A Survey of Multicomponent Mass Diffusion Flux Closures for Porous Pellets: Mass and Molar Forms

Heterogeneous catalysis is of paramount importance in many areas of gas conversion and processing in chemical engineering industries. In porous pellets, the catalytic reactions may be affected by diffusional limitations such that the global rate can be different from the intrinsic reaction rate. In the literature, a number of multicomponent diffusion flux closures have been applied to characterize the diffusion process within different units in chemical process plants. The main purpose of this paper is to outline the derivation of the different diffusion flux models: the rigorous Maxwell–Stefan and dusty gas models, and the simpler Wilke and Wilke–Bosanquet models. Usually the diffusion fluxes are derived and presented with respect to the molar average velocity definition. In this study, also the diffusion flux closures with respect to the mass average velocity definition is outlined. Thus, if the temperature equation and the momentum equation are used in the pellet model, a consistently closed set of pellet equations is obtained on mass basis holding only the mass average velocity. On the other hand, for the closed set of pellet equations on molar basis, the component balances hold the molar averaged velocity whereas the temperature and momentum equations hold the mass average velocity due to the physical laws applied deriving these fundamental balances. Nevertheless, the Maxwell–Stefan and dusty gas models are manipulated and put on the convenient Fickian form. The second purpose of this article is the evaluation of the diffusion flux closures derived. For this purpose, a transient model is developed to describe the evolution of the species composition, pressure, velocity, temperature, total concentration, and fluxes within a spherical pellet. The catalyst problem has been simulated for the methanol dehydration process producing dimethyl ether (DME), with computed efficiency factor values in the range 0.06–0.6 for pellet pore diameters of 0.1–100 nm. Identical results are expected for the mole and mass based pellet equations. However, deviations are obtained in the component fractions comparing the mass and mole based pellet model formulations where the mass fluxes were described according to the Wilke and Wilke–Bosanquet models. On the other hand, the rigorous Maxwell–Stefan and dusty gas models gave identical results.     

Time-property least-squares spectral method for population balance equations

In multiphase chemical reactor analysis the dispersed phase distribution plays a major role in obtaining reliable predictions. The population balance equation is a well established equation for describing the evolution of the dispersed phase. However, the numerical solution of this type of equations is computationally intensive. In this work, a time-property least squares spectral method is presented for solving the population balance equation including breakage and coalescence processes. In this problem, both property and time are coupled in the least squares minimization procedure. Spectral convergence of the L ² least squares functional and L ² error norms in time-property is verified using a smooth solution to the population balance equation.     

NMR study and quantum mechanical calculations on the 2-[(2-aminoethyl)amino]-ethanol-H2O-CO2 system

13C and 1H NMR spectra were obtained for AEEA (2-[(2-aminoethyl)amino]-ethanol)-H2O-CO2 systems and quantum mechanical calculations were carried out for the different AEEA species. The results suggest that the main AEEA species under the conditions studied are free amine, primary carbamate, and secondary carbamate. There is also some indication that a dicarbamate species is formed, this species does however only appear to be formed in small amounts. Comparison between experimental data and quantum mechanical calculations suggest that most AEEA species take on conforms with some degree of intramolecular hydrogen bonding.     

Investigation of the quantitative properties of the quadrupole orthogonal acceleration time-of-flight mass spectrometer with electrospray ionisation using 3,4-methylenedioxymethamphetamine

This paper describes the investigation of the potential of a quadrupole orthogonal acceleration time-of-flight mass spectrometer (Q-TOF) equipped with an atmospheric pressure ionisation interface for quantitative measurements of small molecules separated by reversed phase liquid chromatography. To this end, the detection limits and linear dynamic range in particular were studied in an LC/MS/MS experiment using 3,4-methylenedioxymethamphetamine standards and 3,4-methylenedioxyethylamphetamine for internal standardisation. In a second phase, the experiment was repeated with real biological extracts (whole blood, serum, and vitreous humour). A calibration for 3,4-methylenedioxymethamphetamine and its metabolite 3,4-methylenedioxyamphetamine was prepared in each of these matrices again using 3,4-methylenedioxyethylamphetamine as internal standard. The resulting quantitative data were compared with those obtained by liquid chromatography with fluorescence detection for the same extracts. The Q-TOF results revealed excellent sensitivity and a linear dynamic range of nearly four decades (2-10 000 pg on-column, r(2) = 0.9998, 1/x weighting). Furthermore, all the calibration curves prepared in biological material were superimposable, LC/MS/MS and LC-fluorescence, and the quantitative results for actual samples compared very favourably. It was concluded that the Q-TOF achieves a linear dynamic range for quantitative LC/MS/MS work exceeding that of fluorescence detection and at much better absolute sensitivity. Copyright 1999 John Wiley & Sons, Ltd.     

