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DOE OSTI2023

Quantum algorithms for geologic fracture networks

Abstract Solving large systems of equations is a challenge for modeling natural phenomena, such as simulating subsurface flow. To avoid systems that are intractable on current computers, it is often necessary to neglect information at small scales, an approach known as coarse-graining. For many practical applications, such as flow in porous, homogenous materials, coarse-graining offers a sufficiently-accurate approximation of the solution. Unfortunately, fractured systems cannot be accurately coarse-grained, as critical network topology exists at the smallest scales, including topology that can push the network across a percolation threshold. Therefore, new techniques are necessary to accurately model important fracture systems. Quantum algorithms for solving linear systems offer a theoretically-exponential improvement over their classical counterparts, and in this work we introduce two quantum algorithms for fractured flow. The first algorithm, designed for future quantum computers which operate without error, has enormous potential, but we demonstrate that current hardware is too noisy for adequate performance. The second algorithm, designed to be noise resilient, already performs well for problems of small to medium size (order 10–1000 nodes), which we demonstrate experimentally and explain theoretically. We expect further improvements by leveraging quantum error mitigation and preconditioning.

58 GEOSCIENCES↗

DOE OSTI2022

Leakoff assessment of nanoparticle-stabilized CO 2 foams for fracturing applications

The leakoff of multiphase systems through porous media is a complicated process. In this study, we have designed an experimental setup that is used to assess the leakoff of the liquid and gas phase under pressurized conditions. The novelty of this study is that while most previous studies utilized fluid/gas in the aqueous phase, nanoparticles are introduced in this study, which formed a solid/fluid/gas multiphase system to boost foam performance and reduce leakoff. In the parametric experimental analysis, the effects of foam quality, core permeability, surfactant concentration, and polymer concentration on the dynamic and static leakoff rates of liquid and gas are evaluated. It was found that core permeability affects the leakoff of foam the most with a leakoff coefficient of up to 1.37015 $ft/\sqrt{min}$ for gas and up to 0.1056 $ft/\sqrt{min}$ for liquid under the experiment settings herein. The leakoff rate of gas is generally several magnitudes higher than that of the liquid. When CO 2 gas is present in the foam, the leakoff coefficient falls in the range between 0 and 1.37015 $ft/\sqrt{min}$ for gas, and between 0.0005 and 0.1056 $ft/\sqrt{min}$ for liquid. Finally, the methodology and results of this study shed light on the mechanistic understanding of the leakoff properties of multiphase systems and could be used to assist the design of foam fracturing for reservoir stimulation.

03 NATURAL GAS↗

DOE OSTI2022

Accelerating Hydraulic Fracture Imaging by Deep Transfer Learning

Deep transfer learning has a great success story in computer vision (CV), natural language processing, and many other fields. In this communication, we are going to push forward the deep transfer learning to the hydraulic fracture imaging problem by proposing a two-step approach: 1) train a convolutional neural network (CNN) to reconstruct target geometries by a relatively large amount of approximated field patterns generated from a simplified model and 2) fine-tune the top layers of transferred CNN by a small amount of true field patterns generated through a full model. The advantages include the rapid generation of large amount of data through the simplified model and the high reconstruction accuracy through a careful design of the deep transfer learning. Here, the CNN trained through the deep transfer learning can accurately reconstruct the lateral extent and direction of fractures with unseen conductivity and white Gaussian noise, showing a notable acceleration/accuracy enhancement over the previous CNN trained by mixing a small number of true data into the approximated data as data augmentation.

02 PETROLEUM↗

DOE OSTI2020

CO2 injection with fracturing in geomechanically protected caprock: Task 6 of LLNL's Research Activities to Support DOE's Carbon Storage Program (FWP-FEW0191) (Final Technical Report)

Conventional principles of the design and operation of geologic carbon storage (GCS) require injecting CO 2 below the caprock fracturing pressure to ensure the integrity of the storage complex. In non-ideal storage reservoirs with relatively low permeability, modest injection rates can lead to pressure buildup and hydraulic fracturing of the reservoir and caprock. While the GCS community has generally viewed hydraulic fractures as a key risk to storage integrity, the actual behavior of a caprock hydraulic fracture, particularly from a geomechanical perspective, has not been thoroughly studied. The prevailing method of treating a hydraulic fracture as a high-permeability wing of the storage reservoir might have resulted in erroneous understanding of caprock hydraulic fracture behavior. Comprehensive analyses of monitoring data from the In Salah project suggested that one or more hydraulic fractures may have been created in the reservoir and lower caprock system during injection operations, but did not cause detectable leakage of CO 2 out of the storage complex. This observation coincides with a well-known phenomenon in the oil and gas industry: sedimentary rock formations have many inherent features that naturally protect the formations from unbounded vertical growth of hydraulic fractures.

