead. 2.3. Molecular Reconstruction of Fluids. In an attempt to characterize petroleum cuts from partial analytical data, Hudebine et al. developed a statistical tool, called the entropy maximization approach, that allows creating mixtures of representative molecules with the same properties as those available for the complete fluid.37−39 This approach consists of two steps. In a first step a reference equimolar mixture is constructed containing a large number of molecules. All of the species have the same molar fraction (=1/N, where N is the number of molecules). A stochastic reconstruction method is used to build the molecules: a Monte Carlo sampling method based on a set of distribution functions describing the statistical distribution of structural blocks (e.g., aromatic rings, naphthenic rings, and so on) or molecular characteristics (e.g., the type of molecule, the length of the chain, and the probability of the presence of -CH2- groups, etc.) is employed. For each constructed molecule, the requested properties are calculated, typically using group contribution correlations (e.g., specific gravity, molecular weight, and normal boiling point, etc). The average properties of this equimolar mixture are obtained through mixing rules and compared to the available analyses of the real fluid to modify the parameters of the distribution functions. The equimolar mixture can contain several thousands of molecules. For instance, Verstraete et al. used a set of 5000 molecules to represent an Arabian Light vacuum residue.37 In a second step, starting from the equimolar (or reference) mixture of molecules, the molar fractions are adjusted by using a constrained maximization technique. The objective function to be maximized is the entropy of the fluid, while the constraints are such that the fluid properties are as close as possible to those measured on the real fluid. The molar fraction distribution of the equimolar mixture is uniform. More details about this technique can be found in the literature.37−39 This approach was shown to be useful for rebuilding some petroleum cuts such as gasoline and diesel fuels originating from a fluid catalytic cracking unit and heavy petroleum residue fractions.38,40−42 It has not yet been extended to oxygenated fluids. To our knowledge, this approach has never been used in combination with an EoS. As such, it is probably not adequate because of the very large number of components. However, if combined with a lumping scheme, it could be used as an input so as to produce a limited number of pseudo-components. 2.4. Solvent Fractionation Approaches. Another approach used to characterize petroleum fluids, mainly heavy oils, is solvent fractionation that is based on differences in solubility and polarity between the components. This approach is based on the use of solvents to fractionate the mixtures in terms of chemical families. Each of these chemical classes can be considered as a pseudo-component. An example of such a method is the fractionation of heavy crude oil into saturates, aromatics, resins and asphaltenes (SARA), using n-heptane, acetone, and dimethylformamide.30 The solvent fractionation technique or liquid−liquid extraction has been also applied for bio-oils originating from biomass in many different ways.43 Various research groups have developed their own methods.44−49 In general, the fractionation procedure of pyrolysis oils can be separated into two successive steps. The first step involves the fractionation of bio-oils by

3. PROCEDURE The objective of this work is to propose a single surrogate molecule to describe the thermodynamic behavior of a fluid fraction. For this purpose, we consider that the behavior is driven by a limited number of phenomena which the surrogate molecule must be able to mimick. These can be listed as molecular size and shape (which will drive the excluded volume), molecular polarizability (which is related to the van der Waals forces), permanent dipoles or quadrupoles, and hydrogenbonding capacity. We will consider that simple monofunctional molecules are sufficiently complex to be capable of describing the behavior of such a cut. In order to establish a scheme for determining the chemical structure of an unknown fluid, a large database of monofunctional hydrocarbons and oxygenates belonging to 10 chemical families is compiled (see Table 2). Note that the “alkenes” family is composed of 1-alkenes and methylalkenes; the “alkanes” family includes n-alkanes and methylalkanes; the “alcohols” include both n-alcohols and isoalcohols. C


Article inconvenient to use as such, should be used as an input for lumping

requires detailed information, but potentially to be applied with any model

MW

υL

LVS

n

ε

μ

alkenes alkanes cyclohexanes n-alkylbenzenes aliphatic ethers ketones aldehydes alcohols esters aliphatic acides

