Optimum Steady-State Designs

The design objective is to obtain 95% conversion for fixed fiesh feed flowrates (Fqa and Fob) of 12.6 mol/s and product purilies of both components C and D of 95 mol%. The assumptions, specifications, and steady-state design procedures used for both process flowsheets are the same as used earlier in this chapter. There arc three optimization variables for the conventional multiunit process molar holdup in the reactor Vr, composition of reactant B in the reactor zb. and reactor temperature Tr. 

Conventional Process. In each of the distillation columns of the conventional flowsheet, geometric average relative volatilities are calculated from the reflux-drum and base temperatures. The operating pressure is fixed by specifying the reflux-dmm temperature at 320 K so that cooling water can be used in the condenser. The vapor pressures of the pure components and liquid compositions in the reflux drum and column base are known, so the relative volatilities can be calculated at both locations and averaged. 

Reflux-dmm temperatures are constant for both columns for different values of a39o. However, base temperatures acmally decrease slightly as the reference relative volatilities decrease from case to case. This occurs because of the way we modified the vapor pressures. The vapor pressure constants for component A were held constant. The Bj coefficients of the other three components were modified to make the relative volatilities decrease with temperature. This produces a higher vapor pressure for component D at higher temperatures than it did in the constant relative volatility simation. 

TABLE 3.7 Optimization Results for Conventional Process (Temperature-Dependent tVy) 

ECONOMIC COMPARISON OF REACTIVE DISTILLATION WITH A CONVENTIONAL PROCESS 

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The four types of tubular reactor systems designed in Chapter 5 are investigated for dynamic controllability in this chapter. The four flowsheets are given in Figures 6.1 -6.4 with stream conditions and equipment sizes shown. These are the optimum economic flowsheets for the expensive catalyst cases. A three-bed cold-shot system is shown, but a seven bed system is the optimum steady-state design. As we will show, the seven bed system is uncontrollable. 

If the number of reactors is reduced, the interaction is less and the system can be made closedloop-stable. This is illustrated by considering a system with three adiabatic cold-shot reactors. The optimum steady-state design of the three-stage system is studied (steady-state conditions are given in Fig. 6.3). 

The most beneficial practical use of these models is in the design and optimization of these industrial units. In fact, most industrial unit s design and optimization is based on steady-state design, with the dynamic models developed in a later stage for the design of the proper control loops in order to keep the reactor dynamically operating near its optimum steady-state design in the face of external disturbances. 

Direct comparisons of the conventional multiunit process with the reactive column process at their economic optimum steady-state designs are given in Table 3.5 for five different kinetic cases. The results indicate that the TACs of both design configurations decrease as the value of (ATeq)366 increases. The results also show that the reactive distillation column configuration has lower capital cost and energy cost than the conventional configuration for all kinetic cases. These costs result in lower TAC for the reactive distillation columns compared to the reactor/column/recycle systems. 

The lower gr h in Figure 16.7 compares the economic optimum steady-state design of the column/side reactor process with those of the reactive distillation column and the multiunit conventional process. The reactive distillation column is the most economical alternative for the a39o = 2, where thoe is noreaction/separation temperature mismatch. The column/ side reactor process becomes more attractive as the mismateh of reaction/separation temperatures becomes more severe. The distillation column with a side reactor is economically superior for reference relative volatilities that arc smaller than 1.5 for this case study. 

Control StniCturB CSS. As mentioned in the previous section, it is desirable to use inferential temperature measurements instead of direct composition measurements whenever possible. However, the results show that control structure CS7 is not an effective control structure, at least with the optimum steady-state design studied here. It appears that some direct composition information about the reactant inventory inside the system is required for a more effective control system because the column is designed for neat... 

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. 

The energy cost and the total annual cost (TAC) are also calculated. The reactor volume that minimizes TAC is the optimum economic steady-state design. 

This chapter presents a comparison of the steady-state economics of four alternative tubular reactor systems. The entire process will be considered, not just the reactor in isolation, because the optimum economic steady-state design can be determined only for the entire plant. The type of recycle, the phase of the reaction, and the heat transfer configuration all affect the optimum design. 

Optimum operating conditions and equipment sizes are found. The effect of catalyst cost on the steady-state design is considered. 

For the expensive catalyst, the optimum economic steady-state design has a vessel with seven beds. The TAC is 2.03 x 106 per year, which is about half that of the single adiabatic reactor system. The recycle flowrate is 0.66kmol/s, which is more than that of the interstage-cooled system because of the use for cold feed to provide cooling. The total catalyst in all the beds is 33,800 kg. The optimum bed inlet temperatures range from Ti = 475 K to 7V = 486.9 K. The optimum yRA/ymi ratio is 0.994. 

