Elastic properties of carbonates : measurements and modelling
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This thesis is a multi-scale study of carbonate rocks, from the nanoscale and digital rock investigations to the imaging studies of carbonate reservoir analogues. The essential links between these extremes are the carbonate physical properties and rock-physics models, which are investigated here through the modelling of ultrasonic wave propagation in carbonate samples, focusing on elastic stress sensitivities, saturating fluids and porosity models. Validation of Gassmann fluid substitution in carbonates is also investigated using correlations between core and well log measurements.On the nanoscale, we use the nanoindentation technique in an oolitic limestone to directly measure the calcite Young modulus and derive bulk and shear moduli. We have found a large variation in the calcite bulk modulus, from 56 to 144 GPa. The high values obtained in some oolite rings were interpreted as genetically associated with biologically generated calcite (biocalcite). There are many measurements that achieve these values in brachiopod shells, but none in oolitic limestone. We associate the smaller values with microporosity, which is undetectable by our microCT or even SEM images. On the microscale we use the X-ray microCT images. From these images we can compute oolite elastic parameters using finite difference methods (FDM). In this oolite sample, calcite was segmented in two distinct phases. Nanoindentation provides the elastic parameters for each phase. The results of the modelling are compared with ultrasonic measurements on dry samples.To compute the properties of rocks on fluid-saturated samples, one needs to use fluid substitution methods, such as Gassmann’s equations. However, the applicability of Gassmann’s equations and the fluid substitution technique to carbonate rocks is still a subject of debate. Here we compare the results of fluid substitution applied to dry core measurements against sonic log data. The 36 meters of continuously sampled carbonates data, comes from a cretaceous reservoir buried at a depth of 5000 metres in the Santos Basin, offshore Brazil. Compressional and shear velocities, density and porosity were measured in 50 samples covering the entire interval. We obtain good agreement between the elastic properties obtained from core and log measurements. This shows that Gassmann’s fluid substitution is applicable to these carbonates, at least at sonic log frequencies.Carbonate microstructure is investigated using the stress dependency of shear and compressional wave velocities according to the dual porosity model of Shapiro (2003). The model assumes that the pore space contains two types of pores: stiff and compliant pores. Understanding the parameters of this model for different rocks is important for constraining stress effects in these rocks. The results for a carbonate dataset from the Santos Basin show a good correlation between compliant porosity and dry bulk modulus, total porosity and density for 29 samples of carbonates from the Santos Basin. The correlations seem to be different for different facies distribution, with different trends for mudstone facies and grainstone and rudstone facies. We also performed the same analysis using 66 samples of sandstones of diverse origins (Han et al., 1986): a good correlation appears between compliant porosity and the dry bulk modulus for all samples.If we correlate only the 7 samples from Fontainebleau sandstone, a good correlation also appears between total and compliant porosity. This analysis shows that the correlation is facies dependent also for sandstones.While Gassmann’s equations may be valid for low frequencies, they are not applicable at higher frequencies, where squirt dispersion is significant. We propose a workflow to model wave dispersion and attenuation due to the squirt flow using the geometrical parameters of the pore space derived from the stress dependency of elastic moduli on dry samples. Our analysis shows the dispersion is controlled by the squirt flow between equant pores and intermediate pores (with aspect ratios between 10-3 - 2·10-1). Such intermediate porosity is expected to close at confining pressures of between 200-2000 MPa. We also infer the magnitude of the intermediate porosity and its characteristic aspect ratio. Substituting these parameters into the squirt model, we have computed elastic moduli and velocities of the water-saturated rock and compared these predictions against laboratory measurements of these velocities.The agreement is good for a number of clean sandstones, but much worse for a broad range of shaley sandstones. Our predictions show that dispersion and attenuation caused by the squirt flow between compliant and stiff pores may occur in the seismic frequency band. Confirmation of this prediction requires laboratory measurements of elastic properties at these frequencies.The carbonate system of Telegraph Station, Shark Bay (WA), is a unique environment where coquinas, stromatolites and microbial mats are linked: an excellent analogue to carbonate pre-salt offshore Brazil. We acquired 7.5 km of GPR data and high resolution seismic data in the coquina ridges. They are composed by calcite shells deposited by cyclones, which show excellent high resolution GPR images, being a low loss dielectric medium. Three classes of coquinas were mapped: tabular layers, convex-up crest and washover fan. From the correlation of 14C dating of 50 samples and the mapped events we can estimate an average rate of one event every 13 years. From our interpretation the Holocene regression is continuous but not homogeneous. Carbonate dissolution features, faults, trends and discontinuities were mapped. Analysis of these features helps us understand reservoir porosity and permeability distribution in carbonate deposits, and can be used to constrain reservoir properties in pre-salt carbonates in Brazilian basins.
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