In this work, a mathematical model based on an extended Brinkman equation was used to evaluate the porosity and velocity distribution along the radial direction of a horizontal-flow anaerobic immobilized biomass (HAIB) reactor; the model considers the fluid flow within the bed. The study was performed using two different particle geometries and three tube to-particle diameter ratios (D/d(p)) to understand the effects of the shape and particle size on the flow velocity distribution. The results show that the oscillation in the velocity profile is dependent on the D/d(p) ratio, particle shape and bed porosity. Better results were obtained with irregular shapes, such as hollow cylindrical rings, and a D/d(p) ratio of 10. The model adapted for this study may be a suitable tool for the design and optimization of horizontal flow anaerobic immobilized biomass reactors used in wastewater treatment processes. (c) 2016 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.