Revisiting the Influence of Confinement on the Pressure Drop in Fixed Beds

We study the non-turbulent pipe flow of a Newtonian fluid through a confined porous medium made of randomly arranged spherical particles in the situation where the ratio between the pipe diameter over the particle diameter (D/d) is less than 10. Using experiments and numerical simulations, we examine the relation between the flow rate and the mean pressure gradient as a function of the Reynolds number and particle size, and how it is affected by the presence of the walls. We investigate the intrinsic variability of the measurements in relation to the randomness of the particle arrangement and how such variability is linked to spatial fluctuations of pressure within the bed. We observe that as D/d decreases, the pressure gradient presents a stronger variability, particularly in relation to where measurements are taken within the pipe. The study also quantifies the difference between measuring the pressure drop at the wall versus averaging over the entire volume, finding a small difference of 2.5% at most. We examine how the mean pressure gradient is affected by the lateral walls, finding that the pressure drop follows a consistent 1/Re scaling regardless of the confinement of the bed. Finally, we observe that the pressure gradient balances the force exerted on the solid spheres with a very weak contribution of the wall friction, showing that the role of confinement corresponds to a global effect on the bed arrangement which in turns affects the mean pressure gradient.