Article pubs.acs.org/JPCB
Flash Points of Secondary Alcohol and n‑Alkane Mixtures Zoya N. Esina,*,† Alexander M. Miroshnikov,‡ and Margarita R. Korchuganova† †
Kemerovo State University, 650043 Kemerovo, Russia Kemerovo Institute of Food Science and Technology, 650056 Kemerovo, Russia
‡
ABSTRACT: The flash point is one of the most important characteristics used to assess the ignition hazard of mixtures of flammable liquids. To determine the flash points of mixtures of secondary alcohols with n-alkanes, it is necessary to calculate the activity coefficients. In this paper, we use a model that allows us to obtain enthalpy of fusion and enthalpy of vaporization data of the pure components to calculate the liquid− solid equilibrium (LSE) and vapor−liquid equilibrium (VLE). Enthalpy of fusion and enthalpy of vaporization data of secondary alcohols in the literature are limited; thus, the prediction of these characteristics was performed using the method of thermodynamic similarity. Additionally, the empirical models provided the critical temperatures and boiling temperatures of the secondary alcohols. The modeled melting enthalpy and enthalpy of vaporization as well as the calculated LSE and VLE flash points were determined for the secondary alcohol and nalkane mixtures.
1. INTRODUCTION Solutions of secondary alcohols with n-alkanes are flammable mixtures that may combust, provided that there is a source of ignition. Most mixtures of secondary alcohols with n-alkanes are eutectic and azeotropic mixtures with high enthalpies. Therefore, solutions of secondary alcohols with n-alkanes are of interest as fuel mixtures in the development of alternative energy sources, heat transfer in heating and air conditioning, and other applications. The development of mathematical models for the analysis of environmental conditions that increase the risk of emergencies is an important scientific and practical task. The danger of ignition of mixtures containing combustible substances, such as secondary alcohols, is characterized by their flash point. The flash point is defined as the temperature at which the liquid evaporates and forms a combustible mixture with air. The flash point of the mixture is a critical feature, but there are few experimental data available for mixtures, and the production of such data is expensive and time-consuming.1 Several models for predicting the flash points of mixtures of different types have been previously suggested.2−17 Models developed for ideal solutions are not suitable for nonideal mixtures, which occur most frequently. The general model for predicting the flash point of a mixture is shown in ref 18 and was refined by Liaw et al.19 based on a modified Le Chatelier equation, the Antoine equation, and models for calculating activity coefficients 0 =1 ∑ xiγiPi /Pi,fp
where xi is the mole fraction of the ith component in the liquid; γi is the activity coefficient of component; Pi is the vapor pressure of the ith component of the mixture at a predetermined temperature, T; P0i,fp is the pure fuel vapor pressure of the ith component in its flash point; Ai, Bi, and Ci are the Antoine equation coefficients; and the pressure is expressed in mmHg. The liquid and vapor phase equilibrium partial pressures of the liquid component of the nonideal mixture are assumed to take on the form
pi = xiγiPi To calculate the flash temperature of the solution, the activity coefficient component of the mixture, γi, and the vapor pressure of the ith component of the mixture at its flash point, P0i,fp, must be determined. The flash point, Tfp, of the mixture is a result of the joint solution of eq 1 and the Antoine equation (2). Substitution of the pressure, Pi, in the Antoine equation into the Le Chatelier equation allows for calculation of a flash point for the full range of solution compositions. The main problem is determining the activity coefficients of the components of a nonideal mixture, which can be solved using mathematical modeling techniques. Liaw et al.17 described the results of the calculation and experimental curves depending on the flash point of the composition for ideal systems and the deviation from an ideal mixture. In this paper is a brief description of the UNIFAC (short for UNIversal Functional Activity Coefficient), original UNIFAC, modified UNIFAC-Dortmund 93, and
