Model perfect mixing membrane

They have also modeled a perfectly mixed membrane reactor for the same reaction. For this membrane configuration, the C2 selectivity is essentially 1(X)% for a jo value of less than 0.2 and drops off rapidly with increasing The yield becomes greater as the relative oxygen permeation rate increases. The yield reaches a maximum and then decreases with the permeation rate. There is only a limited range of Jo in which the yield can reach beyond 20%. 

Several authors have already developed methodologies for the simulation of hybrid distillation-pervaporation processes. Short-cut methods were developed by Moganti et al. [95] and Stephan et al. [96]. Due to simplifications such as the use of constant relative volatility, one-phase sidestreams, perfect mixing on feed and permeate sides of the membrane, and simple membrane transport models, the results obtained should only be considered qualitative in nature. Verhoef et al. [97] used a quantitative approach for simulation, based on simplified calculations in Aspen Plus/Excel VBA. Hommerich and Rautenbach [98] describe the design and optimization of combined pervaporation-distillation processes, incorporating a user-written routine for pervaporation into the Aspen Plus simulation software. This is an improvement over most approaches with respect to accuracy, although the membrane model itself is still quite... 

Figure 10.3 Schematic diagram of a single cell or perfect mixing model for a packed-bed membrane shcll-and-tube reactor...

None of the above studies, however, deals with the detailed hydrodynamics in a membrane reactor. It can be appreciated that detailed information on the hydrodynamics in a membrane enhances the understanding and prediction of the separation as well as reaction performances in a membrane reactor. All the reactor models presented in Chapter 10 assume very simple flow patterns in both the tube and annular regions. In almost all cases either plug flow or perfect mixing is used to represent the hydrodynamics in each reactor zone. No studies have yet been published linking detailed hydrodynamics inside a membrane reactor to reactor models. With the advent of CFD, this more complete rigorous description of a membrane reactor should become feasible in the near future. 

The equations derived in the previous section represent penneation rates and flux, and Examples 18.1 and 18.2 are apphcations to a speciflc model. The model assumes the fluid on each side of the membrane to have a constant composition parallel to the membrane. The compositions normal to the membrane are also assumed constant, with the possible exception of composition gradients in the films adjacent to the membrane. The bulk phase compositions on both sides of the membrane had to be given since no material balances were considered. The flow pattern implied in this model is that of perfect mixing (if the film resistances next to the membrane are neglected). Other flow patterns include cross flow, countercurrent flow, and cocurrent flow. 

A membrane separator using 1 mil thickness low-density polyethylene membrane is to be designed for concentrating hydrogen in a hydrogen-methane-carbon monoxide gas mixture. The separator performance may be approximated by a perfect mixing model. The feed flow rate is 1.0 x 10" cnf (STP)/s, and its composition and component permeabilities in polyethylene membrane are given below ... 

The driving force in gas permeation may be expressed in terms of the difference between a component partial pressure on the residue side and the permeate side of the membrane. The feed is introduced to the separator at a high pressure, while the permeate side is controlled at a low pressure. Examples 18.3 and 18.4 use the perfect mixing model for the performance evaluation and the design of two gas permeation processes. 

It is required to design a reverse osmosis unit to process 2500 mVh of seawater at 25°C containing 3.5 wt% dissolved salts, and produce purified water with 0.05 wt% dissolved salts. The pressure will be maintained at 135 atm on the residue side and 3.5 atm on the permeate side, and the temperature on both sides at 25°C. The dissolved salts may be assumed to be NaCl. With the proposed membrane, the salt permeance is 8.0 x 10 m/h and the water permeance is 0.085 kg/rn-.h.atrn. The density of the feed seawater is 1020 kg/m ( of the permeate, 997.5 kg/nv and of the residue (with an estimated salt content of 5 wt%), 1035 kg/rnc Assuming a perfect mixing model and neglecting the mass transfer resistances, determine the required membrane area and calculate the product flow rates and compositions. 

The pressure is 3500 kPa on the residue side and 140 kPa on the permeate side. The composition on the permeate side is specified at 95 mol%. Assuming a perfect-mixing model, calculate the required membrane area. Use a fraction of feed permeated, 0 = 0.15. Calculate the product rates and compositions, and check if 0 needs to be modified. 

Besides the differential equations the complete formulation of the model requires a set of initial and boundary conditions. These must reflect the situation at the interface between measuring solution and enzyme electrode membrane and between membrane and sensor. For the models considered, it is assumed that the measuring solution is perfectly mixed and contains a large amount of substrate as compared to the substrate converted in the enzyme membrane. It has been shown experimentally (Carr and Bowers, 1980) that in measuring solutions diffusion is much more rapid than in membranes. A boundary layer effect is not considered. On the sensor side all electrode-inactive substances fulfill zero flux conditions. If the model contains more than one layer the transfer between the layers may be modeled by using relations of mass conservation. The respective equations will be given in the following sections. 

Apply the perfect-mixing and crossflow models to solve gas permeation problems in membrane modules. 

Models Considering Membrane Diffusion. The following model has been used when assuming that the electrode response is a first-order lag function, the liquid and gas phases are perfectly mixed, there is negligible nitrogen diffusion, and the interfacial area and oxygen concentration in the gas phase are constant (Blazej et al., 2004a Chisti, 1989 Freitas and Teixeira, 2001 Fuchs et al., 1971) ... 

Some of these studies focused on the analysis of equilibrium-limited reactions, namely those in which the conditions of the respective conversion could be enhanced relatively to the value obtained in a conventional reactor, the so-called thermodynamic equilibrium conversion.i i The developed models considered generic equilibrium-limited reactions carried on in membrane reactors with perfectly mixed or plug-flow pattems. In all these studies, the main assumptions considered consisted in isothermal and steady-state operation, Fickian transport across a non-porous membrane with a homogeneously distributed nanosized catalyst with constant diffusion coefficients, Henry s law for describing the equilibrium condition at the interfaces membrane/gas, and equality of local concentrations at the interface polymer phase/catalyst surface. 

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