Andreas Wiegmann

Digital rock physics benchmarks-part II: Computing effective properties

This is the second and final part of our digital rock physics (DRP) benchmarking study. We use segmented 3-D images (one for Fontainebleau, three for Berea, three for a carbonate, and one for a sphere pack) to directly compute the absolute permeability, the electrical resistivity, and elastic moduli. The numerical methods tested include a finite-element solver (elastic moduli and electrical conductivity), two finite-difference solvers (elastic moduli and electrical conductivity), a Fourier-based Lippmann-Schwinger solver (elastic moduli), a lattice-Boltzmann solver (hydraulic permeability), and the explicit-jump method (hydraulic permeability and electrical conductivity). The set-ups for these numerical experiments, including the boundary conditions and the total model size, varied as well. The results thus produced vary from each other. For example, the highest computed permeability value may differ from the lowest one by a factor of 1.5. Nevertheless, all these results fall within the ranges consistent with the relevant laboratory data. Our analysis provides the DRP community with a range of possible outcomes which can be expected depending on the solver and its setup.

A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method

We consider the lattice Boltzmann method for immiscible multiphase flow simulations. Classical lattice Boltzmann methods for this problem, e.g. the colour gradient method or the free energy approach, can only be applied when density and viscosity ratios are small. Moreover, they use additional fields defined on the whole domain to describe the different phases and model phase separation by special interactions at each node. In contrast, our approach simulates the flow using a single field and separates the fluid phases by a free moving interface. The scheme is based on the lattice Boltzmann method and uses the level set method to compute the evolution of the interface. To couple the fluid phases, we develop new boundary conditions which realise the macroscopic jump conditions at the interface and incorporate surface tension in the lattice Boltzmann framework. Various simulations are presented to validate the numerical scheme, e.g. two-phase channel flows, the Young-Laplace law for a bubble and viscous fingering in a Hele-Shaw cell. The results show that the method is feasible over a wide range of density and viscosity differences.

Numerical investigation of a combined lattice Boltzmann-level set method for three-dimensional multiphase flow

We simulate rising bubbles using a hybrid lattice Boltzmann scheme based on the lattice BGK model coupled with the level set method (Thömmes et al., 2009. A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method. Journal of Computational Physics). This method uses special boundary conditions at the interface between the two phases which realise the macroscopic jump conditions on the kinetic level and incorporate surface tension into the model. Previous experience with the approach has already demonstrated that it is feasible over a wide range of density and viscosity differences. We utilise this method to simulate the classical immiscible multiphase problem of rising bubbles driven by buoyancy forces. In particular, simulations with large density ratios are performed. The numerical results are compared with available reference solutions.

Non-Invasive Multi-Scale Imaging and Modelling Using X-Ray Microscopy

Over the last 10-15 years 3 dimensional x-ray microscopy (XRM) has emerged as the leading technology for the non-invasive imaging of materials ranging from the multi-cm to the sub-micron scales. One of the principal challenges when implementing such technology is how to deal with multiscale heterogeneity. Frequently the high resolutions required to capture the fundamental length scales governing physical phenomena come at the sacrifice of a field of view required to capture macroscopic heterogeneity. Multi-scale methods and techniques are required to bridge this gap, allowing for integrated classification, sampling and characterization workflows to be developed. While methodological techniques have been developed which allow for multiple imaging scales and modalities to be integrated, they tend to require significant careful manual interaction for the required image site location and subsequent image registration (e.g. [1]) limiting the utility and applicability of the resulting technique. X-ray microscopy offers unique advantages in solving such a challenge, as the variety of detectors integrated into a single imaging system allows for multiple scales to be proscriptively imaged with minimal user interaction. In this paper we present a novel methodology for integrating multi-scale, non-invasive 3D acquisition and analysis, applied to a heterogenous subsurface sandstone sample using the ZEISS Versa XRM 520 and ORS Visual SI Advanced software. Geological materials provide a unique test for such workflows, as they exhibit strong heterogeneity at all length scales [2].