Internal Mass Transfer Coefficient Research Articles

Mathematical modeling of bioactive extraction from cashew apple: Maxwell-Stefan approach to resolve effect of internal diffusivity and external mass transfer

Every year 2.2 giga-tons of cashew apples are produced and 80 % (unutilized fruit) of them are wasted and contain useful bioactives such as polyphenols and tannins (high molecular weight polyphenols). These bioactives can be separated using extraction: the nutraceutical value of which is of the order of 1 billion USD/year. However, extraction kinetics are normally fitted to simple phenomenological models. These models fail to establish the effect of shrinkage, temperature, thermodynamic parameters, and internal resistances on diffusion of solute. Hence, the objective of this study was to develop a Maxwell-Stefan model that can overcome the above shortcomings and optimize the extraction process of bioactives from cashew apples. The optimized parameters for the extraction process obtained were − solid:solvent ratio- 1:6, particle size (of solid) 125–250 μm, and the extraction temperature as 30 °C. The non-random two liquid (NRTL) activity coefficient model was first used to capture the thermodynamics of extraction effectively, followed by its utilization in the development of Maxwell-Stefan model to resolve the effect of internal diffusivity and external mass transfer coefficient. The model gave a good fit (R2 > 0.90) for all the parameters and could thus predict the extraction data greatly for all operating parameters including temperature, particle size, and solid:solvent ratio. This makes it eminently suitable for scale-up studies.

Mechanism modeling and application of Salvia miltiorrhiza percolation process

Percolation is a common extraction method of food processing industry. In this work, taking the percolation extraction of salvianolic acid B from Salvia miltiorrhiza (Salviae Miltiorrhizae Radix et Rhizoma) as an example, the percolation mechanism model was derived. The volume partition coefficient was calculated according to the impregnation. experiment. The bed layer voidage was measured by single-factor percolation experiment and the internal mass transfer coefficient was calculated by the parameters obtained by fitting the impregnation kinetic model. After screening, the Wilson and Geankoplis, and Koch and Brady formulas were used to calculate the external mass transfer coefficient and the axial diffusion coefficient, respectively. After substituting each parameter into the model, the process of percolation of Salvia miltiorrhiza was predicted, and the coefficient of determination R2 was all greater than 0.94. Sensitivity analysis was used to show that all the parameters studied had a significant impact on the prediction effect. Based on the model, the design space including the range of raw material properties and process parameters was established and successfully verified. At the same time, the model was applied to the quantitative extraction and endpoint prediction of the percolation process.

Intensification of autocatalytic methyl oleate synthesis in continuous flow rotating recycle reactor under hybrid radiation: Process optimization and Scale-up

Intensification of the autocatalytic esterification of methanol with oleic acid for producing methyl oleate (biodiesel) was accomplished using a continuous flow rotating reactor under recycle mode. To exaggerate the biodiesel yield, highly efficient hybrid electromagnetic radiation (near-infrared and microwave irradiation) was used as an energy source. Spherical-shaped nano-zinc-titanate photocatalyst (low band-gap energy: 2.01 eV and low recombination rate) was prepared and utilized in the aforementioned novel reactor. Box-Behnken statistical optimization technique was applied to attain the optimum condition (catalyst concentration 30 wt%, reaction temperature 333 K, methanol: oleic acid mole ratio 11:1, LHSV: 0.20 min−1) resulting in maximum biodiesel yield. Moreover, at optimum rotating speed (∼235 rpm), high external and internal mass transfer coefficients were achieved which rendered a remarkably augmented reaction rate under ideal reactor behavior (Dispersion number: 6.42 × 10−7). A geometric-based COMSOL model was simulated which confirmed uniformity of hybrid irradiation and temperature distribution within the rotating catalytic packed bed; which was applied for the development of a parallel-autocatalytic reaction kinetic model. Langmuir Hinshelwood kinetics of the parallel autocatalytic esterification is well represented in the experimental data (RSSQ=1.52×10-7). Without recycle stream, the reaction exhibited a non-autocatalytic reaction with a lower yield of 79.04 % biodiesel within 0.20 min−1 LHSV, whereas, under recycle mode, the biodiesel yield was increased up to 93.55 % even at a higher LHSV of 0.25 min−1. For larger-scale production of the methyl oleate, the ASPEN PLUS simulator has been deployed for a throughput scale-up factor of 1000 (geometric similarity), which corroborates well with lab-scale yield/reactor performance.

