Experimental Liquid Densities of Red Palm Oil at Pressures up to 150 MPa from (312 to 352) K and Dynamic Viscosities at 0.1 MPa from (293 to 353) K

Abstract

Density and viscosity are fundamental properties necessary for processing of red palm oil (RPO). The main fatty acid constituents of RPO were determined to be palmitic acid (C_16:0), oleic acid (C_18:1), and linoleic acid (C_18:2). Rheology measurements confirmed that RPO behaved as a Newtonian fluid. Viscosities and atmospheric densities of RPO were measured at 0.1 MPa and (293 K to 413) K and correlated with the Rodenbush model (0.05% deviation). Dynamic viscosities of RPO were correlated with the Vogel–Fulcher–Tammann model (0.06% deviation) and Doolittle free volume model (0.04% deviation). High-pressure densities of RPO were measured at (10 to 150) MPa and (312 to 352) K. The Tait equation could correlate the high-pressure densities of RPO to within 0.021% deviation and was used to estimate the thermal expansion as 5.1 × 10⁻⁴ K⁻¹ (at 312 K, 150 MPa) to 4.8 × 10⁻⁴ K⁻¹ (at 352 K, 150 MPa) and isothermal compressibility as 7.3 × 10⁻⁴ MPa⁻¹ (at 352 K, 0.1 MPa) to 3.5 × 10⁻⁴ MPa⁻¹ (at 352 K, 150 MPa). Parameters for the perturbed-chain statistical associating fluid theory equation of state were determined and gave an average of 0.143% deviation in density. The data and equations developed should be useful in high-pressure food processing as well as in applications considering vegetable oils as heat transfer fluids or as lubricants.

1. Introduction

Red palm oil (RPO) is produced via physical refining of crude palm fruits and contains roughly 46% saturated fatty acids, 42% monounsaturated fatty acids, and 12% polyunsaturated fatty acids [1]. In plant oil processing, the viscosity and density are important physical properties of an oil, because they affect applications in high-pressure microfluidics in crystallization [2], high-pressure homogenization in processing of palm-oil-containing foods [3], and separation of phytonutrients with supercritical fluids [4].

Densities and viscosities of plant oils are directly related to lipid structure characteristics, such as type and composition of fatty acid constituents, number of unsaturated constituents, and chain length of fatty acids that constitute their triacylglycerides. Folayan et al. [5] reported that high-linoleic vegetable oil biomass showed cold flow behavior due to high linoleic acid constituents, a high degree of unsaturation, and long chain length. Anitescu et al. [6] reported that optimum fluid volatility and velocity for the 2-D grade diesel fuel oil process could be estimated by the measurement and modeling of oil (palm oil, soybean oil, and rapeseed oil) density and viscosity. In that study, experimental density and dynamic viscosity of oils at atmospheric pressure were used to predict the biodiesel–benzene fluid behavior with the Grunberg–Nissan model [7].

High-pressure densities of oils are prerequisite information for supercritical fluid extraction processes [8], heat transfer, and tribology of lubricants [9]. For instance, Kok et al. [10] found that increased mass transfer of virgin coconut oil and supercritical CO₂ into mangosteen peel was related to the high-pressure density. Regueira et al. [11] measured high-pressure densities of sunflower oil to estimate thermal expansion and isothermal compressibility for applications in power transfer and engine hydraulic fluids. Jasiok et al. [9] measured high-pressure densities of oils for lubricating oil selection and developed a fluctuation theory equation of state to correlate the data.

Even though RPO is of interest to supercritical fluid extraction processing for making functional foods and it is used as a lubricant in food processing machinery in industry due to food safety, experimental densities of RPO at high pressure are unavailable in the literature. In this study, the objective was to measure the density of red palm oil at pressures up to 150 MPa, to measure the viscosity over a wide range of temperatures, and to develop several kinds of correlating equations that are used in the above applications. The Tait equation was used to correlate high-pressure density data and to estimate thermal expansion and isothermal compressibility of RPO. Parameters for the perturbed-chain statistical associating fluid theory (PC-SAFT) equation [12] were determined to allow fundamental description of the pressure–density–temperature behavior of red palm oil and to provide a basis for studying some of the above applications.

2. Materials and Methods

2.1. Materials

Red palm oil (RPO) was supplied by Orifera^TM (Selangor, Malaysia). Fatty acid methyl ester (FAME) mix standards (C8 to C22) were purchased from Sigma-Aldrich Co. (St. Louis, MO, USA).

