Convective Drying of Wastewater Sludge: Introduction of Shrinkage Effect in Mathematical Modeling

Drying of two kinds of wastewater sludge was studied. The first part was an experimental work done in a discontinuous cross-flow convective dryer using 1 kg of wet material extruded in 12-mm-diameter cylinders. The results show the influence of drying air temperature for both sludges. The second part consisted of developing a drying model in order to identify the internal diffusion coefficient and the convective mass transfer coefficient from the experimental data. A comparison between fitted drying curves, well represented by Newton's model, and the analytical solutions of the equation of diffusion, applied to a finite cylinder, was made. Variations in the physical parameters, such as the mass, density, and volume of the dried product, were calculated. This allowed us to confirm that shrinkage, which is an important parameter during wastewater sludge drying, must be taken into account. The results showed that both the internal diffusion coefficient and convective mass transfer coefficient were affected by the air temperature and the origin of the sludge. The values of the diffusion coefficient changed from 42.35 × 10^?9 m² · s^?1 at 160°C to 32.49 × 10^?9 m² · s^?1 at 122°C for sludge A and from 33.40 × 10^?9 m² · s^?1 at 140°C to 28.45 × 10^?9 m² · s^?1 at 120°C for sludge B. The convective mass transfer coefficient changed from 4.52 × 10^?7 m · s^?1 at 158°C to 3.33 × 10^?7 m · s^?1 at 122°C for sludge A and from 3.44 × 10^?7 m · s^?1 at 140°C to 2.84 × 10^?7 m² · s^?1 at 120°C for sludge B. The temperature dependency of the two coefficients was expressed using an Arrhenius-type equation and related parameters were deduced. Finally, the study showed that neglecting shrinkage phenomena resulted in an overestimation that can attain and exceed 30% for the two coefficients.     

Coupling CFD and Diffusion Models for Analyzing the Convective Drying Behavior of a Single Rice Kernel

The drying behavior of a single rice kernel subjected to convective drying was analyzed numerically by solving heat and moisture transfer equations using a coupled computational fluid dynamics (CFD) and diffusion model. The transfer coefficients were computed simultaneously with the external flow field and the internal diffusive field of the grain. The model was validated using results of a thin-layer drying experiments from the literature. The effects of velocity and temperature of the drying air on the rice kernel were analyzed. It was found that the air temperature was the major variable that affected the drying rate of the rice kernel. The initial drying rates (in first 20 min) were 7, 12, and 19% per hour at inlet air temperatures of 30, 45, and 60 ^° C, respectively. Important temperature gradients within the grain existed only in the first few minutes of the drying process. The moisture content gradients reached a maximum value of 11.7% (db) mm ^?1 at approximately 45 min along the short axis in the thickness direction. The variation in the inlet air velocity showed a minor effect on the drying rate of the rice kernel. The heat and mass transfer coefficients varied from 16.57 to 203.46 W·m ^?2·K ^?1 and from 0.0160 to 0.1959 m·s ^?1, respectively. The importance of the computation of the transfer coefficients with the heat and mass transfer model is demonstrated.     

Analysis of the Shrinkage Effect on Mass Transfer During Convective Drying of Sawdust/Sludge Mixtures

Convective drying of wastewater sludges and sawdust/sludge mixtures was studied. The first part of this work was an experimental study performed in a cross-flow convective dryer using 500 g of wet material extruded through a disk with circular dies of 12 mm. The results showed that the sawdust addition has a positive impact on the drying process from a mass ratio of 2/8, on a dry basis, with observed drying rates higher than the original sludge. The second part of this work consisted of developing a drying model in order to identify the internal diffusion coefficient and convective mass transfer coefficient from the experimental data. A comparison was made between fitted drying curves, well represented by the Newton's model, and the analytical solutions of the diffusion equation applied to a finite cylinder. Variations of dimensional characteristics, such as the volume and exchange surface of the sample bed, were obtained by X-ray tomography. This technique allowed us to confirm that shrinkage, which is an important phenomenon occurring during sludge and sawdust/sludge mixture drying, must be taken into account. The results showed that both the internal diffusion coefficient and convective mass transfer coefficient were affected by mixing and sawdust addition. The internal diffusion coefficient changed from 7.77 × 10^?9 m²/s for the original sludge to 7.01 × 10^?9 m²/s for the mixed sludge and then increased to 8.35 × 10^?9 m²/s for the mixture of a mass ratio of 4/6. The convective mass transfer coefficient changed from 9.70 × 10^?8 m/s for the original sludge to 8.67 × 10^?8 m/s for the mixed sludge and then increased to 12.09 × 10^?8 m/s for the mixture of a mass ratio of 4/6. These results confirmed that sawdust addition was beneficial to the sludge drying process as the mass transfer efficiency between the air and material increased. Reinforcing the texture of sludge by adding sawdust can increase the drying rate and decrease the drying time, and then the heat energy supply will be reduced significantly. The study also showed that neglecting shrinkage phenomenon resulted in an overestimation for the internal diffusion coefficient for the convective drying of sludges and sawdust/sludge mixtures.     

