Iron and Steel Division - Graphical Techniques for Adiabatic Staged Systems

Both a graphical and an analytical technique are presented for calculating stream compositions and temperatures in adiabatic staged systems in which solids travel countercurrently to a gas stream. Such a system might be a tower containing several plates, on each of which the descending solid is fluidized by the rising gas stream. Examples are presented in which chemical reactions occur, including the oxidation of SO, by a solid catalyst and the gaseous reduction of iron oxides. COUNTERCURRENT staged processes involving reactions between solid and gas streams are becoming more common. These operations are generally carried out in a series of beds of fluidized solids, with each bed or "plate" acting as a stage. Fig. 1 is a schematic diagram of such a series of stages located in a column, down through which a solids stream moves from stage to stage counter to a rising gas stream. Typical reactions carried out in such systems are the dehydration of aluminum trihydrate, the calcining of limestone, and the gaseous reduction of iron oxides. Calculation of the performance of these counter-current systems rapidly becomes more complex with increases in the number of stages and in the number of chemical reactions occurring. Calcula-tional procedures for isothermal operations of such systems have been described.4 Actual tower operations, however, are generally adiabatic, and in consequence far from isothermal. The object here is to present both graphical and analytical techniques applicable to such adiabatic towers operating continuously and in steady state. In this introductory discussion, the graphical techniques presented are of the McCabe-Thiele type, rather than of the Pon-chon type. In all the examples presented, it will be assumed that both thermal and chemical equilibrium are attained in each bed. The assumption that the gas and solid streams leaving each bed are at the same temperature as the bed is in accordance with the familiar behavior of actual fluidized solid systems. Chemical equilibrium, on the other hand, is not necessarily attained in any given stage between these two streams, even with deep beds, since reaction rates may be slow. In the last section of this paper, discussion is presented of methods suitable for use when chemical equilibrium is not attained. The adiabatic tower in Fig. 1 has "n" stages numbered from 1 to n, starting with the bottom stage as number 1. In analyzing this tower's performance, it is important to express gas flow rates in terms of a key component or element which remains completely within the gas stream throughout the tower. Similarly, solid flow is best expressed in terms of a key compound or element which remains within the solid phase throughout the tower. Thus, in burning limestone with a hot flue gas, the gas flow might be expressed as G, the pound mols of nitrogen flowing through the tower per unit time, while solid flow might be expressed as S, the pound atoms of calcium in all forms in the solid stream per unit of time. Defined in this way, both G and S are constant throughout the tower. The enthalpy of the gas and solid streams are now best expressed in terms of these key components. That is, the gas stream enthalpy H is expressed as Btu in the total gas per mol of the key component in the gas. Similarly, the solids stream enthalpy h is expressed as Btu in the total solid stream per pound mol (or pound atom) of the key component in this stream.