2.2. Gas Chromatography–Flame Ionization Detector (GC-FID)

Fatty acid composition was determined by a gas chromatography–flame ionization detector (GC-FID) (Agilent Technologies 6890N Series Network Gas Chromatograph, Santa Clara, CA, USA) equipped with a BPX70 SGE capillary column (30 m × 320 µm × 0.25 µm). RPO was esterified into methyl esters by following AOCS procedure Ce 2-66 [13] and loaded into an oven at 373 K for 2 min, then heated to 503 K in 6 K min⁻¹. The injection temperature and detector temperature were 523 K. RPOs were injected using split mode (20:1), an injection volume of 1.0 µL, and a total analysis time of 38 min.

2.3. High-Performance Liquid Chromatography (HPLC)

Carotenoid and vitamin E content were analyzed according to the method of Lee et al. [14]. Carotenoid content was determined by high-performance liquid chromatography (HPLC) (Agilent Technologies 1200 chromatographic system, Santa Clara, CA, USA) with a Develosil RP-Aqueous C30 column (250 mm × 4.6 mm, 5 µm) supplied from Hinode-cho Seto, Japan. The mobile phase (acetonitrile/chloroform 80/20% v/v) was delivered isocratically at 1 mL/min and analytes were detected at a 450 nm wavelength with a UV detector. Vitamin E was identified with a Phenomenex Kinetex PFP column (250 mm × 4.6 mm, 5 µm) supplied from Madrid Avenue, Torrance, CA, USA. Methanol and water as the mobile phase were used in gradient mode at 1 mL/min and Ex/Em: 295/330 nm wavelength for detection of analytes with a fluorescence detector.

2.4. Rheology

The shear rate of RPO was measured by a rotational rheometer (Haake, RheoStress 6000, Waltham, MA, USA) to confirm Newtonian behavior and to provide reference values for the Stabinger viscometer. RPO was loaded between a lower plate (222-1891 TMP 60, diameter of 60 mm) and cone that was fixed at a 0.105 mm gap from the attachment (222-1867 cone, C60/2° tilt). One cycle began from (0.1 to 1000) s⁻¹ and then was reversed from (1000 to 0.1) s⁻¹ for two temperatures, 313.2 K and 353.2 K. The shear stress is proportional to shear rate and was determined from the following equations:

$$\eta ={\displaystyle \frac{\tau }{\dot{\gamma }}}$$

(1)

$$\tau =0.0523\dot{\gamma }-0.0065\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}(303.2 \mathrm{K})$$

(2)

$$\tau =0.0108\dot{\gamma }-0.0084\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}(353.2 \mathrm{K})$$

(3)

In Equations (1)–(3), $\eta$ is the dynamic density in units of Pa∙s, $\tau$ is the shear stress in units of Pa, and $\dot{\gamma }$ is shear rate in units of s⁻¹.

2.5. Measurements of Density and Viscosity at Atmospheric Pressure

Measurements of density and viscosity of RPO were conducted with a Stabinger viscometer (Anton Paar, SVM 3000, Graz, Styria, Austria), from (293.15 to 353.15) K at intervals of 10 K increments. The average of eight measurements comprised four cycles. The first cycle started from a low to high temperature and the second cycle from a high temperature to low temperature.

2.6. Viscosity Model

The Rodenbush et al. [15] model was used to determine the relationship between density and viscosity as follows:

$$\rho =D+E{\eta }^{-0.5}$$

(4)

In Equation (4), $\rho$ is density in units of $\mathrm{k}\mathrm{g} {\mathrm{m}}^{-3}$, $\eta$ is viscosity in units of mPa∙s, $D (\mathrm{k}\mathrm{g} {\mathrm{m}}^{-3})$ and $E {(\mathrm{m}\mathrm{P}\mathrm{a}·\mathrm{s})}^{-0.5}$ are fitting parameters. The Vogel–Fulcher–Tammann model [16,17] was used to correlate the viscosity as follows:

$$\eta ={\eta }_{o}exp\left[{\displaystyle \frac{d_1}{T+d_2}}\right]$$

(5)

In Equation (5), $T$ is the absolute temperature, ${\eta }_o$ (mPa∙s), $d_1$ (K) and $d_2$ (K) are the fitting parameters. The Doolittle free volume (FV) model [18] correlated viscosity based on temperature and free volume fraction as follows:

$$\eta =Aexp\left({\displaystyle \frac{B}{f}}\right)$$

(6)

$$f={\displaystyle \frac{V_{s, free}}{V_s}}={\displaystyle \frac{V_{s,}-V_{s, occ}}{V_s}}$$

(7)

