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Software
MAFIC Software Information
 MAFIC
(Matrix and Fracture Interaction Code) uses the finite element method to solve
for flow and transport through FracWorks geological models. MAFIC idealizes
fractures using triangular finite elements, and can alternatively repersent
fractures using 1-D pipe elements. MAFIC provides for dual porosity interaction
using either quadrahedral finite elements or a 1-D approximation based on the
Warren and Root pseudo-steady state approximation. MAFIC uses a pre-conditioned
conjugate gradient solver, with variable bandwidth matrix storage.
MAFIC simulates solute transport and heat transport using a convective particle
tracking approach. Solute dispersion is simulated stochastically using orthogonal,
normally distributed, lateral and transverse dispersion vectors. MAFIC solute
transport includes matrix diffusion, mineral-specific retardation, and sorption
features.
MAFIC was designed to simplify input data requirements while providing maximum
flexibility for the designation of boundary conditions. Input files may be specified
by the user or generated by the FracMan fracture network simulation package.
MAFIC is generally used for fracture networks of 10 to 10,000 fractures, although
it and has been applied for networks of up to 100,000 fractures using triangular
finite elements and 300,000 fractures using pipe elements.
MAFIC Features
| MAFIC |
Features |
| Flow Solution |
Finite Element
Pre-Condioned Conjugate Gradient |
| Transport (Mass and Heat) |
Particle Tracking |
| Fracture Geometry |
Triangular Elements or
Pipe Elements |
| Matrix Geometry |
Quadrahedral Volume Elements,
1-D Warren and Root Approximation, or
1-D Pipe Finite Element |
| Transport Processes |
Advection
Longitudinal and Transverse Dispersion
Matrix Diffusion
Mineral-Specific Sorption
Decay or Biodegredation |
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MAFIC Theory
The MAFIC theory developed below is from the MAFIC manual. Graphics will be
added in the future.
Using continuum principles of mass balance, the diffusivity equation which
describes flow can be written as (Bear, 1972):
 (2-1a)
where: xi = coordinate directions (L)
r = fluid density (M/L3)
m = fluid viscosity (M/LT)
kij = permeability (absolute) (L2)
P = fluid pressure (M/LT2)
g = gravitational acceleration (L/T2)
z = vertical direction (upward) (L)
a = pore compressibility (LT2/M)
F = porosity
b = fluid compressibility (LT2/M)
q = source term (M/T)
t = time (T)
For nearly incompressible fluid (e.g., water), and for flow in two dimensions
(e.g., in a fracture), the mass-conservation of equation (2-1) can be simplified
to a volume-conservation equation:
 (2-1b)
where: S = Fracture Storativity (dimensionless)
h = Hydraulic head (L)
T = Fracture Transmissivity (L2 /T)
q = Source/Sink Term (L/T)
t = Time (T)
 = Two-dimensional
Laplace Operator
MAFIC uses a Galerkin finite element solution scheme to approximate the solution
for Equation (2-1). The finite element approximation to the diffusivity equation
in two-dimensions is given by:
 (2-2)
where: T = fracture transmissivity (L2 /T)
S = fracture storativity (dimensionless)
q = source flux, volume per unit area (L/T)
x = linear or quadratic basis function
R = element area (L2)
h = nodal hydraulic head (L)
t = time (T)
N = number of nodes
This approximation is also used for modeling flow in the rock matrix (see Equation
(2-6). Equation (2-2) can be expressed in matrix notation as:
 (2-3)
where:
MAFIC uses a backwards difference scheme for which Equation (2-3) is written:
 (2-4)
where k = the timestep number
Solution of Equation (2-4) yields the head values at the end of timestep k+1.
[more]
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