58 GEOSCIENCES↗

DOE OSTI2020

Oil and Natural Gas Development near and beneath Uranium Tailings Cells and Other Remediated Sites - 20358

DOE LM is responsible for maintaining remedies at more than 50 remediated sites that require active long-term surveillance and maintenance (LTS and M). Institutional controls (ICs) were established to limit human and environmental exposures to residual contamination by controlling land use, restricting access to potential hazards, and making the public aware of potential dangers from the residual contamination. ICs for each site were developed based on current and foreseeable conditions; however, these controls should evolve to mitigate potential human health and other environmental risks from unanticipated changes in activities or site conditions. Activities conducted beyond the DOE long-term care boundaries by non-DOE parties may impact the effectiveness of ICs or even the long-term stability of disposal cells and groundwater remedies. Several sites that LM manages or that will transfer to LM for LTS and M are in active oil and gas production basins. The sites are associated with uranium ore milling or nuclear test sites and have been remediated or are in the process of remediation and have no ongoing DOE mission. Particularly since 2005, hydraulic fracturing ('fracking') combined with directional drilling has dramatically increased oil and natural gas (oil/gas) production in the United States, now making it the number one hydrocarbon-producing country. Fracking has allowed production from shale and other rocks of low natural permeability that were historically not considered viable oil/gas resources. Also, because wellbores can now be drilled as many as 5 kilometers or more horizontally, hydrocarbons can be recovered from zones without having access to the surface above them. Drilling activity near Rulison, Colorado, the location of an underground nuclear detonation managed by LM, has raised public concerns that remnant radioactivity in the detonation zone could migrate to producing wells and enter the natural gas distribution system. At sites like the Falls City, Texas, Disposal site, transitioned to LM with a split estate, increased production in the region has resulted in wellbores beneath the long-term care boundary of the site. While the DOE license for Falls City was approved by the NRC in 1997 without the acquisition of the subsurface rights, NRC has raised concerns on whether this activity impacts the integrity of the cell and/or groundwater remedies. In Wyoming, LM is anticipating receiving the license for the Bear Creek site and manages the Spook site, both locations of uranium mill tailings disposal cells. These Wyoming sites are in an active region of major oil and gas development. This change in surrounding land use will require LM to work collaboratively with NRC to address these concerns. At several DOE sites radioactive waste, and often intermixed nonradioactive constituents, is permanently isolated in engineered disposal cells. At other sites, residual contamination can be present in groundwater, blast cavities, and infinite amounts within soil. Areas targeted for oil and gas development at the Texas and Wyoming sites range from depths of 2440 to 3350 meters (8000-11000 feet) below ground surface. When most site remedies were designed, oil and gas development was not considered to be an issue within the site boundary. With the more recent uses of directional drilling, fracking, and associated wastewater injections, the evaluative criteria for incoming sites and ICs for managing long-term protectiveness and regulatory compliance are changing. Although DOE surface ownership was previously thought to be a robust IC to prevent surface and subsurface development, particularly at disposal sites, that may no longer be the case. Whereas the subsurface development at Texas and Wyoming sites is currently occurring at thousands of meters beneath the surface, shallower and direct onsite development would be more of a concern for LM. The energy introduced when a well is hydraulically fractured causes microseismic events (magnitude -2 to 1.0) as the fractures propagate but does not directly cause seismic events (earthquakes) of sufficient magnitude to damage surface structures. Additionally, the extent of the hydraulic fractures is limited to the targeted depths, which are far below the surface. However, earthquakes of sufficient magnitude to damage surface structures have been attributed to the injection of wastewater into disposal wells. States that have experienced these effects have enacted regulations that limit the rate and pressures that wastewater can be injected into disposal wells. Items LM may consider are the need for monitoring the volume of water injected into nearby disposal wells and possibly installing seismic stations at sites most susceptible to damage. While the need to demonstrate that no impact from oil and gas extraction activities on a site groundwater remedy or disposal cells will vary from site to site, LM is assessing risk criteria for this activity. Though LM has not experienced an issue yet at a uranium tailings disposal site, it cannot assume that there will be none, and must address NRC concerns. LM is building on past experiences at other sites and beginning to form new processes with the hope that these concepts can be applied for other future sites. (authors)