Drying Characteristics of Barley Grain Dried in a Spouted-Bed and Combined IR-Convection Dryers

A study was performed to determine the drying characteristics and quality of barley grain dried in a laboratory scale spouted-bed dryer at 30, 35, 40, and 45°C and an inlet air velocity of 23 m/s^?1, and in an IR-convection dryer under an infrared radiation intensity of 0.048, 0.061, 0.073, and 0.107 W cm^?2 at an air velocity of 0.5 m/s^?1. The results show that the first, relatively short, phase of a sharp decrease in the drying rate was followed by the phase of a slow decrease. The time of barley drying depended on temperature of inlet air in a spouted-bed dryer and on radiation intensities in an IR-convection dryer. Barley drying at 45°C in a spouted-bed dryer was accompanied by the lowest total energy consumption. The average specific energy consumption was lower and the average efficiency of drying was higher for drying in a spouted-bed dryer. The effective diffusivities were in the range 2.20–4.52 × 10^?11 m² s^?1 and 3.04–4.79 × 10^?11 m²/s^?1 for barley dried in a spouted-bed and in an IR-convection dryer, respectively. There were no significant differences in kernel germination energy and capacity between the two drying methods tested.     

The Effect of External Mass Transfer Resistance during Drying of Fermented Sausage

The drying mechanism of fermented sausages (sucuks) that were cylindrical rod shaped, 40 cm long and 4 cm diameter, during ripening under natural convection conditions at different temperatures (15 to 30°C) was examined. To simulate the experimental drying curves, three empirical models and a diffusional model assuming negligible external mass transfer resistance were evaluated. The drying rate curves of sucuk samples were also simulated taking into account the influence of the external mass transfer resistance. The equation was solved using the trial-and-error solution algorithm developed in this study and the mass transfer coefficient, k _c , and effective moisture diffusivity, D _eff , were simultaneously determined (1.44 × 10^?8 to 1.93 × 10^?8 m/s and 4.30 × 10^?10 to 6.85 × 10^?10 m²/s, respectively). The proposed model considering the effect of external resistance allowed the accurate simulation of the experimental drying data of sucuks at different temperatures.     

Combined Infrared-Convective Drying of Murta (Ugni molinae Turcz) Berries: Kinetic Modeling and Quality Assessment

Murta (Ugni molinae Turcz) berries were dried under convective and combined convective-infrared conditions at 40, 50 and 60°C and 400–800 W in order to determine the drying characteristics and to compare the dried product's quality. To model the drying kinetics, seven mathematical equations were fitted to experimental data. According to statistical tests performed, the Midilli-Kuçuk model best fitted experimental data and was closely followed by the logarithmic model. Effective moisture diffusivity also showed dependency on drying conditions and varied between 7.59 × 10^?10 to 44.18 × 10^?10 m²/s and 11.34 × 10^?10 to 85.41 × 10^?10 m²/s for air-convective drying and combined infrared-convective drying. As to quality attributes of the berries, total surface color difference (ΔE) and total phenolic content (TPC) were determined. It was found that chromaticity coefficients a* and b* changed significantly, showing ΔE to be dependent on the mode of heat supply. TPC under all drying conditions decreased and was significantly different from the initial value in fresh samples. However, at a constant drying temperature, an increase in infrared power enhanced retention of TPC in samples. In particular, working at 40°C/800 W resulted in dried samples with the highest TPC.     

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%.     

