Determination of transverse dispersion coefficients from reactive plume lengths

With most existing methods, transverse dispersion coefficients are difficult to determine. We present a new, simple, and robust approach based on steady-state transport of a reacting agent, introduced over a certain height into the porous medium of interest. The agent reacts with compounds in the ambient water. In our application, we use an alkaline solution injected into acidic ambient water. Threshold values of pH are visualized by adding standard pH indicators. Since aqueous-phase acid-base reactions can be considered practically instantaneous and the only process leading to mixing of the reactants is transverse dispersion, the length of the plume is controlled by the ratio of transverse dispersion to advection. We use existing closed-form expressions for multidimensional steady-state transport of conservative compounds in order to evaluate the concentration distributions of the reacting compounds. Based on these results, we derive an easy-to-use expression for the length of the reactive plume; it is proportional to the injection height squared, times the velocity, and inversely proportional to the transverse dispersion coefficient. Solving this expression for the transverse dispersion coefficient, we can estimate its value from the length of the alkaline plume. We apply the method to two experimental setups of different dimension. The computed transverse dispersion coefficients are rather small. We conclude that at slow but realistic ground water velocities, the contribution of effective molecular diffusion to transverse dispersion cannot be neglected. This results in plume lengths that increase with increasing velocity.