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An efficient finite element technique for modeling transport in fractured porous media: 2. Nuclide decay chain transport
Author(s) -
Huyakorn Peter S.,
Lester Barry H.,
Mercer James W.
Publication year - 1983
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr019i005p01286
Subject(s) - finite element method , porous medium , discretization , matrix (chemical analysis) , fracture (geology) , mechanics , partial differential equation , mathematics , mathematical analysis , porosity , materials science , physics , geotechnical engineering , geology , thermodynamics , composite material
A finite element model is presented for simulation of nuclide decay chain transport in a naturally fractured porous medium system. The model is capable of representing the physical system using a dual‐porosity approach, a discrete fracture approach, or a combination of these two approaches. Advection and hydrodynamic dispersion in the fractures, as well as diffusion in the porous matrix and chain reactions of solute species, can be taken into account simultaneously. An efficient finite element solution technique has been developed to solve a coupled system of governing partial differential equations. Via this technique, spatial discretizations and solutions of systems of algebraic equations for nodal concentration values in fracture and porous matrix domains can be performed separately. The present finite element model has been verified against analytical solutions. Two test problems involving transport of a chain of three components in unfractured and fractured porous media are presented to demonstrate the accuracy and efficiency of the proposed finite element technique. Results indicate that the present numerical model is capable of producing good predictions of breakthrough curves using relatively coarse spatial and temporal discretizations. A major advantage of the present transport model over previous transport models is that the latter are based on a numerical approach that employs overall discretization and simultaneous solution of the entire set of algebraic equations for concentration values in the fracture and porous matrix block domains. Such an approach is not computationally efficient when compared with the present numerical approach, which employs not only separate discretizations of the fracture and porous matrix domains but also direct sequential solutions of much smaller subsets of algebraic equations. Another important practical aspect is that the present model enables more complex problems, involving transverse diffusion into porous matrix and two‐dimensional transport in the fracture flow plane, to be handled without resorting to a fully three‐dimensional grid. In practical applications, CPU time and cost involved in performing a fully three‐dimensional analysis of multiple species transport may be prohibitive.