33 50 7 16 25 26 21 47 47 18

33 50 7 16 25 26 21 47 47 18

39 36 18 17 30 28 13 52 44 9

33 50 7 16 25 26 21 47 47 18

15 27 1 5 7 15 14 37 32 9

15 27 1 5 7 15 14 37 32 9

total

290

290

286

290

162

162

The data are taken from the DIPPR database.23 Symbols: MW, υL, LVS, n, ε, and μ indicate molecular weight (g·mol−1), liquid molar volume (m3·kmol−1), dynamic viscosity (Pa·s), refractive index, dielectric constant, and dipole moment (D), respectively. a

In addition, we have selected a number of analytical descriptors (i.e., measured properties) that we believe are adequate indicators of the molecular interactions we want to describe and which are available in the DIPPR database.23 These descriptors comprise five physical properties, i.e., molecular weight (MW), liquid molar volume (υL), dynamic viscosity (LVS, liquid viscosity), refractive index (n), and dielectric constant (ε). The criteria for choosing these five analytical properties stem from the fact that (i) they are easily measured in the laboratory by current approaches and (ii) they potentially represent the chemical nature of highly polar and hydrogen-bonding components. The dynamic viscosity (LVS, Pa·s) values are calculated at 298.15 K from the correlations available in the DIPPR database. We shall see that it may be used as an indicator of hydrogen-bonding. Heat of vaporization can also be used for that purpose, as discussed by Nath and Bender,51 but very difficult to measure on biomass fluids. The polarizability of a pure compound can be theoretically related to the molar refraction (Rm, m3·kmol−1) which is expressed in terms of refractive index (n) and apparent molar volume (υL) of that compound,52 as shown by

group contribution

lumping on adequate criteria

statistical reconstruction

set of fractions using selected solvents

detailed molecular composition

any analytical data

lumping33,34

molecular reconstruction (Hudebine)37−39

additional measurements needed, typically to determine the functional groups mixing rules

families

Rm =

solvent fractionation44−49

TBP

Table 2. Availability of Experimental Data Per Chemical Family (Number of Compounds for Which Data Are Available)a

pseudo-components characterized by any chosen property large number of molecules

same global approach as volatility curves except that the criterion is chemical affinity rather than volatility

only volatilities; use of cubic EoS

corresponding states based pseudo-components use group contribution to construct pseudo-molecules correlations calculating critical parameters

cutting into temperature intervals and attribution of a density to each cut each fraction is one pseudo-component volatility curves

characterization treatment input data approach

24,25

Table 1. Summary of the Characterization Approaches

description

note

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n2 − 1 MW n2 + 2 ρ

(1) −3

where ρ is the density (kg·m ). In eq 1, the ratio between MW and ρ can be replaced by υL. The molecular weight quantity commonly appears in many characterization approaches in petroleum refining, as well as in developing the group contribution method. Therefore, this property is also used in this work. In addition, the experimental values of dipole moment are also collected in order to validate the calculated values using the Onsager relation (see section 4). The use of this property will be presented in the next section.

4. PHYSICAL OBSERVATIONS ON MOLECULAR INTERACTIONS 4.1. Association. Figure 1 shows that the logarithm of the dynamic viscosity is approximately linear as a function of molecular weight, within a chemical family. Yet, it also strikingly shows that, for a given value of MW, the alcohols and acids have a higher viscosity than the other, non-associating families. It can be argued that the hydrogen bonds within these fluids hinder the shear and require therefore a higher stress for the same effect. D


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than 0.5 log units, thus making it possible to distinguish these two families from the non-associating components. 4.2. Number of Oxygen Atoms. The presence of oxygenated functional groups in molecules results in dipole− dipole intramolecular and/or intermolecular interactions. These interactions can be theoretically measured through Rm which is defined as shown in eq 1.52 It can be assumed that the molar refraction of molecules is an additive property to which each group contributes. Hence, for alkanes, the molar refraction is almost proportional to the number of constitutive groups and can be written as Rm n‐alkanes = 0.0003MW − 0.0007 m 3·kmol−1

(3)

Figure 3 shows that the Rm of molecules depends linearly on the molecular weight. Based on this observation, the molar Figure 1. Dynamic viscosity (LVS) as a function of molecular weight. The LVS values are calculated from the correlations constructed by the DIPPR database.23 The inset indicates the correlation of LVS values of n-alkanes as a function of molecular weight.

