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.

COMPUTATIONAL DOMAIN

ABSTRACT

FLOW THROUGH FRACTURED ROCKS Department of Mechanical & Aeronautical Engineering

Kambiz Nazridoust and Goodarz AhmadiClarkson University, Potsdam, NY 13699-5727

http://www.clarkson.edu/fluidflow/kam/research/

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GOVERNING EQUATIONS

CONCLUSIONS1. 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.

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)

Pressure Drop vs. Flow Rate for Sections (a)-(d)

(a)

Frequency Distributions vs. Passage Size of The Four Fracture Sections Studied

Velocity Magnitude Contours for Section (d)

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 Vector Field for Section (d)

FLOWFIELD SOLUTION

Velocity Magnitude Contours for Section (d) for Different Flow Rates Velocity Vector Field for Section (d) for Different Flow Rates

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Static Pressure Contours for Section (d) for Different Flow Rates Volume Fraction of Water in Water/Oil Flow for Some Instances

Continuity:

Momentum:

Volume of Fluid (VOF):

THREE DIMENSIONAL MODELING(IN PROGRESS)

Comparison of Ratios of the Estimated Pressure Loss Based on Parallel Plate Model to Those Computed from the Numerical Simulation

(b)

(c)

t=250s

t=195s

t=115s

t=70s