Why asymptotic limit of the acid dissolution capacity can lead to a sharp dissolution front in chemical dissolution of porous rocks?

Chongbin Zhao, B. E. Hobbs, A. Ord

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    The use of the asymptotic limit can greatly simplify the theoretical analysis of chemical dissolution front instabilities in fluid-saturated rocks and therefore make it possible to obtain mathematical solutions, which often play a crucial role in understanding the propagation behavior of chemical dissolution fronts in chemical dissolution systems. However, there has been a debate in recent years that the asymptotic limit of the acid dissolution capacity (i.e., the acid dissolution capacity number approaching zero) alone cannot lead to a sharp dissolution front of the Stefan type in the acidization dissolution system, in which the dissolvable minerals of carbonate rocks are chemically dissolved by the injected acid flow. The acid dissolution capacity number is commonly defined as the ratio of the volume of the carbonate rock dissolved by an acid to that of the acid. In this paper, we use four different proof methods, including (i) direct use of the fundamental concepts; (ii) use of the mathematical governing equations of an acidization dissolution system; (iii) use of the different time scaling approach; and (iv) use of a moving coordinate system approach, to demonstrate that the asymptotic limit of the acid dissolution capacity can indeed lead to sharp dissolution fronts of the Stefan type in acidization dissolution systems on a much larger time scale (than the dissolution time scale). Our new finding is that on the reaction time scale, the condition of the conventional time derivative of porosity approaching zero alone can ensure that the acidization dissolution front has a sharp shape of the Stefan type.

    Original languageEnglish
    Pages (from-to)1590-1602
    Number of pages13
    JournalInternational Journal for Numerical and Analytical Methods in Geomechanics
    Volume41
    Issue number15
    DOIs
    Publication statusPublished - 25 Oct 2017

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