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At least 55 records · Page 3

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↗

An Overview of Spray-On Foam Insulation Applications on the Space Shuttle's External Tank: Foam Applications and Foam Shedding Mechanisms

The Columbia Accident Investigation Board (CAIB) concluded that the cause of the tragic loss of the Space Shuttle Columbia and its crew was a breach in the thermal protection system on the leading edge of the left wing. The breach was initiated by a piece of insulating foam that separated from the left bipod ramp of the External Tank and struck the wing in the vicinity of the lower half of Reinforced Carbon-Carbon panel No. 8 at 81.9 seconds after launch. The CAIB conclusion has spawned numerous studies to identify the cause of and factors influencing foam shedding and foam debris liberation from the External Tank during ascent. The symposium on the Thermo-mechanics and Fracture of Space Shuttle External Tank Spray-On Foam Insulation is a collection of presentations that discuss the physics and mechanics of the ET SOFI with the objective of improving analytical and numerical methods for predicting foam thermo-mechanical and fracture behavior. This keynote presentation sets the stage for the presentations contained in this symposium by introducing the audience to the various types of SOFI applications on the Shuttle s External Tank and by discussing the various mechanisms that are believed to be the cause of foam shedding during the Shuttle s ascent to space

Sullivan, Roy M.↗

Numerical Evaluation of Mode 1 Stress Intensity Factor as a Function of Material Orientation For BX-265 Foam Insulation Material

Foam; a cellular material, is found all around us. Bone and cork are examples of biological cell materials. Many forms of man-made foam have found practical applications as insulating materials. NASA uses the BX-265 foam insulation material on the external tank (ET) for the Space Shuttle. This is a type of Spray-on Foam Insulation (SOFI), similar to the material used to insulate attics in residential construction. This foam material is a good insulator and is very lightweight, making it suitable for space applications. Breakup of segments of this foam insulation on the shuttle ET impacting the shuttle thermal protection tiles during liftoff is believed to have caused the space shuttle Columbia failure during re-entry. NASA engineers are very interested in understanding the processes that govern the breakup/fracture of this complex material from the shuttle ET. The foam is anisotropic in nature and the required stress and fracture mechanics analysis must include the effects of the direction dependence on material properties. Material testing at NASA MSFC has indicated that the foam can be modeled as a transversely isotropic material. As a first step toward understanding the fracture mechanics of this material, we present a general theoretical and numerical framework for computing stress intensity factors (SIFs), under mixed-mode loading conditions, taking into account the material anisotropy. We present mode I SIFs for middle tension - M(T) - test specimens, using 3D finite element stress analysis (ANSYS) and FRANC3D fracture analysis software, developed by the Cornel1 Fracture Group. Mode I SIF values are presented for a range of foam material orientations. Also, NASA has recorded the failure load for various M(T) specimens. For a linear analysis, the mode I SIF will scale with the far-field load. This allows us to numerically estimate the mode I fracture toughness for this material. The results represent a quantitative basis for evaluating the strength and fracture properties of anisotropic foam insulation material.

Knudsen, Erik↗

Advances and challenges in CO2 foam technologies for enhanced oil recovery in carbonate reservoirs

Utilization of surfactants for generating foam has the potential for fluid-mobility control during CO2 flooding processes, leading to improved oil recovery. This manuscript is a review of the most important aspects for the design of CO2-foams with mobility control in carbonate reservoirs, including recent advances in novel surfactants and analytical techniques for analysis of surfactant adsorption on carbonate minerals and their thermal stability. Several key parameters and properties regarding foam transport in porous media are reviewed such as, the minimum pressure gradient required for foam generation, the effects of the partition coefficient of a CO2-soluble surfactant on foam transport in rock cores, visualization of foam flow by either microfluidic or PET/CT imaging processes in heterogeneous or fractured systems and the effect of oil on foam transport under reservoir conditions. Also are discussed the most recent advances of two major foam modeling methods, including the semi-empirical STARS foam model and the population balance model, as well as CO2 foam pilot tests and the factors governing their successes.

