Transcript Document

FLOW THROUGH FRACTURED ROCKS
Department of Mechanical & Aeronautical Engineering
Kambiz Nazridoust and Goodarz Ahmadi
Clarkson University, Potsdam, NY 13699-5727
http://www.clarkson.edu/fluidflow/kam/research/
ABSTRACT
Single and multi-phase flows through rock fractures occur in various
situations, such as transport of dissolved contaminants through geological
strata, migration of dense non-aqueous phase liquids through fractured
rocks, sequestration of carbon dioxide in brine-saturated strata, and oil
recovery. The presence of fractures in a reservoir plays a major role in the
fluid flow patterns and the fluids transport. In this study the Brazilian test
technique was employed to induce an extensional fracture with
dimensions of about in a layered Berea (calcite-cemented) sandstone
sample. High-resolution X-ray micro-tomography (CT) imaging was used
to determine the geometry of the fracture. A post-processing code was
developed and used to computationally model the fracture geometry;
Gambit mesh generator was then used to generate an unstructured grid of
about 1,000,000 cells. Single-phase and two-phase flows through the
fracture were studied using FLUENT™ code. The Volume of Fluid (VOF)
model was employed for the case of two-phase flow. Flow patterns
through the induced fracture were analyzed. In geological flow
simulations, flow through fractures is often assumed to occur between
parallel plates. The combination of CT imaging of real fractures and
computational fluid dynamic simulations may contribute to a more
realistic and accurate description of flow through fractured rocks.
GOVERNING EQUATIONS
U j
Continuity:
x j
0
U i
U i
1 P  u'i u' j
 Uj


t
x j
 x i
x j
Momentum:
 q
t
Volume of Fluid (VOF):
 Uj
 q
x j

S q
q
,

q
1
Comparison of Ratios of the Estimated Pressure Loss Based on Parallel
Plate Model to Those Computed from the Numerical Simulation
FLOWFIELD SOLUTION
Pressure Drop vs. Flow Rate for Sections (a)-(d)
THREE DIMENSIONAL MODELING
(IN PROGRESS)
COMPUTATIONAL DOMAIN
(a)
Velocity Magnitude Contours for Section (d)
Velocity Vector Field for Section (d)
(b)
(c)
Fracture Section
Average Passage Width (m)
Standard Deviation (m)
Section (a)
605
300
Section (b)
575
295
Section (c)
590
300
Section (d)
640
310
Velocity Magnitude Contours for Section (d) for Different Flow Rates
Velocity Vector Field for Section (d) for Different Flow Rates
Three Dimensional Model for Fractures: (a) Water Velocity Magnitude Contours for Fracture 1
(b) Water Volume Fraction and Velocity Magnitude Contours for Fracture 2 (c) Volume Fraction
of Air (left) and Water (right)
CONCLUSIONS
t=250s
t=195s
t=115s
t=70s
Frequency Distributions vs. Passage Size of The Four Fracture Sections Studied
Static Pressure Contours for Section (d) for Different Flow Rates
Volume Fraction of Water in Water/Oil Flow for Some Instances
1. Computer simulation technique was capable of capturing the features of
the flow through fractures.
2. The simulation results were in qualitative agreement with the parallel plate
model.
3. The calculated pressure drops were linearly proportional to the flow rates
similar to Darcy’s law.
4. A significant portion of the fracture pressure drop occurred in the areas
with smallest passage width.
5. The order of the magnitudes of the pressure in various sections of the
fracture were consistent with the number of smallest passages that were
present in those sections.