Xiaoxian Zhang

Bio: Xiaoxian Zhang is an academic researcher from Rothamsted Research. The author has contributed to research in topics: Water flow & Lattice Boltzmann methods. The author has an hindex of 26, co-authored 88 publications receiving 2134 citations. Previous affiliations of Xiaoxian Zhang include Scottish Crop Research Institute & Southwest University.

3D stochastic modelling of heterogeneous porous media - applications to reservoir rocks

Abstract: The creation of a 3D pore-scale model of a porous medium is often an essential step in quantitatively characterising the medium and predicting its transport properties. Here we describe a new stochastic pore space reconstruction approach that uses thin section images as its main input. The approach involves using a third-order Markov mesh where we introduce a new algorithm that creates the reconstruction in a single scan, thus overcoming the computational issues normally associated with Markov chain methods. The technique is capable of generating realistic pore architecture models (PAMs), and examples are presented for a range of fairly homogenous rock samples as well as for one heterogeneous soil sample. We then apply a Lattice–Boltzmann (LB) scheme to calculate the permeabilities of the PAMs, which in all cases closely match the measured values of the original samples. We also develop a set of software methods – referred to as pore analysis tools (PATs) – to quantitatively analyse the reconstructed pore systems. These tools reveal the pore connectivity and pore size distribution, from which we can simulate the mercury injection process, which in turn reproduces the measured curves very closely. Analysis of the topological descriptors reveals that a connectivity function based on the specific Euler number may serve as a simple predictor of the threshold pressure for geo-materials.

Domain-decomposition method for parallel lattice Boltzmann simulation of incompressible flow in porous media.

Abstract: The lattice Boltzmann method has proven to be a promising method to simulate flow in porous media. Its practical application often relies on parallel computation because of the demand for a large domain and fine grid resolution to adequately resolve pore heterogeneity. The existing domain-decomposition methods for parallel computation usually decompose a domain into a number of subdomains first and then recover the interfaces and perform the load balance. Normally, the interface recovery and the load balance have to be performed iteratively until an acceptable load balance is achieved; this costs time. In this paper we propose a cell-based domain-decomposition method for parallel lattice Boltzmann simulation of flow in porous media. Unlike the existing methods, the cell-based method performs the load balance first to divide the total number of fluid cells into a number of groups (or subdomains), in which the difference of fluid cells in each group is either 0 or 1, depending on if the total number of fluid cells is a multiple of the processor numbers; the interfaces between the subdomains are recovered at last. The cell-based method is to recover the interfaces rather than the load balance; it does not need iteration and gives an exact load balance. The performance of the proposed method is analyzed and compared using different computer systems; the results indicate that it reaches the theoretical parallel efficiency. The method is then applied to simulate flow in a three-dimensional porous medium obtained with microfocus x-ray computed tomography to calculate the permeability, and the result shows good agreement with the experimental data.

A mass balance based numerical method for the fractional advection‐dispersion equation: Theory and application

Abstract: [1] The inherent heterogeneity of many geophysical systems often gives rise to fast and slow pathways to water and chemical movement, and one approach to model solute transport through such media is the continuous time random walk (CTRW). One special asymptotic case of the CTRW is the fractional advection-dispersion equation (FADE), which has proven to be a promising alternative to model anomalous dispersion and has been increasingly used in hydrology to model chemical transport in both surface and subsurface water. Most practical problems in hydrology have complicated initial and boundary conditions and need to be solved numerically, but the numerical solution of the FADE is not trivial. In this paper we present a finite volume approach to solve the FADE where the spatial derivative of the dispersion term is fractional. We also give methods to solve different boundary conditions often encountered in practical applications. The linear system resulting from the temporal-spatial discretization is solved using a semi-implicit scheme. The numerical method is derived on the basis of mass balance, and its accuracy is tested against analytical solutions. The method is then applied to simulate tracer movement in a stream and a near-saturated hillslope in a naturally structured upland podzol field in northeast Scotland.

Quantitative X-ray tomography

Abstract: X-ray computer tomography (CT) is fast becoming an accepted tool within the materials science community for the acquisition of 3D images. Here the authors review the current state of the art as CT transforms from a qualitative diagnostic tool to a quantitative one. Our review considers first the image acquisition process, including the use of iterative reconstruction strategies suited to specific segmentation tasks and emerging methods that provide more insight (e.g. fast and high resolution imaging, crystallite (grain) imaging) than conventional attenuation based tomography. Methods and shortcomings of CT are examined for the quantification of 3D volumetric data to extract key topological parameters such as phase fractions, phase contiguity, and damage levels as well as density variations. As a non-destructive technique, CT is an ideal means of following structural development over time via time lapse sequences of 3D images (sometimes called 3D movies or 4D imaging). This includes information nee...

Modeling non‐Fickian transport in geological formations as a continuous time random walk

Abstract: [1] Non-Fickian (or anomalous) transport of contaminants has been observed at field and laboratory scales in a wide variety of porous and fractured geological formations. Over many years a basic challenge to the hydrology community has been to develop a theoretical framework that quantitatively accounts for this widespread phenomenon. Recently, continuous time random walk (CTRW) formulations have been demonstrated to provide general and effective means to quantify non-Fickian transport. We introduce and develop the CTRW framework from its conceptual picture of transport through its mathematical development to applications relevant to laboratoryand field-scale systems. The CTRW approach contrasts with ones used extensively on the basis of the advectiondispersion equation and use of upscaling, volume averaging, and homogenization. We examine the underlying assumptions, scope, and differences of these approaches, as well as stochastic formulations, relative to CTRW. We argue why these methods have not been successful in fitting actual measurements. The CTRW has now been developed within the framework of partial differential equations and has been generalized to apply to nonstationary domains and interactions with immobile states (matrix effects). We survey models based on multirate mass transfer (mobile-immobile) and fractional derivatives and show their connection as subsets within the CTRW framework.