Design equation graphical solution

Fig. 15. Graphical solution of the design equation for a cascade of continuous stirred tank reactors.

The concentration has to be introduced in the transformation rate expression and in the general design equation (Equation 2.76) for determining the space time for a required conversion. The space time can always be found by numerical or graphical integration. However, for simple kinetics analytical integration is possible. For the following th order reactions analytical solutions are obtained ... 

To calculate the amoimt of heat that can be removed with heat sink, one can use the natural and forced convection equations from the previous sections. Many physical designers, however, use graphical solutions instead of those based on cinves available from the heat sink manufacturer. Figure 3.11b and Figure 3.11c show the temperature rises for a finned heat sink. Figure 3.11b shows the temperature rise (AT) vs. power dissipated with natural convection whereas Figure 3.11c shows the temperature rise (AT) vs. 

Figure 4-3 Graphical solution of the design equation for an ideal CSTR for the Monod rate equation and the parameter values given in Example 4-8, Part A. Two different steady-state outlet concentrations are possible, Ca = 0.20 and 10 g/1.

Why didn t we see this bizarre behavior, e.g., washout and multiple steady states, previously The reason is that our previous examples involved normal kinetics. In all of our past work, the rate increased monotonically as the reactant concentration increased. In such a case, the graphical solution to the CSTR design equation looks as shown in Figure 4-5. 

Figure 4-5 Illustration of the graphical solution of the design equation for an ideal CSTR for a second-order rate equation. There is only one possible intersection between the —r curve and the...

In order to analyze the behavior of the reactor/exchanger combination, three tools are required an en gy balance on the reactor, an energy balance on the F/P exchanger, and the design equation for the reactor. These equations will have to be solved simultaneously. We will solve them graphically because of the valuable, visual insight that such a solution can provide. 

To obviate the tedious graphical iategration, a simplified design procedure was developed on the basis of Colburn s analytical solution, equation 56. Substitution of the ratio presents no problem because this ratio stays fairly constant ia the tower at the low coaceatratioas for which Figure 12 is... 

Computational fluid dynamics (CFD) programs are more specialized, and most have been designed to solve sets of equations that are appropriate to specific industries. They can then include approximations and correlations for some features that would be difficult to solve for directly. Four major packages widely used are Fluent (http //www.fluent.com/), CFX (now part of ANSYS), Comsol Multiphysics (formerly FEMLAB) (http //www.comsol.com/), and ANSYS (http //www.ansys.com/). Of these, Comsol Multiphysics is particularly useful because it has a convenient graphical-user interface, permits easy mesh generation and refinement (including adaptive mesh refinement), allows the user to add phenomena and equations easily, permits solution by continuation methods (thus enhancing... 

The volume of tabular information necessary to record in detail the thermodynamic data for the paraffin hydrocarbons and their mixtures, as was done for steam, is excessive. It appears hopeful that graphical generalizations typified by the work of Edmister (19) will prove adequate for the less rigorous requirements of design, whereas the Benedict equation of state (4) may be employed where precision is necessary. However, the effective application of this equation of state to compounds containing more than four carbon atoms per molecule still awaits the evaluation of the constants. After the composition and specific volume have been established for a particular state, the solution of equations of state to establish enthalpy and entropy is a straightforward process. 

For a product recovery of 96 percent, optimum solutions were obtained and are presented graphically via design charts. The design charts plot the optimum diafiltration volume and total time cycle as a function of other operating conditions, i.e., initial volume, recovery, membrane area and flux. For a recovery other than 96 percent, the optimum solution can be obtained using the equations developed in this paper in a similar manner. 

A.l Useful Integrals in Reactor Design 921 A.2 Equal-Area Graphical Differentiation 922 A.3 Solutions to Differential Equations 924 A.4 Numerical Evaluation of Integrals 924 A.5 Software Packages 926 ... 

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