(1)
i
ln Pi = Ai − Bi /(T + Ci) © 2015 American Chemical Society
Received: May 21, 2015 Revised: October 7, 2015 Published: October 22, 2015
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DOI: 10.1021/acs.jpcb.5b04872 J. Phys. Chem. B 2015, 119, 14697−14704
Article
The Journal of Physical Chemistry B UNIFAC-Lingby models as well as Bastos and other modified UNIFAC models. Gmehling and Rasmussen calculated the flash points of binary systems, which were used to evaluate the activity coefficients of the UNIFAC model.10 Vidal et al.13 combined the forecasted flash point of Liaw et al.19 with the UNIFAC model to predict the results for strongly nonideal solutions. The minimum flash point of a mixture may drop a few degrees, increasing the risk of explosion, which is often accompanied by a positive deviation of the liquid−vapor equilibrium from Raoult’s law.15 The maximum in the flash point curve of the composition of a solution is linked to a negative deviation from Raoult’s law, which lowers the risk of explosion.16 Models of ideal systems cannot be used for systems that deviate from the ideal because of the interaction of molecules. Among the mixtures of secondary alcohols with n-alkanes, 2-propanol + octane and 2-butanol + octane are imperfect formations with a minimum in the curve of the flash point of the composition. In ref 17, it is noted that the existing thermodynamic models did not accurately describe the system deviation from the ideal. Reference 20 describes a method for calculating the temperature of the flash from the results of a simulation of the liquid−solid equilibrium at constant pressure. The present work aims to predict the flash points of mixtures of secondary alcohols and n-alkanes by the results of the calculation of the vapor−liquid equilibrium (VLE) and liquid−solid equilibrium (LSE).
Integration of eq 3 based on the relationship between enthalpy and boiling point (4) leads to the equation ln P = −A1/T + B1 ln T + C1T + D1
where A1, B1, C1, and D1 are the coefficients of the equation. VLE and LSE can be calculated using various models.17,22,23 Modeled activity coefficients are used for different mixtures of components, such as low or high molecular weight polymers, ionic liquids, etc. The Wilson, NRTL (short for Non-Random Two-Liquid), UNIQUAC (short for UNIversal QUAsiChemical), and UNIFAC models are the most widely used models for binary and multicomponent systems because of their ability to describe many polar and nonpolar systems. These models are currently very popular and can be used to calculate the activity coefficients of the liquid phase in binary and multicomponent systems. Most modeling techniques require the introduction of a significant number of parameters, not only of the pure components but also the parameters describing the interaction, which are mainly determined according to a binary system. Modeling techniques often require complex mathematical calculations, occupying considerable machine time. Moreover, the models do not have a wide range of applications and are limited to one associating agent or applied to the systems with nonpolar components. Associated with these models is the mathematical modeling of interest of the phase diagram liquid−solid and liquid−vapor equilibria for real binary and multicomponent mixtures. The PCEAS (Phase Chart Eutectic and Azeotropic Systems) model24 is based on temperature and enthalpy of fusion data as well as enthalpy of vaporization and boiling point data of the pure components. This method can be used to describe the liquid−solid and liquid−vapor equilibria for real binary and multicomponent systems, including both nonpolar and polar components, molecules with hydrogen bonds, and isomers.25,26 The prediction of the flash point of a system based on eutectic and azeotropic data points is possible using coefficients of association of the components in the liquid and solid phases. To construct a mathematical model of minimizing the Gibbs free energy is entered the solvation parameter λ as the ratio of the number of molecules of component A and component B to the number of molecules in a molecular compound formed in the solution. The difference equation of the state of a binary system, for the real and ideal equilibrium phases, can be represented as27
