Stanislaw Sieniutycz

5 – Uncontrolled Fluid–Solid Systems in Chemistry

In this chapter primary attention is paid to uncontrolled fluid–solid noncatalytic and catalytic systems with particulate solids. The scientific information is largely based on a book in Polish by Szarawara, J., Skrzypek, J., Gawdzik A. 1991. Podstawy Inzynierii Reaktorow Chemicznych ( Fundamentals of Chemical Reactor Engineering ), second ed. Warszawa, WNT, whose English counterpart is not available to date. Basic regimes of a heterogeneous processes (kinetic, diffusional, and intermediate) are distinguished. The notion of chemical resistance is defined and its significance for heterogeneous reactors is exemplified. The so-called model of shrinking grain is formulated and its main implications are described. Some special cases of this model are analytically solved and numerous application examples to industrial processes are presented. Statics and kinetics of sorption processes are considered. The equation of heterogeneous surface kinetics is derived and its “decelerating kinetics” is explained by the detrimental product rates in the denominator of this equation. Effects of concentration and temperature on the general rate of contact reaction are discussed for both exothermal reactions and exothermic reactions. Issues associated with diffusion in porous channels, Thiele modulus, and the influence of internal diffusion on the general chemical rate are discussed. The popular notion of effectiveness coefficient of a contact, attributed to the exploitation of the internal surface of grain, is defined. Charts characterizing internal diffusion under nonisothermal conditions are analyzed. While the effects of catalyst and sorbent deactivation are ignored, the chapter describes the main mechanisms of catalyst decay and, as such, it provides an introduction to further chapters which analyze systems with deactivating sorbents and catalysts to minimize the detrimental effect of catalyst deactivation.

Neural Networks for Emission Prediction of Dust Pollutants

We review the recent applications of artificial neural networks (ANNs) for predicting suspended particulate concentrations in urban air, taking into account meteorological conditions. Described calculations are based on pollution measurements taken in the city of Radom, Poland, in the period 2001–02. PM10 emission and primary meteorological data, which were obtained from the Inspectorate for Environmental Protection (IEP) in Radom, were used to train and test the applied network. Two different methods of emission calculation can be applied. Firstly, an artificial neural network method based on multilayer perceptron with unidirectional information flow is used. Secondly, a hybrid model based on a modified Gaussian model of Pasquilles type and artificial neural network with radial basis function (RBF) is applied. Network architecture and transition function types are described. Statistical assessment of the results is described. In addition, a hybrid model used results which are compared with emission calculations of dust pollution based on a Gaussian model, including various methods of calculation of pollution dispersion coefficients.

Maximum Power Yield in Homogeneous Chemical Systems

This chapter treats approaches, models, and analyzes the rise in optimization of power yield in chemical and biochemical reactors. Nonlinear kinetic models of reacting systems stem from kinetic mass action law, which leads to the identification of two competing unidirectional fluxes in each elementary step of the reaction. Near the thermodynamic equilibrium the approach converges to the standard linear kinetics governed by Onsagers equations. Using these models and methods we then extend to the chemical realm the method of thermodynamic optimization that was developed in earlier chapters for thermal machines. The extended method is aimed at the maximum production of power in isothermal and nonisothermal chemical systems. Some attention is given to analysis of derived dynamic programming algorithms and to development of a generalized approach for complex systems with internal dissipation. Chemical components of power yield are shown to be generated with lowered (imperfect) efficiencies, which are described by “reduced chemical affinities.”

Maximum Conversion in Processes With Chemical Reactions

This chapter reviews basic problems of maximum conversion encountered in typical systems with chemical reactions. The initial continuous problem of the optimal temperature profile for a single reversible reaction in a batch or tubular reactor is easily transformed into its corresponding multistage counterpart where a maximum conversion is sought for a discrete cascade. The experience gained helps to solve generalized optimization problems for parallel and consecutive-parallel reactions in a tubular or batch reactor. The analysis assumes that even a reaction is catalytic, the state of the catalyst remains unchanged when the reaction advances in time, i.e., any phenomena causing catalyst deactivation are absent in the system. Chapter 8 discusses the chemical reactions with catalyst deactivation as well as the associated catalyst regeneration problems.

Outline of Classical Optimization Methods

This chapter provides a brief description of contemporary optimization methods and approaches which are applied throughout this book to improve the performance of thermal, mechanical, chemical, and environmental systems. We optimize profit or cost criteria subject to equality and/or inequality constraints by applying search approaches, methods of static and dynamic optimization, and using some stochastic techniques. With these methods and approaches, we investigate unique optimal properties of neural networks, cascades, multilevel systems of complex topology, etc. Throughout the chapters of this book, optimization problems and goal criteria are formulated, and optimal solutions are found for unit operations and chemical reactors. Our concise review of optimization tools outlines the methods based on differential calculus, Lagrange multipliers, mathematical programming, iterative approaches, dynamic algorithms, and some stochastic optimization techniques. They are applied in the book to processes with energy yield and conversion, modeled with the help of classical and finite-time thermodynamics and second-law approaches. Throughout the book special attention is paid to fluid-solid catalytic systems with particulate solids as well as to complex multiphase reaction-regeneration systems with deactivated sorbents and catalysts.

