Scielo RSS <![CDATA[Brazilian Journal of Chemical Engineering]]> vol. 31 num. 1 lang. es <![CDATA[SciELO Logo]]> <![CDATA[<b>Expression of <i>Saccharomyces cerevisiae</i> </b><b>α</b><b>-glucoside transporters under different growth conditions</b>]]> Important biotechnological processes depend on the efficient fermentation by Saccharomyces cerevisiae yeasts of starch hydrolysates rich in maltose and maltotriose. The rate-limiting step for fermentation of these α-glucosides is the transport across the plasma membrane of the cells. In order to contribute to a better understanding of maltose and maltotriose metabolism by S. cerevisiae, we analyzed the expression of the main α glucoside transporter genes in two different yeast strains grown on media with glucose, maltose or maltotriose as carbon source. Although both yeast strains have higher αglucoside transport activity during growth on maltotriose, our results show similar expression levels of the analyzed genes on either maltose or maltrotriose media. Thus, our results indicate that, although the transport capacity of maltotriose grown cells is higher than that of maltose grown cells, maltotriose cannot be considered a better inducer of αglucoside transporter genes. <![CDATA[<b>The stimulating effects of the addition of glucose on denitrification and removal of recalcitrant organic compounds</b>]]> A laboratory scale aerobic oxidation ditch combined with an anoxic reactor was conducted to treat wastewater from a chemical industrial park in Tianjin, China. The wastewater exhibited a low biodegradability, and the results of gas chromatography mass spectrometry (GC-MS) analysis showed that some recalcitrant organic components are present in the wastewater. Ammonia nitrogen (NH4+-N) removal efficiency of over 90% was obtained. However, the removal efficiencies of total nitrogen (TN) and chemical oxygen demand (COD) were below 16% and 15%, respectively. The addition of glucose to the anoxic reactor in the system increased the removal efficiencies of TN and COD to approximately 72% and 25.57%, respectively. Results of mass balance indicate that about 60% of the external carbon was consumed as electron donor for denitrification, while 40% was consumed as a substrate for co-metabolism. The optimal dose of added glucose was also investigated, which was determined at 0.35 to 1.20 (CODglucose:CODoriginal). <![CDATA[<b>Use of calcined layered double hydroxides for the removal of color and organic matter from textile effluents</b>: <b>kinetic, equilibrium and recycling studies</b>]]> This paper presents data for the synthesis and characterization of layer double hydroxides (LDH) and their use for color and chemical oxygen demand (COD) removal from effluents generated by a textile industry. Adsorption studies with raw and biologically treated (activated sludge) textile effluent showed that the pseudo-second order model best fitted the experimental data, leading to adsorption coefficients of 39.1 and 102.9 mgCOD/gLDH for raw and treated effluents, respectively. The best conditions for color and COD removal were obtained at lower values of temperature and pH (25 °C and pH 7) and, in these conditions, an LDH dose of 10 g/L resulted in color removal efficiencies of 56% for samples of raw and 66% for samples of treated effluent. Recycling studies indicated that the reuse of thermally treated LDH led to a progressive loss in the removal efficiencies of COD and color. The reduction was more pronounced with samples of the raw textile effluent. LDH characterization performed before and after each adsorption and regeneration experiment showed that there was no intercalation of dye molecules in the interlayer region of the LDH, indicating that COD and color removal might be due to the adsorption of organic molecules onto the LDH surface. <![CDATA[<b>Sequencing batch reactor operation for treating wastewater with aerobic granular sludge</b>]]> In this work, the performance of a sequencing batch reactor (SBR) on aerobic granular sludge was studied for urban wastewater treatment. The system was inoculated with aerobic activated sludge collected from a wastewater treatment plant and, after 30 days of operation, the first granules observed had an average diameter of 0.1 mm. The biomass concentration reached a maximum value around 4 g VSS L-1, and COD removal and nitrification efficiency achieved stable values of 90%. The predominant oxidizing ammonium bacteria in the granules were identified as Nitrosomonas spp. <![CDATA[<b>On the prediction of pickup and saltation velocities in pneumatic conveying</b>]]> This paper presents a comparative study of the critical pickup and saltation velocities of particles in horizontal pipelines for pneumatic conveying design. A comparative study is performed using different existing correlations in the literature for the determination of the minimum velocity of transport as a function of the particle and pipe diameter, particle