Internal Mass Transfer Resistance Research Articles

Investigation of the effect of hydraulic retention time on anaerobic digestion of potato leachate in two-stage Mixed-UASB system

In the present paper, potato leachate is introduced into the first reactor, converted to glucose through the hydrolysis process and then into the acetic acid during the acidogenic process and as a feed entered the second reactor, converting to methane and carbon dioxide based on the methanogenic process. For modeling, a kinetic model has been used to justify the two-stage system behavior using MATLAB software. In writing the equations for modeling in the first reactor, variations are taken with time, while in the second reactor, the equations are written in solid and liquid phase and in steady state. The relationship used in most cases to represent the kinetics of bacterial growth is the equation called Monod, which is used in modeling the system. The systems have been investigated at mesophilic temperature and the effect of the reaction's resistance on the boundary layer has been neglected in the concentrations around the granules. According to the modeling, by increasing the residence time and the concentration of input waste, the percentage of removal of organic compounds will increase and fluctuate between the oxygen content of 67–81% and the methane production efficiency will reduce (until less than 0.1 L CH4 g−1 CODremoved−1) that is agreement with laboratory model in 19th day. The results and studies have shown that the modeling performed for a two-stage system can be used in the mesophilic temperature conditions, and the internal mass transfer resistance in the granules is a controlling process.

Drying process and quality characteristics of contact ultrasound reinforced heat pump drying on kiwifruit slices

Contact ultrasound reinforced heat pump drying (CUHPD) experiments of kiwifruit slices were performed to investigate the effect of ultrasound application on drying process, microstructure, and several nutrient components of kiwifruit slices. The results showed that the CUHPD of kiwifruit slices was an internal diffusion-controlled process, in which ultrasound application could improve the dehydration rate significantly, and higher ultrasonic power led to shorter drying time. Scanning electric microscopy results illustrated that the ultrasound treatment could produce more micropores and larger microchannels inside kiwifruit slices, and thus reduce the hardness and brittleness values. Both ultrasonic power and drying temperature could significantly affect the total phenolic content, VC content, and total sugar content. Contact ultrasound application in the heat pump drying (HPD) process was conducive to improve the nutrient contents at all drying temperatures. Hence, contact ultrasound application is a promising way to effectively promote the dehydration rate and to improve the product quality of HPD on kiwifruit slices. Practical applications Heat pump drying (HPD) is one of the modern drying methods and has some excellent advantages such as energy-saving and easy operation. However, it has a certain disadvantage like long drying time for those agricultural materials with great internal mass transfer resistance. In this study, the contact ultrasound reinforcing technology was applied to accelerate internal water transfer and improve the drying rate of HPD on kiwifruits. The results showed that the contact ultrasound application could produce a significant reinforcing effect on internal moisture diffusion and dehydration rate, and then reduce the drying time. The increase in ultrasonic power was conducive to improve dried kiwifruit's quality and protect nutrient components in kiwifruit slices compared with single HPD. Therefore, CUHPD is a promising drying method for kiwifruits and can even be effectively applied for other agricultural product drying.

Dynamics of Water Adsorption from Butanol–Water Vapor in a Biosorbent Packed Column

Drying is essential in the production of biobutanol. In this work, the dynamics of water adsorption from butanol–water vapor mixtures in a fixed bed column were investigated. The biosorbent used in this system was derived from a cellulosic material oat hull. Water adsorption breakthrough curves obtained from the biosorbent packed column were simulated by the Bohart–Adams model and Klinkenberg model. The Klinkenberg model provided a better simulation of the experimental data in comparison with the Bohart–Adams model. The mass transfer coefficient and mass transfer resistances were investigated from the modeling results. The results indicated that the rate of water adsorption was controlled by internal mass transfer resistance. The water adsorption on the biosorbent was visualized with the aid of microscope imaging. This study reveals that water saturated oat hull based biosorbent was regenerated and reused successfully.

