|
Software
Flare
Flow in heterogeneous fractured rock masses is not limited to the integer flow
dimensions defined as linear (1-D), radial (2-D), and spherical flow. A
flow dimension of 2.2 may indicate leaky confined aquifer behavior, while a
dimension of 0.8 may indicate a flow channel in which permeability decreases
with distance from the well. The flow dimension distribution is thus a valuable
measure of rock mass heterogeneity and connectivity. The distribution of transmissivity
and flow dimension can be a key to understanding fluid flow, determining how
far and how fast fluids flow within the fracture network, and how much of the
rock mass is accessed by the fracture network connected to a well.
A series of well tests from different locations in a fracture networks may
exhibit a distribution of flow dimensions rather than a single, characteristic
flow dimension. Examples of flow dimension distributions from well test analyses
of large data sets have been obtained from Japan and Sweden (Geier et al., 1995;
Winberg et al., 1996; Doe et al, 1997).
Flare is a Windows95/NT application to calculate the transmissivity and flow
dimension for FracWorks discrete fracture network (DFN) models. Flare uses the
variation in conductance with distance from the well as an analogue for the
transient hydraulic response. This is based on a direct application of the concept
of flow dimension, as developed by Barker (1985) and others. This approach avoids
the boundary condition effects which limit many numerical simulations of transient
well tests. Flare provides the following features:
- Calculation of variation of conductance with distance from testing well,
- Graphical visualization of the radial distance-conductance relationship
- Graphical assessment of the flow dimension from the radial distance-conductance
relationship.
Flare Algorithm
The inputs to Flare consist of :
- Hydraulic Test Results: A file containing the results of transient
packer test or drill-stem hydraulic test results, expressed as distributions
of interval transmissivity and flow dimension. These are derived from packer
test transient results using fractional dimensional
type curve analyses (Doe, 1991).
- DFN Model: A discrete fracture network (DFN) conceptual
model implemented as a spatial location model, distributions for orientation,
intensity, size, and shape, and analysis of any correlations between these.
The forward modeling approach presented here attempts to reduce the effort
required to get the distribution of dimensions from the DFN model. The approach
concentrates on the variation in the flow path conductance as a function of
radial distance, rather than using simulated hydraulic tests.
Flow dimension is a measure of the power law variation of flow area or conductance
with radial distance. The relationship between the variation in flow path area,
(which is an analog for conductance) with radial distance and the flow dimension
is illustrated.
- For linear (1D) flow, the area (conductance) is constant with radial distance
- For radial (2D) flow, the area (conductance) increases linearly with radial
distance
- For spherical (3D) flow, the area (conductance) increases as radial distance
squared
- For generalized radial flow (nD), the flow area Af (as an analog
of conductance C) increases as a power of radius R equal to the one less than
the flow dimension, according to
C µ Af µ RD-1
(5-6)
In the forward simulation approach, a graph theory search is used to work out
from the borehole into the fracture network to calculate the variation in conductance
with distance from the borehole. This search is carried out as follows:
1. DFN Simulation: A series of realizations of a discrete fracture network
model are generated, using assumed distributions for parameters based on initial
data analysis. The same wells used in the field testing are "completed"
into each of the DFN simulations.
2. Cluster Analysis: A cluster analysis is used to identify all the
fractures which exceed a specified size or transmissivity threshold and which
are connected to well test interval in the simulated well. The result of the
cluster analysis may contain the entire network or it may be only a few fractures
depending on the connectivity of the fracture network.
3. Graph Analysis: The fracture pattern is converted to a pipe network
graph, with each graph element i assigned a length Li and pipe conductance
Ci.. The pipe conductance is calculated as
Ci = Wi Ti (5-7)
where Wi is the flow width achieved in the fracture, and Ti
is the transmissivity of the fracture containing the pipe.
A number of algorithms are available to calculate the flowing width in the
fracture from the geometry of fractures and fracture intersections. For the
present demonstration, the width is calculated based on the geometry of the
traces formed by fracture intersections, with an applied channeling factor Fi,
Wi = ½ Fi (L1i +L2i) (5-8)
L1i and L2i are the lengths of the two traces which define
the fracture intersections.
4. Flow Dimension: Using this approach, a plot of radial distance from
the well against conductance can be derived for any borehole configuration and
DFN model. The slope S of this relationship on a log-log plot provides an estimate
of the flow dimension as,
D = 1+S (5-9)
where S is the non-linear regression fit to the radial distance vs. conductance
plot.
By carrying out this analysis on a series of stochastic realizations of the
DFN model, one can obtain a distribution of packer test flow dimension.
5. Packer Test Transmissivity: The packer test transmissivity Tpi
for each network realization can be approximated by,
Tpi = f ( å Tfj, Di)
(5-10)
where Tfj is the transmissivity of each fracture intersecting the
interval and Di is the packer interval flow dimension calculated
by the equation above.
6. Comparison and Optimization: The distributions of simulated and measured
packer test transmissivity and flow dimension can then be compared to determine
the match between the hydrogeological heterogeneity and connectivity of the
simulated DFN and the in situ rock mass. The DFN can then be calibrated
or conditioned to match the observed behavior.
| 
