Experimental Investigation of Fracture Propagation Behavior Induced by Hydraulic Fracturing in Anisotropic Shale Cores

Hydraulic fracturing is a key technology for the development of unconventional resources such as shale gas. Due to the existence of numerous bedding planes, shale reservoirs can be considered typical anisotropic materials. In anisotropic shale reservoirs, the complex hydraulic fracture network (HFN) formed by the interaction of hydraulic fracture (HF) and bedding plane (BP) is the key to fracturing treatment. In this paper, considering the anisotropic angle, stress state and injection rate, a series of hydraulic fracturing experiments were conducted to investigate the effect of anisotropic characteristics of shale reservoirs on HFN formation. The results showed that the breakdown pressure increased first and then decreased when the anisotropic angle changed at 0°–90°, while the circumferential displacement had the opposite trend with a small difference. When θ = 0°, fracturing efficiency of shale specimens was much higher than that under other operating conditions. When θ ≤ 15°, the bedding-plane mode is ubiquitous in all shale reservoirs. While θ ranged from 30°–45°, a comprehensive propagation pattern of bedding-plane and crossing is presented. When θ ≥ 60°, the HFN pattern changes from comprehensive mode to crossing mode. The propagation pattern obtained from physical experiments were verified by theoretical analysis. The closure proportion of the circumferential displacement was the highest when the propagation pattern was the bedding-plane mode (θ ≤ 15°), following by crossing. The closure proportion was minimum only when the bedding-plane and crossing mode were simultaneously presented in the HFN. The results can provide some basic data for the design in hydraulic fracturing of tight oil/gas reservoirs.

Efficient Solution for Cylindrical Shell Based on Short and Long (Enhanced Vlasov’s) Solutions on Example of Concentrated Radial Force

There is the general feeling among the scientists that everything what could be performed by theoretical analysis for cylindrical shell was already done in last century, or at least, would require so tremendous efforts, that it will have a little practical significance in our era of domination of powerful and simple to use commercial software. Present authors partly support this point of view. Nevertheless there is one significant mission of theory which is not exhausted yet, but conversely is increasingly required for engineering community. We mean the educational one, which would provide by rather simple means the general understanding of the patterns of deformational behavior, the load transmission mechanisms, and the dimensionless combinations of physical and geometrical parameters which governs these patterns. From practical consideration it is important for avoiding of unnecessary duplicate calculations, for reasonable restriction of the geometrical computer model for long structures, for choosing the correct boundary conditions, for quick evaluation of the correctness of results obtained. The main idea of work is expansion of solution in Fourier series in circumferential direction and subsequent consideration of two simplified differential equations of 4th order (biquadratic ones) instead of one equation of 8th order. The first equation is derived in assumption that all variables change more quickly in axial direction than in circumferential one (short solution), and the second solution is based on the opposite assumption (long solution). One of the most novelties of the work consists in modification of long solution which in fact is well known Vlasov’s semi-membrane theory. Two principal distinctions are suggested: a) hypothesis of inextensibility in circumferential direction is applied only after the elimination of axial force; b) instead of hypothesis zero shear deformation the differential dependence between circumferential displacement and axial one is obtained from equilibrium equation of circumferential forces by neglecting the forth order derivative. The axial force is transmitted to shell by means of short solution which gives rise (as main variables in it) to a radial displacement, its angle of rotation, bending radial moment and radial force. The shear force is also generated by it. The latter one is equilibrated by long solution, which operates by circumferential displacement, axial one, axial force and shear force. The comparison of simplified approach consisted from short solution and enhanced Vlasov’s (long) solution with FEA results for a variety of radius to wall thickness ratio from big values and up to 20 shows a good accuracy of this approach. So, this rather simple approach can be used for solution of different problems for cylindrical shells.

A theoretical model for the tread slip and the effective rolling radius of the tyres in free rolling

A rigid–elastic coupling theory for the rolling kinematics of tyres, by which the tread slip, the effective rolling radius and the ply steering of the tyres can be analysed, was formulated. The theory demonstrates that, during free-rolling motion, the coupling between the rotational velocity Ω along the wheel axis and the circumferential displacement gradient generates the longitudinal tread slip, and the coupling between the rotational velocity Ω along the wheel axis and the lateral displacement gradient generates the lateral tread slip and the ply steering. Revisiting the tread slip phenomenon using the newly proposed method numerically proves the kinematic mechanism of the rolling friction. It can be found that the effective rolling radius Re increases with increasing inflation pressure and decreases with increasing load; the sensitivity of Re to the inflation pressure is greater than the sensitivity of Re to the load. The good agreement between the theoretical predictions and the test results for the effective rolling radius of the radial tyres of a car is found. The coupling of the displacement gradient and the rigid rolling kinematics causes non-symmetry of the lateral tread slip which, in turn, leads to the ply steering and the residual aligning moment; these depend on the belt and tread design. The proposed theory and approach provide a quick and powerful tool for analysing the tread slip, the effective rolling radius and the ply steering of the tyres under free rolling.