Enfoques analítico e híbrido neuro-diferencial para la descripción de la remoción de contaminantes de sistemas acuosos

In this study, both analytical and hybrid-neuro-differential formulations were developed for describing the contaminant removal from wastewater by adsorption. The sorption isotherm, expressed as a straight-line equation (single segment or piecewise function) or artificial neural network (ANN), was coupled to the balance equations describing the pollutant transfer in adsorbent and wastewater phases, and their contact interface. The resulting wastewater adsorption remediation model (WARM) is valid for both batch and continuous operations, does not consider a dominant internal or external resistance to mass transfer or instantaneously equilibrated adsorbent, and has an analytical solution when a straight-line isotherm is used. The applicability of current model was tested in the analysis of two experimental datasets from literature describing the removal of the anionic dye direct red 23 (DR23) by graphene oxide (GO) and 4-nitrophenol (4NP) on calcium alginate-multiwall carbon nanotube beads (CAMCNB), where internal and external mass transfer coefficients and sorption isotherm parameters were simultaneously estimated by nonlinear regression. The analytical and hybrid-neuro-differential formulations were further compared with a numerical one where the WARM was coupled to Langmuir isotherm. Besides, the model was also used to explore different scenarios for continuous operation with all tested isotherms. It was demonstrated that the proposed formulations based on straight-line and ANN isotherms achieved a good reproduction of both dynamic and equilibrium experimental data, with similar fitness indices to that obtained with other non-linear equilibrium models.

Performance analysis on open thermochemical sorption heat storage from a real mass transfer perspective

Internal mass transfer coefficient is considered as a key parameter for open thermochemical sorption heat storage which usually has a large margin between theoretical and actual value. This paper aims to analyze the role of mass transfer on system performance prediction. Al2O3 and LiCl composite sorbents are prepared and adsorption behavior is tested through a thermal gravimetric analyzer and a small-scale air duct experiment. An equation of kinetic coefficient is fitted to describe adsorption process more accurate than empirical equation. For simulation, a one-dimensional model is established based on dimensionless number of heat and mass transfer, and similarity theory is built to predict output parameters. Results indicate that the sorbent with 16.44 % salt content reaches 0.39 g·g−1 maximum water uptake on the condition of 20 °C, 80 % relative humidity. It is indicated that the system using composite sorbents has a heat storage density of 345.58 kWh·m−3. Parameters that influence system output power and duration are also investigated. By adjusting air flow rate and sorption length of sorption reactor, the system can achieve temperature rise of 30 °C at the exit and a steady output of 6 h. One striking fact is that mass transfer coefficient can be used to well predict the performance of real open adsorption thermal energy storage system which is also conducive to system design and optimization.

Multi-mode reduced order models for real time simulations of monolith reactors with micro-kinetics

We present a novel procedure for computing washcoat diffusional effects in monolith reactors with detailed micro-kinetic models. First, we show that the short time scales associated with the adsorption/desorption steps of micro-kinetic models requires using a significantly larger number of mesh points within the washcoat to obtain a solution that is independent of the mesh size. Next, we present a multi-mode reduced order model that eliminates the degrees of freedom associated with species diffusion in the washcoat using the local property dependent internal mass transfer coefficient matrix. This matrix is shown to be diagonal for most micro-kinetic models of practical interest and can be calculated accurately. We illustrate the new approach with an example of H2/CO/C3H6 oxidation over a Pt/Al2O3 catalyst with a 20 step micro-kinetic model. Even for this simple single site model, the small time (and length) scales associated with the species adsorption steps make the computation of the mesh size independent solution of the 1＋1D model time consuming. However, the reduced order model leads to an accurate solution while speeding-up calculations by about three orders of magnitude.

Design of Feedback Control Strategies in a Plant-Wide Wastewater Treatment Plant for Simultaneous Evaluation of Economics, Energy Usage, and Removal of Nutrients

Simultaneous removal of nitrogen and phosphorous is a recommended practice while treating wastewater. In the present study, control strategies based on proportional-integral (PI), model predictive control (MPC), and fuzzy logic are developed and implemented on a plant-wide wastewater treatment plant. Four combinations of control frameworks are developed in order to reduce the operational cost and improve the effluent quality. As a working platform, a Benchmark simulation model (BSM2-P) is used. A default control framework with PI controllers is used to control nitrate and dissolved oxygen (DO) by manipulating the internal recycle and oxygen mass transfer coefficient (KLa). Hierarchical control topology is proposed in which a lower-level control framework with PI controllers is implemented to DO in the sixth reactor by regulating the KLa of the fifth, sixth, and seventh reactors, and fuzzy and MPC are used at the supervisory level. This supervisory level considers the ammonia in the last aerobic reactor as a feedback signal to alter the DO set-points. PI-fuzzy showed improved effluent quality by 21.1%, total phosphorus removal rate by 33.3% with an increase of operational cost, and a slight increase in the production rates of greenhouse gases. In all the control design frameworks, a trade-off is observed between operational cost and effluent quality.

