The use of renormalization for calculating effective permeability

There is a need in the numerical simulation of reservoir performance to use average permeability values for the grid blocks. The permeability distributions to be averaged over are based on samples taken from cores and from logs using correlations between permeabilities and porosities and from other sources. It is necessary to use a suitable effective value determined from this sample. The effective value is a single value for an equivalent homogeneous block. Conventionally, this effective value has been determined from a simple estimate such as the geometric mean or a detailed numerical solution of the single phase flow equation.If the permeability fluctuations are small then perturbation theory or effective medium theory (EMT) give reliable estimates of the effective permeability. However, for systems with a more severe permeability variation or for those with a finite fraction of nonreservoir rock all the simple estimates are invalid as well as EMT and perturbation theory.This paper describes a real-space renormalization technique which leads to better estimates than the simpler methods and is able to resolve details on a much finer scale than conventional numerical solution. Conventional simulation here refers to finite difference (or element) techniques for solving the single phase pressure equation. This requires the pressure and permeability at every grid point to be stored. Hence, these methods are limited in their resolution by the amount of data that can be stored in core. Although virtual memory techniques may be used they increase computer time. The renormalization method involves averaging over small regions of the reservoir first to form a new averaged permeability distribution with a lower variance than the original. This pre-averaging may be repeated until a stable estimate is found. Examples are given to show that this is in excellent agreement with computationally more expensive numerical solution but significantly different from simple estimates such as the geometric mean.     

采动诱发岩体移动破坏过程数值模拟研究

本文基于岩石介质的宏观非线性主要是由非均质性和各向异性造成的, 应用新的数值计算软件RFPA(2D), 对采动引起岩体失稳破坏的全过程进了数值模拟研究。     

A Sedimentological Approach to Upscaling

Optimised upscaling in reservoir simulations requires the construction of realistic petrophysical properties that are representative of the heterogeneity in the sedimentary deposits. Reservoir heterogeneities are controlled by the arrangement of various hierarchies of sedimentary facies and their internal bounding surfaces. The conventional sedimentological approach to reservoir upscaling involves subdivision and ranking of various hierarchies of architectural units and associated bounding surfaces of the reservoir sequence according to their geological significance. This global upscaling approach produces realistic scaled up models that retain both the structural and non-structural heterogeneities of the original sedimentological models. Analyses of sedimentary sequences from various depositional environments indicate that the fractional Levy model can adequately describe the heterogeneity and scaling characteristics of individual genetic sediment sequences in the clastic sedimentary system without further subdividing and ranking of the heterogeneous sequences. The heterogeneous nature of each sedimentary system can be quantified by the Levy index parameter, whereas the maximum upscaling magnitude (or upscaling index) for a particular sequence can be determined from the Levy width parameter plot. Depositional modelling mimics the sedimentary processes in a range of scales and honours hierarchies of sedimentary facies and their bounding surfaces. It can be used effectively for upgridding and upscaling in accordance with the stratigraphic framework and sedimentological models. Both the fractional Levy model and the depositional modelling provide quantitative alternatives to the conventional global sedimentological upscaling approach.     

Analysis of relative pressure range influence on the identification quality during computer identification of adsorption system parameters by employing the new multilayer adsorption models

The aim of this work has been to analyze the problems related to the identification of microporous structure parameters of carbonaceous materials. The new methods for microporous structure parameters identification have been explored with special focus on the influence of the analyzed relative pressure range on the reliability of parameters identification. For that purpose, the adsorption isotherm of nitrogen on active carbon for different ranges of relative pressures p/p₀ was analyzed. The conducted research was to provide for an answer to the question of whether the range of the analyzed relative pressures has any effect on the quality of adsorption system parameters identification, as well as what range of the relative pressure permits execution of the reliable identification of microporous structure parameters.     

Living with influenza: Impacts of government imposed and voluntarily selected interventions

Focusing on mitigation strategies for global pandemic influenza, we use elementary mathematical models to evaluate the implementation and timing of non-pharmaceutical intervention strategies such as travel restrictions, social distancing and improved hygiene. A spreadsheet model of infection spread between several linked heterogeneous communities is based on analytical calculations and Monte Carlo simulations. Since human behavior will likely change during the course of a pandemic, thereby altering the dynamics of the disease, we incorporate a feedback parameter into our model to reflect altered behavior. Our results indicate that while a flu pandemic could be devastating; there are coping methods that when implemented quickly and correctly can significantly mitigate the severity of a global outbreak.     