density, solid mass flow rate and particle sphericity. Their limitations and difficulties in predicting those critical velocities are analyzed. For the pickup velocity, an experimental study was also carried out in order to support the analysis. Recommendations are presented on the use of such correlations. <![CDATA[<b>Extensional viscosity measurements of concentrated emulsions with the use of the opposed nozzles device</b>]]> This paper presents results of experimental studies on the apparent extensional viscosity of emulsions. The apparent extensional viscosity measurements were carried out with the use of a customized rheometer which utilizes stagnation flow between two opposing nozzles. Apparent extensional viscosity was determined for emulsions containing 60, 70 and 74 vol.% of dispersed phase. The emulsions were produced using a homogenizer equipped with different dispersing endings that resulted in emulsions characterized by different droplet sizes. The experimental results show that the value of apparent extensional viscosity of the emulsion is significantly influenced by the droplet size and by the concentration of dispersed phase. Apparent extensional viscosity as well as shear viscosity of the emulsions increases with the increase of the dispersed phase concentration and with the decrease of the droplet diameter. It has also been observed that the decrease in the diameter of droplets increases the ratio of the apparent extensional viscosity to the shear viscosity, known as the Trouton ratio. <![CDATA[<b>Non-woven nanofiber chitosan/peo membranes obtained by electrospinning</b>]]> The present work focused on the preparation and morphological characterization of chitosan-based nanofiber membranes, aiming at applications in medical and pharmacological areas. Membranes with nanofiber diameters ranging from 50 - 300 nm were prepared from polymer solutions through the electrospinning process. To stabilize the process, it was necessary to use poly(ethylene oxide) (PEO), which is a biocompatible synthetic polymer. Pure chitosan solutions, as well as chitosan and PEO solution blends, were characterized by their rheological behavior, conductivity, and surface tension measurements. The electrospun fiber thermal characteristics and crystalline structures were investigated through thermogravimetric analysis (TG) and differential scanning calorimetry (DSC). Scanning electron microscopy images (SEM) were used for the morphological evaluations of the membranes. The addition of PEO to the chitosan solutions improved their electrical conductivity, surface tension and viscosity, greatly favoring the electrospinning process. Thus, membranes with 80% chitosan could be electrospun. <![CDATA[<b>Optimization of Pd-B/</b><b>γ</b><b>-Al<sub>2</sub>O<sub>3</sub> catalyst preparation for palm oil hydrogenation by response surface methodology (RSM)</b>]]> Response surface methodology was used to design and evaluate the experimental variables for Pd-B/γ-Al2O3 catalyst preparation. The catalyst was prepared by impregnation and chemical reduction. Thirteen different samples of the catalyst were prepared at different KOH concentrations and annealed at various temperatures, before applying them in palm oil hydrogenation. Hydrogenation was performed on a 0.12% Pd-B/γ-Al2O3 catalyst at a temperature of 393 K, hydrogen pressure of 500 kPa and agitation of 500 rpm for 1 h. The iodine value (IV) and trans fatty acids (TFAs) content responses were measured for each hydrogenated palm oil sample. The predicted models were verified for both responses and found to be statistically adequate. An optimization study was performed on the catalyst preparation variables for minimizing both IV and TFAs content. The Pd-B/γ-Al2O3 prepared under optimized conditions exhibited 47% higher conversion and 22% lower trans-isomerization selectivity than Escat 1241 commercial catalyst. The Pd-B/γ-Al2O3 catalyst preparation variables have a noticeable effect on palm oil hydrogenation conversion and trans-isomerization selectivity. <![CDATA[<b>Clay nanoparticles effects on performance and morphology of poly(vinylidene fluoride) membranes</b>]]> In this study, a comparison between neat poly(vinylidene fluoride) (PVDF) membrane and composite (PVDF-Nanoclay and PVDF-PVP-Nanoclay) membranes is presented. All membranes were synthesized by the phase inversion process, using 18% PVDF, n-methylpyrrolidone as solvent and water as the non-solvent. Demineralized water cross-flow permeation tests were conducted to evaluate the membranes performance. Scanning electron microscopy (SEM) images of the membranes surface and cross-section and water contact angle measurements were used to estimate additives effects on membranes morphology. The results indicate that dopant addition affected membrane permeate flux and morphology. The 4% nanoclay composite membrane resulted in the highest ultrapure water permeability (0.9130 m³.m-2.h-1.MPa-1), lower hydraulic