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

Geophysics ◽  
2011 ◽  
Vol 76 (2) ◽  
pp. N1-N12 ◽  
Author(s):  
Beatriz Quintal ◽  
Stefan M. Schmalholz ◽  
Yuri Y. Podladchikov
Keyword(s):  
Fluid Flow ◽  
Reflection Coefficient ◽  
Analytical Solution ◽  
Quality Factor ◽  
Velocity Dispersion ◽  
Normal Incidence ◽  
Sand Layer ◽  
Partially Saturated ◽  
Fluid Saturation ◽  
Wave Induced

The impact of changes in saturation on the frequency-dependent 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.

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

Geophysics ◽  
2009 ◽  
Vol 74 (1) ◽  
pp. N15-N23 ◽  
Author(s):  
Beatriz Quintal ◽  
Stefan M. Schmalholz ◽  
Yuri Y. Podladchikov
Keyword(s):  
Reflection Coefficient ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Incident Wavelength ◽  
High Attenuation ◽  
Partially Saturated ◽  
Fluid Saturation ◽  
Wide Range ◽  
Wave Induced ◽  
Approximate Equations

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, [Formula: see text], and the corresponding fluid saturation for which [Formula: see text] is minimal. The simple approximate equations provide a better insight into the dependence of [Formula: see text] on basic petrophysical parameters and allow for a fast assessment of the minimal value of [Formula: see text]. 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 [Formula: see text] 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. The reflection coefficient of the layer, caused only by a contrast in attenuation between the layer and the nonattenuating background medium, can be larger than 10% for [Formula: see text] within the layer. The reflection coefficient was calculated with finite difference simulations of wave propagation in heterogeneous, poroelastic solids and in equivalent viscoelastic solids. The reflection coefficient of the layer is also estimated with an analytical solution using a complex velocity for the layer. The numerical and analytical results agree well. Our results indicate that reflection coefficients of gas reservoirs can be significantly increased and frequency dependent in the low-frequency range because of attenuation within the reservoir caused by wave-induced flow.

Numerical modeling and laboratory measurements of seismic attenuation in partially saturated rock

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. L13-L20 ◽  
Author(s):  
Maria Kuteynikova ◽  
Nicola Tisato ◽  
Ralf Jänicke ◽  
Beatriz Quintal
Keyword(s):  
Numerical Modeling ◽  
Seismic Attenuation ◽  
Laboratory Measurements ◽  
Berea Sandstone ◽  
Mesoscopic Scale ◽  
Partially Saturated ◽  
Saturated Rock ◽  
Fluid Saturation ◽  
The Matrix ◽  
Wave Induced

To better understand the effects of fluid saturation on seismic attenuation, we combined numerical modeling in poroelastic media and laboratory measurements of seismic attenuation in partially saturated Berea sandstone samples. Although in laboratory experiments many physical mechanisms for seismic attenuation take place simultaneously, with numerical modeling we separately studied the effect of a single physical mechanism: wave-induced fluid flow on the mesoscopic scale. Using the finite-element method, we solved Biot’s equations of consolidation by performing a quasistatic creep test on a 3D poroelastic model. This model represents a partially saturated rock sample. We obtained the stress-strain relation, from which we calculated frequency-dependent attenuation. In the laboratory, we measured attenuation in extensional mode for dry and partially water-saturated Berea sandstone samples in the frequency range from 0.1 to 100 Hz. All the measurements were performed at room pressure and temperature conditions. From numerical simulations, we found that attenuation varies significantly with fluid distribution within the model. In addition to binary distributions, we used spatially continuous distributions of fluid saturation for the numerical models. Such continuous saturation distribution was implemented using properties of an effective single-phase fluid. By taking into account the matrix anelasticity, we found that wave-induced fluid flow on the mesoscopic scale due to a continuous distribution of fluid saturation can reproduce seismic attenuation data measured in a partially saturated sample. The matrix anelasticity was the attenuation measured in the room-condition dry sample.

scholarly journals Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks — A review

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A147-75A164 ◽  
Author(s):  
Tobias M. Müller ◽  
Boris Gurevich ◽  
Maxim Lebedev
Keyword(s):  
Fluid Flow ◽  
Velocity Dispersion ◽  
Wave Attenuation ◽  
Field Measurements ◽  
Theoretical Models ◽  
Seismic Attenuation ◽  
P Wave ◽  
Induced Flow ◽  
Wave Induced ◽  
Attenuation And Dispersion

