Stanislav Glubokovskikh

Effects of fracture intersections on seismic dispersion: theoretical predictions versus numerical simulations

ABSTRACT The detection and characterisation of domains of intersecting fractures are important goals in several disciplines of current interest, including exploration and production of unconventional reservoirs, nuclear waste storage, CO2 sequestration, and groundwater hydrology, among others. The objective of this study is to propose a theoretical framework for quantifying the effects of fracture intersections on the frequency‐dependent elastic properties of fluid‐saturated porous and fractured rocks. Three characteristic frequency regimes for fluid pressure communication are identified. In the low‐frequency limit, fractures are in full pressure communication with the embedding porous matrix and with other fractures. Conversely, in the high‐frequency limit, fractures are hydraulically isolated from the matrix and from other fractures. At intermediate frequencies, fractures are hydraulically isolated from the matrix porosity but can be in hydraulic communication with each other, depending on whether fracture sets are intersecting. For each frequency regime, the effective stiffness coefficients are derived using the linear‐slip theory and anisotropic Gassmann equations. Explicit mathematical expressions for the two characteristic frequencies that separate the three frequency regimes are also determined. Theoretical predictions are then applied to two synthetic 2D samples, each containing two orthogonal fracture sets: one with and another without intersections. The resulting stiffness coefficients, Thomsen‐style anisotropy parameters, and the transition frequencies show good agreement with corresponding numerical simulations. The theoretical results are applicable not only to 2D but also to 3D fracture systems and are amenable to being employed in inversion schemes designed to characterise fracture systems.

A dual-porosity scheme for fluid/solid substitution

Estimating the impact of solid pore fill on effective elastic properties of rocks is important for a number of applications such as seismic monitoring of production of heavy oil or gas hydrates. We develop a simple model relating effective seismic properties of a rock saturated with a liquid, solid, or viscoelastic pore fill, which is assumed to be much softer than the constituent minerals. A key feature of the model is division of porosity into stiff matrix pores and compliant crack-like pores because the presence of a solid material in thin voids stiffens the rock to a much greater extent than its presence in stiff pores. We approximate a typical compliant pore as a plane circular interlayer surrounded by empty pores. The effect of saturation of the stiff pores is then taken into account using generalized Gassmann’s equations. The proposed model provides a good fit to measurements of the shear stiffness and loss factor of the Uvalde heavy-oil rock at different temperatures and frequencies. When the pore fill is solid, the predictions of the scheme are close to the predictions of the solid squirt model recently proposed by Saxena and Mavko. At the same time, the present scheme also gives a continuous transition to the classic Gassmann’s equations for a liquid pore fill at low frequencies and the squirt theory at high frequencies.

How rough sea affects marine seismic data and deghosting procedures

Most seismic processing algorithms generally consider the sea surface as a flat reflector. However, acquisition of marine seismic data often takes place in weather conditions where this approximation is inaccurate. The distortion in the seismic wavelet introduced by the rough sea may influence (for example) deghosting results, as deghosting operators are typically recursive and sensitive to the changes in the seismic signal. In this paper, we study the effect of sea surface roughness on conventional (5–160 Hz) and ultra-high-resolution (200–3500 Hz) single-component towed-streamer data. To this end, we numerically simulate reflections from a rough sea surface using the Kirchhoff approximation. Our modelling demonstrates that for conventional seismic frequency band sea roughness can distort results of standard one-dimensional and two-dimensional deterministic deghosting. To mitigate this effect, we introduce regularisation and optimisation based on the minimum-energy criterion and show that this improves the processing output significantly. Analysis of ultra-high-resolution field data in conjunction with modelling shows that even relatively calm sea state (i.e., 15 cm wave height) introduces significant changes in the seismic signal for ultra-high-frequency band. These changes in amplitude and arrival time may degrade the results of deghosting. Using the field dataset, we show how the minimum-energy optimisation of deghosting parameters improves the processing result.

Time-lapse full waveform inversion of vertical seismic profile data: Workflow and application to the CO2CRC Otway project

Vertical seismic profile (VSP) is one of the technologies for monitoring hydrocarbon production and CO2 geosequestration. However quantitative interpretation of time-lapse VSP is challenging due to its irregular distribution of source-receiver offsets. One way to overcome this challenge is to use full waveform inversion (FWI), which does not require regular offsets. We present a workflow of elastic FWI applied to offset vertical seismic profile data for the purpose of identification and estimation of time-lapse changes introduced by injection of 15,000 tonnes of CO2-rich gas mixture at 1.5 km depth. Application of this workflow to both synthetic and field data shows that elastic FWI is able to detect and quantify the time-lapse anomaly in P wave velocity with the magnitude of 100-150 m/s.

Optimal bounds for attenuation of elastic waves in porous fluid-saturated media

Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, the bounds are curves in the complex plane. From the general expressions for bounds of effective moduli of viscoelastic mixtures, it is shown that effective bulk and shear moduli of such mixtures must lie between the real axis and a semicircle in the upper half-plane connecting formal lower and upper Hashin-Shtrikman bounds of the mixture of the solid and inviscid fluid of the same compressibility as the Newtonian fluid. Furthermore, it is shown that the bounds on the effective complex bulk and shear moduli of the mixture are optimal; that is, the moduli corresponding to any point on the bounding curves can be attained by the Hashin sphere assemblage penetrated by a random distribution of thin cracks. The results are applicable to a variety of solid/fluid mixtures such as fluid-saturated porous materials and particle suspensions.