Jian, Guoqing↗

Crack Initiation and Growth in Rigid Polymeric Closed-Cell Foam Cryogenic Applications

Cryogenic vessels, such as the Space Shuttle External Tank, are often insulated with closed-cell foam because of its low thermal conductivity. The coefficient of thermal expansion mismatch between the foam and metallic substrate places the foam under a biaxial tension gradient through the foam thickness. The total foam thickness affects the slope of the stress gradient and is considered a significant contributor to the initiation of subsurface cracks. Rigid polymeric foams are brittle in nature and any subsurface cracks tend to propagate a finite distance toward the surface. This presentation investigates the relationship between foam thickness and crack initiation and subsequent crack growth, using linear elastic fracture mechanics, in a rigid polymeric closed-cell foam through analysis and comparison with experimental results.

Sayyah, Tarek↗

Application of Video Image Correlation Techniques to the Space Shuttle External Tank Foam Materials

Results that illustrate the use of a video-image-correlation-based displacement and strain measurement system to assess the effects of material nonuniformities on the behavior of the sprayed-on foam insulation (SOFI) used for the thermal protection system on the Space Shuttle External Tank are presented. Standard structural verification specimens for the SOFI material with and without cracks and subjected to mechanical or thermal loading conditions were tested. Measured full-field displacements and strains are presented for selected loading conditions to illustrate the behavior of the foam and the viability of the measurement technology. The results indicate that significant strain localization can occur in the foam because of material nonuniformities. In particular, elongated cells in the foam can interact with other geometric or material discontinuities in the foam and develop large-magnitude localized strain concentrations that likely initiate failures. Furthermore, some of the results suggest that continuum mechanics and linear elastic fracture mechanics might not adequately represent the physical behavior of the foam, and failure predictions based on homogeneous linear material models are likely to be inadequate.

Hilburger, Mark W.↗

Application of Video Image Correlation Techniques to the Space Shuttle External Tank Foam Materials

Results that illustrate the use of a video-image-correlation-based displacement and strain measurement system to assess the effects of material nonuniformities on the behavior of the sprayed-on foam insulation (SOFI) used for the thermal protection system on the Space Shuttle External Tank are presented. Standard structural verification specimens for the SOFI material with and without cracks and subjected to mechanical or thermal loading conditions were tested. Measured full-field displacements and strains are presented for selected loading conditions to illustrate the behavior of the foam and the viability of the measurement technology. The results indicate that significant strain localization can occur in the foam because of material nonuniformities. In particular, elongated cells in the foam can interact with other geometric or material discontinuities in the foam and develop large-magnitude localized strain concentrations that likely initiate failures. Furthermore, some of the results suggest that continuum mechanics and linear elastic fracture mechanics might not adequately represent the physical behavior of the foam, and failure predictions based on homogeneous linear material models are likely to be inadequate.

Hilburger, Mark W.↗

Modified Mode-I Cracked Sandwich Beam (CSB) Fracture Test

Five composite sandwich panels were fabricated using vacuum assisted resin transfer molding (VARTM). Four of these panels had E-glass/vinylester facesheets and one had carbon/epoxy facesheets. The sandwich panels had different density PVC foam cores. The four E-glass panels had core densities of 80, 100, 130, 200 kg/cu m. The sandwich with carbon/epoxy 3 facesheets had a core with density of 100 kg/cu m. Fracture tests were conducted using a modified Cracked Sandwich Beam (CSB) test configuration. Load displacement curves were obtained for loading and unloading of the specimens during crack growth. Various increments of crack growth were monitored. Critical Strain Energy Release Rates (SERR) were determined from the tests using the area method. The critical values of SERR can be considered the fracture toughness of the sandwich material. The fracture toughness ranged 367 J/sq m to 1350 J/sq m over the range of core densities. These results are compared to the Mode-I fracture toughness of the PVC foam core materials and values obtained for foam-cored sandwiches using the TSD specimen. Finite-element analyses (FEA) were performed for the test configuration and Strain Energy Release Rates were calculated using the Virtual Crack Closure Technique (VCCT). The SERR values determined from the FEA were scaled to the fracture loads, or critical loads, obtained from the modified CSB tests. These critical loads were in close agreement with the test values.

