Comput Geosci DOI 10.1007/s10596-012-9285-3 ORIGINAL PAPER A porosity-gradient replacement approach for computational simulation of chemical-dissolution front propagation in fluid-saturated porous media including pore-fluid compressibility Chongbin Zhao · Lynn B. Reid · Klaus Regenauer-Lieb · Thomas Poulet Received: 11 August 2011 / Accepted: 27 January 2012 © Springer Science+Business Media B.V. 2012 Abstract In dealing with chemical-dissolution-front propagation problems in fluid-saturated porous me- dia, the chemical dissolution front represented by the porosity of the medium may have a very steep slope (i.e., a very large porosity gradient) at the dissolution front, depending on the mineral dissolution ratio that is defined as the equilibrium concentration of the dis- solved minerals in the pore-fluid to the solid molar density of the dissolvable minerals in the solid matrix. When the mineral dissolution ratio approaches zero, the theoretical value of the porosity gradient tends to infinity at the chemical dissolution front. Even for a very small value of the mineral dissolution ratio, which is very common in geochemical systems, the porosity gradient can be large enough to cause the solution hard to converge when the conventional finite element method is used to solve a chemical dissolution C. Zhao (B ) Computational Geosciences Research Centre, Central South University, Changsha 410083, China e-mail: chongbin.zhao@iinet.net.au L. B. Reid · K. Regenauer-Lieb · T. Poulet Western Australian Geothermal Centre of Excellence, CSIRO Division of Earth Science and Resource Engineering, P. O. Box 1130, Bentley, WA 6102, Australia L. B. Reid School of Environmental System Engineering, The University of Western Australia, Crawley, WA 6009, Australia K. Regenauer-Lieb School of Earth and Environment, The University of Western Australia, Crawley, WA 6009, Australia problem in a fluid-saturated porous medium where the pore-fluid is compressible. To improve the convergent speed of solution, a porosity-gradient replacement ap- proach, in which the term involving porosity-gradient computation is replaced by a new term consisting of pore-fluid density-gradient and pressure-gradient com- putation, is first proposed and then incorporated into the finite element method in this study. Through com- paring the numerical results obtained from the pro- posed approach with the theoretical solutions for a benchmark problem, it has been demonstrated that not only can the solution divergence be avoid, but also the accurate simulation results can be obtained when the proposed porosity-gradient replacement approach is used to solve chemical-dissolution-front propagation problems in fluid-saturated porous media including pore-fluid compressibility. Keywords Porosity-gradient replacement · Pore-fluid compressibility · Dissolution front · Chemical dissolution · Instability problem · Porous media 1 Introduction Instability of a nonlinear system is a common phenom- enon in nature. When a nonlinear system is in a stable state, any small perturbation applied to the system can die out with time, so that the system remains in the stable state. However, when a nonlinear system is in an unstable state, any small perturbation applied to the system can grow with time. As a result, the sys- tem will change from the stable state into an unstable state. From the mathematical point of view, when a