2. THEORETICAL METHODS To estimate the temperature of the flash mixture, activity coefficients were generally applied to the liquid phase in equilibrium with the vapor phase. Because the flash point of the mixture may be far below the boiling point in some systems, liquid phase activity coefficients can be used to suitably calculate the LSE. Data on the enthalpies and melting temperatures of the pure components allow us to calculate activity coefficients and make an assessment of the flash point of a binary system in the absence of information on the enthalpies of vaporization and boiling points of the pure components. For some secondary alcohols in the literature, there are no data on the Antoine coefficients. The pressure−temperature curve at the VLE can be found using the Clausius−Clapeyron equation P ΔH vb dP = dT RT 2
(3)
where ΔHvb is the enthalpy of vaporization and R is the universal gas constant. The enthalpy of vaporization can be calculated by the empirical equations depending on the boiling point and the critical parameters.21 To calculate the enthalpy of vaporization, we used the Watson equation ΔH vb2
⎛ 1 − η ⎞n 2 ⎟⎟ = ΔH vb1⎜⎜ ⎝ 1 − η1 ⎠
(5)
2
( −HE/RT 2) dT + (V E/RT ) dP =
∑ xi d ln γi i=1
E
E
where H is the excess enthalpy, V is the excess volume, P is the pressure of the solution, and T is the absolute temperature. The solubility component forming one component phase in a multiphase, multicomponent mixture of condensed matter at a constant pressure can be described by the equation
(4)
d(ln xiγi)/dT = −ΔHi /RT 2
where the subscripts “1” and “2” refer to temperatures 1 and 2, respectively; η = T/Tc is the reduced temperature; and the average values of the exponent n for the alkanes and alcohols are taken to be 0.38 and 0.34, respectively. The exponent n is a function of material properties and is a constant equal to 0.38.21 A satisfactory agreement between the experimental data and the calculation results of pressure on the phase equilibrium curve for alcohols using eqs 3 and 4 is achieved at n = 0.34.33
where ΔHi is the partial molar heat of solution of the ith component in the saturated solution. The excess Gibbs energy in a binary system is represented as 2 E
G = RT ∑ xi ln γi i=1
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DOI: 10.1021/acs.jpcb.5b04872 J. Phys. Chem. B 2015, 119, 14697−14704
Article
The Journal of Physical Chemistry B
Equations 9 and 10 allow us to find the temperature and composition of the solution at the eutectic or azeotrope points. In that case, if the curves of ln γ1 and ln γ2 satisfy thermodynamic consistency, they can be represented in the form of a number of Redlich−Kister
For real systems that can form solvates, the transition to effective mole fractions must be taken into account. If the molecular compounds are formed from pure components in the solution, the total molar mass of the component based on the number of molecules of this type, λi, within the compound can be calculated using the formula μi′ = λiμi, where μi is the molar mass of the pure component. The effective mole fractions of the components of a binary mixture27 are described by z1 = x1/(x1 + λx 2),
ln γ1 = z 2 2[B + C(3z1 − z 2)], ln γ2 = z12[B + C(z1 − 3z 2)]
z 2 = x 2/(x1/λ + x 2)
where B and C are the Redlich−Kister model coefficients, or as an approximation of Van Laar
where λ = λ1/λ2. At constant pressure and low temperature range of phase transitions (melting or boiling), the excess Gibbs energy as a function of the effective mole fraction of the component can be determined from the equation
ln γ1 = A′[B′z 2/(A′z1 + B′z 2)]2 , ln γ2 = B′[A′z1/(A′z1 + B′z 2)]2
where A′ and B′ are the Van Laar model coefficients. According to the eutectic data, the z1eut, z2eut, ln γ1eut, and ln γ2eut coefficients of the Redlich−Kister and Van Laar models can be determined. The dependence of the composition of the solution in the branches of the liquidus temperature is described by
GE = z1[ΔH10(T /T10 − 1)] + z 2[ΔH20(T /T20 − 1)] − RT (z1 ln z1 + z 2 ln z 2) + F(z1)
(6)
ΔH0i
where is the enthalpy of the phase transition (melting or boiling) of the pure ith component; T0i is the transition temperature (melting or boiling) of the pure ith component; i = 1, 2; F(z1) = z1F1(z1) + (1 − z1)F2(z1) is a function selected from the condition of the thermodynamic consistency of the model by the method of Herington and Redlich−Kister27
