J.R. Bourne

Interaction between chemical reactions and mixing on various scales

Abstract The way in which reagents are mixed can have a large influence on the product distribution of a chemical reaction. This has been analysed earlier when micromixing is the limiting mixing step. Additional segregation at a larger scale has only been treated in detail when the local turbulent dispersion of a feed stream was relevant. Here additional segregation due to the finite disintegration rate of large concentration eddies is represented by a feasible structure to describe the environment within which micromixing and chemical reaction take place. The resulting model contains one time constant each for micro- and mesomixing. Their estimation is discussed and applied to predicting the yields of fast complex reactions in plug-flow static mixers and in a semibatch stirred tank reactor under conditions where neither macromixing nor turbulent dispersion were limiting. The comparison with measured yields is good for micromixing and fairly satisfactory for inertial-convective mesomixing. Further research on this step is needed.

Simplification of Micromixing Calculations. I. Derivation and Application of New Model

Abstract The micromixing model reported by us in 1984 consists of a set of partial differential equations to express unsteady diffusion and reaction in deforming laminated structures formed by engulfment in a turbulent fluid. This engulfment—deformation—diffusion (EDD) model has been widely applied to interpret experiments showing an effect of mixing on the product distribution of the reactions between 1-naphthol and diazotized sulphanilic acid. Theoretical arguments and recent experimental results show how the EDD model can be simplified by neglecting deformation and diffusion provided that Sc ⪡ 4000 and F ⪡ 1. The new E model retains fluid engulfment as the rate-determining step in micromixing and contains no arbitrary parameters. Application to two complex reactions has shown that engulfment is also product determining, i.e. the product distribution does not depend on deformation and diffusion. The new E model consists of a set of ordinary differential equations; it is one to two orders of magnitude faster to compute and a wider choice of software is available for its numerical implementation. Micromixing calculations have been simplified and accelerated.

Interactions between mixing on various scales in stirred tank reactors

Abstract Fast, competitive-consecutive reactions exhibit product distributions which are influenced by micro- and macroscale concentration gradients in a reactor. If a reaction is run many times under identical conditions in a semi-batch reactor, except that different feed rates are used, the product distribution is constant at low feed rates, but indicates increasing non-uniformity of composition at higher feed rates. Competition between micromixing and reaction determines product distribution at low feed rates. The additional inhomogeneity appearing at higher feed rates signals a mixing constraint at scales larger than microscopic. The relevant scale is not the macroscopic one of the whole vessel, but rather a mesoscale reflecting the interaction of the plume of fresh feed with its surroundings. Dispersion of this plume has been calculated for homogeneous turbulence, as well as when the mean plume velocity and the turbulence properties in its vicinity were spatially varying. Micromixing and chemical reaction could then be calculated in the concentration field resulting from turbulent dispersion. The relative importance of meso- and micromixing could be expressed by the ratio of their time constants. The description of simultaneous meso- and micromixing developed here successfully predicted product distributions from fast diazo-coupling reactions which had been measured at two scales, two feed points, three concentration levels and various stirrer speeds. The model requires knowledge of the reaction kinetics and the flow field, but does not, however, contain any arbitrary parameters.

The effect of micromixing on parallel reactions

The literature gives little guidance on the factors (e.g. choice of reactor, sequence of adding reagents, imperfect mixing) determining the product distribution of parallel reactions. By considering two irreversible, second-order reactions between three substances, it is shown here how the sequence of adding reagents to a semi-batch reactor will influence the yield when the mixing is perfect as well as when segregation is complete. A mixing model is then applied to predict yields when segregation is partial. Such calculations were made for three mixing sequences when chemically equivalent quantities of the three reagents were employed and when one of the two reactions was instantaneous. The yield then depended upon the mixing sequence, the volume ratio of reagent solutions and the Damkiihler number (this is a ratio of characteristic times for micromixing and chemical reaction). Sodium hydroxide, ferric sulphate and ethyl chloroacetate solutions were contacted in the sequences corresponding to cases 1 and 3 of the modelling. The alkali reacted competitively and the extents of the two parallel reactions were measured after it had been fully consumed. The independent variables were stirrer speed, volume ratio of the two reagent solutions and the concentration level at constant stoichiometric ratio. The effects of these operating variables on the product distribution were well predicted. The stoichiometry of the precipitation of ferric ions in alkaline solution is probably more complex than considered in the modelling and the parallel reactions used here need improvement or possibly replacement. A similar comparison was made between measured and predicted yields of nitrobenzene during the competitive nitration of benzene and toluene. Twelve out of 13 yields measured by Tolgyesi (1965) were satisfactorily predicted.

Investigation of mixing in jet reactors using fast, competitive-consecutive reactions

Although several aspects of turbulent free jets have already been studied, multi-step mixing-controlled reactions in liquid jets were not widely investigated. A network of five well-characterized chemical reactions having a mixing-sensitive product distribution was considered here. A model of turbulent mixing and reaction was first built up. It considers the near-field as well as the fully developed flow regions and includes radial and axial variations in the jet velocity and time-averaged concentrations, axial variation and intermittency in the turbulent energy dissipation rate, expansion of the jet with entrainment and intermittency of its boundary, micromixing controlled by engulfment and inertial-convective decay of segregation (mesomixing). The radical distribution of the energy dissipation rate as well as its axial variation in the near-field region could not be adequately specified from the literature. Two parameters, determined from experiments, were employed to describe this axial profile. The resulting model then predicted well the influences of jet velocity, reagent volume and stoichiometric ratios, reagent concentrations and feed rate on the product distribution. A viscous silicone oil was dispersed in the jet and the measured maximum stable drop size was compared with predictions based on the maximum energy dissipation rates. Measured drops were somewhat smaller and indicated local maxima in the dissipation rate up to 40,000 W/kg. The simple and robust jet reactor is suitable for competitive reactions needing dissipation rates of order 102−104 W/kg to attain high selectivities.

