Transport in Porous Media

, Volume 124, Issue 2, pp 655–679 | Cite as

Exact Solution for Coupled Reactive Flow and Dissolution with Porosity Changes

  • A. Altree-Williams
  • J. Brugger
  • A. Pring
  • P. BedrikovetskyEmail author


We derive exact solution for mineral-dissolution reactive flows in porous media with porosity variations. These conditions are relevant to injection of incompatible liquids into aquifers for disposal or waste storage, rock alteration during well stimulation by acidising or invasion of corrosive, far-from-equilibrium fluids related to ore deposit formation and heap or in situ leaching in mineral processing. Despite the porosity change making the one-dimensional flow equations nonlinear, the problem allows for exact integration, and a novel analytical model is developed. It allows presenting typical curves for breakthrough concentrations and porosity evolution. The exact solution provides a tool for predictive testing of reactive models that account for porosity creation. The analytical model derived exhibits high agreement with laboratory data, which validate the model.


Reactive flow Mineral dissolution Porous media Porosity alteration Mathematical model 

List of symbols



Concentration of mineral in solvent solution


Equilibrium concentration


Axial dispersion (L2 T−1)


Effluent concentration normalized least squares deviation


Normalized least squares deviation


Average porosity normalized least squares deviation


Core length (L)


Time (T)


Dimensionless time, PVI

Tc (X)

Boundary between zones I and II, PVI

Tf (0)

Time of full mineral dissolution at inlet, PVI

Tf (1)

Time of dissolution front breakthrough, PVI


Darcy velocity (L T−1)


Reciprocal to dissolution front speed


Axial coordinate (L)


Dimensionless axial coordinate



Dispersivity (L)


Kinetics number


Kinetic delay time (T)




Normalised porosity



Initial value


Experimental values





The authors are grateful to Eng. T. Russell and A/Prof. Yung Ngothai (The University of Adelaide) for fruitful and encouraging discussions. Many thanks are due to David H. Levin (Murphy, NC, USA) who provided professional English-language editing of this article. The authors thank Australian Research Council for grants DP140102765 and LP150100626. Significant improvement in the quality of the text is due to thoughtful feedback of all seven reviewers.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • A. Altree-Williams
    • 1
  • J. Brugger
    • 2
  • A. Pring
    • 3
  • P. Bedrikovetsky
    • 1
    Email author
  1. 1.University of AdelaideAdelaideAustralia
  2. 2.Monash UniversityMelbourneAustralia
  3. 3.Flinders UniversityAdelaideAustralia

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