Maurice L. Rasmussen

Parameters of Matrix/Fracture Immiscible-Fluids Transfer Obtained by Modeling of Core Tests

This paper was accepted for presentation at the SPE International Oil Conference and Exhibition in Mexico held in Cancun, Mexico, 31 August–2 September 2006, and revised for publication. Original manuscript received for review 8 November 2010. Revised paper received for review 31 March 2011. Paper peer approved 12 April 2011 as SPE paper 104028. Summary Methodology is presented and proved for determination of the best-estimate parameter values affecting the matrix/fracture-interface fluid transfer in naturally fractured reservoirs. Fracture/surface-hindered interface transfer of immiscible fluids is considered between matrix blocks and surrounding natural fractures. Improved matrix/fracture-transfer models are applied on the basis of presumed matrix-block shapes. Analytical solutions and the limiting isotropic-matrix long-time shape factors developed for special boundary conditions are used for interpretation of typical laboratory tests conducted using rectangularand cylindrical-shaped rock samples. Workable equations and straight-line data-plotting schemes are developed for effective analysis and interpretation of laboratory data obtained from various-shaped oil-saturated reservoir-rock samples immersed into brine. Applications concerning the water/air and water/decane systems in laboratory core tests are also presented. The present approach allows rapid determination of the characteristic parameters of the matrix/fracture-transfer models for various-shaped matrix blocks, which are essential for prediction of petroleum recovery from naturally fractured reservoirs. The methodology is verified using various experimental data, and the values of the characteristic parameters (e.g., the average diffusioncoefficient and the interface-skin-mass-transfer coefficient) are determined. The Arrhenius (1889) equation is shown to represent the temperature dependency of these parameters effectively.

Diffusion Effects in Hypersonic Flows with a Ternary Mixture

An evaluation of multi-component diffusion effects in hypersonic flows is presented. A comparison is made of the results obtained from the common simplifying assumption of Fick’s law with the results obtained from the precise constitutive relations stemming from the kinetic theory of gases. To fix the ideas, the flow of a ternary mixture past a flat plate is considered, for which pressure diffusion is negligible. Whereas the precise analysis is more complicated, the results for the mass-fraction distribution can be significantly different from the corresponding simpler analysis stemming from Fick’s Law.

Uniformly valid approximations for non-linear oscillations with small damping

Abstract A uniformly valid zeroth-order approximation is obtained for the general equation y + ϵH ( y ) y + M ( y ) y = 0, where ϵ is a small parameter. The notion of multiple scaling is utilized to set up a systematic approximation scheme. Examples are given for simple polynomials for H ( y ) and M ( y ), which lead to results involving elliptic integrals. Further restrictions allow progress to be made in terms of gamma functions.

On the damping decrement for non-linear oscillations

Abstract The logarithmic damping decrement is obtained as a function of arbitrary non-linear restoring forces and arbitrary, but small, non-linear damping forces. General expressions are obtained for both amplitude-dependent and speed-dependent damping. The special case of a cubic restoring force with quadratic amplitude-dependent damping and the special case of a cubic restoring force with quadratic speed-dependent damping are considered in detail. The results of the analysis suggest how experimental data can be utilized to identify and evaluate the damping parameters for a given non-linear oscillator.

Evaluation of multicomponent diffusion effects in hypersonic flows

An evaluation of multicomponent diffusion effects in hypersonic flows is presented. Of particular interest is a comparison of the results obtained from the common simplifying assumption of Ficks law with the results obtained from the precise constitutive relations stemming from the kinetic theory of gases. To fix ideas, the flow of a ternary mixture past a flat plate is considered, for which pressure diffusion is negligible. Whereas the precise analysis is more complicated, the results for the mass-fraction distribution can be significantly different from the corresponding simpler analyses stemming from Ficks law. (Author)

Perturbation and Finite Difference Solutions for Wave Propagation in Composites with Periodic Stiffness Variations

Wave propagation in composite materials with discrete changes in properties has been extensively studied and is well understood. In contrast, wave propagation in composites with smooth continuous periodic stiffness variations has only begun to be studied [1]. Use of direct analysis techniques for wave propagation in a composite material with varying stiffness has lead to mathematical contradictions and has indicated the need for a different approach [2]. The present study investigated wave propagation in a composite with smooth continuous periodic stiffness variations using perturbation techniques and a model simulation with a refined finite difference method.

Aerodynamic forces of elliptic-cone derived waveriders at hypersonic velocities

The aerodynamic data for two kinds of elliptic-cone derived waveriders are presented and analyzed for a wide range of Mach numbers and angles of attack. The basic shapes of the waveriders are obtained by means of hypersonic small-disturbance theory. Various off-design performances of the waveriders as well as on-design performances are obtained and fully discussed. These aerodynamic data are informative for the design of hypersonic airplanes which are being investigated as future planes. Also from the entropy distributions across the shock layers for elliptic-cones and waveriders, the vortical layer is analyzed and discussed.

The use of invariants in ultrasonic testing

Invariants, mathematical quantities which are independent of coordinate system, are extensively used in solid mechanics. However, they are rarely applied to practical problems. In this work, we show that the sum of the three orthogonally polarized acoustic velocities in any direction in a cubic crystal is an invariant. This observation can be used either as a check to insure the internal consistency of acoustic measurements in these materials or to reduce the number of measurements required. An application of this approach to the simultaneous determination of thickness and orientation in cubic single crystals is presented.

RESONANCE IN FIBER-REINFORCED COMPOSITE MATERIALS WITH SINUSOIDAL STIFFNESS PROPERTIES

Abstract Composite materials reinforced with long fibers can have a unique characteristic: distortion of the reinforcing fibers into wavy patterns which may be beneficial or deleterious, depending on the applications. The effect of the resulting smooth periodic stiffness variation in the material on wave propagation along the fiber direction is the focus of this study. The problem of wave propagation in a material with a smooth periodic stiffness variation is simplified by assuming that the stiffness variation is sinusoidal. The simplified problem is studied by means of an analytic small-perturbation method and a numerical finite-difference scheme. The perturbation analysis reveals that there is a critical excitation frequency for a wavy stiffness material at which resonance occurs in the propagating waves. The finite-difference simulation corroborates the presence of resonance effects at and around the critical frequency. The resonant growth of the propagating waves could result in premature fatigue failure, due to resonance increased loading, or sudden unexpected failure if the resonance induced stresses are large enough.

Evolution of weak waves in inert binary mixtures

The governing Burgers’ equation that describes the evolution of weak one‐dimensional wave fronts in inert binary mixtures is derived.