Lp空间Kantorovich-Vertesi算子逼近的Jackson型估计

考虑了Kantorovich-Vertesi有理插值型算子L^*n,s（f,X,x）对L^p[-1,1]（1≤p≤∞）空间函数逼近的Jackson型估计。并获得了如下逼近阶：‖L^*n,s(f,X,x)-f(x)‖L^p[-1,1]≤Cp,sw(f,1/n 2)L^p[-1,1] （s＞2）。     

Single-crystal growth and characterization of disilver(I) monofluorophosphate(V), Ag2PO3F: crystal structure, thermal behavior, vibrational spectroscopy, and solid-state 19F, 31P, and 109Ag MAS NMR spectroscopy

Single crystals of disilver(I) monofluorophosphate(V), Ag2PO3F (1), were obtained by slow evaporation of a diluted aqueous Ag2PO3F solution. Compound 1 adopts a new structure type and crystallizes in the monoclinic space group C2/c with eight formula units and lattice parameters of a = 9.2456(8) A, b = 5.5854(5) A, c = 14.7840(13) A, and beta = 90.178(2) degrees. The crystal structure of 1 [R(F2 > 2sigma(F2) = 0.0268, wR(F2 all) = 0.0665] is composed of three crystallographically independent Ag+ cations and PO3F2- anions as single building units. The oxygen environment around each of the Ag+ cations is different, with one Ag+ in distorted octahedral (d(Ag-O) = 2.553 A), one in nearly rectangular (d(Ag-O) = 2.445 A), and one in distorted tetrahedral (d(Ag-O) = 2.399 A) coordination. Additional Ag-F contacts to more remote F atoms located at distances >2.80 A augment the coordination polyhedra for the two latter Ag+ cations. The monofluorophosphate anion deviates slightly from C3v symmetry and exhibits the characteristic differences in bond lengths, with a mean of 1.510 A for the P-O bonds and one considerably longer P-F bond of 1.575(2) A. Compound 1 was further characterized by vibrational spectroscopy (Raman and IR) and solid-state 19F, 31P, and 109Ag MAS NMR spectroscopy. The value for the isotropic one-bond P-F coupling constant in 1 is 1JPF = -1045 Hz. Thermal analysis (TG, DSC) revealed a reversible phase transition at 308 degrees C, which is very close to the decomposition range of 1. Under release of POF3, Ag4P2O7 and Ag3PO4 are the thermal decomposition products at temperatures above 450 degrees C.     

First nucleophilic aromatic substitution of annelated pyrazole.

3-Chloropyrazolo[3,4-c]quinoline 5, 3-chloropyrazolo[3,4-c]isoquinoline 6, 1,2-dihydro-1,2-dimethylpyrazolo[3,4-c]quinolin-3-one 8, and 1,2-dihydro-1,2-dimethylpyrazolo[3,4-c]isoquinolin-3-one 10 were obtained by acid-induced nucleophilic aromatic substitution (S(N)H) of H-3 in N-hydroxypyrazolo[3,4-c]quinoline 1b and in N-hydroxy pyrazolo[3,4-c]isoquinoline 3b. In the acid-induced chlorination, 3b was far more reactive than 1b, whereas the related N-hydroxypyrazolo[4,3-c]quinoline 2b and N-hydroxypyrazolo[4,3-c]isoquinoline 4b were completely unreactive toward S(N)H under identical conditions.     

On critical graphs with chromatic index 4

It is shown that the number of vertices of valency 2 in a critical graph with chromatic index 4 is at most 1/3 of the total number of vertices, and that there exist critical graphs with just one vertex of valency 2, but none with exactly two vertices of valency 2. From this bounds for the number of edges are deduced. The paper ends with a presentation of a catalogue of all critical graphs with chromatic index 4 and at most 8 vertices, and all simple critical graphs with chromatic index 4 and at most 10 vertices.