One major cause of elastic wave attenuation in heterogeneous porous media is wave-induced flow of the pore fluid between heterogeneities of various scales. It is believed that for frequencies below [Formula: see text], the most important cause is the wave-induced flow between mesoscopic inhomogeneities, which are large compared with the typical individual pore size but small compared to the wavelength. Various laboratory experiments in some natural porous materials provide evidence for the presence of centimeter-scale mesoscopic heterogeneities. Laboratory and field measurements of seismic attenuation in fluid-saturated rocks provide indications of the role of the wave-induced flow. Signatures of wave-induced flow include the frequency and saturation dependence of P-wave attenuation and its associated velocity dispersion, frequency-dependent shear-wave splitting, and attenuation anisotropy. During the last four decades, numerous models for attenuation and velocity dispersion from wave-induced flow have been developed with varying degrees of rigor and complexity. These models can be categorized roughly into three groups ac-cording to their underlying theoretical framework. The first group of models is based on Biot’s theory of poroelasticity. The second group is based on elastodynamic theory where local fluid flow is incorporated through an additional hydrodynamic equation. Another group of models is derived using the theory of viscoelasticity. Though all models predict attenuation and velocity dispersion typical for a relaxation process, there exist differences that can be related to the type of disorder (periodic, random, space dimension) and to the way the local flow is incorporated. The differences manifest themselves in different asymptotic scaling laws for attenuation and in different expressions for characteristic frequencies. In recent years, some theoretical models of wave-induced fluid flow have been validated numerically, using finite-difference, finite-element, and reflectivity algorithms applied to Biot’s equations of poroelasticity. Application of theoretical models to real seismic data requires further studies using broadband laboratory and field measurements of attenuation and dispersion for different rocks as well as development of more robust methods for estimating dissipation attributes from field data.

scholarly journals Attenuation of Seismic Waves in Partially Saturated Berea Sandstone as a Function of Frequency and Confining Pressure

2021 ◽  
Vol 9 ◽  
Author(s):  
Nicola Tisato ◽  
Claudio Madonna ◽  
Erik H. Saenger
Keyword(s):  
Fluid Flow ◽  
Wave Attenuation ◽  
Confining Pressure ◽  
Berea Sandstone ◽  
Experimental Conditions ◽  
Frequency Dependent ◽  
Near Surface ◽  
Partially Saturated ◽  
Near Surface Geophysics ◽  
Wave Induced

Frequency-dependent attenuation (1/Q) should be used as a seismic attribute to improve the accuracy of seismic methods and imaging of the subsurface. In rocks, 1/Q is highly sensitive to the presence of saturating fluids. Thus, 1/Q could be crucial to monitor volcanic and hydrothermal domains and to explore hydrocarbon and water reservoirs. The experimental determination of seismic and teleseismic attenuation (i.e., for frequencies < 100 Hz) is challenging, and as a consequence, 1/Q is still uncertain for a broad range of lithologies and experimental conditions. Moreover, the physics of elastic energy absorption (i.e., 1/Q) is often poorly constrained and understood. Here, we provide a series of measurements of seismic wave attenuation and dynamic Young’s modulus for dry and partially saturated Berea sandstone in the 1–100 Hz bandwidth and for confining pressure ranging between 0 and 20 MPa. We present systematic relationships between the frequency-dependent 1/Q and the liquid saturation, and the confining pressure. Data in the seismic bandwidth are compared to phenomenological models, ultrasonic elastic properties and theoretical models for wave-induced-fluid-flow (i.e., squirt-flow and patchy-saturation). The analysis suggests that the observed frequency-dependent attenuation is caused by wave-induced-fluid-flow but also that the physics behind this attenuation mechanism is not yet fully determined. We also show, that as predicted by wave-induced-fluid-flow theories, attenuation is strongly dependent on confining pressure. Our results can help to interpret data for near-surface geophysics to improve the imaging of the subsurface.

Numerical simulation of ambient seismic wavefield modification caused by pore-fluid effects in an oil reservoir

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. T41-T52 ◽  
Author(s):  
Marc-André Lambert ◽  
Erik H. Saenger ◽  
Beatriz Quintal ◽  
Stefan M. Schmalholz
Keyword(s):  
Wave Propagation ◽  
Fluid Flow ◽  
Viscoelastic Behavior ◽  
Oil Reservoir ◽  
Noise Mitigation ◽  
Mesoscopic Scale ◽  
High Attenuation ◽  
Fluid Saturation ◽  
Wave Induced ◽  
The Impact

We have modeled numerically the seismic response of a poroelastic inclusion with properties applicable to an oil reservoir that interacts with an ambient wavefield. The model includes wave-induced fluid flow caused by pressure differences between mesoscopic-scale (i.e., in the order of centimeters to meters) heterogeneities. We used a viscoelastic approximation on the macroscopic scale to implement the attenuation and dispersion resulting from this mesoscopic-scale theory in numerical simulations of wave propagation on the kilometer scale. This upscaling method includes finite-element modeling of wave-induced fluid flow to determine effective seismic properties of the poroelastic media, such as attenuation of P- and S-waves. The fitted, equivalent, viscoelastic behavior is implemented in finite-difference wave propagation simulations. With this two-stage process, we model numerically the quasi-poroelastic wave-propagation on the kilometer scale and study the impact of fluid properties and fluid saturation on the modeled seismic amplitudes. In particular, we addressed the question of whether poroelastic effects within an oil reservoir may be a plausible explanation for low-frequency ambient wavefield modifications observed at oil fields in recent years. Our results indicate that ambient wavefield modification is expected to occur for oil reservoirs exhibiting high attenuation. Whether or not such modifications can be detected in surface recordings, however, will depend on acquisition design and noise mitigation processing as well as site-specific conditions, such as the geologic complexity of the subsurface, the nature of the ambient wavefield, and the amount of surface noise.

