Monte carlo simulation of mass transfer in liquid-liquid dispersions

A simulation technique is developed to predict the performance of a two phase liquid-liquid continuous flow stirred tank reactor as an extractor. The dynamics of the dispersed phase droplet interactions and the microscopic interphase mass transfer in the turbulent flow field are digitally simulated using the interval of quiescence method. The use of realistic breakage and coalescence functions together with the natural evolution of the interactive drop population has made it possible to predict the dispersed phase drop size distribution and mass transfer efficiency in a rational manner from the known physicochemical properties of the dispersion and the operating conditions of the extractor.     

New criteria for application of the well-mixed model to gas-liquid mass transfer studies

The well-mixed model presents several advantages for the evaluation of interphase mass transfer rates in gas-liquid contactors: it simplifies the mathematical analysis and eliminates the need for measuring numerous mixing parameters. Although the well-mixed model corresponds to a theoretical concept, it is shown in this paper that, under certain conditions, it can be safely applied to the liquid phase of contactors for the purpose of determining the overall volumetric mass transfer coefficient K_La_L. Based on a computer simulation of absorption and mixing processes, simple criteria were developed that specify the conditions for which the well-mixed model is applicable in practice, for either a semi-batch gas-liquid contactor or a continuous flow absorber at steady-state. The dimensionless group K_La_Lτ_c, where τ_c is the average circulation time in the liquid phase of the contactor, was found to be a key parameter in establishing the validity of the well-mixed model.     

On the relevance of mass transfer limitations in the Fischer-Tropsch slurry process

Satterfield and Huff[1] reported recently on significant mass transfer resistances in the FT slurry process. However, their conclusions are at least partly based on a study with an unsuitable catalyst. In the present communication FT studies with 8 different catalysts and bubble columns, respectively, were analyzed using new and reliable results on hydrodynamic properties. In all cases, mass transfer resistances were found to be small compared to reaction resistances. As long as much more active catalysts are not developed significant mass transfer limitations cannot be expected in the bubble column if operated under appropriate conditions. The absence of mass transfer limitations is mainly a result of the high gas holdups attainable with molten paraffin as liquid phase.     

Wall heat/mass transfer in pulsatile flow

Heat/mass transfer is considered from a solid surface to a fluid undergoing pulsatile flow, consisting of sinusoidal pulsations superimposed on a mean flow. Mass transfer was measured from small strips using the diffusion-controlled electrode method for both non-reversing and reversing flows, corresponding to small and large pulsation amplitudes, respectively. Heat/mass transfer rates from the surface consist of a mean component, with a superimposed oscillatory component that is dependent on the amplitude, α, of the fluctuating wall shear rate, and the dimensionless frequency parameter, F_p. For small α, the amplitude and phase of the first harmonic of the measured transfer rates agree well with the theory of Mizush for all values of F_p. The same is true for larger α (< 1), only when F_p is also large; for large α and small F_p, there is significant deviation from theory. In the latter case, the experimentally measured amplitudes of the second harmonic become large, and the assumptions the theory are no longer valid. For α > 1, flow reversal occurs, and the theory again does not apply. For α < 1, the shapes of the mass transfe time curve are almost sinusoidal, and space-and-time-averaged transfer rates decrease slightly compared to steady flow as α increases. For a > 1, f takes place, and as α increases to about 1.5–2, the average transfer rates increase and become equal to those in steady flow. For α > 2 the tra become greater than the steady flow values and the second harmonic of the fluctuating transfer rate is as significant as the first harmonic. The change of the transfer rate vs time curves is quite significant, with two maxima and minima appearing in a period compared to the single maximum and minimum w characteristic of small α. These changes in average transfer rates and in the shapes of the transfer rate vs time curves are substantial for small va frequency parameter, F_p. As F_p is increased, the changes become less pronounced, and the trend of the data indicates that for F_p large enough, there is no increase in the transfer rate in pulsatile flow, and this appears to be independent of the value of α.     

Turbulent heat and mass transfer in dilute polymer solutions

A new model based on Levich's three-zone model is developed to discuss the turbulent heat and mass transfer in drag-reducing solutions. The proposed model, which has no adjustable parameters and is represented in an explicit form, provides satisfactory predictions of the maximum heat and mass transfer reduction in smooth and rough pipes. The mass transfer to a disk rotating in drag-reducing solutions is also discussed using the proposed model.     

Natural convection mass transfer at cylinders in different positions

Rates of natural convection mass transfer between an electrolyte and horizontal, vertical and inclined cylinders have been determined using an electrochemical technique involving the measurement of limiting currents for the deposition of copper on copper cylinders from acidified cupric sulphate solutions. The data were correlated for different cylinder positions using dimensional analysis. For horizontal cylinders, a single correlation covered both laminar and turbulent conditions, along with existing literature data for the turbulent regime. For vertical cylinders the new correlation agrees closely with the classical vertical plate correlation, and is also compared to heat transfer equations. For inclined cylinders, the new correlation is also compared to existing equations for inclined plates.     