Improvement of the microfluidic microbial fuel cell using a nickel nanostructured electrode and microchannel modifications

In this study, the effect of utilization of a nanostructured nickel based material as a negative electrode on the performance of microfluidic microbial fuel cell (MFC) with Escherichia coli as biocatalyst has been investigated. Designing the microfluidic MFC with nickel nanostructure resulted in a higher volumetric power density of 343 W m−3 compared to the previously published results. The assessment of effective parameters on the electrochemical performance of cell was investigated. The investigation of the hydraulic diameter impact on the power generation proves that reducing the microchannel hydraulic diameter from 1000 to 350 μm minimized the internal mass-transfer resistance, and consequently 32% increase in the maximum surface power density is observed. Replacing the nickel foil with nickel nanostructures resulted in an additional improvement of 67% in the maximum surface power density. The maximum volumetric power density of 343 W m−3 has been obtained for the fabricated MFC with 350 μm hydraulic diameter associating nanostructured morphology. To assess the capability of the microfluidic MFC as a power source of the energy storage devices, the obtained results show that the microfluidic MFC with nickel nanostructure is able to provide about 76% of the total power needed for manganese rechargeable lithium battery.

Mechanistic insight into the adsorption of diclofenac by MIL-100: Experiments and theoretical calculations

The development of high-efficiency adsorbents and the exploration of their adsorption mechanisms are major challenges in environmental remediation. Herein, MIL-100 was prepared, characterized, and utilized for the adsorptive removal of diclofenac sodium (DCF) from aqueous solutions. A high monolayer adsorption capacity of 773 mg g−1 was recorded. The adsorption mechanism was proposed based on different contributions of two types of pore structure of MIL-100 to the adsorption of DCF from aqueous solutions according to the experimental results and theoretical calculation. During adsorption process, DCF (5.2 × 7.4 × 10.3 Å) diffused through the free area of hexagonal pores (8.6 × 8.6 Å) into the cages of MIL-100, whilst it was adsorbed by the pentagonal pores (4.8 × 5.8 Å) preferentially. Internal mass transfer resistance, which was identified as one of the dominant rate-limiting steps by the mass transfer resistance kinetic models based on the Sips model, will be derived from the diffusion process, which was affected by the size-sieving effect of the pore structure of MIL-100. The successful diffusion of DCF into the interior of MIL-100 and the stable configuration between MIL-100 and DCF accounted for the high adsorption capacity. The capture of DCF into MIL-100 also resulted in the pore size distribution variation of adsorbent, which provided vital experimental evidence for the proposed mechanism. This study may offer deeper insights into other pollutants removal by metal-organic frameworks type adsorbents.

Effects of vibration on anammox-enriched biofilm in a high-loaded upflow reactor

An upflow biofilm reactor was operated for 211 days to investigate the effects of vibration on anammox treatment performance. With vibration, the highest nitrogen removal rates (20 kg-N·m−3·d−1) were obtained on day 180. Since the vibration could directly applied on the biofilm, it could release the dinitrogen gas accumulated in the biofilm timely and reduce the internal mass transfer resistance sharply. The specific anammox activity increased by more than 3 times with a higher vibration intensity. Meanwhile, the unique random motion caused by mechanical vibration promotes the production of extracellular proteins. Moreover, the VSS reached 20.97 g·L−1 which was 1.6 times higher than the control reactor. Such enrichment method resulted in a hard and thick anammox biofilm with a special granular morphology, and the nitrite tolerance concentration could reach 500 mg-N·L−1. Operated with an adequate vibration intensity could maintain the biofilm thickness and conducive to improve the stability of the reactor. In addition, this technique also allowed the microorganisms inside the biofilm and those on the surface to reach the same culture conditions. Base on the batch experiments, intermittent vibration caused a decrease in energy consumption from about 7.757 (kW·h)·(kg-N)−1 in group 0-Lv7(60-60) to 0.912 (kW·h)·(kg-N)−1 in group 0-Lv7(5-60). Compared to the internal recycle without vibration, the energy consumption fell by a slice over 65%. Furthermore, the high-throughput sequencing results showed that the relative abundance of Candidatus Kuenenia in reactor 1 increased from 13.2% to 43.9%.

