Modeling and simulation of an acoustic well stimulation method

This paper presents a mathematical model and a numerical procedure to simulate an acoustic well stimulation (AWS) method for enhancing the permeability of the rock formation surrounding oil and gas wells. The AWS method considered herein aims to exploit the well-known permeability-enhancing effect of mechanical vibrations in acoustically porous materials, by transmitting time-harmonic sound waves from a sound source device—placed inside the well—to the well perforations made into the formation. The efficiency of the AWS is assessed by quantifying the amount of acoustic energy transmitted from the source device to the rock formation in terms of the emission frequency and the well configuration. A simple methodology to find optimal emission frequencies for a given well configuration is presented. The proposed model is based on the Helmholtz equation, a sound-hard boundary condition at the casing, and an impedance boundary condition that effectively accounts for the porous solid–fluid interaction at the interface between the rock formation and the well perforations. Exact non-reflecting boundary conditions derived from Dirichlet-to-Neumann maps are utilized to truncate the circular cylindrical waveguides considered in the model. The resulting boundary value problem is then numerically solved by means of the finite element method. A variety of numerical examples are presented in order to demonstrate the effectiveness of the proposed procedure for finding optimal emission frequencies.     

Study on particle removal efficiency of an impinging jet by an image-processing method

 An image-processing method is proposed to obtain the distribution of the removal efficiency of particles on a plate by an air jet. This method can be used to measure particle removal from a flat surface by processing the image of the reflected light from the surface. Factors affecting the particle removal efficiency such as air pressure, distance between the nozzle and the impinging surface and the impinging angle are discussed. Optimal conditions are determined to obtain the most effective particle removal by the air jet. Received: 10 April 2001 / Accepted: 2 August 2001     

Displacement measurement along a line by the diffractographic method

The diffractographic method, a recently developed experimental technique, has been extended to solve the problem of determining the displacement information along the length of a beam. The method, which uses the diffraction of monochromatic light through a variable aperture whose size is a function of the beam displacement, demonstrates that this displacement along a line technique offers a new and accurate method occupying the unique position between point detectors and whole-field procedures.     

Scattering of electromagnetic waves by an acoustic disturbance in the atmosphere

Summary The variations in density associated with an acoustic wave are shown to influence the propagation of an electromagnetic wave. The variation in electric permittivity of the atmosphere caused by an acoustic wave is expressed by the power density of the wave. Under the assumption that the acoustic waves are spherical, the scattered field at large distances is given in terms of definite integrals which are evaluated by means of the method of Stationary Phase. The limiting case of plane acoustic waves is discussed, and two numerical examples are given.     

Some properties of far field patterns of acoustic waves in an inhomogeneous medium

In this paper, the step reduction method is discussed, which was advanced by Prof, Yeh Kai-yuan for calculating a non-uniform beam with various sections. The following result is proved. The approximate solution by this method approaches the true solution if the number of the steps approaches the infinity. However, the measure of the error between the limit solution and the ture solution is not认the pure mathematics sense but in the mechanics sense.     

Calculation of plane equilibrium shapes of thin rods by the method of self-equilibrating variances

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 2, pp. 142–151, March–April, 1994.     

Asymptotic analysis of the equilibrium equation of a fluid-saturated porous medium by the homogenization method

The homogenization of static elasticity equations describing the stress strain state of fluid-saturated porous medium is considered. In this paper, the homogenization method is used to determine the pore pressure transfer tensor, which (a coefficient in the isotropic case) is an important parameter influencing the stress-strain state of fluid-saturated rocks. It shows what a part of the pressure in the fluid is “active” in the formation of macroscopic strains.The pore pressure transfer tensor is calculated for model and real geological specimens. The dependence of this tensor on the porosity, pore shape, and Poisson ratio is investigated. The use of the computational technique for determining the effective properties of rocks shows that it is practically important in the engineering geology.     

