Fractional factorial design study of a pressure swing adsorption-solvent vapor recovery process

A two-level fractional factorial study was performed by computer simulation on the periodic state process performance of a pressure swing adsorption-solvent vapor recovery process (PSA-SVR). The goal was to investigate factor (parameter) interaction effects on the process performance, i.e., interaction effects that cannot be ascertained from the conventional one-at-a-time approach. Effects of seven factors, i.e., the purge to feed ratio, pressure level, pressure ratio, heat transfer coefficient, feed concentration, feed volumetric flow rate and bed length to diameter ratio, on the process performance were investigated. The results were judged in terms of the light product purity, heavy product enrichment (and relative enrichment) and recovery, and bed capacity factor. Only the purge to feed ratio, pressure ratio, and feed concentration had significant effects on the benzene vapor enrichment (and relative enrichment); and no two-factor and higher interactions were observed. The light product purity was affected by all seven factors; and the relative importance of the effect of each factor depended on the levels of the other factors, i.e., significant two-factor interaction effects existed. Two-factor interaction effects also existed on the benzene vapor recovery, although the effects of all seven factors and their interactions were relatively small. The bed capacity factor was affected mainly by the purge to feed ratio, the heat transfer coefficient and the feed concentration; two factor and higher order interaction effects were insignificant. Overall, this study demonstrated the utility of fractional factorial design for revealing factor interactions and their effects on the performance of a PSA-SVR process.Nomenclature BCF bed capacity factor, % - b, b ₀ isotherm parameters, m³/(mol K^0.5) - C _pg gas phase heat capacity, kJ/(kg K) - C _ps solid phase heat capacity, kJ/(kg K) - E enrichment - E _I ideal enrichment - E _R relative enrichment - H heat transfer coefficient, kJ/m² s K) - H heat of adsorption, kJ/mol - k number of factors, or mass transfer coefficient, l/s - l number of levels - L bed length, m - LD bed length to diameter ratio - PF purge to feed ratio - P _H adsorption high pressure, kPa - P _L desorption pressure, kPA - PL pressure level, represented byP _I - PR pressure ratio - q amount adsorbed, mol/kg - q ^xx equilibrium amount adsorbed, mol/kg - q ^xx _j equilibrium amount adsorbed at the feed conditions, mol/kg - r _b bed radius, m - R solvent vapor recovery, % or gas constant, m³ (mole K) - T temperature, K - T ₀ ambient temperature, K - t time, s - u interstitial velocity, m/s - VF volumetric feed flow rate, m³ STP/s - YF feed mole fraction - Y _p light product mole fraction - z axial coordinate, m Greek Symbols _g gas phase density, kg/m³ - _s solid phase density, kg/m³ - bed void fraction     

Optimisation-based simulation of a pressure swing adsorption process

In this paper, an optimisation-based approach is developed for the determination of the cyclic steady-sate (CSS) of a pressure swing adsorption process (PSA). It consists in treating the simulation problem as a single dynamic optimisation problem where the performance index is the CSS condition, the decision variables are the state variables at the start of the cycle and the constraints are given by the process model equations with associated initial conditions. The resulting optimisation problem is solved using a gradient-based non linear programming (NLP) method, e.g. SQP method, where the gradients are computed by means of four different methods: finite differences, numerical and analytical sensitivities and adjoint system methods.     

Effect of variable feed concentration on the performance of a pressure swing adsorption process

Effects of variable feed composition on the performance of a pressure swing adsorption process are analyzed by simulation. Two scenarios are considered. The first, increasing impurity, case considers low impurity concentration in the feed followed by high impurity concentration in the feed. The second, decreasing impurity, case considers high impurity concentration in the feed followed by low impurity concentration in the feed. These results are compared against a case which has an impurity concentration in the feed at an average of the high and the low impurity concentrations. Simulations show that the increasing impurity scenario is expected to perform better, and the decreasing impurity scenario is expected to perform worse than the average feed concentration case.     

Experimental design for copper cementation process in fixed bed reactor using two-level factorial design

This work deals with cementation of copper onto iron grid in a fixed bed reactor. The influence of several parameters is studied, namely: initial concentration of copper [Cu²⁺]₀, temperature and flow rate. Moreover, their influence on the copper cementation reaction is investigated statistically by the experimental design in view of industrial application. The estimation and the comparison of the parameter’s effects are realized by using two-level factorial design. The analysis of these effects permits to state that the most influential factor is initial concentration of copper [Cu²⁺]₀ with an effect of (+2.4566), the second in the order is the temperature with an effect of (+0.18959), the third is the flow rate of the electrolytic solution with an effect of (?0.4226). The significance interactions found by the design of experiments are between initial concentrations of copper ions–flow rate (x₁x₃) with an effect (b₁₃ = +0.6965).     