Analysis of Heat and Mass Transfer during High-Temperature Drying of Pinus radiata

This article describes the analysis of heat and mass transfer coefficients for a single board of Pinus radiata (D. Don) timber over a range of high temperature and superheated steam drying conditions. The calculated heat transfer coefficients were in the range 20 to 60 W m^-2 K^-1. The mass transfer coefficients were of the order of 2 × 10^-8 to 3 × 10^-7 kg m^-2 s^-1, based on the vapor pressure difference, and of the order of 0.002 to 0.04 m s^-1 (expressed in terms of mass transfer velocity) based on vapor concentration difference between the surface of the board and the bulk drying medium.     

SINGLE-LAYER DRYING BEHAVIOR OF MEXICAN TEA LEAVES (CHENOPODIUM AMBROSIOIDES) IN A CONVECTIVE SOLAR DRYER AND MATHEMATICAL MODELING

Single-layer solar drying experiments were conducted for Mexican tea leaves (Chenopodium ambrosioides) grown in Marrakech. An indirect forced convection solar dryer was used in drying the Mexican tea leaves at different conditions such as ambient air temperature (21° to 35°C), drying air temperature (45° to 60°C) with relative humidity (29 to 53%), airflow rate (0.0277 to 0.0556 m ³/s), and solar radiation (150–920 W/m²). The experimental drying curves showed only a falling rate period. In order to select the suitable form of drying curves, 14 mathematical models were applied to the experimental data and compared according to their statistical parameters. The main factor in controlling the drying rate was found to be the temperature. The drying rate equation was determined empirically from the characteristic drying curve. The diffusion coefficient of the Chenopodium ambrosioides leaves was estimated and varied between 1.0209 × 10^?9 and 1.0440 × 10^?8 m ²·s^?1.The activation energy was found to be 89.1486 kJ·mol^?1.     

Drying Kinetics of a Porous Spherical Particle and the Inversion Temperature

A model is presented for drying of a single porous particle with superheated steam and humid air. Experimental data for spherical porous ceramic particle reported in the literature were used for the validation of the model. An inversion temperature at which the evaporation rates within superheated steam and humid air are equal was predicted. The effect of thermophysical properties of the particle (permeability 10^?14 ? 10^?17 m², diameter 3 × 10^?3 ? 10 × 10^?3 m) and operating variables (gas mass flux 0.26 ? 0.78 kg m^?2 s^?1, drying agent temperature 120–200°C) is tested. The inversion temperature is shown to be affected by the thermophysical properties of the porous particle and of the drying agent.     

Filtration and Drying Study of Phosphatidylinositol Fraction from De-Oiled Soy Lecithin

Separation and purification of phosphatidylcholine (PC) and phosphatidylinositol (PI) fractions to their utmost purity is still a challenging task industrially due to the molecular and structural complexity of lecithin molecules. The present study deals with the filtration of the PI-rich fraction followed by drying of the cake for its further purification and value addition. Filtration of the PI-rich fraction was carried out under constant pressure conditions followed by the drying of the cake in a vacuum tray dryer. The average specific cake resistance (α_av) as a function of operating pressure was studied and it showed little variation with respect to the applied pressure differential. The initial solvent content in the cake after filtration was found to be in the vicinity of 1 kg solvent/kg dry solid, which was then subsequently reduced in the drying stage to 0.04 kg solvent/kg dry solid. The drying kinetics of the cake was studied at different drying temperatures in a vacuum tray dryer operated under varying degree of vacuum. The drying rate curve showed a prominent falling rate period with the effective solvent diffusivity in the range of 5.4 × 10^?10 m²s^?1 to 1.42 × 10^?9 m²s^?1within the temperature range of 40–60°C. Critical analysis of the dried PI fraction was carried out in terms of phosphatidylinositol content and color. The drying data were analyzed using various models and Das et al.'s model, the modified Henderson and Pabis model, and the Page model were found to provide the best fit sin terms of root mean square error (RMSE), chi square, and correlation coefficient (R ²).     

