DOI: 10.3303/CET24108005 Paper Received: 11 September 2023; Revised: 11 December 2023 ; Accepted: 7 February 2024 Please cite this article as: Reddy T., Seodigeng T., Musamba B., Rutto H., 2024, Mass Transfer Modelling of Sclerocarya Birrea Kernels in Supercritical Carbon Dioxide, Chemical Engineering Transactions, 108, 25-30 DOI:10.3303/CET24108005 CHEMICAL ENGINEERING TRANSACTIONS VOL. 108, 2024 A publication of The Italian Association of Chemical Engineering Online at www.cetjournal.it Guest Editors: Carlo Pirola, Antonio Espuña Copyright © 2024, AIDIC Servizi S.r.l. ISBN 979-12-81206-08-3; ISSN 2283-9216 Mass Transfer Modelling of Sclerocarya Birrea Kernels in Supercritical Carbon Dioxide Trishen Reddy*, Tumisang Seodigeng, Musamba Banza, Hilary Rutto Department of Chemical and Metallurgical Engineering, Vaal University of Technology, Andries Potgieter Blvd, Vanderbijlpark, Gauteng, 1900, South Africa. tumisangs@vut.ac.za Experimental data was obtained from literature for the supercritical fluid extraction (SFE) process of Sclerocarya birrera kernel oil in supercritical carbon dioxide (CO2). The external mass transfer, diffusion, and axial dispersion coefficients were determined from the experimental values as well as the Sherwood, Reynolds, and Schmidt dimensionless consortiums. The Reynolds number ranged between 8 to 15, indicating that natural convection occurred. The Sherwood and Schmidt numbers were between 2 to 3.4 and 1.6 to 4. Although the solubility of marula oil decreased with an increase in temperature, its effective diffusivity and external mass transfer coefficient increased. However, the external mass transfer coefficient, diffusion coefficient and axial dispersion coefficient decreased with an increase in pressure due to a decrease in binary diffusivity. Even though the density of the solvent increases with pressure, which results in an increase in the diffusivity of the solute in supercritical CO2, the coefficients however decrease. The amount of extract is also amplified by the increase in solvent power. 1. Introduction Sclerocarya birrea is commonly referred to as Marula and is claimed to be the “tree of life” (Welford, Abad & Gericke, 2008). Despite these prerogatives, it is startling that no modelling has been conducted on extracting marula oil from SFE processes. Aside from the extraction process, modelling the process is crucial for design purposes (Louli et al., 2004; Wynn and Clarkson, 2018). The main goal of subjecting experimental data to mathematical modelling is to establish specifications for process design viz., equipment sizing, solvent flow rates, particle size, optimization, process control, troubleshooting and diagnostics. These specifications can provide insight on the practicality of SFE processes on a commercial scale (Melreles et al., 2009; Rasmuson et al., 2014). Honarvar et al. (2013) and Hassim et al. (2021) stress that mathematical modelling is essential for the costing of SFE processes from laboratory to pilot and industrial scale. In addition, applying models that enable experimental data correlation and extrapolation for potential industrial SFE process applications is crucial (Martín et al., 2011). According to Attard et al. (2018), SFE has been used recently to study the extracts of a large number of plant species. Even though a large variety of these plant species have already been used to supplement sustenance and create products with health benefits, many of these species have not yet been explored scientifically and may exhibit novel applications. Therefore, mathematical models must be developed to determine the most viable operating conditions to increase oil output, which can impact the agricultural sector largely. It is important to understand the three fundamental properties viz. the diffusion coefficient of the solute, the viscosity and the density of the supercritical fluid phase to develop mass transfer models (Lim et al., 1989). These properties frequently connect to the pertinent Sherwood, Reynolds and Schmidt dimensionless consortiums (Bernardo‐Gil and Casquilho, 2007). The equations are depicted below (refer to equations 1, 2 and 3). 