∫0
ln ν1 = ΔH10/RT10(1 − T10/T ) − ln γ1 , ln ν2 = ΔH20/RT20(1 − T20/T ) − ln γ2
where ν1 and ν2 are the mole fractions of the first and second solution components to the left and right branches of the liquidus curve, respectively; ln γ1 and ln γ2 are logarithms of the activity coefficients calculated by eq 11. The association of molecules can occur at different phase states and obeys the laws that need to be identified to predict the phase equilibrium. The procedure of thermodynamic consistency of the component activity coefficients allows for the determination of the association coefficients in the liquid phase. When the model association in the solid phase is well-known, details can be obtained from the spectral analysis, providing a more accurate simulation of the liquid−solid phase equilibrium. One of the important problems with the theory of solutions is the simulation of liquid−vapor phase equilibrium in real systems. In this paper, we consider the possibility of calculating the liquid−vapor phase transition at a constant pressure based on the parameters of solvation and association in the liquid, resulting from the calculation of the liquid−solid equilibrium, and a selected model association in vapor. The proposed model based on the optimization of excess thermodynamic functions is universal and can be used to describe the liquid−solid and liquid−vapor phase transitions. The model allows for the calculation of the excess thermodynamic functions, such as Gibbs energy, GE, enthalpy, HE, and entropy, SE. The calculation result of the liquid−vapor equilibrium is dependent on the selected model association in vapor, which can be verified by independent experimental data, such as spectroscopic data. We introduce the coefficient of selfassociation in the vapor phase, τ = τ1/τ2, which is characterized by the ratio of the number of molecules of pure components to form a molecular compound. The obtained data on the coefficients of association in the liquid phase, ki, as well as the accepted model of the association in a vapor allow for the calculation of heat of the phase transition liquid−vapor as ΔHi = kiΔH0i /τi, where ki and τi are the coefficients of association in the liquid and in a vapor, respectively, and ΔH0i is the enthalpy of vaporization of the pure ith component. Because the available literature data on the thermodynamic
1
log γ1/γ2 dz1 = 0
(7)
According to eq 7, the areas bounded by the curve log γ1/γ2 and axes (under and over abscissa axis) should be equal. From the condition of thermodynamic consistency of the constructed model, the ratio k = k1/k2 is determined, which is the ratio of the number of molecules of component A, clustered together to form a solution or directly in the solution, to the number of molecules in the cluster of B. The minimization of excess energy (6) by the internal parameter, λ, leads to Bernoulli’s equation dT /dz1 + f1 (z1)T = f2 (z1)T 2
(8)
where f1 (z1) = α /(ΔH10/R − αz1) f2 (z1) = −[β + ln(1/z1 − 1)]/(ΔH10/R − αz1)
α = (ΔH10 − ΔH20)/R
and β = ΔH20/RT20 − ΔH10/RT10
The solution of eq 8 takes on the form T (z1) = [ΔH10z1 + ΔH20(1 − z1)] /[ΔH10z1/T10 + ΔH20(1 − z1)/T20 − R(z1 ln z1 + (1 − z1) ln(1 − z1))]
(9)
From the extreme condition (9), the following algebraic equation is obtained. 0
0
ln((1 − z1)ΔH1 / R (z1)−ΔH2 / R ) = ΔH10ΔH20(1/T20 − 1/T10)/R2
(11)
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DOI: 10.1021/acs.jpcb.5b04872 J. Phys. Chem. B 2015, 119, 14697−14704
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The Journal of Physical Chemistry B
Table 1. Experimental and Calculated Values of the Enthalpies of Vaporization and Boiling Points of Secondary Alcohols
a
component
ΔHbexp,31 kJ/mol
ΔHbpred,31 kJ/mol
ARD %
ΔHbpred,a kJ/mol
ARD %
Tbexp,31 K
Tbpred,b K
ARD %
Tc,c K
2-propanol 2-butanol 2-pentanol 2-hexanol 2-heptanol 2-octanol
39.850 40.750 41.400 41.010 − 44.400
36.940 38.170 39.880 41.750 − 45.410
7.29 6.34 3.67 1.80 − 2.28
40.012 40.772 41.073 42.393 42.957 44.397
0.410 0.053 0.790 3.370 − 0.007
355.41 372.00 392.15 413.04 431.65 452.95
352.72 374.71 395.35 414.62 432.55 449.11
0.90 0.73 0.83 0.39 0.21 0.84
508.3 536 562.72 588.46 613.22 637.00
Equation 19. bEquation 17. cEquation 18.
Table 2. Antoine Equation Coefficients and Flash Points of the Pure Components flash point
Antoine coefficients component
A
B
C
ref
Tfp, °C
ref
2-propanol 2-butanol 2-octanol pentane hexane heptane octane
18.6929 17.2102 14.7108 15.8333 15.8366 15.8894 15.9426
3640.20 3026.03 2441.66 2477.07 2697.55 2895.51 3120.29
−53.54 −86.65 −150.70 −39.94 −48.78 −53.97 −63.63
31 31 19 19 19 19 19
12.9 ± 0.8 22.0 ± 2.4 74.0 −44.0 −23.0 −5.2 ± 0.5 14.5 ± 1.4
17 17 32 32 32 17 17
Table 3. Coefficients of eq 5 and Flash Points of the Pure Components component
A1
B1
C1
D1
Tfp,32 °C
2-pentanol 2-hexanol 2-heptanol
7178.327 7452.83 7635.027
−2.19344 −1.94571 −2.37303
−0.00889 −0.00887 −0.00758
39.5079 37.99984 39.92242
36.0 50.0 63.0
properties of secondary alcohols are limited and contradictory, the thermodynamic similarity model was used to simulate the melting enthalpy and enthalpy of vaporization.28 The relative molecular weight, M, melting point, Tm, boiling point, Tb, and number of carbon atoms in the molecule, N, were used as parameters. Earlier models of n-alkanes, carboxylic acids, n-alcohols, glycols, glycol ethers, and aldehydes were cited in refs 29 and 30 ΔHm = a(N )/R[MRTm/N ] + b(N )( −1)N + c(N )
The boiling point equation for secondary alcohols is also proposed according to the number of carbon atoms in the molecule Tb = C1N 2 + C2N + C3
where C1, C2, and C3 are the model coefficients determined by the method of least squares. The secondary alcohol model (16) can be represented as
(12)
Tb = −0.6784N 2 + 26.741N + 278.6,
where a(N)/R is the dimensionless parameter of similarity, MRTm/N has the dimensions of molar enthalpy, and b(N) and c(N) have dimensions of J/mol. Equation 12 for the secondary alcohols (3 ≤ N ≤ 13) adopts the following form. (N + 1)MTm ΔHm = + 520N ( −1)N − 3800/N 1.85N
δ = 0.66
(17)
Because the critical temperature is known only for some secondary alcohols, we propose the following correlation Tc = −0.49N 2 + 31.13N + 419.32
(18)
The predictive model for evaporation enthalpy as a function of the critical temperature is given by
(13)
ΔHb =
4MTc + 210( −1)N + 5010, N + 0.47
σ = 211, (19)
δ = 0.31
(14)
The standard deviation, σX, and the average relative error, δX,av, of variable X are given by
where α(N)/R is the dimensionless parameter of similarity, MRTb/N has the dimensions of molar enthalpy, and β(N) and γ(N) have dimensions of J/mol. Equation 14 for the secondary alcohols (3 ≤ N ≤ 13) adopts the following form 5.38MTb ΔHb = + 90( −1)N + 7170, N + 0.47
σ = 2.37,
δ = 0.49
The authors also proposed a model of the enthalpy of vaporization of pure components at the boiling temperature in the form29,30 ΔHb = α(N )/R[MRTb/N ] + β(N )( −1)N + γ(N )
(16)
m
σX =
σ = 325.5,
δX ,av = (15) 14700
∑ j = 1 (X jexp − X jcalc)2 m−1
1 m
m
∑ (|X jexp − X jcalc|/X jexp)·100% j=1 DOI: 10.1021/acs.jpcb.5b04872 J. Phys. Chem. B 2015, 119, 14697−14704
14701
1.0
2-propanol + hexane
−23.00 −22.17 −21.63 −21.90 −20.00 −21.09 −18.10 −20.00 −15.92 −18.37 −13.48 −16.47 −10.49 −12.12 −6.95 −12.12 −2.33 −8.58 3.65 12.90 2-hexanol + hexane −23.00 −22.14 −22.14 −21.45 −21.45 −20.41 −20.75 −18.68 −19.37 −16.26 −17.64 −13.49 −15.22 −10.03 −12.45 −6.57 −10.03 −1.72 −5.88 50.03
2-propanol + pentane
