The paper focuses on the modelling of bromate formation. An axial dispersion model was proposed to integrate the non-ideal mixing, mass-transfer and a kinetic model that links ozone decomposition reactions fromthe Tomiyasu, Fukutomi and Gordon (TFG) ozone decaymodelwith direct and indirect bromide oxidation reactions, oxidation of natural organicmatter and its reactionswith aqueous bromine. To elucidate the role of ammonia an additional set of reactions leading to bromamine formation, oxidation and disproportionation was incorporated in the kinetic model. Sensitivity analysis was conducted to obtain information on reliability of the reaction rate constants used and to simplify the model.
Validation results of a theoretical model that describes the formation of bromate during ozonation of bromide-containing natural waters are presented. An axial dispersion model integrating the nonideal mixing, mass-transfer and a kinetic model that links ozone decomposition reactions from the Tomiyasu, Fukutomi and Gordon ozone decay model with direct and indirect bromide oxidation reactions, oxidation of natural organicmatter and reactions of dissolved organics and aqueous bromine was verified. Themodel was successfully validated with results obtained both at a laboratory and a full scale. Its applicability to different water supply systems was approved.
The quantitative description of an airlift bioreactor, in which aerobic biodegradation limited by carbonaceous substrate and oxygen dissolved in a liquid takes place, is presented. This process is described by the double-substrate kinetics. Mathematical models based on the assumption of plug flow and dispersion flow of liquid through the riser and the downcomer in the reactor were proposed. Calculations were performed for two representative hydrodynamic regimes of reactor operation, i.e. with the presence of gas bubbles only within the riser and for complete gas circulation. The analysis aimed at how the choice of a mathematical model of the process would enable detecting the theoretical occurrence of oxygen deficiency in the airlift reactor. It was demonstrated that the simplification of numerical calculations by assuming the “plug flow” model instead of dispersion with high Péclet numbers posed a risk of improper evaluation of the presence of oxygen deficiency zones. Conclusions related to apparatusmodelling and process design were drawn on the basis of the results obtained. The paper is a continuation of an earlier publication (Grzywacz, 2012a) where an analysis of single-substrate models of the airlift reactor was presented.
A mathematical model of a plane, steady state biofilm, with the use of a single substrate kinetics, was proposed. A set of differential equations was solved. In order to analyse the biofilm’s behaviour, a number of simulations were performed. The simulations included varying process parameters such as detachment coefficient and substrate loading. Two detachment models were taken into consideration: one describing the detachment ratio as proportional to the thickness of the biofilm, and the other one proportional to the thickness of the biofilm squared. The results provided information about substrate and live cell distribution in biofilm and the influence of certain parameters on biofilm behaviour.
In order to investigate the mechanism of adsorption of reactive dyes from the textile industry on ash from heating plant produced by brown coal combustion, some characteristic sorption constants are determined using Langergren adsorption equations for pseudo-ﬁ rst and pseudo-second order. Combined kinetic models of pseudo-ﬁrst order and pseudo-second order can provide a simple but satisfactory explanation of the adsorption process for a reactive dye. According to the characteristic diagrams and results of adsorption kinetic parameters of reactive dyes on ashes, for the applied amounts of the adsorbents and different initial dye concentrations, it can be concluded that the rate of sorption is fully functionally described by second order adsorption model. According to the results, the rate constant of pseudo-second order decreases with increasing initial dye concentration and increases with increasing amount of adsorbent – ash.
The cometabolic biodegradation of 4-Chlorophenol (4-CP) by the Stenotrophomonas maltophilia KB2 strain in the presence of phenol (P) was studied. In order to determine the kinetics of biodegradation of both substrates, present alone and in cometabolic systems, a series of tests was carried out in a batch reactor changing, in a wide range, the initial concentration of both substrates. The growth of the tested strain on phenol alone was described by Haldane kinetic model (mm = 0:9 1/h, Ksg = 48:97 gg/m3, KIg = 256:12 gg/m3, Yxg = 0:5715). The rate of 4-CP transformation by resting cells of KB2 strain was also described by Haldane equation and the estimated parameters of the model were: kc = 0:229 gc=gxh, Ksc = 0:696 gc=m3, KIc = 43:82 gc=m3. Cometabolic degradation of 4-CP in the presence of phenol was investigated for a wide range of initial 4-CP and phenol concentrations (22–66 gc/m3 and 67–280 gg/m3 respectively). The experimental database was exploited to verify the two kinetic models: CIModel taking only the competitive inhibition into consideration and a more universal CNIModel considering both competitive and non-competitive inhibition. CNIModel approximated experimental data better than CIModel.
