Quadratic Model Equation Research Articles

Application of D-optimal design and RSM to optimize the transesterification of waste cooking oil using natural and chemical heterogeneous catalyst

ABSTRACTThis work illustrates a comparative study on the applicability of the natural calcium oxide (CaO) prepared from waste eggshells and chemical CaO as basic heterogeneous catalyst in the transesterification of waste cooking oil (WCO) with methanol for production of biodiesel. Response surface methodology (RSM) based on D-optimal design of experiments was employed to study the significance and interactive effect of methanol-to-oil (M:O) molar ratio, catalyst concentration, reaction time, and mixing rate on biodiesel yield. Second-order quadratic model equations were obtained describing the interrelationships between dependent and independent variables to maximize the response variable (biodiesel yield) and the validity of the predicted models were confirmed. The activity of the produced natural biocatalyst was comparable to that of chemical CaO, producing high yield of biodiesel ≈91 and 98% at 8.57:1 M:O, 3.99 catalyst wt%, 31 min reaction time, and 398.88 rpm mixing rate at 60°C, respectively. Fuel properties of the produced biodiesel were measured and compared with those of Egyptian petro-diesel and international biodiesel standards. The overall biodiesel characteristics either prepared using natural or chemical CaO were comparable and acceptable, encouraging the application of CaO prepared from waste eggshells for production of biodiesel as an efficient, environmentally friendly, sustainable, and low cost heterogeneous catalyst.

Optimization of preparation of CO3O4 by microwave calcination from basic cobalt carbonate

ABSTRACTThe parameters to prepare of Co3O4 by microwave calcination from basic cobalt carbonate were optimized based on the thermal gravity analysis–differential thermal gravity (TG–DTG) using with central composite concept of response surface methodology. A quadratic equation model for decomposition rate was built and rising behaviour of basic cobalt carbonate in fields of microwave and effects of main factors and their corresponding relationships on response were obtained. The results showed that a sample 20% addition of Co3O4 with the basic cobalt carbonate has ability to strongly absorb microwave energy, and the calcination temperature and calcination time significantly affect on the decomposition rate of basic cobalt carbonate in this range studied. The decomposition rate of basic cobalt carbonate was 99.56% under optimum calcination temperature 642.65 K, and calcination time 8.89 min and 4.34 g, respectively. The validity of the model was confirmed experimentally and the results were satisfactory. Furthermore, the Co3O4 was analysed using X-ray powder diffraction. It was feasible to prepare of Co3O4 by microwave calcination from the basic cobalt carbonate though addition of small amounts cobalt oxide.

Effect of Percent Relative Humidity, Moisture Content, and Compression Force on Light-Induced Fluorescence (LIF) Response as a Process Analytical Tool.

The effect of percent relative humidity (16-84% RH), moisture content (4.2-6.5% w/w MC), and compression force (4.9-44.1kN CF) on the light-induced fluorescence (LIF) response of 10% w/w active pharmaceutical ingredient (API) compacts is reported. The fluorescent response was evaluated using two separate central composite designs of experiments. The effect of % RH and CF on the LIF signal was highly significant with an adjusted R (2) = 0.9436 and p < 0.0001. Percent relative humidity (p = 0.0022), CF (p < 0.0001), and % RH(2) (p = 0.0237) were statistically significant factors affecting the LIF response. The effects of MC and CF on LIF response were also statistically significant with a p value <0.0001 and adjusted R (2) value of 0.9874. The LIF response was highly impacted by MC (p < 0.0001), CF (p < 0.0001), and MC(2) (p = 0022). At 10% w/w API, increased % RH, MC, and CF led to a nonlinear decrease in LIF response. The derived quadratic model equations explained more than 94% of the data. Awareness of these effects on LIF response is critical when implementing LIF as a process analytical tool.