A new experimental method to separate interfacial and internal mass transfer on coated adsorbent

This study presents a simple and reasonable experimental methodology for separating the effects of interfacial and internal mass transfers from an overall mass transfer. First, the mass transfer in the range of thickness with negligible internal mass transfer resistance is experimentally observed. It was assumed that the effect of the internal mass transfer can be neglected if the sorption dynamic data of two thin-coated samples correspond with each other. Then, the internal mass transfer resistance is calculated by subtracting the interfacial mass transfer resistance from the overall resistance. The adsorbent, named Wakkanai Siliceous Shale (WSS) impregnated with lithium chloride of 20 wt%, was coated on sample plates with different thicknesses (27 μm, 65 μm, 0.19 mm, 0.38 mm and 0.71 mm). The large pressure jump (LPJ) method was used, and adsorption dynamic characteristics were gravimetrically measured. Based on the experimental data, the adsorption dynamics of composite WSS-coated layers were compared with those of the layers coated by an A-type silica gel to verify the applicability of a composite adsorbent using WSS on adsorption heat pump systems.

Kinetics of Hydrogenation of Acetic Acid over Supported Platinum Catalyst

Petroleum is nonrenewable and contributes to environmental pollution, thus bio-oil can be substituted as a potential alternative. However, bio-oil in its crude form cannot be used directly as fuel since it contains a high proportion of oxygenated, acidic, and reactive compounds such as carboxylic acids. These are known to cause corrosion of vessels and pipework, instability, and phase separation. The heating value of bio-oil can be improved through hydrodeoxygenation (HDO). In this study, the HDO of acetic acid is presented, being a typical model compound found in bio-oil. Kinetic data were obtained over the range of temperature (175–210 °C), hydrogen pressure (20–50 bar), initial acetic acid concentration (0.16–0.521 M), and catalyst loading (0.2–0.5 g), in a 100 mL batch reactor using 4% Pt/TiO2. It was found that catalyst particle sizes < 65 μm and a stirring speed of 1000 min–1 were sufficient to overcome internal and external mass transfer resistances and ensure that the reaction is within the kineti...

H2S adsorption on NaY zeolite

Abstract In this work, high-pressure H2S adsorption data in equilibrium and fixed bed conditions using NaY zeolite as adsorbent were determined. Adsorption and desorption isotherms for different temperatures and H2S partial pressures up to 1.2 bar were obtained experimentally and modelled with Toth and Dubinin-Astakhov equations in order to give information about adsorbate/adsorbent and adsorbate/adsorbate interactions. H2S adsorption in a fixed bed column was achieved for different inlet volumetric flow rates and breakthrough curve data were evaluated considering adsorbed amount, length of mass transfer zone, contributions of internal and external mass transfer resistances and were modelled with Linear Driving Force (LDF) model to estimate adsorbent particle's effective mass transfer coefficient. Equilibrium results indicate maximum uptake capacities are above 6.0 mol kg−1 for highest partial pressures. Isotherms' modeling suggests the predominance of physisorption of H2S in NaY zeolite. However, a hysteresis effect was observed for desorption curves and attributed to H2S chemisorption on zeolite surface, as pointed out by strongly favorable isotherms obtained. Fixed bed adsorption data showed breakthrough curves were nonsymmetrical, which indicated the presence of internal resistance mainly, probably due to the microporosity of adsorbent particle. In accordance, mass transfer zones did not vary significantly with inlet flow rate. Effective intraparticle mass transfer coefficients obtained with LDF model increases as flow rate increases, due to a higher availability of H2S molecules at adsorbent surface, which increases the driven force necessary for mass transfer in the intraparticle region.

