EFFECT OF PORE DIFFUSION IN METHANOL SYNTHESIS

Pore diffusion limitations dampen the sensitivity of temperature runaway to variations in the coolant temperature in methanol synthesis reactors. For an isothermal pellet and low product concentration, the relationship between catalyst effectiveness and the Thiele parameter can be represented with a single curve. However, when equilibrium is approached or at high product concentrations, the relationship between catalyst effectiveness and the Thiele parameter becomes a function of catalyst surface temperature. For large temperature gradients in the catalyst, the effectiveness factor can significantly increase and parametric sensitivity in the relationship between catalyst effectiveness and the Thiele parameter may result.     

EFFECTS OF PORE DIFFUSION ON THE SYNTHESIS OF METHANOL

The hierarchical model concept is applied for solving of the test-problem. Three levels of hierarchy are defined. On the first one the reaction rate at an inner point of a pore in the catalyst pellet is examined. On the 2-nd level, taking pore diffusion into account and introducing the so-called distortion factor, the mean reaction rate concerning a pellet is calculated. On the 3-rd level, the rate of reaction at an inner point of the reactor is given, and the parametric study of industrial reactor is carried out.     

EFFECT OF PORE DIFFUSION ON DEACTIVATING RATES OF SECOND ORDER REACTION

The research and development of catalysts, the design and operation of catalytic reactors are complicated by the phenomenon of catalyst deactivation which is affected by various factors. In this paper, the effect of internal mass transfer resistance in the second order catalytic reaction system of uniform independent deactivation on both reaction and deactivation rates of straight cylindrical pore model has been discussed. In addition, the quantitative relations between effectiveness factor and Thiele modulus in second order reaction and first order deactivation system have been correlated     

ADDITION OF PORE DIFFUSION LIMITATION TO THE “UCKRON-I” KINETIC RATE OF METHANOL SYNTHESIS

Kinetic data with pore diffusion limitation on methanol synthesis were generated by extending the “UCKRON-I” kinetic rate expression. The best fit model and the extended “true” model were compared using their respective rates to simulate temperature profiles in a non-isothermal plug flow tubular reactor.

The objective of this work was to add pore diffusion resistance to the UCKRON-1 kinetic rate for methanol synthesis (Berty, et al. 1983). Kinetic modeling of the data with 5% experimental error added, showed the best model to be that developed from a previous kinetic model (Shalabi, et al. 1983) with apparent activation energy approximately one-half the activation energy at no pore diffusion.

Methods used in this work to determine and evaluate pore diffusion parameters can be utilized for other reaction systems where pore diffusion may play a role in reaction rate.

Temperature profiles estimated from reactor simulation studies showed good argeement between ideal and predicted models for temperature.     

CONFINEMENT EFFECTS ON ADSORPTION AND DIFFUSION OF HEXANE IN NANOPOROUS MCM-41 WITH DIFFERENT PORE SIZES: A MOLECULAR DYNAMICS STUDY

We report the results of molecular dynamics (MD) simulations using a new semi-empirical intermolecular interaction potential on the adsorption and diffusion of hexane in siliceous MCM-41 at 300 K. The potential function is tuned to give an adsorption energy of ? 9.1 kcal/mol, reproducing the experimental value for a corresponding pore size. We investigated MCM-41 models with four different pore sizes and studied loadings from one molecule of hexane up to a loading corresponding to the density of liquid hexane. As a result of confinement in MCM-41, the free energy of adsorption of hexane increases when the pore sizes decrease; for example, the adsorption energy increases from ? 9.1 to 13.7 kcal/mol for the largest to the smallest pore size for a loading of one molecule. Also, the adsorption energy increases by 3–4 kcal/mol for all pore sizes when the loading is increased from one hexane molecule to the density of liquid hexane. The calculated self-diffusion coefficients of hexane in MCM-41 with a pore diameter of 27 Å are in the order of 1 × 10^?5 cm²/s, depending on the loading, which is in reasonable agreement with available experimental data. The self-diffusion coefficients decrease with increasing loadings and when the pore sizes decrease. The average distance between the centers of the mass of hexane molecules in the smallest pores is only marginally less than in the larger pores and in the liquid phase. For low loadings the hexane molecules lie parallel to the pore channel for every pore size. When the loading is increased, they build up concentric rings. These rings of hexane molecules are less well separated from each other in the larger models, and thus their structure more resembles the liquid phase.     