04 OIL SHALES AND TAR SANDS↗

DOE OSTI2022

Methane foam performance evaluation in water-wet unconsolidated porous media: A systematic experimental investigation at elevated pressure and temperature conditions

In the petroleum industry, enhanced oil recovery (EOR) techniques employ foam extensively to establish conformance control in heterogeneous and fractured reservoirs in order to increase the sweep efficiency. In such applications, foam performance evaluation under complex subsurface conditions is pivotal for the effective and optimized deployment of foam treatment. However, there is a scarcity of hydrocarbon gas foam generation and evaluation studies that examine the relationships between foam performance and the critical foam parameters at high-pressure and high-temperature conditions. Here, this study aims at methodically investigating the effects of several foam parameters on methane foam performance in water-wet proppant packs under harsh operating conditions. This is in relation to the technical needs of hydrocarbon foam injection into hydraulically-induced, propped fractures in unconventional oil reservoirs. To this end, a state-of-the-art experimental foam generation apparatus was designed, fabricated, and commissioned. We performed a large number of foam flow experiments on proppant packs using methane gas and different foaming agents at 3500 psi and 115°C. Anionic and amphoteric surfactants were employed to probe the effect of their ionic nature on foam performance. Foam performance sensitivities to various foam generation parameters and operating conditions, such as surfactant concentration, gas fraction, total injection rate, operating pressure, salinity, and proppant pack length were investigated. To this end, steady-state pressure drops across the proppant packs during foam generation and foam's apparent viscosity were measured to quantify the foam performance of surfactants. The results were then analyzed to determine optimum values of the foam parameters and the interplay between these parameters are discussed here. The systematic results achieved from this work are in agreement with the trends available in the literature and provide new insights into complexities of in situ foam generation in water-wet, unconsolidated porous media at extreme reservoir conditions.

03 NATURAL GAS↗

DOE OSTI2025

Recent Advances in Pipeline Integrity for Transporting Blended Hydrogen-Natural Gas

To achieve US decarbonization goals, hydrogen is being considered as an alternative energy source to reduce carbon emissions. Blending hydrogen into existing natural gas pipelines is an intuitive first step to enable near term emission reductions. However, there are numerous challenges and uncertainties that complicate the transition to transporting hydrogen long-distance through existing natural gas pipelines. The main challenge is hydrogen embrittlement (HE), which reduces the ductility, fracture toughness and fatigue resistance of pipeline steels. This work delivers a technical review on HE effects on the material properties of pipeline carbon steels, such as Grade B, X52, X65, X70, X80, and X100. An important aspect of laboratory tests to capture the HE effect is the hydrogen test environment. This includes hydrogen pre-charged specimens tested in air and specimens tested in a hydrogen gas environment. A review of the mechanical properties of pipeline steel in different hydrogen environments determined through tensile testing is given first, which includes HE effects on yield strength, ultimate tensile strength, and ductility for blended hydrogen-natural gas pipelines. Then, the HE effects on fracture toughness and fatigue crack growth resistance are discussed. Last, impacts of HE to pipeline integrity and major technical challenges are discussed.

: Hydrogen Embrittlement↗

DOE OSTI2022

Mesoscale simulations of pressure-shear loading of granular tungsten carbide

Numerical simulations of pressure-shear loading of a granular material are performed using the shock physics code CTH. A simple mesoscale model for the granular material is used that consists of a randomly packed arrangement of solid circular or spherical grains of uniform size separated by vacuum. The grain material is described by a simple shock equation of state, elastic perfectly plastic strength model, and fracture model with baseline parameters for WC taken from previous mesoscale modeling work. Simulations using the baseline material parameters are performed at the same initial conditions of pressure-shear experiments on dry WC powders. Except for some localized flow regions appearing in simulations with an approximate treatment of sliding interfaces among grains, the samples respond elastically during shear, which is in contrast to experimental observations. By extending the simulations to higher shear wave amplitudes, macroscopic shear failure of the simulated samples is observed with the shear strength increasing with increasing stress confinement. The shear strength is also found to be strongly dependent on the grain interface treatment and on the fracture stress of the grains, though the variation in shear strength due to fracture stress decreases with increasing stress confinement. At partial compactions, the transverse velocity histories show strain-hardening behavior followed by formation of a shear interface that extends through the transverse dimensions of the sample. Near full compaction, no strain hardening is observed and, instead, the sample transitions sharply from an elastic response to formation of an internal shear interface. Agreement with experiment is shown to worsen with increasing confinement stress with simulations overpredicting the shear strengths measured in experiment. The source of the disagreement can be ultimately attributed to the Eulerian nature of the simulations, which do not treat contact and fracture realistically.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Systems and methods for locating and imaging proppant in an induced fracture