25 𝑆𝑆ℎ = 𝑑𝑑𝑝𝑝𝑘𝑘𝑓𝑓 𝐷𝐷12 (1) 𝑆𝑆𝑆𝑆 = µ𝑓𝑓 𝑝𝑝𝑓𝑓𝐷𝐷12 (2) 𝑅𝑅𝑅𝑅 = 𝑑𝑑𝑝𝑝𝑝𝑝𝑓𝑓𝑢𝑢 µ𝑓𝑓 (3) Where Sh is the Sherwood number, Sc is the Schmidt number, Re is the Reynolds number, µf is the viscosity of the fluid in Pa.s, u superficial velocity of the supercritical fluid in m.s-1, dp is the particle diameter in m, ρf is the fluid density in kg.m-3, ρs is the solid density kg.m-3 and D12 is the diffusion coefficient in m2.s-1 Dwivedi and Upadhyay (1977) developed the generalized correlation for the Sherwood number and is given by equation 4 below, where C1 and C2 are constants, which can be determined by manipulating the experimental data. 𝑆𝑆ℎ = 𝐶𝐶1𝑅𝑅𝑅𝑅𝐶𝐶2𝑆𝑆𝑆𝑆 1 3� (4) The diffusion coefficient can be obtained using equation 5 below proposed by Wilke and Chang (1955) where KB is the Boltzman constant, T is temperature of the supercritical fluid in Kelvin and r is the molecular radius of the spherical solute. 𝐷𝐷12 = 𝐾𝐾𝐵𝐵𝑇𝑇 6𝜋𝜋𝜋𝜋µ (5) The axial dispersion coefficient can be calculated using the correlation proposed by Funazukuri et al. (1998) as depicted in equation 6 below where Dax is the dispersion coefficient in m2.s-1 and ε is the void fraction. 𝐷𝐷𝑎𝑎𝑎𝑎 = 1.317 (𝜀𝜀 𝑅𝑅𝑅𝑅 𝑆𝑆𝑆𝑆)1.392 �𝐷𝐷12 𝜀𝜀 � (6) 2. Methodology: Mass transfer modelling experimental design The external mass transfer coefficient (Kf), axial dispersion coefficient (Dax) and diffusion coefficient (D12) for marula kernel oil was determined on the solubility of marula oil in supercritical CO2 for the experimental conditions obtained from literature data conducted by Taseski (2015) on marula kernels conducted at 40 to 80 °C and 250 to 450 bar. The density and viscosity of supercritical CO2 were also required in order to compute the external mass transfer coefficient. Chemcad version 8.1.0 was utilised to determine the properties of supercritical CO2 utilising the Benedict-Webb-Rubin-Starling (BWRS) equation of state (EOS). The BWRS EOS is a modified version of the Beattie Bridgeman equation, which better captures the critical properties of pure hydrocrarbons in the gaseous or liquid phase (Benedict et al., 1940). A very straightforward unit operation was generated with an inlet feed of 100 kg.hour-1 comprising of pure CO2. The properties of supercritical CO2 were determined using a pipe with a length of 10 meters, an inside diameter of 0.9 meters, and a roughness factor of 4.572 ×10-5 that was installed under minimal pressure drop. 3. Assumptions made during the calculations The following assumptions were made to enable model calculations • The void fraction could not be calculated because the apparent (bulk) density of marula is unknown and unavailable in literature. It is therefore assumed that the particles are spherical in nature thus having a void fraction within the range of 0.35 to 0.45 (Rolland et al., 2019). • The molecular radius of olive oil was utilised to calculate the dispersion coefficient since the radius of marula (solute) could not be found in literature. Olive oil was utilised since the fatty acid structure of olive oil is similar to that of marula oil. • The void fraction does not change. • The Boltzman constant of 1.380649 x 10-23 m2kg.s-2.K-1 was utilised to calculate the axial dispersion coefficient. • The fluid velocity is uniform during the extraction process. 26 • The superficial velocity was calculated using the dimensions of the extractor that was utilised by Taseski (2015) in which the experimental work was conducted. The area of the extractor was therefore calculated using a diameter of 0.1 meters. • The Sherwood number was calculated using 0.38 and 0.83 for constants C1 and C2 since the Reynolds number was between 2 < Re < 40 and the Schmidt number was between 2 < Sc < 40 (Tan et al., 1988). • A constant CO2 flowrate of 30 kg.hour-1 was utilised for all experimental runs by Taseski (2015). Therefore, the very same flow rate was utilised to calculate the superficial velocity. • The average particle size of the marula kernels of 850µm was utilised as the particle diameter. • A single CO2 property estimate obtained from the simulation data from Chemcad was utilised at the corresponding temperature and pressure calculations, thus overlooking any fluctuations in these parameters. 