In Equations (6) and (7), A$(\mathrm{m}\mathrm{P}\mathrm{a}·\mathrm{s})$ and B$({\mathrm{c}\mathrm{m}}^3 {\mathrm{g}}^{-1})$ are fitting parameters based on the atmospheric viscosities, $f$ is the free volume fraction in units of ${\mathrm{c}\mathrm{m}}^3 {\mathrm{g}}^{-1}$, V_s,free is the free volume, Vs is the liquid volume in units of ${\mathrm{c}\mathrm{m}}^3 {\mathrm{g}}^{-1}$, and V_s,occ is the occupied volume in units of ${\mathrm{c}\mathrm{m}}^3 {\mathrm{g}}^{-1}$. In Equation (7), the free volume can be estimated from the excluded volume of the liquid [19], however, in this study, V_s,occ was treated as a fitting parameter.

2.7. Measurement of Density at High Pressure

Densities at high pressure were measured with a bellows dilatometer under vacuum (ca. 3 Pa) and at ambient temperature as described in previous publications [20,21,22,23,24]. Briefly, RPO was poured into a dilatometer and loaded into the pressure vessel and then the chamber was pressurized. Measurements were made from (313 to 353) K in intervals of 10 K and from (10 to 150) MPa in intervals of 10 MPa. The volume of the bellows was obtained by its linear length expansion or contraction that was measured with a calibrated linear variable differential transformer (LVDT). An additional sequence of measurements was made after the full sequence of measurements from low temperature to high temperature to verify the equipment and the integrity and stability of RPO.

2.8. Tait Equation

In the Tait equation, correlation of density data was made with the following equations:

$$\rho \left(P,T\right)={\displaystyle \frac{\rho (P_o, T)}{1-C ln\left(1+\frac{P}{D(T)}\right)}}$$

(8)

$${\displaystyle \frac{1}{\rho (P_o, T)}}=a_0+a_{1}T+a_2{T}^2$$

(9)

$$D(T)=b_0\mathrm{e}\mathrm{x}\mathrm{p}(-b_{1}T)$$

(10)

In Equations (8)–(10), $\rho$ is the density, $P_o$ is the atmospheric pressure, $T$ is the absolute temperature, $P$ is the pressure, and $C$,$D$, $a_0$, $a_1$, $a_2$, $b_0$, and $b_1$ are fitting parameters. In the analysis with the Tait equation, the coefficient of thermal expansion $\beta$ (K⁻¹) and isothermal compressibility ${\kappa }_{\mathrm{T}}$ (MPa⁻¹) of RPO were calculated from:

$$\beta =-{\displaystyle \frac{1}{\rho }}{\left({\displaystyle \frac{\partial \rho }{\partial T}}\right)}_P={\displaystyle \frac{a_1+{2a}_{2}T}{a_0+a_{1}T+a_2{T}^2}}-{\displaystyle \frac{d_{1}CP}{(D\left(T\right)+P)\left\{1-Cln(1+\frac{P}{D\left(T\right)})\right\}}}$$

(11)

$${\kappa }_{\mathrm{T}}={\displaystyle \frac{1}{\rho }}{\left({\displaystyle \frac{\partial \rho }{\partial P}}\right)}_T={\displaystyle \frac{C}{(D\left(T\right)+P)\left\{1-Cln(1+\frac{P}{D\left(T\right)})\right\}}}$$

(12)

2.9. Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) Equation

In perturbation theory, a fluid corresponding to a hard chain (hc) fluid is used as a reference and perturbations that account for dispersion (disp) or van der Waals forces are summed to form the dimensionless residual Helmholtz function (${\tilde{a}}^{res}$) as follows [12,25]:

$${\tilde{a}}^{res}={\tilde{a}}^{hc}+{\tilde{a}}^{disp}$$

(13)

The equation of state can be determined from the derivative of the Helmholtz function to obtain the compressibility factor as follows:

$$Z=1+Z^{hc}+Z^{disp}$$

(14)

In Equation (14), $Z^{hc}$ is the residual hard chain contribution and $Z^{disp}$ is the residual dispersion contribution. The terms in Equation (14) are defined as follows:

$$Z^{hc}=\overline{m}{Z}^{hs}-\sum _{i=1}^{NC}{x}_i\left(m_i-1\right){\displaystyle \frac{1}{g_{ii}^{hs}\left({\sigma }_{ii}\right)}}\rho {\left({\displaystyle \frac{\partial g_{ii}^{hs}\left({\sigma }_{ii}\right)}{\partial \rho }}\right)}_T$$

