Anisotropy in Fracking: A Percolation Model for Observed Microseismicity

Hydraulic fracturing (fracking) using high pressures and a low viscosity fluid allow the extraction of large quantiles of oil and gas from very low permeability shale formations. The initial production of oil and gas at depth leads to high pressures and an extensive distribution of natural fractures which reduce the pressures. With time these fractures heal, sealing the remaining oil and gas in place. High volume fracking opens the healed fractures allowing the oil and gas to flow the horizontal productions wells. We model the injection process using invasion percolation. We utilize a 2D square lattice of bonds to model the sealed natural fractures. The bonds are assigned random strengths and the fluid, injected at a point, opens the weakest bond adjacent to the growing cluster of opened bonds. Our model exhibits burst dynamics in which the clusters extends rapidly into regions with weak bonds. We associate these bursts with the microseismic activity generated by fracking injections. A principal object of this paper is to study the role of anisotropic stress distributions. Bonds in the $y$-direction are assigned higher random strengths than bonds in the $x$-direction. We illustrate the spatial distribution of clusters and the spatial distribution of bursts (small earthquakes) for several degrees of anisotropy. The results are compared with observed distributions of microseismicity in a fracking injection. Both our bursts and the observed microseismicity satisfy Gutenberg-Richter frequency-size statistics.Comment: 14 pages, 10 figure

Approximation of the acoustic radiation impedance of a cylindrical pipe

Useful approximation formulae for radiation impedance are given for the reflection coefficients of both infinitely flanged and unflanged rigid-walled cylindrical ducts. The expressions guarantee that simple but necessary physical and mathematical principles are met, like hermitian symmetry for the reflection coefficient (identical behaviour of positive and negative frequencies) and causality for the impulse response. A non causal but more accurate expression is also proposed that is suitable for frequency-domain applications. The formulae are obtained by analytical and numerical fitting to reference results from Levine & Schwinger for the unflanged case and extracted from the radiation impedance matrix given by Zorumski for the infinite flanged case.Comment: Journal of Sound and Vibration (2008) accepte

The design and evolution of the beta two-stage-to-orbit horizontal takeoff and landing launch system

The Beta launch system was originally conceived in 1986 as a horizontal takeoff and landing, fully reusable, two-stage-to-orbit, manned launch vehicle to replace the Shuttle. It was to be capable of delivering a 50,000 lb. payload to low polar orbit. The booster propulsion system consisted of JP fueled turbojets and LH fueled ramjets mounted in pods in an over/under arrangement, and a single LOX/LH fueled SSME rocket. The second stage orbiter, which staged at Mach 8, was powered by an SSME rocket. A major goal was to develop a vehicle design consistent with near term technology. The vehicle design was completed with a GLOW of approximately 2,000,000 lbs. All design goals were met. Since then, interest has shifted to the 10,000 lbs. to low polar orbit payload class. The original Beta was down-sized to meet this payload class. The GLOW of the down-sized vehicle was approximately 1,000,000 lbs. The booster was converted to exclusively air-breathing operation. Because the booster depends on conventional air-breathing propulsion only, the staging Mach number was reduced to 5.5. The orbiter remains an SSME rocket-powered stage

Coded excitation of broadband terahertz using optical rectification in poled lithium niobate

We demonstrate coded excitation of broadband terahertz for imaging applications. The encoded transmitter uses optical rectification of femtosecond laser pulses in poled lithium niobate patterned with a 53-bit53-bit binary phase code. The terahertz wave forms are detected by electro-optic sampling in zinc telluride. A digital pulse compression filter decodes the binary wave forms, producing broadband pulses at 1.0 THz1.0THz. A two-dimensional imaging experiment shows comparable performance between the encoded transmitter and a zinc telluride emitter.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87834/2/251105_1.pd

Teacher Leader Administrators: Part 3 Of A Symposium On Teachers As Leaders

In this latest continuation of our multipart symposium on teacher leadership, we examine what happens when self-defined teacher leaders become school administrators. Do teacher leaders who become administrators maintain a teacher identity? Can they remain committed to their vision of teacher leadership when they take on the normative requirements and responsibilities of school administration? Through a conversation with three teachers leaders, we explore the rewards and trials of teaching, the choice to become teacher leaders and then administrators, and the unique challenges that face administrators who deeply value the professional, political, and collaborative work of teachers

In Situ deposition of YBCO high-T(sub c) superconducting thin films by MOCVD and PE-MOCVD

Metalorganic Chemical Vapor Deposition (MOCVD) offers the advantages of a high degree of compositional control, adaptability for large scale production, and the potential for low temperature fabrication. The capability of operating at high oxygen partial pressure is particularly suitable for in situ formation of high temperature superconducting (HTSC) films. Yttrium barium copper oxide (YBCO) thin films having a sharp zero-resistance transition with T( sub c) greater than 90 K and Jc approx. 10 to the 4th power A on YSZ have been prepared, in situ, at a substrate temperature of about 800 C. Moreover, the ability to form oxide films at low temperature is very desirable for device applications of HTSC materials. Such a process would permit the deposition of high quality HTSC films with a smooth surface on a variety of substrates. Highly c-axis oriented, dense, scratch resistant, superconducting YBCO thin films with mirror-like surfaces have been prepared, in situ, at a reduced substrate temperature as low as 570 C by a remote microwave-plasma enhanced metalorganic chemical vapor deposition (PE-MOCVD) process. Nitrous oxide was used as a reactant gas to generate active oxidizing species. This process, for the first time, allows the formation of YBCO thin films with the orthorhombic superconducting phase in the as-deposited state. The as-deposited films grown by PE-MOCVD show attainment of zero resistance at 72 K with a transition width of about 5 K. MOCVD was carried out in a commercial production scale reactor with the capability of uniform deposition over 100 sq cm per growth run. Preliminary results indicate that PE-MOCVD is a very attractive thin film deposition process for superconducting device technology

In-situ deposition of YBCO high-Tc superconducting thin films by MOCVD and PE-MOCVD

Metal-Organic Chemical Vapor Deposition (MOCVD) offers the advantages of a high degree of compositional control, adaptability for large scale production, and the potential for low temperature fabrication. The capability of operating at high oxygen partial pressure is particularly suitable for in situ formation of high temperature superconducting (HTSC) films. Yttrium barium copper oxide (YBCO) thin films having a sharp zero-resistance transition with T(sub c) greater than 90 K and J(sub c) of approximately 10(exp 4) A on YSZ have been prepared, in situ, at a substrate temperature of about 800 C. Moreover, the ability to form oxide films at low temperature is very desirable for device applications of HTSC materials. Such a process would permit the deposition of high quality HTSC films with a smooth surface on a variety of substrates. Highly c-axis oriented, dense, scratch resistant, superconducting YBCO thin films with mirror-like surfaces have been prepared, in situ, at a reduced substrate temperature as low as 570 C by a remote microwave-plasma enhanced metal-organic chemical vapor deposition (PE-MOCVD) process. Nitrous oxide was used as a reactant gas to generate active oxidizing species. This process, for the first time, allows the formation of YBCO thin films with the orthorhombic superconducting phase in the as-deposited state. The as-deposited films grown by PE-MOCVD show attainment of zero resistance at 72 K with a transition width of about 5 K. MOCVD was carried out in a commercial production scale reactor with the capability of uniform deposition over 100 sq cm per growth run. Preliminary results indicate that PE-MOCVD is a very attractive thin film deposition process for superconducting device technology