Characterization of kinetic parameters and mass transfer resistance in an aerobic fixed-bed reactor by in-situ respirometry

An airlift reactor filled with Raschig rings in the downcomer section only was designed to allow for the characterization of biofilm biomass at several superficial liquid velocities. The reactor was inoculated with activated sludge and operated with synthetic wastewater containing acetate. After steady state was reached, the kinetic parameters of the process were determined at each superficial liquid velocity by an in-situ pulse respirometry method. Subsequently, the biofilm contained in the reactor was disaggregated, resuspended in a mineral medium, and reintroduced in the reactor, without Raschig rings, i.e., a standard airlift reactor. The kinetic parameters of the bioprocess were determined again, by the same respirometry method. That strategy allowed for the estimation of apparent and intrinsic kinetic parameters; i.e., with and without mass transfer limitation, respectively. Moreover, the method also allowed for the determination of the internal and external effectiveness factors and mass transfer resistances. The results shown that the hydrodynamic conditions had a strong effect on the kinetic parameters but none on the stoichiometric parameters. The external mass transfer accounted for up to 70% of the total mass transfer resistance. It is concluded that respirometry is a useful tool for the characterization of biofilms, in actual random packing reactors.

Dynamic analysis of the anomalous diffusion in catalyst particles considering chemical reactions with non-linear kinetics

In this work, a generalized reaction-diffusion model useful to study the interactions between anomalous diffusion and chemical reactions in catalyst particles is presented. The fractional reaction-diffusion model considers the linearization of the non-linear reaction kinetic terms, which allows the solution of the mathematical model through the Fourier transform. The proposed methodology can be used for the dynamic analysis of the concentration profiles in the catalytic pellets, including internal and external mass transfer resistances, as well as for the estimation of effectiveness factor (EF). These findings revealed that the analysis of dynamic reaction-diffusion linearized models where the mass transfer is described by the anomalous transport can be analysed in the frequency domain. Two kinetic models, a general power-law and Langmuir-Hinshelwood, were considered. The results demonstrated the effect of use the traditional Fick’s law and the anomalous transport (i.e., subdiffusion or superdiffusion phenomena) in a porous media system, particularly on the space-time concentration profile predictions and the influence on the effectiveness factor of the catalytic particle.

Mathematical modelling applied to the rate-limiting mass transfer step determination of a herbicide biosorption onto fixed-bed columns

ABSTRACTThe herbicide removal of Diuron in a fixed-bed column packed with the Moringa oleifera bark biosorbent was investigated experimentally and through phenomenological mathematical modelling. To understand the physical phenomena involved, the steps of external mass transfer resistance, internal mass transfer resistance and the adsorption phenomenon itself were considered as possible limiting steps in the herbicide mass transfer from the liquid to the solid phase. In the developing process of the internal mass transfer resistance model, two hypotheses were considered: constant mass transfer coefficient and mass transfer coefficient as a function of the herbicide concentration in the biosorbent. The experimental breakthrough curves were obtained for different flow rates and feed concentrations, in order to evaluate the model’s predictive capacity. The mass transfer parameter values of the mathematical models were estimated using the simplex downhill optimization method. The model that considers the resistance a mass transfer internal with parameter Ks variable represented effectively the dynamic behaviour of the herbicide biosorption process in fixed-bed column, in the various evaluated conditions, indicating that this mechanism controls the biosorption process. Thus, the phenomenological mathematical modelling proved to be an analysis important tool, understanding and the herbicide adsorption systems design in a fixed-bed column.

