Complex Process Optimization

However, all of these studies determine only approximate or parameterized optimal control profiles. Also, they do not consider the effect of approximation error in discretizing the ODEs to algebraic equations. In this section we therefore explore the potential of simultaneous methods for larger and more complex process optimization problems with ODE models. Given the characteristics of the simultaneous approach, it becomes important to consider the following topics ... 

Dan F, Grolier JPE (2004) Spectrocalorimetric screening for complex process optimization. In Letcher T (ed) Chemical thermodynamics for industry. Royal Society of Chemistry, Cambridge, p 88... 

Extraction of hemiceUulose is a complex process that alters or degrades hemiceUulose in some manner (11,138). Alkaline reagents that break hydrogen bonds are the most effective solvents but they de-estetify and initiate -elimination reactions. Polar solvents such as DMSO and dimethylformamide are more specific and are used to extract partiaUy acetylated polymers from milled wood or holoceUulose (11,139). Solvent mixtures of increasing solvent power are employed in a sequential manner (138) and advantage is taken of the different behavior of various alkaUes and alkaline complexes under different experimental conditions of extraction, concentration, and temperature (4,140). Some sequences for these elaborate extraction schemes have been summarized (138,139) and an experimenter should optimize them for the material involved and the desired end product (102). 

The first-stage catalysts for the oxidation to methacrolein are based on complex mixed metal oxides of molybdenum, bismuth, and iron, often with the addition of cobalt, nickel, antimony, tungsten, and an alkaU metal. Process optimization continues to be in the form of incremental improvements in catalyst yield and lifetime. Typically, a dilute stream, 5—10% of isobutylene tert-huty alcohol) in steam (10%) and air, is passed over the catalyst at 300—420°C. Conversion is often nearly quantitative, with selectivities to methacrolein ranging from 85% to better than 95% (114—118). Often there is accompanying selectivity to methacrylic acid of an additional 2—5%. A patent by Mitsui Toatsu Chemicals reports selectivity to methacrolein of better than 97% at conversions of 98.7% for a yield of methacrolein of nearly 96% (119). 

Historically, sequential-modular simulators were developed first. They were also developed primarily ia iadustry. They coatiaue to be widely used. la terms of unit operatioas, each module can be made as simple or complex as needed. New modules can be added as needed. Equation-oriented simulators, on the other hand, are able to handle arbitrary specifications and limitations for the entire process dow sheet more dexibly and conveniendy than sequential-modular simulators, and process optimization can also be carried out with less computer effort. 

Biegler, L., Optimization strategies for complex process models. Adv. Chem. Eng. 18, 197 (1992). 

Lorenz T. Biegler, Optimization Strategies for Complex Process Models... 

To illustrate the complexity of process optimization, suppose that we are to scale-up a semibatch stirred-tank reactor for carrying out the following consecutive reactions ... 

Considerable attention should be paid to obtaining samples truly representative of the production process early in method development. Production processes generate mixtures that are far more complex and variable than may be generally realized therefore, a separation developed using an early production sample may prove to be inadequate for a later sample. Minor peaks observed in the chromatogram, whether known or unknown, serve as a record of the consistency of the process and can be used to monitor process changes. Sometimes a particular peak can be associated with a desirable or undesirable property of the product and used for controlled process optimization. 

A particular feature of the whole process is the trade-off between the key intermediates of both mechanistic cycles. While the N—N bond formation (controlled by thermal stability of the mononitrosyl intermediate) is favored by lower temperatures, the 0-0 bond formation step (constrained by endothermic decomposition of the nitrate intermediate) is favored by higher temperatures. Indeed, as revealed by operando IR studies (Figure 2.24), at low temperatures nitrates accumulate on the surface, whereas at high temperatures the surfaces is essentially depleted of the mononitrosyl complexes. The optimal reaction temperature corresponds, therefore, to a subtle balance between the rate of formation of the Cu NO Z surface complex in the early stages, and the rate of decomposition of the CuN03 Z complex in the late stages of the reaction. 

