Fuyong Yan

Physical constraints on c13 and δ for transversely isotropic hydrocarbon source rocks

Based on the theory of anisotropic elasticity and observation of static mechanic measurement of transversely isotropic hydrocarbon source rocks or rock-like materials, we reasoned that one of the three principal Poisson’s ratios of transversely isotropic hydrocarbon source rocks should always be greater than the other two and they should be generally positive. From these relations, we derived tight physical constraints on c13, Thomsen parameter δ, and anellipticity parameter η. Some of the published data from laboratory velocity anisotropy measurement are lying outside of the constraints. We analysed that they are primarily caused by substantial uncertainty associated with the oblique velocity measurement. These physical constraints will be useful for our understanding of Thomsen parameter δ, data quality checking, and predicting δ from measurements perpendicular and parallel to the symmetrical axis of transversely isotropic medium. The physical constraints should also have potential application in anisotropic seismic data processing.

Modeling of effective pressure effect on porous reservoir rocks

Summary Effective pressure effect on porous reservoir formation is one of the most important factors contributing to time-lapse seismic attribute changes. Our research shows that the existing commonly used models tend to overestimate effective pressure effect at high effective pressure, which might cause significant misinterpretation of 4D seismic data. Based on analysis of a large quantity of lab data, a new model that is simpler and has clearer physical meaning was brought up in this study. This new model should be sufficient to describe the effective pressure effect on various porous reservoir rocks.

Characterizing the effect of elastic interactions on the effective elastic properties of porous, cracked rocks

Elastic interactions between pores and cracks reflect how they are organized or spatially distributed in porous rocks. The principle goal of this paper is to understand and characterize the effect of elastic interactions on the effective elastic properties. We perform finite element modelling to quantitatively study how the spatial arrangement of inclusions affects stress distribution and the resulting overall elasticity. It is found that the stress field can be significantly altered by elastic interactions. Compared with a non-interacting situation, stress shielding considerably stiffens the effective media, while stress amplification appreciably reduces the effective elasticity. We also demonstrate that the T-matrix approach, which takes into account the ellipsoid distribution of pores or cracks, can successfully characterize the competing effects between stress shielding and stress amplification. Numerical results suggest that, when the concentrations of cracks increase beyond the dilute limit, the single parameter crack density is not sufficient to characterize the contribution of the cracks to the effective elasticity. In order to obtain more reliable and accurate predictions for the effective elastic responses and seismic anisotropies, the spatial distribution of pores and cracks should be included. Additionally, such elastic interaction effects are also dependent on both the pore shapes and the fluid infill.

Theoretical validation of fluid substitution by Hashin-Shtrikman bounds

Summary In this study, we find that variation of Hashin-Shtrikman bounds caused by pore fluid change is governed by the Biot-Gassmann theory. Also, we have shown that it is generally valid to assume that the relative position of the effective moduli of a rock within the Hashin-Shtrikman bounds is not affected by pore fluid change. Thus HashinShtrikman bounds can be used as a valid fluid substitution tool. Comparing with Gassmann fluid substitution, the velocity predicted by Hashin-Shtrikman bounds generally fits better with the measured data since part of the dispersion is included, and it can be used as a more general pore infill substitution tool.

Practical and robust experimental determination of c 13 and Thomsen parameter δ: Robust experimental determination of δ

We analysed the complications in laboratory velocity anisotropy measurement on shales. There exist significant uncertainties in the laboratory determination of c13 and Thomsen parameter δ. These uncertainties are primarily related to the velocity measurement in the oblique direction. For reliable estimation of c13 and δ, it is important that genuine phase velocity or group velocity be measured with minimum uncertainty. The uncertainties can be greatly reduced if redundant oblique velocities are measured. For industrial applications, it is impractical to make multiple oblique velocity measurements on multiple core plugs. We demonstrated that it is applicable to make multiple genuine oblique group velocity measurements on a single horizontal core plug. The measurement results show that shales can be classified as a typical transversely isotropic medium. There is a coupling relation between c44 and c13 in determining the directional dependence of the seismic velocities. The quasi-P-wave or quasi-S-wave velocities can be approximated by three elastic parameters.We analysed the complications in laboratory velocity anisotropy measurement on shales. There exist significant uncertainties in the laboratory determination of c13 and Thomsen parameter δ. These uncertainties are primarily related to the velocity measurement in the oblique direction. For reliable estimation of c13 and δ, it is important that genuine phase velocity or group velocity be measured with minimum uncertainty. The uncertainties can be greatly reduced if redundant oblique velocities are measured. For industrial applications, it is impractical to make multiple oblique velocity measurements on multiple core plugs. We demonstrated that it is applicable to make multiple genuine oblique group velocity measurements on a single horizontal core plug. The measurement results show that shales can be classified as a typical transversely isotropic medium. There is a coupling relation between c44 and c13 in determining the directional dependence of the seismic velocities. The quasi-P-wave or quasi-S-wave velocities can be approximated by three elastic parameters.

