scholarly journals Approximate Dynamic Programming Based Control of Proppant Concentration in Hydraulic Fracturing

Mathematics ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 132 ◽  
Author(s):  
Harwinder Singh Sidhu ◽  
Prashanth Siddhamshetty ◽  
Joseph Kwon
Keyword(s):  
Mechanical Properties ◽  
Dynamic Programming ◽  
Hydraulic Fracturing ◽  
Young’S Modulus ◽  
Large Scale ◽  
Approximate Dynamic Programming ◽  
Young's Modulus ◽  
Computational Cost ◽  
Control Technique ◽  
Rock Mechanical Properties

Hydraulic fracturing has played a crucial role in enhancing the extraction of oil and gas from deep underground sources. The two main objectives of hydraulic fracturing are to produce fractures with a desired fracture geometry and to achieve the target proppant concentration inside the fracture. Recently, some efforts have been made to accomplish these objectives by the model predictive control (MPC) theory based on the assumption that the rock mechanical properties such as the Young’s modulus are known and spatially homogenous. However, this approach may not be optimal if there is an uncertainty in the rock mechanical properties. Furthermore, the computational requirements associated with the MPC approach to calculate the control moves at each sampling time can be significantly high when the underlying process dynamics is described by a nonlinear large-scale system. To address these issues, the current work proposes an approximate dynamic programming (ADP) based approach for the closed-loop control of hydraulic fracturing to achieve the target proppant concentration at the end of pumping. ADP is a model-based control technique which combines a high-fidelity simulation and function approximator to alleviate the “curse-of-dimensionality” associated with the traditional dynamic programming (DP) approach. A series of simulations results is provided to demonstrate the performance of the ADP-based controller in achieving the target proppant concentration at the end of pumping at a fraction of the computational cost required by MPC while handling the uncertainty in the Young’s modulus of the rock formation.

Manuscript Title: Mechanical and Microstructural Studies of Volcanic Ash Beds in Unconventional Reservoirs

2021 ◽  
Author(s):  
Juan C Acosta ◽  
Mark E Curtis ◽  
Carl H Sondergeld ◽  
Chandra S Rai
Keyword(s):  
Mechanical Properties ◽  
Hydraulic Fracturing ◽  
Young’S Modulus ◽  
Volcanic Ash ◽  
Young's Modulus ◽  
Microstructural Analysis ◽  
Thin Layers ◽  
Ion Milling ◽  
Eagle Ford ◽  
Diagenetic Alteration

Abstract Volcanic ash beds are thin layers commonly observed in the Eagle Ford, Niobrara and, Vaca Muerta formations. Because of their differences in composition, sedimentary structures, and diagenetic alteration, they exhibit a significant contrast in mechanical properties with respect to surrounding formation layers. This can impact hydraulic fracturing, affecting fracture propagation and fracture geometry. Quantifying the mechanical properties of ash beds becomes significant; however, it is a challenge with traditional testing methods. Common logging fails to identify the ash beds, and core plug testing is not possible because of their friability. In this study, nanoindentation was used to measure the mechanical properties (Young's modulus, creep, and anisotropy) in Eagle Ford ash beds, and to determine the contrast with the formation matrix properties. Two separate ash beds of high clay and plagioclase composition were epoxied in an aluminum tray and left for 48 hours curing time. Horizontal and vertical samples of ash beds were acquired and mounted on a metal stub, followed by polishing and broad beam ion milling. Adjacent samples were also prepared for high-resolution Scanning Electron Microscope (SEM) microstructural analysis. The Young's modulus in ash beds ranged from 12 to 24 GPa, with the horizontal direction Young's modulus being slightly greater than that of the vertical samples. The Young's modulus contrast with adjacent layers was calculated to be 1:2 with clay-rich zones and 1:4 with calcite rich zones. The creep deformation rate was three times higher for ash beds compared to other zones. Using Backus averaging, it was determined that the presence of ash beds can increase the anisotropy in the formation by 15-25%. SEM results showed a variation in microstructure between the ash beds with evidence of diagenetic conversion of rhyolitic material into clays. Key differences between the two ash beds were due to the presence of plagioclase and the occurrence of porosity within kaolinite. Overall porosity varied between the two ash beds and adjacent carbonate layers showing a significant increase in porosity. Understanding the moduli contrast between adjacent layers can improve the hydraulic fracturing design when ash beds are encountered. In addition, the presence of these beds can lead to proppant embedment and loss in fracture connectivity. These results can be used for improving geomechanical models.

scholarly journals Static and Dynamic Mechanical Properties of Organic-Rich Gas Shale