Thermodynamic properties of equilibrium air by an exact two-equation model for Euler and Navier–Stokes CFD algorithms

This paper details an exact two-equation procedure to generate pressure, temperature and mass and mole fractions as well as their thermodynamic and Jacobian partial derivatives for five-species neutral equilibrium air. Applicable for arbitrary forms of equilibrium constants and especially designed for explicit and implicit CFD algorithms, the procedure algebraically reduces to two equations the six-equation thermodynamic system comprising the equations for internal energy, law of mass action and conservation of species mass and ratio of oxygen and nitrogen nuclei. This exact algebraic reduction explicitly expresses four mass fractions in terms of nitric oxide mass fraction and temperature, which are then determined through a rapidly converging numerical solution of the internal energy and nitric oxide mass action equations. The procedure then exactly determines the partial derivatives of pressure, temperature and mass fractions analytically. The mathematical formulation also introduces a convenient system non-dimensionalization that makes the procedure uniformly applicable to flows ranging from shock tube flows with zero initial velocity to aerothermodynamic flows with supersonic/hypersonic freestream Mach numbers. Over a wide range of density and internal energy the predicted distributions of mole fractions for the model five species agree with independent published results, while pressure and temperature as well as their partial derivatives remain continuous, smooth and physically meaningful. © 1997 John Wiley & Sons, Ltd.     

Low frequency acoustic properties of bilayer membrane acoustic metamaterial with magnetic oscillator

A bilayer membrane acoustic metamaterial was proposed to overcome the influence of the mass law on traditional acoustic materials and obtain a lightweight thin-layer structure that can effectively isolate low frequency noise. The finite element analysis(FEA) results agree well with the experimental results.It is proved that the sound transmission losses(STLs) of the proposed structures are higher than those of same surface density acoustic materials. The introduction of the magnetic mass block is different from the traditional design method, in which only a passive mass block is fixed on the membrane. The magnetic force will cause tension in the membrane, increase membrane prestress, and improve overall structural stiffness. The effects of the geometry size on the STLs are discussed in detail. The kind of method presented in this paper can provide a new means for engineering noise control.     

Properties of an equilibrium detonation model

A shock wave of zero width is studied as a detonation model in the case when detonation products are in chemical equilibrium behind this shock wave. Together with the well-known properties, some new properties of this model are found. In particular, it is found that there exist weak and strong self-sustaining detonation waves; the latter one propagates in the Chapman-Jouguet regime and corresponds to the point of contact of the Mikhelson line with a new-type adiabat called the extreme adiabat.     

Evolution of the equilibrium states of an inverted pendulum

The influence of the pendulum parameters and the follower force on the evolution of equilibrium states is analyzed using a generalized mathematical model of inverted pendulum. Equilibrium curves are plotted using the parameter continuation method. It is shown that the pendulum with certain values of the angular eccentricity has one or three nonvertical equilibrium positions __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 122–131, March 2007.     

Eigenproblems of two-dimensional acoustic cavities with smoothly varying boundaries by using the generalized multipole method

This paper presents a semi-analytical approach to solve the eigenproblem of a two-dimensional acoustic cavity with smoothly varying boundaries. The multipole expansion for the acoustic pressure is formulated in terms of Bessel and Hankel functions to satisfy the Helmholtz equation in the polar coordinate system. Rather than using the addition theorem, the multipole method and directional derivative are both combined to propose a generalized multipole method in which the acoustic pressure and its normal derivative with respect to non-local polar coordinates can be calculated. The boundary conditions are satisfied by uniformly collocating points on the boundaries. By truncating the multipole expansion, a finite linear algebraic system is acquired. The direct searching approach is applied to identify the natural frequencies using the singular value decomposition technique. Several numerical examples are presented, including those of an annulus cavity, a confocal elliptical annulus cavity and an arbitrarily shaped cavity with an inner elliptical boundary. The accuracy and numerical convergence of the proposed method are validated by comparison with results of the available analytical method and the commercial finite-element code ABAQUS. No spurious eigensolutions are found in the proposed formulation. Due to its semi-analytical character, excellent accuracy and fast rate of convergence are the main features of the proposed method.