Part V – May 1968 - Papers - On Nonisothermal Flow of Gases Through Packed Beds

A method is presented which allows the extension of the Ergun equation for the description of gas flow through packed beds in a nonisothermal regime. The pressure profile in the packed bed is calculated by the establishment of a differential energy balance and the iterative integration of the integral equation thus obtained. The predicted values of the pressure distribution were found to be in excellent agreement with those measured experimentally, under carefully controlled conditions. MANY metallurgical processes are carried out in systems in which a gas stream and particular solids are contacted in a packed bed arrangement under strongly nonisothermal conditions. Ore sintering, the firing of pellets, the operation of regenerators, blast furnace technology may be quoted as examples. Although many aspects of these systems have been extensively studied, an important variable, the pressure distribution and the relationship between pressure head and flow rate, received only little attention to date. The purpose of the paper is to present a brief survey of relevant previous work, followed by a more rigorously formulated model, together with experimental results that afford ready comparison of theoretical prediction with measurement. PREVIOUS WORK A great deal of information is available in the chemical engineering literature on flow phenomena in porous media.' The experimental results pertaining to gas flow were generally interpreted in terms of models based on the analogy with the flow through a pipe of an incompressible, isothermal fluid. Of the numerous, semiempirical correlations that have been proposed to relate pressure drop to the volumetric flow rate, the Ergun equation2 is generally regarded as the most satisfactory: The strong nonisothermality of the metallurgical systems previously mentioned would render the direct applicability of Eq. [I] rather doubtful as both density and viscosity are temperature-dependent. Ergun has used Eq. [I] for estimating the pressure drop in the stack region in the blast furnace by neglecting the viscous term and evaluating the gas density at the integral mean temperature.3 His calculations showed a rather variable agreement with measurements and it was uncertain whether the discrepancy found was attributable to the model or to the inaccuracies often inherent in measurements on an industrial scale. Other work on nonisothermal systems includes studies of the pressure distribution in sinter beds, notably by Voice et a1.4 and Mitchell.5 Mitchell developed a method involving the subdivision of the bed into several zones and assigning average property values (temperature, gas density, and so forth) to each zone. The pressure drop was then calculated for each zone by using an expression analogous to Eq. [I]. This method was an improvement over that described by Voice et al., but even here prediction and measurement differed by as much as 30 pct in certain cases. It would appear that no really satisfactory methods are available for the prediction of pressure drop in packed beds with a strongly nonisothermal regime. The method involving subdivision of the bed into small enough sections, that may be regarded as isothermal, would show promise; however its validity has to be tested by both a rigorous formulation and comparison with experimental data obtained under controlled conditions. In the following a formulation is presented together with experimental data allowing ready practical evaluation of the theory. FORMULATION The mechanical energy balance over an infinitesimal section of a packed bed may be written as follows: