External Mass Transfer Resistance Research Articles

Mass Transfer Resistance and Reaction Rate Kinetics for Carbohydrate Digestion with Cell Wall Degradation by Cellulase.

This paper introduces an enzymatic approach to estimate internal mass-transfer resistances during food digestion studies. Cellulase has been used to degrade starch cell walls (where cellulose is a significant component) and reduce the internal mass-transfer resistance, so that the starch granules are released and hydrolysed by amylase, increasing the starch hydrolysis rates, as a technique for measuring the internal mass-transfer resistance of cell walls. The estimated internal mass-transfer resistances for granular starch hydrolysis in a beaker and stirrer system for simulating the food digestion range from 2.2 × 107 m-1 s at a stirrer speed of 100 rpm to 6.6 × 107 m-1 s at 200 rpm. The reaction rate constants for cellulase-treated starch are about three to eight times as great as those for starch powder. The beaker and stirrer system provides an in vitro model to quantitatively understand external mass-transfer resistance and compare mass-transfer and reaction rate kinetics in starch hydrolysis during food digestion. Particle size analysis indicates that starch cell wall degradation reduces starch granule adhesion (compared with soaked starch samples), though the primary particle sizes are similar, and increases the interfacial surface area, reducing internal mass-transfer resistance and overall mass-transfer resistance. Dimensional analysis (such as the Damköhler numbers, Da, 0.3-0.5) from this in vitro system shows that mass-transfer rates are greater than reaction rates. At the same time, SEM (scanning electron microscopy) images of starch particles indicate significant morphology changes due to the cell wall degradation.

Selective recovery of esterase from Trichoderma harzianum through adsorption: Insights on enzymatic catalysis, adsorption isotherms and kinetics

In recent years, numerous attempts have been made to develop a low-cost adsorbent for selectively recovering industrially important products from fermentation broth or complex mixtures. The current study is a novel attempt to selectively adsorb esterase from Trichoderma harzianum using cheap adsorbents like bentonite (BT), activated charcoal (AC), silicon dioxide (SiO2), and titanium dioxide (TiO2). AC had the highest esterase adsorption of 97.58% due to its larger surface area of 594.45 m3/g. SiO2 was found to have the highest selectivity over esterase, with an estimated purification fold of 7.2. Interestingly, the purification fold of 5.5 was found in the BT-extracted fermentation broth. The functional (FT-IR) and morphological analysis (SEM-EDX) were used to characterize the adsorption of esterase. Esterase adsorption on AC, SiO2, and TiO2 was well fitted by Freundlich isotherm, demonstrating multilayer adsorption of esterase. A pseudo-second-order kinetic model was developed for esterase adsorption in various adsorbents. Thermodynamic analysis revealed that adsorption is an endothermic process. AC has the lowest Gibbs free energy of −10.96 kJ/mol, which supports the spontaneous maximum adsorption of both esterase and protein. In the desorption study, the maximum recovery of esterase from TiO2 using sodium chloride was 41.34 %. Unlike other adsorbents, the AC-adsorbed esterase maintained its catalytic activity and stability, implying that it could be used as an immobilization system for commercial applications. According to the kinetic analysis, the overall rate of the reaction was controlled by reaction kinetics rather than external mass transfer resistance, as indicated by the Damkohler number.

Kinetics of cashew apple drying through mechanistic models and analysis of the effects of drying conditions on the retention of bioactive compounds

AbstractGlobal cashew nut production is nearly 4 million tons per year, valued at 7 billion US dollars. Remarkably, almost the entire cashew apple crop, amounting to 20 million tons annually, goes to waste. However, the cashew apple contains valuable nutraceutical compounds, including tannins, polyphenols, and carotenoids, estimated to be worth 150 million US dollars annually. Due to the highly perishable nature of cashew apples, degradation is a significant issue. In response, the current work has established drying as an effective preservation technique for these bioactive components. The effect of drying temperature on bioactive compounds has been thoroughly investigated. The non‐random two liquid (NRTL) activity coefficient model effectively captures the thermodynamics of the drying process. To facilitate the selection and design of drying equipment, two mechanistic mass transfer models were developed. The first model employs the Maxwell‐Stefan framework to account for internal diffusion, with external mass transfer resistance appearing as a boundary condition. While this model works well for products like grapes, it proved inadequate for explaining the drying behaviour of cashew apples. Consequently, a second model was developed, postulating rapid moisture transport by capillary action within the cashew apple. This model effectively captures the effects of a wide range of operating conditions, using only external mass transfer resistance as the tuneable kinetic parameter. This mechanistic model is more suitable for dryer design compared to conventional phenomenological models like the logarithmic model and the two‐term exponential model.

