Computational simulation for the morphological evolution of nonaqueous phase liquid dissolution fronts in two-dimensional fluid-saturated porous media

Abstract

This paper deals with the computational aspects of nonaqueous phase liquid (NAPL) dissolution front instability in two-dimensional fluid-saturated porous media of finite domains. After the governing equations of an NAPL dissolution system are briefly described, a combination of the finite element and finite difference methods is proposed to solve these equations. In the proposed numerical procedure, the finite difference method is used to discretize time, while the finite element method is used to discretize space. Two benchmark problems, for which either analytical results or previous solutions are available, are used to verify the proposed numerical procedure. The related simulation results from these two benchmark problems have demonstrated that the proposed numerical procedure is useful and applicable for simulating the morphological evolution of NAPL dissolution fronts in two-dimensional fluid-saturated porous media of finite domains. As an application, the proposed numerical procedure has been used to simulate morphological evolution processes for three kinds of NAPL dissolution fronts in supercritical NAPL dissolution systems. It has been recognized that: (1) if the Zhao number of an NAPL dissolution system is in the lower range of the supercritical Zhao numbers, the fundamental mode is predominant; (2) if the Zhao number is in the middle range of the supercritical Zhao numbers, the (normal) fingering mode is the predominant pattern of the NAPL dissolution front; and (3) if the Zhao number is in the higher range of the supercritical Zhao numbers, the fractal mode is predominant for the NAPL dissolution front.

An overview of hydrodynamic studies of mineralization

“…Permeability may increase or decrease through either mechanical or chemical processes, which may also be related to the driving forces (especially deformation), fluid flow and chemical reactions. Generally, a decrease in permeability may be caused by rock deformation (e.g., sediment compaction) or mineral precipitation or cementation, whereas an increase in permeability may be caused by deformation (e.g., fracturing) and mineral dissolution (Bethke, 1985;Ge and Garven, 1992;Xu et al, 2004;Cox, 2005;Zhao et al, 2008bZhao et al, , 2011. It has also been found that rock porosity and permeability may be influenced by temperature (Zhao et al, 1999a).…”

Replacement of annular domain with trapezoidal domain in computational modeling of nonaqueous-phase-liquid dissolution-front propagation problems

“…This means that the finite element method is used to discretize the spatial domain, while the finite difference method is used to discretize the time domain. Since the proposed combination procedure has been verified through simulating both theoretical and experimental benchmark problems in a previous work [12], it can be used to examine how a NAPL dissolution front propagates in both the partial annular domain (in Fig. 1(b)) and the trapezoidal one (in Fig.…”

“…Existing theoretical studies [12] have demonstrated that the intrinsic characteristic time scale of a NAPL dissolution system is about several tens seconds in the order of magnitude, while the intrinsic characteristic length scale of the NAPL dissolution system is about several tens micrometers in the order of magnitude. To simulate the instability phenomenon of a NAPL dissolution front in a computational model, the intrinsic characteristic time is used to determine the time scale at which the NAPL dissolution front is formed, while the intrinsic characteristic length is used to determine the length scale at which the instability of the NAPL dissolution front can be initiated.…”

Effects of domain shapes on the morphological evolution of nonaqueous-phase-liquid dissolution fronts in fluid-saturated porous media

“…Since the dimensionless governing equations of a NAPL dissolution system are highly nonlinear, the segregated algorithm, in which Eqs. (13) to (15) are solved separately and iteratively in a sequential manner, was used to derive the formulation of the proposed numerical procedure (Zhao et al, 2011). For the sake of completeness of this paper, only the final discretized equations of the NAPL dissolution system are given below.…”