Mass transfer trace

Isocratic Elution In the simplest case, feed with concentration cf is apphed to the column for a time tp followed by the pure carrier fluid. Under trace conditions, for a hnear isotherm with external mass-transfer control, the linear driving force approximation or reaction kinetics (see Table 16-12), solution of Eq. (16-146) gives the following expression for the dimensionless solute concentration at the column outlet ... 

Table 3.1 shows the kinetic parameters for cell growth, rate models with or without inhibition and mass transfer coefficient calculation at various acetate concentrations in the culture media. The Monod constant value, KM, in the liquid phase depends on some parameters such as temperature, initial concentration of the carbon source, presence of trace metals, vitamin B solution, light intensity and agitation speeds. The initial acetate concentrations in the liquid phase reflected the value of the Monod constants, Kp and Kp. The average value for maximum specific growth rate (/xm) was 0.01 h. The value... 

By substituting the well-known Blasius relation for the friction factor, Eq. (45) in Table VII results. Van Shaw et al. (V2) tested this relation by limiting-current measurements on short pipe sections, and found that the Re and (L/d) dependences were in accord with theory. The mass-transfer rates obtained averaged 7% lower than predicted, but in a later publication this was traced to incorrect flow rate calibration. Iribame et al. (110) showed that the Leveque relation is also valid for turbulent mass transfer in falling films, as long as the developing mass-transfer condition is fulfilled (generally expressed as L+ < 103) while Re > 103. The fundamental importance of the Leveque equation for the interpretation of microelectrode measurements is discussed at an earlier point. 

Once the initial equilibrium state of the system is known, the model can trace a reaction path. The reaction path is the course followed by the equilibrium system as it responds to changes in composition and temperature (Fig. 2.1). The measure of reaction progress is the variable , which varies from zero to one from the beginning to end of the path. The simplest way to specify mass transfer in a reaction model (Chapter 13) is to set the mass of a reactant to be added or removed over the course of the path. In other words, the reaction rate is expressed in reactant mass per unit . To model the dissolution of feldspar into a stream water, for example, the modeler would specify a mass of feldspar sufficient to saturate the water. At the point of saturation, the water is in equilibrium with the feldspar and no further reaction will occur. The results of the calculation are the fluid chemistry and masses of precipitated minerals at each point from zero to one, as indexed by . 

In Chapter 2 we discussed three special configurations for tracing reaction paths the dump, flow-through, and flush models. These models are special cases of mass transfer that can be implemented within the mathematical framework developed in this chapter. 

The procedure for tracing a kinetic reaction path differs from the procedure for paths with simple reactants (Chapter 13) in two principal ways. First, progress in the simulation is measured in units of time t rather than by the reaction progress variable . Second, the rates of mass transfer, instead of being set explicitly by the modeler (Eqns. 13.5-13.7), are computed over the course of the reaction path by a kinetic rate law (Eqn. 16.2). 

Tracing a kinetic redox path is a matter of redistributing mass among the basis entries, adding mass, for example, to oxidized basis entries at the expense of reduced entries. The stoichiometry of the mass transfer is given by the kinetic reaction 17.3, and the transfer rate is determined by the associated rate law (Eqn. 17.9, 17.12, or 17.21). 

The preceding discussion demonstrates that in order to understand the role(s) of mass transfer with respect to trace element bioaccumulation, the following considerations must be examined ... 

A number of computer programs for generating potential -pH diagrams have been described (49, 50 51). Helgeson (52) describes a method often used within geosciences whereBy compositional changes, mass transfers and the order of appearance of stable and metastable phases are determined in tracing reaction paths from an initial set of conditions to a final state of equilibrium. 

A simulated moving bed system has been proposed for the production of p-cresol from mixtures of cresol isomers even derived from coal tar [52]. Neuzil et al. give details of the development of the adsorbent and desorbent system reviewing balancing mass transfer issues with selechvity [53]. The desorbent for the cresol system is 1-pentanol. For these Hquid adsorptive systems where highly polar molecules are adsorbed and desorbed with polar desorbents, the tolerance of the system for trace polar contaminants is higher because the feed and desorbent can more easily exchange with them on the surface of the zeolites. 

The effects of interfacial monolayers on the extraction from drops are particularly striking. Early work showed that traces of either impurity or surface-active additives can drastically reduce extraction rates even plasticiser, in subanalytical quantities dissolved from plastic tubing by benzene, reduces the mass-transfer rate by about ten times by retarding... 

The rates at which drops and bubbles rise and fall are rather more sensitive to traces of surface-active materials than are the mass-transfer coeflScients 77a, 77b). Whereas, for example, the rate of fall of CCh drops... 

If, however, trace impurities are present to an extent at which there is a stagnant film over the liquid-liquid interface, calculation shows that the mass-transfer rate should vary as with a numerical reduc-... 

A revolving propeller traces out a helix in the fluid. One full revolution moves the liquid a fixed distance. The ratio of this distance to the propeller diameter is known as the pitch. In the case of turbines, pitch is the angle the blades make with the horizontal plane. Propellers are members of the axial class of impeller agitators. The propeller is turned so that it produces a flow toward the bottom of the vessel. Propellers are more frequently used for liquid blending operations than for mass transfer pmposes (Treybal, 1980). 

This problem considers the chemically reactive flow in a long, straight channel that represents a section of an idealized porous media (Fig. 4.32). Assume that the flow is incompressible and isothermal, but that it carries a trace compound A. The compound A may react homgeneously in the flow, and it may react heterogeneously at the pore walls. Overall, the objective of the problem is to characterize the chemically reacting flow problem, including the development of an effective mass-transfer coefficient as represented by a Sherwood number. 

As an example of hydrate nucleation and growth, consider the gas consumption versus time trace in Figure 3. la for an agitated system operated at constant pressure and temperature. An autoclave cell (e.g., 300 cm3) containing water (e.g., 150 cm3) is pressurized with gas and brought to hydrate formation (P, T) conditions. The gas is added from a reservoir to maintain constant pressure as hydrates form with time. The rate of consumption of gas is the hydrate formation rate that can be controlled by kinetics, or heat or mass transfer. 

The CNG process removes sulfurous compounds, trace contaminants, and carbon dioxide from medium to high pressure gas streams containing substantial amounts of carbon dioxide. Process features include 1) absorption of sulfurous compounds and trace contaminants with pure liquid carbon dioxide, 2) regeneration of pure carbon dioxide with simultaneous concentration of hydrogen sulfide and trace contaminants by triple-point crystallization, and 3) absorption of carbon dioxide with a slurry of organic liquid containing solid carbon dioxide. These process features utilize unique properties of carbon dioxide, and enable small driving forces for heat and mass transfer, small absorbent flows, and relatively small process equipment. 

High amounts of asphaltenes and resins require high hydrogen partial pressures and may actually limit the maximum level of hydrodesulfurization, or final traces of sulfur in the residuum may only be eliminated under extremely severe reaction conditions where hydrocracking is the predominant reaction in the process. High asphaltene and resin contents are also responsible for high viscosity (Figure 6-7) which may increase the resistance to mass transfer of the reactants... 

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