Mass balance membrane cells

The permeability class boundary is based indirectly on the extent of absorption (fraction of dose absorbed, not systemic BA) of a drug substance in humans and directly on measurements of the rate of mass transfer across human intestinal membrane. Alternatively, nonhuman systems capable of predicting the extent of drug absorption in humans can be used (e.g., in vitro epithelial cell culture methods). In the absence of evidence suggesting instability in the gastrointestinal tract, a drug substance is considered to be highly permeable when the extent of absorption in humans is determined to be 90% or more of an administered dose based on a mass balance determination or in comparison to an intravenous reference dose. 

The concentration polarization occurring in electrodialysis, that is, the concentration profiles at the membrane surface can be calculated by a mass balance taking into account all fluxes in the boundary layer and the hydrodynamic conditions in the flow channel between the membranes. To a first approximation the salt concentration at the membrane surface can be calculated and related to the current density by applying the so-called Nernst film model, which assumes that the bulk solution between the laminar boundary layers has a uniform concentration, whereas the concentration in the boundary layers changes over the thickness of the boundary layer. However, the concentration at the membrane surface and the boundary layer thickness are constant along the flow channel from the cell entrance to the exit. In a practical electrodialysis stack there will be entrance and exit effects and concentration... 

The retention of membranes are often measured in stirred cells. A mass balance on the cell integrated over time from an initial retentate volume (V ) and initial concentration (Q,) to a final retentate volume (Vf) and final retentate concentration (Cf) yields the following expression for the retention (R) ... 

To capture the dynamics of PEM fuel cell startup it is essential to include the dynamic mass balance for the water content in the membrane, TV . If water accumulation in the hydrophobic gas diffusion layer is neglected, then the water accumulation in the membrane is the difference between the water produced and the net water removed by convection from the anode and cathode, as given by Eq. (3.4). We measure all the quantities on the right-hand side of Eq. (3.4), so we can determine the accumulation rate of water. 

The problem, hence, is governed by the following system of equations. First is the equation of oxygen mass balance in the channel (6.37). Second is the condition of equipotentiality of cell electrodes. Now, however, voltage loss in membrane is not negligible, and this condition reads... 

Figure 10.3 Schematic of three discretized membrane cells with quantities used for mass and energy balances for membrane cell k.

The membrane module is solved by discretizing the membrane area into 100 cells of equal area, and each cell model is given by Equations (10.1) and (10.2). The final set of mass and energy balances for cell k (Figure 10.3) of the membrane unit are as shown in Equations (10.3)-(10.7) ... 

Here, F, Zf and h are, respectively, the molar flow rate, mole fraction of component of i and total enthalpy, all in cell k their subscripts, ret and perm, refer to retentate and permeate streams. Equations (10.4) and (10.5) are mass balances and mass-transfer equations for each of the components present in the membrane feed. The cross-flow model [Equations (10.3)-(10.7)] was implemented in ACM v8.4 and validated against the experimental data in Pan (1986) and the predicted values of Davis (2002). The Joule-Thompson effect was validated by simulating adiabatic throttling of permeate gas through a valve in Aspen Hysys. Both these validations are described in detail in Appendix lOA. 

The molar flux through the differential element of dilute solution compartment in a membrane cell pair in terms of mass balance and current density can be written as follows ... 

Let us consider a two-compartment model (Fig. 1.2) consisting of an intracellular pool (compartment 1) and an extracellular pool (compartment 2). Urea is produced by the intracellular pool and is transported across the cell membrane into the interstitial fluids and then into the blood stream. Mass balance for these two compartments can be expressed as... 

To provide a feel for the quantities involved in a chlor-alkali plant and to allow us to illustrate the size of some of the key equipment, we adopt here a reference plant based on the use of membrane cells and calculate an approximate electrolysis area mass balance. The characteristics of this plant serve as reference material for the specific examples used in later chapters. We defer energy considerations to those later chapters, but we list here all the relevant parameters. 

Fuel cells must carry the costs of conditioning the two reactant gases as well as their own capital charges. Hydrogen requires transport to the anode side of the fuel cells. This is usually by rotary blower, but it also should be possible to operate membrane cells at some positive pressure and then to deliver the hydrogen without mechanical aid. The temperature and water content of the hydrogen must be considered in the overall heat and mass balance. Air and oxygen are candidates for use at the cathodes. The classical balance between cost and efficiency determines the choice. Wth alkaline fuel cells, the carbon dioxide in the air is of concern. It can consume the hydroxide value and contaminate the end product. It is possible to scrub the air to remove the CO2 before... 

Where possible, a single electrolyte compartment in an undivided cell geometry is favored as it considerably simplifies the constmction, electrolyte flow circuit and maintenance needs, while avoiding the potential drop and mass balance problems which can be associated with a microporous separator or ion-exchange membrane. 

For a typical one-molar methanol concentration, the electro-osmotic flux of methanol in the membrane is small as compared to the methanol diffusion. The expression for the crossover current follows from the methanol mass balance in the cell (Kulikovsky, 2002b)... 

A common altemative used where possible is the diafUtration mode with a crossflow UF membrane unit and concentrate recycle (Figure 7.2.5(e)). Here the solution concentration and viscosity are not allowed to increase due to the continuous addition of buffer replacing the permeate volume lost Equations developed in Section 6.4.2.1 for well-stirred UF cells having continuous diafUtration may be used here with appropriate care since we can treat the crossflow UF device as a blackbox far the purpose of an overall process mass balance and solute selectivity analysis. Similarly, the equations developed in Section 6.4.2.1 for a batch concentration process may be utilized here to determine various quantities, such as the yield of macrosolute, retentate concentration, etc. 

Back diffusion of water depends on water concentration on both sides of the membrane, water diffusivity through the membrane, and membrane thickness. Because water concentration is not uniform, it is not easy to explicitly calculate back diffusion for the entire cell or a stack of cells. For the sake of mass balance, back diffusion may be expressed as a fraction, p, of electroosmotic drag. When P = 1, back diffusion is equal to electroosmotic drag, that is, there is no net water transport across the membrane. The coefficient p may be determined experimentally by carefully condensing and measuring water content in both anode and cathode exhaust streams. 

---