Born Scattering Inversion (BSI) systems and methods are disclosed. A BSI system may be incorporated in a well system for accessing natural gas, oil and geothermal reserves in a geologic formation beneath the surface of the Earth. The BSI system may be used to generate a three-dimensional image of a proppant-filled hydraulically-induced fracture in the geologic formation. The BSI system may include computing equipment and sensors for measuring electromagnetic fields in the vicinity of the fracture before and after the fracture is generated, adjusting the parameters of a first Born approximation model of a scattered component of the surface electromagnetic fields using the measured electromagnetic fields, and generating the image of the proppant-filled fracture using the adjusted parameters.

03 NATURAL GAS↗

DOE OSTI2023

Wetting transition and fluid trapping in a microfluidic fracture

Immiscible fluid–fluid displacement in confined geometries is a fundamental process occurring in many natural phenomena and technological applications, from geological CO 2 sequestration to microfluidics. Due to the interactions between the fluids and the solid walls, fluid invasion undergoes a wetting transition from complete displacement at low displacement rates to leaving a film of the defending fluid on the confining surfaces at high displacement rates. While most real surfaces are rough, fundamental questions remain about the type of fluid–fluid displacement that can emerge in a confined, rough geometry. Here, we study immiscible displacement in a microfluidic device with a precisely controlled structured surface as an analogue for a rough fracture. We analyze the influence of the degree of surface roughness on the wetting transition and the formation of thin films of the defending liquid. We show experimentally, and rationalize theoretically, that roughness affects both the stability and dewetting dynamics of thin films, leading to distinct late-time morphologies of the undisplaced (trapped) fluid. Finally, we discuss the implications of our observations for geologic and technological applications.

42 ENGINEERING↗

DOE OSTI2023

Using Homogenized Models to Explore the Effect of Fracture Densities on Weathering

Despite its importance, only a few researchers have incorporated the effects of fracturing into models of reactive transport for rock weathering. Here we explore 2D simulations that describe weathering under conditions of diffusive and advective transport within heterogeneous media consisting of rocky blocks and fractures. In our simulations, the Darcy velocities vary in space and time and depend on weathering processes within the rock matrix. We explore simulations with saturated and unsaturated flow for weathering bedrock that consists of blocks separated by inert or weathered material. The simulations show that a simplified homogenized model can approximate exact solutions for some of the simulated columns and hills and can allow exploration of coupling between flow and reaction in fractured rock. These hillslope simulations document that, even in the presence of 2D water flow, i) an increase in fracture density results in faster weathering advance rates; and ii) the water table locates deeper for a rock system that is weathered and fractured rather than weathered and unfractured. Some of these patterns have also been observed for natural systems. But these simulations also highlight how simplified models that do not use appropriate averaging of heterogeneities can be inaccurate in predicting weathering rate for natural systems. For example, if water flows both vertically and laterally through the vadose zone of a hill, then a prediction of the depth of regolith that is based on modeling strictly unidirectional downward infiltration will be unrealistically large. Likewise, if the fracture density observed near the land surface is used in a model to predict depth of weathering for a system where the fracture density decreases downward, the model will overestimate regolith depth. Learning how to develop accurately homogenized models could thus enable better conceptual models and predictions of weathering advance in natural systems.