A triple porosity scheme for fluid/solid substitution: theory and experiment: Triple porosity scheme for fluid/solid substitution

Quantifying the effects of pore-filling materials on elastic properties of porous rocks is of considerable interest in geophysical practice. For rocks saturated with fluids, the Gassmann equation is proved effective in estimating the exact change in seismic velocity or rock moduli upon the changes in properties of pore infill. For solid substance or viscoelastic materials, however, the Gassmann theory is not applicable as the rigidity of the pore fill (either elastic or viscoelastic) prevents pressure communication in the pore space, which is a key assumption of the Gassmann equation. In this paper, we explored the elastic properties of a sandstone sample saturated with fluid and solid substance under different confining pressures. This sandstone sample is saturated with octadecane, which is a hydrocarbon with a melting point of 28°C, making it convenient to use in the lab in both solid and fluid forms. Ultrasonically measured velocities of the dry rock exhibit strong pressure dependency, which is largely reduced for the filling of solid octadecane. Predictions by the Gassmann theory for the elastic moduli of the sandstone saturated with liquid octadecane are consistent with ultrasonic measurements, but underestimate the elastic moduli of the sandstone saturated with solid octadecane. Our analysis shows that the difference between the elastic moduli of the dry and solid-octadecane-saturated sandstone is controlled by the squirt flow between stiff, compliant, and the so-called intermediate pores (with an aspect ratio larger than that of compliant pore but much less than that of stiff pores). Therefore, we developed a triple porosity model to quantify the combined squirt flow effects of compliant and intermediate pores saturated with solid or viscoelastic infill. Full saturation of remaining stiff pores with solid or viscoelastic materials is then considered by the lower embedded bound theory. The proposed model gave a reasonable fit to the ultrasonic measurements of the elastic moduli of the sandstone saturated with liquid or solid octadecane. Comparison of the predictions by the new model to other solid substitution schemes implied that accounting for the combined effects of compliant and intermediate pores is necessary to explain the solid squirt effects.

Full Waveform Inversion of Time-lapse Offset VSP Data - CO2CRC Otway Project Case Study

Summary Vertical Seismic Profile (VSP) is a useful tool for time-lapse monitoring. We conduct elastic 2D Full Waveform Inversion (FWI) on offset Vertical Seismic Profile (VSP) data to detect and quantify the time-lapse anomaly introduced by the CO2 geosequestration. Two datasets are being studied: a 2D synthetic dataset and the field dataset acquired during the Stage 2C of the CO2CRC Otway project. FWI proves capable of detecting the time-lapse anomaly on both datasets, however, the strength of the anomaly in the field data inversion results is lower than expected from theoretical predictions. We attribute this to 3D effects, which are not taken into account. In the end, FWI proves to be an instrument that fits the monitoring problem well. The inversion of the monitor dataset is significantly quicker than the baseline inversion, which enables the time-lapse anomaly identification shortly after the data acquisition.

Estimation of Intrinsic Q in Finely-layered Media by Wavefield Inversion of VSP Data - Australian North West Shelf Case-study

Seismic waves propagating through attenuative subsurface exhibit amplitude loss and distortion of frequency spectra. Proper description of attenuation process is required to compensate for these effects. Moreover, inelastic attenuation contains information on rock properties and could be utilized in attribute analysis for subsurface characterization. We propose to quantify inelastic (intrinsic) attenuation in horizontally-layered media by wavefield inversion of VSP data with respect to effective interval Q-factors. Impact of short-path multiples in finely-layered subsurface, i.e. scattering at stratigraphic boundaries, and other interference effects are taken into account by forward simulation over a high-resolution elastic model acquired from the well logs (resolution of 1.5m). We present a case study of approximate-zero-offset vertical seismic profile data from Wheatstone offshore site (Northern Shelf of Western Australia). First we describe the algorithm of 1D waveform Q-inversion. Then we validate it on the full-wave synthetics computed for the field survey geometry using a Global Matrix approach (OASES MIT code). Finally, we discuss the results of the Q-inversion application to the field ZVSP dataset versus Q-estimates by Centroid Frequency Shift method.

Double Shell As a Directly Solvable Model of a Micro-inhomogeneous Poroelastic Medium

We consider pore pressure and fluid compressibility effects on rock properties in the case of inhomogeneous solid matrix. For this purpose we propose a model amenable to exact analytical . It consists of similar double-layered spherical shells with a fluid inside. We show how could be realized different values of effective stress coefficient for porosity, give clear interpretation of it. In addition we validate Brown-Korringa approach. Its predictions exactly coincide with the exact solution. At the same time some new theories of poroelasticity gives predictions deviating from the double-shell model results. These theories claim that the porosity pertutbation must be incorporated explicitly in the theory of porous media deformation. We give some possible explanation why this conception is not correct.