| Abstract |
Silica scaling limits the flow rate of the geothermal fluid passing through a powerplant and hence heat and the power that can be extracted from it. The chemical kinetics of silica colloid nucleation and growth are reasonably well understood, but the hydrodynamic transport and the process of binding to solid surfaces are not. A key question is whether the rate at which particles accumulate on the surface is limited by the rate of transport of particles through the fluid near the wall, or by the fraction of particles which form permanent bonds at the surface. Previous work by Dunstall, Zipfel and Brown showed the scale deposited on a cylindrical object placed in flowing geothermal brine varied in thickness from place to place, with thicker deposits forming in the locations where the shear stress is high. This suggests a transport-limited process. This paper reports new computational fluid dynamics (CFD) study which suggests that if electrostatic interactions are ignored, the rate of arrival of silica particles at the surface is several orders of magnitude higher than the observed scaling rate. This suggests only a small fraction (~1 in 105) of the particles arriving at the wall in that experiment actually attach to it, and that the scaling process is limited by the process of bonding with the surface. In an attempt to resolve this contradiction, the theory or particle transport and interaction has been explored. When the wall is coated with silica, colloids in motion near the wall experience electrostatic repulsion. The resultant energy barrier can be calculated from the Derjaguin, Landau, Verwey and Overbeek (DLVO) theory. It is used here to find the stability of a colloidal system under various hydrodynamic conditions: pure Brownian motion (stagnant fluid), laminar and turbulent shear flows. For the conditions of the experiments, the theory predicted that 1 in 104 to 1 in 106 of the particles arriving at the wall would bind permanently to the surface. When multiplied by the transport rate determined from CFD results, the experimentally observed rate of scaling is predicted correctly. The results give a starting point to build a theory of silica colloid transport and deposition. Wall roughness, which is enhanced as ridges of silica scale grow, is shown to enhance the scaling rate significantly. Further calculations and more experimental data are required to integrate roughness into the theory. |