resistance (3.27´10+12.m-1), lower contact angle (87.1º) and highest surface porosity (0.95%). Furthermore, it was verified that the membrane surface porosity increased with increasing clay nanoparticles concentrations. It was observed that the morphology of the membranes with clay nanoparticle addition is characterized by a thin surface layer, with macro-pores, a thin bottom layer, which has a sponge-like structure with micro-pores and a thick intermediate layer, with finger-like pores and macro-pores. It was also verified that the introduction of PVP promotes a denser morphology compared with membranes without it. Based on the SEM surface and cross-sectional images and permeability tests, it became evident that the internal pore morphology plays an important role in membrane performance, because the higher the frequency and extent of the finger-like pores in the intermediate layer the higher is the membrane permeability. These preliminary results indicated that the use of nanoclay as an additive for membrane casting is a promising procedure for improving membrane performance for water and wastewater treatment. <![CDATA[<b>Influence of bloom number and plastifiers on gelatin matrices produced for enzyme immobilization</b>]]> In this study the immobilization of lipase in matrices produced with gelatin with different Bloom values and with the addition of plastifiers was investigated to evaluate the influence of the Bloom value, as well as the capacity of the plastifiers to maintain the enzyme immobilized and the immobilization yield. The results indicated the need for crosslinking of the matrices with glutaraldehyde due to the high solubility in water, explained by the amino acid profile, which confirms the solubility of gelatin. Mannitol showed greater efficiency in the lipase immobilization, since it led to more porous structures and more uniform pores. These structures were also influenced by the gelatin concentration; greater concentrations associated with intermediate concentrations of plastifier led to matrices with a greater immobilization yield (87.92%). The X-ray diffraction analysis revealed that the structure of the immobilization matrices was partially crystalline. <![CDATA[<b>Mixed convection flow by a porous sheet with variable thermal conductivity and convective boundary condition</b>]]> Effects of variable thermal conductivity on the mixed convection flow over a porous stretching surface are investigated. Analysis has been performed subject to the convective boundary conditions. The fluid is electrically conducting in the presence of a uniform applied magnetic field. The resulting problems are computed. The effects of emerging parameters on the velocity and temperature profiles are displayed and discussed. The values of the skin-friction coefficient and local Nusselt number are analyzed numerically. <![CDATA[<b>Study of mixing behavior of cstr using CFD</b>]]> The continuous stirred tank reactor (CSTR) is a widely used equipment in chemical related industries. The flow behaviour of fluid inside the reactor may either change from dispersion to ideal or ideal to dispersion mixing state. It is studied using the computational fluid dynamics (CFD) simulation software ANSYS Fluent. The mixing behaviour is predicted in terms of age distribution function, I (θ). For the CSTR without impeller and baffles, I (θ) is found by the tracer injection method. It is measured and predicted by the impeller swept volume method for the CSTR in the presence of impeller and baffles. The predicted results are found to be in good agreement with the literature experimental data. Effect of rpm of the impeller, Reynolds number and viscosity of the process fluid on the mixing characteristics has been investigated. <![CDATA[<b>Multi-model MPC with output feedback</b>]]> In this work, a new formulation is presented for the model predictive control (MPC) of a process system that is represented by a finite set of models, each one corresponding to a different operating point. The general case is considered of systems with stable and integrating outputs in closed-loop with output feedback. For this purpose, the controller is based on a non-minimal order model where the state is built with the measured outputs and the manipulated inputs of the control system. Therefore, the state can be considered as perfectly known and, consequently, there is no need to include a state observer in the control loop. This property of the proposed modeling approach is convenient to extend previous stability results of the closed loop system with robust MPC controllers based on state feedback. The controller proposed here is based on the solution of two optimization problems that are solved sequentially at the same time step. The method is illustrated with a simulated example of the process industry. The rigorous simulation of the control of an adiabatic flash of a multi-component hydrocarbon mixture illustrates the