Steady-State Design

In the steady-state design application, the flow rates and Gm, and concentrations Yi , Xjn, Yout and Xout will either be specified or established by an overall, steady-state solute balance, where 

Temperatures Tl in and Tq in will also be known. The problem then consists of determining the height of packing required to obtain the above separation. 

Here Klx a (kmol/m s) is the overall mass transfer coefficient for the liquid phase, based on mole fraction in the L-phase, x is the equilibrium liquid phase mole fraction, and Ac is the cross-sectional area of the column (m ). Hence 

It is assumed that there are no heat losses from the column and that there is zero heat exchange between the gas and liquid phases. Consequently the gas phase temperature will remain constant throughout the column. A liquid phase heat balance, for element of volume dV is given by 

The temperature variation throughout the column is important, since this affects the equilibrium concentration x, where 

In order to consider a reasonable system to illustrate a vapor sidestream column, we change the feed stream to contain -butanol (BuOH) instead of water. The normal boiling point of n-butanol is 390.8 K compared with 337.7 K for MeOH. This produces a relative volatility of about 4.4 thus, a vapor sidestream product with only 1 mol% BuOH can be produced with an RR of 1.07. The composition of the liquid on the sidestream drawoff tray is 4.3 mol% BuOH. 

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Constant Flow into Protected Equipment For the steady-state design scenario with a constant, steady flow of fluid from a pressure source that is above the maximum aUowed pressure in the protected equipment, volume is being generated within the equipment at a rate RV = F/ f. Substituting into Eq. (26-21) and noting that the specific volume of the vent stream is l/p, gives the required mass flow rate ... 

The eomplex FCC system involves not only turbomaehinery, but also related proeess eomponents. All of these must be properly designed and sized to operate within system parameters from startup to steady state design point, and through shutdown. System response to emergeney eonditions is also mandatory. Computer simulation is, therefore, an integral part of the design proeess. A eomputer program eapable of this simulation is deseribed below. 

Set the time derivatives in Example 12.6 to zero to find the steady-state design equations for a CSTR with a Michaelis-Menten reaction. An analytical solution is possible. Find the solution and compare it with the solution in Example 12.3. Under what conditions does the quasisteady solution in Example 12.3 become identical to the general solution in Example 12.6 ... 

The general material balance of Section 1.1 contains an accumulation term that enables its use for unsteady-state reactors. This term is used to solve steady-state design problems by the method of false transients. We turn now to solving real transients. The great majority of chemical reactors are designed for steady-state operation. However, even steady-state reactors must occasionally start up and shut down. Also, an understanding of process dynamics is necessary to design the control systems needed to handle upsets and to enable operation at steady states that would otherwise be unstable. 

The steady-state design equations (i.e., Equations (14.1)-(14.3) with the accumulation terms zero) can be solved to find one or more steady states. However, the solution provides no direct information about stability. On the other hand, if a transient solution reaches a steady state, then that steady state is stable and physically achievable from the initial composition used in the calculations. If the same steady state is found for all possible initial compositions, then that steady state is unique and globally stable. This is the usual case for isothermal reactions in a CSTR. Example 14.2 and Problem 14.6 show that isothermal systems can have multiple steady states or may never achieve a steady state, but the chemistry of these examples is contrived. Multiple steady states are more common in nonisothermal reactors, although at least one steady state is usually stable. Systems with stable steady states may oscillate or be chaotic for some initial conditions. Example 14.9 gives an experimentally verified example. 

This equation applies for t > 0 and when t is exactly zero, aout has its steady-state value, which is determined from the steady-state design equation ... 

This section concerns the modelling of countercurrent flow, differential mass transfer applications, for both steady-state and non-steady-state design or simulation purposes. For simplicity, the treatment is restricted to the case of a single solute, transferring between two inert phases, as in the standard treatments of liquid-liquid extraction or gas absorption column design. 

Using the digital simulation approach to steady-state design, the design calculation is shown to proceed naturally from the defining component balance and energy balance equations, giving a considerable simplification to conventional text book approaches. 

The tubular reactor, steady-state design equation is of interest here. The dimensional and dimensionless forms are compared for an nth-order reaction. 

With the exception of this method, all the methods described solve the stage equations for the steady-state design conditions. In an operating column other conditions will exist at start-up, and the column will approach the design steady-state conditions after a period of time. The stage material balance equations can be written in a finite difference form, and procedures for the solution of these equations will model the unsteady-state behaviour of the column. 

For steady-state design scenarios, the required vent rate, once determined, provides the capacity information needed to properly size the relief device and associated piping. For situations that are transient (e.g., two-phase venting of a runaway reactor), the required vent rate would require the simultaneous solution of the applicable material and energy balances on the equipment together with the in-vessel hydrodynamic model. Special cases yielding simplified solutions are given below. For clarity, nonreactive systems and reactive systems are presented separately. 

Continuous binary distillation is illustrated by the simulation example CON-STILL. Here the dynamic simulation example is seen as a valuable adjunct to steady state design calculations, since with MADONNA the most important column design parameters (total column plate number, feed plate location and reflux ratio) come under the direct control of the simulator as facilitated by the use of sliders. Provided that sufficient simulation time is allowed for the column conditions to reach steady state, the resultant steady state profiles of composition versus plate number are easily obtained. In this way, the effects of changes in reflux ratio or choice of the optimum plate location on the resultant steady state profiles become almost immediately apparent. 

AMMONAB - Steady-State Design of a Gas Absorption Column with Heat Effects System... 

In this section we have presented modeling results for industrial type IV FCC units that produce high octane number gasoline from gas oil. Such units consist of two connected bubbling fluidized beds with continuous circulation of the catalyst between the two vessels, the reactor and the regenerator. The steady-state design equations are nonlinear transcendental equations which can be solved using the techniques described in the earlier chapters of the book. 

In this chapter we study the steady-state design of perfectly mixed, continuously operating, liquid-phase reactors. The effects of a wide variety of reaction types, kinetics, design parameters, and heat removal schemes are explored. The important elfects of design conversion and design temperature on heat transfer area and other process parameters are quantitatively studied. 

Several important types of reactions are considered in the following sections. The equations describing each of these systems are developed. The steady-state design of CSTRs with these reactions are discussed, using Matlab programs for hypothetical chemical examples and the commercial software Aspen Plus for a real chemical example. 

Given conversion and parameter values, program calculates % Steady-state design (volume,jacket area, coolant flow and temp)... 

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