Second International Workshop on Rock Physics

The elastic response of a rock and its stress sensitivity are strongly affected by the presence of micro-cracks. Therefore a full characterization and quantification of cracks at the microscale is essential for understanding the rock physics response of rocks under stress. Yet there is no uniquely accepted method to precisely quantify the density and geometrical characteristics of such microstructural features. In this contribution we present results of quantitative analyses of 2D Scanning Electron Microscopy (SEM) images and 3D X-ray micro-tomograms performed on three samples of Carrara Marble artificially cracked by thermal shock. New semi-automatic workflows have been developed to perform these 2D and 3D analyses. The main outcome is the quantification of the micro-cracks’ average length, aspect ratio and density per unit surface (2D) or volume (3D). The results are consistent with the degree of thermal cracking artificially induced on the rock sample prior to the imaging/analysis procedure, i.e., more and wider/longer micro-cracks are measured on samples heated at higher temperature. The results of these quantitative microstructural analyses are also consistent with nuclear magnetic resonance (NMR) data independently acquired on the same samples saturated with water.

University of Southampton Waterfront Campus

Feasibility analysis of seismic monitoring of CO2 sequestration into a saline aquifer involves modelling changes of elastic properties of rocks caused by injection. To estimate the changes in elastic properties by CO2 saturation effects from reservoir simulations, the simulation grid has to be populated with elastic properties. Two workflows are compared regarding their predictions of changes in elastic properties. The comparison shows the importance of the dry rock bulk modulus in predictions of the time-lapse response and how geological information can help improve the estimation of this parameter.

Predicting seismic velocities in fluid-saturated rocks is commonly done using Gassmann equations. For anisotropic media, these equations are expressed in terms of stiffness or compliance tensors. To gain a more intuitive understanding on the impact of fluid on anisotropy, we express Gassmann equations in terms of Thomsen’s anisotropy parameters. Using the derived expressions for anisotropy parameters of fluid-saturated media, we analyse the effect of fluid on two anisotropy patterns, the one caused by aligned fractures embedded in an isotropic porous background and the stress-induced anisotropy pattern. By deriving an approximation of the anellipticity parameter η, we show that if the dry medium is elliptical, the saturated medium is also elliptical but only if the porosity is sufficiently large. This result can provide a way of differentiating between stress- and fracture-induced anisotropy.

In this study we start to look at the causes of electrical anisotropy within the earth. Well log data where both the vertical and horizontal resistivities have been measured is analysed. By exploring different cross plots we can determine those physical properties, such and clay volume, which drive the anisotropy. From this, rock physic models can be built using inclusion modelling.

Development of permeability estimation techniques based on digital image data by means of renormalization group approach (RGA) open the possibility to calculate degree of permeability anisotropy of rocks. In this paper, this technique is applied for three dimensional images obtained from X-Ray μCT (micro computed tomography) scanning devices. New renormalization schemes (NRS) developed by Karim and Krabbenhoft (2010), are also discussed. Experiment and simulation on resistor networks give very good agreement with RGA and NRS for two dimensional cases. Three dimensional models of resistor networks are however different. Calculation of effective permeability for all methods is influenced significantly by the size of smallest block.

An extension of a previously developed, rock physics, model is made that quantifies the relationship between the ductile fraction of a brittle/ductile binary mixture and the isotropic seismic reflection response. Making a weak scattering (Born) approximation and plane wave (eikonal) approximation, with a subsequent ordering according to the smallness of the angle of incidence, a linear singular value decomposition analysis is done to understand the stack weightings, number of stacks, and the type of stacks that will optimally estimate the two fundamental rock physics parameters. It is concluded that the full PP stack and the 'full' PS stack are the two optimal stacks needed to estimate the two rock physics parameters. They dominate over both the second order AVO 'gradient' stack and the higher order (4th order) PP stack.

Elastic wave velocities in rocks vary with stress due to the presence of discontinuities and microcracks within the rock. We analytically derive a model for seismic anisotropy caused by small triaxial stresses applied on a linearly isotropic elastic medium permeated by a distribution of cracks with random orientations. This model predicts ellipsoidal anisotropy and also expresses the ratios of Thomsen’s parameters ε⁄γ as a function of the compliance and Poisson’s ratios in the three orthogonal planes of symmetry. We apply this model to fully estimate the elasticity tensor from log or VSP data and infer P-wave anisotropy from S-wave anisotropy in an area where the anisotropy is known to result from anisotropy of stresses. Besides, this model could be used to differentiate stress-induced anisotropy from that caused by aligned fractures.

An oscillatory pore pressure method for simultaneous measurements of rock transport properties, such as intrinsic permeability and specific storage capacity, and summarize a laboratory setup, being developed for these purposes. The pore pressure pulsing method has been described before by many researchers, however we attempt to examine the relationship between a rock’s transport properties and oscillation parameters, such as amplitude and frequency.

The objective of this study is to describe the limitations of anisotropic rock physics modeling using Ridzki inequalities. Anisotropic rock physics modeling provides the link between seismic anisotropy and anisotropic properties of rocks. However, the limitations of anisotropic rock physics modelling are not well described in the literature. We compare isotropic and anisotropic rock physics models to demonstrate the limitations of anisotropic rock physics modeling. We described the limitations of anisotropic rock physics models by the restrictions of anisotropic seismic properties originally reported by the pioneer of seismic anisotropic modeling, Professor Maurice Ridzki. This study shows that difference between isotropic and anisotropic approximations are increased with increasing complexity of pore structure while isotropic and anisotropic approximations are equal when pore structures are assumed to be spherical. Limitations of anisotropic seismic properties suggest that the Self-Consistent Approximation (SCA) is valid for a maximum porosity of 14%, whereas Differential Effective Medium modeling (DEM) is valid for maximum porosity of 17% when the aspect ratio of the pores is 0.2. Furthermore, we introduce an anisotropic elastic constant which can be used to describe the difference between c12 and c13 in transversely isotropic media.