MULTICOMPONENT LIQUID PHASE ADSORPTION IN BATCH PART I FORMULATION AND DEVELOPMENT OF COMPUTATION ALGORITHMS

Algorithms were developed which can be used to predict the dynamics of multicomponent adsorption in batch. These algorithms were developed on the following bases: (a) the rate of adsorption is controlled by both external and intraparticle diffusion, (b) the intraparticle diffusion is described by either the pore or the surface diffusion models, and (c)the multicomponent adsorption equilibrium behavior can be predicted from the ideal adsorbed solution (IAS)theory. The availability of these algorithms makes it possible to predict concentration histories of batch adsorption processes involving an arbitrarily large number of adsorbates from a minimum amount of base information obtained from single-species adsorption measurements.     

EXPERIMENTAL AND THEORETICAL STUDY OF THE PORE STRUCTURE AND DIFFUSION PROPERTIES OF AN EVOLVING HETEROGENEOUS MATERIAL: APPLICATION TO RADIOACTIVE BITUMINIZED WASTE

Placed in a geological repository, radioactive bituminized waste (BW) could be altered in the long term by water, leading to the release of chemical and radioactive elements. The main difficulty, in terms of experimental characterization, comes from the fact that the BW material evolves in time due to the swelling associated to the water osmotic flux. To overcome this difficulty, a new approach is proposed in this work, based on the leaching of BW samples in aqueous solutions where the chemical activity of water is controlled. These specific leaching conditions allow one to control the swelling of the degraded BW matrix. The chemical activity of water being fixed, the pore structure of the leached BW samples was quantitatively studied by ESEM pictures further treated by image analysis. In parallel, diffusion cells using radioactive tracers were used in order to measure mass transfer characteristics in the leached BW. Coupling image analysis with diffusion experiments for each degradation state leads to a diffusion coefficient-porosity relation that is then compared to standard diffusion models in biphasic materials.     

EXPERIMENTAL AND THEORETICAL STUDY OF THE PORE STRUCTURE AND DIFFUSION PROPERTIES OF AN EVOLVING HETEROGENEOUS MATERIAL: APPLICATION TO RADIOACTIVE BITUMINIZED WASTE

Placed in a geological repository, radioactive bituminized waste (BW) could be altered in the long term by water, leading to the release of chemical and radioactive elements. The main difficulty, in terms of experimental characterization, comes from the fact that the BW material evolves in time due to the swelling associated to the water osmotic flux. To overcome this difficulty, a new approach is proposed in this work, based on the leaching of BW samples in aqueous solutions where the chemical activity of water is controlled. These specific leaching conditions allow one to control the swelling of the degraded BW matrix. The chemical activity of water being fixed, the pore structure of the leached BW samples was quantitatively studied by ESEM pictures further treated by image analysis. In parallel, diffusion cells using radioactive tracers were used in order to measure mass transfer characteristics in the leached BW. Coupling image analysis with diffusion experiments for each degradation state leads to a diffusion coefficient-porosity relation that is then compared to standard diffusion models in biphasic materials.     

THE EFFECT OF PORE DIFFUSION ON THE SHAPE OF THE PH AND TEMPERATURE PROFILES OF IMMOBILIZED ENZYMES

The effect of diffusion on the pH and temperature profiles of immobilized enzymes has been quantitatively assessed using the theory of pore diffusion. The pH profiles of immobilized enzyme systems varied from those of soluble ones to the square root of the relative values of the soluble ones depending on the degree of pore diffusion limitation. Also the decrease in activation energy was predicted quantitatively with considerable accuracy in terms of effectiveness factor. The experimental pH profiles of a few immobilized enzymes were compared with those theoretically predicted.     

MULTICOMPONENT LIQUID PHASE ADSORPTION IN BATCH PART I FORMULATION AND DEVELOPMENT OF COMPUTATION ALGORITHMS

Algorithms were developed which can be used to predict the dynamics of multicomponent adsorption in batch. These algorithms were developed on the following bases: (a) the rate of adsorption is controlled by both external and intraparticle diffusion, (b) the intraparticle diffusion is described by either the pore or the surface diffusion models, and (c)the multicomponent adsorption equilibrium behavior can be predicted from the ideal adsorbed solution (IAS)theory. The availability of these algorithms makes it possible to predict concentration histories of batch adsorption processes involving an arbitrarily large number of adsorbates from a minimum amount of base information obtained from single-species adsorption measurements.     

