Solid-liquid mass transfer measurement

A significant difficulty in characterizing and quantifying gas-liquid, liquid-solid, and gas-liquid-solid mixtures commonly found in bioreactor flows is that the systems are typically opaque (e.g., even an air-water system becomes opaque at fairly low volumetric gas fractions) this necessitates the use of specially designed invasive measurement probes or noninvasive techniques when determining internal flow and transport characteristics. Many of these probes or techniques were developed for a particular type of gas-liquid flow or bioreactor. This chapter first introduces experimental techniques to gauge bioreactor hydrodynamics and then summarizes gas-liquid mass transfer measurement techniques used in bioreactors. 

A significant amount of research has been performed on the measurement of liquid-solid mass transfer [67], Generally, liquid-solid mass transfer in fixed-bed reactors has been studied by five methods dissolution of slightly soluble solids into the liquid [68-73], chemical reaction with significant liquid-solid mass transfer resistance [74], ion exchange followed by an instantaneous irreversible reaction [75], dynamic absorption [76], and electrochemical technique [77-80]. The electrochemical method has certain advantages over the other it facilitates direct and instantaneous measurements of solid-liquid mass transfer and is thus very useful to measure mass transfer fluctuations, especially under pulse flow conditions. 

Later publications have been concerned with mass transfer in systems containing no suspended solids. Calderbank measured and correlated gas-liquid interfacial areas (Cl), and evaluated the gas and liquid mass-transfer coefficients for gas-liquid contacting equipment with and without mechanical agitation (C2). It was found that gas film resistance was negligible compared to liquid film resistance, and that the latter was largely independent of bubble size and bubble velocity. He concluded that the effect of mechanical agitation on absorber performance is due to an increase of interfacial gas-liquid area corresponding to a decrease of bubble size. 

Satterfield150 considers a special case of the above equation, in which the gas-phase resistance is neglected (i.e., the second term on the right-hand side of the above equation is zero) and the catalyst effectiveness factor is assumed to be unity. In this case, a series of measurements of AG/R for various catalyst loadings permits a plot of AG/R versus 1/m to be established. The intercept yields the gas-liquid mass-transfer coefficient and the slope yields a combination of the intrinsic rate constant and the liquid- solid mass-transfer coefficient. 

The structure of wakes behind the gas bubbles affects several aspects (such as holdup, gas-liquid mass transfer, etc.) of three-phase fluidized-bed behavior. The magnitude and composition of such wakes are still not known with any certainty. Wake holdups have been estimated from experimental measurements of gas and solid holdups. It is commonly assumed that the bed can be divided into three regions a liquid fluidized region, a gas-bubble region, and a bubble-wake region and that the bubbles and their wakes travel at the same velocity. Different investigators have, however, assumed different values of hws the ratio of solids holdup in the wake to the solids holdup in the liquid fluidized region. Different methods have been used to calculate wake holdups from the experimental... 

This leads to the concept of mass transfer calculation techniques in scaleup. Figure 36 shows the concept of mass transfer from the gas-liquid step as well as the mass transfer step to liquid-solid and/or a chemical reaction. Inherent in all these mass transfer calculations is the concept of dissolved oxygen level and the driving force between the phases. In aerobic fermentation, it is normally the case that the gas-liquid mass transfer step from gas to liquid is the most important. Usually the gas-liquid mass transfer rate is measured, a driving force between the gas and the liquid calculated, and the mass transfer coefficient, KqO or t a obtained. Correlation techniques use the data shown in Fig. 37 as typical in which KqO is correlated versus power level and gas rate for the particular system studied. 

Equilibrium of adsorption on a solid is characterized by an adsorption isotherm, which shows the concentration on the solid as a function of the concentration in the contacting fluid. A quantitative measure of uptake of a gaseous species by a liquid is the distribution coefficient, defined as the ratio of the concentration on the solid to that in the contacting fluid. If concentration-independent, the coefficient is also called Henry coefficient. Diffusion of a species in a porous solid is expressed in terms of an effective diffusion coefficient, whose value accounts for the retardation by the solid matrix. Mass transfer to or from a solid is expressed in terms of a mass-transfer coefficient, the flux being the product of that coefficient and a concentration difference as "driving force."... 

