Beatriz Quintal

Quasi‐static finite element modeling of seismic attenuation and dispersion due to wave‐induced fluid flow in poroelastic media

[1]xa0The finite element method is used to solve Biots equations of consolidation in the displacement-pressure (u − p) formulation. We compute one-dimensional (1-D) and two-dimensional (2-D) numerical quasi-static creep tests with poroelastic media exhibiting mesoscopic-scale heterogeneities to calculate the complex and frequency-dependent P wave moduli from the modeled stress-strain relations. The P wave modulus is used to calculate the frequency-dependent attenuation (i.e., inverse of quality factor) and phase velocity of the medium. Attenuation and velocity dispersion are due to fluid flow induced by pressure differences between regions of different compressibilities, e.g., regions (or patches) saturated with different fluids (i.e., so-called patchy saturation). Comparison of our numerical results with analytical solutions demonstrates the accuracy and stability of the algorithm for a wide range of frequencies (six orders of magnitude). The algorithm employs variable time stepping and an unstructured mesh which make it efficient and accurate for 2-D simulations in media with heterogeneities of arbitrary geometries (e.g., curved shapes). We further numerically calculate the quality factor and phase velocity for 1-D layered patchy saturated porous media exhibiting random distributions of patch sizes. We show that the numerical results for the random distributions can be approximated using a volume average of Whites analytical solution and the proposed averaging method is, therefore, suitable for a fast and transparent prediction of both quality factor and phase velocity. Application of our results to frequency-dependent reflection coefficients of hydrocarbon reservoirs indicates that attenuation due to wave-induced flow can increase the reflection coefficient at low frequencies, as is observed at some reservoirs.

Low-frequency reflections from a thin layer with high attenuation caused by interlayer flow

The 1D interlayer-flow (or White’s) model is based on Biot’s theory of poroelasticity and explains low-frequency seismic wave attenuation in partially saturated rocks by wave-induced fluid flow between two alternating poroelastic layers, each saturated with a different fluid. We have developed approximate equations for both the minimum possible value of the quality factor, Q , and the corresponding fluid saturation for which Q is minimal. The simple approximate equations provide a better insight into the dependence of Q on basic petrophysical parameters and allow for a fast assessment of the minimal value of Q . The approximation is valid for a wide range of realistic petrophysical parameter values for sandstones partially saturated with gas and water, and shows that values of Q can be as small as two. We ap-plied the interlayer-flow model to study the reflection coefficient of a thin (i.e., between 6 and 11 times smaller than the incident wavelength) layer that is partially saturated with gas and water. ...

Impact of fluid saturation on the reflection coefficient of a poroelastic layer

The impact of changes in saturation on the frequencydependent reflection coefficient of a partially saturated layer was studied. Seismic attenuation and velocity dispersion in partially saturated (i.e., patchy saturated) poroelastic media were accounted for by using the analytical solution of the 1D White’s model for wave-induced fluid flow. White’s solution was applied in combination with an analytical solution for the normal-incidence reflection coefficient of an attenuating layer embedded in an elastic or attenuating background medium to investigate the effects of attenuation, velocity dispersion, and tuning on the reflection coefficient. Approximations for the frequency-dependent quality factor, its minimum value, and the frequency at which the minimum value of the quality factor occurs were derived. The approximations are valid for any two alternating sets of petrophysical parameters. An approximation for the normal-incidence reflection coefficient of an attenuating thin (compared to the wavelength) layer was also derived. This approximation gives insight into the influence of contrasts in acoustic impedance and/or attenuation on the reflectivity of a thin layer. Laboratory data for reflections from a water-saturated sand layer and from a dry sand layer were further fit with petrophysical parameters for unconsolidated sand partially saturated with water and air. The results showed that wave-induced fluid flow can explain low-frequency reflection anomalies, which are related to fluid saturation and can be observed in seismic field data. The results further indicate that reflection coefficients of partially saturated layers (e.g., hydrocarbon reservoirs) can vary significantly with frequency, especially at low seismic frequencies where partial saturation may often cause high attenuation.

Synchrotron-based X-ray tomographic microscopy for rock physics investigations

ABSTRACTSynchrotron radiation X-ray tomographic microscopy is a nondestructive method providing ultra-high-resolution 3D digital images of rock microstructures. We describe this method and, to demonstrate its wide applicability, we present 3D images of very different rock types: Berea sandstone, Fontainebleau sandstone, dolomite, calcitic dolomite, and three-phase magmatic glasses. For some samples, full and partial saturation scenarios are considered using oil, water, and air. The rock images precisely reveal the 3D rock microstructure, the pore space morphology, and the interfaces between fluids saturating the same pore. We provide the raw image data sets as online supplementary material, along with laboratory data describing the rock properties. By making these data sets available to other research groups, we aim to stimulate work based on digital rock images of high quality and high resolution. We also discuss and suggest possible applications and research directions that can be pursued on the basis o...

