Chemical Reaction Engineering in the Chemical Processing of Metals and Inorganic Materials Part II

Korean J. Chem. Eng., 20(3), 415-428 (2003) FEATURED REVIEW Chemical Reaction Engineering in the Chemical Processing of Metals and Inorganic Materials Part II. Chemical Process Modeling and Simulation Hong Yong Sohn† Departments of Metallurgical Engineering and of Chemical and Fuels Engineering, University of Utah, Salt Lake City, Utah 84112, U. S. A. Abstract−In traditional chemical reaction engineering, it is possible to incorporate only the simplified aspects of fluid flow, mixing, and mass/heat transfer into the analysis of chemical reaction rates and reactor design. As a con- sequence of the advent of high-speed, high-capacity computing capacity, complex processes involving chemical reactions have become amenable to analysis and modeling. This has also resulted in the merging of various disciplines of chemical engineering in formulating detailed descriptions of complex processes. Developments that exemplify this trend over the years are discussed in this review. Several examples from the author’s previous work are used to illustrate the application of chemical reaction engineering principles to the modeling and analysis of complex systems involving the chemical processing of metals and other inorganic materials. Key words: Chemical Reaction Engineering, Fluidized-bed Reactor, Gas-particle Flow, Liquid-liquid Emulsion, Process Modeling, Solvent Extraction INTRODUCTION Complex processes involving chemical reactions have become amenable to analysis and modeling thanks to the rapidly increasing computational capacity. Traditional chemical reaction engineering incorporates only the simplified aspects of fluid flow, mixing, and mass/heat transfer into the analysis of chemical reaction rates and processes. As a result, accurate and realistic analyses and simula- tions of many individual aspects of complex processes have not been possible. Thus, the disciplines of chemical reaction engineering and transport phenomena have stood separate, and their aspects Fig. 1. Schematic diagram of the flash smelting process. within a given process were treated individually [Similarly, unit op- erations and transport phenomena were treated separately]. A con- sequence of the availability of high-speed, high-capacity computing the flash smelting process in the production of nonferrous metals capacity has been the merging of these disciplines into the formu- from sulfide minerals. A schematic diagram of this process is given lation of a more detailed description of a complex process. Cur- in Fig. 1. In this process, fine, dried mineral particles and fluxes are rently, many models combine the basic principles of various previ- injected into the furnace with industrial oxygen or oxygen-enriched ously independent sub-disciplines of chemical engineering to for- air. The mineral particles are rapidly ignited and burn in the tur- mulate comprehensive and increasingly more realistic descriptions bulent gas jet. The flash-smelting process has the advantages of rap- of chemical processes. id reaction rate, ease of control, substantial reduction in fuel require- Developments that exemplify this trend over the years in the field ments, and efficient sulfur dioxide capture. of chemical processing of metals and other inorganic materials are Despite the fact that the process has been in commercial use for discussed in this review. The examples will largely be drawn from a long time and is currently the dominant sulfide-smelting process, the work by the author and his coworkers, because of the limita- the design and operation of a flash-smelting furnace has largely re- tions in the scope of the review and time available to prepare this mained an art. This is mainly due to the difficulty of understanding article. Regrettably, therefore, excellent examples by many other and quantifying the complex interactions of the individual sub-pro- researchers have to be left out. cesses involved - the turbulent fluid flow, convective heat and mass transfer, chemical reactions, and radiative heat transfer. FLASH REACTION PROCESSES In our research on an experimental and mathematical modeling investigation of the shaft region of a flash-smelting furnace, we be- An important example of a unit process in metals production is gan by first tearing apart the overall process into identifiable com- ponent processes. We thus recognized a number of important sub- †To whom correspondence should be addressed. processes, as shown in Fig. 2. The model equations were written E-mail: [email protected] based on the continuity of mass and the conservation of momen- 415 416 H. Y. Sohn eral form: − = φ ∇•Γ()ρνφ ∇•()φ∇φ S (1) where φ is the dependent variable, Γφ is the coefficient for the dif- fusive transfer, and Sφ is the source term. Table 1 shows all the gas- phase governing