The transversely isotropic poroelastic wave equation including the Biot and the squirt mechanisms: Theory and application

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 309-318 ◽  
Author(s):  
Jorge O. Parra
Keyword(s):  
Wave Equation ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Seismic Waves ◽  
Transversely Isotropic ◽  
P Wave ◽  
Fluid Properties ◽  
Permeability Anisotropy ◽  
Attenuation And Dispersion ◽  
Maximum Permeability

The transversely isotropic poroelastic wave equation can be formulated to include the Biot and the squirt‐flow mechanisms to yield a new analytical solution in terms of the elements of the squirt‐flow tensor. The new model gives estimates of the vertical and the horizontal permeabilities, as well as other measurable rock and fluid properties. In particular, the model estimates phase velocity and attenuation of waves traveling at different angles of incidence with respect to the principal axis of anisotropy. The attenuation and dispersion of the fast quasi P‐wave and the quasi SV‐wave are related to the vertical and the horizontal permeabilities. Modeling suggests that the attenuation of both the quasi P‐wave and quasi SV‐wave depend on the direction of permeability. For frequencies from 500 to 4500 Hz, the quasi P‐wave attenuation will be of maximum permeability. To test the theory, interwell seismic waveforms, well logs, and hydraulic conductivity measurements (recorded in the fluvial Gypsy sandstone reservoir, Oklahoma) provide the material and fluid property parameters. For example, the analysis of petrophysical data suggests that the vertical permeability (1 md) is affected by the presence of mudstone and siltstone bodies, which are barriers to vertical fluid movement, and the horizontal permeability (1640 md) is controlled by cross‐bedded and planar‐laminated sandstones. The theoretical dispersion curves based on measurable rock and fluid properties, and the phase velocity curve obtained from seismic signatures, give the ingredients to evaluate the model. Theoretical predictions show the influence of the permeability anisotropy on the dispersion of seismic waves. These dispersion values derived from interwell seismic signatures are consistent with the theoretical model and with the direction of propagation of the seismic waves that travel parallel to the maximum permeability. This analysis with the new analytical solution is the first step toward a quantitative evaluation of the preferential directions of fluid flow in reservoir formation containing hydrocarbons. The results of the present work may lead to the development of algorithms to extract the permeability anisotropy from attenuation and dispersion data (derived from sonic logs and crosswell seismics) to map the fluid flow distribution in a reservoir.

Capillary Equilibrium in Porous Materials

1965 ◽  
Vol 5 (01) ◽  
pp. 15-24 ◽  
Author(s):  
Norman R. Morrow ◽  
Colin C. Harris
Keyword(s):  
Mass Transfer ◽  
Fluid Flow ◽  
Porous Materials ◽  
Capillary Pressure ◽  
Chemical Engineering ◽  
Fluid Distribution ◽  
Bulk Fluid ◽  
Fluid Saturation ◽  
Capillary Pressure Curves ◽  
The Relationship

Abstract The experimental points which describe capillary pressure curves are determined at apparent equilibria which are observed after hydrodynamic flow has ceased. For most systems, the time required to obtain equalization of pressure throughout the discontinuous part of a phase is prohibitive. To permit experimental points to be described as equilibria, a model of capillary behavior is proposed where mass transfer is restricted to bulk fluid flow. Model capillary pressure curves follow if the path described by such points is independent of the rate at which the saturation was changed to attain a capillary pressure point. A modified suction potential technique is used to study cyclic relationships between capillary pressure and moisture content for a porous mass. The time taken to complete an experiment was greatly reduced by using small samples. Introduction Capillary retention of liquid by porous materials has been investigated in the fields of hydrology, soil science, oil reservoir engineering, chemical engineering, soil mechanics, textiles, paper making and building materials. In studies of the immiscible displacement of one fluid by another within a porous bed, drainage columns and suction potential techniques have been used to obtain relationships between pressure deficiency and saturation (Fig. 1). Except where there is no hysteresis of contact angle and the solid is of simple geometry, such as a tube of uniform cross section, there is hysteresis in the relationship between capillary pressure and saturation. The relationship which has received most attention is displacement of fluid from an initially saturated bed (Fig. 1, Curve Ro), the final condition being an irreducible minimum fluid saturation Swr. Imbibition (Fig. 1, Curve A), further desaturation (Fig. 1, Curve R), and intermediate scanning curves have been studied to a lesser but increasing extent. This paper first considers the nature of the experimental points tracing the capillary pressure curves with respect to the modes and rates of mass transfer which are operative during the course of measurement. There are clear indications that the experimental points which describe these curves are obtained at apparent equilibria which are observed when viscous fluid flow has ceased; and any further changes in the fluid distribution are the result of much slower mass transfer processes, such as diffusion. Unless stated otherwise, this discussion applies to a stable packing of equal, smooth, hydrophilic spheres supported by a suction plate with water as the wetting phase and air as the nonwetting phase. SPEJ P. 15ˆ

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