Equations, design

Energy consumption can firstly be ignored in the membrane module design. The following assumptions are adopted for the derivation of design equations  

Plug flows with negligible axial dispersion for both the shell- and lumen-side streams 

Isothermal operation also no temperature gradients are present in the membrane module 

Engineering Aspects of MIEC Hollow Eiber Membranes for Oxygen Production 267 

The governing equations for different operations of the module are based on the mass conservations in the lumen- and the shell-side, respectively and are given as follows  

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Cyclone Efficiency. Most cyclone manufacturers provide grade-efficiency curves to predict overall collection efficiency of a dust stream in a particular cyclone. Many investigators have attempted to develop a generalized grade-efficiency curve for cyclones, eg, see (159). One problem is that a cyclone s efficiency is affected by its geometric design. Equation 15 was proposed to calculate the smallest particle size collectable in a cyclone with 100% efficiency (157). 

Entrance andExit SpanXireas. The thermal design methods presented assume that the temperature of the sheUside fluid at the entrance end of aU tubes is uniform and the same as the inlet temperature, except for cross-flow heat exchangers. This phenomenon results from the one-dimensional analysis method used in the development of the design equations. In reaUty, the temperature of the sheUside fluid away from the bundle entrance is different from the inlet temperature because heat transfer takes place between the sheUside and tubeside fluids, as the sheUside fluid flows over the tubes to reach the region away from the bundle entrance in the entrance span of the tube bundle. A similar effect takes place in the exit span of the tube bundle (12). 

For the air—water system, the Lewis relation shows that r = 1. Under these conditions, the two parenthetical terms on the right-hand side of equation 33 ate enthalpies, and equation 33 becomes the design equation for humidification operations ... 

The simplification of equation 33 to equation 34 is possible only if r = 1 that is, foi simple monoatomic and diatomic gases. Foi other systems the design equation can be obtained by a direct rearrangement of equation 33. 

M. V. Arastoopour, M. V. Modi, D. V. Punwani, and A. T. Talwalker,M Keview of Design Equations for Dilute Phase Gas-Solids Hori ntal Conveying Systems for Coal and Belated Material, Powder and Bulk SoHds Conference, Philadelphia, 1979. 

If data on several furnaces of a single class are available, a similar treatment can lead to a partially empirical equation based on simphfied rules for obtaining (GS )r or an effective A. Because Eq. (5-178) has a structure which covers a wide range of furnace types and has a sound theoretical basis, it provides safer structures of empirical design equations than many such equations available in the engineering hterature. 

When it is known that Hqg varies appreciably within the tower, this term must be placed inside the integr in Eqs. (5-277) and (5-278) for accurate calculations of hf. For example, the packed-tower design equation in terms of the overall gas-phase mass-transfer coefficient for absorption would be expressed as follows ... 

This equation shows that for 5 percent maldistribution, the pressure drop across the holes shoiild be about 10 times the pressure drop over the length of the pipe. For discharge manifolds with K = 0.5 in Eq. (6-147), and with 4/E/3D 1, the pressure drop across the holes should be 10 times the inlet velocity head, pV V2 for 5 percent maldistribution. This leads to a simple design equation. 

The function of the decouplers is to compensate for the undesirable process interactions represented by Gpi9 and Gp9i. Suppose that the process transfer functions are all known. Then the ide design equations are ... 

These decoupler design equations are very similar to the ones for feedforward control in an earlier section. In fact, decoupling can be interpreted as a type of feedforward control where the input signal is the output of a feedback controller rather than a measured load variable. 

In principle, ideal decouphng eliminates control loop interactions and allows the closed-loop system to behave as a set of independent control loops. But in practice, this ideal behavior is not attained for a variety of reasons, including imperfect process models and the presence of saturation constraints on controller outputs and manipulated variables. Furthermore, the ideal decoupler design equations in (8-52) and (8-53) may not be physically realizable andthus would have to be approximated. 

Overall Heat-Transfer Coeffieient The basic design equation for a heat exchanger is... 

Thermal Design If the controUing resistance for heat and mass transfer in the vapor is sensible-heat removal from the cooling vapor, the following design equation is obtained ... 

Thermal design concerns itself with sizing the equipment to effect the heat transfer necessaiy to cany on the process. The design equation is the familiar one basic to all modes of heat transfer, namely,... 

By rearrangement, this can be made into a design equation as follows ... 

Numerical values for for use in the general design equation may be calculated from experimental data by... 

Approximate design equations apphcable only to the case of pure physical desorption are developed later in this sec tion for both packed and plate stripping towers. A more rigorous approach using distiUation concepts may oe found in Sec. 13. A brief discussion of desorption with chemical reac tion is given in the subsec tion Absorption with Chemical Reaction. ... 

The number of transfer units can be calculated from the adiabatic design equation, Eq. (14-46) ... 

For example, the packed-tower design equation for a dilute system in which gas-phase reaciant A is being absorbed and reacted with liquid-phase reagent B is... 

For an isothermal absorber involving a dilute system in which a liquid-phase mass-transfer limited first-order irreversible chemic reaction is occurring, the packed-tower design equation is derived as... 

When one of these three conditions is apphcable, the appropriate design equation can be obtained by substitution into Eq. (14-71), followed by integration of the resulting relationship. 

Pickiug up the solids at the bottom of the tank depends upon the eddies and velocity fluctuations in the lower part of the tank and is a different criterion from the flow pattern required to keep particles suspended and moving in various velocity patterns throughout the remainder of the vessel This leads to the variables in the design equation and a relationship that is quite different when these same variables are studied in relation to complete uniformity throughout the mixing vessel. 

This, then, is our final design equation. It shows how the survival probability depends on both the stress (rand the volume V of the component. In using it, the first step is to fix on an acceptable failure probability, Pp 0.3 for chalk, 10 for the cutting tool, 10 for the vacuum-chamber window. The survival probability is then given by P = 1 -. ... 

D. Caleulate the eomponent values and ratings from the design equations using your partieular set of operating eonditions. 

Application of the Design Equations to Packed Liquid Chromatography Columns and Open Tubular Gas Chromatography Columns... 

At the end of this chapter you will find three annexes. The first of these is a list of nomenclature used in the chapter. There are quite a few design equations that are summarized in the foregoing sections and, hence, you will need to refer to this... 

Modeling of Chemioal Kinetios and Reaotor Design Equation 3-42 is resolved into partial fraetions as... 

The type of optimum reaetor that will proeess 200 m /hr is a eon-tinuous flow stirred tank reaetor (CFSTR). This eonfiguration operates at the maximum reaetion rate. The volume V[ of the reaetor ean be determined from the design equation ... 

For the ideal reactors considered, the design equations are based on the mass conservation equations. With this in mind, a suitable component is chosen (i.e., reactant or product). Consider an element of volume, 6V, and the changes occurring between time t and t + 6t (Figure 5-2) ... 

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