Smith, S. A.↗

Tuscaloosa Marine Shale Laboratory

The Tuscaloosa Marine Shale (TMS) in Louisiana and Mississippi is an Upper Cretaceous source rock formation sandwiched between the sands of the upper and lower Tuscaloosa sections. The TMS is believed to be the source rock for underlying prolific Tuscaloosa sand formation. The TMS has an unproven estimate of 7,000,000,000 bbls of recoverable oil while its current total average production is about 3,000 bbls of oil per day in 2017. In 2013 and 2014, more than 80 wells were drilled horizontally into the TMS that were fractured using multi-stage fracturing technology. The results from this have been mixed, but recent production for several wells show an appealing initial oil production rate of more than 1000 bbl/day. The preliminary core analysis by industry partners and a few literature studies shows that the TMS is one of the most clay-rich and sensitive shales to water. Due to these and other technical problems, there is high risk for the economic development of TMS compared to other shale plays. The experiences of major industrial players in the TMS show the necessity of open and collaborative efforts to better understand the critical gaps in the development of this challenging and potentially highly economic shale play to enable more cost-efficient and environmentally-sound recovery from this unconventional liquid-rich shale play. The overall objective of this project is to form a consortium of science and industry partners to address the following six major objectives using scientific and technical approaches: 1. To improve wellbore integrity by better understanding the sources of the wellbore instability issues, proposing innovative mud and cement design for the TMS. 2. To improve formation evaluation using laboratory techniques for the evaluation of mineralogical composition, organic content, and produced-water chemistry as well as well log and geophysical analysis. 3. To determine the role of geologic discontinuities on fracture growth and shale creep behavior using digital image correlation technique. 4. To investigate the application of stable CO 2 foam and super-hydrophobic proppants for improved reservoir stimulation. 5. To better understand the nature of water/hydrocarbon/CO 2 flow in clay and organic-rich formation and the role of water/fluid interaction on recovery. 6. To prepare better socio-economic environment for TMS development by community engagement. Subsequently, the TMS virtual laboratory conducted testing and analysis of various properties of rock and formation fluids from the TMS, including but not limited to the following: Analyzing reports and logs to better understand the source of wellbore instability in TMS wells; Experiments to design a customized cement based on TMS requirements; Experiments to obtain the mineralogical and geochemical composition of TMS samples; Seismic analysis of TMS geophysical data to better predict total organic carbon (TOC) content and brittleness in TMS; Well log analysis to better estimate the TOC and geo-mechanical properties of TMS; Experiments on formation water to understand the chemistry of produced water; Experiments to determine the role of lamination and natural fractures on fracture propagation or rock deformation using digital image correlation technique in in-direct tensile tests, semi-circular bend test and creep tests Experiments to determine the stability and rheological properties of nanoparticle-stabilized CO 2 foam in TMS rock samples; Experiments to determine fluid dynamics in un-propped TMS fractures and the role of nano-coating of proppants on fluid dynamics in fractures with proppants; Micro-fluidics experiments to enhance the understanding of fluid dynamics in tight liquidrich pores with high clay content; Socio-economic studies to better engage communities in TMS development.