Influence of feed pipe diameter on mesomixing in stirred tank reactors

The product distribution of competitive reactions depends upon how the reagents are mixed when reaction is fast relative to mixing. Different mixing scales are considered here. The rate of micromixing is determined by the engulfment of small fluid elements. Mesomixing refers to the turbulent dispersion of a feed stream shortly after it enters a reactor. Turbulence creates the concentration field within which micromixing proceeds. The source of this field is the feed pipe, which had previously been modelled as a point, resulting in a Gaussian distribution of concentration downstream from the feed pipe outlet. This pipe can however be sufficiently large so that it represents a finite source: the relevant solution of the turbulent dispersion equation is given and contains a new dimensionless group, namely the ratio of the velocities inside and outside the feed pipe. With incresing size of the feed pipe opening it is predicted that (a) the critical feed time of a semi-batch reactor should decrease, thereby raising the productivity, and (b) when mesomixing is important and the feed time is constant, reagents should mix faster. These predictions were verified in experiments whereby sodium hydroxide was added through feed pipes of 1, 2, 3, 4 and 5 mm bore to a mixture of hydrochloric acid and ethyl monochloroacetate in a 0.021 m3 stirred tank reactor. It was also confirmed that product distribution is independent of the feed pipe, when only micromixing controls. Backmixing of reagents from the tank into the feed pipe occurred with the larger openings when the feed time was long. It was directly visualized and could have a large effect on product distribution. The modelling of micromixing and mesomixing does not include backmixing, which should be studied in more detail.

Self-tuning control of crystal size distribution in a cooling batch crystallizer

Abstract In this paper the theoretical basis of a control scheme, previously implemented on a laboratory scale potash alum batch cooling cystallizer (Rohani , Can. J. chem. Engng , in press, 1990), is presented. A comparison is made between the experimental and simulation results. A mathematical model of a seeded batch cooling crystallizer equipped with a fines dissolving loop and a fines suspension measuring device is developed. The mean crystal size and the coefficient of variation of an ideal batch crystallizer are derived analytically and it is shown that a batch crystallizer utilizing the proposed control scheme approaches the ideal case. Using the traditional control schemes based on operation along an optimal cooling trajectory results in a terminal CSD far from the ideal case. It is also shown that due to the time-varying characteristics of a batch crystallizer, a minimum variance self-tuning controller renders tighter control and improves the product CSD to a larger extent (a smaller coefficient of variation and a larger mean crystal size of the weight distribution) when compared with a conventional PI-controller.

The effect of imperfect mixing on an idealized kinetic fermentation model

Abstract Mixing patterns in stirred reactors are analyzed in this study from the point of view of the hysteresis behavior of final product rate as a function of the intermediate concentration in the sequential reaction A → B → C . A two-tank system model with an internal recycle stream is studied, in order to simulate the effect of imperfect mixing in a single batch reactor. The extent of mixing between positions at which product and intermediate species concentrations are measured in the reactor is revealed in both the direction of the hysteresis function and the relative magnitude of the inscribed area. Another approach, which apparently simplifies the analysis, is to measure the concentration of B in each of the two tanks and cross-plot the two variables. This latter technique not only avoids the errors resulting from differencing the data, but also leads to correlations between the circumscribed areas and the degree of mixing.

Design and characterization of a multistage, mechanically stirred column absorber

Abstract A multistage, mechanically stirred column absorber has been designed and built with a modular construction, based on preliminary experiments with a test column. The column has been characterized as a gas-liquid contactor by its gas holdup, gas and liquid axial dispersion, mixing times, oxygen transfer coefficients and power consumptions, determined as a function of gas velocity, liquid velocity and impeller speed for one and two impellers per stage. Gassed power was correlated with ungassed power, gas rate and impeller speed. The gas phase axial mixing was essentially plug flow and the liquid phase axial mixing varied between 5 and 12 equivalent stages. Oxygen transfer coefficients were correlated with power consumptions and aeration rates by the equation K L a γ (P/V) a (υ sg ) b . The oxygen transfer coefficients with single stiffer stages were 25% above those for the double stirrer stages for equal power consumption and gas rates. Except for the low aeration and high power consumption extremes, the column showed superior oxygen transfer performance. in comparison to tubular loop and tank fermenters.

A study of disproportionation effects in semi-batch foams—II. Comparison between experiment and theory

Abstract The degradation of foam generated in a semi-batch system, operating under high retention times, has been monitored. Under the experimental conditions particular to the study, the rate of degradation with respect to foam height and the total foam height itself are seen to be sensitive functions of the solubility of the filler gas and of the sparging rate. The first of these is explained in terms of the larger role of interbubble gas diffusion at higher gas solubilities, whereas the second is attributed to the varying residence time of the bubbles with regard to a particular height in the foam bed. Further, the dynamic simulation procedure described in Part I of this work is seen to follow the experimental trends rather well.