Tracking Diverse Minerals, Hungry Organisms, and Dangerous Contaminants Using Reactive Transport Models

Abstract

Despite the vast technological and manufacturing innovations of the Second Industrial Revolution (~ 1870 to 1914), the chemical engineer of the 1930s still relied heavily on trial and error to optimize the design of industrial processes, from chemical separations and petroleum refining to combustion engines (Inger 2001). The question these engineers sought to answer was seemingly simple: how long did a fluid or gas need to stay in the reactor to achieve maximum conversion? The answer was also simple, in principle: the time the fluid or gas spends in the reactor should be longer than the timescale of the chemical reaction(s). Quantitative understanding, however, required the development of mathematical constructs. To address this problem, a young assistant professor at Göttingen University (Germany), Gerhard Damköhler, explored an extension of similarity theory to “nondimensionalize” the governing equations of reactive flows. What emerged was a set of dimensionless numbers that bears his name: the Damköhler (Da) numbers. The Da compares the timescale for solute or gas transport (i.e., how long it takes for a hypothetical particle of fluid or gas to traverse the reactor) to the timescales for the reactions to go to completion, i.e., how long it takes to complete a set of reactions as governed by the kinetics and thermodynamics that set the rates of reactions and final concentrations (Damköhler 1936). In this sense, the ratio reflected in the Da number is useful in that it defines the competition between transport and reaction (Fig. 1). Although developed in the context of chemical engineering, this concept is equally valid for the interactions between the reactions and transport processes below our feet, i.e., in the Earth’s upper crust.