Solution Of Mass Transfer Equations Research Articles

Numerical simulation of ozonation in hollow-fiber membranes for wastewater treatment

In this study, we developed a comprehensive modeling framework for simulation of ozonation process using combination of artificial intelligence and computational fluid dynamics (CFD). The process is carried out in a hollow-fiber membrane contactor in which the concentration data of ozone was obtained by solution of mass transfer equations, and then the results were used for artificial intelligence modeling. We used three different machine learning models to predict concentration of ozone (C) in a system based on its coordinates, i.e., r and z. The models were optimized using the Bat Algorithm (BA) and were trained on a dataset consisting of over 10,000 data points. The three models developed were Support Vector Regression (SVR), Decision Tree Regressor, and Orthogonal Matching Pursuit (OMP). These models were evaluated using three common metrics — Mean Squared Error (MSE), R-squared (R2), and Mean Absolute Error (MAE). Our results indicated that the SVR model overperformed the other two models in terms of all evaluation metrics. Specifically, the SVR model achieved an MSE of 0.003, an R2 of 0.998, and an MAE of 0.046. The Decision Tree Regressor and OMP models achieved less favorable results with MSEs of 0.007 and 0.221, R2 scores of 0.996 and 0.878, and MAEs of 0.056 and 0.359, respectively.

Numerical solution of the parabolic multicomponent convection–diffusion mass transfer equations by a splitting method

ABSTRACTThe splitting method used in a previous study for the numerical solution of mass transfer equations in ternary systems is generalized to mixtures with n-components. The diffusion coefficients are considered constant. Theoretical results about the stability of the method are presented, as well as numerical simulations for mixtures with n = 4, 5, and 6. The numerical experiments confirmed the theoretical results and show good numerical performances. Moreover, multicomponent diffusion effects without an imposed concentration gradient are investigated for mixtures with n = 4, 5, and 6 components.

Analysis of mass transfer equations during solid-liquid extraction and its application for vanilla extraction kinetics modeling

Rigorous dimensionless analysis and analytical solution of mass transfer equation (punctual and space averaged) governing the solid-liquid extraction dynamic were performed. Analytical solutions result in continuous and analytical maps between solute mass fractions in extract with respect to time which were used both for solute diffusivity estimation and process modeling. In order to validate the models, experimental extraction at equilibrium of 1 cm long vanilla beans pieces were obtained at 0.1, 0.2, 0.3 and 0.4 g vanilla/mL solvent (60% w/w ethanol-water) and 30, 40 and 50 °C; and extraction kinetics were developed at 0.1 g/mL and 30, 40 and 50 °C. Apparent equilibrium constant and solute effective diffusivity estimation were performed by linear regression on experimental results. Apparent equilibrium constant was 0.86, and diffusivities were 1.22, 1.98, and 2.43 × 10−11 m2/s at 30, 40 and 50 °C respectively. Diffusivities and analytical solutions predicted the experimental results at 30 and 50 °C with 0.3, and 0.4 g/mL respectively.

Evolution of stresses and permeability of fractured-and-porous rock mass around a production well

The authors model deformation and mass transfer in jointed and porous rock mass around a production well. The modeling based on the concept of a continuum with double porosity uses an original method with finite difference solution of mass transfer equations and analytical solution of pore elastoplasticity equations. From the numerical experiments, dimensions of irreversible deformation zones in the well bore zone grow with the parameter Bio. The estimate of the reservoir permeability decline in the course of operation, obtained from the pore elasticity and pore plasticity models, qualitatively agrees with the in situ observation data.

An Effective Moisture Diffusivity Model Deduced from Experiment and Numerical Solution of Mass Transfer Equations for a Shrinkable Drying Slab of Microalgae Spirulina

From experimental data, Spirulina effective moisture diffusivity was analytically estimated by considering two diffusion regions and the product shrinkage. Then, the moisture diffusivity was deduced from the numerical solutions of mass transfer equations by minimizing the difference between experimental and simulated drying curves and by taking into account the slab thickness variation. The range of moisture diffusivity used for simulations was estimated from minimal and maximal values of experimental effective diffusivities and calculation started with the mean value of experimental effective diffusivities. Identified effective diffusivities ranged from 1.79 × 10−10 to 6.73 × 10−10 m2/s. These diffusivities increased strongly with drying temperature and decreased slightly with moisture content. A suitable model correlating effective diffusivity, temperature, and moisture content was then established. Effective diffusivities given by this model were very close to experimental ones with a relative difference ranging from 0.5 to 24%.

Numerical simulation of CO2 absorption into aqueous methyldiethanolamine solutions

The CO2 absorption rate into aqueous N-methyldiethanolamine solutions was measured using a stirred cell with a flat gas-liquid interface. The measurements were performed in the temperature range of 293.15 to 333.15 K for various amine concentrations and CO2 partial pressures. A numerical model of mass-transfer with complex chemical reactions based on the film theory was developed to interpret the experimental results. The model predictions have been found to be in good agreement with the experimental values of CO2 absorption rates. A comparison is made between the enhancement factor predicted from the detailed model and the approximate solution of mass transfer equations with chemical reaction. The numerical results indicate that under the present experimental conditions, the effect of the reaction between CO2 and OH− on the observed mass transfer rates is negligible. The detailed mass transfer model was used for simulating the CO2 absorption process in terms of the enhancement factor under a variety of operating conditions.