(15)

$$\overline{m}=\sum _{i=1}^{NC}{x}_i{m}_i$$

(16)

$$Z^{hs}={\displaystyle \frac{{\xi }_3}{(1-{\xi }_3)}}+{\displaystyle \frac{{3\xi }_1{\xi }_2}{{{\xi }_0(1-{\xi }_3)}^2}}+{\displaystyle \frac{{3\xi }_2^3-{\xi }_3{\xi }_2^3}{{\xi }_0{(1-{\xi }_3)}^3}}$$

(17)

$$g_{ii}^{hs}={\displaystyle \frac{1}{(1-{\xi }_3)}}+\left({\displaystyle \frac{d_i{d}_i}{d_i+d_i}}\right){\displaystyle \frac{{3\xi }_2}{{(1-{\xi }_3)}^2}}+{\left({\displaystyle \frac{d_i{d}_i}{d_i+d_i}}\right)}^2{\displaystyle \frac{{2\xi }_2^2}{{(1-{\xi }_3)}^3}}$$

(18)

$$\begin{gathered} {\rho \left({\displaystyle \frac{\partial g_{ii}^{hs}\left({\sigma }_{ii}\right)}{\partial \rho }}\right)}_T={\displaystyle \frac{{\xi }_3}{{(1-{\xi }_3)}^2}}+\left({\displaystyle \frac{d_i{d}_i}{d_i+d_i}}\right)\left({\displaystyle \frac{{3\xi }_2}{{(1-{\xi }_3)}^2}}+{\displaystyle \frac{{6\xi }_2{\xi }_3}{{(1-{\xi }_3)}^3}}\right) \\ +{\left({\displaystyle \frac{d_i{d}_i}{d_i+d_i}}\right)}^2\left({\displaystyle \frac{{4\xi }_2^2}{{(1-{\xi }_3)}^3}}+{\displaystyle \frac{{6\xi }_2^2{\xi }_3}{{(1-{\xi }_3)}^4}}\right) \end{gathered}$$

(19)

$${\xi }_n={\displaystyle \frac{\pi }{6}}\rho \sum _{i=1}^{NC}{x}_i{m}_i{d}_i^n, n\in \left\{0, 1, 2, 3\right\}$$

(20)

$$\rho ={\displaystyle \frac{6}{\pi }}\eta {\left(\sum _{i=1}^{NC}{x}_i{m}_i{d}_i^3\right)}^{-1}$$

(21)

In Equations (15)–(21), $i$ is the single pure component of oil, NC is the number of components (NC = 1), ${\xi }_n$ is equal to the packing fraction, $x_i$ is the mole fraction of chains of a single pure component $i$ ($x_i=1$), $\overline{m}$ is the mean segment number of molecule $i$, $m_i$ is the number of segments in a chain of molecule $i$, $g_{ii}^{hs}$ is the radial pair distribution function of molecule $i$ in a hard sphere system, superscript hs indicates quantities of the hard sphere system, $\rho$ is the total number density of molecule $i$ ${\mathrm{\AA }}^{-3}$, and temperature-dependent segment diameter $d_i(T)$ is calculated in units of Å by the following equation [12]:

$$d_i(T)={\sigma }_i\left[1-0.12exp\left(-{\displaystyle \frac{3{\epsilon }_i}{kT}}\right)\right]$$

(22)

In Equation (22), ${\sigma }_i$ is temperature-independent segments in units of $\mathrm{\AA }$, ${\displaystyle \frac{{\epsilon }_i}{k}}$ is dispersion energy divided by the Boltzmann constant in units of K, ${\epsilon }^i$ is pair potential in units of $\mathrm{J}$, k_B is the average kinetic energy of one particle related to absolute temperature (1.380649 × 10⁻²³ $\mathrm{J} {\mathrm{K}}^{-1}$), and $T$ is absolute temperature in units of $\mathrm{K}$. The dispersion contribution $Z^{disp}$ is given by the following equations:

$$Z^{disp}=-2\pi \rho {\left({\displaystyle \frac{\partial \left(\eta I_1\right)}{\partial \eta }}\right)}_{T,n}\overline{m^2\epsilon {\sigma }^3}-\pi \rho \overline{m}\overline{m^2{\epsilon }^2{\sigma }^3}\left(C_1{\left({\displaystyle \frac{\partial \left(\eta I_2\right)}{\partial \eta }}\right)}_{T,n}+C_2{\eta I}_2\right)$$

(23)

$$\overline{m^2\epsilon {\sigma }^3}=\sum _{i=1}^{NC}{x}_i{m}_i\left({\displaystyle \frac{{\epsilon }_{ii}}{kT}}\right){\sigma }_{ii}^3$$