Low-dimensional models for real time simulations of monolith reactors with dual washcoat layers

We present a novel and accurate procedure with local property dependent internal and external mass transfer coefficient matrices for real time simulations of monolith reactors with dual washcoat layers. Our approach extends the prior work based on the Thiele matrix method for accurately describing the washcoat diffusional effects in single layered systems. It combines the vector form of the multi-scale averaged model with calculation of the local property dependent internal, external and cross-Sherwood number matrices for multi-component systems. We illustrate the usefulness of the reduced order model using the example of a dual-layered model system with first washcoat layer of selective catalytic reduction (SCR) catalyst and second washcoat layer of lean NOx trap (LNT) catalyst. We determine the mesh size independent solutions of the full 1+1D detailed model and compare the same with that obtained with the reduced order model. We show that the proposed method has the same accuracy as the mesh size independent detailed solution while speeding up calculations by about three orders of magnitude for the example studied, and possibly by several more orders of magnitude for real systems with complex and detailed micro-kinetic models to describe the storage and reactions in the catalytic layers.

The effects of copigments, sulfur dioxide and enzyme on the mass transfer process of malvidin-3-glucoside using a modelling approach in simulated red wine maceration scenarios

Maceration is fundamental to producing high quality red wine through the extraction of components from grape, including pigments of importance to wine colour. The effects of copigments and commonly used winemaking additives (maceration enzyme, SO2) on the extraction of malvidin-3-O-glucoside (M3G) were modelled under simulated maceration conditions. Copigments (gallic acid, rutin, caffeic acid) did not significantly facilitate the mass transfer process of M3G nor colour extraction, with caffeic acid having significantly lower values. Importantly, SO2 showed the most positive effects on both mass distribution constant and internal mass transfer coefficient of M3G, with temperature and ethanol having less of an impact. Significant interactions of the experimental factors were observed, however, and SO2, temperature, and ethanol were found to play predominant roles in the extraction phenomena. Comparatively, maceration enzyme or rutin (most impactful copigment) did not exhibit as much of an influence on the mass transfer process of M3G.

Mathematical Description of the Process of Adsorption of Metal Ions by Modified Zeolites in Adsorbers with a Fixed Adsorbent Layer

The solution of the problem of mathematical description of the processes occurring directly in the adsorber apparatus with a fixed layer of the solid phase and comparisons of the results with known classical representations is presented. The following characteristics were calculated: equivalent particle diameter of the sorbent, permissible fictitious velocity of wastewater, adsorber diameter, hydraulic resistance, Reynolds criterion, Prandtl test, Nusselt mass transfer criterion, external and internal mass transfer coefficients, mass transfer coefficients (including taking into account longitudinal mixing), general number of transfer units. The calculation was made taking into account that in the adsorber under consideration the fixed layers of adsopbent are located on cassettes, the distance between which is 0.01 m, which affects some characteristics of the adsorber apparatus with a fixed layer of a solid phase (modified zeolite).

Numerical analysis on the performance of an SCR monolith reactor

An SCR catalyst is used as an example to investigate the effects of the washcoat diffusion limitation on the performance of monolith reactors. One-dimensional model and three-dimensional CFD model with and without washcoat diffusion limitation were established. The washcoat diffusion was modeled by using an effective diffusivity in the washcoat region (CFD modeling) and the internal mass transfer coefficient between the interface and the interior of the washcoat (One-dimensional modeling). The results show that numerical models with washcoat diffusion limitation give more accurate NO concentration prediction than the numerical models without washcoat diffusion limitation. Using the ratios of internal mass transfer resistance and reaction resistance to estimate the washcoat diffusion limitation, the correlation between the temperature and the washcoat limitation is discussed. Detailed comparisons of the 1-D model and CFD model are conducted.

Reduced order models with local property dependent transfer coefficients for real time simulations of monolith reactors

We present a novel and accurate reduced order model with local property dependent internal and external mass transfer coefficients for real time simulations of monolith reactors. We compare the accuracy of the present approach with other reduced order models in the literature and with exact (numerical) solution of the detailed washcoat diffusion model. We illustrate the application of the reduced order models with three examples: a four reaction model of a three-way catalytic converter (TWC) to determine the steady-state as well as transient behavior in real time; a simplified TWC model with oxygen storage and release, and the case of three reversible reactions with linear kinetics. We show that the use of local property dependent transfer coefficients in terms of the Jacobian of the reaction rate vector leads to the best accuracy followed by its diagonal approximation, followed by the asymptotic (slow reaction) approximation for the internal Sherwood number. It is shown that the proposed method has sufficient accuracy for most practical applications, especially in the washcoat diffusion controlled regime, while speeding up the calculations by orders of magnitude compared to detailed washcoat diffusion models.