Fractional factorial design in modeling of polyethyleneimine modified magnetic yeast composites for the removal of uranium with various background ions

Journal of Radioanalytical and Nuclear Chemistry - Polyethyleneimine (PEI) modified magnetic yeast biomaterials composites (MY@SiO2-PEI) were prepared through a two-step solution polymerization...     

A factorial design for optimizing a flow injection analysis system

The use of a factorial design for the response exploration of a flow injection (FI) system is described and illustrated by FI spectrophotometric determination of paraquat. Variable response (absorbance) is explored as a function of the factors flow rate and length of the reaction coil. The present study was found to be useful to detect and estimate any interaction among the factors that may affect the optimal conditions for the maximal response in the optimization of the FI system, which is not possible with a univariate design. In addition, this study showed that factorial experiments enable economy of experimentation and yield results of high precision due to the use of the whole data for calculating the effects.     

A factorial design for optimizing a flow injection analysis system

The use of a factorial design for the response exploration of a flow injection (FI) system is described and illustrated by FI spectrophotometric determination of paraquat. Variable response (absorbance) is explored as a function of the factors flow rate and length of the reaction coil. The present study was found to be useful to detect and estimate any interaction among the factors that may affect the optimal conditions for the maximal response in the optimization of the FI system, which is not possible with a univariate design. In addition, this study showed that factorial experiments enable economy of experimentation and yield results of high precision due to the use of the whole data for calculating the effects.     

Application of factorial design to the study of xylitol production from eucalyptus hemicellulosic hydrolysate

This study deals with the bioconversion of xylose into xylitol by Candida guilliermondii FTI 20037 using eucalyptus hemicellulosic hydrolysate obtained by acid hydrolysis. The influence of various parameters (ammonium sulfate, rice bran, pH, and xylose concentration) on the production of xylitol was evaluated. The experiments were based on multivariate statistical concepts, with the application of factorial design techniques to identify the most important variables in the process. The levels of these variables were quantified by the response surface methodology, which permitted the establishment of a significant mathematical model with a coefficient determination of R ²=0.92. The best results (xylitol=10.0 g/L, yield factor=0.2 g/g, and productivity=0.1 g/[L·h]) were attained with hydrolysate containing ammonium sulfate (1.1 g/L), rice bran (5.0 g/L), and xylose (initial concentration of 60.0 g/L), after 72 h of fermentation. The pH of fermentation was adjusted to 8.0 and the inoculum level utilized was 3 g/L.     

Application of factorial design to improve a FIA system for penicillin determination

A potentiometric FIA system for penicillin determination, employing penicillinase [E.C. 3.5.2.6] immobilized on silica gel, packed into a reactor, was improved by the use of statistically designed experiments. A two-level and three-factor factorial was used to find the best working conditions evaluating the influence of some parameters on the signal response of the system and the number of determinations per hour. These parameters were analyzed individually obtaining two level of the variables to be used in the factorial design: length of the reactor (1.5 and 2.0 cm), carrier flow rate (1.6 and 2.2 ml min⁻¹) and sample volume (100 and 150 μl). The pure error on the measurements was estimated by authentic repetitions. The ideal working conditions taking into account a compromise between the best response signal and the number of determinations per hour (with the same importance) being chosen the level of factors: length of reactor 1.5 cm, carrier flow rate 2.2 ml min⁻¹ and sample volume of 150 μl. Under these conditions the system allowed to analyze was about 45 samples per hour, during 73 days, with a standard deviation of 2.4% at concentration range between 10⁻¹ and 10⁻³ mol l⁻¹.     

Simulation of pressure swing adsorption modules having laminated structure

A mathematical model was formulated for the bulk separation of binary gas mixtures in micro-structured pressure swing adsorption (PSA) modules consisting of parallel channels lined with adsorbent. Axial and radial dispersion in the gas phase and mass transfer resistance in the adsorbent phase were taken into consideration. The partial differential equations governing the concentration profiles in the gas and adsorbent phases were solved by orthogonal collocation. The model enabled the prediction of the concentration profiles in both the gas and adsorbent phases (as a function of location and time), the product purity and the separation efficiency. The effects of model parameters and operating conditions on the module performance were investigated. Simulation of oxygen enrichment from air by molecular sieve 13X indicated that long modules with thin layers of adsorbent, narrow gas flow channel heights and large numbers of flow channels give the best separation.     

