Reservoir description using dynamic parameterisation selection with a combined stochastic and gradient search

There is a correspondence between flow in a reservoir and large scale permeability trends. This correspondence can be derived by constraining reservoir models using observed production data. One of the challenges in deriving the permeability distribution of a field using production data involves determination of the scale of resolution of the permeability. The Adaptive Multiscale Estimation (AME) seeks to overcome the problems related to choosing the resolution of the permeability field by a dynamic parameterisation selection. The standard AME uses a gradient algorithm in solving several optimisation problems with increasing permeability resolution. This paper presents a hybrid algorithm which combines a gradient search and a stochastic algorithm to improve the robustness of the dynamic parameterisation selection. At low dimension, we use the stochastic algorithm to generate several optimised models. We use information from all these produced models to find new optimal refinements, and start out new optimisations with several unequally suggested parameterisations. At higher dimensions we change to a gradient-type optimiser, where the initial solution is chosen from the ensemble of models suggested by the stochastic algorithm. The selection is based on a predefined criterion. We demonstrate the robustness of the hybrid algorithm on sample synthetic cases, which most of them were considered insolvable using the standard AME algorithm.     

Static deformation of two welded monoclinic elastic half-spaces due to a long inclined strike-slip fault

Static deformation of two monoclinic elastic half-spaces in welded contact due to a long inclined strike-slip fault situated in one of the half-spaces is studied analytically and numerically. Closed-form algebraic expressions for the displacement at any point of the medium are obtained. The variation of the displacement at the interface with the horizontal distance from the fault is studied. The effect of anisotropy on the displacement field is examined. It is found that while the anisotropy of the source half-space has a significant effect on the displacement at the interface, the anisotropy of the other half-space has only a marginal effect.     

A Comparison of Two-Phase Dynamic Upscaling Methods Based on Fluid Potentials

Although a number of methods for calculating dynamic pseudo-functions have been developed over the years, there is still a lack of understanding as to why a certain method will succeed in some cases but fail in others. In this paper, we describe the results of an assessment of several upscaling methods, namely the Kyte and Berry (KB) method, the Stone method, the Hewett and Archer (HA) method and the Transmissibility-Weighted (TW) method. We have analyzed the equations for deriving the methods and investigated the results of numerical simulations of gas displacing oil, in a variety of models to enable us to gain new insights into these, and related, upscaling methods. In particular, some novel observations on methods based on fluid potential are presented and the issue of using predicted fluid mobilities as a criterion of accuracy of an upscaling method is clarified.     

Torsional vibrations of elastic foundation on saturated media

A comprehensive analytical solution is developed to examine the torsional vibration of an elastic foundation on a semi-infinite saturated elastic medium for the first time. First, the governing equations of saturated media are solved by use of Hankel transform techniques. Then, based on the assumption that the contact between the foundation and the half-space is perfectly bonded, this dynamic mixed boundary-value problem can lead to dual integral equations, which are further reduced to the standard Fredholm integral equations of the second kind and solved by numerical procedures. Numerical examples are given at the end of the paper. The numerical results indicate that the response of the elastic foundation strongly depends on the material and geometrical properties of both the saturated soil-foundation system and the load acting on the foundation. In most of the cases, the dynamic behavior of an elastic foundation on saturated media significantly differs from that of a rigid plate bearing on the elastic half-space.     

Surface vibration due to a sequence of high speed moving harmonic rectangular loads

The transmission of vibrations over the surface of the ground, due to high-speed moving, vertical harmonic rectangular loads, is investigated theoretically. The problem is three-dimensional and the interior of the ground is modelled as an elastic half-space or a multilayered ground. The transformed solutions are obtained using the Fourier transform on the space variable. A new damping model in the spatial wavenumber domain, presented in Lefeuve-Mesgouez et al. [J. Sound. Vibr. 231 (2000) 1289] is used. Numerical results for the displacements on the surface are presented for loads moving with speeds up to and beyond the Rayleigh wave speed of the half-space.