Mass transfer circuits

Once again, application of the Ohm s law analogy allows construction of mass transfer circuits to describe a specific drying application. The mass flow through the circuits derived from Fig. 2 can be described using... 

As shown in Fig. 13-92, methods of providing column reflux include (a) conventional top-tray reflux, (b) pump-back reflux from side-cut strippers, and (c) pump-around reflux. The latter two methods essentially function as intercondenser schemes that reduce the top-tray-refliix requirement. As shown in Fig. 13-93 for the example being considered, the internal-reflux flow rate decreases rapidly from the top tray to the feed-flash zone for case a. The other two cases, particularly case c, result in better balancing of the column-refliix traffic. Because of this and the opportunity provided to recover energy at a moderate- to high-temperature level, pump-around reflirx is the most commonly used technique. However, not indicated in Fig. 13-93 is the fact that in cases h and c the smaller quantity of reflux present in the upper portion of the column increases the tray requirements. Furthermore, the pump-around circuits, which extend over three trays each, are believed to be equivalent for mass-transfer purposes to only one tray each. Bepresentative tray requirements for the three cases are included in Fig. 13-92. In case c heat-transfer rates associated with the two pump-around circuits account for approximately 40 percent of the total heat removed in the overhead condenser and from the two pump-around circuits combined. 

Checking the absence of internal mass transfer limitations is a more difficult task. A procedure that can be applied in the case of catalyst electrode films is the measurement of the open circuit potential of the catalyst relative to a reference electrode under fixed gas phase atmosphere (e.g. oxygen in helium) and for different thickness of the catalyst film. Changing of the catalyst potential above a certain thickness of the catalyst film implies the onset of the appearance of internal mass transfer limitations. Such checking procedures applied in previous electrochemical promotion studies allow one to safely assume that porous catalyst films (porosity above 20-30%) with thickness not exceeding 10pm are not expected to exhibit internal mass transfer limitations. The absence of internal mass transfer limitations can also be checked by application of the Weisz-Prater criterion (see, for example ref. 33), provided that one has reliable values for the diffusion coefficient within the catalyst film. 

Besides mass transfer limitations, it is very important in electrochemical promotion experiments to compute the maximum mass-balance allowable rate enhancement. This is intimately related to the conversion of the limiting reactant under open circuit conditions, as the conversion of the latter cannot exceed 100%. In this respect keeping the open circuit conversion as low as possible (normally by using a small amount of catalyst) allows the system to exhibit a pronounced rate enhancement ratio. 

Smirnov VI (1964) A course of higher mathematics, vol II. Pergamon, London Stephan PS, Busse CA (1992) Analysis of the heat transfer coefiicient of grooved heat pipe evaporator walls. Int 1 Heat Mass Transfer 35 383-391 Tuckerman D (1984) Heat transfer micro stracture for integrated circuits. Dissertation, Stanford University, Stanford... 

Much of the optimization of the solvent extraction plant can be achieved in the pilot plant testing. As noted earlier on the subjeet of proeess design, one must investigate the dependence of the dispersion and eoaleseence char-aeteristies and their effect on extraction and phase separation. Also, such variables as metal concentration, equilibrium pH (or free aeidity or free basieity), salt concentration, solvent concentration (extraetant, diluent, and modifier), and temperature have to be studied to determine their effect on mass transfer. Although many of the variables can be tested in the pilot plant, many circuits are not optimized until the full-scale plant is in operation. 

The vapor density, like the vapor pressure, can be used as a thermodynamic potential whose total change around a closed path is zero. According to this argument, the effect of the above five factors on vapor density can be mathematically expressed and summed to zero. Beginning at the product water outlet, move to salt water by adding M, compress the salt water to pressure p, and subject it to the thermal loss of latent heat transfer, the diffusion loss of mass transfer, and the viscous loss of pressure in cellophane and manifold passages. This returns the path to fresh water and a closed circuit. 