Kinetics studies on the ascorbic acid extraction from roselle (Hibiscus sabdariffa) calyces

The effect of processing conditions of roselle (Hibiscus sabdariffa) calyces on the vitamin C content of the extracts was studied to develop models that best describe the process. The extraction parameters are the processing time (5, 10, 15 mins), process temperature (30oC, 50℃, 75℃ and 100℃), and calyx-water mass ratio (1:50, 1:20 and 1:10). These samples were tested for ascorbic acid using the spectrophotometric method. Statistical analysis was conducted on the experimental results and regression models were developed. A total of six mathematical models were selected for the description of vitamin C extraction from the calyces. The results showed that time, temperature and calyx-water mass ratio have a linear significant effect (p ≤ 0.01); while time-temperature and temperature-ratio had a significant (p ≤ 0.05) interaction effect; time and temperature had a significant (p ≤ 0.05) quadratic effect on the vitamin C content of the extract. Pseudo-first-order gave the highest overall coefficient of determination R2 and lowest overall root mean square error (RMSE). The activation energy of vitamin C ranged from 3 to 8.4 kJ; the effective diffusion coefficient ranged from 1.5×10-9 to 5.0×10-7 m 2 s -1 ; while mass diffusivity ranged from 3.11×10-5 to 8.6×10-4 ms-1 . The Biot number calculated ranged between 33.93 and 541.94 which showed that there is an insignificant external mass transfer resistance.

Comprehensive analysis of water vapor sorption kinetics and mechanisms using biosorbent pellets from canola meal and oat hull

Agricultural residues, specifically canola meal (CM) and oat hull (OH), have been innovatively utilized to develop biosorbents for sorbing water vapor from the air. These biomaterials are comprised of hydrophilic functional groups that effectively perform air dehydration. Air, being non-polar, was used as a model gas in this study to simulate gas dehydration. In the current research, these materials were formed into pellets to produce high-quality biosorbents with controlled size, shape, and enhanced moisture uptake capacity. CM (309.48 mg/g) and OH (233.07 mg/g) pellets had higher or comparable water sorption capacities than commercialized adsorbents used for drying gases. The mixed-order kinetic model described the sorption process well and identified both mass transfer and sorption on active site steps (R 2 > 0.991 and χ 2 < 16.0). Regarding the OH pellet, sorption on active sites was the predominant kinetic mechanism at the beginning, followed by intraparticle diffusion until equilibrium. However, sorption on CM pellets was delayed at 4.2 min at the initial stage, owing to the external mass transfer resistance; then, intraparticle diffusion controlled the process until equilibrium. Adding sodium lignosulfonate (LSNa) lowered the initial sorption rate but enhanced the water uptake and strength of pellets. The addition of LSNa resulted in a 25% and 14% increase in the water uptake capacity of oat hull and canola meal pellets, respectively; conversely, it also caused an increase in the delay time for sorption on CM pellets at the beginning of the process, extending it to 9.50 min.

A Kinetic Non-Steady-State Analysis of Immobilized Enzyme Systems Without External Mass Transfer Resistance

In this paper, a non-steady-state non-linear reaction diffusion in immobilized enzyme on the nonporous medium is considered for its mathematical analysis. The non-linear terms in this model are related to the Michaelis-Menten kinetics. For the considered model, the approximate analytical expressions of the substrate concentration and the effectiveness factor for the various geometric profiles of immobilized enzyme pellets are obtained using homotopy perturbation method (HPM). The obtained approximate analytical expressions proved to be fit for all values of parameters. Numerical solutions are also provided using the MATLAB software. When comparing the analytical and the numerical solutions, satisfactory results are noted. The effects of Thiele modulus and Michaelis-Menten kinetic constants on the effectiveness factor are also analyzed.