application of the robust controller. The dynamic simulation of this process is performed using EMSO - Environment Model Simulation and Optimization. Finally, a comparison with a linear MPC using a single model is presented. <![CDATA[<b>Detection and on-line prediction of leak magnitude in a gas pipeline using an acoustic method and neural network data processing</b>]]> Considering the importance of monitoring pipeline systems, this work presents the development of a technique to detect gas leakage in pipelines, based on an acoustic method, and on-line prediction of leak magnitude using artificial neural networks. On-line audible noises generated by leakage were obtained with a microphone installed in a 60 m long pipeline. The sound noises were decomposed into sounds of different frequencies: 1 kHz, 5 kHz and 9 kHz. The dynamics of these noises in time were used as input to the neural model in order to determine the occurrence and the leak magnitude. The results indicated the great potential of the technique and of the developed neural network models. For all on-line tests, the models showed 100% accuracy in leak detection, except for a small orifice (1 mm) under 4 kgf/cm² of nominal pressure. Similarly, the neural network models could adequately predict the magnitude of the leakages. <![CDATA[<b>Optimizing the control system of cement milling: process modeling and controller tuning based on loop shaping procedures and process simulations</b>]]> Based on a dynamical model of the grinding process in closed circuit mills, efficient efforts have been made to optimize PID controllers of cement milling. The process simulation is combined with an autoregressive model of the errors between the actual process values and the computed ones. Long term industrial data have been used to determine the model parameters. The data include grinding of various cement types. The M - Constrained Integral Gain Optimization (MIGO) loop shaping method is utilized to determine PID sets satisfying a certain robustness constraint. The maximum sensitivity is considered as such a criterion. Both dynamical parameters and PID sets constitute the inputs of a detailed simulator which involves all the main process characteristics. The simulation is applied over all the PID sets aiming to find the parameter region that provides the minimum integral of absolute error, which functions as a performance criterion. For each cement type a PID set is selected and put in operation in a closed circuit cement mill. The performance of the regulation is evaluated after a sufficient time period, concluding that the developed design combining criteria of both robustness and performance leads to PID controllers of high efficiency. <![CDATA[<b>Investigation of adsorption of the dyestuff astrazon red violet 3rn (basic violet 16) on montmorillonite clay</b>]]> In this study, color removal by absorption from synthetically prepared wastewater was investigated using montmorillonite clay by adsorption. As dyestuff Astrazon Red Violet 3RN (Basic Violet 16) was used. Experimental parameters selected were pH, temperature, agitation speed, initial dyestuff concentration, adsorbent dosage and ionic strength. It was established that adsorption rate increased with increasing pH, temperature, dye concentration and agitation speed, but decreased with increased ionic strength and adsorbent dosage. Adsorption equilibrium data obtained by a series of experiments carried out in a water bath were employed with common isotherm equations such as Langmuir, Freundlich, Temkin, Elovich and Dubinin-Radushkevich. It was found that the Langmuir equation appears to fit the equilibrium data better than the other models. Furthermore, the fit of the kinetic data to common kinetic models such as the pseudo-first-order, second-order, Elovich and intraparticle diffusion models was tested to elucidate the adsorption mechanism. Kinetic data conformed to the pseudo-second-order model, indicating chemisorptions. In addition, the thermodynamic parameters activation energy, Ea, enthalpy ΔH*, entropy, ΔS*, and free energy change, ΔG*, were calculated. The values of the calculated parameters indicated that physical adsorption of ARV on the clay was dominant and that the adsorption process was endothermic. <![CDATA[<b>High performance maleated lignocellulose epicarp fibers for copper ion removal</b>]]> Natural lignocellulosic fiber epicarp extracted from the babassu coconut (Orbignya speciosa) was chemically modified through reaction with molten maleic anhydride without solvent, with incorporation of 189.34 mg g-1 of carboxylic acid groups into the biopolymer structure. The success of this reaction was also confirmed by the presence of carboxylic acid bands at 1741 and 1164 cm-1 in the infrared spectrum. Identically, the same group is observed through 13C NMR CP/MAS in the solid state, via high field signals in the 167 pm region. Both the precursor and the immobilized maleated