58 GEOSCIENCES↗

Cryogenic Temperature-Gradient Foam/Substrate Tensile Tester

The figure shows a fixture for measuring the tensile strength of the bond between an aluminum substrate and a thermally insulating polymeric foam. The specimen is meant to be representative of insulating foam on an aluminum tank that holds a cryogenic liquid. Prior to the development of this fixture, tensile tests of this type were performed on foam/substrate specimens immersed in cryogenic fluids. Because the specimens were cooled to cryogenic temperatures throughout their thicknesses, they tended to become brittle and to fracture at loads below true bond tensile strengths. The present fixture is equipped to provide a thermal gradient from cryogenic temperature at the foam/substrate interface to room temperature on the opposite foam surface. The fixture includes an upper aluminum block at room temperature and a lower aluminum block cooled to -423 F (approx. -253 C) by use of liquid helium. In preparation for a test, the metal outer surface (the lower surface) of a foam/substrate specimen is bonded to the lower block and the foam outer surface (the upper surface) of the specimen is bonded to the upper block. In comparison with the through-the-thickness cooling of immersion testing, the cryogenic-to-room-temperature thermal gradient that exists during testing on this fixture is a more realistic approximation of the operational thermal condition of sprayed insulating foam on a tank of cryogenic liquid. Hence, tensile tests performed on this fixture provide more accurate indications of operational bond tensile strengths. In addition, the introduction of the present fixture reduces the cost of testing by reducing the amount of cryogenic liquid consumed and the time needed to cool a specimen.

Vailhe, Christophe↗

Structural concepts for future space transportation orbiters

Two structural concepts for a fully reusable STS orbiter are compared with respect to weight and the ability to satisfy structural goals. The cryogenic propellant tanks for both concepts use welded, blade-stiffened aluminum skins for leak-free containment and compatibility with LOX and LH2. The tanks are sized primarily by pressure, although some areas are sized by bending and fracture mechanics considerations. The tank concept is regarded as state-of-the-art, even though it requires a closed cell foam insulation with a dry air purge to prevent air liquefaction and ice formation. It is noted that the foam will require testing to verify its design life for use in the STS. One concept has nonintegral tanks suspended inside an insulated aluminum airframe and thrust structure. Here, a durable thermal protection system external insulation is mechanically attached to the airframe, allowing a buckled skin design. The other concept uses a novel structural arrangement consisting of a separate tank/thrust structure that supports a hot advanced-carbon-carbon aeroshell structure.

Taylor, A. H.↗

Strengthening of phosphate ceramic foam by silicon carbide whiskers

The influence of additions of SiC whiskers on the elastic modulus and flexural strength of phosphate ceramic foam is assessed. It is shown that the incorporation into the material composition of even small amounts (2.4 vol%) of SiC whiskers enhances the impact toughness and heat resistance of the ceramic foam. A 12.3 vol% of SiC whiskers leads to a more than threefold increase of the flexural strength. Strengthening of the phosphate ceramic foam is due to the fact that the whiskers hinder the propagation of matrix crack by increasing the work of matrix fracture. The whiskers reinforce only that volume of material which is occupied by solid matter, whereas they do not reinforce the pores.

Schetanov, B. V.↗

Using Natural Gas Liquids to Recover Unconventional Oil and Gas Resources (Final Report)

