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This work gives tools to overcome the difficulty to determine experimentally physical properties for vegetable oils within the range of temperature typically observed during the injection phase in a diesel engine. Knowing vegetable oils ’ physical properties to these range s of temperature is of fundamental importance when modeling their combustion in diesel engine. However, vegetable oils ’ experimental physical properties data are rare in the literature for temperature above 523 K. This paper describes experimental measurements an d estimation methods for density, dynamic viscosity, thermal conductivity and heat capacity of vegetable oils for this particular range of temperature. The methodology uses several correlative methods using group contribution approach for each property and compares experimental data with predicted one to select the more accurate model. This work has shown the rapeseed and jatropha oils ’ physical properties can be satisfactorily predicted as a function of temperature using group contribution approach.

In the last three decades, several studies have shown the potential of pure vegetable oils as fuel in diesel engines and burners [

Many studies, mostly experimental, have described the mechanisms of evaporation and combustion of vegetable oils under different conditions of temperature and pressure [

Vegetable oils are mainly used for food purposes and therefore there are few data in literature on their physical properties up to 450 K. This lack of data had to be overcome by experimental measurements and predictions for industrial use of vegetable oils. The main objective of this work is to determine experimentally vegetable oils density, viscosity, thermal conductivity and heat capacity up to 523 K and hence to predict the same physical properties for temperature above 523 K by means of predictive methods based on group contribution approach. At least two group contribution methods were tested for rapeseed and Jatropha oil density, viscosity, thermal conductivity and heat capacity which can be obtained experimentally or available in the literature. The physical properties above mentioned are evaluated as a function of temperature and the models which give very good agreement with literature or experimental data obtained in this work will be retained. The contribution of this work is to provide rapeseed and Jatropha experimental physical properties and predictive one by group contribution methodology that can be applied to others vegetable oils. Group contribution method has been used in recently works to estimate vegetable oils density [

The critical properties such as critical temperature, critical pressure or critical volume are very important because they are involved in determining the physical properties mentioned above. Then, the critical properties and normal boiling point will be firstly determined by correlative method.

Experimental tests were carried out at CIRAD Biomass Energy Laboratory (UR BioWooEB) in Montpellier (France), with the collaboration of the ‘‘Laboratoire de Physique et de Chimie de l’Environnement’’ (Burkina Faso), and the PROMES-CNRS laboratory of Perpignan (France).

Jatropha curcas oil was obtained from agricultural producers in Burkina Faso. Rapeseed oil is commercially available and was purchased in a refined standard state from a food reseller in France.

The physical and chemical characteristics in standard conditions of jatropha curcas and rapeseed oils used in this study were determined at BioWooEB. They are listed in

Density (kg/m^{3} at 288 K) | Kinematic viscosity (mm^{2}/s at 313 K) | Flash point (K) | Surface tension (N/m) | Low heating value (MJ/kg) | Carbon residue (%) | |
---|---|---|---|---|---|---|

Rapeseed oil | 925 | 34.9 | 483 | 32.9 | 37.1 | 0.39 |

Jatropha oil | 940 | 34 | 498 | - | 36.3 | - |

carbon residue was measured by performing the NF EN ISO 10370 operation in a furnace of 773 K. Some of these physical properties were determined at the IESPM on the request of the unit BioWooEB.

The fatty acid composition was determined by gas chromatography, using a Agilent 6890 GC type with a FID detector and a CP-WAX 58CB column (25 m × 0.32 mm × 0.2 µm). The fatty acid composition of the oils is reported in

In this section the experimental methods used to characterize the considered oils in the 298 - 523 K temperature range are described. The different methods or devices used in this work for the determination of density, dynamic viscosity, thermal conductivity and heat capacity of rapeseed and jatropha oils are listed in

The details of method 3 ω can be obtained in the following literature [

A model that could predict pure vegetable oils physical properties based on the knowledge of their fatty acid composition would be useful in their direct use as fuel or in the optimization of biodiesel production processes or for the blending with others suitable products. On the basis of the fatty acid composition of the vegetable oils, the group contribution methods are known to be a powerful tool for predicting physical properties when experimental data are not available [

