Numerical Calculation of Equivalent Permeability Tensor for Fractured Vuggy Porous Media Based on Homogenization Theory

A numerical procedure for the evaluation of equivalent permeability tensor for fractured vuggy porous media is presented.At first we proposed a new conceptual model,i.e.,discrete fracture-vug network model,to model the realistic fluid flow in fractured vuggy porous medium on fine scale.This new model consists of three systems:rock matrix system,fractures system,and vugs system.The fractures and vugs are embedded in porous rock,and the isolated vugs could be connected via discrete fracture network.The flow in porous rock and fractures follows Darcy’s law,and the vugs system is free fluid region.Based on two-scale homogenization theory,we obtained an equivalent macroscopic Darcy’s law on coarse scale from fine-scale discrete fracture-vug network model.A finite element numerical formulation for homogenization equations is developed.The method is verified through application to a periodic model problem and then is applied to the calculation of equivalent permeability tensor of porous media with complex fracture-vug networks.The applicability and validity of the method for these more general fractured vuggy systems are assessed through a simple test of the coarse-scale model.

Optimization of Permeability Tensor Characteristics of Anisotropic Reservoir and Well Pattern Parameters

The problems of well pattern arrangement, well array direction, and well array spacing ratios for anisotropic reservoirs were studied using tensor analysis. The problems were formulated as a bilevel programming model which was solved using a genetic algorithm. The results show that if the permeability in one direction is much higher than in another direction, the wells should be aligned along the high permeability direction. The analysis provides a theoretical foundation for well pattern arrangement in fractured reservoirs as well as in channel sand reservoirs.

A REVISED SOLUTION OF EQUIVALENT PERMEABILITY TENSOR FOR DISCONTINUOUS FRACTURES

The equivalent permeability tensor is essential to the application of the equivalent porous media model in the numerical seepage simulation for fractured rock masses. In this paper, a revised solution of the equivalent permeability tensor is proposed to represent the influence of the fracture connectivity in discontinuous fractures. A correction coefficient is involved to reflect the com- plex seepage flow type through the rock bridge. This correction coefficient is back analyzed from single-hole packer tests, based on the Artificial Neural Network （ANN） back analysis and the Finite Element Method （FEM） seepage simulation. The limitation of this back analysis algorithm is that the number of single-hole packer tests should be equal or greater than the number of fracture sets, and three is the maximum number of the fracture sets. The proposed solution and the back analysis algorithm are applied in the permea- bility measurement and the seepage simulation for the Xiaowan arch dam foundation.

Anisotropic Variation Law of Rock Permeability with the Burial Depth of Limestone

Permeability tensors of both macrofracture and microfracture Systems weremeasured progressively along the depth of limestone formations at severed sites. It was found thatthe principal permeability values K_x, K_y and K_z in these permeability tensors all decreasesimultaneously and logarithmically with depth. However, the limestone aquifers are composed of anupper region where the larger permeability ellipsoid is upright or prolate and characterized byK_z>K_x and K_z>K_y, a transitional zone, and a lower zone whose smaller permeability ellipsoid ishorizontal or oblate and characterized by K_z>K_x and K_z>K_y. The inversion of the permeabilityellipsoids in direction indicates that the anisotropy of rock permeability with the depth oflimestone formations has evidently changed. The anisotropic variation law of permeability tensors ina macrofracture system displays a similar pattern with that in a microfracture system. It is nextto impossible to examine the rock permeability tensor of the aquifer just by measuring the hydraulicparameters of macrofracture system directly, unless the limestone aquifer is exposed on or near theearth's surface. Therefore, the permeability tensors of a macrofracture system at any depth may beindirectly and roughly determined from the gaugeable permeability tensors of the microfracturesystem by conversion. This anisotropic variation law of rock permeability with depth is of greatsignificance in the study of three-dimensional fracture water flow the huge carbonate formations andin the research on the conditions of karst development and karst distribution.

Magnetic resonance imaging and cell-based neurorestorative therapy after brain injury

Restorative cell-based therapies for experimental brain injury, such as stroke and traumatic brain injury,substantially improve functional outcome. We discuss and review state of the art magnetic resonance imaging methodologies and their applications related to cell-based treatment after brain injury. We focus on the potential of magnetic resonance imaging technique and its associated challenges to obtain useful new information related to cell migration, distribution, and quantitation, as well as vascular and neuronal remodeling in response to cell-based therapy after brain injury. The noninvasive nature of imaging might more readily help with translation of cell-based therapy from the laboratory to the clinic.

An Efficient Numerical Model for Immiscible Two-Phase Flow in Fractured Karst Reservoirs

Numerical simulation of two-phase flow in fractured karst reservoirs is still a challenging issue.The triple-porosity model is the major approach up to now.However,the triple-continuum assumption in this model is unacceptable for many cases.In the present work,an efficient numerical model has been developed for immiscible two-phase flowin fractured karst reservoirs based on the idea of equivalent continuum representation.First,based on the discrete fracture-vug model and homogenization theory,the effective absolute permeability tensors for each grid blocks are calculated.And then an analytical procedure to obtain a pseudo relative permeability curves for a grid block containing fractures and cavities has been successfully implemented.Next,a full-tensor simulator has been designed based on a hybrid numerical method(combining mixed finite element method and finite volume method).A simple fracture system has been used to demonstrate the validity of our method.At last,we have used the fracture and cavity statistics data fromTAHE outcrops in west China,effective permeability values and other parameters from our code,and an equivalent continuum simulator to calculate the water flooding profiles for more realistic systems.

A hybrid simulation approach to evaluate stimulation micro-seismic events and production potential of fractured geothermal reservoirs

This study presents an integrated approach to simulate fluid flow and to predict the micro seismic eventsduring stimulation and circulation of cold water over a longer term in geothermal reservoirs. The integrated approach based on new three dimensional fully coupled thermo-poroelastic numerical model forevaluation of energy recoverable. In the presented approach, the fracture aperture due to fractureslippage is calculated by shear and dilation. The shear slippage is controlled by the concept of shearfailure using linear Mohr-Coulomb criterion. The numerical model is validated against an analytical Oda’smodel for permeability tensor calculation and against an analytical solution for thermo-poroelasticmodel. The heat transfer between the rock and fluid is modelled by using the conductive heat transferwithin the reservoir rock and convective heat transfer in discrete fractures. The thermal stress changesare included in the model to be studied by using roughness induced shear displacement principle in aporo-thermo-elastic environment. The fracture aperture changes are estimated by using an analyticalmodel based on the distributed dislocation technique. The roughness of fracture surfaces is used in thecalculation of residual fracture aperture. The presented approach is used to study the potential ofpermeability enhancement for Habanero geothermal reservoir at a depth of 3600 m. The result show thatthe increasing in tensile effective stress tend to increase the fracture aperture within the zone of cooling.This increasing in fracture aperture led to significant changes in pressure distribution (decrease inimpedance) and hence, increase in the flow rate.