−44.00 −42.85 −42.54 −42.22 −40.97 −41.28 −39.40 −39.71 −37.20 −37.52 −34.38 −34.69 −31.24 −31.55 −27.16 −28.10 −21.20 −23.40 −11.78 12.90 2-hexanol + pentane −44.00 −43.78 −43.17 −42.01 −42.40 −40.84 −41.23 −38.52 −39.68 −35.41 −37.35 −31.92 −34.60 −27.26 −31.44 −23.00 −27.26 −16.40 −21.83 50.03
−5.20 −5.83 −4.18 −5.60 −3.24 −5.36 −2.06 −4.65 −0.64 −3.71 0.78 −2.53 2.43 −1.35 4.32 −0.17 6.45 1.96 8.81 12.9 2-hexanol + heptane −5.20 −4.29 −4.29 −3.67 −3.67 −2.74 −3.05 −1.50 −1.81 0.67 0.05 3.16 2.22 5.95 4.71 9.05 7.19 13.40 10.92 50.03
2-propanol + heptane 14.50 9.84 12.68 9.03 11.26 8.62 10.04 8.42 9.84 8.21 9.84 8.21 9.84 8.42 9.43 8.62 8.42 9.23 6.59 12.90 2-hexanol + octane 14.50 14.91 14.91 15.45 15.45 15.99 16.26 17.07 17.62 18.70 19.24 20.87 21.14 22.77 23.31 24.93 25.20 28.19 27.91 50.03
2-propanol + octane −44.00 −42.87 −42.54 −42.21 −42.21 −41.21 −39.55 −39.55 −37.23 −36.90 −34.56 −33.58 −31.25 −30.26 −26.94 −26.27 −20.96 −20.96 −10.67 22.00 2-heptanol + pentane −44.00 −43.08 −43.08 −41.83 −42.66 −40.59 −41.84 −38.11 −40.59 −34.80 −38.94 −31.07 −36.45 −26.10 −34.38 −21.14 −31.90 −14.51 −28.17 61.23
2-butanol + pentane −23.00 −21.96 −21.96 −21.38 −21.38 −20.80 −20.51 −19.35 −19.06 −17.32 −17.32 −15.00 −15.00 −12.39 −12.68 −9.78 −10.36 −5.72 −7.17 22.00 2-heptanol + hexane −23.00 −22.04 −22.04 −21.29 −21.29 −20.18 −20.55 −18.69 −19.06 −16.08 −16.83 −12.73 −14.22 −9.39 −11.99 −5.67 −9.39 −0.09 −6.04 61.23
2-butanol + hexane −5.20 −4.83 −4.32 −4.58 −3.30 −3.81 −2.98 −3.05 −0.76 −1.52 1.02 0.26 3.06 2.04 5.35 3.82 7.64 6.36 10.94 22.00 2-heptanol + heptane −5.20 −4.07 −4.07 −3.39 −3.39 −2.72 −2.39 −1.04 −1.04 1.32 1.32 4.01 3.67 7.03 6.36 10.40 8.72 15.11 12.08 61.23
2-butanol + heptane 14.50 12.25 14.17 12.02 13.09 12.02 12.66 12.23 13.09 12.65 14.17 13.31 15.24 13.95 15.89 14.60 14.46 15.89 14.38 22.00 2-heptanol + octane 14.50 15.29 15.58 15.88 16.18 16.77 17.66 17.96 19.45 20.04 22.12 22.42 25.39 24.79 28.65 27.46 32.22 31.33 36.97 61.23
2-butanol + octane −44.00 −42.88 −42.88 −42.16 −42.52 −41.08 −41.80 −39.28 −40.36 −36.40 −38.22 −32.80 −36.76 −29.20 −34.60 −24.88 −32.44 −19.12 −29.20 36.00 2-octanol + pentane −44.00 −42.99 −42.55 −41.68 −40.81 −40.37 −38.63 −37.76 −36.45 −34.27 −33.40 −29.91 −29.91 −24.68 −24.68 −19.44 −17.70 −12.03 −3.75 74.00
2-pentanol + pentane −23.00 −22.12 −22.12 −21.48 −21.48 −20.53 −20.53 −18.94 −18.94 −17.03 −17.03 −14.49 −14.81 −11.31 −12.58 −8.45 −10.67 −3.99 −7.49 36.00 2-octanol + hexane −23.00 −21.78 −21.39 −21.39 −19.81 −20.20 −17.84 −18.23 −15.48 −15.48 −12.32 −11.93 −8.38 −8.38 −3.66 −4.05 3.83 1.86 11.23 74.00
2-pentanol + hexane −5.20 −4.37 −4.37 −4.08 −3.80 −3.24 −2.96 −2.11 −1.54 −0.41 −0.15 1.84 2.41 4.10 4.39 6.65 6.36 10.03 8.90 36.00 2-octanol + heptane −5.20 −4.319 −3.59 −3.59 −1.809 −2.52 0.00 −0.72 2.50 1.79 5.73 5.01 9.31 8.24 14.33 12.18 21.50 11.56 34.40 74.00
2-pentanol + heptane
14.50 14.07 14.56 14.32 15.04 14.56 15.77 15.29 17.00 16.50 18.69 17.72 20.39 19.18 22.33 20.66 23.79 22.82 25.98 36.00 2-octanol + octane 14.50 15.54 16.18 16.18 17.77 17.14 19.69 18.73 22.24 20.96 25.11 23.52 28.94 27.34 34.68 29.90 40.10 34.68 51.31 74.00
2-pentanol + octane
The upper value of the temperature of the flash was obtained by calculating the activity coefficients for the liquid−vapor equilibrium, whereas the lower value of the results was obtained by calculating the liquid−solid equilibrium.