Fatty acids | Formula | Rapeseed oil | Jatropha oil |
---|---|---|---|

Oleic (C18:1) | C_{18}H_{34}O_{2} | 60.78 | 41.64 |

Linoleic (C18:2) | C_{18}H_{32}O_{2} | 19.22 | 32.53 |

Linolenic (C18:3) | C_{18}H_{30}O_{2} | 8.92 | 0.00 |

Palmitic (C16:0) | C_{16}H_{32}O_{2} | 4.78 | 16.00 |

Stearic (C18:0) | C_{18}H_{38}O_{2} | 1.35 | 6.05 |

Other minor fatty acids | - | 4.95 | 3.77 |

Physical Properties | Density | Dynamic viscosity | Thermal conductivity | Heat capacity |
---|---|---|---|---|

Device/Method | Pycnometer | Rheometer ARES-G2 | 3 ω Method | DSC Setaram C80 |

In this study, rapeseed and jatropha oils critical properties were estimated by using correlative methods that are based on group-contribution approach. Marrero and Gani (MG) method was used [

For this method, each critical property is estimated by a function f which depends, on the one hand on the different contributions of the functional groups at different levels as shown in the Equation (1) and on the other hand on the primary properties. The functions used for this work are listed in

f ( X ) = ∑ i N i C i + w ∑ j M j D j + z ∑ k O k E k (1)

f(X) is a function of the property X to be estimated, and i, j and, k refer to the first, second and third order groups defined in the group contribution method. N_{i} and M_{j} are the number of the i-th first order group, and the j-th second order group, respectively, present in the molecule, and C and D are the fitted contributions to the first and second order groups, respectively.

The approach used is based on the rapeseed and jatropha oils fatty acid composition: each fatty acid has been fragmented into several chemical groups and the contribution of each group is taken into account to get the contribution of the corresponding fatty acid. Then, the rapeseed or Jatropha oils critical properties can be estimated satisfactorily by taking into account their composition in fatty acids. For these different physical properties, at least two methods most suited for vegetable oils were considered and the best of them was retained.

Density estimation

There are several methods that can be used to estimate liquid density of pure or mixture compound [

According to Gunn Yamada’s estimation method, the pure compound liquid density is evaluated as follows Equations (2) to (6). The temperature range of this correlation extends from a reduced temperature of 0.20 to just below the critical temperature.

Properties | Function f | Constants |
---|---|---|

Boiling Point | f ( X ) = exp ( T b / T b o ) | T b o = 222 . 543 K |

Critical Temperature | f ( X ) = exp ( T c / T c o ) | T c o = 231 . 239 K |

Critical Pressure | f ( X ) = ( P c − P c l ) 0.5 − P c 2 | P c 1 = 5.9827 bar , P c 2 = 0.108998 bar − 0. 5 |

Critical volume | f ( X ) = V c − V c o | V c o = 7.95 cm 3 / mol |

1 ρ = V s c V R ( o ) ( 1 − ω Γ ) (2)

where

V s c = 1 ρ r e f V R ( o ) ( T r e f ) [ 1 − ω Γ ( T r e f ) ] (3)

and Γ = 0.29607 − 0.09045 T R − 0.04843 T R 2 (4)

and ω is the acentric factor and is calculated using Equation (5)

P c V c R T C = 0.291 − 0.080 ω (5)

where P_{c}, T_{c} and V_{c} are the critical pressure, temperature and volume, respectively. T_{ref} is a reference temperature, generally ambient temperature, ρ_{ref} is the density at the reference temperature.

V R ( O ) = 0.33593 − 0.33593 T R + 1.51941 T R 2 − 2.02512 T R 3 + 1.11422 T R 4 (6)

for temperature ranges corresponding to 0.2 ≤ T R ≤ 0.8 where T_{R} is the reduced temperature with T R = T T C . In this study, reference data are these obtained experimentally at 298 K from this study.

