Claudio Madonna

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 new Seismic Wave Attenuation Module to experimentally measure low-frequency attenuation in extensional mode

A Seismic Wave Attenuation Module is developed to experimentally measure the attenuation in extensional-mode QE−1 and the Youngs modulus of copper jacketed, 60 mm long and 25.4 mm in diameter samples in a gas medium (Paterson) rig. The new module is suitable for natural rock samples and was tested under confining pressure up to 50 MPa and room temperature. The module is designed to operate at a strain < 10−6, for which rocks behave linearly. To calculate attenuation, both the applied force and the bulk shortening of the sample are measured employing linear variable differential transformers. This technique allows measuring samples with a high degree of heterogeneity. Attenuation at low-seismic frequencies (10−2–102 Hz) is obtained for rocks at dry and various saturation conditions. We present a series of measurements on Berea sandstone in a room-dry condition and saturated with different fluids: water and glycerine solutions with viscosities of 10 cP and 22 cP, respectively, at a confining pressure of 10 MPa and with a pore pressure of 1 MPa. The accuracy of the attenuation data expressed as a phase shift is 0.0019 rad.

An overview of laboratory apparatuses to measure seismic attenuation in reservoir rocks

Intrinsic wave attenuation at seismic frequencies is strongly dependent on rock permeability, fluid properties, and saturation. However, in order to use attenuation as an attribute to extract information on rock/fluid properties from seismic data, experimental studies on attenuation are necessary for a better understanding of physical mechanisms that are dominant at those frequencies. An appropriate laboratory methodology to measure attenuation at seismic frequencies is the forced oscillation method, but technical challenges kept this technique from being widely used. There is a need for the standardization of devices employing this method, and a comparison of existing setups is a step towards it. Here we summarize the apparatuses based on the forced oscillation method that were built in the last 30 years and were used to measure frequency-dependent attenuation in fluid-saturated and/or dry reservoir rocks under small strains (10 −8 ‐10 −5 ). We list and discuss important technical aspects to be taken into account when working with these devices or in the course of designing a new one. We also present a summary of the attenuation measurements in reservoir rock samples performed with these apparatuses so far.

Synchrotron-based X-ray tomographic microscopy for rock physics investigations

ABSTRACTSynchrotron radiation X-ray tomographic microscopy is a nondestructive method providing ultra-high-resolution 3D digital images of rock microstructures. We describe this method and, to demonstrate its wide applicability, we present 3D images of very different rock types: Berea sandstone, Fontainebleau sandstone, dolomite, calcitic dolomite, and three-phase magmatic glasses. For some samples, full and partial saturation scenarios are considered using oil, water, and air. The rock images precisely reveal the 3D rock microstructure, the pore space morphology, and the interfaces between fluids saturating the same pore. We provide the raw image data sets as online supplementary material, along with laboratory data describing the rock properties. By making these data sets available to other research groups, we aim to stimulate work based on digital rock images of high quality and high resolution. We also discuss and suggest possible applications and research directions that can be pursued on the basis o...

Integrated numerical and laboratory rock physics applied to seismic characterization of reservoir rocks

A good understanding of the effect of rock and pore-fluid properties on seismic waves is necessary for the characterization of a subsurface hydrocarbon reservoir from a seismic data set. Information about the rock and fluids in the reservoir can be obtained, for example, through well logging and laboratory tests with samples cored from the wellbore. Together with seismic data, this information can be extrapolated for the entire dimension of the reservoir to provide valuable quantitative estimates for production. Additionally, this information can be extrapolated in time for monitoring the spatial redistribution of fluids during production. Making such space and time extrapolations more accurate using seismic data is the main goal of rock physics. For that, identifying and understanding the physical processes taking place in a reservoir rock at different scales is an important step and the subject of our article.