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Hui Li ◽  
Chi Dong ◽  
Hongwei Yu ◽  
Xin Zhao ◽  
Yan Li ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Dynamic Properties ◽  
Confining Pressure ◽  
Dynamic Mechanical Properties ◽  
Eagle Ford Shale ◽  
Eagle Ford ◽  
Dynamic Mechanical ◽  
Rock Mechanical Properties

Rock mechanical properties are critical for drilling, wellbore stability, and well stimulation. There are usually two laboratory methods to determine rock mechanical properties: static compression tests and acoustic velocity measurements. Rocks are heterogeneous, so there are significant differences between static elastic constants and the corresponding dynamic ones. Usually, static test results are more representative than dynamic methods but the static tests are time consuming and costly. Dynamic methods are nondestructive and less expensive, which are practical in the laboratory and field. In this paper, we compare the static and dynamic elastic properties of Eagle Ford Shale by triaxial compressive tests and ultrasonic velocity tests. Correlations between static and dynamic elastic properties are developed. Conversion from dynamic mechanical properties to static mechanical properties is established for better estimating reservoir mechanical properties. To better understand the relationship of static and dynamic mechanical properties, 30 Eagle Ford Shale samples were tested. According to the test results, the dynamic properties are considerably different from the static counterparts. For all tested samples, static Young’s modulus is lower than dynamic Young’s modulus, ranging from 55% to 90%. The difference of the static and dynamic Young’s moduli decreases with the increasing of confining pressure. The reason may be because the microcracks closed in high confining pressure. Correlations between static and dynamic Young’s modulus are developed by regression analysis, which are crucial to understand the rock mechanical properties and forecast reservoir performance when direct measurement of static mechanical properties is not available or expensive. There are no strong correlations between static and dynamic Poisson’s ratios observed for the tested samples. Two potentially major reasons for the discrepancy of the static and dynamic properties of Eagle Ford Shale are discussed. Lithology and heterogeneity may be the inherent reasons, and external causes are probably the difference in strain amplitude and frequency.

Mechanical properties of FeAlSi powders prepared by mechanical alloying from different initial feedstock materials

2019 ◽  
Vol 107 (2) ◽  
pp. 207 ◽  
Author(s):  
Jaroslav Čech ◽  
Petr Haušild ◽  
Miroslav Karlík ◽  
Veronika Kadlecová ◽  
Jiří Čapek ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Mechanical Alloying ◽  
Young’S Modulus ◽  
Milling Time ◽  
Young's Modulus ◽  
Element Model ◽  
X Ray Diffraction ◽  
X Ray ◽  
Powder Particles ◽  
Complete Homogenization

FeAl20Si20 (wt.%) powders prepared by mechanical alloying from different initial feedstock materials (Fe, Al, Si, FeAl27) were investigated in this study. Scanning electron microscopy, X-ray diffraction and nanoindentation techniques were used to analyze microstructure, phase composition and mechanical properties (hardness and Young’s modulus). Finite element model was developed to account for the decrease in measured values of mechanical properties of powder particles with increasing penetration depth caused by surrounding soft resin used for embedding powder particles. Progressive homogenization of the powders’ microstructure and an increase of hardness and Young’s modulus with milling time were observed and the time for complete homogenization was estimated.

scholarly journals First principles computation of composition dependent elastic constants of omega in titanium alloys: implications on mechanical behavior

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. Salloom ◽  
S. A. Mantri ◽  
R. Banerjee ◽  
S. G. Srinivasan
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
First Principles ◽  
Young's Modulus ◽  
Group Vi ◽  
Group V ◽  
Β Phase ◽  
Ti Alloys ◽  
Ω Phase ◽  
Stabilizer Concentration

AbstractFor decades the poor mechanical properties of Ti alloys were attributed to the intrinsic brittleness of the hexagonal ω-phase that has fewer than 5-independent slip systems. We contradict this conventional wisdom by coupling first-principles and cluster expansion calculations with experiments. We show that the elastic properties of the ω-phase can be systematically varied as a function of its composition to enhance both the ductility and strength of the Ti-alloy. Studies with five prototypical β-stabilizer solutes (Nb, Ta, V, Mo, and W) show that increasing β-stabilizer concentration destabilizes the ω-phase, in agreement with experiments. The Young’s modulus of ω-phase also decreased at larger concentration of β-stabilizers. Within the region of ω-phase stability, addition of Nb, Ta, and V (Group-V elements) decreased Young’s modulus more steeply compared to Mo and W (Group-VI elements) additions. The higher values of Young’s modulus of Ti–W and Ti–Mo binaries is related to the stronger stabilization of ω-phase due to the higher number of valence electrons. Density of states (DOS) calculations also revealed a stronger covalent bonding in the ω-phase compared to a metallic bonding in β-phase, and indicate that alloying is a promising route to enhance the ω-phase’s ductility. Overall, the mechanical properties of ω-phase predicted by our calculations agree well with the available experiments. Importantly, our study reveals that ω precipitates are not intrinsically embrittling and detrimental, and that we can create Ti-alloys with both good ductility and strength by tailoring ω precipitates' composition instead of completely eliminating them.