EFFECTS OF SOLUTE ADSORPTION ON HINDERED DIFFUSION UPTAKE RATES IN FINITE BATH EXPERIMENTS

This work investigates the effects of solute adsorption on hindered diffusion behavior in porous catalysts. A mathematical model describing the adsorptive diffusion process is developed. The model, termed the shrinking pore model, incorporates the local reduction in catalyst pore diameter due to the adsorption of solute molecules on the pore walls. The influence of the adsorbed solute layer is found to depend on two additional parameters, reflecting the relative degree of adsorption and molecule/pore size ratio. Hindered diffusion experiments are performed for diffusion controlled adsorptive uptakes of two solute molecules, quinoline and polystyrene, from cyclohexane on a porous catalyst. Comparison of the experimental data and model simulation results shows that for the larger polystyrene solute the shrinking pore model better represents the uptake behavior than the conventional model which assumes constant catalyst properties, e.g. pore diameter, during the uptake process. Experimental measurements were found to be in good agreement with model simulations after accounting for additional hindered diffusional effects due to an adsorbed solute layer on the pore walls. The additional hindrance due to the adsorbed solute was found to be very significant for the uptake of the larger polystyrene solute, whereas it was not significant for the smaller quinoline solute.     

A MATHEMATICAL MODEL CHARACTERIZING THE DIFFUSION PROPERTIES OF MICROCAPSULES

Composite techniques are developed for numerical solutions of partial differential equations (PDE's) by the combinations of different solutions. The combination can be global or local depending on the usage of the composite. A global composite is one in which the composite solution is not utilized in any continued calculations of the different numerical solutions. Global composites are space by space combinations, i.e., the solutions are obtained over the entire space of independent variables. For local combinations, on the other hand, the composite is used in the continued calculations of the different solutions. Therefore, the local procedure is a line by line algorithm where the different solutions are combined and become the initial values for the continued calculations of the different solutions.

Composites considered are (i) global extrapolation, (ii) local extrapolation and local stabilization, (iii) alternating direction methods, and (iv) acceleration. By extrapolation the solution over the space of independent variables is calculated and combined with solutions for successively smaller grid spacings, characterized by h_m . Global extrapolation is applied to the finite difference solution of PDE's and shown to be effective for reducing the truncation error (TE) of fixed difference methods. On the basis of computation time the spacing sequence h₀ (m + 1) is shown to reduce the TE more efficiently than fco/2m for more than two extrapolations, where /i0 characterizes the largest spacing.     

孔隙对陶瓷球接触疲劳寿命的影响分析

本文通过陶瓷球接触疲劳寿命试验，分析了陶瓷球孔隙对陶瓷球接触疲劳寿命的影响，提出了提高陶瓷球接触疲劳寿命的方法。     

固定化静止酵母细胞的扩散─反应特性的模拟

测定了聚丙烯酰胺包埋酵母的固定化细胞中葡萄糖和乙醇的有效扩散系数，研究了葡萄糖和乙醇对于悬浮静止酵母细胞反应动力学的影响．计算了固定化静止细胞中酵母细胞的存活分数，考察了具有不同细胞包埋量及不同厚度的固定化细胞的反应特性。用组分的有效扩散系数、悬浮细胞的反应动力学及固定化细胞的细胞存活分数很好地模拟了具有内扩散影响的固定化细胞的反应结果。     

STRUCTURAL AND PARAMETRIC SENSITIVITY OF “UCKRON-1” TEST PROBLEM

The sensitivity of a specified tabular reactor to thermal runaway is simulated using a model for the UCKRON-1 Test Problem. Parametric sensitivity was increased by the increase of coolant temperature and by the increase of inlet temperature and pressure. Extension of the Test Problem by the water-gas shift reaction reduced the productivity and sensitivity of the reactor. Addition of the water-gas reaction represents the sensitivity for runaway to the structure of the model. These observations lead to a strategy for maximizing the methanol production within a range where thermal runaway does not occur.     