Modeling and optimization of MBSE and MBSS of a multicomponent metallic solution in HF contactors is discussed in ref. [77]. A short-cut method for the design and simulation of two-phase HF contactors in MBSE and MBSS with the concentration-dependent overall mass-transfer and distribution coefficients taking into account also reaction kinetics was suggested by Kertesz and Schlosser [47]. Comparison of performance of the MBSE and MBSS circuit with pertraction through ELM in case of phenol removal presented Reis [78] and for copper removal Gameiro [79]. 

V and b = 0.18 V dec-1 for the current density expressed in amperes m-2. Both processes occur without any mass transfer with an efficiency of 100% in each electrode, (a) Determine the open-circuit potential of the system, (b) Determine the potential difference needed to obtain a production of Cl2 of 2.5 g hr-1, (c) If the overpotential for the evolution of H2 on the cathode in the solvent S is -1.25... 

Electrochemical reactions consist of electron transfer at the electrode surface. These reactions mainly involve electrolyte resistance, adsorption of electroactive species, charge transfer at the electrode surface, and mass transfer from the bulk solution to the electrode surface. Each process can be considered as an electric component or a simple electric circuit. The whole reaction process can be represented by an electric circuit composed of resistance, capacitors, or constant phase elements combined in parallel or in series. The most popular electric circuit for a simple electrochemical reaction is the Randles-Ershler electric equivalent... 

When we begin to investigate an electrochemical system, we normally know little about the processes or mechanisms within the system. Electrochemical impedance spectroscopy (EIS) can be a powerful approach to help us establish a hypothesis using equivalent circuit models. A data-fitted equivalent circuit model will suggest valuable chemical processes or mechanisms for the electrochemical system being studied. From Chapter 1, we know that a fuel cell is actually an electrochemical system involving electrode/electrolyte interfaces, electrode reactions, as well as mass transfer processes. Therefore, EIS can also be a powerful tool to diagnose fuel cell properties and performance. 

Ahn et al. have developed fibre-based composite electrode structures suitable for oxygen reduction in fuel cell cathodes (containing high electrochemically active surface areas and high void volumes) [22], The impedance data obtained at -450 mV (vs. SCE), in the linear region of the polarization curves, are shown in Figure 6.22. Ohmic, kinetic, and mass transfer resistances were determined by fitting the impedance spectra with an appropriate equivalent circuit model. 

In the circuit, Rs is the electrolyte resistance, CPE indicates the double-layer capacitance, Rc, is the methanol oxidation charge-transfer resistance, while R1 and Cl are the mass transfer related resistance and capacitance (mainly due to methanol adsorption or CO coverage). The physical expression of these parameters can be deduced from the reaction kinetics. In the methanol oxidation reaction, the overall charge transfer rate is the sum of each charge-transfer step (rct). The Faradaic resistance (Rj) equals the inverse of the DC polarization curve slope ... 

According to the equivalent circuit, at zero frequency the Faradaic resistance equals the sum of the charge-transfer resistance and the mass transfer resistance ... 

Figure 6.65. Equivalent circuit of a typical DMFC anode. f i and Ci are membrane resistance and capacitance, Rct and Cai are charge-transfer resistance and double-layer capacitance, andf 3 and C3 are mass-transfer-related resistance and capacitance.

From the previous discussion, equilibrium relations required for process circuit analysis are evidently in ortant. To achieve equilibrium requires equipment infinite in size, which is a physical and economical in jossibility. We must be satisfied wifii an economical approach to equilibriimi conditions. In some cases, because of rapid mass transfer or chemical reaction, the difference between actual and equilibrium conditions is insignificant. 

As described in the subsequent chapters in Part m, models for the impedance response can be developed from proposed hypotheses involving reaction sequences (e.g., Chapters 10 and 12), mass transfer (e.g., Chapters 11 and 15), and physical phenomena (e.g.. Chapters 13 and 14). These models can often be expressed in the mathematical formalism of electrical circuits. Electrical circuits can also be used to construct a framework for accounting for the phenomena that influence the impedance response of electrochemical systems. A method for using electrical circuits is presented in this chapter. 

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