(24)

$$\overline{m^2{\epsilon }^2{\sigma }^3}=\sum _{i=1}^{NC}{x}_i{m}_i{\left({\displaystyle \frac{{\epsilon }_{ii}}{kT}}\right)}^2{\sigma }_{ii}^3$$

(25)

$$C_1={\left(1+\overline{m}{\displaystyle \frac{8\eta -{2\eta }^2}{{\left(1-\eta \right)}^4}}+(1-\overline{m}){\displaystyle \frac{20\eta -27{\eta }^2+12{\eta }^3-2{\eta }^4}{{\left[\left(1-\eta \right)\left(2-\eta \right)\right]}^2}}\right)}^{-1}$$

(26)

$$C_2={\left({\displaystyle \frac{\partial C_1}{\partial \eta }}\right)}_{T, n}=-C_1^2\left(\overline{m}{\displaystyle \frac{-4{\eta }^2+20\eta +8}{{\left(1-\eta \right)}^5}}+(1-\overline{m}){\displaystyle \frac{2{\eta }^3+12{\eta }^2-48\eta +40}{{\left[\left(1-\eta \right)\left(2-\eta \right)\right]}^3}}\right)$$

(27)

$$\left({\displaystyle \frac{\partial \left(\eta I_1\right)}{\partial \eta }}\right)=\sum _{i=0}^6{a}_i\left(\overline{m}\right)\left(i+1\right){\eta }^i$$

(28)

$$\left({\displaystyle \frac{\partial \left(\eta I_2\right)}{\partial \eta }}\right)=\sum _{i=0}^6{b}_i\left(\overline{m}\right){\left(i+1\right)\eta }^i$$

(29)

In Equations (23)–(29), $\eta$ is the reduced density ($\eta ={\xi }_3$), $\overline{m^2\epsilon {\sigma }^3}$, $\overline{m^2{\epsilon }^2{\sigma }^3}$ are functions of molecule $i$, $C_1$ is shorthand notation for a function, $C_2$ is a function for the derivative of $C_1$, and $I_1,I_2$ are integrals of the perturbation theory given by Equations (28) and (29) and thus the compressibility factor can be obtained from the Helmholtz function using standard thermodynamic relationships [12], while $a_i\left(\overline{m}\right)$ and $b_i\left(\overline{m}\right)$ are computational coefficients:

$$a_i\left(\overline{m}\right)=a_{0i}+\left({\displaystyle \frac{\overline{m}-1}{\overline{m}}}\right)a_{1i}+\left({\displaystyle \frac{\overline{m}-1}{\overline{m}}}\right)\left({\displaystyle \frac{\overline{m}-2}{\overline{m}}}\right)a_{2i}$$

(30)

$$b_i\left(\overline{m}\right)=b_{0i}+\left({\displaystyle \frac{\overline{m}-1}{\overline{m}}}\right)b_{1i}+\left({\displaystyle \frac{\overline{m}-1}{\overline{m}}}\right)\left({\displaystyle \frac{\overline{m}-2}{\overline{m}}}\right)b_{2i}$$

(31)

In Equations (30) and (31), $a_{00}$to $a_{26}$ and$b_{00}$to $b_{26}$ are a set of 42 universal constants of the model that is based on pure components [12]. Parameters ${\sigma }_{ii}$ and ${\epsilon }_{ii}$ are determined by Berthelot–Lorentz combining rules for a pair of unlike segments:

$${\sigma }_{ii}={\displaystyle \frac{1}{2}}\left({\sigma }_i+{\sigma }_i\right)$$

(32)

$${\epsilon }_{ii}=\left(1-k_{ii}\right)\sqrt{{\epsilon }_i{\epsilon }_i}$$

(33)

In Equations (32) and (33), $k_{ii}$ is a binary interaction parameter that does not apply for this work ($k_{ii}=0$), because the oils studied are considered to be a single type of triglyceride molecule.

2.10. Objective Function

The following objective functions were used for determining model parameters: Average relative deviation ($ARD$) of calculated ($calc$) and experimental ($exp$) viscosities ($\eta$) and densities ($\rho$) were applied as objective functions in calculating fitting parameters of the Rodenbush et al. [15] model:

$$ARD={\displaystyle \frac{1}{N}}\sum _{i=1}^N\left|{\displaystyle \frac{{\eta }_{calc,i}-{\eta }_{exp,i}}{{\eta }_{exp,i}}}\right|\times 100\%$$

(34)

$$ARD={\displaystyle \frac{1}{N}}\sum _{i=1}^N\left|{\displaystyle \frac{{\rho }_{calc,i}-{\rho }_{exp,i}}{{\rho }_{exp,i}}}\right|\times 100\%$$

(35)

In Equations (34) and (35), $N$ is number of data and $i$ is an index. The objective function of Equation (34) was used to minimize the deviation of experimental and calculated viscosity by correlation of Vogel–Fulcher–Tammann and Doolittle free volume models. For the Tait equation, atmospheric pressure density data with multiple linear regression was used to determine parameters ($a_0$, $a_1$, $a_2$) and high-pressure density data with non-linear minimization of Equation (35) were used to determine parameters ($b_0$, $b_1, C$).