a
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
x1, mol 0 0.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0 0.1
x1, mol
Table 4. Flash Point Tfp (°C) Values in Secondary Alcohol and n-Alkane Systems According to LSE and VLEa
The Journal of Physical Chemistry B Article
DOI: 10.1021/acs.jpcb.5b04872 J. Phys. Chem. B 2015, 119, 14697−14704
Article
The Journal of Physical Chemistry B where Xj is the enthalpy of the phase transition or temperature; j = 1, 2, ..., m; and m is the number of experimental data.
3. RESULTS AND DISCUSSION This paper presents the results of the calculation of flash points in secondary alcohol + n-alkane mixtures based on the characteristics of the liquid−solid and liquid−vapor equilibria. Table 1 shows the thermodynamic characteristics of the secondary alcohols. For the calculation of the flash point of a binary mixture of a secondary alcohol and an n-alkane, Antoine equation coefficients were taken from the literature,19,31 as well the flash points of the pure components in the literature17,32 (Table 2). In the literature, the Antoine equation coefficients for 2-pentanol, 2-hexanol, and 2-heptanol are unknown; therefore, from eqs 3 and 4, the dependences on the boiling point (17), melting enthalpy (13), and enthalpy of vaporization (15) are calculated. Table 3 shows the coefficients of eq 5 used for calculating the vapor pressure and flash point32 for these components. Table 4 shows the parameters of the flash points of the secondary alcohol + n-alkane systems according to the liquid− vapor and liquid−solid equilibria. Figures 1 and 2 show the calculated results of the liquid− vapor phase diagram as well as the experimental and calculated
Figure 3. Liquid−vapor phase diagram of the octane + 2-butanol system at normal pressure.
Figure 4. Comparison of predicted and experimental flash points for the octane + 2-butanol system. The solid line is according to calculated data of the liquid−vapor equilibrium; points are experiment.17
PCEAS model) data for the flash points of the octane + 2-butanol system. The average absolute deviation of the flash point of the experiment is calculated by the formula Figure 1. Liquid−vapor phase diagram of the 2-propanol + octane system at normal pressure.
ΔTfp =
∑ |Tfpexp − Tfppred|/m m
T pred fp
where is calculated from the PCEAS model, Texp fp is the experimental value, and m is the number of experimental data. Reference 17 describes the deviation of the calculated flash points of the experiments for different models (NRTL Wilson, original UNIFAC, UNIFAC-Dortmund, UNIFAC-Lingby, and Bastos). The average absolute deviation between the calculated and experimental flash points, ΔTfp, by the different models is for the octane + 2-propanol system in the range from 0.39 to 1.32 °C and for the octane + 2-butanol system in the range from 0.26 to 1.00 °C. ΔTfp by the PCEAS model is for the octane + 2-propanol system 1.66 °C and for the system octane + 2-butanol 1.15 °C, which is comparable in magnitude to the accuracy of calculations by known models. Figures 5and 6 show the calculation results of the phase diagram and the liquid−vapor flash point according to the PCEAS model for the 2-pentanol + heptane system. Figures 7 and 8 show the calculation results of the phase diagram and the liquid−vapor flash point according to the PCEAS model for the 2-pentanol + octane system. The curves in Figures 6 and 8 show the comparison of flash temperatures to the composition of the mixture obtained according to the VLE and LSE, demonstrating the similarity of
Figure 2. Comparison of predicted and experimental flash points for the 2-propanol + octane system. The solid line is according to calculated data of the liquid−vapor equilibrium; points are experiment.17
(from the PCEAS model) data for the flash points of the 2-propanol + octane system. Figures 3 and 4 show the calculated liquid−vapor phase diagram as well as the experimental and calculated (by the 14702
DOI: 10.1021/acs.jpcb.5b04872 J. Phys. Chem. B 2015, 119, 14697−14704
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Figure 5. Liquid−vapor phase diagram of the 2-pentanol + heptane system at normal pressure.