The evaluation of whether a compound may associate can therefore be based on the difference between the dynamic viscosity of the compound and that of the corresponding homomorph. The homomorph is defined as the hypothetic nalkane that has the same molecular weight as the investigated compound. A mathematical relationship (eq 2) can be drawn for estimating the dynamic viscosity of the n-alkanes as a function of molecular weight:

Figure 3. Molar refraction as a linear function of the molecular weight. The linear equation is exclusively based on n-alkane data.

log(LVS)homomorph = −0.000015(MW)2 + 0.012105MW − 4.474094

refraction of hydrocarbons (Rmhomomorph) will be approximately calculated from the correlation between Rm and the molecular weight for n-alkanes that is presented in eq 3. When a polar group (e.g., oxygenated functional groups) is present in the molecule, the molar refraction can be written as

(2)

If we define Δlog(LVS) = log(LVS) − log(LVS)homomorph, it is possible to visualize the result of Δlog(LVS) as a function of molecular weight for the various families, as shown in Figure 2. Alcohols and n-aliphatic acids have a value of Δlog(LVS) larger

Rm = Rmhomomorph + ΔRm

(4)

where Rmhomomorph is the molar refraction contribution of the homomorph, again defined as the molecular weight equivalent hydrocarbon. ΔRm can be seen as the contribution of the oxygenated functional groups. As a consequence, the contribution to the molar refraction by the oxygenated functional groups can be determined using ΔRm = Rm − Rmhomomorph. Figure 4 shows that ΔRm is (almost) independent of molecular weight (within the uncertainty range). In addition, this figure allows distinguishing among chemical families such as hydrocarbons, molecules containing one oxygen atom (ketones, esters, and alcohols, etc.), and molecules containing two oxygen atoms (esters, acids, and so on). The results shown in Figure 4 can be used in addition to the observation of Figure 2 to distinguish, for hydrogen-bonding families, between alcohols (one oxygen atom) and n-aliphatic acids (two oxygen atoms). It can be observed on Figure 4 that the lines are not straight. This could have been corrected if a different fit had been chosen in eq 3, but, unfortunately, because the minima in the curves do not occur at identical molecular weights, the overlap between zones would have been much larger. The reason for this limitation is probably due to the fact that Rm does not exactly obey the

Figure 2. Difference between the dynamic viscosity of the compound and that of the homomorph. The latter is defined as the inert substance (n-alkanes in this work) having the same molecular weight as the compound investigated. For example, Δlog(LVS) of 1-butanol having MW = 74 g·mol−1 is calculated by the difference of log(LVS)1‑butanol and log(LVS)homomorph which can be obtained by using eq 2. E


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Figure 4. Contribution to molar refraction by the oxygenated functional groups ΔRm as a function of molecular weight. The value is the difference between the molar refraction of the molecule investigated and that of the molecular weight equivalent hydrocarbon part, calculated by using eq 3.

Figure 5. Comparison between the dipole moment calculated by using eq 5 and the experimental data taken from the DIPPR database.23

mRD = MW(n − 1.475)

additive group contribution principle that is postulated here. Some aromatic molecules having large molecular weight deviate slightly from the area which is found for nonpolar hydrocarbon (the value ΔRm > −0.002 m3·kmol−1). In addition, some one oxygen containing molecules, i.e., aliphatic ethers, are found in the zone for nonpolar hydrocarbons. 4.3. Polarity. For the type of molecules considered in this work, the dipole−dipole interactions are mainly due to the oxygenated functional groups. The dipole moment is a measure of the magnitude of this type of intermolecular interaction.53 There are many theories concerning the molecular dipole moment.54 Theoretically, the dipole moment is known to be related to the dielectric constant (ε) and the refractive index (n). Equation 5, developed by Onsager,55 expresses the relationship between these properties.

