Chapter 8 - Thermodynamics and Optimization of Practical Processes

Abstract

In this chapter, we show that contemporary mathematics provides powerful methods and algorithms for continuous and discrete theories of optimal control, which constitute suitable theoretical and computational tools when evaluating extremal or optimal properties of practical systems. Physical or economic problems can be treated by methods of optimal control. One can also perform studies that seek thermodynamic limits and studies that evaluate how to improve existing technological units or networks. The role of thermodynamic optimization approaches is defined within the family of practical optimization problems. Mathematical aspects of static and dynamic methods of optimization are briefly characterized. Optimal control theory is central to formulating and solving problems of optimal trajectories and optimal decisions required by availability analysis, entropy source minimization, finite-time thermodynamics, thermo-economics, and routine economics. The difficulties in many control theoretic approaches to practical control processes can be overcome by applying averaged optimization methods developed by a group of Russian scientists. The relative merits of these approaches are discussed. Focusing on chemical and mechanical engineering applications, some recent papers on entropy generation minimization, thermodynamic optimization, finite-time thermodynamics and thermo-economics are reviewed. In particular, references are given to some sorption models of catalyst decay and reactivation and related optimization problems. Other examples refer to the application of optimization theory to multistage drying processes with granular fluidizing solids, treated by discrete methods of optimal control. Selected references and analyses are given for optimization of still other processes and operations.