Juan C. Gottifredi

Isothermal effectiveness factor—II: Analytical expression for single reaction with arbitrary kinetics, geometry and activity distribution

Abstract A previously presented method[1], to predict isothermal effectiveness factor with a single complex reaction in isothermal slab pellets is extended to encompass much more complex and general situations. In this work the geometry of the pellet can be arbitrary and a non uniform distribution of the catalyst is considered. Though the previously presented method[1] has had to be slightly modified to predict with great accuracy the effectiveness factor, (with less than 3% deviation from the exact values), an almost general and very simple algebraic expression is deduced to predict effectiveness factor values within 10% of their respective exact values. Thus for many applications in engineering design and catalytic reactor simulation, this simple general expression can be extremely useful since only one easily generated parameter is needed, as shown throughout the present contribution.

Thermodynamics of the absorption of hydrocarbon vapors in polyethylene films

Abstract Solubility of n-butane, n-pentane, n-hexane and n-heptane vapors in polyethylene membranes was measured with an accurate gravimetric technique as a function of temperature, within the range of 258 to 318 K, and relative vapor pressure of hydrocarbons (up to 0.95). The results are analyzed with the scope of establishing a unique expression to predict the solubility of the hydrocarbon vapors. It is shown that such an expression exists and can be used with a fair degree of accuracy to estimate both solubility and solubility coefficients, in spite of the marked deviation of the experimental results from Henrys law. The effect of temperature over the whole range investigated is also well correlated, and the isoplethic heat of absorption was calculated, showing that its values are independent both of temperature and solubility. The Flory-Huggins theory was also used to analyze experimental results and the values of the interaction parameter were calculated, which can be used in turn to predict solubility and solubility coefficients of hydrocarbon vapors.

Isothermal effectiveness factor—I: Analytical expression for single reaction with arbitrary kinetics. Slab geometry

Abstract An analytical simple algebraic expression for isothermal effectiveness factor (η) in a porous pellet is presented. Arbitrary kinetic expressions are investigated and the external mass transfer effect is also considered. The resulting analytical expression is found after matching asymptotic expressions of η valid for large and small values of Thiele modulus. The agreement between approximated and numerical results is surprisingly good. For most cases analyzed maximum deviation are below 3% for power law type kinetic expressions provided the reaction order is greater than 0.5. More severe limitation arises for Langmuir-Hinshelwood kinetic expressions. In actual facts the proposed analytical expressions is unable to predict effectiveness factor greater than one. Nevertheless, as will be shown in future works, this very simple procedure can be safely used to predict the effectiveness in more complex situations such as those where activity distribution must be considered or where the kinetic parameters will be function of composition and/or spatial coordinates.

The analysis of sorption data of organic vapors in polymeric membranes through novel theories

Abstract Analysis of sorption data of hydrocarbon vapors in polyethylene and polypropylene films using Flory-Huggins, UNIFAC. Michael-Hausslein and Flory-Rehner theories are presented. Basically two models are used, one deduced with UNIFAC and Michael-Hausslein (UNIFAC-M-H) approach and the other with UNIFAC and Flory-Rehner (UNIFAC-F-R) theory. Prediction of penetrant activity values through these theories fit quite well the experimental results with errors ranging between 4.7 and 10.8%. The mean arithmetic values of the fraction of elastically effective chain in the amorphous region are f =0.4915 and f =0.3354 for polypropylene (PP) and polyethylene (PE), respectively. The experimental results with polypropylene are correlated, establishing a unique expression to predict solubility and solubility coefficient. The dependence of solubility in polypropylene over the whole range of temperature it is also presented.

Mechanical properties of a high amylose content corn starch based film, gelatinized at low temperature Propriedades mecânicas de filme a base de amido de milho de alto teor de amilose gelatinizado em baixa temperatura

Summary In the present study, a better knowledge of the influence of plasticizer content, storage relative humidity and film thickness on the mechanical properties of high amylose corn starch based films gelatinized at low temperature, is presented. The mechanical properties, tensile strength and percentage of elongation at break of high amylose corn starch films plasticized with glycerol were evaluated using tension tests. The films exhibited an increase in elongation and a decrease in tensile strength with increasing plasticizer concentration. When the glycerol level was high, some fissures were detected in the dry films, possible due to phase separation (starch-glycerol) phenomena. Film crystallinity is related to the reorganization capacity of the polymer chain, and thus the relative film crystallinity should increase with plasticizer content (glycerol and water). The mechanical properties were found to be strongly dependent on the water content due to the hydrophilic nature of starch films. The influence of moisture sorption on tensile strength was similar to that of plasticization with glycerol. The relationship between polymer chain mobility and water content explained this behavior. Elongation suffered a different effect and maximum values were reached at 45% relative humidity. The final drop in elongation was due to a softening of the structure at high relative humidity. The thicker the film the longer the drying time required, leading to greater relative crystallinity due to the corresponding increase in the possibility for chain reorganization. As a consequence, linear increases in tensile strength and elongation were observed with film thickness over the whole range studied (30 to 100 µm).

Effectiveness factors and selectivity for parallel catalytic reactions with Langmuir-Hinshelwood kinetics

Les reactions ont lieu dans un reacteur catalytique a lit fixe. Les calculs sont menes par la methode des perturbations

General diagnostic criteria for transport limitation in porous solid chemical reactions

Abstract Theoretical criteria for establishing the absence of heat and mass transport limitations are of fundamental importance in chemical reactor engineering. Many criteria have been proposed in the past, but they cover only particular situations. This work shows that only two general expressions are needed to establish the absence of either intraparticle or interphase mass and heat transport. They encompass all previous theoretical findings and cover new cases. Moreover, when properly applied, the procedure can be used to generate useful criteria for systems with more than one reaction.

An approximate expression for predicting concentration and temperature profiles inside a catalyst pellet

The scope of this contribution is to develop an approximate expression based on the available information, since η (effectiveness factor) values are related to the slope of concentration in a region near the surface. Since η values can be accurately predicted, it is possible to build up an approximate expression that also describes the profiles inside the particle

Heat transfer to power-law fluids flowing in pipes and flat ducts with viscous heat generation

Abstract This paper aims to show the application of the analytical approach presented recently by Gottifredi [ Int. J. Heat Mass Transfer 26 , 1215–1220 (1983)] to the generalized Graetz—Nusselt problem, in order to estimate the mixing-cup temperature of a power-law fluid which is flowing through a duct whose walls are maintained at constant temperature. Steady and laminar flow conditions as well as constant thermophysical properties of the fluid are assumed. The effect of heat generation by viscous dissipation is also considered. The technique is very simple and a unique expression of the mixing-cup temperature valid for both cylindrical and plane geometries is generated. This expression provides results which are in good agreement with those reported by previous authors in the whole range of Graetz numbers (0 ⩽ Gz ⩽ ∞).

Effectiveness factor and selectivity estimation for a parallel reaction system

Abstract The case of double parallel reaction scheme taking place in a porous catalytic pellet is analyzed. Effectiveness factor expressions for both reactions are derived after matching asymptotic solutions strictly valid for small and large values of the Thiele moduli. It is assumed that the kinetics of both reactions follow a general irreversible power law model, that isothermal conditions prevail and that external m Approximate results in terms of effectiveness factors compare fairly well with exact results obtained by numerical integration of the differential equa