This document presents final technical findings for the project Using Natural Gas Liquids to Recover Unconventional Oil and Gas Resources (FE0031782). The project is part of the U.S. Department of Energy Oil and Gas Program to develop and advance technologies that can significantly improve the recovery efficiencies of unconventional oil and gas resources. The overall objective of this project is to improve the ultimate recovery from unconventional oil and gas (UOG) resources in the United States by developing a method for using unrefined natural gas liquids (NGLs) as treatment fluids to improve hydrocarbon production. Horizontal extended-lateral drilling coupled with high volume hydraulic fracturing has significantly increased production from UOG resources in the U.S. However, the recovery efficiency is low compared to the estimated oil and gas in place. Recent data indicate that less than 10% of the oil in the liquid-rich UOG reservoirs is produced. Alternative completion methods using NGLs could increase production (Battelle, 2016; Wan et al., 2013; Wan, 2013; Downey et al, 2021); however, field validation tests are needed to develop an approach that is economical, efficient, and compatible in the UOG setting to advance towards commercial deployment. This project aims to develop and field test a method to improve recovery of oil resources in UOG shale plays by using Y-Grade NGLs, or a similar combination of NGLs, as treatment fluids. Refined NGLs have been used as a hydraulic treatment fluid in UOG plays for decades and are shown to be particularly effective because their miscibility with oil allows oil to flow more freely; however, the use of Y-Grade (unrefined) NGLs has not been studied. The use of Y-Grade NGLs would be advantageous over refined NGLs because Y-Grade NGLs do not require infrastructure or investment in refining and are already being produced from many UOG reservoirs. The concept was tested and monitored in the field at a commercial well site owned by project partner Hopco, Ltd. The project team, which consists of multiple oil and gas operators, Linde Gas North America LLC (Linde) and the Ohio Division of Geological Survey (ODGS), has extensive experience with oil and gas production in the Appalachian basin and the ability to work together quickly to solve technical issues and research needs. A key part of the proposed work was the use of existing wells for field testing and monitoring. A total of four wells (three vertical and one horizontal) were available for this project. One of the vertical wells was utilized as the test well for the NGL treatment test. A nearby vertical well was used for microseismic monitoring. The remaining vertical well and the horizontal well provided a baseline for typical UOG production in the oil window of the Utica/Point Pleasant (UPP). Major technical tasks of the project include characterization of the geotechnical properties of the UPP with an emphasis on the field site; design and planning for the NGLs testing; field testing and monitoring; analysis and integration of field data; and economic and resource/reserve assessment. The Shoman monitoring well and Doughty NGL treatment well were successfully plugged back during September-October 2020 in preparation for treatment and monitoring. A nitrogen diagnostic fracture injection test (DFIT) was completed on the Doughty well on July 22, 2021, consisting of 133,000 scf (91 Bbl.) of nitrogen. A nitrogen foam frac was completed in the Utica-Point Pleasant interval on August 17, 2021 with funding from outside sources. A microseismic monitoring array was installed in the Shoman well and monitored microseismic activity during the Doughty well frac job. Y-Grade NGL injection commenced on August 26, 2021. A total of 215 Bbl. was injected but the job was shut down due to a small leak on the suction hose on the pump truck. The Y-Grade treatment resumed on August 27, 2021 and an additional 726 Bbl. of Y-Grade NGL was injected at a well head pressure of 3850 psi. Total volume of injected Y-Grade over the two days of injection was 941 Bbl. The well was shut-in for 17 days following injection to allow the Y-Grade NGLs to soak on the formation. Y-Grade treatment flow back commenced on 9/13/2021 on a weekly basis. Production data, including surface pressures, oil, nitrogen, natural gas, and flow times was measured and recorded. Periodic gas samples were collected and analyzed to determine composition of flowback gas. As of July 2022, the treatment well had produced 726 Bbl of oil and 2,888 mcf gas. In August 2022, tubing and packer in the well were removed and a pump was installed to enhance oil recovery. Currently, the operator is producing the well about 2 days a week for a few hours. The performance of the NGL treatment test was evaluated based on reservoir simulations of the treatment process, processing of well testing data, analysis of micro seismic monitoring data, and production data analysis. This analysis suggested that oil production in the small test would continue through 2025. Upscaling the treatment to a horizontal Utica Point-Pleasant well would allow more oil recovery, but the process would involve more investment, services, and operational support. An economic analysis was conducted for scenarios aimed at upscaling the NGL treatment process for more typical horizontal UPP wells in the Appalachian Basin.

02 PETROLEUM↗

Columbia Accident Investigation Board Report. Volume Four

This is Volume Four of a set of six reports produced by NASA and other organizations which were provided to the Columbia Accident Investigation Board (CAIB) in support of its inquiry into the February 1, 2003 destruction of the Space Shuttle Columbia. The Technical Documents included in this volume are: Appendix F.1 Water Absorption by Foam; Appendix F.2 Follow the TPS; Appendix F.3 MADS Sensor Data; Appendix F.4 ET Cryoinsulation; Appendix F.5 Space Shuttle STS-107 Columbia Accident Investigation, and External Tank Working Group Final Report - Volume 1.