Comparative study of the batch adsorption kinetics and mass transfer in phenol-sand and phenol-clay adsorption systems

This study was aimed at evaluating the kinetics and mass transfer of phenol adsorption onto sand and clay sediments. The adsorption studies were carried out in batch mode. The results showed that the time taken to attain equilibrium in the adsorption of phenol onto sand and clay sediments are 21 and 27 h, respectively. At an equal given time, clay sediments relatively had higher adsorption of phenol than sand sediments, which can be ascribed to its large surface area and higher porosity. The kinetic data adjusted well to the pseudo-first-order and Elovich kinetic models; however, Elovich kinetic model best describe the phenol adsorption kinetics. Mass transfer models were applied to the adsorption data to evaluate the rate-limiting step in the adsorption of phenol onto the sand and clay sediments. The values of the external mass transfer coefficient and diffusion coefficient were estimated from the models. Biot number was determined using the estimated internal mass transfer (intraparticle diffusion) coefficient and the external mass transfer coefficient. From the applied models and the calculated Biot number, the results revealed that the mechanism of phenol adsorption onto sand and clay sediments was not only by intraparticle diffusion but also by film diffusion.

Kinetic study on CO2 adsorption behaviors of amine-modified co-firing fly ash

Abstract Coal and biomass fly ash was impregnated with tetraethylenepentamine (TEPA) to prepare solid CO2 sorbent. Experimental CO2 adsorption capacities of the sorbent in fixed-bed column were fitted to several kinetic equations. The modified Avrami fractional kinetic model could accurately predict the CO2 adsorption kinetic behaviors of the sorbent under different conditions. CO2 adsorption rate increases with the increase in temperature, initial CO2 concentration and gas flow rate, as a result of the decreased CO2 diffusion resistance. A mathematical model was proposed and demonstrated to well predict the CO2 adsorption breakthrough curves in the fixed-bed column. Effects of temperature, initial CO2 concentration and gas flow rate on the mass transfer kinetic behaviors of the desired sorbent were investigated. The positive effect of these factors on promoting the overall mass transfer coefficient and the internal mass transfer coefficient is not significant. The external mass transfer coefficient will be remarkably reinforced with the increase in these operating parameters, due to the change in viscosity and density of the gas phase and the reduced external mass transfer resistance. Internal mass transfer process is determined as the rate-limiting step for CO2 adsorption. The results will lay the groundwork for future scale-up application of the sorbent in post-combustion CO2 capture.

Study on supercritical fluid extraction of solanesol from industrial tobacco waste

Extraction of solanesol from industrial tobacco waste using supercritical CO2 was studied. The extraction yield was obtained at various pressures, temperatures, CO2 flow rates and mean particle diameters. The content of solanesol in extract was determined by HPLC analysis. The broken and intact cell model was successfully applied to both the tobacco extraction kinetics and solanesol extraction kinetics. The internal mass transfer coefficients were computed for both extracts and solanesol at various experimental conditions. The extraction rate of solanesol was found higher than that of tobacco extract, indicating that shorter extraction time resulted in higher selectivity of solanesol. Furthermore, a pretreatment with a solvent of n-hexane:95% ethanol at 4:6 volumetric ratio was tried at a selected experimental condition to improve the selectivity of solanesol. A final product with solanesol content of 0.44 was obtained. Consequently, this study provides a new route for generating solanesol from industrial tobacco waste.

Dibenzothiophene removal from model fuel using an acid treated activated carbon

ABSTRACTSulfur containing compounds are one of the most concerning pollutants in fossil fuels. The increasing rate of fuel consumption around the globe reveals the necessity of further purification of the fuels. In this study, application of adsorption process in removing dibenzothiophene from a model fuel is investigated. A granular activated carbon is treated with aqueous solution of nitric acid and implemented as the sorbent. Treatment of the activated carbon with nitric acid resulted in increasing the adsorption capacity of the activated carbon. Freundlich and TÓth isotherms are capable of sufficiently describing the equilibrium data. Investigation of the kinetics of the process is carried out using the homogeneous surface diffusion model. Internal and external mass transfer coefficients are 9.3917 × 10-6 m2/min and 1.4153 × 10-2 m/min for the virgin activated carbon (VAC) and 4.8738 × 10-6 m2/min and 5.2529 × 10-2 m/min for acid treated activated carbon (AAC), respectively.

