Engineered Capabilities of 3D-Printed Models Analyzing Subsurface Fracture Parameters due to Fluid FlowAlexander J. Wirtz, The College of Idaho; Earl D. Mattson, Idaho National Laboratory

Abstract   The hydraulic fracturing of rocks in the subsurface, created by a pressurized liquid such as a mix of water, sand, and other chemicals, has proven to be an efficient way to obtain oil, natural gas, and other fluids from the subsurface. Despite the success of fluid recovery, understanding the interaction and response of these fractures due to their inaccessibility has proven to be difficult in the field. Understanding these mechanisms with laboratory experiments are also difficult due to the heterogeneities within rock samples. 3D printing of laboratory experiments has the potential to be an alternative substitute testing matrix for these fracture experiments. 3D-printed fracture models allow researchers to design the fracture characteristics, reproduce the unique specimens, embed sensors, and create known heterogeneous structures within the printed model. For this poster presentation, overall 3D-printing techniques are discussed, engineered design complications are investigated, and a prototype design of a subsurface-fracture system has been analyzed.

Background

3D-Printing

Acknowledgements

Conclusions/Future Work

Experiment

Model ProcessFigure 1: Simple enhanced geothermal system . Pressurized water moves down into the fracture system to capture heat in the rock and is then pumped out for clean energy use.

This work was supported in part by the U.S. Department of Energy, Office of Science, and Office of Workforce Development for Teachers and Scientists (WDTS) under the Science Undergraduate Laboratory Internships Program (SULI). Special thanks to Idaho National Laboratory (INL), Mitchell Plummer, Robert Ristrem, and Ashley Lambson of Idaho National Laboratory, Brian Hoffmann of Intermountain3D, Battelle Energy Alliance (BEA), and the INL Energy Resource Recovery & Sustainability Research Department.

Three dimensional printing or 3D-Printing is an additive manufacturing process in which a machine, under computer control, ‘prints’ a material in successive layers to create a physical object. A 3D-scanner or CAD is used to design objects of various geometries in which a 3D-printer can use to print individual layers, bottom-up, of that object using various printing techniques (Techniques: Figures 3-9, photo credit to Loughborough University’s Additive Manufacturing Research Group).

Figure 2: Computer-aided design model of a simple geothermal system on AutoDesk Inventor® Pro. The well travels down into a very narrow fracture connecting the well to the other exiting well. Pressurized liquid will travel down one well, interact with the fracture, and exit the other well. Model includes threading at the top of the wells.

Figure 9: Directed Energy Deposition.

Figure 8: Sheet Lamination.

Figure 7: Powder Bed Fusion.

Figure 6: Material Jetting. Most useful method with multi-material ability. Plastic, Ceramics, etc.

Figure 5: Material Extrusion. Most popular method. Creates plastics and polymers.

Figure 4: Binder Jetting. Uses a liquid binder adhesive to bind powdered material. Creates plastics, polymers, metals, and even glass.

Figure 3: Vat Photopolymerisation. Usually executed with Stereolithography technology. Creates plastics and polymers. High accuracy.

Enhancing subsurface permeability through the use of hydraulic stimulation allows the extraction of energy-producing fluids from low permeable reservoirs. For example, engineered geothermal systems inject cold water into one well, capturing heat from the rock while flowing through the fracture system, to be then pumped out by other wells and used to generate electricity. (Figure 1). A scale model can be created via computer-aided design (CAD) using software such as Autodesk Inventor® Pro (Figure 2), printed on a 3D-printer, and be used to understand the fracture’s response to the pressurized fluid, heat transfer, and the resulting stress and strain on the fracture.

Figure 10: Thin stress (top left) and strain (bottom left) sensors’ size compared to a penny.

Figure 11: Wedge, injection, and glued sensor installation methods (left to right) with FlexiForce stress sensors.

Benefits:• Simple construction of reproducible fracture

structure models• Incorporation of multiple materials• Engineering of complicated geometries• Inexpensive and quick to print models• Range of materials available for printingLimitations:• Small sensors needed due to model size (Fig. 10)• No standard method to install sensors (Fig. 11) • Sensors are inaccessible after printed in object• Scaling of laboratory model results/properties to

field conditions is difficult• Mechanical parameters for printed material are

not well published

• Numerous 3D-printing technologies were evaluated as to their ability to print experimental fracture models

• Embedding sensors in 3D-printed models is not trivial; a printer with the capability to print sensors themselves into models will be necessary for the best representation of a fracture model

• Experimental results should provide more knowledge about how pressurized fractures in a system interact with each other

• Future work will develop a scaling methodology to represent real fracture systems for the 3D-printed models using various combinations of ceramic and composite materials to simulate heterogeneities in a reservoir

An experimental fracture-interaction prototype was designed (Fig. 12) and printed with a polylactic acid material on a MakerBot Replicator Z18 3D-printer. The model includes three parallel fractures (aperture of 1mm, separation of 3mm) where the outer two fractures are subject to a known pressure while measuring the middle fracture’s change in permeability (Eq. 1). Fracture transport models will be tested if this model can predict the reduced permeability in fractures as the inner fracture’s walls are compressed (Fig. 13) due to the outer two fractures’ pressure. Equation 2 was used to estimate and design the fracture’s wall deflection.

Figure 12: Horizontal cross-section of the fracture interaction model designed in AutoDesk Inventor® Pro.

𝒅𝒎𝒂𝒙=𝑪 (𝟏−𝝂𝟐) (𝒑𝒃𝟒

𝑬𝒕𝟑 )

Figure 13: Square plastic plate. Uniform load. All edges fixed.

Equation 2: Deflection due to a square plastic plate where dmax is the max deflection, C is a condition constant, ν is Poisson’s ratio, p is pressure, b is side length, E is the elastic modulus, and t is the thickness between fractures.

𝑸𝒍 =

𝒑𝒃𝟑

𝟏𝟐𝝁𝑳Equation 1: Fluid flow rate between two parallel plates where Q is the fluid flow rate, l is the length of opening, p is the uniform pressure, b is the aperture, μ is the dynamic viscosity of the fluid, and L is the length the fluid travels.