2.11. Optimal Parameter Analysis

For density and viscosity models, Equations (2)–(8), the ARD% values were plotted against a single fitting parameter and the remaining parameters were adjusted to confirm a global minimum. Optimization of the fitting parameter set was performed step-wise according to the sequences’ change in the equations. In Equation (2), initially the $D$ parameter value was set equal to zero and the $E$ value was optimized and afterwards the two parameters ($D$, $E$) were optimized together. This was applied to Equations (2)–(8).

3. Results and Discussion

3.1. Characterization of Red Palm Oil

Characterization of red palm oil (RPO) fatty acid composition by GC-FID analyses is shown in

Table 1. Analysis of fatty acid constituents in red palm oil (RPO).

Fatty Acid Content (%)
Oils	Mw (g mol−1)	C8:0	C10:0	C12:0	C14:0	C16:0	C16:1	C18:0	C18:1	C18:2	C18:3	C20:0	C22:0	C24:0
RPO	866.10	0.03	0.04	0.32	0.90	21.60	0.26	3.20	56.60	16.00	0.40	0.50	0.10	0.10

. The main fatty acid constituents of RPO were determined to be palmitic acid (C_16:0), oleic acid (C_18:1), and linoleic acid (C_18:2). The RPO has similar main fatty acid constituents to palm oil (Table S1), while RPO constituents are different from those of other common plant oils. According to its constituents, RPO should have similar physical properties to palm oil as discussed below.

Figure 1 shows the shear stress versus shear rate curve of RPO (Figure 1a) and residuals of straight-line fits (Figure 1b) measured with a rotational. As shown in Figure 1a, the shear stress was directly proportional to the shear rate at both 303.2 K and 353.2 K, meaning that RPO behaves as a Newtonian fluid.

Measurements of dynamic viscosities and atmospheric densities for red palm oil (RPO) at (293 to 353) K are shown in

Table 2. Dynamic viscosities and atmospheric densities of red palm oil at (293 to 353) K.

T (K)	η (mPa∙s)	ρ a (kg m−3)
293.15	84.24 ± 0.147	912.14
303.15	53.53 ± 0.081	905.39
313.15	35.99 ± 0.044	898.63
323.15	25.38 ± 0.024	891.85
333.15	18.63 ± 0.015	885.13
343.15	14.14 ± 0.011	878.41
353.15	11.05 ± 0.010	871.70

^a Combined expanded uncertainty for density and viscosity were estimated as 1 kg m⁻³ and 0.73%, respectively, with a level of confidence of 0.95 (k = 2).

. Combined extended uncertainties in density and viscosity were estimated to be 1 kg m⁻³ and 0.73%, respectively, at a 95% level of confidence.

Figure 2a shows dynamic viscosities and atmospheric densities of red palm oil (RPO) measured with a Stabinger viscometer and correlated with the Rodenbush et al. [15] model. As shown in Figure 2a, the Rodenbush et al. [15] model could correlate the experimental RPO densities well (0.05%) and when the set of parameters was used to predict the viscosities, an average deviation of 0.08% was obtained. The Rodenbush model was able to correlate both viscosity and density as shown by the ARD values in

Table 3. Parameters and statistical details of Rodenbush et al. [15] model, Vogel–Fulcher–Tammann (VFT) model, Doolittle free volume (FV) model for red palm oil.

Model	Parameters		$\mathit{A}\mathit{R}\mathit{D}$ (%)
			Density	Viscosity
Rodenbush et al. [15]	$D$ (kg m−3)	934.0360	0.0505	0.0771
	$E$ ${(\mathrm{m}\mathrm{P}\mathrm{a}·\mathrm{s})}^{-0.5}$	−209.6053
VFT	${\eta }_o$ ($\mathrm{m}\mathrm{P}\mathrm{a}·\mathrm{s}$)	0.1063
	$d_1$ (K)	914.5262	-	0.0609
	$d_2$ (K)	−156.1386
FV	$V_{s, occ} ({\mathrm{c}\mathrm{m}}^3{\mathrm{g}}^{-1})$	0.9893
	$A (\mathrm{m}\mathrm{P}\mathrm{a}·\mathrm{s})$	0.1440	-	0.0436
	$B ({\mathrm{c}\mathrm{m}}^3{\mathrm{g}}^{-1})$	1.2358

. It should be noted that the VFT and FV models provide a set of parameters that allow them to predict RPO densities via the Rodenbush et al. [15] model.