equations. The standard k-ε model was used to represent gas-phase turbulence. The particle phase was described using the Lagrangian framework, the governing equation being listed in Table 2. Further details of the model equations can be found else- where [Hahn and Sohn, 1990; Perez-Tello et al., 2001]. The next sub-process we tackled was the gas-particle reactions - the oxidation of sulfur and iron in the mineral particles. To describe the ignition transient as well as the main combustion period follow- Fig. 2. Components of mathematical modeling of the flash-smelting the ignition, information on the intrinsic kinetics of the mineral ing process. particle oxidation is needed. This information was obtained by car- rying out separate experiments [Chaubal and Sohn, 1986]. Appro- tum and energy for the gas and the particle phases [Hahn and Sohn, priate measures were taken to ensure determination of the intrinsic 1990; Perez-Tello et al., 2001]. The gas phase was described from kinetics. After the particle becomes molten in the flash furnace, the the Eulerian point of view. The time-averaged equations for the con- particle temperature is sufficiently high that the overall rate of reac- servation of fluid properties can be expressed in the following gen- tion can be described by the mass-transfer rate of oxygen from the Table 1. Gas-phase equations ∂ ∂ ∂ ∂ ∂φ ∂ ∂φ ∂ ∂φ ()ρ φ + ()ρ φ + ()ρ φ − Γ − Γ − Γ = φ ------ gug ------ gvg ------ gwg ------φ------ ------φ------ ----- φ------ S Equation ∂x ∂y ∂x ∂x ∂x ∂y ∂y ∂z ∂z φ φΓφ S p Continuity 1 0 Sm (A-1) ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ − p + ug + vg + wg −2 + + u x-Momentum u µ ------ ------ µ ------- ------ µ ------- ----- µ --------- ---------()ρ k ρ g S (A-2) g e ∂x ∂xe ∂x ∂ye ∂x ∂ze ∂x 3∂x g g x p ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ − p + ug + vg + wg −2 + + v y-Momentum v µ ------ ------ µ ------- ------ µ ------- ----- µ --------- ---------()ρ k ρ g S (A-3) g e ∂y ∂xe ∂y ∂ye ∂y ∂ze ∂y 3∂y g g y p ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ − p + ug + vg + wg −2 + + w z-Momentum w µ ------ ------ µ ------- ------ µ ------- ----- µ --------- ---------()ρ k ρ g S (A-4) g e ∂z ∂xe ∂z ∂ye ∂z ∂ze ∂z 3∂x g g z p µ σ −ρ ε Turbulent kinetic energy k e/ k G g (A-5) εµσ ()ε⁄ ()− ρ ε Dissipation rate e/ ε k C1G C2 g (A-6) µ σ f Sulfur mass fraction f e/ f Sp (A-7) ηµσ η Reacted oxygen ratio e/ η Sp (A-8) ∂ ∂ ∂ h + h + p + p + p + h Enthalpy h µ /σ Q Q u ------ v ------ w ------ S (A-9) g e h rp rg g∂x g∂y g ∂z p where: ∂ 2 ∂ 2 ∂ 2 ∂ ∂ 2 ∂ ∂ 2 ∂ ∂ 2 =µ ug +vg +wg +ug + vg +ug + wg +vg + wg G t2 ------- ------- --------- ------- ------- ------- --------- ------- --------- (A-10) ∂x ∂y ∂z ∂y ∂x ∂z ∂x ∂z ∂y µ µ µ e = t + l (A-11) µ ρ 2 ε t =Cµ g k / (A-12) m f − η Sp =Sp Sp (A-13) Table 2. Particle-phase equations 〈〉 ρ d V 3 g 1 − − + − ------------ = --- ---- ---- 〈〉〈〉()〈〉〈〉 () Motion mp mp CDρ U V U V mp mg g (B-1) dt 4 pdp 2 = t 2 t p Particle dispersion (cloud model) σ ()t 2v'∫ 〈〉()t ∫ R ()τ dτdt (B-2) ii 0 i 1 0 ii 1 j = q dni = r − v Species mass balance ------- ∑Rij, Ri (B-3) dt j = 1 d = + − − Energy ---- ()m h H Q Q H (B-4) dt p p r rp p v May, 2003 Chemical Reaction Engineering in the Chemical Processing of Metals and Inorganic Materials 417 bulk gas. was fed through a series combination of a screw feeder and a vi- The ability of the computer model to describe the dispersion of bratory feeder to minimize the pulsing of the solid feed. Five 250-W the particles in the turbulent gas jet of a flash-smelting furnace shaft spotlighting halogen lamps were placed on either side of the cham- was verified by the use of a non-reacting model system [Yasuda ber as the light source, and a black cloth was used for background. and Sohn, 1995]. This work was done using a room-temperature The photograph showed the particles as white spots on the black model apparatus by combining a photographic method and a com- background. A sample of the comparison between the experimen- puter image-analysis technique. The observation chamber was a tal and computed results is shown in Fig. 3. It is noted that the com- rectangular box made of acrylic plates and lined with glass plates puter model yields the particle number density in the units of num- to prevent the particles from sticking to the wall. The height of the ber per unit volume, whereas the photographic data gave it as num- chamber was 1.22 m, and the width and length were both 0.61 m. ber per unit projected area. Thus, the computed data were con- A steady flow of a gas-particle jet was injected from the center of verted by integrating through the depth of the system. As can be the ceiling through a variety of injector and withdrawn through an seen, the agreement is quite satisfactory, thus verifying the validity outlet at the bottom of the chamber.

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