fluid flow absence of fluid flow = effective thermal conductivity of a packed bed in the = thermal conductivity of gas = natural logarithm = logarithm to base 10 = number of samples = probability density function = log population standard deviation = temperature = bulk temperature of the bed = wall temperature of the heater = superficial air velocity = minimum fluidization velocity = distance from heat transfer surface Greek Letters 6 = interval length € = void fraction (effective) €1 €2 e = time ee 0; 4 cc, = viscosity of gas IT = 3.1415926 Pe = emulsion (packet) density Po = density of gas PS = solid density oi = void fraction of a loosely packed bed = void &action of a densely packed bed = emulsion (packet) residence time = root-square average emulsion (packet) residence = log sample mean of residence times time by Equation (3) = log sample standard deviation SCOPE The principal objective of this work was to develop an analytical procedure for predicting the critical velocity for slurry transport in pipelines. The prediction of the critical velocity, defined as the minimum velocity demarcating flows in which the solids form a bed at the bottom of the pipe from fully suspended flows, is an eminently practical Correspondence concerning this work should be addressed to Ram M. Turian. Anil problem in itself. However, the analytical approach des-R. Oroskar is now in the Deptutment of Chemical Engineering, University of Wisconsin, Madison, Wisconsin 53706. ooO1-1541 -80 -3462 -0550 ~ $01.05cribed here derives its broader relevance from the fact that it constitutes an attempt to establish a better understanding of the complex problem of slurry transport.

A new model for porous media comprised of monosized, or nearly monosized grains, is developed. In applying this model to a packed bed, the bed is assumed to consist of a series of statistically identical unit bed elements each of which in turn consists of a number of unit cells connected in parallel. Each unit cell resembles a piece of constricted tube with dimensions which are random variables. The problem of flow through each unit cell is reduced, subject to reasonable assumptions, to the determination of the flow in an ALKlVlADES C. PAYATAKES CHI TlEN and RAFFI M. TURIAN infinitely long periodically constricted tube. The solution of this flow problem is given in a companion publication. This model, together with the solution of the flow through it, can be used for the modeling of processes which take place in the void space of a bed.As a preliminary test, theoretical friction factor values, based on the proposed model, were compared with experimental ones for two different beds and found to be in good agreement even in the region of high Reynolds numbers where the nonlinear inertia terms are significant. SCOPEThe main purpose of this paper is to present a new model for porous media of the type represented by randomly packed beds of monosized, or nearly monosized, grains. The model has been developed as a first step in

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Pressure drop correlations for flow of slurries in pipelines were developed for each of the following four flow regimes: flow with a stationary bed, saltation flow, heterogeneous flow, and homogeneous flow. A total number of 2 848 data points, comprised of 1912 collected from the published literature together with 936 taken using our own test pipelines and relating to ranges of the pertinent variables extensive enough to span all four flow regimes were used as the basis of these correlations. Also, these data were used in developing an associated quantitative regime delineation scheme. The correlations provide an improved predictive capability over previously available procedures and are also broader in scope. The delineation procedure developed here permits straightforward classification of the data according to the flow regime prevailing, and it is moreover inclusive of all the data and is self-consistent.

A simulation procedure for predicting the dynamic behavior of a deep bed filter over the entire practicable range of filter operation is developed. The method is based on synthesizing available quantitative results relating to filtration, and to porous media flows, within an overall framework which views the process to consist of two principal stages dominated by appropriate limiting deposition modes. Evaluation of the results through comparison with available data indicates, to the extent the nature of these types of data permits, that the method is surprisingly effective and even capable of predicting on satisfactorily quantitative basis some intricate details of observed filter behavior. CHI SCOPEThis work is concerned with the development of a simulation procedure capable of predicting the dynamic behavior of a deep bed filter over the broadest practicable range of the pertinent variables involved, including, in particular, the value of the specific deposit. The method presented here was developed by assimilating available quantitative results relating to porous media flows, and to filtration, in the context of a conceptual framework which views the process, and its progressive evolution, to consist of two consecutive stages, each dominated by an appropriate limiting deposition mode. This picture of the process is supportable on the basis of observed filter behavior and does, moreover, provide the means for integrating results based on the two main collector types (the spherical and the constricted tube models) into the overall simulation scheme. The method we present incorporates the transformation, first suggested by Herzig et al. (1970), which reduces the governing conservation equations into a set of ordinary differential equations, thereby leading to considerable savings in computational effort. CONCLUSIONS AND SIGNIFICANCEDeep bed filtration is a subject which has, in recent years, developed a rich and varied literature. Despite the dramatic progress in our understanding which this has produced, a comprehensive method capable of predicting the dynamic behavior of a filter over its entire operational span has remained out of reach. No doubt the uncertainties surrounding some aspects of the nature of the deposition process, particularly the critical ones relating to the nature of the distribution of the deposited matter within the media and its evolution with progressive deposition, have stood as the main impediments obstructing progress towards such a general predictive scheme. In this work this problem is resolved by postulating an overall picture of the filtration process which views it to consist of two consecutive stages: a first stage dominated by deposition according to a smooth coating mode and assumed to endure until the specific deposit attains a prescribed transition value, followed by a second stage corresponding to transition to deposition by the constriction clogging mode. This picture of the process, though somewhat idealized, is in the main consistent with observed filter behavior.However...