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Permeability measurement
For our permeability measurement we used two methods: steady state and transient pulse. The steady state technique uses either a constant flow or a constant pore pressure gradient provided by two servo-controlled cylinders. Two symmetrical measures of permeability were performed by switching the flow direction in the sample. Permeability was then inferred using Darcy’s law: 𝑄𝑆=−𝑘Δ𝑃𝜂𝐿 (1-16).
Where Q is the fluid flow (m3s-1), S the sample area (m2), L the sample length (m), η the dynamic viscosity of the pore fluid (Pa·S), Δ𝑃𝐿 is the pore fluid pressure gradient (Pa). However, this method can only measure a permeability 𝑘≥10−18m2.
Transient pulse is used when permeability is lower (<10−18m2). The fluid pressure on one side of the sample is instantaneously increased by Δ𝑃. This allows us to measure the fluid diffusion through the sample. Δ𝑃 decays exponentially with time until equilibrium pressure is reached in the sample. Assuming the system geometry is known, the permeability could be computed from the time it takes for this transient pressure pulse to reach the equilibrium (Brace et al. 1968).
𝑘=𝛼𝜂𝛽𝐿𝑆(11𝑉𝐴+1𝑉𝐵).
Stress-dependent permeability
Transport properties, (permeability and diffusivity) have been observed to be strongly stress-dependent (Nur et al. 1980; Yilmaz et al. 1994). Gavrilenko and Gueguen (1989) developed a model of pressure-dependent permeability, connecting permeability with statistical distribution of crack geometry. More recently, Yilmaz et al. 1994 suggested a model in which the diffusion coefficient 𝐷 is related to the pore fluid pressure 𝑃 by 𝐷=𝐷0𝑒𝜅𝑝 (1-59) κ is the permeability compliance, defined and dicussed in 1.2.6.
Strain and ultrasonic instrumentation
Four groups of strain gauges are glued at different positions directly on the sample. (Figure 2 in appendix). Each group is composed of one axial gauge and one radial gauge. Strain gauges Tokyo Sokki TML FCB 2-11 are employed. The axial strain a , and radial strain r are both averaged across the four strain gauges in each orientation. The volumetric strain is deduced as 2 v a r =+ . Neoprene tubing is used to separate the sample from the oil of the confining medium. Then, 12 P-wave sensors (PI 255 PI Ceramics, 1 MHz resonance frequency) and 4 polarized S-wave sensors (Shear PZT plate) are glued directly on the surface of the rock and sealed with a two-component epoxy (Figure 2 in appendix). The network of ultrasonic sensors used allows us to record i) acoustic emissions (passive mode) and ii) the evolution of the ultrasonic velocities in different directions (active mode). For the ultrasonic wave velocity survey, a 250 V high-frequency signal is pulsed every 2 minutes on each sensor while the others are recording. In passive mode, these sensors can record the acoustic emissions (AE) that take place in the sample. The AEs are amplified at 40 dB and can be discretely recorded with a maximum rate of 12 AE/s. (Schubnel et al., 2006, 2007; Brantut et al., 2011; Ougier-Simonin et al., 2011; Nicolas et al., 2016).
Properties of samples heat-treated at different temperatures
The samples were heat-treated at different temperatures: 500°C, 850°C, 930°C and 1100°C. The evolution of the P-wave velocity and permeability as functions of the temperature of the heat treatment are shown in Figure 2.3. In addition, we invert the P-wave velocity to obtain the crack density, as defined by 𝜌 = Σ 𝑙𝑖 𝑁 𝑉, where 𝑙𝑖 is the length of the i-th crack and N is the total number of cracks embedded in the representative elementary volume V. When the crack length is smaller than the wavelength, effective medium theory is an appropriate method (Ougier- Simonin et al., 2010). The effective elastic properties are mainly controlled by cracks (Gueguen and Kachanov 2012). A noninteractive assumption is employed (Kachanov, 1994).
Noninteractive effective medium theory has been shown to be valid when cracks are distributed randomly and crack density does not exceed 0.2-0.3 (Kachanov, 1994; Sayers and Kachanov, 1995; Gueguen and Sarout, 2009). The details of the inversion in crack density are given in the appendix “Crack density inversion method – Isotropic case” (Ougier-Simonin et al. 2010; Mallet et al. 2014; Fortin et al., 2011; Nicolas et al., 2016).