La-, Mn- and Fe-Doped Zirconia Washcoats Deposited on Monolithic Reactors via Sol-Gel Method: Characterization and Evaluation of their Mass Transfer Phenomena and Kinetics in Trichloroethylene Combustion

Abstract La-, Mn- and Fe-doped ZrO2 was synthesized using the sol-gel method, washcoated on cordierite monoliths and used in trichloroethylene (TCE) combustion. A sol from sol-gel synthesis method was used to obtain the zirconia washcoatings. The washcoatings deposited on the cordierite monolith materials were characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), Fourier transform infrared (FT-IR) spectroscopy and N2 physisorption measurements, being the crystalline phase determination the most correlate with the catalytic activity. The washcoat properties were correlated to their performance in trichloroethylene combustion. The catalytic washcoatings contained a mixture of crystalline tetragonal ZrO2 and monoclinic ZrO2, and the monoclinic phase exhibited strong interactions with the α-cordierite crystalline phase. For the kinetic tests, the mass transfer into the washcoated monolith channels was evaluated using a recently developed model for the internal mass transfer coefficients for diffusion and reactions in catalytic monoliths. This model involves three resistances. In a plot of the overall resistance as function of the Thiele modulus was determinate that he reaction occurred in the kinetically controlled regime. The kinetic data were fit to two Langmuir–Hinshelwood (LH) models, and the reaction rate was fitted as a function of the trichloroethylene inlet concentration. The adsorption parameters obtained with both LH models were validated based on thermodynamic criteria for the changes in the standard enthalpy of adsorption(${\Delta}H_{ads}^0$) and standard total entropy of adsorption (${\Delta}S_{ads}^0$). It was found that adsorbed TCE and oxygen atoms should be more mobile over the catalyst, which had a higher proportion of tetragonal phase than monoclinic phase of zirconia. The La, Fe-doped catalyst exhibited the highest activity, mainly due the presence of tetragonal zirconia.

Thermal Modeling of Indirect Solar Drying System: An Experimental Validation

The expressions for crop and moist air temperatures, drying rate and efficiency of indirect solar drying with phase change material (PCM) storage systems in quasi-steady state conditions have been derived. The analysis is based on the basic energy balance for the system. A computer model has been developed to predict the performance of the solar dry-ers. Experimental validation of the thermal model has been carried out by using modified heat transfer coefficients. Internal heat and mass transfer coefficients have been evaluated with PCM for March 24, 2014 in Varanasi, India. A fair agreement has been observed between theoretical and experimental results by using the modified internal heat and mass transfer coefficients.

Thermal Modeling of Indirect Solar Drying System: An Experimental Validation

ABSTRACTThe expressions for crop and moist air temperatures, drying rate and efficiency of indirect solar drying with phase change material (PCM) storage systems in quasi-steady state conditions have been derived. The analysis is based on the basic energy balance for the system. A computer model has been developed to predict the performance of the solar dryers. Experimental validation of the thermal model has been carried out by using modified heat transfer coefficients. Internal heat and mass transfer coefficients have been evaluated with PCM for March 24, 2014 in Varanasi, India. A fair agreement has been observed between theoretical and experimental results by using the modified internal heat and mass transfer coefficients.

Two-structured solid particle model for predicting and analyzing supercritical extraction performance

Solid extraction process, using the supercritical fluid, is a modern science and technology, which has come in vogue regarding its considerable advantages. In the present article, a new and comprehensive model is presented for predicting the performance and separation yield of the supercritical extraction process. The base of process modeling is partial differential mass balances. In the proposed model, the solid particles are considered twofold: (a) particles with intact structure, (b) particles with destructed structure. A distinct mass transfer coefficient has been used for extraction of each part of solid particles to express different extraction regimes and to evaluate the process accurately (internal mass transfer coefficient was used for the intact-structure particles and external mass transfer coefficient was employed for the destructed-structure particles). In order to evaluate and validate the proposed model, the obtained results from simulations were compared with two series of available experimental data for extraction of chamomile extract with supercritical carbon dioxide, which had an excellent agreement. This is indicative of high potentiality of the model in predicting the extraction process, precisely. In the following, the effect of major parameters on supercritical extraction process, like pressure, temperature, supercritical fluid flow rate, and the size of solid particles was evaluated. The model can be used as a superb starting point for scientific and experimental applications.