Effect of pore geometry on Gassmann fluid substitution

Although there is no assumption of pore geometry in derivation of Gassmann’s equation, the pore geometry is in close relation with hygroscopic water content and pore fluid communication between the micropores and the macropores. The hygroscopic water content in common reservoir rocks is small, and its effect on elastic properties is ignored in the Gassmann theory. However, the volume of hygroscopic water can be significant in shaly rocks or rocks made of fine particles; therefore, its effect on the elastic properties may be important. If the pore fluids in microspores cannot reach pressure equilibrium with the macropore system, assumption of the Gassmann theory is violated. Therefore, due to pore structure complexity, there may be a significant part of the pore fluids that do not satisfy the assumption of the Gassmann theory. We recommend that this part of pore fluids be accounted for within the solid rock frame and effective porosity be used in Gassmann’s equation for fluid substitution. Integrated study of ultrasonic laboratory measurement data, petrographic data, mercury injection capillary pressure data, and nuclear magnetic resonance T2 data confirms rationality of using effective porosity for Gassmann fluid substitution. The effective porosity for Gassmann’s equation should be frequency dependent. Knowing the pore geometry, if an empirical correlation between frequency and the threshold pore-throat radius or nuclear magnetic resonance T2 could be set up, Gassmann’s equation can be applicable to data measured at different frequencies. Without information of the pore geometry, the irreducible water saturation can be used to estimate the effective porosity.

Reply to Joel Sarout’s comment on “Physical constraints on c13 and δ for transversely isotropic hydrocarbon source rocks”

We thank Joel Sarout for his perspective reading of our paper (Sarout 2016). First, we want to state explicitly that the physical constraints on c13 are not theoretical constraints; they are heuristic constraints based on observation of laboratory static measurement and physical intuition concerning the explanation of the behavior of a certain amount of hydrocarbon source rocks, to the author’s knowledge. As the title suggests, they only applied to hydrocarbon source rocks whose elastic properties can be described by transverse isotropy. This point is also emphasized in the discussion part of our paper.

Pore Aspect Ratio Spectrum Inversion from Ultrasonic Measurements and Its Application

We have conducted simultaneous ultrasonic velocity and pore volume change measurements on a carbonate rock sample. By including of pressure dependent porosity data, we have improved Cheng’s pore aspect ratio spectrum inversion methodology and made the inverted pore aspect ratio spectrum more realistic. Tang’s unified velocity dispersion and attenuation model is modified and extended to poroelastic media with complex pore structure under undrained condition. Using improved pore aspect ratio spectra inversion methodology and modified Tang’s model, we have explored the potential application of pore aspect ratio spectrum in prediction of seismic wave dispersion and attenuation.

Some consideration about fluid substitution without shear wave velocity

Summary When S-wave velocity is absent, approximate Gassmann equation using P-wave modulus is recommended by Mavko (1995) to calculate the fluid saturation effects. Using both lab data and log data, our study shows that the approximate Gassmann equation might introduce significant error in fluid saturation effect prediction except for unconsolidated rocks. Using S-wave velocity estimated by existing techniques, with same input parameters, the exact Gassmann equation should provide more reliable estimation of fluid saturation effect than that predicted by approximate Gassmann equation.

Study of Potential Gas Eruption By Seismic Survey In Lake Kivu

We have investigated potential risk of gas eruption by air gun operation in a seismic survey on the Lake Kivu, East Africa, which contains a huge amount of gas dissolved in the water zone below a depth of 260 m. Measured data suggest that gas nucleation and bubble growth in a large body of water require super-saturated condition (pressure significantly lower than the bubble pressure (B. P.) and significant long relaxation time (> 1 second). Initial homogeneous gas nucleation in water enhances viscous behavior of gas exhaustion from a large body of water. Therefore, a seismic survey on the lake surface will not likely trigger gas outburst from the Lake Kivu.