Application of factorial design to SMC viscosity build-up

Summary The thickening behavior of SMC varies with formulation and operating conditions. During the SMC compounding process, alkaline oxides such as MgO, Mg(OH)₂, CaO, Ca(OH)₂ are added to the formulation to yield the viscosity build-up from a flowable paste to a semi-solid sheet. The thickening curve of SMC can be divided into three stages: 1. The initial thickening period for the wetting process, 2. The middle thickening rate period for viscosity increasing, 3. The final viscosity period for the molding process. By means of factorial design with an appropriate objective set-up, one is able to define the influence of each factor on thickening curves. Combined with the experimental work on some individual factors, the maturation control system can be further understood and the proper thickening rates can be obtained.     

Application of the factorial design of experiments to biodiesel production from lard

Synthesis of biodiesel from lard was carried out using potassium hydroxide as a catalyst. A 3² factorial design of experiments was used. The effects of agitation speed and catalyst concentration were studied. A regression model was obtained to predict the methyl ester concentration and adequately describe the experimental range studied.     

Application of factorial experimental design to study the influence of polymerization conditions on the yield of polyaniline powder

Influences of chemical oxidation polymerization conditions on the yields of polyaniline powder were investigated. These chemical oxidation polymerization conditions included polymerization time, concentration of HNO₃, mol ratio of ammonium persulfate/aniline (APS/AN), and polymerization temperature. If polymerization time, concentration of HNO₃, mol ratio of APS/AN, and polymerization temperature were 60 min, 1.0 M, 1.0, and 0°C, respectively, then the yield of emeraldine base form polyaniline powder was around 78.1%. The yield of polyaniline powder increased significantly with the polymerization time, concentration of HNO₃, and the mol ratio of APS/AN. A 2³ factorial experimental design was applied to study the main, two‐factor interaction, and three‐factor interaction effects of polymerization time, concentration of HNO₃, and mol ratio of APS/AN on the yield of polyaniline powder. According to the definition, the sequence of the main effects on the yield of polyaniline powder, in ascending order, is concentration of HNO₃ < mol ratio of APS/AN < polymerization time. The sequence of the two‐factor interaction effects on the yield of polyaniline, in ascending order, is concentration of HNO₃ vs. mol ratio of APS/AN < polymerization time vs. concentration of HNO₃ < polymerization time vs. mol ratio of APS/AN. Meanwhile, the prediction equation by definition is: ? = 0.287+0.145X₁+0.091X₂+0.121X₃+0.023X₁X₂+0.111X₁X₃+0.002X₂X₃+0.003X₁X₂X₃. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 1571–1580, 2002     

Application of chitosan to cobalt recovery: Evaluation by factorial design of experiments

A natural polymer in a commercially available form (chitosan) has been tested using a factorial design of experiments for its application to cobalt recovery either in hydrometallurgy and in analytical separations. A simple mechanically stirred system has been used, evaluating the influence of the contact time, iron(II), cobalt (II), chitosan concentration, salinity, and pH in the separation. The pH value has a dramatic influence on the metal recovery from a negligible amount of metals at pH = 1.0 to a quantitative sorption at pH = 3.0. Linear relationships between sorbed metal and the variables have been determined at constant pH value and a quantitative evaluation of the metal recovery at different pH values can be performed using the maximum sorption capacity of the chitosan (a₀) and the selectivity for both metals. The obtained results allow the evaluation of the recovery of metals using chitosan as solid phase.     

Application of the factorial design of experiments to hydrothermal synthesis of lithium iron phosphate

The mathematical model of lithium iron phosphate prepared by hydrothermal method was established by factor experimental design. The effect of individual variables and their interactions were studied by the main effects plot and Interaction plot. The influence of ascorbic acid dosage on the discharge specific capacity was greater than the hydrothermal time and the hydrothermal temperature, and the influence degree of the latter two was equivalent and the interaction effect of hydrothermal time and ascorbic acid dosage has the greatest influence on the discharge specific capacity in three interaction effects. The optimized hydrothermal condition was hydrothermal time of 9 hours, hydrothermal temperature of 210°C and ascorbic acid dosage of 1.5 mmol in the experimental design range, with the initial discharge specific capacity of 0.1 C as 152.5 mAh g⁻¹. The corresponding characterization was performed using electrochemical methods, XRD, SEM, and TEM. This study provided a protocol to factorially design better experiments to achieve excellent battery criterion in the context of lithium iron phosphate preparation.     