Binary and ternary distillation in a stirred mass transfer cell

A continuous flow stirred cell operating at point conditions has been developed for the study of mass transfer in distillation. Results for the methanol-isopropanol and methanol-ethanol binary systems showed that 85–100% of the resistance to mass transfer resided in the vapour phase, and that the vapour side coefficients correlated well with those obtained in the same cell for gas phase controlled absorption. Flux rates for the ternary system methanol-ethanol-isopropanol were in fair agreement with those predicted from the binary data, using a modified form of the Krishna-Standart theory. It is concluded that the experimental technique shows considerable promise, but requires further development to overcome discrepancies in the interfacial heat balance.     

A new model of mass transfer in a rotating disc contactor

A new model of oxygen transfer using a rotating disc contactor, half immersed in wastewater in a trough, is presented. The boundary-layer theory is used to estimate the liquid-film thickness on the disc while submerged. The oxygen transfer rate calculated from the model showed good agreement with observations, hence showing improvement compared to the previous model which has not been supported by observations.     

Effect of bubble interaction on interphase mass transfer in gas fluidized beds

A non-interfering technique has been used to measure the concentration of ozone in pairs of bubbles injected into a bed of inactive 390 μm glass beads fluidized by ozone-free air. The transfer of the ozone tracer from the bubble phase to the dense phase is enhanced when compared to the transfer from isolated bubbles in the same particles and the same column. Bubble growth is also greater for the case where pairs of bubbles are introduced than when bubbles are present in isolation. Enhancement of interphase mass transfer for interacting bubbles in the present work and in previous studies incr with particle size and can be explained in terms of enhancement of the throughflow (or convective) component of transfer while the diffusive component unaltered. This mechanism leads to new equations for estimating interphase mass transfer in freely bubbling fluidized beds.     

Ionic mass transfer rate of CuSO4 in electrodialysis

Ionic mass transfer rate of copper ion in the ion exchange membrane electrodialysis at limiting current density has been studied using a planar flow electrodialyzer consisted of a cation exchange membrane and an anion exchange membrane. Their effective area is 4 × 5 cm². The effects of flow rate, viscosity of electrodialysate solution and thickness of electrodialyzer to the ionic mass transfer rate have been studied. An empirical correlation equation (Nu)_exp. = 4.57 × Re^0.333 Sc^0.307 (de/L)^O.33 is obtained. It fitted well with the theoretical performance equation (NU)_theor.= 3.70 × (Re · Sc · de/L), which is derived from the Nernst-Planck Equation based on the assumption that mass transfer in the concentration boundary layer in the desalting compartment is controlling.     

Promotion of CO2 mass transfer in carbonate solutions

A general, physico-chemical analysis of mass transfer rate promotion in the system CO₂-potassium carbonate-water-promoter is presented. Different possible mechanisms of promoter action including homogeneous catalysis, “shuttle” mechanism and surface reactions are discussed and classified. A unified picture of promoter chemistry is presented, showing that differences between inorganic and organic promoters are predominently quantitative, not qualitative.The “shuttle” mechanism is analyzed for absorption. The analysis leads to the prediction that the CO₂ mass transfer rate may be influenced by the liquid hold up. This is related to the fact that, although the reaction in the interface region may be fast enough to enhance the mass transfer rate, the different reaction in the bulk may not be fast enough to maintain chemical equlibrium. This complex type of chemical absorption process has not been considered previously in the literature.     

A quin-diagonal algorithm to describe mass transfer and backmixing in extraction

Specific algorithms are especially effective and economical when used to solve sets of linear-algebraic equations when the coefficients of the equations are adjacent to the diagonal elements. The Thomas algorithm is well known and has been used in many areas of chemical engineering when “tridiagonal” sets of equations are encountered. A similar algorithm is developed for use when the coefficients take a quin(5)-diagonal configuration. Its application to multistage mass transfer operations is demonstrated and the effects of deviation from equilibrium and backmixing are illustrated for multistage extraction operations.     

Two-phase gas-liquid flow in rectangular channels

The results of investigation of hydraulics in a two-phase gas—liquid flow in vertical and horizontal rectangular channels have been presented in the paper.Flow regime maps have been worked out and a method for calculating the pressure drop in a two-phase mixture flow has been proposed.The methods applied in a two-phase flow in pipes have been used to describe the results of investigations, after adopting the correction for the difference between the flow in rectangular channels and that in pipes.     

Effects of mass transfer on the performance of slurry reactors used for fischer-tropsch synthesis

The influence of mass transfer on the H₂/CO ratio in the liquid phase of a slurry reactor used for Fischer-Tropsch synthesis has been analyzed theoretically. It is determined that even under circumstances where the gas-liquid mass-transfer resistance is a small fraction of the overall resistance, differences in the solubilities and diffusivities of H₂ and CO can give rise to liquid-phase H₂/CO ratios which differ substantially from that of the gas fed to the reactor. The direction and magnitude of the change in the liquid-phase H₂/CO ratio is dependent on the H₂-CO consumption ratio, the interfacial area for mass transfer from the bubble phase, the Damkohler number, and the space velocity of the feed gas.