Modeling and Scale-Up of Mixing- and Temperature-Sensitive Chemical Reactions

A review of published measurements of yield for complex chemical reactions in mixed reactors of various types and methods of modeling and simulating such reactions for the purpose of reactor scale-up shows the extent of progress that has been made. Reaction kinetics for very fast competitive reactions are usually difficult and expensive to determine. Many reaction processes must be scaled up from bench- and/or pilot-scale experiments that produce yield data under various mixing conditions. the variables that strongly affect the yield results are the reaction types and their rates, feed point in the reactor, feed injection velocity and scale, mixing reactor type, and intensity of mixing induced. Because temperature affects the rates of many chemical reactions, the effects of exothermic reactions are examined. Simulation methods that aim at accounting for all these variables, as well as more approximate methods that are easier and quicker to use, are reviewed. an approach to scale-up is proposed that involves a series of yield calculations for conditions ranging from perfectly mixed to full simulation of the mixed vessel or flow mixer. These may be progressively compared with experimental yields, and the ratios of rate constants and their absolute values are adjusted to give yields close to those of bench and pilot experiments. the rate constant ratios and absolute values may in this way be bracketed (maximum and minimum values) for use in doing the scale-up computations. General conclusions based on the current knowledge of mixing effects on chemical reactions and a correlation based on dimensional analysis that incorporates most of the above variables are presented. © 2005 American Chemical Society

Turbulence measurements in polymer solutions using hot-film anemometry

Hot-film anemometry was used to study the detailed structure of turbulence (intensities, energy spectra, and auto-correlations) in Newtonian solvents, non-drag reducing polymer solutions, and drag reducing polymer solutions. This was done in two smooth wall tubes with diameters of 1.0 inch and 2.0 inches. A probe traversing mechanism was used for measurements at radial positions from the center to as near the wall as possible for both the film probes (r/a=0.85 in the 2-inch tube) and the impact tubes (r/ a=0.98). The impact tubes were used to measure velocities for film probe calibration. The solvents used in this investigation were toluene, cyclohexane, and benzene. Three concentrations of a medium molecular weight polyisobutylene (Vistanex L-80, molecular weight about 720,000) in cyclohexane, two concentrations of the same polymer in benzene, two concentrations of a high molecular weight polymethyl methacrylate (Plexiglas, molecular weight about 1,500,000) in toluene, one concentration of a low molecular weight polymethyl methacrylate (V-100 molding powder, molecular weight about 110,000) in toluene, three concentrations of a high molecular weight polyisobutylene (Vistanex 1-200, molecular weight about 4,700,000) in toluene, and one concentration of the same polymer in cyclohexane were used. In the liquids not showing drag reduction a viscous and/ or elastic effect was found for both turbulence intensities and energy spectra. Turbulence intensities were higher and energy spectrum frequencies were lower for the polymer solutions of high viscosity. Unfortunately the most viscous solutions were also elastic. So purely viscous liquid studies will be necessary to distinguish between elastic and viscous effects. During drag reduction it was found that the energy spectra changed little from purely viscous solvents. The turbulence intensities, however, showed very unusual effects. The intensities relative to friction velocity increased at low drag ratio values (high drag reduction), rather than remain constant as expected from mixing length considerations. This behavior was dependent upon the degree of mechanical polymer degradation, lower intensities occurring for fresh than for degraded solutions during drag reduction. Normal stress differences (P₁₁ - P₂₂) were measured for two of the solutions used in this investigation, one showing drag reduction at attainable flow rates in the l-inch tube, the other showing drag reduction only in 0.5-inch and smaller tubes. Both solutions yielded normal stress differences of about the same level. A quantitative viscoelastic mechanism of drag reduction was tested using the viscosity and normal stress data for the two solutions discussed above. The drag reduction mechanism demonstrated the relative effects of elasticity and viscosity on drag reduction. The adequate prediction of drag ratios for two solutions at two flow rates in each of two tube sizes demonstrated the validity of the mechanism and the reasonableness of the assumptions made --Abstract

Experimental Measurements and Simulation of Mixing and Chemical Reaction in a Stirred Tank

Effects of mixing on the rate of second-order chemical reactions have been studied by measuring the time-average degree of conversion at enough points in a steady-state, continuous-flow stirred reactor to provide comparisons with numerical simulations of the same reactions using a standard Reynolds-averaged turbulence simulation code with an added closure. The reactants were introduced in widely separated feed streams in order to provide a difficult test for the measurements and simulations. Concentration and segregation measurements were made with two fluorescence based methods - one remote and one using a fiber optic probe. The rates of mixing and reaction were simulated using the Corrsin mixing term and the Spalding segregation production term with the Paired-Interaction reaction closure term

Comparison Of Lagrangian Time Correlations Obtained From Dispersion Experiments And From Space‐time Correlation Functions

No Abstracts. Copyright © 1969 American Institute of Chemical Engineer

Hot‐film Anemometry Measurements Of Turbulence In Pipe Flow: Organic Solvents

Longitudinal turbulence intensities, autocorrelations, and energy spectra have been measured in the flow of toluene, benzene, and cyclohexane in smooth, round 1‐ and 2‐in. I.D. tubes. These measurements were made with a constant‐temperature hot‐film anemometer and covered radial positions from the center to r/a = 0.85 in the 2‐in. tube and to r/a = 0.75 in the 1‐in. tube. The turbulence intensity data were found to be similar to those obtained for air in a 10‐in. pipe by Laufer. A slight diameter effect was observed, the intensities in the 1‐in. tube being slightly lower than those in the 2‐in. tube at equal Reynolds numbers. The energy spectra were similar to the spectrum reported by Lee and Brodkey for water. The spectra reached higher frequencies at the lowest measurable energy levels for higher velocities. There was little effect of tube diameter or radial position on the spectra from the center to r/a = 0.85. A short inertial subrange with a log‐log slope of −5/3 seemed evident in high velocity spectra, and the log‐log slope of −7 was approached at high frequencies by the lowest velocity spectrum. The peak energy dissipation frequencies for all the energy spectra measured were approximately proportional to bulk mean velocity to the 1.4 power with little effect of tube diameter or radial position from the center to r/a = 0.85. Integral scales of the turbulence were proportional to bulk mean velocity to a power less than one for a given tube. These measurements indicated that the ratio of integral scale to pipe diameter is not a function of Reynolds number only. Microscale values were relatively independent of velocity and pipe diameter. Copyright © 1967 American Institute of Chemical Engineer

Equity Returns Around Extreme Loss: A Stochastic Event Approach

We define an extreme loss event as a daily return at the left tail of negative two standard deviations of all daily returns for a specific stock. Prior studies focus on the relationship between extreme losses and specific anticipated announcements. Our study identifies the extreme loss events after they are randomly realized, and examines the return patterns of the equities in question on stochastic event setups. We investigate the daily returns of 2,651 stocks traded in the U.S. equity markets and identified 217,990 extreme loss events from the 1950s to early 2019. Our findings show that after an extreme loss, an asset realizes, on average, a daily return of 0.8459% on the first day, and 1.8099% cumulatively in the following 5-day window. We attribute the fast recovery to the investors’ overreaction. This suggests an extreme loss reversal trading strategy. Our confirmation suggests that behavioral bias may not be corrected or eliminated through arbitrage