Analysis of granulation kinetics was carried out using a laboratory disc granulator with a diameter D of 0.5 m. A liquid binder was delivered to the tumbling bed at a constant flow rate with a nozzle generating droplets with a size of approx. 4-5 mm. Fine-grained chalk was used as a model of raw material and water or disaccharide solution with concentrations of 20 - 40% as a wetting liquid. Different times of droplet delivery ranging from 2 to 6 min were utilized. Granulometric composition of the bed for selected lengths of process, bed moisture and the moisture of individual size-fractions were assessed. Mass of granulated material, which was transferred from nuclei fraction to other size fractions was determined on the basis of mass balance analysis and the assessment of liquid migration between fractions. The influence of disaccharide concentration in wetting liquid on the aforementioned phenomena was also examined.
A mathematical model of waste tyre pyrolysis process is developed in this work. Tyre material decomposition based on a simplified reaction mechanism leads to main product lumps: noncondensable (gas), condensable (pyrolytic oil) and solid (char). The model takes into account kinetics of heat and mass transfer in the grain of the shredded rubber material as well as surrounding gas phase. The main reaction routes were modelled as the pseudo-first order reactions with a rate constant calculated from the Arrhenius type equation using literature values of activation energy determined for main tyre constituents based on TG/DTG measurements and tuned pre-exponential parameter values obtained by fitting theoretical predictions to the experimental results obtained in our laboratory reactor. The model was implemented within the CFD software (ANSYS Fluent). The results of numerical simulation of the pyrolysis process revealed non-uniformity of sample’s porosity and temperature. The simulation predictions were in satisfactory agreement with the experimentally measured mass loss of the tyre sample during pyrolysis process investigated in a laboratory reactor.
The study analyses application possibilities of filtration and thickening models in evaluation of papermaking suspension drainage rate. The authors proposed their own method to estimate the drainage rate on the basis of an existing Ergun capillary model of liquid flow through a granular material. The proposed model was less sensitive to porosity changes than the Ergun model. An empirical verification proved robustness of the proposed approach. Taking into account discrepancies in the published data concerning how the drainage velocity of papermaking suspension is defined, this study examines which of the commonly applied models matches experimental results the best.
Ozonation is a heterogeneous process of chemical absorption often controlled by a gas-liquid mass transfer rate. This paper presents the results of kinetics in a reaction between phenylphenol isomers and ozone. The degradation of phenylphenol isomers during ozonation proceeds quite fast. In order to avoid the influence of mass transfer limitation the kinetics experiments were conducted in a homogenous liquid-liquid system. The second-order rate constants were determined using classical and competition methods, which are especially recommended for fast reactions. The determined rate constants at pH 2 using the two different methods are almost the same. The increase of pH causes an increase of rate constants for the reaction of phenylphenol isomers with ozone.
The studies showed that alkaline lipase from Pseudomonas fluorescens enables an irreversible transesterification of vinyl esters to give enantiomeric excess (eeR) of about 80% using vinyl butyrate as acyl donor and diisopropyl ether as a solvent, at partially optimized conditions. For the native lipase the process was adequately described by a five-parameter Ping-Pong Bi Bi model for both enantiomers plus expression accounting for the formation of enzyme-acyl donor complex, but for the same lipase supported on mesoporous materials of SBA-15-Oc type, R-product inhibition also had to be taken into account. The use of hydrophobic support increased by more than two-fold the rate of the S-solketal conversion but even more that of R-solketal. Thus the immobilization of lipase had very positive effect on the process kinetics but decreased its enantioselectivity.
A kinetic model to describe lovastatin biosynthesis by Aspergillus terreus ATCC 20542 in a batch culture with the simultaneous use of lactose and glycerol as carbon sources was developed. In order to do this the kinetics of the process was first studied. Then, the model consisting of five ordinary differential equations to balance lactose, glycerol, organic nitrogen, lovastatin and biomass was proposed. A set of batch experiments with a varying lactose to glycerol ratio was used to finally establish the form of this model and find its parameters. The parameters were either directly determined from the experimental data (maximum biomass specific growth rate, yield coefficients) or identified with the use of the optimisation software. In the next step the model was verified with the use of the independent sets of data obtained from the bioreactor cultivations. In the end the parameters of the model were thoroughly discussed with regard to their biological sense. The fit of the model to the experimental data proved to be satisfactory and gave a new insight to develop various strategies of cultivation of A. terreus with the use of two substrates.
