Economic Optimum Steady-State Design

The economic design objective is to minimize total annual cost, given feed conditions, and desired product specifications. The two product specifications are 99.5 mol% water in the distillate and 12 mol% water in the bottoms. The Aspen Design Spec/Vary feature is used to attain these specifications by varying the distillate flow rate and the reflux ratio. The Aspen Tray Sizing feature is used to determine the diameter of the column. A tray spacing of 2 ft is used to determine column height. 

The economic parameters and sizing relationships given in Chapter 4 are used to determine heat-exchanger areas (reboiler and condenser), capital investment, and energy cost. Total annual cost (TAC) takes the total capital investment, divides by a payback period (3 years), and adds the annual cost of reboder energy. 

The minimum TAC case shown in Table 8.3 is the 120-stage column. However, the reduction in TAC between this case and the 100-stage column is 1 %. Therefore, the 100-stage column is used in the control study discussed in the next section. 

---

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. 

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. 

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. 

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... 

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. 

Another consideration is the dynamic controllability of a process design. If there are no uncertainties or disturbances, then the optimum economic design normally occurs at a constraint. An actual process cannot be operated at a constraint, because any disturbance may force the system to violate the constraint (a product purity limit, for example). In this case, the desired steady-state operating point must be backed-off from the economic optimum so that the control strategy can tolerate disturbances. The basic idea is shown in Fig. 9. 

The impact of several design parameters has been explored. Control performance worsens when the steady-state economic optimum design, consisting of a large feed-effluent heat exchanger and a small furnace, is used. The most robust control is obtained when a small FEHE and a large furnace are employed. 

Of course, this suggests that it may be possible to modify the process operating conditions (recycle flow rates) or the process design parameters (reactor holdup) and move away from the steady-state economic optimum point to be able to use control structure 2 with its advantages of allowing production rate to be directly set and not requiring a composition measurement. 

There is an engineering trade-off between the number of trays and the reflux ratio. An infinite number of columns can be designed that produce exactly the same products, but have different heights, different diameters, and different energy consumptions. Selecting the optimum column involves issues of both steady-state economics and dynamic controllability. 

In the Ryan-Doherty paper, the number of stages in the azeotropic column is given as 36, and the number of stages in the recovery column is given as 30. A similar flowsheet was used in a control study of these two columns. No consideration of the steady-state economic optimum design was considered in that study. The feed stage locations assumed in that study (using Aspen notation) were... 

I hope the examples will clearly demonstrate that the development of a steady-state economically optimum process is only half the job and answers only half the vital questions. The design in not complete and intelligent management decisions about what process to build cannot be made until dynamic performance is evaluated. 

Most of the treatments in the above books are qualitative and concepmal in namre, emphasizing VLLE issues and alternative configurations. Few of these books present in-depth rigorous designs that achieve optimum economic criteria. None of these books deal with the control and operation of azeotropic distillation systems. Detailed discussions of these two areas are the main contribution of this book. Rigorous steady-state and dynamic simulation tools (Aspen Plus and Aspen Dynamics) are used for design calculations and rigorous dynamic simulations. 

---