A comprehensive heat-transfer model and associated simplified scaling laws are developed and verified using a pilot-scale, directly fired rotary kiln with a slumping bed of dry or wet, 6-mm clay sorbent particles. The kiln operating conditions examined include: rotation rate (0.1-0.9 rpm), percent fill fraction (3-8), feed moisture content (0-20 wt.%), and inner-wall temperature (190"-790"C). The model is used to determine the relative importance of several heat-transfer mechanisms, including radiation, gas-to-solid convection, and wall-to-solid convection. Simple scaling laws are also developed for water vaporization. Generally good agreement is obtained between theory and experiment without adjusting any model parameters. Further, the simplified scaling laws provide a reasonable estimate of the pilot scale performance. The key conclusions of this study for kilns at the conditions examined are (1) water exerts a profound effect on the solids thermal profile, (2) simple geometrical scaling is not sufficient, (3) the assumption of a well mixed (radially isothermal) solids bed for the heat transfer analysis is appropriate, (4) a dimensionless group, which is a function of temperature, can be defined giving the relative importance of radiative and convective modes of heat transfer, and (5) moisture vaporization rates can be roughly approximately by assuming that the water vaporizes at the boiling point at a rate controlled by the rate of heat transfer to the bed. The implications of the scaling laws for scale-up and kiln design are also examined.
NOMENCLATURE
Ei w Eo w G a thermal diffusivity of solid burden, m2/s, Acco, v area of covered inner wall for one f zone participating in convection be-Fw s tween wall and burden, m 2. A s exposed surface of solid burden for one zone at gas-solid interface, m 2. F wg A w area of inner wall, excluding area covered by solid burden, for one zone, m 2. Fsg Cpd s heat capacity of dry solids, J/kg β’ K. Cpw s heat capacity of wet solids, J/kg β’ K. d kiln i.d., m. Gg' z~ H v heat of vaporization of water, J/kmol. A Z zone width, m. hg s Eg emissive power of gas, W/m 2. hi gs