4. Results and Discussion The Kf, Dax and D12 values for marula kernel oil was determined from the SFE experimental values, together with the Sherwood, Reynolds and Schmidt dimensionless consortiums presented in Table 1 below. Table 1: The correlated parameters obtained for the mass transfer model for marula kernel oil. Experiment Pressure (bar) Temperature (°C) Density (kg.m-3) Viscosity (Pa.s) Superficial velocity (m.s-1) D12 (10-8 m2.s-1) Sc Sh kf (m.s-1) Dax (m2.s-1) 1 250 40 880 0.00008660 0.00121 3.12 3.159 2.799 0.0187 0.00071 2 250 60 787 0.00006928 0.00135 4.15 2.127 2.267 0.0201 0.00074 3 250 75 712 0.00005896 0.00149 5.09 1.630 1.987 0.0216 0.00078 4 350 40 935 0.00010039 0.00114 2.69 3.993 3.129 0.0180 0.00069 5 350 60 863 0.00008338 0.00123 3.44 2.804 2.564 0.0189 0.0007 6 350 75 808 0.00007334 0.00131 4.09 2.217 2.255 0.0198 0.00071 7 450 40 975 0.00011223 0.00109 2.41 4.787 3.42 0.0176 0.00068 8 450 60 913 0.00009477 0.00116 3.03 3.425 2.816 0.0183 0.00068 9 450 75 867 0.00008448 0.00123 3.55 2.744 2.482 0.0189 0.00069 4.1. The effect of pressure on the mass transfer coefficient at constant temperature The mass transfer coefficients of marula kernel oil in supercritical CO2 were determined as a function of pressure at a constant temperature of 40, 60 and 75 ° C. It should be emphasized that the experiments were not carried out isothermally and that the values in figures 1a, b and c were extrapolated from the experimental results. Figure 1: The effect of pressure on a) Diffusion coefficient b) Axial Dispersion coefficient c) External mass transfer coefficient Figure 1a, b and c show that at higher pressures, the effect of pressure on the coefficients was less significant. Given that these parameters change more quickly at lower pressures, the sudden diffusivity shift at low pressures suggests that solvent density and viscosity are crucial parameters affecting the mass transfer coefficients (Liong et al., 1992). It can also be seen from figure 1b that the values of the axial dispersion coefficient at the highest pressure of 450 bar differed marginally at the various isotherms. In contrast, the diffusion and external mass transfer coefficients were at their lowest at 450 bar; however, they differed largely. Pressure (Bar) 200 250 300 350 400 450 500 D 12 ( m 2 s-1 ) 2,0e-8 2,5e-8 3,0e-8 3,5e-8 4,0e-8 4,5e-8 5,0e-8 5,5e-8 40 °C 60 °C 75 °C Pressure (bar) 200 250 300 350 400 450 500 D ax ( m 2 s-1 ) 0,00066 0,00068 0,00070 0,00072 0,00074 0,00076 0,00078 0,00080 40 °C 60 °C 75 °C Pressure (bar) 200 250 300 350 400 450 500 k f ( m s-1 ) 0,017 0,018 0,019 0,020 0,021 0,022 40 °C 60 °C 75 °C 27 The relationship between pressure and the coefficients are therefore inversely proportional. similar trends were observed by many studies correlating to the findings observed for marula oil. For example, Raspo et al. (2008) noticed the same trends in a study on the diffusion coefficients of solids in supercritical CO2. The external mass transfer coefficient was also noted to be lower at higher pressures on a study conducted by Lin et al. (2013) on the mass transfer coefficients and correlation of supercritical CO2 extraction of Sarawak black pepper. Honarvar et al. (2013) noted that the axial dispersion coefficient and mass transfer coefficient decreased with increased pressure. The authors explain that at higher pressures, there is a decrease in binary diffusivity. Leila et al. (2022) conducted experimental and mathematical modelling data of green process of essential oil extraction in supercritical CO2. The authors found the very same trends to that of marula oil in relation to the mass transfer coefficient. They explain why the mass transfer coefficient decreases with an increase in pressure by stating that the density increases with pressure, thus increasing the solute's diffusivity in the supercritical CO2. The coefficient Kf drops as a result, but the amount of extract is amplified by the increase in solvent power. This may suggest that while pressure itself has a negative impact on the coefficient Kf, the external mass transfer's resistance has a minimal impact on the total amount of mass transfer. 