Finite Rate Optimization of Steady Thermal Units

This chapter offers an advanced synthesizing approach to power yield and power limits in various thermal power generators, such as thermal and solar engines. Thermodynamic principles determine the converters efficiency and the generated power. Static and dynamical power systems are investigated. Dynamical models take into account the gradual downgrading of a resource, caused by power delivery. Analytical modeling includes conversion efficiencies expressed in terms of driving fluxes. Products of efficiencies and driving fluxes determine the power yield and power maxima. While the static optimization of industrial and practical systems requires the use of the differential calculus and Lagrange multipliers, dynamic optimization involves variational calculus and dynamic programming. The results of power maxima provide limiting indicators for thermal and solar power generators. They are more exact than classical reversible limits of thermal energy transformation. Following the present procedure, in later chapters ( Chapters 6 and 9 Chapter 6 Chapter 9 ), which deal with reacting mixtures, balances of mass and energy will serve to derive power yield in terms of the active part of chemical affinity. A generalized approach will then be applied to flow engines driven by fluxes of heat and chemical reagents.

Optimizing Reactor–Regenerator System With Catalytic Parallel-Consecutive Reactions

The subject of this investigation is a system with a moving deactivating catalyst, composed of a co-current tubular reactor and a catalyst regenerator whose (catalytic) product is supplemented by a small flux of the fresh catalyst. For temperature-dependent catalyst deactivation, the optimization problem is formulated in which a maximum of a process profit flux is achieved by the best choice of temperature profile, best catalyst recycle ratio, and best catalyst activity after regeneration. A set of parallel-consecutive reactions, A+B→R A + B → R and R+B→S R + B → S , with desired product R is taken into account. A relatively unknown, powerful algorithm, in which a suitably defined discrete Hamiltonian is constant along the optimal path, is applied for optimization. Properties of optimal solutions are discussed. It is shown that an increase of the unit cost of catalyst regeneration or an increase of the catalyst recycle ratio cause optimal temperatures which save the catalyst, as the optimal temperature profiles are then shifted towards lower temperatures. Finally, these profiles reach isothermal shape at the level of minimum allowable temperature and then it is not further possible to control the reactor process by the temperature profile. Thus the catalyst activity after regeneration, as well as the average catalyst activity in the reactor, decrease when the unit catalyst regeneration cost increases. This is a form of catalyst saving, as the catalyst deactivation rate becomes reduced when average catalyst activity is not allowed to decrease quickly. It is important that this form of catalyst saving appears in the region where any saving of the catalyst by an optimal choice of temperature profile is impossible. For small values of the catalyst recycle ratio, the catalyst regenerator should be removed from the system. In this case, the renewal of the catalyst takes place exclusively due to a fresh catalyst input.

Maximum Principle and Other Criteria of Dynamic Optimization—An Unconventional Approach

In this theoretical chapter, Bellmans optimality principle and the method of dynamic programming are used to develop various algorithms of dynamic optimization. Both continuous and discrete systems are considered. Pontryagins maximum principle is derived and described as the most common and most effective tool which serves to optimize control engineering systems. The analysis is focused on the formulation and application of the so-called Caratheodory−Boltyanskii criteria (functions B ( x , t , u ) and A n ( x n , t n , u n , θ n )), transformed by the authors to the canonical equations and other forms of the necessary and locally sufficient optimality conditions. Various cases of transversality conditions are derived and discussed. Modified versions of the maximum principle are briefly described.

Reactors With Catalyst Decay and Regeneration

In this chapter the method of Pontryagins maximum principle is applied to optimize some chemical lumped parameter and distributed parameter systems with the catalyst decay described by a simple model of the first-order, temperature-independent deactivation. Continuous and discrete algorithms with either ordinary or partial differential equations along with appropriate boundary conditions are employed to calculate optimal temperature profiles in reactors with deactivating catalyst. The state equations contain two state variables: reaction extent, x (or concentration c ), catalyst activity, a , and temperature, T , as a single control. The distributed system theory serves to obtain an analytical solution for extremum temperature control in a fixed bed reactor with a first-order reaction and the first-order catalyst deactivation. Application of the distributed algorithm shows that an optimal profile for the effective reaction constant, k eff ( t ), is formed as the result of prescribed activity distributions, initial w p ( τ ) and final w k ( τ ). When the chronological time t k increases, the effective reaction rate constant corresponds to higher reaction temperatures. A decrease in the operation time causes time-dependent temperature profiles T ( τ , t ). This function may appear because of too high temperatures at the final moments of the process, which may cause excessive corrosion of the reactor material. Therefore, a generalized optimization problem with constrained temperature control is formulated and solved for short-duration processes. The solution is supplemented by an analysis of a cycle composed of an infinite number of deactivation and regeneration steps working sequentially in a steady cyclic operation.

Optimizing Circulation Reactor With Deactivating Catalyst

In this chapter an optimal solution is obtained and analyzed for a reactor with catalyst recycle and chemical reactions running in the presence of concentration-independent catalyst deactivation. A co-current tubular reactor working with controlled temperature profile and yielding a desired product R is investigated for a set of catalytic reactions A+B→R A + B → R and R+B→S R + B → S subject to temperature-dependent catalyst deactivation. A dynamic optimization algorithm searches to maximize flux profit achieved by the best choice of the temperature profile and residence time of reactants. The rates of reactions are described for each reagent by expressions containing ( T -dependent) rate constants, concentrations of reagents, catalyst activity, as well as catalyst concentration in the reacting suspension. The difference between velocities of reagents and velocities of solid catalyst particles (slip) is taken into account in the computational model.