Response Surface Optimization of the Thermal Acid Pretreatment of Sugar Beet Pulp for Bioethanol Production Using Trichoderma viride and Saccharomyces cerevisiae

Worldwide nowadays, relying on the second generation bioethanol from the lignocellulosic feedstock is a mandatory aim. However, one of the major drawbacks for high ethanol yield is the physical and chemical pretreatment of this kind of feedstock. As the pretreatment is a crucial process operation that modifies the lignocellulosic structure and enhances its accessibility for the high cost hydrolytic enzymes in an attempt to maximize the yield of the fermentable sugars. The objective of this work was to optimize and integrate a physicochemical pretreatment of one of the major agricultural wastes in Egypt; the sugar beet pulp (SBP) and the enzymatic saccharification of the pretreated SBP using a whole fungal cells with a separate bioethanol fermentation batch processes to maximize the bioethanol yield. The response surface methodology was employed in this study to statistically evaluate and optimize the conditions for a thermal acid pretreatment of SBP. The significance and the interaction effects of the concentrations of HCl and SBP and the reaction temperature and time were studied using a three-level central composite design of experiments. A quadratic model equation was obtained to maximize the production of the total reducing sugars. The validity of the predicted model was confirmed. The thermally acid pretreated SBP was further subjected to a solid state fermentation batch process using Trichoderma viride F94. The thermal acid pretreatment and fungal hydrolyzes were integrated with two parallel batch fermentation processes of the produced hydrolyzates using Saccharomyces cerevisiae Y39, that yielded a total of ≈ 48 g/L bioethanol, at a conversion rate of ≈ 0.32 g bioethanol/ g SBP. Applying the proposed integrated process, approximately 97.5 gallon of ethanol would be produced from a ton (dry weight) of SBP.

A Simpler Energy Transfer Efficiency Model to Predict Relative Biological Effect for Protons and Heavier Ions.

The aim of this work is to predict relative biological effectiveness (RBE) for protons and clinically relevant heavier ions, by using a simplified semi-empirical process based on rational expectations and published experimental results using different ion species. The model input parameters are: Z (effective nuclear charge) and radiosensitivity parameters αL and βL of the control low linear energy transfer (LET) radiation. Sequential saturation processes are assumed for: (a) the position of the turnover point (LETU) for the LET–RBE relationship with Z, and (b) the ultimate value of α at this point (αU) being non-linearly related to αL. Using the same procedure for β, on the logical assumption that the changes in β with LET, although smaller than α, are symmetrical with those of α, since there is symmetry of the fall off of LET–RBE curves with increasing dose, which suggests that LETU must be identical for α and β. Then, using iso-effective linear quadratic model equations, the estimated RBE is scaled between αU and αL and between βU and βL from for any input value of Z, αL, βL, and dose. The model described is fitted to the data of Barendsen (alpha particles), Weyrather et al. (carbon ions), and Todd for nine different ions (deuterons to Argon), which include variations in cell surviving fraction and dose. In principle, this new system can be used to complement the more complex methods to predict RBE with LET such as the local effect and MKM models which already have been incorporated into treatment planning systems in various countries. It would be useful to have a secondary check to such systems, especially to alert clinicians of potential risks by relatively easy estimation of relevant RBEs. In clinical practice, LET values smaller than LETU are mostly encountered, but the model extends to higher values beyond LETU for other purposes such as radiation, protection, and astrobiology. Considerable further research is required, perhaps in a dedicated international laboratory, using a basket of different models to determine what the best system or combination of systems will be to make proton and ion beam radiotherapy as safe as possible and to produce the best possible clinical results.

Effect of Tapped Density, Compacted Density, and Drug Concentration on Light-Induced Fluorescence Response as a Process Analytical Tool

The effect of tapped density, compacted density, and fluorescent drug concentration on the light-induced fluorescence (LIF) response is reported. The fluorescent response to powder mixtures containing 0.25%-10.00% w/w fluorescent active pharmaceutical ingredient (API) was evaluated over a density range of about 0.641-1.370 g/cm(3) . Blend concentrations up to 4.00% w/w API showed a linear trend in LIF response with increasing tapped and compacted density. API concentrations of 4.00% w/w or greater exhibited a negative parabolic trend in LIF response. The LIF responses were fitted to a quadratic model equation that included an interaction term between material density and API concentration (adjusted R(2) = 0.975 and p < 0.0001). All model terms were highly significant, including the material density-API concentration interaction (p < 0.0001). Being aware of the sensitivity of the LIF response to material density changes and the related changes in apparent concentration are important in implementing LIF as a process analytical tool for processes such as blending, roller compaction, and tableting.

