Gray-scale Lattice Boltzmann – an attempt to bridge multiple length scales

Understanding and controlling the flow of fluids through porous media such as rocks, fibres, granular media and paper is of fundamental significance to a variety of industries such as oil and gas, chemical production, health and sanitary products. Numerical modelling of this physical process can be difficult not only because of the complex, three- dimensional topology of the porous medium but also because of computational limitations. For example, shale rocks which is now being intensively investigated for its oil and gas resources have porosity over a wide range of length scales from nano-metres up to millimetres. It has been shown that the micro-porosity is fundamental to the fluid movement through the rock. However, current numerical models, which work off computed tomo- graphical (CT) scans of the rock will be excessively large if they are to fully model all length scales which may span six or more orders of magnitude. Here we consider the development of a lattice Boltzmann (LB) technique which may be able to solve the fluid flow over a wide range of length scales. In the past LB techniques have proven to be ideal to model fluid flow in complex porous media since it can readily import and process digital data from CT scans. Hence the fluid flow field is quickly determined and permeabilities can be predicted. However, when the CT data contains micro- porosity, the conventional LB method is not applicable and a modified LB method needs to be developed. Here we consider a gray-scale LB method which works on voxels which are not fully void or solid but something in between, i.e. each voxel is partially resistant to fluid flow. We firstly outline the model, then validate it on test cases and then demonstrate its applicability on real porous media. We develop models not only for single phase fluid flow, but also multiphase fluid flow (i.e. a gas and a liquid) as well as a temperature model, where the temperature field is advected by the fluid flow. For all these cases the models are developed and validated and then demonstrated on realistic media. It is shown that the gray-scale LB model may be able to solve for fluid flow through multiple length scales – a difficult computational problem which is of increasing significance in many real-world applications

Generation of amorphous carbon and crystallographic texture during low-temperature subseismic slip in calcite fault gouge

Identification of the nano-scale to micro-scale mechanochemical processes occurring during fault slip is of fundamental importance to understand earthquake nucleation and propagation. Here we explore the micromechanical processes occurring during fault nucleation and slip at subseismic rates (∼3 × 10−6 m s–1) in carbonate rocks. We experimentally sheared calcite-rich travertine blocks at simulated upper crustal conditions, producing a nano-grained fault gouge. Strain in the gouge is accommodated by cataclastic comminution of calcite grains and concurrent crystal-plastic deformation through twinning and dislocation glide, producing a crystallographic preferred orientation (CPO). Continued wear of fine-grained gouge particles results in the mechanical decomposition of calcite and production of amorphous carbon. We show that CPO and the production of amorphous carbon, previously attributed to frictional heating and weakening during seismic slip, can be produced at low temperature during stable slip at subseismic rates without slip weakening

Saturation effects on the joint elastic-dielectric properties of carbonates

We used a common microstructural model to investigate the cross-property relations between elastic wave velocities and dielectric permittivity in carbonate rocks. A unified model based on validated self-consistent effective medium theory was used to quantify the effects of porosity and water saturation on both elastic properties (compressional and shear wave velocities) and electromagnetic properties (dielectric permittivity). The results of the forward models are presented as a series of cross-plots covering a wide range of porosities and water saturations and for microstructures that correspond to different predominant aspect ratios. It was found that dielectric permittivity correlated approximately linearly with elastic wave velocity at each saturation stage, with slopes varying gradually from positive at low saturation conditions to negative at higher saturations. The differing sensitivities of the elastic and dielectric rock properties to changes in porosity, pore morphology and water saturation can be used to reduce uncertainty in subsurface fluid saturation estimation when co-located sonic and dielectric surveys are available. The joint approach is useful for cross-validation of rock physics models for analysing pore structure and saturation effects on elastic and dielectric responses

Evaluation of Damage Mechanisms and Skin Factor in Tight Gas Reservoirs

Tight gas reservoirs normally have production problems due to very low matrix permeability and significant damage during well drilling, completion, stimulation and production. Therefore, they may not flow gas at optimum rates without advanced production improvement techniques. The main damage mechanisms and the factors that have significant influence on total skin factor in tight gas reservoirs include mechanical damage to formation rock, plugging of natural fractures by mud solid particles invasion, relative permeability reduction around wellbore as a result of filtrate invasion, liquid leak-off into the formation during fracturing operations, water blocking, skin due to wellbore breakouts, and the damage associated with perforation. Drilling and fracturing fluids invasion mostly occurs through natural fractures and may also lead to serious permeability reduction in the rock matrix that surrounds the natural or hydraulic fractures.This study represents evaluation of different damage mechanisms in tight gas formations, and examines the factors that can have significant influence on total skin factor and well productivity. Reservoir simulation was carried out based on a typical West Australian tight gas reservoir in order to understand how well productivity is affected by each of the damage mechanisms such as natural fractures plugging, mud filtrate invasion, water blocking and perforation

Data-constrained characterization of sandstone microstructures with multi-energy X-ray CT

A data-constrained non-linear optimization approach has been developed to characterize microscopic distributions of mineral phases and pores in a sandstone sample using X-ray CT data sets acquired at 35keV and 45keV beam energies as constraints. The approach minimizes discrepancy between the expected and measured linear absorption coefficients and maximizes Boltzmann distribution probability. It enables integration of both the 3D X-ray CT data-constraints and global level information, and leads to more accurate predictions of microscopic 3D compositional distributions in material samples. Permeability simulations and comparisons with experimentally measured porosity indicate that DCM characterisation agrees reasonably with experimental observations. However, segmentation of CT images leads to under-estimation of porosity and permeability

Determination of effective grain geometry for electrical modeling of sedimentary rocks

Accurate electrical modeling of sedimentary rocks is crucial for the interpretation of electrical survey data and must take into account the geometric information of the rock grains. We have developed an incremental model for the multiphase electrical conductivity of sedimentary rocks on the theoretical basis of differential effective medium models. The developed incremental model was first validated on clean and clay-rich sandstones and then applied to simulate the conductivity of five digitally created rock samples with different spectra of grain aspect ratios. The conductivity is calculated as a function of water conductivity at full water saturation, and an effective grain aspect ratio for a two-phase medium is determined to reproduce the electrical behavior of the digital rocks. It was found that the effective grain aspect ratio can either be determined analytically or estimated from the aspect ratio spectrum. A link between the obtained effective grain aspect ratio and the cementation coefficient widely used in petrophysics has been established. The cementation coefficient increases with the decrease of the grain aspect ratio (increasing the z-axis depolarization factor) and grain conductivity and the increase of sample porosity. It showed that the cementation coefficient can be interpreted as a measure of the connectivity of pores as well as the conductivity of the grains. Our results gave us new insights into the physical meanings of the grain aspect ratio and cementation coefficient, which could be used to facilitate the electrical modeling or interpretation of reservoir rocks