A kinetic non-steady state analysis of immobilized enzyme systems with external mass transfer resistance

&lt;abstract&gt;&lt;p&gt;The goal of this paper is to utilize the homotopy perturbation method (HPM) and Laplace transform to provide an approximate analytical expression to the non-linear time-dependent reaction diffusion equation arising in a mathematical model of an immobilized enzyme system with external mass transfer resistance. This mathematical model is a non-steady, non-linear reaction diffusion equation based on Michaelis–Menten kinetics. Approximate analytical expressions are also provided for various geometries of the enzyme catalytic pellets, namely, planar, cylindrical, and spherical. Obtained semi-analytical expressions are proven to fit for all the parameters appearing in the system and for all the geometries of enzyme catalytic pellets. When comparing the numerical and approximate analytical solutions, satisfactory results are obtained. Also, approximate analytical expressions of the effectiveness factor (EF) of the immobilized system are presented, and the effect of parameters on the EF is also analyzed.&lt;/p&gt;&lt;/abstract&gt;

Mass transfer studies on the solvent-free lipase-catalyzed partial hydrolysis of palm oil in packed-bed reactor

Packed-bed reactor (PBR) is widely employed for enzyme-mediated reactions at an industrial scale because the reactor configuration enables reusability of the biocatalyst with ease, thereby reducing the overall operating expenses. However, mass transfer limitation remains a key challenge in fixed-bed column systems, especially at large scale. Therefore, the present study investigated the external mass transfer effects on solvent-free lipase-catalyzed partial hydrolysis reaction and aimed to develop a mass transfer model for the operation. The influence of volumetric flow rate, one of the crucial operating parameters affecting the external mass transfer resistance, was examined. Results demonstrated increasing the flow rate led to an increase in hydrolysis reaction with the highest reaction rate observed at 5 ml min-1 . A dimensionless mathematical mass transfer model of Colburn factor, JD = K(Re)n-1 which is a function of Reynolds and Schmidt numbers, was then proposed to simulate the enzymatic partial hydrolysis reaction of palm oil in PBR. The mass transfer model was analyzed with different n values and results revealed that the mass transfer correlation of JD=0.92(Re)-0.2 was able to predict the experimental data accurately. The model developed could describe the dominance of mass transfer effects besides providing useful information for the scale-up design of industrial reactor.

Fixed-bed column adsorption modeling using Zr biocomposites for fluoride removal

ABSTRACT This research involved conducting continuous adsorption experiments to assess fluoride elimination from drinking water achieved by utilizing biocomposites created from the peels of oranges and apples, which were impregnated with zirconium (Zr), to form BOP-Zr and BAP-Zr, respectively. The findings from the experimental data indicate that BOP-Zr and BAP-Zr are effective biosorbents with a solid ability to remove fluoride selectively. Additionally, these biosorbents were found to be stable, as they do not release Zr into the treated water. Notably, these environmentally friendly biosorbents are derived from renewable sources and enhance the value of waste materials. The study employed various empirical models, including Bohart-Adamas, Thomas, Yoon-Nelson, BDST, Clark, Yan, and Woolborska, to elucidate the mechanisms and crucial parameters involved in fluoride adsorption within packed bed columns. The Yan model demonstrated the highest correlation among these models, indicating a chemical adsorption process with kinetics following a pseudo-second-order pattern. BOP-Zr and BAP-Zr exhibited a maximum adsorption capacity of 59.3 and 47.5 mg/g, respectively, under a flow rate of 4 mL/min and an inlet fluoride concentration of 25 mg/L. The analysis of mass transfer coefficients revealed that the primary step governing the adsorption procedure was diffusion through pores. Consequently, the study conclusively establishes that BOP-Zr and BAP-Zr biocomposites, originating from lignocellulosic biomass remains, present a practical and competitive choice for eliminating fluoride from water. These materials surpass waste materials in performance and rival more expensive options in efficiency and performance.

