Transport and Elastic Properties of Fractal Media

We investigate the influence of fractal structure on material properties. We calculate the statistical correlation functions of fractal media defined by level-cut Gaussian random fields. This allows the modeling of both surface fractal and mass fractal materials. Variational bounds on the conductivity, diffusivity and elastic moduli of the materials are evaluated. We find that a fractally rough interface has a relatively strong influence on the properties of composites. In contrast a fractal volume (mass) has little effect on material properties.Comment: 10 pages, 6 figure

Quantitative properties of complex porous materials calculated from X-ray μCT images

A microcomputed tomography (μCT) facility and computational infrastructure developed at the Department of Applied Mathematics at the Australian National University is described. The current experimental facility is capable of acquiring 3D images made up of 20003 voxels on porous specimens up to 60 mm diameter with resolutions down to 2 μm. This allows the three-dimensional (3D) pore-space of porous specimens to be imaged over several orders of magnitude. The computational infrastructure includes the establishment of optimised and distributed memory parallel algorithms for image reconstruction, novel phase identification, 3D visualisation, structural characterisation and prediction of mechanical and transport properties directly from digitised tomographic images. To date over 300 porous specimens exhibiting a wide variety of microstructure have been imaged and analysed. In this paper, analysis of a small set of porous rock specimens with structure ranging from unconsolidated sands to complex carbonates are illustrated. Computations made directly on the digitised tomographic images have been compared to laboratory measurements. The results are in excellent agreement. Additionally, local flow, diffusive and mechanical properties can be numerically derived from solutions of the relevant physical equations on the complex geometries; an experimentally intractable problem. Structural analysis of data sets includes grain and pore partitioning of the images. Local granular partitioning yields over 70,000 grains from a single image. Conventional grain size, shape and connectivity parameters are derived. The 3D organisation of grains can help in correlating grain size, shape and orientation to resultant physical properties. Pore network models generated from 3D images yield over 100000 pores and 200000 throats; comparing the pore structure for the different specimens illustrates the varied topology and geometry observed in porous rocks. This development foreshadows a new numerical laboratory approach to the study of complex porous materials

3D imaging and flow characterization of the pore space of carbonate core samples

Carbonate rocks are inherently heterogeneous having been laid down in a range of depositional environments and having undergone significant diagenesis. They are particularly difficult to characterise as the pore sizes can vary over orders of magnitudes and connectivity of pores of different scales can impact greatly on flow properties. For example, separate vuggy porosity in an underlying matrix pore system can increase the porosity, but not the permeability and lead to large residual oil saturations due to trapping in vugs. A touching vug network can have a dramatic effect on permeability and lead to higher recoveries. In this paper we image a range of carbonate core material; from model carbonate cores to core material from outcrops and reservoirs via 3D via micro-CT. Image-based calculations of porosity, MICP and permeability on 3D images of the carbonate systems are directly compared to experimental data from the same or sister core material and give good agreement. The carbonate systems studied include samples with well connected macroporous systems and other where the macroporosity is poorly connected. Simulation of permeability on these systems and direct analysis of local flow properties within the system allows one to directly illustrate the important role of the connectivity of macropores on flow properties. Pore network models generated from the images illustrate the varied topology obtained in different carbonate samples and show a dramatic difference when compared to clastic samples. Many carbonate samples can include a significant proportion of microporosity (pores of 2 microns or less in extent) which are not directly accessible via current micro-CT capabilities. We discuss how one can map the structure and the topology of microporous regions crucial in studies of flow, production and recovery in carbonates. A hybrid numerical scheme is developed to measure the contribution of microporosity to the overall core permeability. Overall these results show the important role of identifying the connectivity of the pore sizes in dictating the single phase flow properties. Implications to two phase relative permeability and recovery are briefly discussed

