With the advent of high-speed computers and innovative numerical methods, mathematical models have been gaining considerable importance in recent years. The application of mathematical modeling in process engineering has been confined so far to model validation studies only, and simulation, in the strictest sense, has remained virtually a neglected area. Studies related to the numerical simulation of process equipment, particularly on a commercial scale, are therefore called for. One such investigation is reported in the present work on a primary reformer, a vital equipment in the ammonia fertilizer industry. The study deals with the development of a complete mathematical model of the reformer and its validation using the data obtained on an industrial reformer. It is demonstrated through the subsequent simulation program how important design information could be derived from the mathematical model.

The thermotropic liquid crystal (LC), 4,4‘-diheptylazoybenzene (HAB), exhibiting isotropic nematic and smectic phases, is investigated through 129Xe NMR and density studies. The temperature dependence of 129Xe chemical shifts and spin−lattice relaxation times (T 1) of the xenon gas dissolved in HAB have shown clear signatures of the phase transitions. We have applied an extended pairwise additive model to the smectic phase of HAB to account for the measured temperature dependence of chemical shifts. It is inferred that the LC−xenon molecular pair correlations have a significant effect on the shielding anisotropy in the nematic and smectic phases whereas they are negligible in the isotropic phase. The isotropic and anisotropic parts of the nuclear shielding and their dependences on liquid crystalline ordering (orientational and translational), density, and temperature are deduced for both the nematic and smectic phases. It is found that the shielding anisotropy is primarily due to orientational ordering of the LC molecules. In the smectic phase, xenon atoms preferentially occupy interlayer spacings rather than their interiors, leading to an increase in the isotropic part of the shielding. The activation energies (E a) associated with xenon dynamics in different phases are deduced from T 1 measurements. Despite the denser packing of molecules in the smectic phase, the E a in this phase is lower than that of the nematic phase. This finding is in agreement with the conclusions drawn from the analysis of the chemical shift data.

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