58 GEOSCIENCES↗

DOE OSTI2020

A Pilot-Scale Evaluation of Natural Gas-Based Foam at Elevated Pressure and Temperature Conditions

Abstract Nitrogen (N2) and Carbon Dioxide (CO2) foams have been used as hydraulic fracturing fluids for several decades to reduce water usage and minimize damage in water-sensitive reservoirs. These foam treatments require gases to be liquefied and transported to site. An alternative approach would be to use natural gas (NG) that is readily available from nearby wells, pipelines, and processing facilities as the internal, gaseous phase to create a NG-based foam. Hydraulic fracturing with NG foam is a relatively inexpensive option, makes use of an abundant and often wasted resource, and may even provide production benefits in certain reservoirs. As part of an ongoing development project sponsored by the Department of Energy (DOE), the surface process to create NG foam is being developed and the properties of NG foam are being explored. This paper presents recent results from a rigorous pilot-scale demonstration of NG foam over a range of operating scenarios relevant to surface and bottomhole conditions with a variety of base-fluid mixtures. The Pilot-scale Foam Test Facility (PFTF) used in these investigations is first described. The PFTF is capable of generating foamed fluids at pressures up to 7,500 psig and at temperatures in excess of 300°F. Then, results from several investigations aimed at proving NG foam at conditions relevant to the field are presented. NG foam was characterized using rheology measurements and flow visualization techniques. Experiments were performed to investigate the texture and stability of NG foam generated by two different mixing methods: one using a custom designed tee to match mixing velocities in the field where the gas phase is jetted into the aqueous stream, and another to ensure comprehensive mixing for laboratory analysis. Parametric studies were conducted to explore the effects of flow rate, foam quality, and temperature on the stability of NG foam. Moreover, different fluid preparations were used to investigate the effect of base fluid and additive concentrations on the stability of NG foams. Additional laboratory studies that investigated foam stability with produced water and multicomponent NG mixtures are also reported. The NG foams explored in these investigations exhibited typical, shear-thinning behavior observed in rheological studies of N2- and CO2-based foams. The measured viscosity and observed stability indicate that NG foams are well suited for fracturing applications. Like other foams, NG foam exhibits sensitivity to operating temperature characterized by a decrease in apparent viscosity as temperature increases. Rapid foam breakdown was observed at significantly elevated temperatures exceeding 290°F. In addition to fluid characterization, these investigations also yielded several key lessons that should be applied to future field demonstrations of NG foam.

Beck, Griffin↗

DOE OSTI2021

Systems and methods for locating and imaging proppant in an induced fracture

Aldridge, David F.↗

DOE OSTI2022

Jan-Dec 2021 IC Project: w20_earthquake (Yearly Report)

The simulations conducted under this IC project used an in-house code developed at Los Alamos National Laboratory called HOSS (Hybrid Optimization Software Suite) and its extended version called HOSS-FSIS (fluid-structure interaction solver). HOSS has been under development in LANL’s Geophysics Group since 2004 and was used to simulate the signal propagation in pieces of material with pre-existing defects and also to simulate the near source effects of above ground nuclear explosions. One of the key feature of HOSS is that it is superior to pure finite element method and discrete element method implementations because it allows for a natural transition from continuum to discontinuum when the material breaks or fractures.

58 GEOSCIENCES↗

DOE OSTI2021

Mechanical Behavior of Hybrids with Hyper-Connected Molecular Networks

Our research is focused on fundamental studies related to the molecular design, synthesis, characterization and modeling of molecular-reinforced hybrid glass films for superior mechanical and fracture properties. Molecular-reinforced hybrid glass films exhibit unique electro-optical properties while maintaining excellent thermal stability. They have important technological application for emerging nanoscience and energy technologies including anti-reflective and ultra-barrier layers in photovoltaics, display technologies, as well as quantum technologies. However, they are often inherently brittle in nature, do not adhere well to adjacent substrates, and exhibit poor mechanical properties. Furthermore, a robust understanding of the underlying mechanisms of deformation, fracture and fatigue has been lacking particularly given their mechanically fragile nature. The related lack of structure-property relationships between molecular structure, mechanical properties and processing represents a fundamental challenge to their integration into device technologies, compromises their thermomechanical reliability and has thwarted efforts to improve mechanical and, particularly, fracture properties.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Numerical study of the effect of propped surface area and fracture conductivity on shale gas production: Application for multi-size proppant pumping schedule design

