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ISBN Prices are subject to change without notice. Journal RSS feed. Sign up for new issue notifications. The viscoplastic self-consistent VPSC large strain polycrystal plasticity theory proved to be very useful for modelling the deformation in Earth materials. In contrast to most metals, rocks are composed of low-symmetry minerals with few slip systems. Also, most minerals have a high strain-rate sensitivity.
Consequently, different orientations deform at different rates, contrary to the assumptions of the traditional Taylor model. The self-consistent method has been applied to predict textures and microstructures in many mineral systems and some highlights will be reviewed. Starting at the surface of the Earth, ice deforms mainly by basal slip. Texture patterns observed in experiments and in the large polar ice sheets are well predicted with the VPSC model. In sediments, concentrations of salt halite deform by buoyant upwelling into salt domes.
Calcite has been an excellent example to illustrate how textures measured in natural rocks can be used to infer the deformation history in the Earth's crust. At Ekofisk, over-pressure depletion led to reservoir compaction which induced overburden deformation and seafloor subsidence which led to detrimental effects on the production equipment and to the platforms resting on the seafloor.
In addition to that, when the pressure declined this led to significant reduction in the production rates during the late 's and early 's see e. In the secondary production phase, recognized by seawater injection, pressure support was provided to maintain the pressure gradient through the oil-field and to reduce the effective stresses and corresponding compaction to pre-production times.
Seawater injection has until now been a great financial success because, in addition to maintain a pressure gradient and to reduce the effective stress, the seawater imbibes from fractures into water-wet chalk matrix where it displaces the oil, an effect leading to increased oil production [ 11 , 12 ].
However, for chalks, time-dependent creep effects are significant. At Ekofisk, for example, since the seawater injection started in the mids it took several years before the reservoir pressure and stress conditions were increased to pre-production level. The prevailing compaction and seafloor subsidence after re-pressurization indicate that not only stress and pressure effects drive deformation, but also the chemical nature of the pore fluid. In addition, the yield stresses, at which irreversible deformation occurs during stress-strain load experiments, are significantly altered by the chemistry of the pore fluids [ 16 ].
As such, the exact way in which pore fluid chemistry impacts chalk mechanics is multi-faceted, as both long-term and short-term chemical processes may occur simultaneously. At these conditions they showed that when seawater is injected into chalk reservoirs it becomes supersaturated with respect to magnesium bearing minerals, e. In addition, precipitation of the Mg-bearing carbonate minerals drives dissolution of calcium-carbonate, which subsequently leads to an excess amount of Ca-ions in the aqueous solution.
These excess ions bind to the sulfate ions in the seawater to form calcium-sulfate, such as anhydrite. Chalks have a varying degree of CaCO 3 -purity. The impurity is often associated with silicate-bearing minerals such as quartz and various forms of clay. When dissolution of pre-existing quartz is taken into account, the geochemical calculations show that magnesium-bearing silicates such as tremolite and talc are also formed.
As such, calculations and direct rock-observations have shown that chalk is prone to chemical rock-fluid reactions at high temperatures [ 17 ]. The rate of deformation with time is linked to mineral alteration see e. Any dissolution related to solid-volume changes may affect the bulk volume directly. Since these mineral reactions, expected when MgCl 2 are flooded through chalks, are associated with density increase, the total volumetric deformation can be partitioned into a solid volume and a pore volume component.
Depending on how the solid volume and pore volume changes, the porosity may change in a non-intuitive way [ 17 ]. It is the chemical potential, related to the Gibbs free energy, which governs the chemical stability of minerals, with temperature and pressure as state variables. In granular systems, where there are large spatial variations in the local stress level, the difference between the externally applied forces over the bulk area may be significantly smaller than the stresses at the solid-solid contacts.
The Biot coefficient, measured to be in the range of 0. These stresses may end up to be 5— times the externally imposed load see later in this paper. However, the appropriate pressure to be used in the geochemical calculations may range from the pore pressure, in the lower end typically 0.
This range in the appropriate thermodynamic pressure at grain contacts are therefore significant, and may therefore lead to spatial differences in the solubility of the different minerals within the porous rock. The stress-driven dissolution at grain contacts is termed pressure solution and has been used to understand the long-term creep experiments see [ 22 , 23 ] for a review. Croize et al.
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Sub-critical crack growth, where cracks propagate at imposed stresses below a critical level due to the chemical interplay between the fluids and rock surface close to the crack tip [ 25 ], may also be an effective driver of deformation and grain re-organization. In addition, the adsorption of sulfate in the diffusive double layer sets up a disjoining pressure at the grain contacts that leads to a reduction in the attractive van der Waals forces.
This mechanism has been shown to significantly alter the mechanical properties and rates of deformation in chalks [ 16 ]. It is important to note that the deformation, due to grain re-organization and porosity reduction, alters the flow pattern. As the material deforms, fresh mineral surfaces are exposed to the non-equilibrium brine, which again increases the chemical reactions there. Hence, deformation could be important for the total chemical reaction measured in the ion concentration of the effluent water concentration.
Many experiments from the University of Stavanger have been performed at these temperatures previously, since the temperature coincide with the temperature at Ekofisk and Valhall reservoir chalk fields at the Norwegian Continental Shelf. Each experiment is denoted OBSV with a number suffix for identification.
Chalk is a sedimentary rock with high calcium carbonate CaCO 3 content. Cylindrical plugs were drilled from a chalk block, before being radially adjusted to diameters D 0 and cut to lengths L 0. The bulk volumes V b were estimated according to the volume of a cylinder.
The plugs were then placed in a vacuum cabinet before being saturated with distilled water, and the saturated weight of each plug was measured M sat , 0. The porosity estimate from mass difference measurements was performed both before and after the experiment. Based on previous experience in related geochemistry, pycnometry, saturation and dry mass estimates, the porosity of connected pores is equal to the overall porosity of the chalk sample [ 17 ].
The solid density can be used to estimate the volume of the solids V s , so that the porosity can be estimated before and after test according to:. The average mineral density was estimated from the dry mass divided by the solid volume.http://web-qi.com/760-tracking-skype-on.php
Earth's mantle: New numerical tool describes rock deformation
The chalk plugs were mounted into a triaxial cell that allowed for continuous measurements of the axial strains during the injection of reactive fluids at elevated stresses, pressures and temperatures see Figure 1. The pore pressure was controlled by a back-pressure regulator ensuring constant pore pressure at 0. The back-pressure regulator allowed for continuous sampling of the effluent water throughout the test period. Figure 1. Top Sketch of the tri-axial cell [ 17 ] and an overview of the gauges, pumps and flow-loop in the experimental setup Bottom.
The triaxial cell has been designed to have a balanced piston, meaning that the confining oil pressure can migrate to a chamber above the piston [see confining pressure outlet in Figure 1 ] to inhibit piston movement unless an additional piston pressure, that overcomes the friction pressure, is added in the upper chamber. The piston friction and the area factor is not the same for all the triaxial cells used. The piston friction is measured in each case, typically depending on temperature and confining pressure, and it takes on values between 0. The area factor varies for the different chalk core diameters and the design of each setup.
It varies between the values of 1. The piston pressure was kept 0. The 0. During this phase, elastic and plastic parameters were measured from stress-strain plots. The initial steps from 1 to 4 lasted 3 days.
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