Membranes Operating equations

The jfipervap term in Equation (9.2) and Equation (9.5) can be derived in terms of /3evap, membrane permeabilities, and membrane operating conditions using the standard solution-diffusion model from Chapter 2. The membrane fluxes can be written as... 

During UF membrane operation, there is a volume rejection. Thus, ultrafiltration data can be presented in terms of volume concentration ratio (VCR) or concentration factor (CF) as shown by the following equation ... 

Undoubtedly, this new kind of integrated approach is well representative of what should be membrane engineering, with final objectives clearly defined, the right hypothesis and choice of simple equations for modeling, a realistic representation of real complex solutions and the set-up of efficient simulation tools involving successive intra- and extrapolation steps. It appears to be easily extended to other membrane operations, in other fields of applications. It should provide stakeholders with information needed to make their decision costs, safety, product quality, environment impact, and so on of new process. Coupled with the need to check the robustness of the new plant and the quality of final output, it should constitute the right way to develop the use of membranes as essential instruments for process intensification with industrial units at work. 

Wardius [51] extended the advancing front model to be employed to multistage mixer-settler systems for liquid membrane operations. They presented a zero order solution to the perturbation equations based on the model developed by Ho et al. [29]. The emulsion globule residence time distribution in each mixer was assumed to be exponential and the fractional utilization of internal reagent was given by... 

The model assumes that the driving force for diffusion depends on the difference between the partial pressures of each component across the membrane as described in the following equation for steady-state operation [Equation (10.1)]. 

If we pick a value of Mx we can determine n(M . ) and calculate Xp. Then we can generate the RT curve including nonlinear osmotic pressure and concentration polarization. If the membrane module is perfectly mixed, the operating equation is... 

In the absence of experimental data for extended temperature range, the 30°C sorption data and Equation 9.13 are generally assumed as applicable to membranes operating at a higher temperature of 80°C. The variation of water content in Nafion-117 with water activity is plotted in Figure 9.10. 

There are two other aspects of importance in practical ultrafiltration processing time and the membrane area. A brief treatment of processing time with a view to minimizing it will be considered now. The processing time depends on a variety of factors the total volume to be processed the concentration of retained solids, especially if it leads to gel polarized operation (equation (6.3.143)) the mode of operation (continuous, batch, etc.) (Cherytm, 1986). One approach suggested by Ng et al. (1976) employs the gel-polarized condition and perfect rejection of the protein i for continuous diafiltration operation ... 

A slight decrease in solvent flux was also observed after 50 h of continuous operation at transmembrane pressure of 0.5 bar. This observation can be explained by the internal pore clogging and external surface fouling due to insoluble iron oxide/hydroxide precipitation that reduced the pore size of the membrane. Such phenomena have been extensively studied and reported in the literature (Tansel et al., 2000). Taking into account the adverse effects on the permeation property that occurred for long duration of membrane operation, the Hagen-Poiseuille equation is written as follow ... 

In both of these pieces of apparatus, isothermal operation and optimum membrane area are obtained. Good temperature control is essential not only to provide a value for T in the equations, but also because the capillary attached to a larger reservoir behaves like a thermometer, with the column height varying with temperature fluctuations. The contact area must be maximized to speed up an otherwise slow equilibration process. Various practical strategies for presetting the osmometer to an approximate n value have been developed, and these also accelerate the equilibration process. 

Basic Principles of Operation RO and NF are pressure-driven processes where the solvent is forced through the membrane by pressure, and the undesired coproducts frequently pass through the membrane by diffusion. The major processes are rate processes, and the relative rates of solvent and sohite passage determine the quality of the product. The general consensus is that the solution-diffusion mechanism describes the fundamental mechanism of RO membranes, but a minority disagrees. Fortunately, the equations presented below describe the obseiwed phenomena and predict experimental outcomes regardless of mechanism. 

Salt flux across a membrane is due to effects coupled to water transport, usually negligible, and diffusion across the membrane. Eq. (22-60) describes the basic diffusion equation for solute passage. It is independent of pressure, so as AP — AH 0, rejection 0. This important factor is due to the kinetic nature of the separation. Salt passage through the membrane is concentration dependent. Water passage is dependent on P — H. Therefore, when the membrane is operating near the osmotic pressure of the feed, the salt passage is not diluted by much permeate water. 

Equations (22-86) and (22-89) are the turbulent- and laminar-flow flux equations for the pressure-independent portion of the ultrafiltra-tion operating curve. They assume complete retention of solute. Appropriate values of diffusivity and kinematic viscosity are rarely known, so an a priori solution of the equations isn t usually possible. Interpolation, extrapolation, even precuction of an operating cui ve may be done from limited data. For turbulent flow over an unfouled membrane of a solution containing no particulates, the exponent on Q is usually 0.8. Fouhng reduces the exponent and particulates can increase the exponent to a value as high as 2. These equations also apply to some cases of reverse osmosis and microfiltration. In the former, the constancy of may not be assumed, and in the latter, D is usually enhanced very significantly by the action of materials not in true solution. 

The foregoing equations assume that membrane performance is time independent. In some cases, a noticeable reduction in permeability occurs over time primarily due to membrane fouling. In such cases, design and operational provisions are used to maintain a steady performance of the system (Zhu et a ., 1997). 

The permeation dosimeter operates on the principle that the rate at which a gas permeates a given membrane is a fixed value, and the total mass of the gas that is transported through the membrane is a function of the concentration of the gas in the ambient atmosphere and the time of exposure. The quantity of analyte collected is given by equation (8.8)... 

A more detailed explanation of these equations can be found in Elardee [4]. The close monitoring of cell voltages is expected to enable operators to observe problems with membrane blistering and potentially dangerous situations such as membrane tears before they become dangerous or explosive. 

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