Calibration of the Site-Scale Saturated Zone Flow Model Page: 44 of 120
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and q, is the solute source or sink given by
q, = Cq. (Eq. 7)
The reactive-transport module of FEHM also contains rock/solute interactions and aqueous
speciation reactions. These features are not used in the present study, but for a complete
description, the reader is referred to Viswanathan et al. (1998).
A control-volume finite-element (CVFE) approach is used in FEHM. The CVFE method has
been used extensively in petroleum reservoir engineering (Forsyth 1989). The CVFE method
treats the potentials in a finite-element approach while the control-volume aspect allows local
mass conservation and upstream weighting (Verma and Aziz 1997). Quadrilaterals and triangles
in two dimensions and hexahedra and tetrahedra in three dimensions are divided into volumes
associated with gridblocks and areas associated with interblock distances. The gridblock
volumes are the Voronoi volumes (Forsyth 1989) associated with each gridblock. Voronoi
volumes are also called perpendicular bisector (PEBI) volumes. The Voronoi volume is formed
by boundaries that are orthogonal to the lines joining adjacent gridblocks and that intersect the
midpoints of the lines (Verma and Aziz 1997). Any point within a Voronoi volume is closer to
its associated gridblock than to any other node in the grid. The CVFE representation of Equation
1 is
Am- As , - kpi(as)(Ai Y F (1P + Pq
V. At de ) 2 )(x3X3)+imass=0 i=1,N (Eq.8)
where
A, and dg are the area and distance between connected nodes i andj
At is the timestep size
V is the Voronoi volume of node i
xk,] is the cartesian coordinate for node j in the k direction
Nis the number of nodes.
The CVFE method can be shown on simple elements with constant properties to be equivalent to
traditional finite-element methods.
The stiffness coefficients (e.g., elements of the stiffness matrix) of the traditional finite-element
method can be interpreted as a linear function of the area through which the fluid passes
traveling from one node to its neighbor. A stiffness coefficient uses the area of the boundary of
the Voronoi volume that intersects the line joining adjacent nodes. LaGriT V1.0 (STN: 10212-
1.0-00) is designed to produce CVFE grids.
These terms are used to form control-volume difference equations for the conservation
equations. This method is not traditional because equation parameters are defined by node, not
element, but the method leads to an intuitive understanding of the numerical method.
In FEHM, the nodal definition of equation parameters leads naturally to a separation of the
nonlinear and purely geometric parts. This separation is explained in detail in Zyvoloski (1983)MDL-NBS-HS-000011, Rev 00, ICN 01
June 20011
44
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Zyvoloski, G. A. Calibration of the Site-Scale Saturated Zone Flow Model, report, June 28, 2001; Las Vegas, Nevada. (https://digital.library.unt.edu/ark:/67531/metadc776938/m1/44/: accessed April 30, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.