Transient Kinetics of Slag Metal Reactions
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IN modern pyrometallurgical reactors, the overall reaction rate is generally accelerated through either stirring of the bath to promote mass transfer or increasing the interfacial area between phases, normally through gas injection.[1] At low levels of stirring, the interfacial area between slag and metal phases is unchanged and relatively simple equations can be used to model the overall kinetics of a particular reaction system. For example, in the case of mass-transfer control in one of the phases, a first-order ordinary differential equation can be employed:[2] A ðCB CI Þ dCB area drive ½1 ¼ V 1 ¼ volume resistance dt k where CI is the concentration of reacting species at interface (mol/m3), CB is the concentration of reacting species in the bulk (mol/m3), A is the interfacial area (m2), V is the volume of the phase (m3), k is the interfacial mass-transfer coefficient (m/s), and t is time (s). Normally, CI is set by an equilibrium relationship between the slag and metal and k is calculated using a semiempirical relationship.[2] This type of equation is valid when there is little variation in mass-transfer conditions, interfacial area, and equilibrium drive with time. However, it is common G.A. BROOKS, Professor, and M.A. RHAMDHANI, Lecturer, are with the Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Melbourne, VIC 3122, Australia. Contact e-mail: [email protected] K.S. COLEY, Professor, is with the Department of Materials Science and Engineering, McMaster University, Hamilton, ON L8S 4L7, Canada. SUBAGYO, Associate Professor, is with the Department of Mechanical and Industrial Engineering, Gadjah Mada University, Yogyakarta 55281, Indonesia. Y. PAN, Research Scientist, is with CSIRO Minerals, Clayton South, VIC 3169, Australia. This article is based on a presentation given at the International Symposium on Liquid Metal Processing and Casting (LMPC 2007), which occurred in September 2007 in Nancy, France. Article published online September 3, 2008. METALLURGICAL AND MATERIALS TRANSACTIONS B
in industrial operations for slag chemistry to change with time, as flux additions are carried out and refractories dissolve into the slag, though there is little theoretical treatment of this type of problem in the literature. Desulfurization in ladle metallurgy is an example of this type of transient problem, where the equilibrium drive is changing with time and mixing is nonuniform. A summary of the Subagyo et al. treatment of this problem is provided in this article.[3] In the case of processes with high-speed gas injection, such as oxygen steelmaking, a large volume of droplets is generated, resulting in complex multiphase regions within the reactor. The regions in top blown oxygen steelmaking are shown schematically in Figure 1. In these processes, the relationships between gas dynamics, fluid properties, mass transfer, and overall kinetics are complex, and simple uniform steady-state equations do not accurately describe the kinetics of the process. The overall kinetics for a
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