Two-resistance mass transfer model for the adsorption of various dyestuffs onto chitin

The kinetics of the adsorption of various dyestuffs onto chitin have been studied. The dyestuffs used are Neoland Blue 2G, Eriochrome Flavine A, and Solophenyl Brown 3RL and a number of process variables were considered, such as adsorbent mass and dye concentration. The mass transfer model is based on the assumption of a pseudoirreversible isotherm and two resistances to mass transfer. These are external mass transfer and internal pore diffusion mass transfer. The rate of adsorption of dyestuffs onto chitin can thus be described by an external mass transfer coefficient and a pore diffusion coefficient. The external mass transfer coefficients are 5.0 × 10^?5, 5.0 × 10^?5, and 1.0 × 10^?5 m·s^?1 and the pore diffusivities are 3.0 × 10^?10 and 4.0 × 10^?11 m²·s^?1 for Neolan Blue 2G, Eriochrome Flavine A, and Solophenyl Brown 3RL, respectively.     

Modeling Superheated Steam Vacuum Drying of Wood

Abstract

A two-dimensional mathematical model developed for vacuum-contact drying of wood was adapted to simulate superheated steam vacuum drying. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady-state mass conservation of dry air. A drying test conducted on sugar maple sapwood in a laboratory vacuum kiln was used to infer the convective mass and heat transfer coefficients through a curve fitting technique. The average air velocity was 2.5 m s^?1 and the dry-bulb temperature varied between 60 and 66°C. The ambient pressure varied from 15 to 11 kPa. Simulation results indicate that heat and mass transfer coefficients are moisture content dependent. The simulated drying curve based on transfer coefficients calculated from boundary layer theory poorly fits experimental results. The functional relation for the relative permeability of wood to air is a key parameter in predicting the pressure evolution in wood in the course of drying. In the case of small vacuum kilns, radiant heat can contribute substantially to the total heat transfer to the evaporative surface at the early stages of drying. As for conventional drying, the air velocity could be reduced at the latter stage of drying with little or no change to the drying rate.     

Estimation of Effective Moisture Diffusivity of Okra for Microwave Drying

The effect of microwave output power and sample amount on effective moisture diffusivity were investigated using microwave drying technique on round okra (Hibiscus esculentus L.). The various microwave output powers ranging from 180 to 900 W were used for the determination of effective moisture diffusivity for constant sample amount of 100 g okra. To examine the effect of sample amount on effective moisture diffusivity, the samples in the range of 25–100 g were dried at constant microwave output power of 360 W. By increasing the microwave output powers and decreasing the sample amounts, the effective moisture diffusivity values ranged from 20.52 × 10^?10 to 86.17 × 10^?10 and 34.87 × 10^?10 to 11.91 × 10^?9 m²/s^?1, respectively. The modeling studies were performed to illustrate the relationship between the ratio of the microwave output power to sample amount and effective moisture diffusivity. The relationship between drying constant and effective moisture diffusivity was also estimated.     

Water vapor sorption and diffusion in wheat straw particles and their impact on the mass transfer properties of biocomposites

This work intends to decipher the role of hydrophilic fillers, wheat straw fibers (WSF), on the water vapor transfer properties (sorption and diffusion) of biocomposites based on poly(3‐hydroxybutyrate‐co‐3‐hydroxyvalerate), (PHBV) as matrix. Transfer in biocomposites, measured using dynamical vapor sorption measurement, is correlated to the transfer properties of each individual constituent and to the specific structural arrangements induced by the presence of particles inside the matrix. Increasing amounts of WSF particles in the PHBV matrix lead to an increase of the water vapor sorption (WVS) of the resulting composites. This is attributed to the high sorption of hydrophilic WSF as compared to that of the neat PHBV matrix. Water vapor diffusion in composites (around 0.13 × 10^?11 m² s^?1 at 20°C whatever the filler content) is always lower than in the neat matrix (0.26 × 10^?11 m² s^?1) although wheat straw displays high diffusivity values (1.84 × 10^?11 m² s^?1). Such unexpected behavior is related to (1) changes of structure and properties of the WSF particle once embedded in the PHBV matrix, (2) changes in the polymer matrix structure and properties in contact with fibers, and also (3) to the representativeness of the filler diffusivity, which is difficult to appraise. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43329.     