CRYOINSULATION↗

Probabilistic Multi-Factor Interaction Model for Complex Material Behavior

Complex material behavior is represented by a single equation of product form to account for interaction among the various factors. The factors are selected by the physics of the problem and the environment that the model is to represent. For example, different factors will be required for each to represent temperature, moisture, erosion, corrosion, etc. It is important that the equation represent the physics of the behavior in its entirety accurately. The Multi-Factor Interaction Model (MFIM) is used to evaluate the divot weight (foam weight ejected) from the external launch tanks. The multi-factor has sufficient degrees of freedom to evaluate a large number of factors that may contribute to the divot ejection. It also accommodates all interactions by its product form. Each factor has an exponent that satisfies only two points - the initial and final points. The exponent describes a monotonic path from the initial condition to the final. The exponent values are selected so that the described path makes sense in the absence of experimental data. In the present investigation, the data used were obtained by testing simulated specimens in launching conditions. Results show that the MFIM is an effective method of describing the divot weight ejected under the conditions investigated. The problem lies in how to represent the divot weight with a single equation. A unique solution to this problem is a multi-factor equation of product form. Each factor is of the following form (1 xi/xf)ei, where xi is the initial value, usually at ambient conditions, xf the final value, and ei the exponent that makes the curve represented unimodal that meets the initial and final values. The exponents are either evaluated by test data or by technical judgment. A minor disadvantage may be the selection of exponents in the absence of any empirical data. This form has been used successfully in describing the foam ejected in simulated space environmental conditions. Seven factors were required to represent the ejected foam. The exponents were evaluated by least squares method from experimental data. The equation is used and it can represent multiple factors in other problems as well; for example, evaluation of fatigue life, creep life, fracture toughness, and structural fracture, as well as optimization functions. The software is rather simplistic. Required inputs are initial value, final value, and an exponent for each factor. The number of factors is open-ended. The value is updated as each factor is evaluated. If a factor goes to zero, the previous value is used in the evaluation.

Abumeri, Galib H.↗

Subsurface mechanical damage of fused silica glass during grinding by various sub-aperture tools with and without ultrasonics

The subsurface mechanical damage (SSD) depth after grinding fused silica glass with a comprehensive set of sub-aperture fixed abrasive grinding tools [cup, wheel, belt, pad, and rotary face mill (with and without ultrasonics)] and process parameters has been statistically measured using the taper wedge technique and evaluated. Consistent with a previously reported grinding model [J. Non-Cryst. Solids 352, 5601–5617 (2006) Crossref , Materials Science and Technology of Optical Fabrication (Wiley & Sons, 2018)], based on the sliding indentation fracture by sliding particles or asperities where the normal load per particle determines the depth of the fracture (and ultimately the overall SSD depth), the dominant factor controlling SSD depth was found to be the abrasive size regardless of the tool type and process conditions. Compared to full aperture grinding methods, the overall SSD depth was higher using the sub-aperture tools, likely due to the higher effective pressure and higher load per particle distribution. Here, in addition to abrasive size, a significant reduction in SSD depth was achieved by: (1) reducing the load distribution on the abrasive particles via increase in contact area and/or decrease in mechanical loading; (2) using a more compliant host tool medium; and (3) in what we believe is a more novel way, using ultrasonics. Combining low abrasive size, larger contact area, and a compliant host, the 6 µm diamond in a resin matrix (Trizact) on a foam pad led to very low SSD depth (~ 4.6 µm), relatively fast grinding rate (186 mm 3 /h), and little or no figure degradation. This grinding tool/process is an attractive choice for final grind, resulting in significantly reduced polish out (i.e., “grey out”) times. With the rotary face mill tool, the use of ultrasonics consistently led to a SSD depth reduction (ranging from 17%–34%). A new fracture mechanics-based model, to the best of our knowledge, where the relevant normal load is parallel to the feed direction, has been developed to explain how ultrasonics leads to lower SSD depth. The key factors, supported by finite element stress analysis and load measurements, are (1) the initiation of fractures at higher z heights during the tool’s ultrasonic vertical oscillations, thus propagating less deep into workpiece; (2) reduction in load (and therefore reduction in fracture propagation distance) due to smaller tool-workpiece feed direction contact area (again caused by higher heights relative to depth of cut); (3) upward movement of the tool during oscillation leads to fracturing toward the surface instead into the depth; and finally (4) at tool’s lowest point of oscillation cycle, there may not be enough time for the fracture to propagate to its full length.

Optics and optical instruments↗