Adsorption model development for mass transport characteristics of MFEP structure by physisorption method

A novel heterogeneous contacting structure, microfibrous entrapped particles (MFEP) structure, was developed to intensify chemical processes including heterogeneous catalytic reactions and the gas–solid adsorption process. MFEP is characterized by its extremely high heat and mass transfer efficiency, which is critical for thermal and/or mass transfer limited reactions. To investigate the mass transport characteristics of MFEP, a physisorption (hexane adsorption onto activated carbon) was used as a probe process. A theoretical adsorption model was developed based on the linear driving force approximation and constant pattern behavior. Mass transfer mechanisms including external diffusion, intraparticle molecular diffusion, Knudsen diffusion, and surface diffusion, were considered in the model. This model was then used to analyze the experimental breakthrough data and calculate the mass transfer coefficient. The experimental results showed that for MFEP with a particle diameter of approximately 200 µm, the volumetric mass transfer coefficient is more than 10 times higher than that of a packed bed. Combining the experimental results and theoretical analysis, it was also found that in the particle diameter range of 2000 to 100 µm, the system’s mass transfer resistance is primarily the result of both the external and internal mass transfer resistances. This leads to the conclusion that decreasing the particles size can effectively increase the mass transfer rate. However, when the particle size is less than 100 µm, axial dispersion becomes the rate-limiting resistance, potentially reducing the residence time of the adsorbate in the adsorbent bed. The current study was aimed at understanding the mass transfer behavior in the MFEP structure, and optimizing of MFEP for specific heterogeneous contacting applications.

Simulation of a closed low-pressure honeycomb adsorber for thermal energy storage

The efficient implementation of renewable energy sources necessitates thermal energy storages. For domestic as well as industrial applications thermal energy storages based on closed adsorption are studied. Against this background, a closed low-pressure honeycomb adsorber is numerically examined in this work. The examined adsorber contains stacked layers of honeycomb blocks with rectangular channels which are separated by heat exchanger plates. Zeolite 13X and water is assumed as the adsorption pair. The focus of this work is solely on the adsorption process. The numerical model applies a one-dimensional model for the single channels of the honeycomb blocks. The one-dimensional model has been presented in a previous work of the authors. To account for transversal heat conduction in the honeycomb cross-section, the one-dimensional model equations are extended by heat source/sink terms. In addition, the mass transport equation is modified for rectangular channel flow. The results demonstrate that the heat and mass transfer and the adsorption processes are strongly coupled and can be only understood by their interaction. Regarding modelling aspects, it is found that the spatial variations of temperature and pressure as well as the local deviation from adsorption equilibrium are significant. Hence, no equilibrium assumptions should be made. Further, the minor rarefaction effect of slip should be considered. With respect to the application, the analysis yields, that the thermal power can be optimized by variation of the honeycomb geometry parameters, e.g. channel size. The local optimum is a result of the inverse dependencies of the external and internal mass transfer resistance on the channel size. Interestingly, the optimum for peak and mean power do not coincide in general. Finally, it is found that the thermal power can be controlled effectively by the inlet pressure.

Kinetic modeling of catalytic esterification of non-edible macauba pulp oil using macroporous cation exchange resin

Conversion of non-edible oils through heterogeneous catalysis and their kinetic aspects are essential in order to produce economically viable biodiesel. Especially for oils containing high Free Fatty Acids (FFA) content since those cannot be viably converted through homogenous catalysis. Herein, the heterogeneous catalytic esterification kinetics of macauba pulp acid oil was exploited. The reaction tests were conducted in a stirred batch reactor with ethanol, and a cation exchange resin (Purolite® CT275)as a catalyst. The reaction kinetics was modeled based on a pseudo-homogeneous (PH) model of second order, showing good agreement with the experimental data acquired under different reaction conditions. The reaction progress was monitored by validated HPLC and GC methods. The internal and external mass transfer resistances were evaluated, and show that the rate limiting step is the surface reaction. To assess the catalyst stability, scanning electron microscopy was performed on both fresh and spent (after 10 reaction cycles) catalysts; reuse of catalyst was conducted without further treatment. The catalyst recycling demonstrates good performance where 85% of its performance was retained, and the SEM images show that the materials were structurally stable. Because the Pseudo-Homogeneous model properly described the kinetic aspects of the esterification process it was possible to estimate thermodynamic parameters by using the Arrhenius plot. The activation energy of the forward reaction was determined as 44.0 kJ/mol, while for the reverse reaction was 11.7 kJ/mol. Therefore, the kinetic and thermodynamic descriptions along with the catalyst stability upon several cycles without any further treatment reflect the viability of these resins for industrial application in the energy sector. Furthermore, combining these features with the low cost of macauba pulp acid oil, we conclude that the process is suitable for scaling up studies.