IMAGING OF PORE SCALE DISTRIBUTION OF FLUIDS AND WETTABILITY

ABSTRACT Wettability has a profound effect on reservoir recovery and productivity. It determines the microscopic distribution of fluids in the pore-space which, in turn, determine important global multiphase properties such as capillary pressure, relative permeability, residual saturation and resistivity index. Complexities in pore-space geometry, rock-fluid and fluidfluid interactions have limited descriptions of wettability to highly simplified model systems and wettability in real porous systems remains a poorly understood phenomenon. This paper utilizes two new techniques which have the potential to greatly improve our understanding of wettability in real porous systems. The first is a technique to reproducibly clean and modify the surface energy of clastic and carbonate cores to produce well defined wettability states. The second is a technique for directly imaging the pore-scale distribution of fluids in reservoir cores using high resolution tomography and a newly developed 3D registration technique which allows voxel perfect alignment of a set of images of the same core. We present results for a preliminary study of drainage and imbibition in Fontainebleau sandstone, sucrosic dolomite and oomoldic grainstone cores at well defined wettability states using air and water to demonstrate the applicability of the techniques. The imaged fluid distributions show that gas is preferentially located in larger pores with water occupying smaller pores. The gas saturations measured compare well with those calculated from the imaged fluid distributions. The imaged pore-scale fluid distributions are also compared with predictions based on computations made directly on dry images of the pore-space and in equivalent network models. The computations use simple percolation concepts to model the pore-scale distributions. Drainage saturations and fluid distributions compare well with invasion percolation. Imbibition fluid distributions compare well with ordinary percolation. The comparisons show, for the first time, the feasibility of testing the validity of network models for multi-phase flow by directly comparing model fluid saturations with imaged saturations in real systems on a pore-to-pore basis

The combination of carboxy-terminal propeptide of procollagen type I blood levels and late gadolinium enhancement at cardiac magnetic resonance provides additional prognostic information in idiopathic dilated cardiomyopathy - A multilevel assessment of myocardial fibrosis in dilated cardiomyopathy

Aims To determine the prognostic value of multilevel assessment of fibrosis in dilated cardiomyopathy (DCM) patients. Methods and results We quantified fibrosis in 209 DCM patients at three levels: (i) non-invasive late gadolinium enhancement (LGE) at cardiac magnetic resonance (CMR); (ii) blood biomarkers [amino-terminal propeptide of procollagen type III (PIIINP) and carboxy-terminal propeptide of procollagen type I (PICP)], (iii) invasive endomyocardial biopsy (EMB) (collagen volume fraction, CVF). Both LGE and elevated blood PICP levels, but neither PIIINP nor CVF predicted a worse outcome defined as death, heart transplantation, heart failure hospitalization, or life-threatening arrhythmias, after adjusting for known clinical predictors [adjusted hazard ratios: LGE 3.54, 95% confidence interval (CI) 1.90-6.60; P < 0.001 and PICP 1.02, 95% CI 1.01-1.03; P = 0.001]. The combination of LGE and PICP provided the highest prognostic benefit in prediction (likelihood ratio test P = 0.007) and reclassification (net reclassification index: 0.28, P = 0.02; and integrated discrimination improvement index: 0.139, P = 0.01) when added to the clinical prediction model. Moreover, patients with a combination of LGE and elevated PICP (LGE+/PICP+) had the worst prognosis (log-rank P < 0.001). RNA-sequencing and gene enrichment analysis of EMB showed an increased expression of pro-fibrotic and pro-inflammatory pathways in patients with high levels of fibrosis (LGE+/PICP+) compared to patients with low levels of fibrosis (LGE-/PICP-). This would suggest the validity of myocardial fibrosis detection by LGE and PICP, as the subsequent generated fibrotic risk profiles are associated with distinct cardiac transcriptomic profiles. Conclusion The combination of myocardial fibrosis at CMR and circulating PICP levels provides additive prognostic value accompanied by a pro-fibrotic and pro-inflammatory transcriptomic profile in DCM patients with LGE and elevated PICP

No viscous fingers in heterogeneous porous media

We have carried out computer simulation of miscible displacements in porous media in which the permeabilities vary spatially according to a fractional Brownian motion. This distribution induces long-range correlations and bas been found to describe the permeabilities of heterogeneous rocks. Our simulation shows that conventional viscous fingers, which are the result of the contrant $M$ between the viscosities of the displacing and displaced fluids, and are usually found in laboratory experiments, do not exist. Displacement patterns and efficiency are controlled by the heterogeneities, and the viscosity contrast $M$, varied here between 1 and $\alpha$, han essentially no effect

Percolation thresholds on elongated lattices

We investigate the percolation thresholds of both random and invasion percolation in two and three dimensions on elongated lattices; lattices with a geometry of L^(d−1) × nL in d dimensions, where n denotes the aspect ratio of the lattice. Scaling laws for the threshold and spanning cluster density for random percolation are derived and simulation confirms the behaviour. A direct relationship between thresholds obtained for random percolation and invasion percolation is given and verified numerically.

Finite size scaling for percolation on elongated lattices in two and three dimensions

We derive scaling laws for the percolation properties of an elongated lattice, i.e., those with dimensions of L^(d-1)×nL in d dimensions, where n denotes the aspect ratio of the lattice. Based on statistical arguments it is shown that, in the direction of the extension, the percolation threshold scales approximately as ln n^(1/a) in both two and three dimensions. Extensive Monte Carlo simulations of the site percolation model confirm this scaling behavior. It is further shown that the density of the incipient infinite cluster at the percolation threshold scales differently in two and three dimensions.