The aim of the present theme issue was to study the influence of ultrasound enhancement on the kinetics of osmotic dehydration and the effect of convective drying from the point of view of drying time and quality of dried products. Apple fruit was used as the experimental material. The kinetics of osmotic dehydration with (UAOD) and without (OD) ultrasound enhancement were examined for 40% fructose and sorbitol solutions. The effective dehydration time of osmotic process was determined. Preliminary dehydrated samples with OD and UAOD were next dried convectively with (CVUS) and without (CV) ultrasound assistance. The influence of OD and UAOD on the kinetics of CV and CVUS drying was analysed. The parameters of water activity and colour change were measured for the assessment of product quality after drying process.
Steel is a versatile material that has found widespread use because of its mechanical properties, its relatively low cost, and the ease with which it can be used in manufacturing process such as forming, welding and machining. Regarding to mechanical properties are strongly affected by grain size and chemical composition variations. Many industrial developments have been carried out both from the point of view of composition variation and grain size in order to exploit the effect of these variables to improve the mechanical proprieties of steels. It is also evident that grain growth are relevant to the mechanical properties of steels, thus suggesting the necessity of mathematical models able to predict the microstructural evolution after thermo cycles. It is therefore of primary importance to study microstructural changes, such as grain size variations of steels during isothermal treatments through the application of a mathematical model, able in general to describe the grain growth in metals. This paper deals with the grain growth modelling of steels based on the statistical theory of grain growth originally developed by Lücke  and here integrated to take into account the Zener drag effect and is therefore focused on the process description for the determination of the kinetics of grain growth curves temperature dependence.
The aim of this article is to present a modern method of convective drying intensification caused by the external action of ultrasound. The purpose of this study is to discover the mechanism of ultrasonic interaction between the solid skeleton and the moisture in pores. This knowledge may help to explain the enhancement of drying mechanism affected by ultrasound, particularly with respect to biological products like fruits and vegetables. The experimental kinetics tests were conducted in a hybrid dryer equipped with a new ultrasonic generator. The drying kinetics curves determined on the basis of drying model developed by the author were validated with those by the ones obtained from experimental tests. The intensification of heat and mass transfer processes due to ultrasound induced heating effect and vibration effect are analysed. The obtained results allow to state that ultrasound makes drying processes more effective and enhance the drying efficiency of biological products without significant elevation of their temperature.
A catalytic combustion of organic admixtures of air belongs to the basic technologies of gas purification. A macrokinetics of admixtures combustion over the porous catalysts was described. The theoretical approach is in agreement with standard description of macrokinetics of the catalytic processes. The relationship between the fundamental magnitudes: observed process rate r*, reaction rate r in the kinetic zone, and a coefficient of the surface utilization η in the form r*= r · η have been described. These magnitudes combines the Thiele module φ. A kinetics equation for the isothermal and non-isothermal conditions was provided. The influence of mass and heat transfer in the catalyst grain on the course of the process was described by means of the surface utilization coefficient η. An equation describing this coefficient for both isothermal and non-isothermal conditions was given. The second part of this work concerns the application of theory. When the composition of purified gas is continuously varied, a quantitative approach is rather impossible. The theory was used for the qualitative analysis of process on the basis of the experimental results. A fulfillment of the first-order kinetics means that the degree of admixtures conversion does not depend on their initial concentrations. A non-isothermicity of the catalyst grain is expressed in such a way that the process rate observed over the large porous grains of the catalyst can be higher than the reaction rate in the kinetic zone. A temperature deference between the catalyst grains and flowing gas causes that the reactor can be stably operated at varied concentrations of admixtures and temperature over a relatively wide range. It was also demonstrated that the flammable admixtures may advantageously influence the conversion of hardly combustible admixtures
The paper presents results of research on cobalt and nickel ions removal from monocomponent solutions using Purolite ion exchange resins. It has been shown that C 160 ion exchange resin has the best sorption properties for both ions (Qe – 72.5 mg Co/g and 88.2 mg Ni/g). Regeneration process of this ion exchanger has high efficiency, achieving about 93% for cobalt ions and about 84% in case of nickel ions. It has been shown that the use of ion exchange method with suitable ion exchange resins guarantees effective removal of cobalt and nickel ions from solutions with very high concentrations corresponding to contents of these metals in industrial wastewaters (e.g. galvanic). In case of C 160 ion exchange resin, after the sorption process is carried out in one 50 minute cycle, the cobalt concentration decreased from about 30 000 mg/L to about 9 500 mg/L (approx. 68%), whereas nickel concentration reached about 6 300 mg/L (approx. 79%). Studied chelating resins don’t have such high sorption capacities. In their case, it is required to convert cobalt and nickel ions into complex forms. The kinetics of studied processes were described by pseudo-second order equations.