Simulating the Moisture Diffusion and Evaporation of Sawdust during Convective Drying using the Spatial Reaction Engineering Approach

AbstractThe spatial reaction engineering approach (S‐REA) was used to simulate hot air drying of sawdust. The studies extended the previous work reported in literature where the sawdusts were dried using hot air at 70 °C, 80 °C, and 90 °C. The simulated results were found to agree well with the experimental moisture content (R2 &gt; 0.98) and temperature (R2 &gt; 0.82) profiles. In a further analysis using S‐REA, the spatial profiles of moisture content and vapor concentration were generated to understand better the physics behind. Simulation also revealed that the external mass transfer resistance was more dominant as compared to the internal diffusion resistance. The vapor concentrations were observed peaked at time range of about 10 800– 18 000 s and dropped thereafter upon further heating. This observation could be supported by the variation in the vapor effective diffusivities where peak diffusivity values typically occur after most of the moisture evaporates towards the end of drying.

Kinetic analysis of an ionic liquid-based metal extraction process using a single droplet extraction column

In this study a liquid-liquid extraction (LLX) process has been investigated based on experimental analysis and kinetic modelling. The purpose of this investigation is (1) to understand the mass transfer behaviour, (2) to determine the rate limiting step via evaluating different mass transfer models, and (3) to estimate the mass transfer and kinetic parameters. This has been discussed in the context of the extraction of Co by the ionic liquid (IL) [P8888][Oleate] as an example of LLX with chemical reaction. Mass transfer models, with and without a chemical reaction, are evaluated based on a statistical cross-validation method. The following operational parameters are included in the analysis: column lengths, droplet diameter, droplet rising velocity and continuous and dispersed phase concentrations on Co uptake. This method reveals that a single parameter representing the external mass transfer resistance can describe the forward extraction of Co (i.e., into the IL) for the whole data set sufficiently accurate (error ±30%) regardless of the studied operational conditions. Back-extraction of Co from pre-loaded IL droplets shows a different transfer mechanism. Now the mass transfer in the dispersed IL phase dominates the process which is attributed to a change of the physical properties of the pre-loaded IL.

Influence of ultrasound-pretreated convective drying of Roselle (Hibiscus sabdariffa L) leaves on its drying kinetics and nutritional quality

The drying kinetics and the nutritional qualities of Roselle (Hibiscus sabdariffa L) leaves as affected by ultrasound pretreatment during hot air drying were investigated in this work. Ultrasound frequency and power at 20 kHz and 600 W, respectively, were used for the experiment. Roselle leaves were subjected to ultrasound pretreatment in distilled water for 0 min (untreated), 5 min (UD5), 10 min (UD10) and 15 min (UD15) before hot air drying. The result showed that UD15 samples had about 47% reduction in drying time compared with the untreated samples. The effective moisture diffusivity of the treated and untreated samples ranged from 1.21 to 3.29 × 10−1m2/s. The Page and Logarithmic models best described the drying behavior for the untreated and treated samples respectively. The values of the mass transfer Biot number (ratio of internal mass transfer resistance to external mass transfer resistance) for all the samples ranged from 0.9032 to 1.2391. The samples of UD10 and UD5 had the highest amount of carotenoid and vitamin C contents, respectively, amongst the untreated and treated samples. The total color change of the treated samples were significantly lower than the untreated samples after drying. Drying of Roselle leaves is usually done using convective drying method with its attendant's effects such as long drying time, loss of nutrients and high energy usage. But this work showed that application of ultrasound pretreatment during drying of Roselle leaves can significantly reduce the drying time and at the same time retain the nutritional quality of the dried treated samples.