Ihmels and Gmehling [

ρ = M w V = M w ∑ n i Δ v i (7)

where M_{W} is the molecular weight and V the molar volume. The molar volume is obtained by summing up all the group volume contributions Δν_{i} with n_{i} the number of group i appearing in the compound, while Δν_{i} is expressed as a polynomial function of absolute temperature:

Δ v i = A i + B i T + C i T 2 (8)

where the units are K for temperature and cm^{3}・mol^{−1} for Δν_{i}. Group functional and there parameters A_{i}, B_{i} and C_{i} can be seen in this literature [

The molecular weight of vegetable oils can be estimated using Equation (9):

M w = 3 ∑ x i M w i + 38.0488 [

Dynamic viscosity estimation

The most important methods used for dynamic viscosity estimation of pure compounds are based on group contribution models proposed by Jöback-Lydersen’s [

Jöback-Lydersen’s method used a simple correlation given by Equation (10):

μ = M w ⋅ exp [ ∑ Δ μ a − 597.82 T + ∑ Δ μ b − 4.294 ] [

where Δμ_{a} and Δμ_{b} are Jöback groups’ contributions which are given and T is the temperature. No temperature limitations are specified for this method except for the fact that the temperature must be less than the critical.

For Morris’s Method, the dynamic viscosity μ_{L} can be estimated using Equation (11) to Equation (12).

log 10 μ L μ + = J ( 1 T R − 1 ) (11)

where J = ( 0.577 + ∑ Δ μ M ) 1 / 2 (12)

Δμ_{M} represents the group contributions factors which are given and μ^{+} is compound class group contribution. This method is limited to temperatures less than 0.8 times the critical temperature.

Thermal conductivity estimation

For thermal conductivity estimation of rapeseed and jatropha oils respectively, two methods based on group contribution method proposed by Sastri, and Sato-Riedel [_{L} by Equation (13) below:

λ L = λ b a m (13)

where m is given by Equation (14)

m = 1 − ( 1 − T R 1 − T b r ) n (14)

and λ_{b} is calculated using the group contribution method Equation (15):

λ b = ∑ Δ λ b + ∑ Δ λ c o r r (15)

Δλ_{b} is the group contribution value of the different groups and Δλ_{corr} is a correction factor which may be required for some compounds. “a” and “n” are constants. Excepted for alcohols and phenols (where a = 0.856 and n = 1.23) the values for these constants are respectively 0.160 and 0.20 for most compounds [_{br} is the ratio of the boiling temperature and the critical temperature.

Sato-Riedel method is based on the equation of Sato-Riedel Equation (16) as follow:

λ = 1.1053 ∗ ( 3 + 20 ( 1 − T R ) 2 / 3 ) ( 3 + 20 ( 1 − T b r ) 2 / 3 ) ∗ M w 1 / 2 (16)

The upper temperature limit for Sato-Riedel method is the critical point and thermal conductivity will not be calculated at temperatures above this.

Heat capacity at constant pressure (C_{p}) estimation

Two methods were selected to estimate the heat capacity at constant pressure. The most accurate method was chose by comparing the values of the estimated properties with experimental values of this study. Zong et al. [

C P l = ∑ A N f r a g , A C P , A l ( T ) (17)

where C P , A l = A 1 , A + A 2 , A T (18), A_{1}_{,}_{A} and A_{2,A} are parameters of temperature dependent correlation for fragment A and T is the temperature (K), and N_{frag}_{,A} is the number of fragments A in the component. The detail of Zong et al. method and the others parameters can be found in the following references [

Ceriani et al. [

C P i l = ∑ k N k ⋅ ( A k + B k T ) (18)

where N_{k} is the number of group k in the molecule and A_{k}, B_{k} are parameters obtained from the regression. The detail of Ceriani et al. [

No temperature limit was found for Ceriani et al. and Zong et al. methods.

For all the physical properties, the Average Relative Deviation (ARD) which formula given by Equation (19) is used to evaluate the accuracy of the different studied methods and for the validation of the estimated values.

ARD ( % ) = 1 N ∑ 1 N 100 ∗ | E x p V − E s t V | / E x p V (19)

where N is the number of data points, Exp_{V} is experimental value, Est_{V} is estimated value.

To test the reliability of MG method, the estimated values of this study have been compared with literature data. However, there are literature data for only canola oil which is another variety of rapeseed oil and then is used for comparison.

Physical Properties | T_{B} (K) | T_{C} (K) | P_{C} (bar) | V_{C} (cm^{3}/mol) | |
---|---|---|---|---|---|

Rapeseed oil | This study* | 638.01 | 811.02 | 14.17 | 1.05 |

Literature [ | 626.10 | 818.95 | 12.85 | 1.04 | |

ARD (%) | 1.90 | 0.96 | 10.27 | 1.25 | |

Jatropha oil | This study* | 634.51 | 838.39 | 14.35 | 1.03 |

Literature [ | 623.60 | 837.47 | 13.02 | 1.03 | |

ARD (%) | 1.75 | 0.10 | 10.21 | 0.68 |

*values of parameters calculated by the authors using the Marrero-Gani’s method.

