Response to “Comments on Abrupt-Interface Solution for Carbon Dioxide Injection into Porous Media by Dentz and Tartakovsky (2008)” by Lu et al.

Abstract

In their Comment, the authors raise an important issue of the validity of the analytical (Dentz and Tartakovsky 2008) and semi-analytical (Nordbotten et al. 2005) solutions describing migration of supercritical CO2 that is being injected into a deep geological formation. Indeed, any mathematical model (including the two-phase immiscible flow model employed in the Comment) is an abstraction, whose fidelity to a physical phenomenon it purports to describe can be established only through observation. Unlike standardmulti-phase flowmodels, which rely on a number of implicit and often unstated physical conjectures whose validity is hard to ascertain a priori (e.g., Adler and Brenner1988; Gray andHassanizadeh 1998, among others), the solutions of Dentz and Tartakovsky (2008) and Nordbotten et al. (2005) are based on the following premise: