Membrane separation mass balance

Excel was then used to generate the membrane area, mass balance, energy consumption and operating cost simultaneously over the range of recovery (10-90%), temperature (25-90°C) and permeate presstrre (up to 1.5 bar). The permeate that produced the lowest specific operating cost ( /kg H2 separated) and met the purity specification for a certain recovery was selected and the corresponding membrane area and energy consumption recorded. The objective fimction for the optimization (minimization) was... 

Because oxygen from the tank is completely dry, the amount of water at the stack inlet is equal to the amount of water vapor at the stack outlet. This also means that the amount of liquid water separated at the stack outlet is equal to water generated in the stack, plus any net water transport from the anode through the membrane. The mass balance equation is ... 

A complete or global tissue distribution model consists of individual tissue compartments connected by the blood circulation. In any global model, individual tissues may be blood flow-limited, membrane-limited, or more complicated structures. The venous and arterial blood circulations can be connected in a number of ways depending on whether separate venous and arterial blood compartments are used or whether right and left heart compartments are separated. The two most common methods are illustrated in Figure 3 for blood flow-limited tissue compartments. The associated mass balance equations for Figure 3A are... 

The situation is somewhat different with porous membranes, where the permselectivities for all components do not equal zero but exhibit certain values determined in most cases by the Knudsen law of molecular masses. In general, when porous membranes are used as separators in a membrane reactor next to the catalyst or the reaction zone (Figure 7.2a), it has been shown experimentally (Yamada et al. 1988) and theoretically (Mohan and Govind 1986, 1988a, b, Itoh et al. 1984, 1985) that there is a maximum equilibrium shift that can be achieved. On the basis of simple mass balances one can calculate that this maximum depends on, besides the reaction mechanism, the membrane permselectivities (the difference in molecular weights of the components to be separated) and it corresponds to an optimum permeation to reaction-rate ratio for the faster permeating component (which is a reaction product). 

Chemical species can transfer between phases, and this represents the coupling between the mass-balance equations. This geometry looks like a membrane reactor in which a permeable area A (dashed lines) separates the phases, but all multiphase reactors can be described by this notation. 

Chemical equilibrium and analysis of a mixture. A remote optical sensor for C02 in the ocean was designed to operate without the need for calibration.21 The sensor compartment is separated from seawater by a silicone membrane through which C02, but not dissolved ions, can diffuse. Inside the sensor, C02 equilibrates with HCO3 and CO3-. For each measurement, the sensor is flushed with fresh solution containing 50.0 pM bromothymol blue indicator (NaHIn) and 42.0 pM NaOH. All indicator is in the form HIn-or In2 near neutral pH, so we can write two mass balances (1) [HIn ] + [In2-] = Fln = 50.0 pM and (2) [Na"] = FNa = 50.0 pM + 42.0 pM = 92.0 pM. HIn- has an absorbance maximum at 434 nm and In2 has a maximum at 620 nm. The sensor measures the absorbance ratio RA = A620/A434 reproducibly without need for calibration. From this ratio, we can find C()2( [Pg.420]

A fundamental innovative aspect of chemical MRs is the separation operated by means of the membrane. In fact, the mass-balance equations have to take into account the mass transfer due to the permeation through the membrane the other terms being the same present in mass-balance equations of TRs. Figure 13.4 introducing reaction paths for MSR at different values of hydrogen permeance shows a very large difference with the permeance and also with the path of a TR. 

The permeability is a property of the membrane material of the separating layer, whereas the permeance is also a property of the product membrane in its entirety considering thickness, the eventual support, defects, and so on. For this reason, the permeance will be used instead of permeability in subsequent mass-balance equations. 

Fundamental aspects of chemical membrane reactors (MRs) were introduced and discussed focusing on the peculiarity of MRs. Removal by membrane permeation is the novel term in the mass balance of these reactors. The permeation through the membrane is responsible for the improved performance of an MR in fact, higher (net) reaction rates, residence times, and hence improved conversions and selectivity versus the desired product are realized in these advanced systems. The permeation depends on the membranes and the related separation mechanism thus, some transport mechanisms were recalled in their principal aspects and no deep analysis of these mechanisms was proposed. 