biopolymers presented nearly the same thermal stability and similar crystallinity to cellulose. However, the pendant carboxylic groups have the ability to remove copper with maximum sorption through a batchwise process at pH 6.0, as expected from the point of zero charge, determined to be 6.45. The sorption kinetic data were fitted to pseudo-first order, pseudo-second order, Elovich-chemisorption and intra-particle diffusion models and the equilibrium data were fitted to the Langmuir, the Freundlich and Tenkim isotherm models. Taking into account a statistical error function and determination coefficients, the data were fit to the pseudo-first and pseudo-second order kinetic and Langmuir isotherm models, with a maximum sorption capacity of copper ions of 55.09 mg g-1. This value suggests the application of this biopolymer with incorporated carboxylate groups as a favorable agent for copper removal from appropriate systems. <![CDATA[<b>Batch removal of manganese from acid mine drainage using bone char</b>]]> The present study investigated batch kinetics and the batch equilibrium of manganese removal from acid mine drainage (AMD) using bone char as an adsorbent. Equilibrium tests revealed that the Langmuir-based maximum manganese uptake capacity was 22 mg g-1 for AMD effluents and 20 mg g-1 for laboratory solutions at a pH ranging from 5.5 to 5.7. The pseudo-second order model best described the manganese kinetics within bone char. Manganese removal was mainly influenced by the operating variables of the solid/liquid ratio and the pH of the aqueous phase. In fact, metal uptake was favored at nearly neutral pH values. The effect of particle size and temperature proved to be insignificant for the investigated operating range. This work also evaluated the mechanism for manganese removal using bone char. Results showed that intraparticle diffusion is the main rate-limiting step; however, additional contributions from boundary layer diffusion may well affect this removal when particles of smaller sizes are used. The final concentration of fluoride and other metals present in the AMD effluent was in agreement with the concentration limit set forth by Brazilian legislation. The present study demonstrated that bone char is a suitable material to be used for the removal of manganese from AMD effluents. <![CDATA[<b>Study of CaCl<sub>2 </sub>as an agent that modifies the surface of activated carbon used in sorption/treatment cycles for nitrate removal</b>]]> The efficiency of the application of a chemically-modified activated carbon surface was investigated. The purpose of this study was to examine the effect of treatment with CaCl2 solution at a concentration of 2000 mg.L-1 on the sorption of nitrate ions from aqueous solutions in successive sorption/t reatment cycles. The sorbent was initially subjected to chemical treatment with CaCl2 and subsequently to the sorption process. Nine sorption cycles were performed. The concentrations of nitrate ions in the solution were measured by UV-Vis spectrophotometry before and after sorption. The results show that treatment with CaCl2 caused a significant increase in the percentage removal for each treatment step, reaching a removal rate of 80% of nitrate in the solution after nine cycles. <![CDATA[<b>Biosorption study of Ni<sup>2+ </sup>and Cr<sup>3+</sup> by <i>Sargassum filipendula</i></b>: <b>kinetics and equilibrium</b>]]> In this work, the biosorption of Cr3+ and Ni2+ by Sargassum filipendula pre-treated with CaCl2 was studied. Kinetic and equilibrium experiments were carried out for mono- and multi-component solutions in a batch reactor at pH 3.0 and 30 ºC. The results from the kinetic experiments showed that Cr3+ adsorbs slower than Ni2+. This behavior was explained by means of a mechanistic analysis, which showed that Cr3+ uptake presented three adsorption stages, whereas Ni2+ adsorption presents only two. The mono-component equilibrium data, along with binary kinetic data obtained from mono-component experiments, showed that, although the kinetics for Cr3+ removal are slower, the biomass had a stronger affinity for this ion. Almost all Ni2+ is desorbed from the biomass as Cr3+ adsorbs. The binary equilibrium data also presented this behavior. The binary data was also modeled by using modified forms of the Langmuir, Jain and Snoeyink, and Langmuir-Freundlich isotherms. However, the prediction obtained presented low accuracy. An alternative modeling with artificial neural networks was presented and the results showed that this technique could be a promising tool to represent binary equilibrium data. The main contribution of this work was to obtain experimental data for Cr3+/Ni2+ adsorption, which is a system rarely found in the literature and that provides information that could be used in process modeling and simulation. <![CDATA[<b>Kinetic modelling of cadmium and lead removal by aquatic mosses</b>]]> Because biosorption is a low cost and effective