(6)

where 1.475 is the extrapolated value of n when the molecular weight of compounds is extremely high. Figure 6 represents mRD values as a function of molecular weight. It is observed that mRD is almost independent of the

⎛ n2 − 1 ⎞ MW ⎛ ε − 1 ⎞ MW NA ⎛ 3ε(n2 + 2) ⎞ μ2 ⎜ ⎟ =⎜ 2 + ⎜ ⎟ ⎟ ⎝ε + 2⎠ ρ 9ε0kB ⎝ (2ε + n2)(n + 2) ⎠ T ⎝n + 2⎠ ρ

(5)

where μ is the dipole moment (C·m); T is temperature (K); kB = 1.381 × 10−23 J·K−1 is the Boltzmann constant; NA = 6.022 × 1023 mol−1 is the Avogadro number; ρ is the density (kg·m−3); and ε0 = 8.854 × 10−12 F·m−1 is the free space permittivity. Based on the Onsager expression (eq 5), the dipole moment of molecules can be theoretically calculated from n and ε. This equation performs quite nicely for a large number of compounds, as can be observed in Figure 5. On the top of this figure, the CO group belonging to aldehydes and ketones has, as expected, the largest dipole moment. All O C−O groups (esters) exhibit equivalent values of dipole moments, and the smallest dipole moment for polar molecules is found for aliphatic ethers (C−O−C). This result may be useful in predicting the dipole moment, and therefore identifying the family of non-associating polar compounds. 4.4. Aromatics. The aromatic ring features a quadrupole rather than a dipole. Riazi and Daubert56,57 observed that the aromatics’ refractive index behaves in a way different from that of other molecules. They proposed the use of the parameter m, labeled mRD in this work, in order to identify the presence of such aromatic groups in molecules. According to Riazi and Daubert, the presence of aromatic groups in the molecule is verified by the positive value of mRD. The parameter mRD (g· mol−1) is defined as shown in

Figure 6. Value mRD, calculated by using eq 6, as a function of molecular weight.

molecular weight. The results shown in Figure 6 allow us to distinguish the n-alkylbenzenes whose mRD values are always positive. In addition, it should be noted that some oxygenated molecules such as phenylacetate, 2-phenylpropionaldehyde, and acetonephenone which also contain an aromatic group similarly exhibit a positive value for mRD. Thus, the approach proposed by Riazi and Daubert56,57 is very useful for determining the presence of an aromatic group in the molecule investigated.

5. MOLECULAR RECONSTRUCTION The criteria that have been identified in section 4 could be used for reconstructing a representative molecule as a pseudocomponent for which the five required properties are available (MW, υL, LVS, n, and ε). This representative molecule is assumed to be a linear molecule possibly containing a functional group which may be aromatic or oxygenated. Therefore, this approach necessitates as the first step to identify the chemical family. From the physical observations presented in section 4, a characterization scheme is proposed in F


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Figure 7. Characterization scheme for identifying some functional groups including alcohols, acids, ethers, esters, aldehydes, ketones, aromatics, and hydrocarbons.

6, a positive value of mRD is evidence of the presence of this functional group in the molecule. It is now possible to distinguish among chemical families including alcohols, n-aliphatic acids, aliphatic ethers, esters, aldehydes and ketones, aromatics, and hydrocarbons. 5.2. Determination of the Alkyl Chain. The second step for constructing a representative molecule is to add an alkyl chain to the functional group previously identified using the characterization scheme (Figure 7). It is assumed that this scheme, which was established for monofunctional linear molecules, is sufficient for our purpose: we will thus construct a monofunctional representative molecule whose five characteristic properties will match as closely as possible the imposed values. Therefore, an alkyl chain constituted of one or two CH3 and CH2 groups is added to the functional group. The procedure of adding an alkyl chain is realized as follows. First, the number of CH3 groups found at the end of the molecular chain must be determined. Depending on the type of the functional group in the molecule chain, the number of methyl groups will be 1 or 2, as summarized in Table 4.

order to distinguish the chemical families considered in this work (i.e., hydrocarbons and oxygenated compounds) through the use of the five properties. The second step is to add an alkyl chain which is based on the availability of the molar weight. It should be noted that this approach is based on the assumption that (1) the investigated fluid is previously separated and every fraction is sufficient for the measurements and (2) the five properties for each fraction are available in order to define a model molecule for the thermodynamic properties calculations. 5.1. Identification of the Chemical Family. The proposed characterization scheme is shown graphically in Figure 7. The first step in this scheme is to distinguish the selfassociating molecules (alcohols and n-aliphatic acids) from the non-associating ones. On the basis of the dynamic viscosity and the molecular weight of molecules, the difference between the dynamic viscosity of the molecule investigated and that of the homomorph having the same molecular weight (eq 2) is calculated. Δlog(LVS) ≥ 0.5 (Pa·s) is an indication of the associating molecules including the alcohols and n-aliphatic acids. These two classes will be then distinguished based on ΔRm which is calculated by using eqs 1, 3, and 4. The alcohols are identified when the calculated ΔRm value is greater than −0.006. Similarly, ΔRm ≤ − 0.0006 is the range valid for naliphatic acids. The remaining oxygenated compounds (i.e., not selfassociating) and hydrocarbons (non-associating) are recognized using the values of the dielectric constant, refractive index, and liquid molar volume. As such, the dipole moment of these molecules will be calculated using eq 5. As shown in Figure 5, these compounds are identified considering the range of the dipole moment values. Table 3 summarizes the value ranges for these non-associating families. The identification of aromatic groups present in molecules is based on the use of the parameter mRD. As observed in Figure