4.2. The effect of temperature on the mass transfer coefficient at constant pressure The mass transfer coefficients of marula kernel oil in supercritical CO2 were determined as a function of temperature at a constant pressure of 250, 350 and 450 bar. Notably, the experiments were not carried out isobarically and that the values in figures 2a, b and c were extrapolated from the experimental results. The effect of temperature on the coefficients will be discussed in conjunction with density and pressure. Figure 2: The effect of temperature on a) Diffusion coefficient b) Axial Dispersion coefficient c) External mass transfer coefficient According to Reddy et al. (2022), the solubility of marula oil decreases with an increasing temperature, however from figures 2a, b and c, one can observe that temperature had an opposing effect on the diffusion, axial and mass transfer coefficient which had increased when the temperature was elevated. The findings also show that as the pressure increased, the reliance of the diffusion coefficient on temperature reduced which is also indicated by the decrease in the slopes for the diffusion, dispersion, and mass transfer coefficients when the pressure was elevated. The rising temperature dependency of the fluid density as the pressure approaches the critical pressure may be related to the increased temperature dependence of the diffusion coefficient at lower pressures (Liong et al., 1992). Ahmed et al. (2012) conducted extraction and modelling of Algerian rosemary essential oil using supercritical CO2 and studied the extraction temperature and pressure effect on oil yield. The authors found that an increasing temperature increased the external mass transfer coefficient. The effects of temperature is therefore an important parameter affecting both the yield of marula oil as well as masss transfer (Reddy et al., 2023). Ahmed et al. (2012) go on to explain the importance of mass transfer on the yield of oil and state that the external mass transfer resistance controls the extraction dynamics during the early stages of the extraction process. However, Leila et al. (2022) argue that the resistance of the external mass transfer has an insignificant effect on the total mass transfer. The findings also agree with Rai et al. (2014) who found that mass transfer coefficient increased with temperature due to the greater diffusivity in supercritical CO2 at higher temperatures. Therefore, when the temperature rises, the rate of mass transfer of the solute to the bulk liquid phase also increases. ln (Temperature, Kelvin) 5,74 5,76 5,78 5,80 5,82 5,84 5,86 ln ( D 12 , m 2 s-1 ) -17,6 -17,4 -17,2 -17,0 -16,8 -16,6 250 bar 350 bar 450 bar ln (Temperature, Kelvin) 5,74 5,76 5,78 5,80 5,82 5,84 5,86 ln ( D ax , m 2 s-1 ) -7,32 -7,30 -7,28 -7,26 -7,24 -7,22 -7,20 -7,18 -7,16 -7,14 250 bar 350 bar 450 bar ln (Temperature, Kelvin) 5,74 5,76 5,78 5,80 5,82 5,84 5,86 ln ( k f , m s-1 ) -4,05 -4,00 -3,95 -3,90 -3,85 -3,80 250 bar 350 bar 450 bar 28 4.3. Dimensionless numbers The values for the dimensionless numbers for extracting marula kernel oil are presented in Table 2 below. The table also includes additional ratios and interaction calculations of the terms. Table 2: Values of dimensionless numbers for the extraction of marula kernel oil. Experiment Pressure (bar) Temperature (°C) Re Sc Sh εReSc εDaxD12-1 (Sh/Sc)1/3 1 250 40 10.419 3.159 2.799 14.813 56.122 0.295 2 250 60 13.024 2.127 2.267 12.462 44.123 0.355 3 250 75 15.305 1.630 1.987 11.223 38.135 0.406 4 350 40 8.988 3.993 3.129 16.149 63.289 0.261 5 350 60 10.822 2.804 2.564 13.654 50.101 0.305 6 350 75 12.303 2.217 2.255 12.276 43.209 0.339 7 450 40 8.0404 4.787 3.42 17.319 69.760 0.238 8 450 60 9.521 3.425 2.816 14.675 55.393 0.274 9 450 75 10.681 2.744 2.482 13.190 47.749 0.302 The Reynolds number ranged between 8 to 15. Grosso et al. (2010) state that natural convection occurs at low Reynolds numbers for high soluble solutes fed in extractors with an upward configuration. Puiggené, Larrayoz and Recasens (1997) state that a low Reynolds numbers fall between 10 and 100, and that the liquid side exhibits a strong resistance in relation to the mass transfer coefficient, which becomes smaller when the Velocity is elevated. del Valle et al. (2006) found that the Reynolds number was within the range of 4.74