Figure 8. Flash point of the 2-pentanol + octane system. The olive line is according to calculated data of the liquid−solid equilibrium; the black line is according to calculated data of the liquid−vapor equilibrium.
Figure 6. Flash point of the 2-pentanol + heptane system. The olive line is according to calculated data of the liquid−solid equilibrium; the black line is according to calculated data of the liquid−vapor equilibrium.
Figure 9. Flash point of the acetic acid + hexanol system. The olive line is according to calculated data of LSE; the blue line is according to calculated data of VLE at k1/k2 = 5/16, τ1/τ2 = 1.25/8; the red line is according to calculated data of VLE at k1/k2 = 5/16, τ1/τ2 = 2.5/8; points are experiment.1
Figure 7. Liquid−vapor phase diagram of the 2-pentanol + octane system at normal pressure.
Figure 10. Flash point of the octane + butanol system olive line is according to calculated data of LSE. The blue line is according to calculated data of VLE at k1/k2 = 1/6, τ1/τ2 = 0.5/3; the red line is according to calculated data of VLE at k1/k2 = 1/6, τ1/τ2 = 1/3; points are experiment.17
the curves for some systems and estimating the temperature of the flash according to the LSE. There are no experimental data on the flash points for these mixtures in the literature. The results of the calculation of the flash points of the mixture depend on the scheme of association in vapor. Molecules of acetic acid form associates in the vapor phase; therefore the effect of the association cannot be neglected. Strong coupling in the vapor phase of acetic acid was considered in the literature,34 based on the chemical theory35 and the Hayden−O’Connell equation.36 The association scheme in vapor was adopted for the acetic acid + hexanol system, with k1/k2 = 5/16, τ1 = k1/4 = 1.25, and τ2 = k2/2 = 8; and for the octane + butanol system, with k1/k2 = 1/6, τ1 = k1/2 = 0.5, and τ2 = k2/2 = 3.
Figures 9 and 10 show graphs of the flash points of the acetic acid + hexanol and octane + butanol systems. As can be seen, Figures 9 and 10 show that calculation of the flash points according to the VLE depends on the association scheme in vapor. The results of calculation of the flash points according to the LSE are in good agreement with the experimental data.1,17 The graphs in Figure 10 with the formation of the flash point maximum and minimum allow us to estimate the degree of danger of ignition mixtures. 14703
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4. CONCLUSION To predict the flash points of binary liquid mixtures of secondary alcohols and n-alkanes, a liquid−vapor and liquid− solid equilibrium modeling method was applied under isobaric conditions, based on the minimization of excess Gibbs energy of solvation parameters. We used eqs 13, 15, and 19 to calculate the enthalpies of melting and the vaporization enthalpies of secondary alcohols. The PCEAS model allowed for the determination of activity coefficients required to calculate the flash point. The predicted flash points for some systems, e.g., 2-propanol + octane and 2-butanol + octane, showed the best results when determined by the coefficients according to the activity of the liquid−vapor equilibrium rather than the liquid− solid equilibrium. For many systems, the results of the flash point calculations according to the liquid−vapor and liquid− solid equilibria are very similar (Table 4).
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AUTHOR INFORMATION
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[email protected]. Tel.: +7(384-2) 54-27-70. Notes
The authors declare no competing financial interest.
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REFERENCES
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