##### Research in Theoretical Rock Physics is currently ongoing in the following areas:

- Seismic signatures of patchy saturation
- Modelling of attenuation and dispersion due to squirt flow in rocks saturated with viscous and viscoelastic fluid
- Modelling elastic properties of fractured reservoirs
- Modelling stress-dependent properties of rocks

##### Seismic Signatures of Patchy Saturation

**A major effort of the group is focused on the study of the effects of patchy saturation on seismic signatures.**

This effort is partially funded by the ARC Discovery Project Seismic response of partially saturated petroleum reservoir zones: towards quantitative recovery monitoring.

The main objective is to quantify the effect of random spatial distribution of fluid patches in hydrocarbon reservoirs. The approach is based on the general theory of heterogeneous poro-elasticity developed by CRGC over the last decade. The aim of the current effort is to build a general model for elastic properties of partially saturated rock with a given statistical distribution of fractures and with arbitrary contrast between the properties of the two fluids (e.g., gas and liquid).

We are also performing a series of fluid injection experiments with X-ray Computer Tomography and ultrasonic control to validate the theoretical findings. The effect of capillary forces on the elastic properties of partially saturated rocks is also being explored. On field scale, the results of theoretical research have been applied to time-lapse logs acquired at the Nagaoka CO2 storage site.

**Researcher(s):**

Prof. Boris Gurevich

Dr. Stanislav Glubokovskikh

Prof. Maxim Lebedev

##### Modelling of attenuation and dispersion due to squirt flow in rocks saturated with viscous and viscoelastic fluid

**We have developed a new squirt flow model in which all parameters can be independently measured or estimated from measurements.**

The pore space of the rock is assumed to consist of stiff porosity and compliant (or soft) pores present at grain contacts. The effect of isotropically distributed soft pores is modelled by considering pressure relaxation in a disk-shaped gap between adjacent grains. This derivation gives the complex and frequency-dependent effective bulk and shear moduli of a rock, in which the soft pores are liquid-saturated and stiff pores are dry. The resulting squirt model is consistent with Gassmann’s and Mavko-Jizba equations at low and high frequencies, respectively. As expected, the dispersion and attenuation are the strongest at low effective stress and become much weaker at higher effective stress.

More recently we developed a much more general model, in which the pore fill can be fluid, solid or a viscoelastic substance. In this model a typical compliant pore is approximated by a plane circular interlayer surrounded by empty stiff pores. The effect of saturation of the stiff pores is then taken into account using generalised Gassmann’s equations. The proposed model is consistent with our earlier models for fluid saturated rocks and provides an accurate approximation for rocks saturated with a solid and viscoelastic substances such as heavy oils. The model has been tested using ultrasonic measurements on a sandstone sample saturated with octadecane in both liquid and solid form.

**Researchers:**

Dr. Stanislav Glubokovskikh

Prof. Boris Gurevich

##### Modelling Elastic Properties of Fractured Reservoirs

**A major effort of the rock physics group is directed towards modelling attenuation, dispersion and frequency dependent anisotropy of porous reservoirs permeated by aligned fractures.**

Over the last decade, this group has developed a methodology of fluid substitution in fractured reservoirs, which is based on the combination of anisotropic Gassmann equations and Schoenberg’s linear slip parameterisation of the effect of fractures on rock properties. Between 2003 and 2006, the group developed a model for attenuation and dispersion of P-waves propagating perpendicular to a periodic system of parallel planar fractures and validated this model with numerical simulations using a poroelastic extension of reflectivity method. These simulations helped to extend the attenuation/dispersion model to randomly spaced fractures and to oblique incidence.

The group developed a model for seismic attenuation and dispersion caused by the presence of sparsely distributed finite (penny-shaped and slit) fractures in the porous reservoirs. The model is based on the combination of Biot’s theory of poroelasticity with the ideas of a multiple scattering theory. The current effort in this area is focused on the deeper understanding of the implications of this theory and its extensions to:

- Oblique incidence;
- Shear waves;
- Higher fracture densities;
- Arbitrary aspect ratios.

While all of the above models are designed for a single set of aligned fractures, real reservoirs often contain multiple fracture sets. Moreover, similar phenomena (fluid flow between pores and fractures) lead to frequency dependent attenuation and dispersion in isotropic rocks with micro-cracks, compliant grain contacts, etc. These effects are being studied by extending the aligned fracture models to arbitrary angular distributions of fractures.

Recently these models have been extended to finite thickness and tested against numerical simulations

**Researcher(s):**

Dr. Stanislav Glubokovskikh

Prof. Boris Gurevich

##### Modelling stress-dependent properties of rocks

**Stress is one of the major causes of anisotropy in the earth and understanding it is important for imaging, reservoir characterisation and monitoring.**

There is a need to be able to distinguish stress-induced from fracture-induced anisotropy. In recent years, we have developed theoretical models of stress-induced anisotropy of rocks. We first considered an isotropic linearly elastic medium (porous or nonporous) permeated by a distribution of discontinuities with random (isotropic) orientation (such as randomly oriented compliant grain contacts or cracks). When this isotropic rock is subjected to a small compressive stress (isotropic or anisotropic), the number of cracks along a particular plane is reduced in proportion to the normal stress traction acting on that plane.

This effect is modelled using the Sayers-Kachanov noninteractive approximation. The model predicts that such an anisotropic crack closure yields elliptical anisotropy, regardless of the value of the ratio of the normal to shear compliance. It also predicts the ratio of Thomsen’s anisotropy parameters as a function of the compliance ratio and Poisson’s ratio of the unstressed rock. The model is tested using laboratory data. In addition, it has been extended to large stresses, and also to a general triaxial stress state (leading to orthotropic symmetry).

The results can potentially be used for differentiating between stress and fracture-induced anisotropy, and also for predicting P-wave anisotropy from S-wave anisotropy; the latter may be estimated from shear-wave splitting as measured by modern sonic logs or VSP.

**Researchers:**

Dr. Stanislav Glubokovskikh

Prof. Boris Gurevich