Experimental design methodology applied to study a diamond purification process

The synthesis of graphite at higher pressure and temperature conditions in the presence of a catalyst–solvent metallic alloy is a commonly applied process for industrial diamond production. The product obtained after this synthesis is an agglomerate composed by diamonds crystals, metallic particles, non-transformed graphite and other compounds. The diamond extraction from the agglomerates is known as purification. In this work the diamond purification process by alkaline melt was studied by statistical methods. It was shown that the alkaline melt could be a very efficient process and environmentally correct procedure for diamond purification.     

Application of a simulated annealing algorithm to design and optimize a pressure-swing distillation process

The design and optimization of pressure-swing distillation (PSD) have a critical impact on its economics. An optimization method based on simulated annealing algorithm (SAA) was proposed. The move generator and cooling schedule of the SAA were discussed, and suitable parameter settings were investigated. Two cases of PSD with and without heat integration were optimized by the SAA-based optimization method using procedures of pressure specified and pressure optimized. The results of the process without heat integration were compared with conventional optimization methods. For the acetone-methanol system, the total annual cost (TAC) shows a 5.69% decrease with the pressure specified and a 17.32% decrease with the pressure optimized. For the methanol-chloroform system, the TAC shows a 1.79% decrease with the pressure specified and a 9.04% decrease with the pressure optimized. The SAA-based optimization method has the advantages of a high probability to obtain the global optimum, automatic calculation, and less computing time.     

Application of graph theory to process design and analysis

Graph Theory and related computational techniques have been applied to a wide range of problems in process design and analysis to facilitate visualization, formulation, computation and interpretation. These applications are illustrated with selected examples. Most problems of practical importance are of such size and complexity that their solution requires using algorithms on a computer. Many problems we encountered in the last 20 years were solved using pollynomial time algorithms. We are now likely to have to conend with some harder and some ill-defined problems, which call for different approaches. Recent development in computational complexity theory provides us with a very useful perspective and some valuable tools, which we did not have 10 years ago. Alternatives for dealing with these hard but practically important problems are outlined and discussed in this paper.     

Full factorial experimental design to study the devulcanization of ground tire rubber in supercritical carbon dioxide

In this study a 2⁴ factorial design was employed to investigate the supercritical CO₂ devulcanization process of ground tire rubber from end of life tires performed using diphenyl disulfide (DD) as devulcanizing reagent.The aim of the experimental design was to investigate the influence on the process of temperature, pressure, amount of devulcanizing reagent, treatment time and their interactions.The crosslink density, sol fraction, gel fraction and sulfur content were chosen as experimental responses. Multiple linear regression was used for modeling the relationship between each response and the process variables. Reduced regression models were obtained for each response, considering only the significant variables and interactions. The predicted results from these reduced models showed good agreement with the experimental values.Temperature, amount of DD and DD–temperature interaction resulted the relevant parameters for the process. On the contrary, the influence of treatment time, pressure and all other interactions proved to be negligible.These results have an important outcome since this devulcanization process can be carried out in a short time and at relatively low pressure, with subsequent energy saving.     

A factorial design applied to polypropylene functionalization with maleic anhydride

Maleic anhydride functionalized PP was prepared in a melt-mixer according to a factorial design. Two levels of maleic anhydride concentration (MA), dicumyl peroxide concentration (DCP), reaction time, and temperature were employed. The isolated and interaction effects of these variables on the degree of functionalization and molecular weights were analyzed. The products were characterized by Fourier transform infrared spectroscopy (FTIR), gel permeation chromatography (GPC), titration, and torque measures. The reaction time showed no appreciable effect within the studied range (10 to 20 minutes); however, the other three factors showed significant main effects. MA and temperature presented an important interaction effect on the degree of functionalization and molecular weights. The highest degrees of functionalization were found to be related to the smallest molecular weights.     