Application of D-optimal Design and RSM to Optimize the Transesterification of Waste Cooking Oil Using a Biocatalyst Derived from Waste Animal Bones and Novozym 435

This study was performed to investigate the applicability of the basic heterogeneous fluorapatite catalyst prepared from waste animal bones in the transesterification of waste cooking oil with methanol for production of biodiesel. Response surface methodology based on D-optimal design of experiments was employed to study the significance and interactive effect of methanol to oil (M:O) molar ratio, catalyst concentration, reaction time, and mixing rate on biodiesel yield using the prepared fluorapatite and Novozym 435. Quadratic model equations were obtained describing the interrelationships between dependent and independent variables to maximize the response variable (biodiesel yield) and the validity of the predicted models were confirmed. The optimum combination for transesterification were determined to be 7.35:1 and 6:1 M:O, 4.35 and 8.8 catalyst wt%, 91 and 96 min, and 331 and 394 rpm at 60°C, for prepared fluorapatite and Novozym 435, respectively, with maximum biodiesel yield of ≈ 96 and 62%, respectively. Fuel properties of the produced biodiesel and its blends with petro-diesel were measured and compared with those of Egyptian petro-diesel and international biodiesel standards. Acceptable agreement was observed, encouraging application of fluorapatite prepared from waste animal bones for production of biodiesel as an alternative or complementary to petro-diesel.

Applying Factorial Design and Response Surface Methodology to Enhance Microbial Denitrogenation by Tween 80 and Yeast Extract

In this study the effect of yeast extract as a conitrogen source and Tween 80 as a commercial and available nonionic surfactant on microbial denitrogenation MDN of carbazole by Bacillus clausii BS1 was investigated. The central composite design matrix and response surface methodology were applied in designing the batch experiments to evaluate the interactive effects of these two parameters on MDN. Quadratic model equations have been predicted finding out how significant the effects of these variables (factors) and their interactions are in practice. The validity of the predicted models was confirmed. The MDN efficiency increased from ≈88% without yeast extract or Tween 80 to ≈95% in presence of optimum concentration of 0.868 g/L yeast extract and 0.861% (v:v) Tween 80, which would represent a major economic improvement in low-margin, high-volume refining processes.

Waste Eggshells for Production of Biodiesel from Different Types of Waste Cooking Oil as Waste Recycling and a Renewable Energy Process

Based on 3-levels-D-optimal design, involving as factors: methanol:oil, molar ratio; catalyst concentration, wt%; reaction time, min; and type of waste cooking oil, a statistical design of experiments strategy was performed to evaluate and investigate the biodiesel production process from different types of waste cooking oil using CaO prepared from waste eggshells. MATLAB software was employed for experimental design and data analysis. An empirical quadratic regression equation model was obtained describing the interrelationships between dependent and independent variables to maximize the response variable (biodiesel yield). The optimum values of the selected predictor variables were obtained by solving the quadratic model equation using LINGO software. They were found to be: methanol:oil, 9.15:1 molar ratio; catalyst concentration, 7.728 wt%; and reaction time, 75 min, regardless of the type of waste cooking oil used as the feedstock. The qualification and yield of biodiesel were comparable to those prepared using chemical CaO and immobilized standard enzyme Novozym 435.

Modeling Fluoride Adsorption on Cerium-Loaded Cellulose Bead—Response Surface Methodology, Equilibrium, and Kinetic Studies

