The effect of microstructure and nonlinear stress on anisotropic seismic velocities

Recent work in hydrocarbon reservoir monitoring has focused on developing coupled geomechanical/fluid-flow simulations to allow production-related geomechanical effects, such as compaction and subsidence, to be included in reservoir models. To predict realistic time-lapse seismic signatures, generation of appropriate elastic models from geomechanical output is required. These elastic models should include not only the fluid saturation effects of intrinsic, shape-induced, and stress-induced anisotropy, but also should incorporate nonlinear stress-dependent elasticity. To model nonlinear elasticity, we use a microstructural effective-medium approach in which elasticity is considered as a function of mineral stiffness and additional compliance is caused by the presence of low-aspect ratio displacement discontinuities. By jointly inverting observed ultrasonic P- and S-wave velocities to determine the distribution of such discontinuities, we assessed the appropriateness of modeling them as simple, planar, penny-shaped features. By using this approximation, we developed a simple analytical approach to predict how seismic velocities will vary with stress. We tested our approach by analyzing the elasticity of various sandstone samples; from a United Kingdom continental shelf (UKCS) reservoir, some of which display significant anisotropy, as well as two data sets taken from the literature.

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Gassmann's equation and fluid‐saturation effects on seismic velocities

Geophysics ◽

10.1190/1.1707059 ◽

2004 ◽

Vol 69 (2) ◽

pp. 398-405 ◽

Cited By ~ 143

Author(s):

De‐hua Han ◽

Michael L. Batzle

Keyword(s):

Upper And Lower Bounds ◽

Fluid Substitution ◽

Seismic Velocities ◽

Critical Porosity ◽

Fluid Saturation ◽

Gassmann’S Equation ◽

Physical Insight ◽

Velocity Changes ◽

Saturation Effects ◽

Insight Into

Gassmann's (1951) equations commonly are used to predict velocity changes resulting from different pore‐fluid saturations. However, the input parameters are often crudely estimated, and the resulting estimates of fluid effects can be unrealistic. In rocks, parameters such as porosity, density, and velocity are not independent, and values must be kept consistent and constrained. Otherwise, estimating fluid substitution can result in substantial errors. We recast the Gassmann's relations in terms of a porosity‐dependent normalized modulus Kn and the fluid sensitivity in terms of a simplified gain function G. General Voigt‐Reuss bounds and critical porosity limits constrain the equations and provide upper and lower bounds of the fluid‐saturation effect on bulk modulus. The “D” functions are simplified modulus‐porosity relations that are based on empirical porosity‐velocity trends. These functions are applicable to fluid‐substitution calculations and add important constraints on the results. More importantly, the simplified Gassmann's relations provide better physical insight into the significance of each parameter. The estimated moduli remain physical, the calculations are more stable, and the results are more realistic.

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Discrimination between pressure and fluid saturation changes from marine multicomponent time‐lapse seismic data

Geophysics ◽

10.1190/1.1620633 ◽

2003 ◽

Vol 68 (5) ◽

pp. 1592-1599 ◽

Cited By ~ 45

Author(s):

Martin Landrø ◽

Helene Hafslund Veire ◽

Kenneth Duffaut ◽

Nazih Najjar

Keyword(s):