As shown in _{B}, T_{C} and V_{C} confirming the reliability of MG method. Large deviations were only observed for critical pressure in both cases. Poling et al. [

The experimental data of this work for physical properties of rapeseed and Jatropha oils, for the temperature range 298 to 523 K, using the different methods and devices above mentioned are given in

Physical property | Density (kg/m^{3}) | Dynamic viscosity (mPa∙s) | Thermal conductivity (W/m.K) | Heat capacity (J/g.K) | ||||
---|---|---|---|---|---|---|---|---|

Mesasurement error | 0.051 | 0.10 | 0.012 | 0.037 | ||||

Temperature (K) | rapeseed oil | Jatropha oil | rapeseed oil | Jatropha oil | rapeseed oil | Jatropha oil | rapeseed oil | Jatropha oil |

298 | 911.462 | 914.99 | 134.868 | 88.839 | 0.1654 | 0.1681 | 2.0294 | 2.0373 |

303 | 908.117 | 911.294 | 97.7675 | 63.5536 | 0.1648 | 0.1670 | 2.0313 | 2.0642 |

323 | 894.735 | 896.51 | 39.6956 | 24.8646 | 0.1617 | 0.1630 | 2.0739 | 2.1903 |

343 | 881.353 | 881.726 | 21.9229 | 13.4007 | 0.1587 | 0.1591 | 2.1512 | 2.3228 |

363 | 867.971 | 866.942 | 14.0706 | 8.4454 | 0.1559 | 0.1555 | 2.2398 | 2.4377 |

383 | 854.589 | 852.158 | 9.8750 | 5.8414 | 0.1533 | 0.1521 | 2.3227 | 2.5197 |

403 | 841.207 | 837.374 | 7.3539 | 4.2976 | 0.1508 | 0.1489 | 2.3891 | 2.5622 |

423 | 827.825 | 822.59 | 5.7129 | 3.3041 | 0.1485 | 0.1460 | 2.4345 | 2.5674 |

443 | 814.443 | 807.806 | 4.5808 | 2.6254 | 0.1464 | 0.1433 | 2.4605 | 2.5458 |

463 | 801.061 | 793.022 | 3.7645 | 2.1402 | 0.1444 | 0.1408 | 2.4750 | 2.5171 |

483 | 787.679 | 778.238 | 3.1551 | 1.7807 | 0.1426 | 0.1385 | 2.4920 | 2.5094 |

503 | 774.297 | 763.454 | 2.6872 | 1.5067 | 0.1409 | 0.1364 | 2.5319 | 2.5595 |

523 | 760.915 | 748.67 | 2.3195 | 1.2927 | 0.1394 | 0.1346 | 2.6212 | 2.7129 |

the case of density, when the temperature increases, the molecules disperse and the fluid expands in occupying a larger space. As the mass of the fluid remains identical, this expansion causes a decrease in the density. However, the specific heat of the two oils increases along with increasing temperature. This trend confirms the experimental results obtained by Morad et al. [

Property | Estimation method | ARD (%) | data points | |
---|---|---|---|---|

Rapeseed oil | Jatropha oil | |||

Density | Gunn Yamada | 2.05 | 3.73 | 16 |

Ihmels et al. Gmehling | 2.30 | 2.45 | 16 | |

Dynamic Viscosity | Jöback-Lydersen | 28.39 | 20.42 | 14 |

Morris | 32.42 | 58.93 | 14 | |

Thermal conductivity | Sastri | 5.05 | 1.29 | 14 |

Sato-Riedel | 34.30 | 39.32 | 14 | |

Heat Capacity | Zong et al. | 6.18 | 7.75 | 14 |

Ceriani et al. | 19.03 | 12.18 | 14 |

of the two correlatives methods. However, in view of the purpose of this work, Gunn Yamada correlative method is recommended for extrapolation of density at high temperatures typically observed during the injection phase in diesel engine. Ihmels et al.’s method is then recommended for determined edible vegetable oils properties for food purposes.