Subgroup analysis of zero-inflated Poisson regression model with applications to insurance data

Customized personal rate offering is of growing importance in the insurance industry. To achieve this, an important step is to identify subgroups of insureds from the corresponding heterogeneous claim frequency data. In this paper, a penalized Poisson regression approach for subgroup analysis in claim frequency data is proposed. Subjects are assumed to follow a zero-inflated Poisson regression model with group-specific intercepts, which capture group characteristics of claim frequency. A penalized likelihood function is derived and optimized to identify the group-specific intercepts and effects of individual covariates. To handle the challenges arising from the optimization of the penalized likelihood function, an alternating direction method of multipliers algorithm is developed and its convergence is established. Simulation studies and real applications are provided for illustrations.     

Vortex pinning: A probe for nanoscale disorder in iron-based superconductors

The pinning of quantized flux lines, or vortices, in the mixed state is used to quantify the effect of impurities in iron-based superconductors (IBS). Disorder at two length scales is relevant in these materials. Strong flux pinning resulting from nm-scale heterogeneity of the superconducting properties leads to the very disordered vortex ensembles observed in the IBS, and to the pronounced maximum in the critical current density j_c at low magnetic fields. Disorder at the atomic scale, most likely induced by the dopant atoms, leads to “weak collective pinning” and a magnetic field-independent contribution j_c^coll. The latter allows one to estimate quasiparticle scattering rates.     

Magnetic resonance imaging in laboratory petrophysical core analysis

Magnetic resonance imaging (MRI) is a well-known technique in medical diagnosis and materials science. In the more specialized arena of laboratory-scale petrophysical rock core analysis, the role of MRI has undergone a substantial change in focus over the last three decades. Initially, alongside the continual drive to exploit higher magnetic field strengths in MRI applications for medicine and chemistry, the same trend was followed in core analysis. However, the spatial resolution achievable in heterogeneous porous media is inherently limited due to the magnetic susceptibility contrast between solid and fluid. As a result, imaging resolution at the length-scale of typical pore diameters is not practical and so MRI of core-plugs has often been viewed as an inappropriate use of expensive magnetic resonance facilities. Recently, there has been a paradigm shift in the use of MRI in laboratory-scale core analysis. The focus is now on acquiring data in the laboratory that are directly comparable to data obtained from magnetic resonance well-logging tools (i.e., a common physics of measurement). To maintain consistency with well-logging instrumentation, it is desirable to measure distributions of transverse (_T2$T_2$) relaxation time–the industry-standard metric in well-logging–at the laboratory-scale. These _T2$T_2$ distributions can be spatially resolved over the length of a core-plug. The use of low-field magnets in the laboratory environment is optimal for core analysis not only because the magnetic field strength is closer to that of well-logging tools, but also because the magnetic susceptibility contrast is minimized, allowing the acquisition of quantitative image voxel (or pixel) intensities that are directly scalable to liquid volume. Beyond simple determination of macroscopic rock heterogeneity, it is possible to utilize the spatial resolution for monitoring forced displacement of oil by water or chemical agents, determining capillary pressure curves, and estimating wettability. The history of MRI in petrophysics is reviewed and future directions considered, including advanced data processing techniques such as compressed sensing reconstruction and Bayesian inference analysis of under-sampled data. Although this review focuses on rock core analysis, the techniques described are applicable in a wider context to porous media in general, such as cements, soils, ceramics, and catalytic materials.     

How to count strong adsorption sites by gas chromatography?

Summary A simple gas chromatographic method is presented for the determination of the quantity of the strongest adsorption sites on an adsorbent's surface. The method consists of the blockage of the sites with quasi-irreversibly adsorbed, known amount of a strongly interacting compound and subsequent measuring of the retention of a hydrocarbon during the presence of the blocking compound in the column. Heterogeneity of chromatographic grade silicas is investigated with this method.     

On the visualization of heterogeneous plastic strains by Moiré interferometry

Moiré interferometry is a valuable tool for investigations of the mechanics of materials. It is characterized by high-sensitivity and full-field capability. In this paper, the applicability of moiré interferometry and microscopic magnification to the visualization of the heterogeneous nature of the plastic strains in a polycrystalline material is considered. Plastic deformation of a coarse-grained aluminum is considered in detail.