Microstructural observations of the heat-treated samples
The microstructures are shown in Figure 2.4. In the sample heat-treated at 500°C (Figure 2.4A, 2.4B), few cracks can be observed. In the samples heated at 800°C (Figure 2.4C, 2.4D) and 930°C (Figure 2.4E, 2.4F), cracks surrounding the large inclusions with lengths of 50 μm-200 μm can be observed, including intergranular and intragranular cracks. Small cracks begin to appear in the matrix. Partial melting occurs above 500°C; the details and effects of partial melting are presented in section 3.2. The sample treated at 1100°C shows the highest crack density (Figure 2.4G, 2.4H). In particular, in the matrix (Figure 2.4H), the number of cracks with lengths ranging between 1 μm and 20 μm is greatly increased, and most cracks are located at the boundaries of the crystal grains of quartz, tridymite and plagioclase. Overall, the evolution of the microstructure is in good agreement with the evolution of the P-wave velocity and the permeability (Figure 2.3).
Tri-axial deformation of non-heat-treated andesite and heat-treated andesite
Triaxial deformation tests were performed at confining pressures of 5 MPa, 15 MPa and 30 MPa under dry conditions at room temperature. The differential stress and mean stress are plotted versus axial strain and volumetric strain, respectively, in Figure 2.6.
The samples under confining pressures varying between 5 MPa and 30 MPa are deformed in the brittle regime. The differential stress reaches a peak stress followed by macroscopic failure. The peak stress is observed to increase with confining pressure: the maximum differential stress increases by 20% as the confining pressure increases from 5 MPa to 15 MPa and increases by 27% as the confining pressure increases from 5 MPa to 30 MPa. Note that at the beginning of the loading, the stress-strain curves (Figure 2.6) are almost linear, which indicates that the number of pre-existing cracks is very small.
Another result of interest is the identification of the D’ point, which is the point where volumetric strain reverses (Figure 2.6). Beyond D’, dilatancy dominates over compaction [Heap et al. 2014]. The differential stress for D’ increases as the confining pressure is increased from 5 MPa to 30 MPa. The stress state of D’ increases by 22% as the confining pressure increases from 5 MPa to 15 MPa and increases by 50% as the confining pressure increases from 5 MPa to 30 MPa.
Ultrasonic velocity evolution of heat-treated andesite
The P-wave velocity evolution during the triaxial deformation of heat-treated andesite samples under confining pressures of 0 MPa, 15 MPa and 30 MPa is shown in Figure 2.9. In Figure 2.9, the evolution of P-wave velocities along different traces from 0° to 53° (Figure 2.7.a) is plotted. A clear difference can be observed in comparison with Figure 2.7.b: for heat-treated samples, the P-wave velocity increases at the beginning of loading, indicating the closure of pre-existing cracks (Stage I). This observation agrees with the stress-strain curve of heat-treated andesite samples, which is concave at the beginning of loading.
During stage II (from C’ to D’), the P-wave velocity reaches a plateau. There is competition between pre-existing crack closure and new crack nucleation and propagation. The onset of dilatancy (point C’) corresponds to new crack nucleation. Point C’ is determined from both acoustic data and mechanical data, as shown in Figure 2.9. Regarding the acoustic data, point C’ corresponds approximately to the stage where the radial P-wave velocity stops increasing. At stage III, from point D’ to the failure point, a clear decrease in P-wave velocities is observed as well as clear P-wave anisotropy indicating the propagation and nucleation of mainly axial cracks.
Effect of heat treatment on the microstructure: partial melting
The question is: where does the melt go? Figure 2.11 shows that the melt seals some cracks, especially the cracks with the largest apertures. We also observe that bubbles are distributed in the melt in agreement with the observations of Simmons and Richter [1976], Swanenberg [1980], and Roedder [1981], indicating that the bonding strength is recovered. The melt flows into the cracks, and as it cools, the glass bonds the two surfaces of cracks. Bubbles are clearly observed in the SEM (Figure 2.6). Since the spherical bubbles represent relatively stable pore shapes, we refer to the bubble planes as being strength recovered.