Thermogravimetric measurements of liquid vapor pressure

A method was developed using thermo-gravimetric analysis (TGA) to determine the vapor pressure of volatile liquids. This is achieved by measuring the rate of evaporation (mass loss) of a pure liquid contained within a cylindrical pan. The influence of factors like sample geometry and vapor diffusion on evaporation rate are discussed. The measurement can be performed across a wide range of temperature yielding reasonable results up to 10 kPa. This approach may be useful as a rapid and automatable method for measuring the volatility of flavor and fragrance raw materials.     

Development of a quick leaching test for monolithic materials by using factorial design

A quick leaching test procedure for monolithic waste materials has been developed by a Nordic expert group using experimental factorial design. The Dutch quick leaching test proposal in which the wetting time of the test specimen is reduced by applying vacuum was chosen as a starting point. The influence of the following parameters were studied: vacuum, stirring, open or closed vessel, water renewal frequency, leachant quality and laboratory or batch differences. The study was performed with test specimens prepared from a cement stabilised soil containing As, Cr and Cu. The test specimens were immersed in water and the water was renewed at certain time intervals. The study clearly showed that the use of vacuum had a strong effect on the release rate and that the open vessel lowered the pH-values of the eluates due to uptake of carbon dioxide in the water. The results also indicate higher emissions when stirring was applied. The following test conditions are recommended: application of vacuum prior to testing, use of closed test vessel, use of stirring, a test time of 3 days with four water renewals after 15 min vacuum steps, and then after e.g. 2 h, 23 h and 3.2 days, use of demineralised water as leachant. The amount of water must be selected according to the size of the test specimen. A liquid to surface (L/A) ratio of 5-10 ml cm(-2) is recommended. All four eluates collected are filtered and analysed.     

Application of factorial design to study of heavy metals biosorption by waste biomass from beverage distillery

A full factorial design leading to 20 sets of sorption runs was conducted to study the influence of four variables (bleaching earth and biomass concentrations, pH, and sorption time) on the iron, nickel, and chromium removal from stainless steel effluent using waste biomass from a beverage industry. Similar factor effects and interactions were found for each metalinvolved in this biosorption study, and the main factors were pH (positive effect) and biomass concentration (negative effect). Response surface methodology was adopted and an empirical linear polynomial model constructed on the basis of the specific uptake (mg of metal/g of biomass as dry weight) for each metal species. Under optimized process conditions (pH 4.0, biomass concentration of 2.0 g/L, absence of Celite), uptake values of 155 mg of Fe/g, 38 mg of Cr/g, and 0.4 mg of Ni/g were achieved after 3 h. This corresponded to a reduction in heavy metals concentration of approx 94% for Cr, 57% for Fe, and 25% for Ni.     

Production of oxygen enriched air by rapid pressure swing adsorption

A novel rapid pressure swing adsorption (RPSA) process is described for production of 25–50% oxygen enriched air. The embodiment consists of one or more pairs of adsorbent layers contained in a single adsorption vessel. The layers undergo simultaneous pressurization-adsorption and simultaneous depressurization-purge steps. A total cycle time of 6–20 seconds is used. The process yields a very large specific oxygen production rate and a reasonable oxygen recovery for production of 20–50 mole% oxygen enriched gas.It is demonstrated by a simple mathematical model of isothermal single adsorbate pressure swing ad(de)sorption concept on a single adsorbent particle that the specific production rate of a PSA process cannot be indefinitely increased by reducing the cycle time of operation when adsorbate mass transfer resistances are finite.     

Carbon dioxide sorbents with propylamine groups-silica functionalized with a fractional factorial design approach

