Extending a Gray Lattice Boltzmann Model for Simulating Fluid Flow in Multi-Scale Porous Media

Abstract A gray lattice Boltzmann model has previously been developed by the authors of this article to simulate fluid flow in porous media that contain both resolved pores and grains as well as aggregates of unresolved smaller pores and grains. In this model, a single parameter is introduced to prescribe the amount of fluid to be bounced back at each aggregate cell. This model has been shown to recover Darcy-Brinkman flow but with effective viscosity and permeability correlated through the model parameter. In this paper, we prove that the model parameter relates to the fraction of the solid phase of a sub-pore system for a specific set of bounce-back conditions. We introduce an additional parameter to the model, and this enables flow simulation in which cases with variable effective viscosity and permeability can be specified by selecting the two parameters independently. We verify and validate the model for layered channel cases and mathematically analyze fluid momentum and energy losses for the single- and two-parameter models to explain the roles of the parameters in their conservation. We introduce a strategy to upgrade our model to an isotropic version. We discuss the fundamental differences between our model and the Brinkman body-force LBM scheme

Integrating GIS and spatial statistical tools for the spatial analysis of health-related data.

Spatial Statistical Analysis (SSA) and Geographical Information Systems (GIS) are instrumental in many areas of geographical study. However, their use tends to be separate one from another. This has prevented their potential in many application areas from being realised. This research is an attempt to bring the two technologies together for a specific application area - health research. There are two research objectives. The first and main objective is to construct a software package - SAGE - by integrating necessary SSA techniques with ARC/INFO, a GIS, to enable the user to undertake a coherent study of area-based health-related data. The second objective is to evaluate and demonstrate SAGE through a case study. A range of SSA techniques was identified to be useful for addressing typical health questions. A three-tier client-server model was suggested and argued to be the most appropriate for integration as it takes advantages of both the loose-coupling and close-coupling approaches. Under this model, a SSA component forms the client, while ARCH/INFO functions as the server. They are linked through the middle tier - the linking agent. The development of SAGE provided experiences useful for developing a generic SSA module in the future for any GIS that confonns to a set of well-defined standard application interfaces. An empirical study of colorectal cancer (CRC) incidence for the city of Sheffield using SAGE is presented. It shows the usefulness of the SAGE regionalisation tool in constructing an appropriate regional framework for subsequent data analyses and of both exploratory and confirmatory spatial data analysis in exploring the characteristics of CRC incidence. Some weaknesses of SAGE are identified, while remedies for them are suggested. Future work is recommended. The SAGE User Guide, related publications and the SAGE source and executable code as well as the data used in the case study are enclosed for reference

Gravitation-Based Edge Detection in Hyperspectral Images

Edge detection is one of the key issues in the field of computer vision and remote sensing image analysis. Although many different edge-detection methods have been proposed for gray-scale, color, and multispectral images, they still face difficulties when extracting edge features from hyperspectral images (HSIs) that contain a large number of bands with very narrow gap in the spectral domain. Inspired by the clustering characteristic of the gravitational theory, a novel edge-detection algorithm for HSIs is presented in this paper. In the proposed method, we first construct a joint feature space by combining the spatial and spectral features. Each pixel of HSI is assumed to be a celestial object in the joint feature space, which exerts gravitational force to each of its neighboring pixel. Accordingly, each object travels in the joint feature space until it reaches a stable equilibrium. At the equilibrium, the image is smoothed and the edges are enhanced, where the edge pixels can be easily distinguished by calculating the gravitational potential energy. The proposed edge-detection method is tested on several benchmark HSIs and the obtained results were compared with those of four state-of-the-art approaches. The experimental results confirm the efficacy of the proposed method

Determining reservoir intervals in the Bowland Shale using petrophysics and rock physics models

An evaluation of prospective shale gas reservoir intervals in the Bowland Shale is presented using a wireline log data set from the UK's first shale gas exploration well. Accurate identification of such intervals is crucial in determining ideal landing zones for drilling horizontal production wells, but the task is challenging due to the heterogeneous nature of mudrocks. This heterogeneity leads to stratigraphic variations in reservoir quality and mechanical properties, and leads to complex geophysical behaviour, including seismic anisotropy. We generate petrophysical logs such as mineralogy, porosity, and organic content and calibrate these to the results of core studies. If ‘reservoir quality’ is defined by combined cut-offs relating to these parameters, we find that over 100 m of reservoir quality shale is present in the well, located primarily within the upper section. To examine the link between geophysical signature and rock properties, an isotropic rock physics model is developed, using effective medium theories, to recreate the elastic properties of the shale and produce forward-looking templates for subsequent seismic inversion studies. We find that the mineralogical heterogeneity in the shale has a profound impact on modelled elastic properties, obscuring more discrete changes due to porosity, organic content and water saturation and that the best reservoir quality intervals of the shale bear a distinctive response on rock physics cross-plots. Finally, we consider the density of natural fractures in the shale by developing an anisotropic rock physics model to reflect high-angle fractures observed on micro-imagery logs. We invert crack density using shear wave splitting well log data and find a crack density of up to 4 per cent which correlates well with micro-imagery observations. Our work further supports previous authors’ core-based studies in concluding that the Bowland Shale holds good reservoir characteristics, and we propose that there are multiple intervals within the shale that could be targeted with stacked horizontal wells, should those intervals’ mechanical properties also be suitable and there be adequate stress barriers between to restrict vertical hydraulic fracture growth. Finally, our rock physics templates may provide useful tools in interpreting pre-stack seismic data sets in prospective areas of the Bowland Shale and picking the best locations for drilling wells

Research on stress sensitivity of fractured carbonate reservoirs based on CT technology

Fracture aperture change under stress has long been considered as one of primary causes of stress sensitivity of fractured gas reservoirs. However, little is known about the evolution of the morphology of fracture apertures on flow property in loading and unloading cycles. This paper reports a stress sensitivity experiment on carbonate core plugs in which Computed Tomography (CT) technology is applied to visualize and quantitatively evaluate morphological changes to the fracture aperture with respect to confining pressure. Fracture models were obtained at selected confining pressures on which pore-scale flow simulations were performed to estimate the equivalent absolute permeability. The results showed that with the increase of confining pressure from 0 to 0.6 MPa, the fracture aperture and equivalent permeability decreased at a greater gradient than their counterparts after 0.6 MPa. This meant that the rock sample is more stress-sensitive at low effective stress than at high effective stress. On the loading path, an exponential fitting was found to fit well between the effective confining pressure and the calculated permeability. On the unloading path, the relationship is found partially reversible, which can evidently be attributed to plastic deformation of the fracture as observed in CT images