The preparation and efficacy of SrO/CeO2 catalysts for the production of dimethyl carbonate by transesterification of ethylene carbonate

The need for eco-friendly fuels has given a fillip to search for new molecules and their cost-effective synthesis. A series of ceria-strontium (CexSr1−xO2; x = 0 to 1) catalysts were prepared by a citric acid assisted sol–gel method. These catalysts were characterized by BET, XRD, SEM-EDAX, ICP-MS, FTIR, NH3-TPD and CO2-TPD techniques and tested for the synthesis of dimethyl carbonate (DMC) in a batch reactor for the transesterification of ethylene carbonate (EC). The activity of the synthesized catalysts was found to be closely related to basic and acidic sites, and the surface area of the catalysts. The catalyst, Ce0.6Sr0.4, showed highest basicity and acidity, and was found to be most effective in the formation of DMC from transesterification of EC. Reactions were carried out by varying the particle size (50–800 μm) and agitation speed (200–600 rpm) for minimizing the internal mass transfer resistance and the external mass transfer resistance, respectively. Further, Ce0.6Sr0.4 catalyst was used to optimize the reaction conditions such as methanol/EC molar ratio (in the range of 4–12), catalyst dose (in the range of 2–5 wt% of EC), reaction time (in the range of 2–6 h) and temperature (in the range of 100–180 °C) for DMC yield and EC conversion. At the optimum conditions of methanol/EC molar ratio of 8, 3 wt% of catalyst, 5 h reaction time and 150 °C temperature, the DMC selectivity was 87% and EC conversion of 82%, with a reaction rate of ∼0.547 mol/L.h (with respect to EC). The reusability of the Ce0.6Sr0.4 catalyst for EC conversion with turn-over frequency and DMC selectivity were also studied.

NiMg/Ceria-Zirconia Cylindrical Pellet Catalysts for Tri-reforming of Surrogate Biogas

Cylindrical NiMg/Ce0.6Zr0.4O2 pellet catalysts with two different sizes (large, radius = 1.59 mm; small, radius = 0.75 mm) were produced by extrusion of powder catalysts. The small catalyst pellets had a higher specific surface area, pore volume, average pore size, radial crush strength, and resistance to breakage than the large pellets. Tri-reforming tests with surrogate biogas were conducted at 3 bar and 882 °C, with the feed molar ratios of CH4:CO2:air fixed at 1.0:0.7:0.95 and the H2O/CH4 molar feed ratio varied (0.35–1.16). The small catalyst pellets exhibited lower internal mass-transfer resistance and higher coking resistance compared to the large pellets. CO2 conversion decreased and H2/CO molar ratio increased with the increase of H2O/CH4 molar feed ratio, which are consistent with the trends predicted by thermodynamic equilibrium calculations. The results indicate that the NiMg/Ce0.6Zr0.4O2 catalyst pellets are promising for commercial scale applications.

Influence of surface morphology on the performance of nanostructured ZnO-loaded ceramic honeycomb for syngas desulfurization