scholarly journals Tailoring a Low Young Modulus for a Beta Titanium Alloy by Combining Severe Plastic Deformation with Solution Treatment

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3467
Author(s):  
Anna Nocivin ◽  
Doina Raducanu ◽  
Bogdan Vasile ◽  
Corneliu Trisca-Rusu ◽  
Elisabeta Mirela Cojocaru ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Mechanical Properties ◽  
Plastic Deformation ◽  
Severe Plastic Deformation ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Solution Treatment ◽  
Young Modulus ◽  
Orthopedic Implants ◽  
Beta Titanium Alloy

The present paper analyzed the microstructural characteristics and the mechanical properties of a Ti–Nb–Zr–Fe–O alloy of β-Ti type obtained by combining severe plastic deformation (SPD), for which the total reduction was of etot = 90%, with two variants of super-transus solution treatment (ST). The objective was to obtain a low Young’s modulus with sufficient high strength in purpose to use the alloy as a biomaterial for orthopedic implants. The microstructure analysis was conducted through X-ray diffraction (XRD), scanning electron microscopy (SEM), and high-resolution transmission electron microscopy (HRTEM) investigations. The analyzed mechanical properties reveal promising values for yield strength (YS) and ultimate tensile strength (UTS) of about 770 and 1100 MPa, respectively, with a low value of Young’s modulus of about 48–49 GPa. The conclusion is that satisfactory mechanical properties for this type of alloy can be obtained if considering a proper combination of SPD + ST parameters and a suitable content of β-stabilizing alloying elements, especially the Zr/Nb ratio.

scholarly journals Phase Formation, Microstructure and Mechanical Properties of Mg67Ag33 as Potential Biomaterial

Metals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 461
Author(s):  
Konrad Kosiba ◽  
Konda Gokuldoss Prashanth ◽  
Sergio Scudino
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Equilibrium Phase ◽  
Antibacterial Properties ◽  
Equilibrium Phase Diagram ◽  
Compressive Yield Strength ◽  
X Ray ◽  
Fine Grained ◽  
Equilibrium Phases

The phase and microstructure formation as well as mechanical properties of the rapidly solidified Mg67Ag33 (at. %) alloy were investigated. Owing to kinetic constraints effective during rapid cooling, the formation of equilibrium phases is suppressed. Instead, the microstructure is mainly composed of oversaturated hexagonal closest packed Mg-based dendrites surrounded by a mixture of phases, as probed by X-ray diffraction, electron microscopy and energy dispersive X-ray spectroscopy. A possible non-equilibrium phase diagram is suggested. Mainly because of the fine-grained dendritic and interdendritic microstructure, the material shows appreciable mechanical properties, such as a compressive yield strength and Young’s modulus of 245 ± 5 MPa and 63 ± 2 GPa, respectively. Due to this low Young’s modulus, the Mg67Ag33 alloy has potential for usage as biomaterial and challenges ahead, such as biomechanical compatibility, biodegradability and antibacterial properties are outlined.

scholarly journals Effect of Nanopores on Mechanical Properties of the Shape Memory Alloy

Micromachines ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 529
Author(s):  
Chunzhi Du ◽  
Zhifan Li ◽  
Bingfei Liu
Keyword(s):  
Mechanical Properties ◽  
Constitutive Model ◽  
Shape Memory ◽  
Young’S Modulus ◽  
Residual Strain ◽  
Surface Effect ◽  
Young's Modulus ◽  
Strain Curve ◽  
Stress Strain ◽  
Strength Limit

Nanoporous Shape Memory Alloys (SMA) are widely used in aerospace, military industry, medical and health and other fields. More and more attention has been paid to its mechanical properties. In particular, when the size of the pores is reduced to the nanometer level, the effect of the surface effect of the nanoporous material on the mechanical properties of the SMA will increase sharply, and the residual strain of the SMA material will change with the nanoporosity. In this work, the expression of Young’s modulus of nanopore SMA considering surface effects is first derived, which is a function of nanoporosity and nanopore size. Based on the obtained Young’s modulus, a constitutive model of nanoporous SMA considering residual strain is established. Then, the stress–strain curve of dense SMA based on the new constitutive model is drawn by numerical method. The results are in good agreement with the simulation results in the published literature. Finally, the stress-strain curves of SMA with different nanoporosities are drawn, and it is concluded that the Young’s modulus and strength limit decrease with the increase of nanoporosity.

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