A novel cerium-loaded cellulose nanocomposite bead (CCNB) is synthesized and tested for fluoride adsorption. The optimization of the process under the cooperative influence of different experimental variables was made employing response surface methodology (RSM). It is found from fractional factorial design (FFD) that among the different experimental variables, only adsorbent dose, temperature, and pH are significant. At the optimum condition (adsorbent dose 1 g L−1, temperature 313 K, pH 3.0), a maximum fluoride adsorption of 94 % was observed for an initial fluoride concentration of 2.5 mg L−1. A quadratic polynomial model equation based on central composite design (CCD) was built to predict the extent of adsorption. The result of the analysis of variance (ANOVA) shows high coefficients of determination (correlation coefficient; R 2 = 0.9772, adjusted R 2 = 0.9545, and adequate precision = 18.1045) and low probability value (Prob > F, 0.001) which signifies the validity of the model. The equilibrium adsorption data conformed to the Tempkin isotherm, having higher R 2 and lower SE value, among the Langmuir, Freundlich, and Tempkin equations at different temperatures. The adsorption data was found to fit well the second-order rate equation with film diffusion governing the overall rate. The activation energy value was calculated to be 16.74 kJ mol−1. Fluoride can be eluted from fluoride-loaded CCNB using alkali. CCNB can be reused at least for five successive operations.

Process optimization for vacuum distillation of Sn–Sb alloy by response surface methodology

Based on the molecular interaction volume model (MIVM), the vapor–liquid phase equilibrium of Sn–Sb alloy was calculated, which was used to predict the element distribution of Sn–Sb alloy between vapor and liquid phase during vacuum distillation. A central composite design (CCD) was used to optimize the process parameters influencing the content of Sn in liquid phase and the direct yield of Sn. The studied parameters were distillation temperature, feeding materials and soaking time. Two quadratic mathematical model equations were derived for predicting the content of Sn in liquid phase and the direct yield of Sn. The analysis of variance (ANOVA) shown that distillation temperature was the most significant factor affecting the separation of Sn–Sb alloy. In the process optimization, while the direct yield of Sn equal to 92%, the maximum content of Sn in liquid phase should be 99.66 wt.% under the conditions of 1531 K, 137 g and 46 min. The confirmation test values of 91.22% and 99.43 wt.% were fair agreement with the predicted data, which demonstrated that these models were very good and can be used for parameter optimization in vacuum distillation.

Activated Carbon Production from Agricultural Biomass Using Response Surface Method (RSM) for Cd (II) Removal

The production of activated carbon (AC) from sugarcane bagasse (SCB) was carried out using central composite design of response surface method to run a limited number of experiments with the possibility of revealing the interaction of three selected factors of temperature, time and nitrogen/steam flowrate at different levels. Two second order quadratic regression model equations were developed using statistical analysis with Design Expert® software. The models were used for the prediction of removal of Cd2+ and carbon yield. Correlation coefficients (R2) were 0.957 for removal and 0.985 for yield, showing the sufficiency of the model in predicting response within 13 experimental runs. Characterization of the product with optimal performance which was produced at 900oC, with nitrogen/steam flow of 100 mL/min and activation time of 30 minutes, was carried out. The performance showed this AC sample was able to remove 62.42% Cd2+ from an aqueous solution with concentration 2 mg/L within 2 hours at optimized conditions. Experimental results indicated that AC from SCB had good prospect for Cd2+ removal.

Response surface optimization of milling parameters for synthesis of carbon nanotubes/Al5083 by powder metallurgy

Carbon nanotube/Al5083 composite material has been synthesized by powder metallurgy. And the yield strength has been predicted by mathematical models. The parameters such as milling time, rotary speed and carbon nanotube concentration are considered independent variables. The experiments were carried out based on the central composite design. The experimental results were analyzed by the analysis of variance, which revealed that the quadratic model was statistically significant. And the optimal milling parameters were 104 min milling time, 798 r/min rotary speed and 2.95 wt% carbon nanotube concentration. Under these conditions, the predicted yield strength was 179 MPa. The quadratic equation model can also predict the maximum yield strength at different concentrations of carbon nanotubes. By comparing the predicted yield strength by the Orowan strengthening model and the coefficient of thermal expansion model, it was shown that the coefficient of thermal expansion model overestimated yield strength. And the increase in strength can be explained by the Orowan strengthening mechanism.