Laboratory‐based seismic attenuation in Fontainebleau sandstone: Evidence of squirt flow

At seismic frequencies (1–100 Hz), we studied attenuation in the laboratory using the forced oscillation method. We adopted the longitudinal mode of oscillation, which yields the Youngs modulus and the corresponding attenuation, here defined as the inverse quality factor. A Fontainebleau sandstone with a porosity of 8% and a permeability of 12 mD was saturated with different fluids and investigated at the confining pressures of 5, 10, and 15 MPa. At all the measured confining pressures, while attenuation was zero for the dry sample, for partial and full water saturation, it gradually increased from nearly zero to ~0.02 with increasing frequency. The sample was then fully saturated with glycerin-water mixtures of varying viscosities, up to that of glycerin (8, 92, 485, and 1414 cP). At the confining pressure of 5 MPa, a bell-shaped attenuation curve peaking at ~6 Hz with a magnitude of ~0.11 was observed when the sample was fully saturated with glycerin (1414 cP). A decrease in viscosity of the saturating fluid shifted the attenuation curve to higher frequencies, and an increase in confining pressure caused a decrease in the overall magnitude of attenuation. The data obtained for glycerin were compared to a simple squirt flow model with sufficient agreement, implying that squirt flow is the dominant mechanism responsible for the observed attenuation.

Application of differential effective medium, magnetic pore fabric analysis, and X-ray microtomography to calculate elastic properties of porous and anisotropic rock aggregates

Application of differential effective medium, magnetic pore fabric analysis, and X-ray microtomography to calculate elastic properties of porous and anisotropic rock aggregates

Porosity evolution at the brittle-ductile transition in the continental crust: Implications for deep hydro-geothermal circulation

Recently, projects have been proposed to engineer deep geothermal reservoirs in the ductile crust. To examine their feasibility, we performed high-temperature (up to 1000 °C), high-pressure (130 MPa) triaxial experiments on granite (initially-intact and shock-cooled samples) in which we measured the evolution of porosity during deformation. Mechanical data and post-mortem microstuctural characterisation (X-ray computed tomography and scanning electron microscopy) indicate that (1) the failure mode was brittle up to 900 °C (shear fracture formation) but ductile at 1000 °C (no strain localisation); (2) only deformation up to 800 °C was dilatant; (3) deformation at 900 °C was brittle but associated with net compaction due to an increase in the efficiency of crystal plastic processes; (4) ductile deformation at 1000 °C was compactant; (5) thermally-shocking the granite did not influence strength or failure mode. Our data show that, while brittle behaviour increases porosity, porosity loss is associated with both ductile behaviour and transitional behaviour as the failure mode evolves from brittle to ductile. Extrapolating our data to geological strain rates suggests that the brittle-ductile transition occurs at a temperature of 400 ± 100 °C, and is associated with the limit of fluid circulation in the deep continental crust.

Low frequency measurements of seismic wave attenuation in Berea sandstone

We have designed and set up a pressure vessel for 250 mm long and 76 mm in diameter cylindrical samples to measure seismic wave attenuation in rocks at frequencies between 0.01 and 100 Hz and to verify the occurrence of fluid-flow induced by stress field changes. A dynamic stress is applied at the top of the rock cylinder by a piezoelectric motor generating either a stress step of several kPa in few milliseconds or a mono-frequency force. A load cell measures force and a strain sensor the bulk axial shortening across the sample. Five pressure sensors are buried at different heights of the cylinder to measure pore pressure changes related to stress field changes. The sample is sealed in a pressure vessel that can reach confining pressures of 25 MPa. We present datasets collected at room pressure and temperature. Three attenuation data curves measured on reference samples demonstrate the accuracy of the apparatus. A test of the influence of the static stress applied on the sample on the attenuation measurements and measurements conducted for frequencies between 0.1 and 50 Hz with strain < 5e-6 on partially saturated Berea sandstone are presented. Timeevolution pore-pressure curves due to stress field changes are also given.

A theory on thermal spalling of rocks with a focus on thermal spallation drilling

Thermal cracking of rocks is an intensively studied topic in different research areas and for various engineering problems. In this context, we present a modeling approach which describes thermal spalling of rocks with a focus on thermal spallation drilling. This drilling technology uses high thermal loads to locally destruct the surface of the rock formation. With the presented model, the operating conditions which are required to initiate spalling of rocks can be estimated. Additionally, a Spallability number is introduced allowing a categorization of rocks according to their ability to spall. The presented model is based on linear fracture mechanics and the stress intensity concept. It evaluates if a crack with a certain geometry embedded in a rock with specific properties propagates during exposure to different heat loads and external pressures. Thereby, rapid heat transfer processes are coupled with induced thermal stresses and fracture mechanics in rocks.