Seismic Low-frequency Anomalies In Multiple Reflections From Thinly-layered Poroelastic Reservoirs

Seismic low-frequency (1-10 Hz) anomalies in multiple reflections can be related to hydrocarbon-saturated rocks with high values of attenuation. We study reflections in the low-frequency range from a poroelastic layered reservoir embedded in an elastic background medium, using Biot’s theory and 1D finite-difference modeling of wave propagation. In this model, the reservoir has a constant thickness and consists of a variable number of alternating pairs of fluid-saturated layers. For few layers (coarse layers), the reflections from the reservoir are identical when we compare results for poroelastic and equivalent elastic layers. For many layers (thin layers), the results are considerably different. When we choose, for example, the impedance of the background medium similar to the elastic Backus-averaged impedance of the reservoir, the reflections disappear in the elastic case, while in the poroelastic they become significant, due to velocity dispersion caused by wave-induced viscous fluid flow and attenuation between layers (interlayer-flow model).

Detection of a viscoelastic inclusion using spectral attributes of the quasi-stationary seismic surface response

This study investigates the feasibility of detecting a viscoelastic inclusion in the subsurface by analyzing the seismic wavefield at the mediums surface. A synthetic quasi-stationary wavefield is generated by random body wave sources at depth. The seismic response at the surface is then analyzed in the frequency domain for lateral variations of two specific spectral attributes. The results show that an inclusion with anomalous attenuation properties can create spectral attribute anomalies in the quasi-stationary background wavefield at the surface. This is even the case in the presence of a shallow low velocity layer. The study provides physical theoretical support for the contention that spectral anomalies in the ambient background wavefield can occur due to anomalously high attenuation properties of hydrocarbon reservoirs.

Synchrotron-based X-ray Tomographic Microscopy for Rock Physics Investigations

Synchrotron radiation X-ray tomographic microscopy is a non-destructive method providing ultra-high-resolution 3D digital images of rock microstructures. We describe this method and, to demonstrate its wide applicability, present 3D images of very different rock types: Berea sandstone, Fontainebleau sandstone, dolomite, calcitic dolomite, and three-phase magmatic glasses. For some samples, full and partial saturation scenarios are considered using oil, water, and air. The rock images precisely reveal the 3D rock microstructure, the pore space morphology, and the interfaces between fluids saturating the same pore. We provide the raw image data sets as online supplementary material, along with laboratory data describing the rock properties. By making these data sets available to other research groups, we aim to stimulate work based on digital rock images of high quality and high resolution. We also discuss and suggest possible applications and research directions that can be pursued on the basis of our data.

Effects of permeability barriers and pore fluids on S-wave attenuation

We numerically perform stress relaxation experiments using Biot’s equations for consolidation of poroelastic media to study seismic attenuation of S-waves caused by wave-induced fluid flow. Our model consists of periodically distributed mesoscopic-scale circular heterogeneities with lower porosity and permeability than the background, which contains 80% of the total pore space of the medium. This model represents a hydrocarbon reservoir, where the background is fully saturated with oil or gas (or water, for comparison), and the low porosity heterogeneities are always saturated with water. Varying the dry bulk and shear moduli in the medium, a tendency is observed in the relative behavior of the S-wave attenuation among the different saturation scenarios. First, in the gas-saturated media the S-wave attenuation is very low and much lower than in the oil-saturated or in the fully water-saturated media. Second, at low frequencies the S-wave attenuation is significantly higher in the oil-saturated media than in the fully water-saturated media. Additionally, we observed that impermeable barriers in the background can cause a significant increase in S-wave attenuation. Based on the theory of wave-induced fluid flow, our results suggest that S-wave attenuation could be used as an indicator of fluid content and permeability changes in a reservoir.

S-wave Attenuation Caused By Wave-induced Fluid Flow

We study seismic wave attenuation (1/Q) caused by the physical mechanism of wave-induced fluid flow. Relaxation experiments are numerically performed to solve Biot’s equations of consolidation. The experiments yield stress-strain relations used in a post-processing step to calculate the complex moduli of 2D poroelastic media with mesoscopic-scale heterogeneities. Attenuation is then determined from the complex moduli. In our model, the rock is represented by a medium containing circular heterogeneities of much lower porosity and permeability than the homogeneous background. The background contains 80% of the total pore space in the medium and is fully saturated with oil, gas, or water, while the heterogeneities are always fully saturated with water. We observe that the S-wave attenuation in the medium with 80% of oil is much higher than in the one with 80% of gas, and at low seismic frequencies (< 10 Hz), the S-wave attenuation in the medium with 80% of oil is also much higher than in the one with 100% of water. This occurs because the maximum value of the S-wave attenuation is shifted to lower frequencies with increasing fluid viscosity. Additionally, we observe that S-wave attenuation can be high (e.g., Q = 16) when the porous and permeable background has also a much more compliant solid frame than the low-porosity, low-permeability heterogeneities.