## Reactor Engineering And Flow Modeling

All industrial chemical processes are designed to transform cheap raw materials to high value products (usually via chemical reactions). A 'reactor', in which such chemical transformations take place, has to carry out several functions such as bringing reactants into intimate contact (to allow chemical reactions to occur), providing an appropriate environment (temperature and concentration fields, catalysts) for an adequate time and allowing for the removal of products. Chemical reactor engineering includes all the activities necessary to evolve the best possible hardware and operating protocol of the reactor to carry out the desired transformation of raw materials (or reactants) to value added products. A reactor engineer has to ensure that the reactor hardware and operating protocol satisfy various process demands without compromising safety, the environment and economics. To realize this, the reactor engineer has to establish a relationship between reactor hardware and operating protocols and various performance issues (Fig. 1.1).

Successful reactor engineering requires expertise from various fields including thermodynamics, chemistry, catalysis, reaction engineering, fluid dynamics, mixing and heat and mass transfer. The reactor engineer has to interact with chemists to understand the basic chemistry and peculiarities of the catalyst. Based on such an understanding and proposed performance targets, the reactor engineer has to abstract the information relevant to identifying the characteristics of the desired fluid dynamics of the reactor. The reactor engineer then has to conceive suitable reactor hardware and operating protocols to realize this desired fluid dynamics in practice. Thus, fluid

dynamics plays a pivotal role in establishing the relationship between reactor hardware and reactor performance.

To establish the relationship between reactor hardware and reactor performance, it is necessary to use a variety of different tools/models. Creative application of the best possible tools is required to evolve the best possible hardware configuration and operating protocol for the reactor under consideration. Various tools for modeling chemical kinetics and reactions are already well developed and routinely used in practice. This activity constitutes the major part of conventional chemical reaction engineering. Several excellent textbooks discussing these tools are available (for example, Aris, 1965; Levenspiel, 1972; Westerterp et al., 1984; Naumann, 1987). Most models falling in this category make use of drastic simplifications when treating the reactor fluid dynamics. Indeed, sophisticated models and theories are available to predict the interaction between chemistry and transport processes such as mixing, heat and mass transfer. However, these models rarely attempt to rigorously relate transport properties with the reactor hardware and operating protocol. For a specific chemistry/catalyst, the reactor performance is a complex function of the underlying transport processes. These transport processes are, in turn, governed by the underlying fluid dynamics, and therefore by a variety of design and operating parameters of the process equipment. In conventional reaction engineering, experimental and semi-theoretical methods (like cold flow simulations or tracer studies) are used to relate fluid dynamics and mixing with reactor hardware and operating parameters. The information obtainable from these methods is usually described in an overall/global parametric form. This practice conceals detailed local information about turbulence and mixing, which may ultimately determine reactor performance. This approach essentially relies on prior experience and trial and error methods to evolve suitable reactor hardware. These tools, therefore, are increasingly perceived as being expensive and time consuming ways of developing better reactor technologies. It is necessary to adapt and develop better techniques and tools to relate reactor hardware with fluid dynamics and resultant transport processes.

Over the years, aerospace engineers, who are most concerned with the task of establishing the relationship between the hardware and resulting fluid dynamics, have developed and routinely use computational fluid dynamics. Computational fluid dynamics (CFD) is a body of knowledge and techniques used to solve mathematical models of fluid dynamics on digital computers. In recent years, chemical engineers have realized that, although establishing a relationship between reactor hardware and fluid dynamics is less central (compared to aerospace engineers) to their role, it is no less important. With the development of high performance computers and advances in numerical techniques and algorithms, chemical engineers have started exploiting the power of computational fluid dynamics tools. Considering the central role of reactors in chemical process industries, there is tremendous potential for applying these tools for better reactor engineering. If applied properly, computational flow modeling (CFM) may reduce development time, leading to reduced time to market, shorter payback time and better cash flow. It is, however, necessary to adapt CFD techniques and to develop a computational flow modeling approach to apply them to chemical reactor engineering. This book is written with the intention of assisting practicing engineers and researchers to develop such an approach. Individual aspects of chemical reactor engineering and computational flow modeling (CFM) are discussed and related in a coherent way to convey and clarify the potential of computational flow modeling for reactor engineering research and practice. The emphasis is not on providing a complete review but is on equipping the reader with adequate information and tips to undertake a complex flow-modeling project. The focus is on modeling fluid flows and developing tractable reactor engineering models. Numerical issues are dealt with in adequate detail to provide appreciation of the important aspects and to guide the development and incorporation of new models into available solvers. Readers interested in developing their own complete solvers may refer to specialized books on CFD (for example, Ferziger and Peric, 1995; Patankar, 1980).

