Similarity solution of axisymmetric flow in porous media

Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate. (c) 2005 Elsevier Ltd. All rights reserved.

A new equation for macroscopic description of capillary rise in porous media

Capillary rise in porous media is frequently modeled using the Washburn equation. Recent accurate measurements of advancing fronts clearly illustrate its failure to describe the phenomenon in the long term. The observed underprediction of the position of the front is due to the neglect of dynamic saturation gradients implicit in the formulation of the Washburn equation. We consider an approximate solution of the governing macroscopic equation, which retains these gradients, and derive new analytical formulae for the position of the advancing front, its speed of propagation, and the cumulative uptake. The new solution properly describes the capillary rise in the long term, while the Washburn equation may be recovered as a special case. (C) 2004 Elsevier Inc. All rights reserved.

Stochastic modelling and simulations for solute transport in porous media

A stochastic model for solute transport in aquifers is studied based on the concepts of stochastic velocity and stochastic diffusivity. By applying finite difference techniques to the spatial variables of the stochastic governing equation, a system of stiff stochastic ordinary differential equations is obtained. Both the semi-implicit Euler method and the balanced implicit method are used for solving this stochastic system. Based on the Karhunen-Loeve expansion, stochastic processes in time and space are calculated by means of a spatial correlation matrix. Four types of spatial correlation matrices are presented based on the hydraulic properties of physical parameters. Simulations with two types of correlation matrices are presented.

Prediction of slurry transport in SAG mills using SPH fluid flow in a dynamic DEM based porous media

DEM modelling of the motion of coarse fractions of the charge inside SAG mills has now been well established for more than a decade. In these models the effect of slurry has broadly been ignored due to its complexity. Smoothed particle hydrodynamics (SPH) provides a particle based method for modelling complex free surface fluid flows and is well suited to modelling fluid flow in mills. Previous modelling has demonstrated the powerful ability of SPH to capture dynamic fluid flow effects such as lifters crashing into slurry pools, fluid draining from lifters, flow through grates and pulp lifter discharge. However, all these examples were limited by the ability to model only the slurry in the mill without the charge. In this paper, we represent the charge as a dynamic porous media through which the SPH fluid is then able to flow. The porous media properties (specifically the spatial distribution of porosity and velocity) are predicted by time averaging the mill charge predicted using a large scale DEM model. This allows prediction of transient and steady state slurry distributions in the mill and allows its variation with operating parameters, slurry viscosity and slurry volume, to be explored. (C) 2006 Published by Elsevier Ltd.

Three-dimensional simulation of the rolling of a saturated fibro-porous media

This paper describes recent advances made in computational modelling of the sugar cane liquid extraction process. The saturated fibro-porous material is rolled between circumferentially grooved rolls, which enhance frictional grip and provide a low-resistance path for liquid flow during the extraction process. Previously reported two-dimensional (2D) computational models, account for the large deformation of the porous material by solving the fully coupled governing fibre stress and fluid-flow equations using finite element techniques. While the 2D simulations provide much insight into the overarching cause-effect relationships, predictions of mechanical quantities such as roll separating force and particularly torque as a function of roll speed and degree of compression are not satisfactory for industrial use. It is considered that the unsatisfactory response in roll torque prediction may be due to the stress levels that exist between the groove tips and roots which have been largely neglected in the geometrically simplified 2D model. This paper gives results for both two- and three-dimensional finite element models and highlights their strengths and weaknesses in predicting key milling parameters. (c) 2005 Elsevier B.V. All rights reserved.

Quantitative prediction of phase diagrams for polymer partitioning in aqueous two-phase systems

Published polymer distribution data for aqueous poly(ethylene glycol)/dextran mixtures have been reassessed to illustrate the feasibility of their quantitative characterization in terms of the Flory-Huggins theory of polymer thermodynamics. Phase diagrams predicted by this characterization procedure provide better descriptions of the experimental data than those based on an earlier, oversimplified treatment in similar terms. (C) 2003 Wiley Periodicals, Inc.

The effect of the CaO/SiO2 ratio on the phase equilibria in the ZnO-“Fe2O3”-(PbO + CaO + SiO2) system in air: CaO/SiO2 = 0.1, PbO/(CaO + SiO2) = 6.2, and CaO/SiO2 = 0.6, PbO/(CaO + SiO2) = 4.3

Experimental studies on phase equilibria in the multi-component system PbO-ZnO-CaO-SiO2-FeO-Fe2O3 in air have been conducted to characterize the phase relations of a complex slag system used in the oxidation smelting of lead and in typical lead blast furnace sinters. The liquidus in two pseudoternary sections ZnO-Fe2O3-(PbO + CaO + SiO2) with the CaO/SiO2 weight ratio of 0.1 and the PbO/(CaO + SiO2) weight ratio of 6.2, and with CaO/SiO2 weight ratio of 0.6 and the PbO/(CaO + SiO2) weight ratio of 4.3, have been constructed.

Endogenous amino acid flow in the avian ileum: quantification using three techniques

The aim of the present study was to compare the protein-free diet, guanidinated casein (GuC) and enzyme hydrolysed casein (EHC) methods for the quantification of endogenous amino acid (AA) flow in the avian ileum. Growing broiler chickens (5 weeks old) were used. All three assay diets were based on dextrose, and in the GuC and EHC diets GuC or EHC were the sole source of N. Endogenous AA flows determined with the use of protein-free diet were considerably lower (P < 0.05) than those determined by the GuC and EHC methods. The, total endogenous AA flows determined by the GuC and EHC methods were almost 3-fold greater (P < 0.05) than those determined by the protein-free diet. The endogenous AA values obtained from GuC and EHC methods were similar (P >0.05), except for the flow of arginine, which was lower (P < 0.05) in the EHC method. Glutamic acid, aspartic acid, threonine and glycine were the predominant endogenous AA present in digesta from the distal ileum. The contents of methionine, histidine and cystine were lower compared with other AA. The method of determination had no effect on the AA composition of endogenous protein, except for threonine, glutamic acid, lysine, arginine and cystine. The concentrations of threonine and arginine were lower (P < 0.05) and that of lysine was higher (P < 0.05) with the EHC method compared with the other two methods. The concentration of glutamic acid was greater (P < 0.05) and that of cystine was lower (P < 0.05) in the EHC and GuC methods compared with the protein-free diet method. The results showed that the ileal endogenous flows of N and AA are markedly enhanced by the presence of protein and peptides, above those determined following feeding of a protein-free diet. It is concluded that the use of EHC and GuC methods enables the measurement of ileal endogenous losses in chickens under normal physiological conditions.

Adaptive phase measurements in linear optical quantum computation

Photon counting induces an effective non-linear optical phase shift in certain states derived by linear optics from single photons. Although this non-linearity is non-deterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode-so-called 'single-rail' logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to 'dual-rail' logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state a alpha/0 > + beta/1 > can be prepared deterministically.