Optimizing polyimide cure using infrared spectroscopy and a factorial design

The cure of a polyimide derived from pyromellitic dianhydride (PMDA) and oxydianiline (ODA) has been studied using infrared spectroscopy. A factorial experimental design, combined with regression analysis, was used to find the optimum curing conditions. It was shown that five micron films can be cured by heating at 230–250°C for times of five minutes or longer, while samples cured initially at 150°C did not cure completely when heated to higher temperatures.     

Design and optimization of a dividing wall column by factorial design

A factorial design methodology was applied to the design of a dividing wall column, solving the complex multivariable problems and simultaneously optimizing the interacting variables to achieve the best design with respect to total annual cost. Column structure was practically optimized with a minimum of simulation runs. The proposed design method was tested in the design and optimization of an NGL recovery system; it allowed interactions between variables to be identified and quantified. The column system designed by the proposed method reduced reboiler energy consumption and total annual cost by 28.23% and 25.49%, respectively, in case 1, and those by 25.63% and 18.85%, respectively, over conventional distillation in case 2.     

Application of factorial experimental design to the study of the suspension polymerization of β‐cyclodextrin and epichlorohydrin

The suspension polymerization of β‐cyclodextrin (β‐CD) with epichlorohydrin (EP) has been studied using a fractionated factorial design with two levels and six variables (β‐CD:EP molar ratio, NaOH concentration, temperature, stirring speed, delay time before paraffin addition, and β‐CD concentration). Different variables, such as the amount of β‐CD in the product, particle size, degree of swelling, and sorption capacity, have been analyzed as the responses for the synthesized polymers. The experimental design approach permitted to select the optimal conditions of synthesis depending on the desired features of the product. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 3393–3402, 2006     

Study of the process of stirred ball milling of poorly water soluble organic products using factorial design

The objective of this work was to investigate the mechanism of very fine grinding in a wet ball mill as a function of process parameters, i.e. rotation speed of the mill and grinding medium bead size. The ball mill used was a Dynomill and the grinding medium consisted of zirconium oxide beads. The product is a poorly water-soluble organic compound. Laser diffraction was used to analyze the particle size distribution.During grinding the average particle diameter of the product was reduced to a minimum size, which was constant within the range of tested operating conditions.The grinding parameters were studied to control the grinding process with respect to the required grinding time for reaching the minimum particle size and wear of the set-up.The grinding time was strongly dependent on the grinding medium bead size and on the rotation speed. The grinding process became faster when the rotation speed increased and the grinding medium bead size decreased. The wear of the set-up, and therefore the contamination of the final product with heavy metals, strongly increased with the rotation speed. A similar trend was observed with an increase of grinding medium bead size. The degradation rate of the product was not significant in the range of grinding parameters studied.     

Ceramic suspension optimization using factorial design of experiments

The influence of organic phases (binder and two plasticizers) on ZnO slip viscosity and the properties of green tape were studied using design of experiments (DOE). Analysis of the results show no significant influence of the three components on slip viscosity and green tape density, but joint influence of two factors—binder polyvinyl butyral (PVB) and plasticizer polyethylene glycol (PEG)—is significant on green tape adhesion to the substrate tape of casting machine.     

析因分析法分析酶标板筛选结果

目的利用析因分析法对筛选酶标板数据进行分析。方法应用析因分析法探讨厂家、批次及板列分布3个自变量主效应或交互效应对酶标板A_(450-620)值的影响。结果厂家(P0.001)和板列分布(P=0.003)均对酶标板A_(450-620)值的主效应显著,二者的交互作用(P0.001)对酶标板A_(450-620)值也有影响。结论酶标板A_(450-620)值与厂家、板列分布及二者交互作用相关。     

Application of generic principles of process intensification to solution crystallization enabled by a task-based design approach

The design of current industrial crystallizers is strongly focussed on optimization of known types of crystallization equipment. These crystallizers harbour various physical phenomena, which are strongly entangled. The application of generic principles of process intensification (PI) to crystallization processes requires individual control over physical phenomena. A new design method is applied that exploits elementary processing functions as building blocks for design instead of existing equipment, which enables the application of generic principles of PI. Innovations in the field of crystallization to manipulate shear forces, manipulate nucleation rates with external fields, and improve control over solvent removal with membranes are key technologies. A case study demonstrates the application of task-based design for solution crystallization. The results show how task-based design leads to high modularization of the process representation and model architecture. In addition, task-based design enables the application of generic PI principles, which results in a large flexibility to manipulate final product quality. Future needs include generalization of task-based design for crystallization and development of novel technologies for single task manipulation.     

A study of antifungal antibiotic production by Thermomonospora sp MTCC 3340 using full factorial design

The three independent variables, viz concentration of carbon source (glucose), concentration of nitrogen source (soybean meal) and temperature of incubation were found to be the most important for production of antifungal antibiotic by the isolate Thermomonospora sp MTCC 3340 from one‐factor‐at‐a‐time study. These variables were varied at three levels in a total number of 27 experiments designed using full factorial design. The results on analysis using the statistical software SPSS (version 6.0) indicated that the optimum combination of the three factors for the maximum yield of the antibiotic was concentration of carbon source (glucose) 2%, concentration of nitrogen source (soybean meal) 1% and temperature of incubation 30 °C. A close fit between experimental and predicted values of the antifungal yield was obtained using one of the modes derived from the statistical analysis, indicating that this model was applicable to this production. Copyright © 2003 Society of Chemical Industry     

Electrochemical treatment of methyl parathion based on the implementation of a factorial design

Commercial methyl parathion was treated by an electrochemical method using Ti/Pt as anode, Stainless Steel 304 as cathode and sodium chloride as electrolyte. Based on a number of preliminary experiments, a factorial experimental procedure was designed in order to optimize the electrolysis efficiency, in terms of removed COD and energy consumed kW h per kg of removed COD. The parameters examined were the temperature, the stirring rate of the brine solution, the input rate of the organic material, the current density, the electrolyte concentration and the concentration of Fe ²⁺ ions added. In the experimental range studied, the lower energy consumption measured was 6.61 kW h ( kg COD _r) ^–1 and the higher COD reduction measured was 86.3. From a mathematical model, the optimum conditions for the electrochemical treatment of MeP for 2.03 kW h ( kg COD _r) ^–1 were found to be Input rate of MeP 4300 mg COD min^–1, NaCl concentration 4.5, 4 g l^–1 of added FeSO₄, current density 0.47 A cm^–2, temperature 45 °C and stirring rate 400 rpm. An experiment was conducted under these optimum conditions which resulted in a satisfactory removal of the organic load (in terms of COD, BOD ₅). Furthermore, a significant improvement in the COD/BOD₅ ratio was achieved, rendering the effluent amenable to further biological treatment.     

Mineralization of phenol by a heterogeneous ultrasound/Fe-SBA-15/H2O2 process: Multivariate study by factorial design of experiments

A novel heterogeneous catalyst has been used for the oxidation of aqueous solutions of phenol by catalytic wet peroxide oxidation assisted by ultrasound irradiation. This composite catalyst material that contains crystalline hematite particles embedded into a mesostructured SBA-15 matrix was used successfully in the oxidation of phenol by heterogeneous Fenton and photo-Fenton processes. Ultrasound is found to enhance the activity of the catalyst in the process, without prejudice to the stability of the iron supported species. The influence of different variables, such as hydrogen peroxide concentration or catalyst loadings in the reaction was studied by factorial design of experiments. Catalyst loadings of 0.6 g L⁻¹ and a concentration of hydrogen peroxide close to twice the stoichiometric amount yield a remarkable organic mineralization, accompanied by excellent catalyst stability. The coupled US/Fe-SBA-15/H₂O₂ process at room temperature is revealed as a promising technique for wastewater treatment.