Mixed transport/reaction control of gypsum dissolution kinetics in aqueous solutions and initiation of gypsum karst

Abstract

Experiments with gypsum in aqueous solutions at 25°C, low ionic strengths, and a range of saturation states indicate a mixed surface reaction and diffusional transport control of gypsum dissolution kinetics. Dissolution rates were determined in a mixed flow/rotating disc reactor operating under steady-state conditions, in which polished gypsum discs were rotated at constant speed and reactant solutions were continuously fed into the reactor. Rates increase with velocity of spin under laminar conditions (low rates of spin), but increase asymptotically to a constant rate as turbulent conditions develop with increasing spin velocity, experiencing a small jump in magnitude across the laminar–turbulent transition. A linear dependence of rates on the square root of spin velocity in the laminar regime is consistent with rates being limited by transport through a hydrodynamic boundary layer. The increase in rate with onset of turbulence accompanies a near discontinuous drop in hydrodynamic boundary layer thickness across the transition. A relative independence of rates on spinning velocity in the turbulent regime plus a nonlinear dependence of rates on saturation state are factors consistent with surface reaction control. Together these behaviors implicate a `mixed' transport and reaction control of gypsum dissolution kinetics. A rate law which combines both kinetic mechanisms and can reproduce experimental results under laminar flow conditions is proposed as follows: R=k t 1−Ω ± b +ζ 1− 1+ 2(1−Ω ± b ζ 1/2 where k t is the rate coefficient for transport control, and Ω ± b is the mean ionic saturation state of the bulk fluid. The dimensionless parameter ζ(=D m ± eq /2δk + where m ± eq=mean ionic molal equilibrium concentration, D is the diffusion coefficient through the hydrodynamic boundary layer, δ equals the boundary layer thickness and k + is the rate constant for surface reaction control) indicates which process, transport or surface reaction, dominates, and is sensitive to the hydrodynamic conditions in the reactor. For the range of conditions used in our experiments, ζ varies from about 1.4 to 4.5. Rates of gypsum dissolution were also determined in situ in a cavern system in the Permian Blaine Formation, southwestern Oklahoma. Although the flow conditions in the caverns were not determinable, there is good agreement between lab- and field-determined rates in that field rate magnitudes lie within a range of rates determined experimentally under zero to low spin velocities A numerical model coupling fluid flow and gypsum reaction in an idealized circular conduit is used to estimate the distance which undersaturated solutions will travel into small incipient conduits before saturation is achieved. Simulations of conduit wall dissolution show end-member behaviors of conduit formation and surface denudation that depend on flow boundary conditions (constant discharge or constant hydraulic gradient) and initial conduit radius. Surface-control of dissolution rates, which becomes more influential with higher fluid flow velocity, has the effect that rates decrease more slowly as saturation is approached than otherwise would occur if rates were controlled by transport alone. This has the effect that reactive solutions can penetrate much farther into gypsum-bearing karst conduits than heretofore thought possible, influencing timing and mechanism of karst development as well as stability of engineered structures above karst terrain.