Analysis of Effective Roughness Length of Calcium Carbonate Scales Using Darcy Friction

We investigate the effect of brine solution composition on the effective roughness length (K_s). This is relevant to the oil and gas industry, for instance, because a common way to monitor scale formation (CaCO₃) growth is by measuring the pressure drop in pipes or other equipment and analyzing how it varies over the course of its lifetime in the field. Often, a constant value for the roughness is assumed to be used with the Darcy-Weisbach equation. With this assumption, an estimate is made for the internal local pipe diameter and, indirectly, the thickness of deposited material. However, data on K_s is lacking due to experimental difficulties in controlling scale formation at high Reynolds number flows. Additionally, the effect of flow acceleration or deceleration—consequence of varying diameter—on the pressure drop is usually neglected.



To this end, we conducted 44 experiments with varying combinations of flow rate and water ionic composition, making sure that each individual condition was set up at least twice. The experimental rig consists of a 65m long circular pipe with a 10mm internal diameter. Eleven different pressure meters are positioned equally spaced along its length. Immediately downstream of such pressure gauges are removable sections designed to allow us to assess the scale thickness from SEM images. Then, we perform an one-dimensional momentum balance to calculate the wall shear stresses and, consequently, the Darcy friction factor. Finally, from the Colebrook-White equation, K_s is determined.