It should also be noted that optimization of POCL detection is a relatively complex process due to the number of variable parameters in the reaction. Most papers dealing with practical applications of the POCL reaction also feature some degree of optimization studies. In addition, a number of studies have focused specifically on the optimization process [125-134], and Hadd and Birks [135] have recently summarized the most important aspects in a comprehensive overview. 

The reactions (518->-517 + 517 ) or (518 516 517 + 517 ) are complex processes and require optimization and the use of special procedures in each particular case. If the starting nitronates or nitroso acetals are unsubstituted at the C-3 atom, the target 3-halomethyl-oxazines can be synthesized in satisfactory yields, although diastereomers (517) and (517 ) are unseparable in some cases. In the presence of a substituent R (see entry 14), the yield of the product is substantially lower, whereas the reaction is diastereoselective. 

Copper production is quite a complex process to plan and to schedule due to the many process interdependencies (shared continuous casters and cranes, emission level restrictions, limited material availability, to name a few). This makes it very difficult to foresee the overall consequences of a local decision. The variability of the raw material has alone a significant impact on the process, various disturbances and equipment breakdowns are common, daily maintenance operations are needed and material bottlenecks occur from time to time. The solution that is presented here considers simultaneously, and in a rigorous and optimal way, the above mentioned aspects that affect the copper production process. As a consequence, this scheduling solution supports reducing the impact of various disturbance factors. It enables a more efficient production, better overall coordination and visualization of the process, faster recovery from disturbances and supports optimal... 

Models can be written in a variety of mathematical forms. Figure 2.3 shows a few of the possibilities, some of which were already illustrated in Section 2.1. This section focuses on the simplest case, namely models composed of algebraic equations, which constitute the bulk of the equality constraints in process optimization. Emphasis here is on estimating the coefficients in simple models and not on the complexity of the model. 

The costs of dissolved-phase recovery and treatment involve a series of tradeoffs between the quantity of water pumpage necessary to accomplish the task and the concentration of dissolved chemicals that require treatment. Optimization of these factors is often a complex process that requires evaluation of several design options. 

The centralized control can be approached using different techniques pole-placement, optimal control and loop decoupling. When the whole state is not accessible, a motivation to introduce a state observer is discussed. A detailed example when all state variables are accessible, i.e. when the state observer it is not necessary, has been explained. It is important to remark that the previously cited techniques are not widely used in CSTR control. This is due to the fact that these procedures require non-intuitive matrix tuning and computations, which are not familiar in the process industry. Nevertheless, for complex processes, these procedures can be the only solution to the control problem, when a limited set of sensors are available. 

High-energy ball milling is a complex process, which requires optimization of many parameters to assure repeatability of nanostructure from batch to batch. To illustrate this complexity we can list the important parameters that must be decided when conducting the process in the magnetic A.O.C. model Uni-Ball Mill ... 

Said this, we can let the reader to recall Fig. 1.15, where we depicted amorphous-like phase regions at grain boundaries as the pathways open for preferential diffusion of hydrogen atoms. Apparently, an alloy can benefit from some fraction of amorphous phase to improve kinetics of hydrogen absorption, but complete amorphization of crystalline lattice lowers capacity for storing hydrogen [156]. Mechanochemical activation is therefore a complex process where kinetic and thermodynamic effects must be firstly well understood, and then optimized. 

For process optimization problems, the sparse approach has been further developed in studies by Kumar and Lucia (1987), Lucia and Kumar (1988), and Lucia and Xu (1990). Here they formulated a large-scale approach that incorporates indefinite quasi-Newton updates and can be tailored to specific process optimization problems. In the last study they also develop a sparse quadratic programming approach based on indefinite matrix factorizations due to Bunch and Parlett (1971). Also, a trust region strategy is substituted for the line search step mentioned above. This approach was successfully applied to the optimization of several complex distillation column models with up to 200 variables. 

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