Post-processing of a lavender flowers solvent extract using supercritical CO2 fractionation

BackgroundSupercritical Fluid Extraction (SFE) was performed using an unconventional material, the solid extract of lavender flowers obtained by liquid solvent extraction and subsequent solvent elimination. MethodsSystematic extraction experiments were carried out at 8 MPa and 40 °C, and the extract was fractionated in semi-continuous mode in the SFE plant. To understand mass transfer phenomena driving the process, CO2 mass flow rates ranging between 0.60 and 1.50 kg/h were used, and yield vs. time curves were obtained. Significant findingsFractionation produced a cuticular waxes selective precipitation in the first separator and the floral fragrance in the second separator. The most abundant species in the extract were τ-cadinol (13%), lavandulol (10.5%), β-caryophyllene (10%), viridiflorene (8.5%), isocaryophyllene (6%), cedrenalol (4.5%), linalool (4%) and 1,8-cineol (4%). The fragrance contained no waxes, indicating that the fractionation was successful. At higher mass flow rates (from 0.90 to 1.50 kg/h), an asymptotic extraction yield of 5.2% w/w was obtained; whereas, at lower mass flow rates, the extraction yield was lower (2.3% w/w) since the vegetable bed was not completely wetted by the extraction fluid. The overall results indicated that an external mass transfer resistance controlled the process.

Assessment of biodegradation kinetics and mass transfer aspects in attached growth bioreactor for effective treatment of brilliant green dye from wastewater

In this study, Bacillus licheniformis immobilized with low-density polyethylene (LDPE) was employed to degrade Brilliant Green (BG) dye from wastewater in a packed bed bioreactor (PBBR). Bacterial growth and extracellular polymeric substance (EPS) secretion were also assessed under different concentrations of BG dye. The impacts of external mass transfer resistance on BG biodegradation were also evaluated at different flow rates (0.3–1.2 L/h). A new mass transfer correlation JD=5.71NRe-0.3 was proposed to study the mass transfer aspects in attached-growth bioreactor. The intermediates, namely 3- dimethylamino phenol, benzoic acid, 1–4 benzenediol, and acetaldehyde were identified during the biodegradation of BG and, subsequently degradation pathway was proposed. Han - Levenspiel kinetics parameters μmax and Ks were found to be 0.185 per day and 115 mg/L, respectively. The new insight into mass transfer and kinetics support the design of efficiently attached growth bioreactor to treat a wide range of pollutants.

Modeling and simulation of trickle bed reactors for the purification of 1-butene

Abstract In this contribution, a mathematical model of an industrial trickle-bed reactor employed in the purification of a C4 cut by selective hydrogenation of acetylenic or dienes compounds to obtain high purity 1-butene is presented. A reaction network of ten reactions is included in the model, with kinetics expressions and parameter estimation obtained from previous experimental studies on a commercial catalyst. Internal mass transfer resistances in the catalyst particles are significant; therefore the reaction-diffusion equations must be solved. External mass transfer resistances in the liquid phase were retained, while those in the vapor phase were negligible. The model was employed to analyze the reactor behavior by varying the inlet molar flow rate of hydrogen, the operating pressure, inlet temperature and the level of activity of the catalyst, taking into account its deactivation. It was demonstrated that the mass transfer resistances, inside and outside the catalyst particles, have a significant impact on the selectivity, but a careful operation of the reactor can improve the selectivity and extent the catalyst life. On the other hand, an alternative system was proposed, with two beds and a distributed input of H2, which led to a significant improvement in the selectivity.

Experimental study and kinetic modeling of methanol conversion to propylene with co-feeding of C4 and C5/C6 hydrocarbon cuts over a ZSM-5 catalyst.

Extensive experimental data were used to develop a comprehensive kinetic model for the methanol to propylene (MTP) process over a ZSM-5 catalyst. Preliminary experiments were performed to determine the reaction conditions that would ensure the absence of external (film) and internal mass transfer resistances. The kinetic experiments were subsequently carried out at 420-500 °C under conditions where mass transfer limitations were absent. A detailed reaction network was proposed for the MTP process based on the experimental product distribution and various reported kinetic models in the literature. According to the first series of experiments (without C4 and C5/C6 recycle streams) conducted at various temperatures, the best yield for propylene production was achieved at 480 °C with a water to methanol ratio of 0.7. Subsequently, kinetic experiments were performed at 480 °C and a water to methanol ratio of 0.7 using feeds with different amounts of C4 and C5/C6 hydrocarbons as recycle streams. Species material balances for the integral tubular reactor along with power-law rate functions and the Arrhenius equation for rate constants were employed in an optimization algorithm to obtain the kinetic parameters. The predictive ability of the model was checked against experimental data, and the kinetic parameters were validated by additional experiments.

