George B. DeLancey

An optimal catalyst activation policy for poisoning problems

Abstract Pontryagins minimum principle is used to calculate the optimum distribution of active material throughout a single pellet that is uniformly experiencing activity decay. The definition of optimality is based upon balancing catalyst costs against the net return from reactant conversion. The optimal policy is full activation to a fractional depth with an inert core, the depth depending upon the Thiele parameter, poisoning time constant, operating time, and an economic parameter. An isothermal, first order, irreversible reaction is considered. Auxiliary calculations of the effectiveness factor are given for the reaction rate in the nonisothermal pellet with the catalyst distribution found to be optimal in the isothermal case. The results of the pellet calculations are utilized in numerically calculating a uniform activation policy that is optimal for a homogeneously poisoned bed. The definition of optimality is on the same basis as that for the single pellet and the results depend upon the same physical parameters in addition to the time constant for convection in the tube relative to that for diffusion in the pellets. Four regimes of behavior arise depending upon catalyst costs: (i) the reactor cannot be operated economically, (ii) only partial activation policies are economical, a single one being optimal, (iii) both partial and full activation schemes are economical, with one of the former being optimal, and (iv) full activation is optimal but the reactor can be operated economically with partially activated pellets. The results for both the single pellet and the packed tube are viewed as the homogeneous poisoning limit of many practical problems and are believed to reflect the major characteristics of more complicated poisoning mechanisms.

A diffusion model and optimal cell loading for immobilized cell biocatalysts

A diffusion model based on the random pore model is derived for immobilized cell biocatalysts and verified with 19 sets of experimental diffusion data. The predicted effective diffusivity relative to that for the support matrix reflects a quadratic dependence on the cell loading and contains a single parameter that depends on the intracellular diffusivity and the chemical partitioning coefficient. The model is used to predict optimal cell loadings that maximize the total reaction rate in an immobilized cell biocatalyst. A rule of thumb based on the diffusion model is obtained to the effect that the cell loading should be at least (1/3) for single reactions regardless of the kinetics and diffusional resistances. A means of calculating improved lower bounds is provided for cases where the cellular diffusional resistance is known but the kinetics are not. The optimal cell loadings for reversible first-order and for Michaelis-Menten kinetics are presented and demonstrated to be within the range of conditions of practical interest.

Optimum density and composition for catalytic pellets

Abstract Optimization calculations are applied to the problem of selecting either a microporous support from the viewpoint of available surface area or a macroporous support from the viewpoint of permeability in order to achieve the largest reaction rate in a pellet of fixed geometry. A single reversible reaction of first order is considered under isothermal conditions. The calculations are carried out with a proposed diffusion model which can successfully correlate diffusion data in pellets formed from single supports over a wide range of conditions. Optimum compositions are determined for pellets formed from both supports at a fixed density. Optimum densities are calculated for pellets of fixed composition. The combined problem of optimum density and composition is also treated and is shown to reduce to one of the individual problems. The results include both local maxima in the reaction rate and maxima on the boundary of allowable values of composition and density. The location of the maxima depend upon the kinetic and diffusional characteristics of the supports and the diffusional parameters of the pellet.

The effect of thermal diffusion in multicomponent gas absorption

The contribution of thermal diffusion to interfacial mass transfer rates is examined in multicomponent gas absorption systems. Each interfacial flux is expressed as the product of the isothermal expression corresponding to the bulk temperature of the liquid and a dimensionless correction factor that includes the pure heat effects in multicomponent absorption and the contributions of thermal diffusion. It is shown that when the influence of thermal diffusion is to increase the interfacial mass flux, it is opposite to the heat effect and that the two effects may cancel within a realistic range of values of the thermal diffusion coefficient. A monotonic trend to greater significance of thermal diffusion with the number of components being absorbed is illustrated. This trend is shown to be very rapid for the more dilute species in the mixture. Examples based on the absorption of propane, n-pentane, and n-hexane by paraffin oil are treated. The error induced in the correction factor for the flux of n-pentane by neglecting thermal diffusion when adding propane and n-hexane is less than 6·1 per cent, but the corresponding result for propane is 59·2 per cent for a thermal diffusion coefficient of 1· X 10−7 g/(cm sec °K) for each species.

Transmembrane distribution of substrate and product during the bioreduction of acetophenone with resting cells of Saccharomyces cerevisiae

The average volumetric intracellular concentrations of acetophenone and phenethyl alcohol were determined during the bioreduction of acetophenone using resting cells of Saccharomyces cerevisiae in aqueous solutions at 30 degrees C. The behavior of their distribution coefficients (ratio of intracellular to extracellular concentrations) during the bioreduction process was evaluated with different cell preparation and extracellular conditions. The distribution coefficient of acetophenone was found to be in the range of 2.3-4.0. The distribution coefficient of phenethyl alcohol was found to be in the range of 1.3-1.8. Both the distribution coefficients were correlated significantly only with the physiological state of the resting cells as reflected by the relative cell mass (0.65-1.09). The correlation is approximately linear with the largest slope for the toxic reagent, acetophenone. No significant effects on the distribution coefficients were experimentally observed or were present in a regression analysis for the concentrations of acetophenone (0-0.30% v/v), phenethyl alcohol (0-0.20% v/v), ethanol (1.60-2.25% v/v), the extracellular pH (pH 2-7), or the presence of the salts: KCl, KH2PO4, MgSO4, NaCl, and CaCl2 (each 0-0.1 M) in the medium. Different cell initialization times (0-6 days) and initialization conditions were also included.

Multicomponent film-penetration theory with linearized kinetics—II. Particular cases and tests

The matrix results required for the evaluation of all interfacial flows at the film theory limit are presented for the multiple reaction system A → C ⇄ B with linear kinetics and the single reaction system A + 2B ⇄ C with linearized kinetics. The yield of C is calculated in the former case and the enhancement factor for A is calculated in the latter case when B is nonvolatile and the reaction is irreversible. The single reaction, A + 2B ⇄ C, as well as A + B ⇄ C + D, is considered further for testing the linearized solution against the exact numerical calculations of the enhancement factor with the nonlinear kinetics. The results indicate that the linearization theory can be applied with a maximum error of 10 per cent and, in most cases, with a considerably smaller error over the complete range of gas—liquid contact times.

Catalyst effectiveness in sulfur dioxide oxidation

The sensitivity of the relationship between catalyst effectiveness in SO2 oxidation and the Thiele parameter to: (1) the kinetic expression with respect to the presence or absence of strong SO3 inhibition, (2) the activation energy in the range of 16–32 kcal/g mol, (3) the conversion of SO2 up to 90%, (4) the temperature at the exterior surface of the pellet in the range of 450–600°C, and (5) the feed composition ranging from 6–10% SO2 in air, was investigated. A nonisothermal model was used and the calculations were carried close to equilibrium. Far from equilibrium, the relationship is essentially unaffected except by conversion at the pellet surface for the case of strong product inhibition. Close to equilibrium, the relationship is significantly influenced by conversion, temperature, and the inlet composition but the form of the kinetics is not important. The activation energy is not a significant variable. Catalyst size, surface area, and density were not specified while it was necessary to fix the ratios of the transport properties for the calculations. The properties of the American Cyanamid V2O 5 catalyst were used for this purpose.