Mesoporous silica particles (Davisil) were functionalized with aminopropyltriethoxysilane (APTES) in a fractional factorial design with 19 different synthesis and uptake experiments. The number of amino groups and the uptake of CO(2) were optimized in a 2(V)(5-1) design. Most important to functionalization was the amount of water present during synthesis, the reaction time, and pretreating the silica with a mineral acid; certain two-way interactions were shown to be statistically significant as well. Modifications performed at 110 or 80 °C showed no significant differences concerning amine content or uptake of CO(2). Properly choosing center points for the discrete variables is problematic and is somewhat related to the lack of fit with respect to CO(2) uptake; the regression was good. Solid-state (29)Si NMR showed that the APTES was mainly fully condensed. Specific surface areas did not correlate with the number of n-propylamine groups on the silica, which is indicative of differential levels of heterogeneity in the coverage of propylamines. The uptake of CO(2) and N(2) was measured from -20 to 70 °C and from 0 to 1 bar and parametrized by the Freundlich isotherm. Amine-modified silica adsorbed significant amounts of CO(2), especially at the low partial pressure, which is important for CO(2) capture from flue gas. At such pressures, samples with a high density of amine (4 amines/nm(2)) showed a much higher uptake of CO(2) than did those with densities of ～2-3 amines/nm(2), reflecting differential tendencies to form propylammonium-propylcarbamate ion pairs; these require close proximity among amine groups to form. Water affected the uptake of carbon dioxide in different ways. Certain samples took up more moist CO(2) gas than dry CO(2), and others took up less moist CO(2) than dry CO(2), which is indicative of differential tendencies toward water adsorption. We conclude that experimental design is a time-efficient approach to the functionalization of silica with propylamine groups.     

Application of sequential factorial design and orthogonal array composite design (OACD) to study combination of 5 prostate cancer drugs

Prostate cancer is one of the most common cancers among men in the United States. It is also a major leading cause of cancer death among men of all races. In order to treat prostate cancer, drug combinations are often applied. Drug combinations target at different pathways of cells can potentially lead to higher efficacy and lower toxicity due to drug synergy. In this paper, we sequentially applied a two-level design and a follow-up orthogonal array composite design (OACD) to investigate combinations of five anti-cancer drugs, namely, doxorubicin, docetaxel, paclitaxel, cis-dichlorodiamine platinum and dihydroartemisinin. Our initial screening using a two-level full factorial design identified doxorubicin and docetaxel as the most significant drugs. A follow-up experiment with an OACD revealed more complicated drug interactions among these 5 anti-cancer drugs. Quadratic effects of doxorubicin and paclitaxel appeared to be significant. A further investigation on contour plots of all the two-drug pairs indicated that combination of doxorubicin and docetaxel are the most effective companion, while the combination of cis-dichlorodiamine platinum and dihydroartemisinin showed unknown antagonistic effects which diminished the individual drug anti-cancer efficacy. These observations have significant practical implications in the understanding of anti-cancer drug mechanism that can facilitate clinical practice of better drug combinations.     

Optimization of inulinase production by Kluyveromyces marxianus using factorial design

Factorial design and response surface techniques were used to optimize the culture medium for the production of inulinase by Kluyveromyces marxianus. Sucrose was used as the carbon source instead of inulin. Initially, a fractional factorial design (2^5–1) was used in order to determine the most relevant variables for enzyme production. Five parameters were studied (sucrose, peptone, yeast extract, pH, and K₂HPO₄), and all were shown to be significant. Sucrose concentration and pH had negative effects on inulinase production, whereas peptone, yeast extract, and K₂HPO₄ had positive ones. The pH was shown to be the most significant variable and should be preferentially maintained at 3.5. According to the results from the first factorial design, sucrose, peptone, and yeast extract concentrations were selected to be utilized in a full factorial design. The optimum conditions for a higher enzymatic activity were then determined: 14 g/L of sucrose, 10 g/L of yeast extract, 20 g/L of peptone, 1 g/L of K₂HPO₄. The enzymatic activity in the culture conditions was 127 U/mL, about six times higher than before the optimization.     

A study of physicochemical and biopharmaceutical properties of amoxicillin tablets using full factorial design and PCA biplot

The variables that influence the tablets obtained by direct compression method deserve to be studied to minimize formulations costs and to improve the physicochemical and biopharmaceutical properties of the compacts. Here, we explore the adjuvants effects on amoxicillin tablet formulations considering multiple responses, and indicate the most suitable formulation composition. A 2(3) full factorial design was built to different amoxicillin formulations, each one containing three replicate batches, and eight responses (physicochemical and biopharmaceutical parameters) were obtained. The microcrystalline cellulose (MCC) type Avicel PH-102 (low) or PH-200 (high), the absence (low) or presence (high) of spray-dried lactose (LAC), and the absence (low) or presence (high) of disintegrant (DIS) were the levels investigated. The more relevant responses to the distinct formulations from the experimental design were hardness, friability, and the amount of amoxicillin dissolved during the first hour. PCA biplot indicated high values of amount of drug dissolved in 60 min as advantageous responses for the investigated amoxicillin tablet formulations and high values of friability as not desirable. Considering the individual response evaluation, the most suitable amoxicillin tablet formulation should present in its composition the MCC type Avicel PH-102 (low level) and the superdisintegrant agent (DIS high level), croscarmellose sodium, but no LAC (low level).