Influence of Modal Coupling on the Nonlinear Vibration of Simply Supported Cylindrical Panels

The aim of this paper is to analyse the influence of the nonlinear modal coupling on the nonlinear vibrations of a simply supported cylindrical panel excited by a time dependent transversal load. The cylindrical panel is modeled by the Donnell nonlinear shallow shell theory and the lateral displacement field is based on a perturbation procedure. The axial and circumferential displacement are described in terms of the obtained lateral displacement, generating a precise low-dimensional model that satisfies all transversal boundary conditions. The discretized equations of motion in time domain are determined by applying the standard Galerkin method. Various numerical techniques are employed to obtain the cylindrical panel resonance curves, bifurcation scenario and basins of attraction. The results show the influence of geometry and the nonlinear modal coupling on the nonlinear response of the cylindrical panel.

Study on Dynamic Response of Cylindrical Shells under Combined Load

In order to study the dynamic response of the cylindrical shell structure which is similar to the missile cabin under the combined effects of axial compressive load and radial aerodynamic load, the equilibrium equation of dynamic response of cylindrical shell is derived based on the Hamiltons principle. The displacement response of cylindrical shell is calculated through employing the numerical method. The calculation results show that the axial displacement response and the radial displacement response of cylindrical shell are much greater than the circumferential displacement response; the radial displacement will be maximum when the excitation frequencies are 285Hz, 594Hz, 1039Hz, 1062Hz, 1093Hz, 1962Hz and 1987Hz; the axial displacement will be maximum when the corresponding excitation frequencies are 81Hz and 294Hz; the peak values of displacement response in non-load plane are not all obtained at the resonance frequency and a certain effect is generated due to the modal coupling.

Analysis of Cylindroid Shell Subject to Internal Linearly-Increased Pressure

Close cylindroid shells are widely used in many industrial branches. Membrane theory of shells is used to take an analytical solution to investigate the internal force distributions and deformation laws of such shells. The result shows that, under the condition of two-point simple supports, among three force components(meridional forceT1, circumferential forceT2, and shear forceT12),T1is the dominant one, which is negative (compressional) in the vicinity of the neutral axis, and becomes positive (tensional) after being away from the neutral axis. The shear forceT12is rather like a sine curve, which changes its sign at the neutral axis. This type of shear force distribution leads to a warp deformation within the cylinder.T2is always the tensional force, and when comparing to the other two components, it is too small to be dominant in shell designing. Somewhat similar to the three force components, among the three deformation components, the normal displacementwis the extreme one, and also it varies acutely. The circumferential displacementvis much less thanw, which is compressive below the neutral axis, and becomes tensile above the neutral axis. In the nearby of neutral axis,vis nearly zero. Compared towandv, the meridional displacementuis always the minimal.

Flexible Sensor for McKibben Pneumatic Artificial Muscle Actuator

The demand for flexible, lightweight McKibben pneumatic artificial muscles (McKibben actuators) has been increasing for power assistance equipment used for assisting and rehabilitating the elderly. To accurately control this equipment, the length of the actuator should be measured. However, the equipment becomes heavier and less flexible when a rigid sensor, such as a potentiometer or an encoder, is used. The sensor should be flexible in order to take advantage of the favorable properties of the McKibben actuator. The aim of this study is to measure the length of the actuator without loss of its advantages. We propose a method of estimating the length from the circumferential displacement, which can be measured by a sensor made of electroconductive, flexible rubber. Higher accuracy is obtained by measuring the circumferential displacement than by measuring the axial displacement using this sensor. The sensor’s flexibility enables us to accurately control the actuator without any loss of flexibility or increase in weight. Furthermore, the sensor does not require the attachment of any rigid fixtures. The accuracy of the estimate is successfully evaluated and the usefulness of the proposed method is verified through its application to a multi-link arm driven by the McKibben actuator.

Stress Evaluation of a Short, Medium and Long Stem Proximal Fill Femoral Implants

The femoral stem of a traditional total hip arthroplasty is believed to be essential for fixation and stability. Stems achieve early stability in a non-physiological fashion by a combination of friction and circumferential displacement of bone, similar to that of a nail being impacted into a piece of wood. In contrast, the “Revelation” femoral prosthesis, produced by DJO Surgical Corporation, relies upon a proximal lateral expansion (“Lateral Flare” design concept) to achieve stability.

Ultrasonic Flexural Torsional Guided Wave Focusing in Pipe

Ultrasonic flexural torsional guided wave properties, including the excitation and propagation have been studied recently. Natural focusing is one of the major characteristics exhibited by partial loading excitation. With the aid of phased array transducer we propose a wave focusing method to enhance the signal to noise ratio and defect resolution in pipe inspection. With time delays and amplitudes applied to different elements constructive wave interference at specific point can be achieved in order to focus wave energy. Focusing effect is examined by angular profile, which is the circumferential displacement distribution.

Nonlinear Vibrations and Multiple Resonances of Fluid-Filled, Circular Shells, Part 1: Equations of Motion and Numerical Results

The response-frequency relationship in the vicinity of a resonant frequency, the occurrence of travelling wave response and the presence of internal resonances are investigated for simply supported, circular cylindrical shells. Donnell’s nonlinear shallow-shell theory is used. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The problem is reduced to a system of four ordinary differential equations by means of the Galerkin method. The radial deflection of the shell is expanded by using a basis of four linear modes. The effect of internal fluid is also investigated. The equations of motion are studied by using a code based on the Collocation Method. The present model is validated by comparison of some results with others available. A water-filled shell presenting the phenomenon of 1:1:1:2 internal resonances is investigated for the first time; it shows intricate and interesting dynamics. [S0739-3717(00)01204-6]