Table 4. Number of CH3 groups, structure of the Surrogate Molecule and Molecular Weight of the Functional Group (MWfg) for the Various Functional Groups As Selected by the Characterization Scheme (Figure 7)

Table 3. Summary for the Range of Dipole Moment Values for Non-associating Familiesa families

value range of dipole moment (D)

hydrocarbons aliphatic ethers esters aldehydes and ketones

0≤μ≤1 1 < μ ≤ 1.6 1.6 < μ ≤ 2.4 2.4 < μ ≤ 3.6

functional group (fg)

no. of CH3 groups

alcohols (OH) aliphatic acids (COOH) aliphatic ethers (O) aliphatic esters (COO) aldehydes and ketones (CO)a hydrocarbons aromatics

1 1

CH3(CH2)n OH CH3(CH2)n COOH

17 45

2 2

CH3(CH2)n O(CH2)m CH3 CH3(CH2)n COO(CH2)m CH3

16 44

2

CH3(CH2)n CO(CH2)m CH3

28

2 1

CH3(CH2)n CH3 (C6H5)aro (CH2)n CH3

77

molecular typeb

MWfg

a

Aldehydes will be treated as ketones because they cannot be distinguished (Figure 5). bNote: n and m are numbers of CH2 groups.

Next, the number of the CH2 groups must be determined. This is done on the basis of the molecular weight, using the closest integer to MW − MWfg − nCH3 MWCH3 nCH2 = MWCH2 (7)

a

The dipole moments are calculated using the onsager’s relation as shown in eq 5. G


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The value Δlog(LVS) smaller than 0.5 indicates that the representative molecule is non-associating. It means that this molecule will contain neither the functional group of alcohols nor that of acids. (b) Next, the dipole moment μ of the fluid at the temperature of 298.15 K is calculated by using eq 5:

where MW, MW fg , MW CH 2 , and MW CH 3 correspond respectively to the molecular weight of the cut to be represented, the functional group identified, the CH2 group (MWCH2 = 14), and the CH3 group (MWCH3 = 15). nCH2 and nCH3 are the numbers of the CH2 and CH3 groups, respectively.

6. SOME EXAMPLES In this section, we will illustrate how to generate, by using the proposed characterization scheme in section 5 (Figure 7), a representative molecule which represents a regular diesel (given as B0) and a biodiesel (given as B100). The approach for reconstructing a representative molecule is validated by comparing the solubility of water in these two fluids with the predicted values by using either a predictive equation of state or data from the literature. Table 5 presents values for some

2

2

μ=

biodiesel B100

MW

240

290

g·mol−1

υL

0.287

0.328

m3·kmol−1

LVS

0.00210

0.00394

Pa·s

n

1.46471

1.45627

ε

2.35

3.26

ρ η

834.8 2.52

883.3 4.463

symbol

density kinematic viscosity

(

3ε(n2 + 2) (2ε + n2)(n + 2)

)

1 T

With use of Figure 7 or Table 3, this value of the dipole moment indicates that the representative molecule is a hydrocarbon (without oxygenated group). (c) In order to check the presence of aromatic groups, the parameter mRD is calculated by using eq 6: mRD = 240 × (1.46471 − 1.475) = −2.4696

unit

b

property molecular weight molar liquid volumec dynamic viscosityd refractive index dielectric constant

NA 9ε0kB

= 0.6988 D

Table 5. Values of Physicochemical Properties for the Regular Diesel B0 and Biodiesel B100a regular diesel B0