Pore Pressure ◽

Seismic Data ◽

Water Saturation ◽

Synthetic Data ◽

Time Lapse ◽

Seismic Survey ◽

Data Sets ◽

Amplitude Variation With Offset ◽

Fluid Saturation ◽

Pressure Changes

Explicit expressions for computation of saturation and pressure‐related changes from marine multicomponent time‐lapse seismic data are presented. Necessary input is PP and PS stacked data for the baseline seismic survey and the repeat survey. Compared to earlier methods based on PP data only, this method is expected to be more robust since two independent measurements are used in the computation. Due to a lack of real marine multicomponent time‐lapse seismic data sets, the methodology is tested on synthetic data sets, illustrating strengths and weaknesses of the proposed technique. Testing ten scenarios for various changes in pore pressure and fluid saturation, we find that it is more robust for most cases to use the proposed 4D PP/PS technique instead of a 4D PP amplitude variation with offset (AVO) technique. The fit between estimated and “real” changes in water saturation and pore pressure were good for most cases. On the average, we find that the deviation in estimated saturation changes is 8% and 0.3 MPa for the estimated pore pressure changes. For PP AVO, we find that the corresponding average errors are 9% and 1.0 MPa. In the present method, only 4D PP and PS amplitude changes are used in the calculations. It is straightforward to include use of 4D traveltime shifts in the algorithm and, if reliable time shifts can be measured, this will most likely further stabilize the presented method.

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Pressure-dependent seismic velocities based on effective compliance theory and an asperity deformation model

Geophysics ◽

10.1190/geo2012-0041.1 ◽

2012 ◽

Vol 77 (6) ◽

pp. D229-D243 ◽

Cited By ~ 10

Author(s):

Kai Gao ◽

Richard L. Gibson

Keyword(s):

Pressure Dependence ◽

Laboratory Data ◽

Confining Pressure ◽

Time Lapse ◽

Hertzian Contact ◽

Deformation Model ◽

Seismic Velocities ◽

Power Law Distribution ◽

S Wave ◽

Effective Compliance

Seismic velocities of rocks depend strongly on confining pressure, which is often explained by the fracture compliances changes within the rocks. It is important to have an accurate model describing the relations between confining pressure and seismic velocities for applications such as time-lapse reservoir characterization. We propose a new model to address this problem by combining the existing effective compliance theory with new solutions for the pressure dependence of fracture compliances. Specifically, we assume the fracture contact surface can be represented by a set of elastic hemispheres with radii following power-law distribution, and the pressure dependence of seismic velocities can be expressed through pressure-dependent normal and tangential fracture compliances that are derived from Hertzian contact theory. Joint data fittings of P- and S-wave velocity laboratory data show that our model is accurate. We also implement fluid substitution using our model to explain the similar stress-induced velocity variations of fluid-saturated fractured rocks.

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Field measurements of fracture characteristics on a wave-cut platform

Interpretation ◽

10.1190/int-2020-0132.1 ◽

2021 ◽

Vol 9 (2) ◽

pp. T453-T462

Author(s):

Thomas Loriaux ◽

James Verdon ◽

J.-Michael Kendall ◽

Alan Baird ◽

James Wookey

Keyword(s):

High Tide ◽

Seismic Refraction ◽

Field Measurements ◽

Time Lapse ◽

Natural Fracture ◽

Effective Density ◽

Seismic Velocities ◽

S Wave ◽

Fracture Characteristics ◽

The Impact

We have used seismic refraction surveys of a wave-cut platform from a field site in South West England to characterize the impact of natural fracture networks on seismic velocities and anisotropy. Time-lapse surveys were performed as the high tide ebbed to investigate the seismic effects of the water draining from the rock. We also deployed a drone to map the fracture sets from the air. Azimuthal variations in the P- and S-wave velocities reflect the orientation of the main east–west-oriented joint set. Seismic velocities increased as the water drained, an effect attributed to a reduction in the effective density of the medium. The ratio of fracture normal ([Formula: see text]) to tangential ([Formula: see text]) compliance ([Formula: see text]), which can be used as a proxy for fracture saturation and permeability, was observed to increase from [Formula: see text] to [Formula: see text], primarily driven by a drop in [Formula: see text]. These variations are attributed to a decrease in the water content of the main fracture set as the tide retreats.

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Streamline-Based Time-Lapse-Seismic-Data Integration Incorporating Pressure and Saturation Effects

SPE Journal ◽

10.2118/166395-pa ◽

2017 ◽

Vol 22 (04) ◽

pp. 1261-1279 ◽

Cited By ~ 10

Author(s):

Shingo Watanabe ◽

Jichao Han ◽

Gill Hetz ◽

Akhil Datta-Gupta ◽

Michael J. King ◽

...