Dynamic viscosities of RPO at (293 to 353) K and 0.1 MPa were correlated with the Vogel–Fulcher–Tammann (VFT) and Doolittle free volume (FV) models (Table 3) and residuals of all models are plotted in Figure 2b. The VFT and FV models could correlate the experimental RPO viscosities at low deviations (0.04 to 0.06)%, however, the residuals of VFT and FV models showed systematic deviations (quadratic) that indicate that additional terms could be added to the models, because about half of the residuals fall outside of the 95% confidence interval (Figure S1).

The 95% confidence interval (Figure S1) was similar for all models which means that the correlation of the data is not so different. Residuals of the FV model all fall within the 95% confidence interval (Figure S1), which means the FV model is the most reliable among the correlating equations (Figure S2).

The dynamic viscosities and atmospheric densities of RPO were compared with palm oil, sunflower oil, soybean oil, and corn oil (Figure S3). From Figure S3, viscosities of RPO and palm oil were high, with low densities, while those of sunflower oil and corn oil were low, with high densities. This means that fluid behavior of RPO was similar to that of palm oil at atmospheric pressure [26].

3.2. High-Pressure Densities of Red Palm Oil (RPO)

Table 4. Measurement of liquid densities ^a for red palm oil at (312 to 351) K and (10 to 150) MPa.

	T (K)
	312.1	321.9	331.9	341.8	351.9	312.0 b
P (MPa)	$\rho \left(P_o, T\right)$ (kg m−3)
10	904.5	898.2	891.9	885.5	879.2	904.6
20	910.0	903.7	897.6	891.5	885.4	909.9
30	915.0	909.0	903.0	897.2	891.2	914.9
40	919.8	913.9	908.2	902.5	896.7	919.7
50	924.5	918.6	913.0	907.5	901.8	924.3
60	928.7	923.1	917.6	912.3	906.7	928.6
70	932.9	927.4	922.1	916.8	911.5	932.9
80	937.0	931.6	926.3	921.1	915.8	936.9
90	940.8	935.5	930.4	925.2	920.2	940.7
100	944.5	939.2	934.2	929.2	924.2	944.4
110	948.1	942.8	937.9	933.1	928.2	948.1
120	951.7	946.4	941.5	936.9	932.0	951.6
130	955.1	949.9	945.1	940.5	935.7	955.0
140	958.3	953.2	948.4	944.0	939.3	958.2
150	961.6	956.5	951.8	947.3	942.8	961.4

^a Standard uncertainties are $u\left(T\right)=0.1$K, $u\left(P\right)=0.1$ MPa for $10\le P\le 80$ MPa and $u\left(P\right)=0.25$ MPa for $90\le P\le 200$ MPa, and combined expanded uncertainty with a 0.95 level of confidence ($k=2$) is $U_c\left(\rho \right)=1.3$ kg m⁻³. ^b Measurements at this temperature were made after completing the series of measurements from 312.1 K (minimum temperature) to 351.9 K (maximum temperature).

shows the measurement of high-pressure density for red palm oil (RPO) at (312 to 351) K and (10 to 150) MPa. For Table 4, high-pressure liquid densities of RPO increased with increasing pressure. The last column in

Table 5. Summary of Tait equation parameters and average relative deviation (ARD) for experimental liquid densities of oils at high pressure.

		$\mathit{\rho }({\mathit{P}}_{\mathit{o}},\mathit{T})$		$\mathit{D}(\mathit{T})$
	${\mathit{a}}_0$	${\mathit{a}}_1$	${\mathit{a}}_2$	${\mathit{b}}_0$	${\mathit{b}}_1$	$\mathit{C}$	$\mathit{A}\mathit{R}\mathit{D} (\mathit{\%})$	Ref.
	$({\mathrm{m}}^3 {\mathrm{k}\mathrm{g}}^{-1})$	$({\mathrm{m}}^3 {\mathrm{k}\mathrm{g}}^{-1} {\mathrm{K}}^{-1})$	$({\mathrm{m}}^3 {\mathrm{k}\mathrm{g}}^{-1} {\mathrm{K}}^{-2})$	MPa	${\mathrm{K}}^{-1}$
RPO	8.756 × 10−4	6.951 × 10−7	1.995 × 10−10	6.484 × 102	4.563 × 10−3	9.514 × 10−2	0.021	This work

is a replicate run after completing the series of density measurements and shows that the oil maintained its integrity, because the maximum density differences observed were 0.1 kg m⁻³ to 0.2 kg m⁻³.

