Finite element modeling of fluid–rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins Original Research Article

In order to use the finite element method for solving fluid–rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins effectively and efficiently, we have presented, in this paper, the new concept and numerical algorithms to deal with the fundamental issues associated with the fluid–rock interaction problems. These fundamental issues are often overlooked by some purely numerical modelers. (1) Since the fluid–rock interaction problem involves heterogeneous chemical reactions between reactive aqueous chemical species in the pore-fluid and solid minerals in the rock masses, it is necessary to develop the new concept of the generalized concentration of a solid mineral, so that two types of reactive mass transport equations, namely, the conventional mass transport equation for the aqueous chemical species in the pore-fluid and the degenerated mass transport equation for the solid minerals in the rock mass, can be solved simultaneously in computation. (2) Since the reaction area between the pore-fluid and mineral surfaces is basically a function of the generalized concentration of the solid mineral, there is a definite need to appropriately consider the dependence of the dissolution rate of a dissolving mineral on its generalized concentration in the numerical analysis. (3) Considering the direct consequence of the porosity evolution with time in the transient analysis of fluid–rock interaction problems, we have proposed the term splitting algorithm and the concept of the equivalent source/sink terms in mass transport equations so that the problem of variable mesh Peclet number and Courant number has been successfully converted into the problem of constant mesh Peclet and Courant numbers. The numerical results from an application example have demonstrated the usefulness of the proposed concepts and the robustness of the proposed numerical algorithms in dealing with fluid–rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins.