Title: “Ultra-high resolution tomography for nanoscale mechanics and fracturing of chalk”
Description: Chalk is a biogenic limestone that constitutes a large portion of the underground in the Øresund-Skagerrak-Kattegat region. Both drinking water and hydrocarbon reservoirs are hosted in chalk and thus it is essential to understand how depletion of a reservoir will affect the mechanical strength of the underground. To assess the mechanical properties of a reservoir rock, the most common method is to drill a meter long core and take smaller inch sized core plugs for standard laboratory testing. While these standard tests deliver values for properties such as Young’s modulus, Poisson’s ratio and yield strength, they essentially treat the rock as a black box. For example, two core plugs having the same porosity may exhibit very different values for Young’s modulus, which standard mechanical testing cannot attribute to any intrinsic feature of the rock. It is thus necessary to actually look into the rock’s microstructure to determine how different pore morphologies lead to different mechanical properties. The most promising method to retrieve a 3D image of the pore space of chalk is X-ray nanotomography.
Chalk consists of the remains of ancient algae (coccoliths) which are shield-like calcium carbonate structures (a few micrometres in diameter) protected by a thin layer of organics. This organic layer keeps the coccoliths from recrystallizing which means that depending on the rock forming conditions a percentage of the initial coccoliths still remain intact today. Thus, the pore space between the grains is often less than a micrometre wide which necessitates ultra-high resolution imaging. This resolution (less than 100 nm optical resolution) can be achieved using synchrotron based X-ray nanotomography at a number of synchrotrons around the world, e.g. SPring-8 (Japan), ESRF (France) and Swiss Light Source.
We have already recorded some preliminary tomography data (Fig. 1a) of chalk from a quarry outside Aalborg, Denmark using ptychographic X-ray nanotomography, a newly developed form of tomography, pioneered at the Swiss Light Source. The voxel size in this data set is around 21 nm, which seems to be sufficient to resolve all the essential features of the pore network. From a subvolume (Fig. 1b) of this data set, we constructed a volume mesh, imported it into finite element software (Fig. 1c) and set up a uniaxial tension simulation. From the resulting deformed mesh, we were able to derive the strain in the sample. Dividing the applied stress by the resulting strain leads to a constant, the Young’s modulus that can be directly compared to results from laboratory scale testing. Our sample size is of course many orders of magnitude smaller and hardly representative for the whole rock. Sampling different locations in the data leads to different subvolumes with different porosity and thus different Young’s modulus. Plotting Young’s modulus versus porosity for all subvolumes then produces a rock specific porosity-elasticity relationship that can indeed be compared to laboratory scale testing and has already shown some promising
results. However, we need to provide more data to support our claim that nanoscale mechanical simulations can be used to deliver results that are meaningful on the centimetre scale.
This project will thus start with looking into different types of chalk and correlating the recorded pore morphology to rock type and mechanical properties. Furthermore, it is necessary to confirm our finite element simulations by comparing them to other methods. Our partners from the University of Oslo, Dag Dysthe and his group, will be filling exactly that gap. One of Dag’s PhD students is working with a related mechanical simulation technique called peridynamics. In contrast to finite elements, peridynamics is based on integral equations and not partial differential equations, which allows studying plastic deformation e.g. fracturing. Hence, with the supervision of Dag, we will be able to go beyond the elastic limit set by our simulation methods and thereby get a big step closer to more realistic model of what happens in a chalk reservoir during depletion.
Ultra-high resolution X-ray tomography of chalk: Slice of tomography data on chalk from an outcrop in Aalborg, Denmark (a) and 3D visualization of a small subvolume of the data set (b); finite element simulation of confined uniaxial compression (blue axis) on a subvolume of tomography data showing the resulting stress along the blue axis as colour code (c).