( εε +− 21 ) MWρ − ( nn +− 21 ) MWρ

The negative value of mRD indicates that this representative molecule contains no aromatic groups. (d) As a conclusion, the representative molecule should be composed of the CH2 and CH3 groups. (2) Reconstruct the representative molecule (a) Based on the molecular weight of the regular diesel (MW = 240 g·mol −1 ), the representative molecule will be reconstructed by using the group contribution concept. Based on Table 4, this representative molecule will have two groups of CH3 at each end of the chain. The number of CH2 groups will be determined by using eq 7.

kg·m−3 mm2·s−1

nCH2 =

a

The values are provided by the Physics and Analysis direction of IFP Energies nouvelles.58 bThe property values are used to calculate the molar liquid volume and dynamic viscosity. cThe molar liquid volume is calculated by dividing the molecular weight (g·mol−1) by the density (kg·m−3). dThe dynamic viscosity (Pa·s) is calculated by multiplying the kinematic viscosity (m2·s−1) with the density (kg·m−3).

MW − 15nCH3 14

=

240 − 15 × 2 = 15 14

(b) As a result, the reconstructed molecule has two terminal CH3 groups and 15 CH2 groups. Therefore, the representative molecule for the regular diesel B0 is n-heptadecane. 6.2. Biodiesel B100. The representative molecule for the biodiesel B100 will be constructed by using the proposed characterization scheme in section 5 (Figure 7). The reconstruction procedure consists of the following steps. (1) Identif y the f unctional group in the representative molecule (a) First, the dynamic viscosity of the homomorph is calculated by using eq 2:

physicochemical properties for the regular diesel B0 and the biodiesel B100. All of the measures are supplied by the Physics and Analysis direction of IFP Energies nouvelles.58 6.1. Regular Diesel B0. According to the characterization scheme (Figure 7), the procedure of reconstructing a representative molecule of this fluid is performed, as follows: (1) Identif y the functional group in the representative molecule (a) First, the dynamic viscosity of the homomorph is calculated by using eq 2:

log(LVS)homomorph = −0.000015 × (290)2 + 0.012105 × 290 − 4.474094 = −2.225

log(LVS)homomorph

Then, the difference Δlog(LVS) between the dynamic viscosity of B100 and that of the homomorph is calculated:

2

= −0.000015 × (240) + 0.012105 × 240 − 4.474094

Δlog(LVS) = log(LVS) − log(LVS)homomorph

= −2.433

Then, the difference Δlog(LVS) between the dynamic viscosity of B0 and that of the homomorph is calculated:

= log(0.00394) + 2.225 = −0.180

Δlog(LVS) = log(LVS) − log(LVS)homomorph

The value Δlog(LVS) smaller than 0.5 indicates that the representative molecule is non-associating. (b) Next, the dipole moment μ of the fluid at the temperature of 298.15 K is calculated by using again eq 5:

= log(0.00210) + 2.433 = −0.245 H


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Energy & Fuels

taken from Nguyen-Huynh et al.18 and Nguyen et al.59 The GC-PPC-SAFT parameters of n-heptadecane and ethyl hexadecanoate are calculated by using the group contribution method as presented in ref 19. It was also possible to identify directly some experimental data for the water solubility in these molecules. They are also provided in Table 6. It is found at first that the water solubility calculated by using both the GC-PPC-SAFT and PSRK models is close to the values found for the same systems in literature. The water content at saturation in the real fluids however is generally somewhat larger. The reason may be found in the fact that the regular diesel B0 is not only made of alkanes but can contain up to 30% by volume of aromatics. A calculation with the GCPPC-SAFT model has been done considering that diesel fuel contains a binary undecylbenzene in n-heptadecane. The predicted values of water solubility depending on the aromatic content are presented in Table 7. It shows that the presence of up to 30% aromatics can double the water content at saturation.