method for treating metal-bearing wastewaters, understanding the process kinetics is relevant for design purposes. In the present study, the performance of the aquatic moss Fontinalis antipyretica for removing cadmium and lead from simulated wastewaters has been evaluated. Five kinetic models (first-order, pseudo-first-order, Elovich, modified Ritchie second-order and pseudo-second-order) were fitted to the experimental data and compared. Previously, the effect of parameters such as the initial solution pH, contact time, and initial metal ion concentration on biosorption was investigated. The initial pH of the solution was found to have an optimum value in the range of 4.0-6.0. The equilibrium sorption capacity of cadmium and lead by Fontinalis antipyretica increased with the initial metal concentration. For an initial metal concentration of 10 mg L-1, the uptake capacity of the moss, at equilibrium, is the same for both metals (4.8 mg g-1). Nevertheless, when the initial concentration increases up to 100 mg L-1, the uptake of Pb(II) was higher than 78%. The pseudo-second order biosorption kinetics provided the better correlation with the experimental data (R² ≥ 0.999). <![CDATA[<b>Solvent recovery from soybean oil/n-butane mixtures using a hollow fiber ultrafiltration membrane</b>]]> The aim of this work was the study on the separation of soybean oil/n-butane mixtures using a commercial hollow fiber ultrafiltration membrane (50 kDa). Oil/n-butane mixtures with mass ratios of 1:1 and 1:3 (wt), with the feed pressures of 5, 7 and 10 bar and transmembrane pressure of 1 bar were studied. Rejections of oil between 21 to 97.2%, oil fluxes between 0.04 and 0.98 kg/m² h and n-butane fluxes between 4 and 46 kg/m² h were observed, strongly influenced by the feed concentration. The increase in oil/n-butane mass ratio caused an increase in oil rejection and a decrease in the permeate flux of oil for most assays. The increase in the operating pressure caused an increase in oil flux and a consequent decrease in oil rejection. No degradation was observed in the membrane module during the operation with this non-aqueous feed stream, as confirmed by integrity tests. <![CDATA[<b>Solid-liquid stable phase equilibria of the ternary systems MgCl<sub>2</sub> + MgB<sub>6</sub>O<sub>10</sub>+ H<sub>2</sub>O AND MgSO<sub>4</sub> + MgB<sub>6</sub>O<sub>10</sub> + H<sub>2</sub>O at 308.15 K</b>]]> The solubilities and the relevant physicochemical properties of the ternary systems MgCl2 + MgB6O10 + H2O and MgSO4 + MgB6O10 + H2O at 308.15 K were investigated using an isothermal dissolution method. It was found that there is one invariant point, two univariant curves, and two crystallization regions of the systems. The systems belong to a simple co-saturated type, and neither double salts nor solid solutions were found. Based on the extended HW model and its temperature-dependent equations, the single-salt Pitzer parameters β(0), β(1), β(2) and CØ for MgCl2, MgSO4, and Mg(B6O7)(OH)6, the mixed ion-interaction parameters θCl,B6O10, θSO4,B6O10, ΨMg,Cl,B6O10, ΨMg,SO4,B6O10 of the systems at 308.15 K were fitted, In addition, the average equilibrium constants of the stable equilibrium solids at 308.15 K were obtained by a method using the activity product constant. Then the solubilities of the ternary systems are calculated. The calculated solubilities agree well with the experimental values. <![CDATA[<b>Simulation of ethanol extractive distillation with mixed glycols as separating agent</b>]]> Extractive distillation is an alternative for ethanol dehydration processes that has been shown to be more effective than azeotropic distillation and, in close proximity, to be very competitive against the process that uses adsorption with molecular sieves. Glycols have been shown to be the most effective solvents in extractive distillation, mainly ethylene glycol and glycerol. In this work, an extractive distillation column was simulated with the Aspen Plus software platform, using the RadFrac module for distillation columns, to investigate the effect on the separation of the ethylene glycol-glycerol mixture composition, the separating agent feed stages, the separating agent split stream feed, and the azeotropic feed temperature. The NRTL model was used to calculate the phase equilibrium of these strongly polar mixtures. A rigorous simulation of the extractive distillation column finally established was also performed, including a secondary recovery column for the mixture of solvents and a recycle loop, to simulate an industrially relevant situation. This simulation allowed establishing the complete parameters to dehydrate ethanol: the optimal stage for separating agent feed is stage 4; the most adequate composition for the glycols mixture is 60 mol% ethylene glycol and 40 mol% glycerol. Finally, energetically efficient operating conditions for each one of the columns were established through a preliminary pinch analysis.