Optimal economic steady-state design

These numbers show that the optimal economic steady-state design is the multiple-stage reactor system. The higher the conversion, the larger the economic incentive to have multiple stages. At 95 percent conversion, the capital cost of a three-CSTR process is 67 percent that of a one-CSTR process. At 99 percent conversion, the cost is only 38 percent. Thus, if only steady-state economics is considered, the design of choice in these numerical cases is a process with two or three CSTRs in series. 

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 optimization of a reactive distillation column has a large number of design variables. The following specihcations and assumptions are made to reduce the number of design optimization variables in the economic steady-state design ... 

It has been recognised for long time that the performance of a plant depends much more on its design characteristics than on the sophistication of the control algorithms. The practice showed also that the optimal steady state design is not always the best in operation. Only slightly more expensive alternative could posses much better dynamic properties, and become more profitable when the cost of time is taken into account. Hence, there is always a trade-off between steady state economics and controllability. 

Simultaneous design is defined as the development of a chemical process by considering both steady-state economics and dynamic controllability at all stages of flowsheet synthesis. The basic notion is that the dynamics of the process are vitally important in its ability to operate efficiently and safely and to make on-specification products with little product-quality variability. There is no guarantee that a process flowsheet that has been developed to optimize some steady-state economic objective will provide good plantwide dynamic performance. 

Several different specifications in items 2-5 will be used to investigate the effects of product quality, conversion, and recycle impurities on the economically optimal steady-state design. However, these do not affect the general stmcture of the design procedure. 

Some recent applications have benefited from advances in computing and computational techniques. Steady-state simulation is being used off-line for process analysis, design, and retrofit process simulators can model flow sheets with up to about a million equations by employing nested procedures. Other applications have resulted in great economic benefits these include on-line real-time optimization models for data reconciliation and parameter estimation followed by optimal adjustment of operating conditions. Models of up to 500,000 variables have been used on a refinery-wide basis. 

Although, as explained in Chapter 9, many optimization problems can be naturally formulated as mixed-integer programming problems, in this chapter we will consider only steady-state nonlinear programming problems in which the variables are continuous. In some cases it may be feasible to use binary variables (on-off) to include or exclude specific stream flows, alternative flowsheet topography, or different parameters. In the economic evaluation of processes, in design, or in control, usually only a few (5-50) variables are decision, or independent, variables amid a multitude of dependent variables (hundreds or thousands). The number of dependent variables in principle (but not necessarily in practice) is equivalent to the number of independent equality constraints plus the active inequality constraints in a process. The number of independent (decision) variables comprises the remaining set of variables whose values are unknown. Introduction into the model of a specification of the value of a variable, such as T = 400°C, is equivalent to the solution of an independent equation and reduces the total number of variables whose values are unknown by one. 

This book is intended for use by students in senior design courses in which dynamics and control are incorporated with the traditional steady-state coverage of flowsheet synthesis, engineering economics, and optimization. A modern chemical engineering design course should include all three aspects of design (steady-state synthesis, optimization, and control) if our students are going to be well-prepared for what they will deal with in industry. 

The main objective of this section is to provide a quantitative example in which the besf process is not the optimal steady-state economic design. In this example reactor system, temperature control is the measure of product quality. For this type of system, dynamic controllability is improved by increasing the heat transfer area in the reactor. 

This theory will now be applied to the multiobjective design cases for the MTBE column. The reference design used for the sake of comparison is the structure previously introduced in chapter 7. This structure corresponds to a reactive distillation column for the synthesis of MTBE. The spatial design variables were obtained by steady-state optimization of the unit s economic performance. For background information, the reader is referred to section 6.2. The relevant parameters and schematic representation of the optimized design are given in table 8.4 and figure 8.7, respectively. 

The previous steps are based on steady-state economics only, and in the final selection other factors must also be considered, inlcuding their controllability properties. This may change the order of candidate controlled variables. Hopefully, at least one of the control structures that was acceptable from a steady-state economic point of view, is also acceptable from a dynamic point of view. Otherwise, one may consider design changes in order to improve the controllability, or consider the need for in-line optimizing control. 

The approach yields a steady-state control strategy design that is optimized for the particular economics and disturbance structures used, explicitly trading off reduced engineering costs against a potential drop in operational flexibility. 

---