μ = 1.6908 D

With use of Figure 7 or Table 3, this value of the dipole moment indicates that the representative molecule is an ester. (c) In order to check the presence of aromatic groups, the parameter mRD is calculated by using eq 6: mRD = 290 × (1.45627 − 1.475) = −5.4317

The negative value of mRD indicates that this representative molecule contains no aromatic groups. (d) As a conclusion, the representative molecule should be composed of the CH2, CH3, and COO (ester) groups. (2) Reconstruct the representative molecule (a) Based on the molecular weight of the regular diesel MW = 290 g·mol −1 ), the representative molecule will be reconstructed by using the group contribution concept. Based on Table 4, this representative molecule will have two groups of CH3 at each end of the chain. The number of CH2 groups will be determined by using eq 7. nCH2 =

MW − 15nCH3 − nCOO 14

=

Table 7. Influence of Undecylbenzene on Saturation Water in the Binary Mixture with n-Heptadecane and Undecylbenzenea

290 − 15 × 2 − 44 = 15.43 14

volume fraction of aromatics (%) molar fraction of water (%) mass fraction of water (ppm mass)

This value is rounded down to 15. (b) As a result, the reconstructed molecule has two groups of CH3, 15 groups of CH2, and one group of COO. Considering that most biodiesels are ethyl esters, we will consider as representative molecule for the regular diesel B0 ethyl hexadecanoate CH3−(CH2)14−COO−CH2−CH3. The choice of methyl heptadecanoate could have been done equally well, with very similar results. 6.3. Validation of the Proposed Approach. The approach for reconstructing the representative molecules (i.e., n-heptadecane for B0 and ethyl hexadecanoate, also known as ethyl palmitate, for B100) is validated by investigating three different properties for the two fluids. 6.3.1. Water Saturation. The water saturation in the real fluids is compared with that of the representative molecules. Table 6 summarizes the experimental values of the water solubility for the regular diesel and biodiesel and the calculated values for the water solubility in the aqueous solution of the representative molecules by using the GC-PPC-SAFT model and the PSRK model. The group contribution−polar perturbed chain−statistical associating fluid theory (GC-PPC-SAFT) model parameters are

6.3.2. Density. The proposed approach in this investigation is validated on the comparison of the GC-PPC-SAFT-based prediction of liquid densities of both fluids with their experimental data. The experimental values of both representative molecules (i.e., n-heptadecane for B0 and ethyl hexadecanoate for B100) as found in the DIPPR23 database are provided in Table 8 as well as the predictions using the GCPPC-SAFT model. As shown in Table 8, the surrogate molecules behave similarly to the original fluids. Table 8. Deviation of the Predicted Densities at 25 °C for the Regular Diesel and Biodiesel (B0) and Biodiesel (B100) on the Basis of the Representative Molecules density (kg·m−3) regular diesel (B0)

1690

representative molecule calculated with GC-PPC-SAFT calculated with PSRK from referencesb

n-heptadecane 31 75 53 (at 25 °C)18

ethyl hexadecanoate 966 1717 141359

biodiesel (B100)

experimental data

834.8

883.3

representative molecule calculated with GC-PPC-SAFTa from DIPPR23

n-heptadecane 826.3 773.35

ethyl hexadecanoate 875.3 857.37

a

The densities are calculated by dividing the molecular weight (g· mol−1) by the liquid molar volumes (m3·kmol−1).

biodiesel (B100)

80

30 0.092 69

The molar fraction of water is calculated by using the GC-PPC-SAFT model.

solubility of water by mass (ppm) experimental dataa

10 0.067 50

a

Table 6. Summary of the Experimental and Calculated Values of the Water Solubility for the Regular Diesel (B0) and Biodiesel (B100), at 20 °C and 1 atm regular diesel (B0)

0 0.050 38

6.3.3. Boiling Temperature. This property has been investigated because it is generally available, but the approach suggested in this work is not sufficient to reproduce the volatility curve that is observed with real fluids: for this, a mixture of pseudo-components would be needed, which was not the scope of this work. Nevertheless, we propose in Table 9 some numbers that may help the reader in evaluating the limits of the methodology. For the diesel fuel, the boiling temperature of the surrogate molecule lies within the (large) range of the volatility curve. Biodiesel B100 is easier to compare because in

a

The experimental data (the water content at the saturation in the real fluids) is supplied by the Physics and Analysis direction of IFP Energies nouvelles.58 bThese values are the water solubilities in the binary systems with the representative molecules. I


Article

Energy & Fuels

It must be stressed that the proposed approach cannot be used to compute the full phase envelope of the biomass fluid. For this, several fractions must be characterized separately and combined into a multicomponent mixture. A procedure is proposed in Figure 8, where several routes can be followed