A facile seeding-growth protocol was employed to immobilize nanostructured ZnO with nanorod and nanosheet morphologies (ZnO-nR and ZnO-nS, respectively) on cordierite-mullite honeycomb support. By varying the hexamethylenetetramine (HMTA) concentration, Zn precursor, and number of growth cycles during synthesis, different nanorod sizes, nanosheets textures and ZnO layers were obtained. The ZnO-loaded honeycombs were characterized using FESEM, EDX and XRD indicating that the immobilized layer of nanostructured ZnO was highly-crystalline with a thickness of ∼1µm. The synthesized nanostructured ZnO-loaded honeycombs and a commercial ZnO sorbent were applied for removal of sulfur compounds (H2S and COS) from syngas at 400°C. The ZnO-nS showed significantly longer breakthrough time (BTTS) and higher total sulfur sorption capacity (48.7mgg−1 ZnO, BTTS=75.4min) than the ZnO-nR (9–12mgg−1 ZnO, BTTS=23–25min) and commercial ZnO sorbent (4.6mgg−1 ZnO, BTTS=6.8min). The superior sorption capacity of ZnO-nS was attributed to the significantly better surface coverage and higher crystallinity of ZnO nanosheets on the honeycomb. The introduction of additional ZnO nanosheets layers (up to 3 layers) through repeated growth process increased the ZnO loading to ∼1.5±0.1mgmm−1 (from ∼0.9±0.1mgmm−1 in the single layer) but resulted in poorer performance (11.6mgg−1 ZnO, BTTS=24.6min) compared to ZnO-nS. This was due to the increased internal mass transfer resistance and decreased density of the effective reactive sites. The mechanism of ZnO-nS formation is also proposed to provide further insights. Overall, the ZnO-nS showed better regenerability, lower mass transfer resistance, and higher sorption capacity compared to the commercial ZnO and ZnO-nR sorbents indicating that it has a promising potential for syngas desulfurization.

Kinetics of lipase-catalysed methyl gallate production in the presence of deep eutectic solvent

Production of methyl gallate (MG), which is an important phenolic acid ester for pharmaceutical industry, was carried out by Novozym 435-catalysed transesterification of propyl gallate (PG) with methanol in a deep eutectic solvent. Reaction parameters governing substrate molar ratio, enzyme concentration, temperature and agitation rate were investigated batch-wise in choline chloride:glycerol-water binary mixture. The results were evaluated in terms of conversion of PG, yield of MG and hydrolysis of PG to gallic acid. 10% (w/w) of water was found to be favourable in the reaction medium for low hydrolysis percent. The highest conversion (17.4%) and yield (60.4%) but the lowest hydrolysis (2%) after 120 h of transesterification were found at PG/methanol molar ratio of 1:6, enzyme concentration of 40 g/L, 50 °C and 200 rpm. A kinetic model based on the Ping-Pong Bi–Bi mechanism for transesterification of PG was proposed with the assumption that there were no internal and external mass transfer resistances.

Phenomenological mathematical modeling of heavy metal biosorption in fixed-bed columns

A phenomenological mathematical modeling has been applied in order to describe the dynamic behavior of the biosorption of heavy metals in fixed-bed columns. The mathematical model hereby proposed was evaluated on experimental breakthrough curves of the ions Cu(II), Ni(II) and Zn(II) in monocomponent systems using the residue of alginate extraction from Sargassum filipendula as biosorbent. Some authors have studied mathematical models to describe the biosorption of heavy metals, however, in most cases, they have fitted the models to the experimental data without evaluating the prediction capacity of the model in different operational conditions. This capacity is inherent of phenomenological models. Therefore, in addition to the breakthrough curves used to obtain the kinetic parameters of the models, an extra set of breakthrough curves has been studied outside the range evaluated for the fitted parameters in order to validate the model. The equilibrium data for the three studied ions was adequately represented by the Langmuir isotherm. The quantity of Ni(II) removed was very similar to the quantity related to the Zn(II) removal and the removal of Cu(II) ions was far superior than the other ions. The high values for the breakthrough time obtained for the Cu(II) ions represent a high removal efficiency and affinity with the biomass. The mathematical model was able to predict the dynamic behavior of removal for the three investigated ions, indicating that the internal mass transfer resistance is the rate limiting-step. The validation of the model demonstrated the prediction capacity in the different evaluated conditions, characterizing it as a useful tool when analyzing and designing heavy metal biosorption processes in fixed-bed columns.