The information in this book is organized to facilitate the central task of a reactor engineer, that is, relating reactor hardware to reactor performance. This chapter provides a brief introduction to the contents to be covered in detail in subsequent chapters. Here, the roles of flow modeling and computational flow modeling are discussed in the context of reactor engineering. Various aspects of chemical reaction and reactor engineering are discussed in Section 1.1 to clearly define the role of flow modeling in overall activity. Computational flow modeling, its advantages and limitations are discussed in Section 1.2. Introduction to the use of CFM for reactor engineering is given in Section 1.3. This chapter, as a whole, will be used to appreciate and identify the potential of CFM for reactor engineering.

The theoretical and numerical basis of computational flow modeling (CFM) is described in detail in Part II. The three major tasks involved in CFD, namely, mathematical modeling of fluid flows, numerical solution of model equations and computer implementation of numerical techniques are discussed. The discussion on mathematical modeling of fluid flows has been divided into four chapters (2 to 5). Basic governing equations (of mass, momentum and energy), ways of analysis and possible simplifications of these equations are discussed in Chapter 2. Formulation of different boundary conditions (inlet, outlet, walls, periodic/cyclic and so on) is also discussed. Most of the discussion is restricted to the modeling of Newtonian fluids (fluids exhibiting the linear dependence between strain rate and stress). In most cases, industrial reactors are operated under a turbulent flow regime. Introduction to turbulence and various approaches (direct numerical simulations or DNS, large eddy simulations or LES and Reynolds averaged Navier-Stokes equations or RANS simulations) to modeling turbulent flows are discussed in Chapter 3. Turbulence models based on the RANS approach are discussed in more detail, with special consideration to reactor engineering applications. For several industrial applications, multiphase reactors are used, which involves contacting more than one phase. Various approaches to modeling such multiphase flows are discussed in Chapter 4 with special emphasis on dispersed multiphase flows. The interactions between chemical reactions and fluid dynamics are discussed in Chapter 5.

Model equations governing flow processes relevant to reactor engineering applications are quite often complex, non-linear and coupled. More often than not, analytical solutions are not possible and numerical methods are required to obtain a solution to the model equations. The numerical methods relevant to solving model equations are discussed in Chapters 6 and 7. Chapter 6 covers use of the finite volume method to solve generic flow models. Various aspects of the finite volume method such as discretization schemes, grid arrangements, implementation of boundary conditions and algorithms for handling pressure-velocity coupling are discussed in detail. Applications of these methods to solve turbulent flows, multiphase flows and reactive flows are discussed in Chapter 7. Guidelines for making appropriate selection of the available techniques based on the objective at hand are discussed. Practical ways of estimating errors in numerical solutions of model equations are discussed. The methodology and the desired qualities of computational tools required to implement these numerical methods on a digital computer to solve model equations are discussed in Chapter 8.

Part III of the book discusses the overall methodology of using computational flow modeling for reactor engineering. The necessity of using a hierarchy of modeling tools and establishing a clear relationship between the objectives of reactor engineering and the computational flow model is illustrated with the help of examples. The importance of a physical understanding of the system for facilitating rational simplification of the problem, formulation of appropriate boundary conditions and identification of key issues is emphasized. The information discussed in Part I and Part II is used to evolve a systematic methodology for linking reactor hardware with reactor performance. The methodology is illustrated with the help of some practical examples.

Details of the application of computational flow modeling to different types of reactors are discussed in Part IV. A separate chapter is devoted to three major reactor types used in chemical industries, namely, stirred reactors, bubble column reactors and fluidized bed reactors. Applications to fixed bed reactors and other miscellaneous reactor types are briefly discussed in Chapter 13. Recent work on modeling the complex fluid dynamics in these reactors is critically reviewed. The modeling approaches and the flow results obtained therefrom are evaluated from the point of view of their application to reactor engineering. Limitations of the current state of knowledge in describing the complex underlying physics of some of the flows relevant to reactor engineering are discussed. Despite such limitations, suggestions are made for making the best use of these computational flow models for reactor engineering applications.

The Epilogue recapitulates the lessons learnt from our experience of applying computational flow modeling while addressing practical reactor engineering problems. The advantages of using CFM and the probable pit falls are re-emphasized. Some comments on future trends in computational flow modeling and its application by the chemical/reactor engineering community are included.

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