Two-peak approximation in kinetic capillary electrophoresis

Kinetic capillary electrophoresis (KCE) constitutes a toolset of homogeneous kinetic affinity methods for measuring rate constants of formation (k(+)) and dissociation (k(-)) of non-covalent biomolecular complexes, C, formed from two binding partners, A and B. A parameter-based approach of extracting k(+) and k(-) from KCE electropherograms relies on a small number of experimental parameters found from the electropherograms and used in explicit expressions for k(+) and k(-) derived from approximate solutions to mass transfer equations. Deriving the explicit expressions for k(+) and k(-) is challenging but it is justified as the parameter-based approach is the simplest way of finding k(+) and k(-) from KCE electropherograms. Here, we introduce a unique approximate analytical solution of mass transfer equations in KCE termed a "two-peak approximation" and a corresponding parameter-based method for finding k(+) and k(-). The two-peak approximation is applicable to any KCE method in which: (i) A* binds B to form C* (the asterisk denotes a detectable label on A), (ii) two peaks can be identified in a KCE electropherogram and (iii) the concentration of B remains constant. The last condition holds if B is present in access to A* and C* throughout the capillary. In the two-peak approximation, the labeling of A serves only for detection of A and C and, therefore, is not required if A (and thus C) can be observed with a label-free detection technique. We studied the proposed two-peak approximation, in particular, its accuracy, by using the simulated propagation patterns built with the earlier-developed exact solution of the mass-transfer equations for A* and C*. Our results prove that the obtained approximate solution of mass transfer equations is correct. They also show that the two-peak approximation facilitates finding k(+) and k(-) with a relative error of less than 10% if two peaks can be identified on a KCE electropherogram. Importantly, the condition of constant concentration of B is always satisfied in macroscopic approach to studying kinetics at equilibrium (MASKE) whether or not B is in excess to A* and C*, and, thus, the two-peak approximation is applicable to MASKE. It completes a toolset of fitting-free methods for processing MASKE data and makes MASKE a simple practical method for finding k(+) and k(-) of "fast", "slow", and "intermediate-rate" non-covalent interactions.

Solution of an inverse problem for mass transfer in a drying process in a magnetic field

In this study, mass transfer in deformed porous materials is investigated theoretically and analytical solutions of mass transfer equations for investigated materials are derived. In order to determine the variation of porosity degree of the material versus time and to estimate the region where the variation of effective diffusion coefficient is regular, an inverse ill-posed problem is solved by considering the experimental data concerned with the drying of the porous material. The numerical calculations of concentration profiles and experimental results concerned with the drying of the materials in a magnetic field are given.

Osmotic dehydration of tilapia fillets in limited volume of ternary solutions

In this study, water activity, moisture content reduction and solute uptake kinetics as well as mass transfer in osmotic dehydration of tilapia (Oreochromis niloticus) fillets were studied, using limited volumes (solution/fillet ratio: 4/1) of ternary solutions (salt–sugar–water) at different initial sucrose (0–100 g in 100 g of water) and salt (0–35.14 g in 100 g of water) concentrations at 20 °C. The multicomponent effective diffusion coefficients were calculated by fitting the experimental values to analytical solution of mass transfer equations with a limited solution/fillet ratio. Previously, the effective diffusion coefficients of salt and sugar in tilapia muscle were calculated using a binary system. A very good fit between the mathematical model and experimental values was observed. The binary coefficients obtained were: for sodium chloride, D 11, 0.91×10 −9 m 2 s −1 and sucrose, D 22, 0.22×10 −9 m 2 s −1, and the calculated cross-term coefficients, D 12 and D 21, were −0.12×10 −9 and 0.06×10 −9 m 2 s −1, respectively.

Analytical solution of mass transfer equation considering shrinkage for modeling food-drying kinetics

In order to obtain a simplified equation for the mathematical description of drying kinetics, an analytical solution of a mass transfer equation with concentration-dependent shrinkage and a constant average water diffusivity was proposed. Experimental drying curves of 4 × 4 cm 2 mango slices, with 0.5, 1.0 and 1.5 cm thicknesses and 10 cm long cassava parallelepipeds with 1, 2 and 3 cm thicknesses, at different air temperatures (50°C, 60°C and 70°C) and 3 m/s of air velocity, were obtained in order to fit the proposed model by non-linear least-squares. The proposed model solutions reproduced with moderate accuracy the numerical solution of mass transfer equation, and the experimental drying curves with r 2=0.92 for mango and 0.97 for cassava. An evident deviation from experimental behavior was observed at moisture contents below 5% in a semi-log scale. Using the average water diffusivity and shrinkage obtained with the proposed model, an accurate simulation of experimental drying curves was obtained at low-air velocities (0.5 and 1.75 m/s).

Analytical Solution of Mass Transfer Equation with Interfacial Resistance in Food Drying

ABSTRACT A simplification of boundary conditions of the mass transfer equation in food drying was obtained. An average distribution constant between food and air humidity was introduced. With this simplification and analytical solution for the mass transter equation with interfacial resistance was; found. and a medihcd Bi number is proposed: Thc analytical solution for infinite flat slab was comparcd to the numcrical solution without the simplification. The analytical solution showed a good approximation to thc numerical solution. The equation oblained from thc analytical solution predicted ha1 for modified Bi numbers greater han 30. the drying curve bccamcs indcpcndcnt o f thc boundary conditions, which means that drying is diffusion controlled. Experimental drying curves of carrots were obtained at modified Bi numbers between 10 and 60. The crperimenwl drying cumes did not show statistical diffcrencc for modified Bi numbcrs grcater than 40, which approaches to the same limit predicted by the analytical ...