The accuracy of the experimental measurements by considering the imperfections of the geometry and the precision of the rheometer was estimated to be in the order of 10%. Two estimation methods have been discussed. In

For temperatures lower than 350 K, large errors result, as illustrated on both figures for the two methods. This is due to the fact that Jöback-Lyderson and Morris viscosity correlations [

Therefore, for low temperatures, deviations can be observed. In the same range of temperature, experimental values of viscosity are higher than estimated ones obtained by Jöback-Lyderson and Morris. The two methods give similar accuracies and tend to underestimate vegetable oil dynamic viscosity but the method of Jöback-Lyderson yields the smallest errors.

When the temperature increases from 350 K, relative deviations become smaller and the experimental and estimated curves tend to overlap, especially with the method of Jöback-Lyderson. For higher accuracy, the Jöback-Lyderson method can be selected. In the literature [

Two estimation methods have been discussed: Sastri and Riedel methods [

Method | Error (%) | Oil | Reference |
---|---|---|---|

Photoacoustic | 2 | Sunflower | [ |

3 | Soybean | ||

Thermal analyser | 1 | Sunflower (21˚C) | [ |

1,8 | Sunflower (68.7˚C) | ||

1.2 | Soybean (21˚C) |

Sastri method. Riedel method overestimates the rapeseed and jatropha oils thermal conductivity. Then, Sastri method gives good agreement between predicted thermal conductivity and experimental thermal conductivity data in the studied temperature range. The higher agreement of Sastri method with experimental values is probably due to the fact that this correlative method involves the contribution of functional groups as well as correction factors, whereas the Riedel method involves only a reference value and a reduced temperature.

Two methods for estimating liquid heat capacities were considered.

[

In addition, while the curve of the three methods evolves linearly, the experimental one varies first linearly and then changes the slope from 450 K. This clearly shows that from a certain temperature the nature of the oil evolves. This confirms the results of our previous studies which showed that, starting from a certain temperature depending on the oil, the nature of the latter evolved following the thermal decomposition of the triglycerides it contains.

For each recommended estimation model, the curves of the physical properties as well as the ARDs of the two oils can differ depending on the physical property under consideration. The rapeseed and jatropha oils are substantially different in their fatty acid composition. Indeed, according to the

This work gives tools to overcome the difficulty to determine experimentally physical properties for vegetable oils within the range of temperature typically observed during the injection phase in diesel engine. Based on experimental physical properties of pure vegetable oils determined in this study and existing theoretical models, this work has shown that, within the range 298 to 523 K, rapeseed and jatropha oils’ physical properties can be satisfactorily predicted as a function of temperature using group-contribution approach. In this temperature range, it was found that for the prediction of oil density, the Gunn Yamada method was the most accurate, and in line with our experimental data, with an ARD of 1.34 for Rapeseed oil and 0.04 for Jatropha oil. Dynamic viscosity was found to be well-predicted by the Jöback-Lyderson method above 350 K. The calculated ARD of 28.39 for Rapeseed oil and 20.42 for Jatropha oil is much higher because of the large deviation observed at lower temperatures. Thermal conductivity and Heat Capacity were respectively found to be well predicted by Sastri and Zong et al. methods with ARD lower than 7.75 for both Rapeseed and Jatropha oils.

Further studies to be conducted on vegetable oils having extreme fatty acid composition will allow correlating more specifically the evolution up to 523 K of a given physical property to the composition of oils.

A.S. Zongo expresses his gratitude to French Cooperation in Burkina Faso who, through the Service for Cooperation and Cultural Action (SCAC), financed this study by awarding an internship fellowship in 2017 at CIRAD Montpellier.

The authors declare no conflicts of interest regarding the publication of this paper.

Zongo, A.S., Vaïtilingom, G., Daho, T., Caillol, C., Hoffmann, J.-F., Piriou, B., Valette, J., Segda, B.G. and Higelin, P. (2019) Temperature Dependence of Density, Viscosity, Thermal Conductivity and Heat Capacity of Vegetable Oils for Their Use as Biofuel in Internal Combustion Engines. Advances in Chemical Engineering and Science, 9, 44-64. https://doi.org/10.4236/aces.2019.91004