The Optimization of Biodiesel Production from Waste Frying Sunflower Oil Using a Heterogeneous Catalyst

This study was performed to optimize a base heterogeneous CaO catalyzed transesterification process for biodiesel production from waste frying sunflower oil. Response surface methodology based on central composite face centered design was employed to statistically evaluate and optimize the conditions for maximum production of biodiesel and study the significance and interaction of methanol to oil (M:O) molar ratio, catalyst concentration and reaction time on biodiesel yield. A quadratic model equation was obtained for biodiesel production and the validity of the predicted model was confirmed. The optimum combination for transesterification was determined to be 7.05:1 M:O, 8.21 CaO wt% and 1.5 h at 60°C, and mixing rate of 300 rpm. The maximum predicted and actual biodiesel yield was 92.2 and 93%, respectively. The reusability of used CaO was investigated and recorded sufficient biodiesel production up to four cycles. The fuel properties of the produced biodiesel were measured and compared with those of Egyptian petro-diesel and international biodiesel standards. Acceptable agreement was observed, encouraging application of biodiesel as an alternative or complementary to petro-diesel.

Optimization and kinetics of nutrient removal from wastewater by chemical precipitation of struvite

Nutrient removal by the precipitation of struvite from synthetic municipal wastewater was tested. Response surface methodology with the Box–Behnken experimental design was employed to determine the optimal phosphorus removal efficiency with the influencing process variables of pH, temperature, magnesium to phosphorus molar ratio, mixing speed (rpm), and organic contents. Under the values of pH, temperature, Mg to P ratio, mixing, and organic content of 9.86, 26.5°C, 1.64, 80 rpm, and 1,020 mg sugar/l, respectively, optimum phosphorus (PO4-P) removal efficiency of 90.1% was obtained. Results of analysis of variance indicated that the quadratic model predicts the responses adequately with the five factors that coded the process variables. The effects the factors have on the amount of PO4-P removal were ranked (with their relative scores) in the descending order of pH (11.8), Mg:P ratio (6.2), organic content (2.4), mixing speed (1.1), and temperature (0.5), where the ranking quantifications were according to the respective coefficients of the factors in the quadratic model equation. Removal of nitrogen (NH4-N) was limited by equal molar amount of PO4-P removed and thus the remaining NH4-N must be subsequently treated using usual nitrogen removal processes.

Optimization on Response Surface Methodology for Preparing V2O5 from Industrial Ammonium Metavanadate

AbstractIn order to obtain the vanadium pentoxide, the process of vanadium pentoxide preparation by calcination from industrial ammonium metavanadate was further investigated. The effects of calcination temperature and calcination time were studied. The conditions of technique to prepare vanadium pentoxide in flakes by calcination from industrial ammonium metavanadate were optimized using a central composite design of response surface methodology. A quadratic equation model for field was built and effects of main factors and their corresponding relationships were obtained. The statistical analysis of the results showed that in the range studied, the rate of weight loss of the industrial ammonium metavanadate was significantly affected by the calcination temperature and calcination time. The results showed that the optimum conditions of ammonium metavanadate calcination were as follows: sample mass 15 g, calcination temperature 900 °C, calcination time 2.4 h, the rate of weight loss 85.1%. In addition, the sample was characterized by XRD and SEM. The SEM analysis and XRD showed the product was layer structure. According to results from analysis of variance, the value of the determination coefficient (R2 = 0.9417) indicates that the model was a good fit that 94.17% of the variation could be explained well by the model.

The Optimization of Bio-diesel Production from Waste Frying Oil Using Response Surface Methodology and the Investigation of Correlations for Changes in Basic Properties of Bio-petro-diesel Blends

Bio-diesel is derived from renewable sources and is steadily gaining attention and significance for use as an alternative or in blends with petro-diesel. In this study, bio-diesel was produced by alkaline-catalyzed transesterification process of waste frying oil at 60°C and 300 rpm. Response surface methodology, based on a central composite design, was employed to statistically evaluate and optimize the conditions for maximum conversion to bio-diesel and to study the significance and interaction of methanol to oil molar ratio, catalyst concentration, and reaction time on bio-diesel yield. A quadratic model equation was obtained for bio-diesel conversion by multiple regression analysis and the validity of the predicted model was confirmed. The optimum combinations for transesterification were determined to be methanol to oil, 9:1; catalyst amount, 0.6%; and reaction time, 1 h. The optimum and actual bio-diesel yields were 99.13 and 98.90%, respectively. The fuel properties of the produced bio-diesel and bio-petro-diesel blends were measured and compared with those of petro-diesel and the American Society for Testing and Materials standards for bio-diesel and bio-petro-diesel blends, and acceptable agreement was observed. Correlations were also established to describe the changes of basic properties of the produced fuel with the volumetric percentage of the bio-diesel for the bio-petro-diesel blends.