Table 9. Deviation of the Predicted Boiling Temperatures for the Regular Diesel and Biodiesel (B0) and Biodiesel (B100) on the Basis of the Representative Molecules average boiling temperature (°C) regular diesel (B0)

biodiesel (B100)

experimental data

184.5−356.3a

346b

representative molecule from DIPPR23

n-heptadecane 302

ethyl hexadecanoate 331

The B0 diesel fluid is a mixture of components of many different volatilities, which results in a volatility curve rather than a single boiling temperature. The initial and final distillation temperatures are provided here. bNo volatility curve of the B100 fuel is available, but we know it is a narrow mixture of methyl esters: it contains essentially C18 acid methyl esters, with a majority of methyl linoleate, which boils at 346 °C (DIPPR23 values). This is why this value is chosen here. a

Figure 8. Proposition of the methodology for characterizing bio-oils.

depending on the type of available data. All routes end with molecular reconstruction of a number of pseudo-components (surrogate molecules) based on the identified descriptors (block 4). Properties of molecules reconstructed this way can then be estimated with any predictive equation (block 5). The relevant properties can be accessed using two possible paths depending on the type of data. If data originate from a detailed molecular description, one may expect having access to all properties of the molecules considered. The lumping procedure (block 3) will allow limiting the compositional description to a reasonable number of pseudo-components whose properties can be accessed through averaging rules. If the data originating from various sources are used, the maximum entropy molecular reconstruction algorithm37−39 can be used to produce a typical detailed molecular composition (block 1). A subsequent lumping is needed in order to reduce the number of pseudocomponents. If finally the analytical procedure allows a fractionation of the bio-oil into representative samples (for example by liquid−liquid extraction through a series of solvents), then the samples can be submitted to a number of measurements that will provide the required descriptors (block 2).

our case it is essentially composed of methyl linoleate, of which the boiling temperature is known. The reason for the observed difference in boiling temperature may be related to the fact that the surrogate molecule chosen is an ethyl ester, rather than a methyl ester. In fact, a closer look shows that the main reason is because the number of carbon atoms in the surrogate molecule is one less than that of methyl linoleate (18 instead of 19). Going back to the construction of the pseudo-molecule, this is directly related to the molecular weight that made us conclude nCH2 = 15.43, which we rounded to 15. If the measurement had been a little bit higher, we would have chosen correctly nCH2 = 16. Nevertheless, the results are acceptable.

7. CONCLUSION The main target of this work is to propose a characterization methodology for a given biomass fraction. The procedure aims at using measurable properties for quantifying chain length, polarity, and hydrogen-bonding capacity. It leads to the selection of a surrogate molecule that is expected to behave in the same way as the initial biomass fraction. The five following properties have been selected to that end: molecular weight, liquid molar volume, dynamic viscosity, refractive index, and dielectric constant. We call these properties analytical descriptors. They have been selected in view of the ease of measurements on highly oxygenated mixtures: high temperature properties (such as, e.g., boiling temperature) are avoided. The approach has been validate on three properties: (1) Water saturation is an interesting property as it is easy to measure and is fully independent from the characterization procedure. We can therefore state that it is a predictive test. (2) Density provides a second test. This one is not fully predictive because density measurements are used in the characterization procedure. (3) The boiling temperature is tested because of its availability. This is also a predictive test as no volatility information is used. Yet, the use of a single surrogate molecule is clearly not adapted to describing the volatility curve of a fluid mixture. Hence, the proposed procedure is expected to provide reasonable results for so-called “global properties” where the contributions of all mixture components are somehow averaged. It is validated here on two mixtures (regular diesel and biodiesel). Unfortunately, only non-hydrogen-bonding fluids have been investigated so far.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was funded by the Tuck foundation chair on “Thermodynamics for Biofuels” at IFPEN. We gratefully acknowledge the contribution of several investigators (Nadège Charon, Isabelle Brunella, Denis Defiolle, and Emmanuelle Trela-Baudot) to the measurements of the analytical descriptors and water saturation needed for evaluating the approach.

■

REFERENCES

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Characterization Scheme for Property Prediction of Fluid Fractions

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