THE “UCKRON-1” TEST PROBLEM FOR REACTION ENGINEERING MODELING

Testing kinetic models against a “true” and detailed kinetic expression was the aim of the Workshop on Kinetic Model Development at the Denver AIChE Meeting in August, 1983. For this purpose an artificial reaction mechanism was created, based on the known thermodynamics of the methanol synthesis as a framework. The kinetic rate laws, that were derived from this mechanism, were made thermodynamically consistent by achieving agreement between equilibrium constants calculated at various temperatures from the given, real original thermodynamic relationship and those calculated from the detailed reversible kinetic expressions.

Using the artificial kinetics as the "true" one, CSTR experiments were simulated. The results of a statistically designed set of experiments were published after 5% random error was added to the data. Participation was invited for all interested to correlate the data, develop kinetic models and to calculate the performance of the specified reactor.

The results of 19 submitted entries are summarized with the conclusion that the models had more differences than were expected, but their predictive values were not as different as was anticipated, if the extreme high production rates due to thermal runaways are not considered. This in turn points out the necessity to check models experimentally, in pilot plant, not only for predicted optimum, but also for calculated runaway conditions. Models which did not capture the true character of this reaction failed to predict the onset of runaway reactions.     

THE TWO-THIRDS POWER MODEL FOR PREDICTING DIFFUSION COEFFICIENTS IN LIQUIDS

Most of the models found in the literature for predicting diffusion coefficients in liquids take the viscosity of the solution as inversely proportional to the diffusivity. A model (previously derived for sucrose-water system)which considers the viscosity raised to the two-third power, is evaluated here using published data for the Benzene—Cylohexane, Ethanol-Water and Acetone-Chloroform systems. These results, and results for the sucrose-water system are compared with the experimental values, and with those obtained using the Hartley—Crank equation. Better agreement with the experimental values at low and in the middle of the concentration range was found when diffusivities were calculated using the model proposed than when using the Hartley-Crank equation.     

MOLECULAR DIFFUSION OF VOLATILE-LIQUID VAPORS INTO AIR

Diffusion coefficients of vapors diffused into stagnant air were determined at room temperature and atmospheric pressure. Experimental data on diffusion coefficients were obtained from the steady-state open-tube evaporation method modified for this study. No fresh air is passed over the top end of a diffusion tube, and amounts of volatile liquids evaporated in the diffusion tube are measured with a balance rather than a change of the liquid level in a diffusion tube. Experimental molecular diffusion coefficients are obtained by applying experimental data of mass losses of volatile liquidsversusevaporation durations to a diffusion equation developed suitable for the novel open-tube evaporation method. Three main experimental errors of the novel open-tube evaporation method are described in detail. Predicted diffusion coefficients are calculated with the Wilke-Lee method and compared with experimental values obtained from this diffusion study.     

活性炭孔结构及润湿性对混合型超级电容器电化学性能的影响

以Ni（OH）2和活性炭为正负极组成复合电化学电容器。用氮吸附和接触角测定润湿性以恒流充、放电等表征方法，研究孔径、比表面积、浸润性对混合电容器电化学性能的影响。结果表明：高润湿性的活性炭有利于电容器容量的提高；具有较多中孔含量的活性炭有利于电容器大电流充放电性能的提高。     

ON BROWNIAN DYNAMICS WITH HYDRODYNAMIC WALL EFFECTS: A PROBLEM IN DIFFUSION NEAR A FIBER,AND THE MEANING OF THE NO-FLUX BOUNDARY CONDITION

An analysis is presented of the steady-state diffusion of spherical Brownian partcles through an effectively infinite expanse of fluid perforated by a circular cylindrical fiber. Detailed Stokes-flow calculations quantify the solute-fiber hydrodynamic interaction in three regimes covering the full range of solute-fiber separations, and lead to an approximate expression for the position-dependent diffusion dyadic. Thereafter, solution of the pertinent Brownian dynamic problem yields the perturbation caused by the fiber to a linear variation of the solute concentration. The results illustrate a general conclusion, derivable by simple scaling arguments, that the normal derivative of the solute concentration must tend to zero with decreasing solute-wall gap ε as [ln(1/ε)]^?1