Solute transport in solution conduits exhibiting multi-peaked breakthrough curves

Abstract

► We derive a mathematical model to fit a dual-peaked breakthrough curve. ► We develop a series of experiments to examine the physical cause of dual peaks in breakthrough curves. ► We fit the mathematical model to a real-world tracer test. ► The mathematical model provides valuable insight regarding subsurface flow conditions in karst aquifers. ► The experiments suggest some caution in applying the mathematical model. Solute transport in karst aquifers is primarily constrained to solution conduits where transport is rapid, turbulent, and relatively unrestrictive. Breakthrough curves generated from tracer tests are typically positively-skewed and may exhibit multiple peaks. In order to understand the circumstances under which multi-peaked positively skewed breakthrough curves occur, physical experiments utilizing single- and multiple-flow channels were conducted. Experiments also included waterfalls, short-term solute detention in pools, and flow obstructions. Results demonstrated that breakthrough curve skewness nearly always occurs to some degree but is magnified as immobile-flow regions are encountered. Multi-peaked breakthrough curves occurred when flow in the main channel became partially occluded from blockage in the main channel that forced divergence of solute into auxiliary channels and when waterfalls and detention in pools occurred. Currently, multi-peaked breakthrough curves are fitted by a multi-dispersion model in which a series of curves generated by the advection–dispersion equation are fitted to each measured peak by superimposing the measured breakthrough curve to obtain a combined model fit with a consequent set of estimated velocities and dispersions. In this paper, a dual-advection dispersion equation with first-order mass transfer between conduits was derived. The dual-advection dispersion equation was then applied to the multi-peaked breakthrough curves obtained from the physical experiments in order to obtain some insight into the operative solute-transport processes through the acquisition of a consequent set of velocities, dispersions, and related parameters. Successful application of the dual-advection, dispersion equation to a tracer test that exhibited dual peaks for a karst aquifer known to consist of two connected but mostly separate conduits confirmed the appropriateness of using a multi-dispersion type model when conditions warrant.