Simulation of a Combined Isomerization Reactor & Pressure Swing Adsorption Unit

The Total Isomerization Process developed by Union Carbide in 1970 (Gary, 1987) for the conversion of normal paraffin's to their isomers consists of a reactor followed by a PSA unit each operating at similar pressures and temperatures. The combination of these two operations in one unit in a Pressure Swing Adsorption Reactor (PSAR) process may provide an increased throughput and a significant cost saving in ancillary equipment.The simulation of a mathematical model linking the catalyst packed-bed and the adsorbent packed-bed is reported. The catalyst is a Pd/Y-zeolite and the adsorbent is 5A zeolite. The simulated feed consists of 17% each of n- and isopentane with the remainder being hydrogen. The mathematical model assumes dispersed plug-flow in both sections, constant velocity in the reactor section but varying in the adsorber, with mass transfer in the adsorber section due to external fluid film resistance and macropore diffusion in series. The fraction of the total column length occupied by the catalyst (denoted by ) is accounted for in the model by solving numerically using orthogonal collocation on finite elements. Parameters varied are the ratio of catalyst/column length (), temperature range (506–533 K), high pressure (15–20 bars), with the low pressure held constant at 2 bars. The catalyst/column ratio has a strong effect at low temperatures. The optimum catalyst/column length ratio appears to be controlled by the low pressure step and occurs at = 0.7 for the assumptions used in this work.     

Generating M-Indeterminate Probability Densities by Way of Quantum Mechanics

Probability densities that are not uniquely determined by their moments are said to be “moment-indeterminate,” or “M-indeterminate.” Determining whether or not a density is M-indeterminate, or how to generate an M-indeterminate density, is a challenging problem with a long history. Quantum mechanics is inherently probabilistic, yet the way in which probability densities are obtained is dramatically different in comparison with standard probability theory, involving complex wave functions and operators, among other aspects. Nevertheless, the end results are standard probabilistic quantities, such as expectation values, moments and probability density functions. We show that the quantum mechanics procedure to obtain densities leads to a simple method to generate an infinite number of M-indeterminate densities. Different self-adjoint operators can lead to new classes of M-indeterminate densities. Depending on the operator, the method can produce densities that are of the Stieltjes class or new formulations that are not of the Stieltjes class. As such, the method complements and extends existing approaches and opens up new avenues for further development. The method applies to continuous and discrete probability densities. A number of examples are given.

     

Probing the formation of bicyclo[4.2.0]octan-1-ols

Reaction of lithium enolates of simple ketones with (+/-)-phenyl vinyl sulfoxide has potential for the convergent construction of complex fused ring systems containing a bicyclo[n.2.0]alkan-1-ol. The formation of sulfinylbicyclo[4.2.0]octan-1-ols 1-3 from the lithium enolate of cyclohexanone with (+/-)-phenyl vinyl sulfoxide or (R)-(+)-p-tolyl vinyl sulfoxide 18 was used to probe the mode of this novel cyclization reaction. Using phenyl vinyl sulfoxide, variations in the reaction lighting and solvent were investigated, in conjunction with radical trapping (TEMPO) and isotope labeling (deuterium) experiments. Cyclization to form sulfinylbicyclooctanols 1-3 is likely to proceed via an intermediate that ring closes to the bicycloalkanol anion 11 and was presently favored by the use of solvents such as THF or DME.     

Minimal paramount matrices

A real symmetric matrix of order n, n ? 2, is said to be paramount if each proper principal minor is not less than the absolute value of any other minor built from the same rows. A paramount matrix is minimal ¹ if reducing any of the diagonal entries removes the matrix from the paramount class. Minimal paramount matrices arise in the n-port realization problem of circuit theory. A condition is found that is equivalent to the minimality of a paramount matrix. Conditions are also found that guarantee that the inverse of an invertible minimal paramount matrix is itself minimal.     

Intrinsic adsorption properties of CO2 on 5A and 13X zeolite

Data for the adsorption of CO₂ on 5A (CaA) and 13X (NaX) zeolite are critically evaluated. In addition, fresh data for the adsorption of CO₂ on 13X zeolite is reported. Three intrinsic properties are examined: q _max , the saturation loading, K _H , the Henry constant, and (?ΔH) _q , the isosteric heat of sorption. Below a reduced temperature T _r , of 0.9, the q _max values for both 5A and 13X zeolites are similar to theoretical values that may be derived using zeolitic crystallographic properties and the sorbate density calculated using the Rackett equation. For the region 0.9 ≤ Tr ≤ 1.0, the calculated q _max values exceed the theoretical values similarly calculated, indicating that the molecules have a smaller molar volume than in a similar liquid phase. This is a similar result to that observed in ionic liquids. Linear regressed equations are derived for q _max for the region 0.9 ≤ Tr ≤ 1.25. The Henry constant values for 5A are remarkably consistent for the five studies examined, with a correlation coefficient, R, of 0.999 for the van’t Hoff equation, but for the seven studies examined in 13X the data is more disperse as indicated by a correlation coefficient R of 0.899 for the van’t Hoff equation. The values of (?ΔH) _q , the isosteric heat of sorption are in agreement with the literature. An explanation is advanced for the discrepancy between the higher heats of sorption values obtained calorimetrically from those obtained from isosteric adsorption studies. Finally, the fresh data is observed to fit the Toth model with regression coefficients of 0.999. However, the parameters obtained for the Toth equation by regression are significantly different from the intrinsic properties derived earlier, indicating the difficulty of deriving intrinsic parameters from isotherm fits.     

Selective mono reduction of bis-phosphine oxides under mild conditions

Bis-phosphine oxides can be selectively reduced to bis-phosphine monoxides under exceptionally mild conditions using triflic anhydride and a thiol.     

Effects of Turbulence, Evaporation and Heat Release on the Dispersion of Droplets in Dilute Spray Jets and Flames

The dispersion characteristics of a selection of non-evaporating non-reacting, evaporating non-reacting, and reacting dilute spray jets issuing in ambient air (Gounder et al, Combust Sci Technol 182:702–715, 2010; Masri and Gounder, Combust Flame 159:3372–3397, 2010) and in a hot coflow (Oloughlin and Masri, Flow Turbul Combust 89:13–35, 2012) are analysed. Other than the cases found in those contributions, two additional sprays of kerosene have been investigated in order to systematically study the effects of evaporation. The burners are well designed such that boundary conditions may be accurately measured for use in numerical simulations. The dynamics and dispersion characteristics are analysed by conditioning results on the droplet Stokes numbers and by systematically investigating changes in dispersion and dynamics as a function of carrier air velocity, liquid loading, ignition method, and location within the flame or spray jet. The tendency for droplet dispersion defined by the ratio of radial rms velocity to axial mean velocity varies significantly between reacting and non-reacting flows. However, dispersion is found to be largely unaffected by evaporation. The total particle concentration, or number density of droplets within the spray has also been used as a direct measure of spray dispersion with the effect of evaporation on a turbulent polydisperse spray being isolated by investigating acetone and kerosene sprays with similar boundary conditions. The rate of change of droplet size with radial position is almost identical for the kerosene and acetone cases. The dispersion characteristics, closely related to the ‘fan spreading’ phenomenon are dependant on the carrier air velocity and axial location within the spray.