Harold A. Wright

Determination of coalescence frequencies in liquid—liquid dispersions: effect of drop size dependence

Abstract The size dependence of the drop coalescence frequency is investigated by measurement of transient drop size distributions in purely coalescing systems (with negligible drop break-up). A two-pronged approach is employed to estimate the bivariate coalescence frequency function, using such experimental data. First, coalescence frequency expressions derived from mechanistic models of the relative motion of the drops are evaluated based on their ability to predict the experimental transient size spectra. Second, experimental drop size distributions which exhibit a property known as self-similarity are analyzed through an inverse problem in order to extract the coalescence frequency function directly from the data. Results indicate that the coalescence frequency of small droplets (10–50 μm in diameter) is lower than that predicted from a constant coalescence efficiency model. In addition, experiments show that, given favorable initial conditions, self-similar drop size distributions can be manifest. In the cases where similarity behavior is observed, the frequencies obtained from the inverse problem are in qualitative agreement with the mechanistic models that describe the data best.

Operating strategies for Fischer-Tropsch reactors: A model-directed study

A comprehensive parametric study for a Fischer-Tropsch (FT) synthesis process has been conducted to investigate the relation between process parameters and reactor characteristics such as conversion, selectivity, multiplicity, and stability. A flexible model was employed for this purpose, featuring the dependence of Anderson-Shultz-Flory (ASF) factor on composition and temperature. All variable process parameters in industrial FT reactors were subject to variation, including reaction temperature, reactor pressure, feed ratio, inlet mass flux, feed temperature, heat transfer coefficient, catalyst concentration, catalyst activity, etc. While typical trade-off was encountered in most cases, i.e., the change of a parameter in one direction enhances one aspect but deteriorating another, the change of feed conditions gave some promising results. It has been found that decreasing the feed rate (or increasing the residence time) and/or lowering the feed concentration can successfully enhance the conversion up to more than 90% for our specific case, without hurting the product selectivity as well as effectively condense the region of multiple steady states. The benefits and limitations accompanied with the variation of the parameters were discussed in detail and a rational start-up strategy was proposed based on the preceding results. It is shown that the decrease of inlet mass flux (say, 85% decrease of the feed rate or 60% decrease of the feed concentration from the nominal condition chosen here) or the decrease of H2/CO ratio (specifically, below about 0.25), or their combination can eliminate multiple steady states. The resulting unique relation between temperature and manipulated variable (i.e., coolant flow rate) appears to assure a safe arrival at the target condition at the start-up stage.

Multiplicity and sensitivity analysis of Fischer–Tropsch bubble column slurry reactors: plug-flow gas and well-mixed slurry model

Existence of multiple steady states of Fischer–Tropsch (FT) synthesis has been reported experimentally as well as theoretically even in simple stirred tank slurry reactors. Bhattacharjee, Tierney, and Shah (1986) have found steady-state multiplicity in product distribution and heat generation rate in their experiments on supported ruthenium catalyst. Shah, Dassori, and Tierney (1990) have subsequently provided an explanation of this observation based on the analysis of heat generation and dissipation curves. They maintained that ignition should be avoided since, once it occurs, the normal FT synthesis reaction would be switched to the methane-forming mode seemingly never to return. This is because the catalyst could su=er serious deactivation on exposure to the high temperature resulting from the ignition. Recently, Song, Ramkrishna, Trinh, andWright (2003) have reported more complex experimental observations for an FT stirred tank slurry reactor with cobalt catalyst. The operating state of the FT process suddenly jumps from the normal wax-producing mode to the undesirable methane-forming mode accompanying the abrupt temperature lift. This multiplicity behavior is peculiar in the following two senses: (i) this happens sporadically, not always, and (ii) the normal wax-producing mode was, contrary to the interpretation by Shah et al. (1990), eventually recovered after a couple of hours. A plausible scenario explaining this peculiar multiplicity behavior was proposed by Song et al. (2003) using rigorous nonlinear analysis. It was found that decrease of the Stanton number for heat transfer (StH ) could be responsible for the @rst jump, while a decrease of the DamkA ohler

Inverse Problems of Aggregation Processes

The coagulation frequency is the key ingredient in the population balance (Smoluchowski) equation of coagulation kinetics. An inverse problem is formulated to extract the coagulation frequency from transient size distributions when these distributions are self-similar. Two numerical examples illustrate the procedure. The first demonstrates the inverse problem for the recovery of singular coagulation frequencies, while the second shows the procedure when self-similarity is approximate. Transient droplet coagulation experiments in a turbulent flow field have been performed. The resulting size distributions are observed to be self-similar. The inverse problem is used to determine the drop coagulation frequency. This frequency shows significant deviation from the coagulation frequencies derived from simple models of drop-drop interactions in a turbulent flow field.