Modelling of Cr(VI) removal from polluted groundwaters by ion exchange

This work reports the viability and modelling of the removal of Cr(VI) from polluted groundwaters by means of ion exchange using the resin Lewatit MP‐64. Feed groundwaters that contained Cr(VI) at an average concentration of 2431 mg dm^?3 and 1187 mg dm^?3 of chloride and 1735 mg dm^?3 of sulfate as main anions were acidified to a pH of 2.0 prior to the removal process. Dynamic experiments were carried out in a fixed bed column with feed waters at flow rates in the range of 2.78 × 10^?7 m³ s^?1 to 5.55 × 10^?7 m³ s^?1. Regeneration was achieved with NaOH (2 mol dm^?3). From the experimental results, the equilibrium of the ion exchange reaction was successfully modelled, obtaining an equilibrium constant (K′_AB) = 44.90. Finally, a mass balance that included mass transfer resistances in the liquid and solid phases was developed and from the comparison between simulated and experimental data the value of the effective intraparticle diffusivity (D_s) was determined as 1.43 × 10^?12 m² s^?1. Copyright © 2004 Society of Chemical Industry     

Characterization of isotherms and thin-layer drying of red kidney beans,Part II: Three-dimensional finite element models to estimate transient mass and heat transfer coefficients and water diffusivity

Three-dimensional finite element models with consideration of shrinkage and irregular shape were developed to estimate the relationships among the transient heat and mass transfer coefficients, the transient water diffusivity, and the temperature and moisture content of the red kidney beans being dried under different drying conditions. An equation was developed to calculate the transient mass transfer coefficient using the measured time–moisture content data. This calculated transient mass transfer coefficient was further used to calculate the transient heat transfer coefficient. To verify the predicted temperature on the surface of the red kidney beans, surface temperature was measured using a handhold infrared thermometer. These measured temperature and time–moisture content data were used to determine the transient water diffusivity using the least square method when the red kidney bean kernel experienced a shrinkage during drying. Strong relationship among the transient heat and mass transfer coefficients, the water diffusivity, and the ratio of the transient heat and mass transfer coefficients was revealed. This relationship could be used to predict temperature and moisture content of the red kidney beans during the entire drying period. The Lewis number?=?27, and the ratio of the transient heat over mass transfer coefficients was 10765?J?m^?3?k^?1 at 30 and 40°C, and 10729?J?m^?3?k^?1 at 50°C. Shrinkage did not significantly influence the value of the estimated transient water diffusivity.     

Kinetics and Mass Transfer during Atmospheric Freeze Drying of Red Pepper

Drying is applied for moisture removal to allow safe and extended storage. Red pepper (Capsicum annum) samples were heat pump dried in fluidized bed at different air temperatures. A slightly modified solution of the diffusion equation was used to describe the kinetics and drying rates of red pepper. The model well described the low- and medium-temperature drying processes. The determined effective mass diffusivities varied from 0.7831 to 4.0201 × 10^?9 m²/s and increased consistently with drying air temperature. The mass diffusivity was correlated to temperature by linear regression with coefficient of determination equal to 0.999 and negligible standard error.     

Microwave drying of wastewater sludge: Experimental and modeling study

This study investigates experimentally and using mathematical modeling the microwave drying of wastewater sludge with determination of moisture diffusivity at different drying conditions. The drying behavior was observed at different power levels (480, 840, and 1,080 W) and different initial masses (90, 120, and 150 g). The observed drying kinetics were divided into three parts: a short adaptation period, a long constant drying rate period, and a falling drying rate period. The maximum drying rate was observed during the constant rate period. Mainly, the results show that the drying rate decreases with the initial mass increase (from 0.45 kg·kg^?1·min^?1 for 90 g to 0.25 kg·kg^?1·min^?1 for 150 g) and increases with an increase in power level (from 0.15 kg·kg^?1·min^?1 at 480 W to 0.45 kg·kg^?1·min^?1 at 1,080 W). The measurement of the sample dimensions shows that shrinkage can occur and, depending on the drying conditions, it ranged between 0.42 and 0.37 of the sample initial volume. Presenting a more accurate solution of the diffusion model by incorporating shrinkage and finite dimensions of the sample is the novelty of this study. The drying conditions influenced the diffusion coefficient, which ranged from 1.53 × 10^?7 to 7.67 × 10^?7 m²s^?1. Similar to the drying rate, the diffusion coefficient was directly proportional to the power level and inversely proportional to the initial mass. Activation energy was determined using an Arrhenius relationship of the diffusion coefficient as a function of the ratio initial mass to the power level.