Table 6.8 shows the optimum economic steady-state design for the hot reactor system when the catalyst cost is 100/kg. The important steady-state design parameters for this hot reaction system are a total catalyst weight of 11,880 kg, a recycle flow of 0.27kmol/s, a tube diameter of 0.0592 m, and a heat transfer area of 401 m2. The design optimization variables used are the same as discussed in Chapter 5. The TAC of the optimum design is 770,000 per year. 

The optimum steady-state economic design was determined with these new kinetic parameters, and the parameters are given in Table 7.4. The FS2 flowsheet is used with a ratio (2p,/2totai = 0.1. The impact of the kinetic parameters on the optimum design is striking. The hotter reaction requires a much larger recycle flowrate and a higher reactor inlet temperature for the same reactor exit temperature 7 ollt = 500 K. These lead... 

The optimum economic steady-state design of a two-column direct-separation sequence is shown in Figure 12.18. The number of trays, feed tray locations, and reflux ratios were varied in each column to find the configuration giving the minimum TAC. An additional... 

The practical advantages gained from the use of steady-state models in design, optimization, and operation of catalytic reactors are tremendous. It is estimated that about 80—85% of the success of the process depends on the steady-state design and the remaining 15—20% depends on the successful dynamic control of the optimum steady state. These estimates are, of course, made for a process operating smoothly with conventional control which is not model based. However, in certain cases, inefficient dynamic control may cause temperature runaway or a complete shutdown of the process. 

For most continuous processes operating under steady-state conditions, dynamic models are used to design appropriate control loops that minimize the deviation of the process dynamically from the optimum steady-state... 

This book studies a broad spectmm of real azeotropic distillation separation methods for a variety of industrially important chemical systems. Economically optimum rigorous steady-state designs are developed for many of these chemical systems. Then practical control structures are developed that provide effective load rejection in the face of typically large disturbances in throughput and feed composition. Trade-offs between steady-state energy savings and dynamic controllability (product quality variability) are demonstrated. 

Steady-state designs of reactive distillation columns are developed that are economically optimum in terms of total annual cost, which includes both energy and capital costs. The economics of reactive distillation columns are quantitatively compared with conventional multiunit processes over a range of parameter values (chemical equilibrium constants,... 

There are also control implications. As we will see in later chapters, the dynamic controllability of a reactive distillation column is improved by adding more reactive trays. Thus, as is true in many chemical processes, there is a conflict between steady-state design and dynamic controllability. The column with 9 reactive trays is the steady-state economic optimum. However, as we will demonstrate in Chapter 10, a column with 13 reactive trays provides better dynamic performance in terms of the ability to maintain conversion and product purities in the face of disturbances in throughput and feed compositions. 

Finally, the value of the reactor temperature is changed over a wide range, and steps 2 -13 are repeated for each temperature. The minimum for the TAG is selected as the optimum economically steady-state design for the given (Kb,q)s66 value and the given relative volatility relationship. 

A wide range of (7Teq)366 values is explored in this section. Optimum economic steady-state designs of both the reactive distillation process and the conventional multiunit process are developed and compared in terms of TAC. 

In the previous section, the optimum economic steady-state designs of reactive distillation columns were quantitatively compared with conventional multiunit systems for a wide range of chemical equilibrium constants. Relative volatilities (a = 2) were assumed constant. Reactive distillation was shown to be much less expensive than the conventional process. In this section we explore how temperature-dependent relative volatilities affect the designs of these two systems. 

Finally, the minimum TAC is selected as the optimum economical steady-state design for the given a39o value. 

Reaction and separation temperamres cannot be set independently in a conventional reactive distillation column. If a ternperamre mismatch exists between the temperature favorable for reaction and those favorable for separation, other alternative flowsheets should be considered. The results shown in this chapter demonstrate that the use of a distillation column with external side reactors can provide a more economical process because the distillation column and the side reactors can be operated at their optimum temperamres. Both steady-state design and dynamic control of these systems were explored. 

Steady-state mechanism. Consider the oxidation of RufNHj) by CL, which is believed to occur by the scheme shown below at constant pH. Imagine that one does a series of experiments with [Ru(NHs)g+ ] [O2]. Derive the steady-state rate law. Could these experiments equally well have had the reverse inequality of concentrations Should [RulNH.O ] also be adjusted (how and why) What apparent rate constant could be obtained from the concentration conditions that you consider optimum How would you design a longer series of experiments, and what rate constants could be obtained from the data If the data were examined graphically, what quantities would be displayed on the axes to obtain linear plots, and how would the rate constants be obtained from them ... 

Use sliders for Npiate, Fplate and R to determine the optimum design conditions for the column. For this the array index [i] can be chosen for the X axis to obtain steady-state axial profiles. 

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