The selectivity should be greater than 20 to accomplish significant separation of species / from species j. For a completely mixed membrane system, the external mass balance yields... 

Eor a complete description of the separation process, it is necessary to include the mass balances in the emulsion reservoirs as well as the interfacial equilibrium expression at the feed-membrane side. 

C) Equations (20.6-13)-(20.6-23) are inconvenient to use for the case in Fig. 20.6-4tr where the membrane area is given, but the stage-cut is unknown. Direct numerical integration or the mass balance eqontions is preferred Tor this arrangement, which will be shown later for a hollow.fiber separator. 

Consider separation of a binary mixture in a membrane module with the crossflow pattern shown in Figure 9.3. The feed passes across the upstream membrane surface in plug flow with no longitudinal mixing. The pressure ratio and the ideal separation factor are assumed to remain constant. Film mass-transfer resistances external to the membrane are assumed to be negligible. A total mass balance around the differential-volume element gives... 

Traditionally, it was believed that RCMs were only suitable for equilibrium-based separations and could not be used for the representation of kinetically based processes [15]. However, the differential equations which describe a residue curve are simply a combination of mass balance equations. Because of this, the inherent nature of RCMs is such that they can be used for equilibrium- as well as non-equilibrium-based processes. This now allows one to consider kinetically based processes, such as reactive distillation (see Chapter 8) as well as membrane separation processes. 

However, in spite of the known advantages and applications of liquid membrane separation processes in hollow-fiber contactors, there are scarce examples of industrial application. The industrial application of a new technology requires a reliable mathematical model and parameters that serve for design, cost estimation, and optimization purposes allowing to accurate process scale-up. " The mathematical modeling of liquid membrane separation processes in HFC is divided into two steps (1) the description of the diffusive mass transport rate and (2) the development of the solute mass balances to the flowing phases. 

To conclude, one should note that the mass balances can also be modified by using permselective or specific membranes in some industrial processes. A good example of such applications includes the use of anionic and cationic membranes to desalinate sea water or other methods of separation or purification. 

For it to be useful, we need to couple Pick s law with mass balances. The first case considered is steady-state diffusion with no convection in the direction of diffusion. This is an inportant practical case for measuring diffusion coefficients, studying steady-state evaporation and steady-state permeation of gases and liquids in membranes, and in design of distillation and some other separation processes. The second case we consider is unsteady diffusion with no convection in the direction of diffusion, which is of practical significance in controlled-release drug delivery and in some batch reactors and separation processes. 

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. 

Consequently, it has been considered the most basic model to describe the separation of metallic components using hollow fiber membranes, which consists of a set of coupled differential equations corresponding to the mass balances of the metallic... 

It has previously been indicated (see Table 8.2) that membrane-based gas separation processes, while still of considerable complexity, can be modeled at the level of ODEs. This is because the principal transport resistance resides within the membrane itself and because the mass balances need therefore be concerned only with concentration changes in the direction of flow. These equations, however, must be supplemented by force balances to take account of the nonlinear pressure drop associated with permeation processes. The resulting set of ODEs will generally have to be solved numerically. We do not take up this problem here but instead acquaint the reader with two important system parameters that provide useful information for a preliminary assessment of these operations. These parameters are the pressure ratio ( ) and the membrane selectivity a. 

Note Using equation (6.4.122a) in mass balance (6.4.120b) for spedes A, we obtain tbe equation corresponding to (6.2.44) for a continuous stirred tank separator having one membrane surface.)... 

The above discussions pertain to models assuming three regions the dense phase, bubble phase and separation side of the membrane. The membrane is assumed to be inert to the reactions. There are, however, cases where the membrane is also catalytic. In these situations, a fourth region, the membrane matrix, needs to be considered. The mass and heat balance equations for the catalytic membrane region will both contain reaction-related terms. 

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