Hydraulic fracturing is a technique extensively used in the oil and gas industry, where water, proppant (sand) and additives are injected into unconventional reservoirs to enhance the recovery of shale hydrocarbon. Although some previous studies have developed pumping schedules that maximize gas production for a single-size proppant, there are very few studies that consider the effect of varying proppant diameters across pumping stages on shale gas production. Motivated by this, we carried out an extensive sensitivity analysis to determine the effect of different proppant diameters on the average fracture conductivity (FC), average propped surface area (PSA) and cumulative shale gas production volume. We found out that the cumulative shale gas production volume depends on both the average PSA and average FC. We also found out that small-diameter proppant resulted in higher average PSA and lower average FC, whereas large-diameter proppant resulted in lower average PSA and higher average FC. Hence, we designed a multi-size proppant pumping schedule considering both of these parameters into account for simultaneously propagating multiple fractures to maximize shale gas production from unconventional reservoirs. Since the size of injected proppant particles determines the average PSA and average FC for the propped hydraulic fractures, we developed a novel framework called Sequentially Interlinked Modeling Structure (SIMS) to predict the average PSA, average FC and cumulative shale gas production volume at the end of 10 years for a given pumping schedule. Then, we used this SIMS framework to obtain a multi-size proppant pumping schedule that maximizes shale gas production. In closing, we demonstrated that the obtained pumping schedule gives a cumulative shale gas production volume greater than the values obtained from the existing pumping schedules.

03 NATURAL GAS↗

DOE OSTI2021

Evaluating proxies for the drivers of natural gas productivity using machine-learning models

We report the extensive development of unconventional reservoirs using horizontal drilling and multistage hydraulic fracturing has generated large volumes of reservoir characterization and production data. The analysis of this abundant data using statistical methods and advanced machine-learning (ML) techniques can provide data-driven insights into well performance. Most predictive modeling studies have focused on the impact that different well completion and stimulation strategies have on well production but have not fully exploited the available in situ rock property data to determine its role in reservoir productivity. We have used machine-learning techniques to rank rock mechanical properties, microseismic attributes, and stimulation parameters in the order of their significance for predicting natural gas production from an unconventional reservoir. The data for this study came from a hydraulically fractured well in the Marcellus Shale in Monongalia County, West Virginia. The data classes included measurements aggregated by well completion stage that included (1) gas production, (2) well-log-derived measurements including bulk density, elastic moduli, shear impedance, compressional impedance, brittleness, and gamma measurements, (3) microseismic attributes, (4) long-period long-duration (LPLD) event counts, (5) fracture counts, and (6) stimulation parameters that included the fluid injection volume and average pumping pressure. To identify observable proxies for the drivers of gas production, we evaluated five commonly used ML approaches including multivariate adaptive regression spline, Gaussian mixture model, random forest, gradient boosting, and neural network. We selected five variables including LPLD event count, seismogenic b-value, hydraulic diffusivity, cumulative moment, and fluid volume as the features most likely to impact gas productivity at the stage level in the study area. The data-driven selection of these parameters for their importance in determining gas production can help reservoir engineers design more effective hydraulic-fracture treatments in the Marcellus Shale and other similar unconventional reservoirs. Plain language summary: We use machine-learning methods and data-driven selection of reservoir parameters to rank and better understand their importance in determining gas production, which can help reservoir engineers design more effective hydraulic-fracture treatments in the Marcellus Shale and other similar unconventional reservoirs.

58 GEOSCIENCES↗

DOE OSTI2025

Role of Intersections in Fracture Connectivity

Networks of intersecting fractures often provide the flow paths through subsurface reservoirs. Assessing network connectivity is challenging because fracture intersections compose a vanishingly small fraction of the network void volume. In this paper, motivated by 3D X-ray imaging of the simplest element of fracture network, that is, two orthogonal fractures, we perform a percolation and finite-size scaling analysis to study the connectivity provided by fracture intersections. The conditions when an intersection enhances connectivity across a sample depend on spatial correlations in the fracture aperture distributions, on the stress state, and on the direction of flow. Here we consider three flow directions: (a) across intersections, (b) parallel to intersections and (c) around corners. For (a), intersections provide minimal enhancement of connectivity because they contribute little additional void area. For (b), intersections increase the probability of a connected path near threshold by enabling 3D connected pathways that are not possible in parallel fractures. Flow around corners, (c), is fundamentally the result of the intersection connecting two fractures in series and spatial correlations are broken around corners, suppressing the connectivity relative to (a). When the connected fractures are stressed equally, a joint percolation threshold emerges that continues to have scale invariance. However, when the fractures are stressed unequally, the system has mixed percolation without clearly defined percolation thresholds. In all cases, percolation probabilities are found to be scale dependent which has important consequences for the connectivity of larger fracture networks composed of the fundamental element studied here.

02 PETROLEUM↗