Keyword(s):

High Resolution ◽

Finite Difference ◽

Seismic Data ◽

History Matching ◽

Flow Simulation ◽

Time Lapse ◽

Production Data ◽

Reservoir Properties ◽

Fluid Saturation ◽

Saturation Effects

Summary We present an efficient history-matching technique that simultaneously integrates 4D repeat seismic surveys with well-production data. This approach is particularly well-suited for the calibration of the reservoir properties of high-resolution geologic models because the seismic data are areally dense but sparse in time, whereas the production data are finely sampled in time but spatially averaged. The joint history matching is performed by use of streamline-based sensitivities derived from either finite-difference or streamline-based flow simulation. For the most part, earlier approaches have focused on the role of saturation changes, but the effects of pressure have largely been ignored. Here, we present a streamline-based semianalytic approach for computing model-parameter sensitivities, accounting for both pressure and saturation effects. The novelty of the method lies in the semianalytic sensitivity computations, making it computationally efficient for high-resolution geologic models. The approach is implemented by use of a finite-difference simulator incorporating the detailed physics. Its efficacy is demonstrated by use of both synthetic and field applications. For both the synthetic and the field cases, the advantages of incorporating the time-lapse variations are clear, seen through the improved estimation of the permeability distribution, the pressure profile, the evolution of the fluid saturation, and the swept volumes.

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Reservoir characterization based upon the onset of time-lapse amplitude changes

Geophysics ◽

10.1190/geo2014-0076.1 ◽

2015 ◽

Vol 80 (1) ◽

pp. M1-M14 ◽

Cited By ~ 10

Author(s):

Donald W. Vasco ◽

Andrey Bakulin ◽

Hyoungsu Baek ◽

Lane R. Johnson

Keyword(s):

Large Scale ◽

Reservoir Characterization ◽

Reference Model ◽

Rock Physics ◽

Time Lapse ◽

Seismic Velocities ◽

Reservoir Properties ◽

Fluid Saturation ◽

Seismic Amplitudes ◽

Physics Model

Time-lapse geophysical monitoring has potential as a tool for reservoir characterization, that is, for determining reservoir properties such as permeability. Onset times, the calendar times at which geophysical observations begin to deviate from their initial or background values, provide a useful basis for such characterization. We found that, in contrast to time-lapse amplitude changes, onset times were not sensitive to the exact method used to related changes in fluid saturation to changes in seismic velocities. As a consequence of this, we found that an inversion for effective permeability based upon onset times was robust with respect to variations in the rock-physics model. In particular, inversions of synthetic onset times calculated using Voigt and Reuss averaging techniques, but inverted using sensitivities from Hill’s averaging method, resulted in almost identical misfit reductions and similar permeability models. All solutions based on onset times recovered the large-scale, resolvable features of the reference model. Synthetic tests indicated that reliable onset times can be obtained from noisy seismic amplitudes. Testing also indicated that large-scale permeability variations can be recovered even if we used onset times from seismic surveys that were spaced as much as 300 days apart.

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An Experimental and Modeling Study on the Response to Varying Pore Pressure and Reservoir Fluids in the Morrow A Sandstone

International Journal of Geophysics ◽

10.1155/2012/726408 ◽

2012 ◽

Vol 2012 ◽

pp. 1-17 ◽

Cited By ~ 3

Author(s):

Aaron V. Wandler ◽

Thomas L. Davis ◽

Paritosh K. Singh

Keyword(s):