Most of published papers regard exclusively the hydrodynamics of an air-water system and the determination of the gas-liquid interfacial area a, the gas-liquid kj a and the liquid-solid kga mass transfer parameters in aqueous solutions. In this paper we present some experimental results on hydrodynamics and mass transfer parameters a and kj a, measured by the chemical technique with two or-... 

Because the mechanism of mass transfer changes so significantly when a reaction takes place, it is dangerous to measure gas-to-liquid mass transfer and liquid-to-solid mass transfer independently and then combine them for gas-to-liquid-to-solid (kajcLw as resistances in series according to... 

The correlations for solid fluid interfaces in Table 8.3-3 are much like their heat transfer equivalents. More significantly, these less important, fluid-solid correlations are analogous but more accurate than the important fluid-fluid correlations in Table 8.3-2. Accuracies for sohd fluid interfaces are typically average 10% for some correlations like laminar flow in a single tube, accuracies can be 1 %. Such precision, which is truly rare for mass transfer measurements, reflects the simpler geometry and more stable flows in these cases. Laminar flow of one fluid in a tube is much better understood than turbulent flow of gas and liquid in a packed tower. 

The HTE characteristics that apply for gas-phase reactions (i.e., measurement under nondiffusion-limited conditions, equal distribution of gas flows and temperature, avoidance of crosscontamination, etc.) also apply for catalytic reactions in the liquid-phase. In addition, in liquid phase reactions mass-transport phenomena of the reactants are a vital point, especially if one of the reactants is a gas. It is worth spending some time to reflect on the topic of mass transfer related to liquid-gas-phase reactions. As we discussed before, for gas-phase catalysis, a crucial point is the measurement of catalysts under conditions where mass transport is not limiting the reaction and yields true microkinetic data. As an additional factor for mass transport in liquid-gas-phase reactions, the rate of reaction gas saturation of the liquid can also determine the kinetics of the reaction [81], In order to avoid mass-transport limitations with regard to gas/liquid mass transport, the transfer rate of the gas into the liquid (saturation of the liquid with gas) must be higher than the consumption of the reactant gas by the reaction. Otherwise, it is not possible to obtain true kinetic data of the catalytic reaction, which allow a comparison of the different catalyst candidates on a microkinetic basis, as only the gas uptake of the liquid will govern the result of the experiment (see Figure 11.32a). In three-phase reactions (gas-liquid-solid), the transport of the reactants to the surface of the solid (and the transport from the resulting products from this surface) will also... 

The development of the electrodynamic balance and other particle traps has made it possible to perform precise measurements of the properties of small particles by focusing on the single particle. The variety of processes and phenomena that can be investigated with particle traps is quite extensive and includes gas/liquid and gas/solid chemical reactions, chemical spectroscopies, heat and mass transfer processes, interfacial phenomena, thermodynamic properties, phoretic forces, and other topics of interest to chemical engineers. 

Finally, in Fig. 3.4-12 [24], a comparison is given for the overall, gas-based, mass transfer coefficient for several liquid-to-gas and solid-to-gas packed beds and column systems. In Fig. 3.4-12, for a given data point, the vertical distance up to the Tan et al. [27] correlation (which is for a solid-to-fluid boundary layer) would provide a measure of the liquid-side mass-transfer resistance associated with the liquid. This is so because amount of the large gas... 

In high pressure work, slurry reactors are used when a solid catalyst is suspended in a liquid or supercritical fluid (either reactant or inert) and the second reactant is a high pressure gas or also a supercritical fluid. The slurry catalytic reactor will be used in the laboratory to try different catalyst batches or alternatives. Or to measure the reaction rate under high rotational speeds for assessing intrinsic kinetics. Or even it can be used at different catalyst loadings to assess mass transfer resistances. It can also be used in the laboratory to check the deactivating behaviour. 

Chemical or mass transfer criteria Criteria for fluid mixing evaluation that involves measuring the rate of chemical reactions or rates of mass transfer across liquid, gas, or solid interfaces. 

Similar SECM experiments can be performed using a simple (unassisted) IT process [41]. In this case, both the top and the bottom phases contain the same ion at equilibrium. The micropipet tip is used to deplete concentration of this common ion in the top solvent near the ITIES. The depletion results in the IT across the ITIES, which produces positive feedback. Any solid surface (or a liquid phase containing no specific ion) acts as an insulator in this experiment. The mass transfer rate for IT measurements by SECM is similar to that for heterogeneous ET measurements, and the standard rate constants in excess of 1 cms-1 should be measurable. 

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