The extracellular polymeric substance (EPS) produced from Rhizobium radiobacter F2, designated as EPSF2, was investigated as a biosorbent for the removal of Pb(II) and Zn(II) from aqueous solution. The optimum biosorption pH values were 5.0 for Pb(II) and 6.0 for Zn(II). Kinetics study revealed that the biosorption followed pseudo-first-order model well, and the equilibrium data fit the Langmuir model better. The adsorbed metal ions could be effectively desorbed by HCl. Desrobed EPSF2 regained 80% of the initial biosorption capacity after five cycles of biosorption-desorption-elution. These results demonstrated that EPSF2 could be a promising alternative for Pb(II) and Zn(II) removal from aqueous solution.
This paper concerns convective drying of carrot preliminary dehydrated in aqueous solutions of three types of osmotic agents (sucrose, fructose, glucose). Three solution concentrations (20, 40 and 60%) were examined to work out efficient conditions of osmotic dewatering. The parameters such as water loss (WL), solid gain (SG) and osmotic drying rate (ODR) indicating the real efficiency of osmotic dehydrations (OD) were determined. The samples dehydrated with osmotic solutions underwent further convective drying to analyze influence of dehydration process on drying kinetics and final products quality. The quality of products was assessed on the basis of visual appearance of the samples and colorimetric measurements. It was found that osmotic pretreatment improves significantly the final product quality as the samples were less deformed and their colour was better preserved compared to samples, which had not been preliminarily dehydrated. Preliminary dehydration, however, did not influence significantly the overall drying time of the samples.
The kinetics of the reaction between CO2 and methyldiethanolamine in aqueous solutions have been studied using the stopped-flow technique at 288, 293, 298 and 303 K. The amine concentration ranged from 250 to 875 mol·m-3. The overall reaction rate constant was found to increase with amine concentration and temperature. The acid base catalysis mechanism was applied to correlate the experimentally determined kinetic data. A good agreement between the second order rate constants for the CO2 reaction with MDEA computed from the stopped-flow data and the values reported in the literature was obtained.
Results for microcrystalline cellulose pyrolysis are presented, which includes thermogravimetric measurements and kinetic analysis of experimental data. The effect of sample mass size and heating rate on estimated values of activation energy and pre-exponential factor is demonstrated and a simple modification of procedure is proposed that allows for the correct values of kinetic parameters regardless of the experimental conditions. The efficiency of the proposed method is confirmed for two endothermic chemical reactions. A method of nonlinear regression is used for calculation of kinetic parameters for a single or TG curve or several curves simultaneously.
The results of activity studies of four catalysts in methanol synthesis have been presented. A standard industrial catalyst TMC-3/1 was compared with two methanol catalysts promoted by the addition of magnesium and one promoted by zirconium. The kinetic analysis of the experimental results shows that the Cu/Zn/Al/Mg/1 catalyst was the least active. Although TMC-3/1 and Cu/Zn/Al/Mg/2 catalysts were characterised by a higher activity, the most active catalyst system was Cu/Zn/Al/Zr. The activity calculated for zirconium doped catalyst under operating conditions was approximately 30% higher that of TMC-3/1catalyst. The experimental data were used to identify the rate equations of two types - one purely empirical power rate equation and the other one - the Vanden Bussche & Froment kinetic model of methanol synthesis. The Cu/ZnO/Al2O3 catalyst modified with zirconium has the highest application potential in methanol synthesis.
This paper presents a method of describing an airlift bioreactor, in which biodegradation of a carbonaceous substrate described by single-substrate kinetics takes place. Eight mathematical models based on the assumption of liquid plug flow and axial dispersion flow through the riser and the downcomer in the reactor were proposed. Additionally, the impact of degassing zone with assumed complete mixing on the obtained results was analyzed. Calculations were performed for two representative hydrodynamic regimes of reactor operation, i.e. with the presence of gas bubbles only within the riser and for complete gas circulation. The conclusions related to the apparatus design and process performance under sufficient aeration of the reaction mixture were drawn on the basis of the obtained results.