High-pressure densities of red palm oil (RPO) at (312 to 351) K and (10 to 150) MPa were correlated with the Tait equation (Figure 3a) and residuals were plotted (Figure 3b). As shown in Figure 3a, the Tait equation could correlate the trends of the data at low deviations (0.021%), however, the residuals (Figure 3b) showed quadratic dependence in pressure that implies that an additional term in pressure could be added to the model, especially since about half of the residuals fall outside of the 95% confidence interval.

High-pressure densities of red palm oil (RPO) were correlated with the PC-SAFT equation (Figure 4a) and residuals were plotted (Figure 4b). As shown in Figure 4a, the PC-SAFT model could correlate the trends of the data with moderate deviations (0.143%), however, the residuals (Figure 4b) showed quadratic dependence in pressure as well as a systematic deviation in temperature, indicating that additional terms in temperature and density could be added to the model, because about one third of the residuals fall outside of the 95% confidence interval.

Comparing the Tait and the PC-SAFT equations, it is clear that the Tait equation gives deviations that are roughly seven times lower than those of the PC-SAFT equation for liquid density correlation. Nevertheless, deviations in density with either equation are relatively low compared with cubic equations of state (e.g., 2% to 6%) and the molecular parameters of the PC-SAFT equation allow it to be applied to calculate other physical properties as well as phase equilibria of mixtures.

Table 5 shows a summary of Tait equation parameters and ARD values for high-pressure density of RPO. In Table 5, the optimal parameter values (Figure S4) of RPO were close to those of palm oil (Table S2), but different from those of olive oil, despite RPO having similar fatty acid constituents to palm oil and olive oil (Table S1).

Table 6. Summary parameter and statistic details of Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) model with molecular weight of red palm oil (RPO) for correlation of liquid densities at high pressure.

Oils	Mw (g mol−1)	$\mathit{m}$	$\mathit{\sigma }$ (Å)	$\mathit{\epsilon }/{\mathit{k}}_{\mathit{B}}$ (K)	ARD (%)	Ref.
RPO	821.7	34.003	3.400	277.35	0.143	This Work

shows the PC-SAFT model parameters and ARD values for high-pressure RPO densities. In Table 6, the PC-SAFT $\sigma$ parameter of RPO is slightly larger than those of palm oil or olive oil (Table S3), but the $\epsilon /k_B$ parameter of RPO was in between their values (Table S3), which means that the interaction strength $\epsilon /k_B$ parameter is the main reason for the differences in the densities of these oils.

Figure 5 shows derivative properties of red palm oil (RPO) derived from the Tait equation. The thermal expansion decreased with increasing temperature (Figure 5a) and the isothermal compressibility decreased with increasing pressure (Figure 5b). The thermal expansion of RPO was lower than that of palm oil at a given pressure (Figure S5a) and the isothermal compressibility was lower than that of palm oil at a given temperature (Figure S5b). These differences in derivative properties between RPO and palm oil (Figure S5) are as high as 10% depending on conditions of temperature and pressure and may be important for some applications where low thermal expansion and low compressibility are required.

4. Conclusions

In this study, high-pressure densities and densities and viscosities at atmospheric pressure were measured for red palm oil (RPO). Shear rate versus shear stress measurements showed that RPO had Newtonian behavior with maximum shear stress (52 Pa) and shear rate (1000 s⁻¹) at 303 K. The viscosity and density of RPO could be correlated with Vogel–Fulcher–Tammann (VFT) and Doolittle free volume (FV) models at deviations lower than about 0.08%. For high-pressure densities, the Tait equation provided data correlation with low deviations (0.02%). Variation of the thermal expansion and isothermal compressibility of RPO with temperature and pressure estimated with the Tait equation showed typical trends for vegetable oils. From analysis of the residuals, it is likely that high-pressure density data correlation with the Tait equation can be improved by adding another parameter in pressure. Although molecular parameters for RPO could be estimated for the PC-SAFT equation of state, systematic deviations (0.14%) in density were apparent in both temperature and pressure. Correlation of high-pressure density data with the PC-SAFT equation can probably be improved by fitting isotherms and examining the temperature dependence of the fitted parameters.