Transport in Porous Media 27: 99–118, 1997. 99 c 1997 Kluwer Academic Publishers. Printed in the Netherlands. Wall Region Porosity Distributions for Packed Beds of Uniform Spheres with Modified and Unmodified Walls JON D. MCWHIRTER 1 , MICHAEL E. CRAWFORD 2 and DALE E. KLEIN 2 1 College of Engineering, Box 8060, Idaho State University, Pocatello, ID 83209 U.S.A. e-mail: mcwhjon@if.if.isu.edu 2 Department of Mechanical Engineering, University of Texas at Austin, U.S.A. (Received: 26 March 1996; in final form: 27 November 1996) Abstract. A mathematical derivation of the porosity (local void fraction) distribution near the walls of packed beds of uniform spheres is presented. This investigation supports the study of methods of reducing or eliminating the so-called wall effect, or bypass flow, which accompanies the increase in porosity when spheres come in contact with a solid boundary. Limiting the amount of bypass flow is important in certain applications such as in packed bed nuclear reactors where bypass flow allows some coolant to avoid the high power density core region. Four basic porosity distributions are determined. The first investigates the case where spheres against a flat wall are packed in the tightest possible packing density. This density is then reduced by changing the sphere spacing until the minimum porosity matches that obtained experimentally. In the other cases, the effect of various ways of embedding spheres in the wall on the wall region porosity is examined. By partially embedding spheres in the wall, the porosity at the wall is reduced and the most direct cause of the bypass flow is thereby eliminated. The porosity is found by evaluating the ratio of the solid area to total area in a plane which is parallel to the wall. The local porosity is derived as a function of distance from the wall in the region within one-half a sphere diameter from the wall. The average porosity of the wall region is also calculated. This research has application to flow situations such as packed bed chemical reactors, pebble bed nuclear reactors and flow in packed beds. Key words: packed bed, bypass flow, well effect. Nomenclature area. sphere diameter. container diameter. unoccupied normal distance from wall. dimensionless distance from wall, . normal distance from wall. sphere radius, 2. spacing parameter. volume. radius of circle formed by intersection of a sphere with a plane parallel to a wall. local distance from sphere center normal to a wall. angle between specific planes. porosity.