An investigation of biodiesel production from wastes of seafood restaurants.

This work illustrates a comparative study on the applicability of the basic heterogeneous calcium oxide catalyst prepared from waste mollusks and crabs shells (MS and CS, resp.) in the transesterification of waste cooking oil collected from seafood restaurants with methanol for production of biodiesel. Response surface methodology RSM based on D-optimal deign of experiments was employed to study the significance and interactive effect of methanol to oil M : O molar ratio, catalyst concentration, reaction time, and mixing rate on biodiesel yield. Second-order quadratic model equations were obtained describing the interrelationships between dependent and independent variables to maximize the response variable (biodiesel yield) and the validity of the predicted models were confirmed. The activity of the produced green catalysts was better than that of chemical CaO and immobilized enzyme Novozym 435. Fuel properties of the produced biodiesel were measured and compared with those of Egyptian petro-diesel and international biodiesel standards. The biodiesel produced using MS-CaO recorded higher quality than that produced using CS-CaO. The overall biodiesel characteristics were acceptable, encouraging application of CaO prepared from waste MS and CS for production of biodiesel as an efficient, environmentally friendly, sustainable, and low cost heterogeneous catalyst.

Microwave-low-pressure process (MWLP): An effective technology applied in extraction of total polyphenols

Abstract: The microwave-low-pressure process (MWLP) of total polyphenols from Chaenomeles speciosa fruit was studied, and the advantages of MWLP were further evaluated by comparing with ultra high pressure (UHP) and microwave-assisted extraction (MAE). The influences of liquid/solid ratio, extraction time, pressure, and ethanol concentration on the performance of MWLP were investigated. Thereafter, the interactive variables were further optimized by the stepwise multiple quadratic regression model on the basis of the previous univariate analysis. The results showed that temperature as an intermediate variable in MWLP significantly affected the yields of polyphenols and 3-o-caffeoyl-quinic acid, which was determined by pressure and ethanol concentration. The optimized parameters were proved to be valid because the results predicted by the stepwise multiple quadratic regression model equations fit well with the experimental results. Compared with UHP, the predominance of MWLP was that the extraction time was shortened and the cost of extraction equipment was lowered. MWLP is an effective technology since MWLP was superior to MAE based on extraction yield, solvent loss and reproducibility. Keywords: Microwave-low-pressure process (MWLP), total polyphenols, Chaenomeles speciosa fruit, model optimization, performance evaluation DOI: 10.3965/j.ijabe.20130604.010 Citation: Hu Z Q, Jia L L, Yue T L. Microwave-low-pressure process (MWLP): An effective technology applied in extraction of total polyphenols. Int J Agric & Biol Eng, 2013; 6(4): 84－95.

Application of response surface methodology to optimize degradation of polyacrylamide in aqueous solution using heterogeneous Fenton process

Response surface methodology was employed to investigate the individual and interaction effect of the independent variables on the degradation of polyacrylamide (PAM) in aqueous solution by heterogeneous Fenton process with Fe2+–Al2O3 catalyst. pH, catalyst and H2O2 dosage were chosen as independent variables, and the degradation of PAM was chosen as the response value. A predictive polynomial quadratic equation model was developed by ANOVA as well as analysing the response surface plots and their corresponding contour plots. Response surface analysis results showed that the chosen variables had important correlation with the degradation of PAM in aqueous solution. The optimum conditions of heterogeneous Fenton process were determined to be pH of 4.80, 0.82g L−1 catalyst and 20.64 mmol L−1 H2O2, under which the degradation ratio of PAM (initial concentration 1000 ppm) reached 95.68%. The adequacy of the model for predicting the optimum response values was verified by the experiment effectively. After five recycle, the Fe2+–Al2O3 still maintain high catalysis activity.