Part VI – June 1969 - Papers - Heat and Gas Flow Interactions in Nonisothermal Packed Beds. Part I-Fixed Bed Systems

Heat and gas flow interactions in nonisothermal packed beds were examined in the paper. A study was made of the response of the system to a step or pulse change in the inlet gas temperature, with a fixed value of the overall pressure drop across the bed. Under these conditions the heat flow and fluid flow transients are coupled because the convective heat transfer rate is alfected by the mass flow rate of the gas which, in turn, for a fixed pressure drop will depend on the temperature profile in the system. The Problem was stated in terms of differential equations, which were integrated numerically. The parameters used in the computation were so chosen to reflect the operation of the stack region of blast furnaces and sinterbeds. The computed results showed that the pressure drop-flou1 relationships and the rate of progress of the temperature fronts (waves) were strongly interrelated and were also markedly affected by variations in particle size and in void fraction. MANY metallurgical processes involve the contact of solid particles with a gas stream in a packed bed arrangement under nonisothermal conditions. Examples are shaft furnaces, regenerators, pebble heaters, and the sinter process. Although the heat and mass transfer aspects of packed bed processing have been extensively studied, the associated flow phenomena and in particular the effects of nonisothermality on the flow, have received little attention to date. :In fact, most of the previous workers considered the flow rate of the carrier gas time invariant and independent of the heat or mass transfer processSzekely and carr2 have shown that the pressure drop-flow relationships in nonisothermal packed beds may be strongly affected by the temperature profile within the system. These authors have devised a method for relating the pressure drop to flow for a given temperature profile. thus providing an extension of the Ergun equation to steady nonisothermal systems. Finally, in a recent paper willmot3 examined the response of regenerators to externally imposed changes in the gas flow rate. Both these investigations were somewhat specialized since, in general, neither the temperature distribution nor the gas flow rate may be regarded as truly independent variables, thus the heat transfer and the fluid flow problems have to be solved simultaneously. The work reported here is divided into two parts: in Part 1 the general formulation is given and a detailed discussion is presented of fixed bed systems. Part is devoted to systems in which a gas and particulate solids are contacted in a counter flow arrangement. FORMULATION Consider a nonisothermal fixed packed bed, extending from through which a gas is flowing. The problem is to develop a relationship between pressure drop and gas flow (with the gas flow being the dependent variable) and to evaluate the rate at which a change in the gas temperature, imposed at the inlet, travels through the system. Let us consider an infinitesimal section of the bed and establish differential heat, mass, and mechanical energy balances over this region. In addition, relationships are needed describing the temperature dependence of gas density (equation of state) and the temperature dependence of viscosity. These may be written as: where c, and are constants. It is noted that in this formulation we neglected any temperature gradients within the solid particles, thus assuming these to be either sufficiently small or of sufficiently high thermal conductivity to meet this condition. The justification and consequences of this assumption will be mentioned in the discussion.