Optimization of the solution of mass- and heat transfer models in capillary-porous media

Extraction efficiency is determined by mass and heat transfer processes in the liquid-solid system. In order to determine the optimal conditions for the extracting process, it is necessary to make up a mathematical model which reliably describes mass and heat exchange processes. In our study there are equations of mass and heat transfer, which occur during extracting process. They allow to determine numerically the process parameters and describe the resistance shares of external mass transfer much easier than in other methods of calculation. Further development of the outlined ideas leads to a new content of the concepts of kinetic coefficients of mass and heat transfer. To prove the accuracy of the calculation method, the share of external mass transfer resistance was calculated when extracting soybean oil with extraction gasoline and dichloroethane. The described calculation method for extracting process features may be used for designing extraction equipment, technology development and technological characterizing of process. Taking into account the identified system features, it is possible to reduce the solution to a particular form and mathematically describe a specific mass and heat exchange process. This makes it possible to determine the optimal conditions and increase the efficiency of the extracting process.

Catalytic hydrogenolysis over Cu-based oxide derived from hydrotalcite-like structured materials: Reaction condition optimization and artificial neural network modelling

In this study, the catalytic activity of Cu-derived oxide catalysts in glycerol hydrogenolysis was investigated and the effect on the selectivity of 1,2-propanediol (1,2-PDO) with the different Cu/Al molar ratios was observed. The glycerol conversion/1,2-PDO selectivity was found to be dependent on the metallic sites and surface acidity of the Cu-based catalyst. The surface acidity and metallic sites of Cu nanoparticles were significantly improved with the increase of Cu/Al mole fraction in the catalyst. The efficiency of the Cu-derived oxide catalyst was attributed to the well-dispersed Cu and the presence of acidic sites. As expected, the Cu-based oxide catalyst (3CuAl) showed remarkable catalytic performance for 1,2-PDO synthesis with the highest turnover frequency (TOF) from the hydrogenolysis reaction. It is observed that the Cu-derived oxide catalyst is stable and efficient under strident reaction conditions in the presence of water and high temperature (aqueous glycerol solution (20 wt%), 210 °C, 40 bar). Moreover, the reaction conditions for glycerol hydrogenolysis in the presence of active 3CuAl were optimized to maximize the selectivity of 1,2-PDO with TOF. In addition, overcoming the limitation due to the external mass transfer resistance was investigated. The rate of glycerol consumption was subjected to kinetic analysis, which revealed a zero-order relationship on glycerol concentration, indicating that adsorbed glycerol was the most tightly bonded organic adsorbate. Further, the experimental reaction data was validated through the developed artificial neural network (ANN) model.

Reaction and Kinetic Studies of Immobilized Enzyme Systems: Part-I Without External Mass Transfer Resistance

Reaction and Kinetic Studies of Immobilized Enzyme Systems: Part-I Without External Mass Transfer Resistance

Kinetics, mass transfer, and thermodynamics of Ethyl Hexanoate synthesis using heterogeneous catalyst

The present work delineates insight into the heterogeneous esterification of hexanoic acid to Ethyl Hexanoate. Efficacy was tested using Indion-225H and Amberlyst-15 as a catalyst. The effect of various process parameters such as mole ratio, temperature, catalyst loading, and speed of agitation was investigated for maximum ester conversion. A maximum yield of 81.31% was obtained in 4 h of reaction time at optimized values of 70 °C, 1:3, Hexanoic acid: Ethanol mole ratio, 12% catalyst loading, and 10% molecular sieves at an agitation speed of 300 rpm. The possibility of internal and external mass transfer resistance was evaluated. Effective diffusivity De-A was calculated as 3.58 × 10–11 m2/s. The energy of activation was calculated as 40.39 kJ mol-1. Kinetic and adsorption equilibrium constants were investigated for the LHHW model. Thermodynamic parameters such as enthalpy of activation, Gibbs free energy, and entropy of activation were predicted. Functional groups were confirmed using infrared spectroscopy.