SEM and EBSD reveal that the melt content is an amorphous phase that contains Fe, K, and Mg. Partial melting probably results from the presence of smectite, which has lowered melting point of other minerals. Indeed, the melting point of pyroxene and plagioclase is 1400°C, whereas smectite melts at temperatures of 400-500°C.
Table of contents :
Chapter Ⅰ Methodology and Theoretical Background
1.1 Methodology
1.1.1 Experiment apparatus
1.1.2 Strain and ultrasonic measurements
1.1.3 The brittle regime: definition of the stress states C’ and D’
1.1.4 Ultrasonic measurements and acoustic emission (AE)
1.1.5 Velocity model for AE hypocenter location
1.1.6 Acoustic location algorithm
1.1.7 Permeability measurement
1.2 Theoretical background
1.2.1 Fracture mechanics
1.2.2 Effective Medium Theory
1.2.3 Wing crack model
1.2.4 Subcritical crack growth
1.2.5 Stress-dependent permeability
1.2.6 Construction of a nonlinear diffusion equation
Chapter Ⅱ Physical and Mechanical Properties of Thermally Cracked Andesite Under Pressure
2.1 Introduction
2.2 Material & Methods
2.2.1 Materials
2.2.2 Experimental Methods
2.3 Results
2.3.1 Properties of samples heat-treated at different temperatures
2.3.2 Mineralogical effects of heat treatment on andesite
2.3.3 Tri-axial deformation of non-heat-treated andesite and heat-treated andesite
3.3.4 Ultrasonic velocity evolution of heat-treated andesite
2.4 Discussion
2.4.1 Effect of the heat treatment on the crack density
2.4.2 Effect of heat treatment on the microstructure: partial melting
2.4.3 Effect of heat treatment on mechanical strength
2.5 Conclusions and Perspectives
2.6 Appendix
Chapter Ⅲ Influence of Hydrothermal Alteration on The Elastic Behavior and Failure of Heat-Treated Andesite from Guadeloupe
3.1 Introduction
3.2 Material and methods
3.2.1 Starting material, heat-treatment and artificial alteration
3.2.2 Characterization of mineral sand chemical contents
3.2.3 Petrophysical properties
3.2.4 Experimental Apparatus
3.3 Results
3.3.1 Evolution of mineralogy with heat-treatment and alteration
3.3.2 Evolution of petrophysical properties with heat-treatment and alteration
3.3.3 Evolution of the elastic behaviour under hydrostatic stress with heat-treatment and alteration
3.3.4 Evolution of the mechanical behaviour during triaxial loading and failure with heat-treatment and alteration
3.4 Discussion
3.4.1 Alteration, porosity and density
3.4.2 Can smectite precipitation in cracks explain the mechanical behaviour?
3.4.3 Modelisation
3.4.4 Implications
3.5 Conclusion
Chapter Ⅳ Fluid-Injection Induced Rupture in Thermally Cracked Andesite at Laboratory Scale
4.1 Introduction
4.2 Material & Methods
4.2.1 Materials
4.2.2 Experiment Methods
4.3. Results
4.3.1 Mechanical properties of heat-treated andesite under hydrostatic loading
4.3.2 Differential loading of heat-treated andesite sample under saturated condition.
4.3.3 Fluid injection induced rupture on heat-treated andesite sample
4.4 Discussion
4.4.1 Crack density inverted from hydrostatic loading under dry condition
4.4.2 Aspect ratio/crack length/crack aperture inverted from hydro-loading under saturated conditions
4.4.3 Fluid injection into heat treated saturated andesite sample
4. 5 Conclusions
Chapter Ⅴ Permeability Evolution and Its Effect on Fluid Pressure Temporal Spatial Distribution during Fluid Injection
5.1 Introduction
5.2 Methodology
5.2.1 Sample preparation
5.2.2 Experiment apparatus
5.2.3 Optical Fibers
5.3 Results
5.3.1 Fluid pressure temporal spatial distribution
5.3.2 Permeability variation space & time
5.3.3 A clear heterogeneity of crack development (CT images)
5.4 Discussion
5.4.1 boundary condition
5.4.2 Equation setup
5.4.3 Solution of pore pressure at different positions and time
5.5 Conclusions
Conclusions
References .