Pore Pressure ◽

Wave Velocity ◽

Oil Recovery ◽

Laboratory Experiments ◽

Time Lapse ◽

P Wave ◽

Well Logs ◽

S Wave ◽

Core Samples ◽

Fluid Saturation

In mature oil fields undergoing enhanced oil recovery methods, such as CO2injection, monitoring the reservoir changes becomes important. To understand how reservoir changes influence compressional wave (P) and shear wave (S) velocities, we conducted laboratory core experiments on five core samples taken from the Morrow A sandstone at Postle Field, Oklahoma. The laboratory experiments measured P- and S-wave velocities as a function of confining pressure, pore pressure, and fluid type (which included CO2in the gas and supercritical phase). P-wave velocity shows a response that is sensitive to both pore pressure and fluid saturation. However, S-wave velocity is primarily sensitive to changes in pore pressure. We use the fluid and pore pressure response measured from the core samples to modify velocity well logs through a log facies model correlation. The modified well logs simulate the brine- and CO2-saturated cases at minimum and maximum reservoir pressure and are inputs for full waveform seismic modeling. Modeling shows how P- and S-waves have a different time-lapse amplitude response with offset. The results from the laboratory experiments and modeling show the advantages of combining P- and S-wave attributes in recognizing the mechanism responsible for time-lapse changes due to CO2injection.

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Estimation of changes in saturation and pressure from 4D seismic AVO and time-shift analysis

Geophysics ◽

10.1190/1.3549756 ◽

2011 ◽

Vol 76 (2) ◽

pp. C1-C17 ◽

Cited By ~ 53

Author(s):

Mario Trani ◽

Rob Arts ◽

Olwijn Leeuwenburgh ◽

Jan Brouwer

Keyword(s):

Seismic Data ◽

Order Approximation ◽

Random Noise ◽

A Priori ◽

Time Lapse ◽

Time Shift ◽

Reliable Estimate ◽

S Wave ◽

Fluid Saturation ◽

Avo Attributes

A reliable estimate of reservoir pressure and fluid saturation changes from time-lapse seismic data is difficult to obtain. Existing methods generally suffer from leakage between the estimated parameters. We propose a new method using different combinations of time-lapse seismic attributes based on four equations: two expressing changes in prestack AVO attributes (zero-offset and gradient reflectivities), and two expressing poststack time-shifts of compressional and shear waves as functions of production-induced changes in fluid properties. The effect of using different approximations of these equations was tested on a realistic, synthetic reservoir, where seismic data have been simulated during the 30-year lifetime of a water-flooded oil reservoir. Results found the importance of the porosity in the inversion with a clear attenuation of the porosity imprint on the final estimates in case the porosity field or the vertically averaged porosity field is known a priori. The use of a first-order approximation of the gradient reflectivity equation leads to severely biased estimates of changes in saturation and leakage between the two different parameters. Both the bias and the leakage can be reduced, if not eliminated, by including higher-order terms in the description of the gradient, or by replacing the gradient equation with P- and/or S-wave time-shift data. The final estimates are relatively robust to random noise, as they present fairly high accuracy in the presence of white noise with a standard deviation of 15%. The introduction of systematic noise decreases the inversion accuracy more severely.

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Elastic properties of two VTI shale samples as a function of uniaxial stress: Experimental results and application of the porosity-deformation approach

Geophysics ◽

10.1190/geo2016-0459.1 ◽

2017 ◽

Vol 82 (6) ◽

pp. C201-C210 ◽

Cited By ~ 8

Author(s):

Viacheslav A. Sviridov ◽

Sibylle I. Mayr ◽

Serge A. Shapiro

Keyword(s):

Elastic Properties ◽

Pore Space ◽

Uniaxial Stress ◽

Data Sets ◽

Seismic Velocities ◽

Transverse Isotropic ◽

Compliant Parts ◽

Stress Dependent ◽

Deformation Approach ◽

Stress Dependency

Shale is a complex medium composed of clay, other mineral phases, and a pore space. The combined elastic properties of these components control the effective (anisotropic) properties of the composite solid. The factor that is the most dependent on the stress field is the structure of the pore space, which greatly influences the elastic properties of the medium. We have further developed and experimentally validated the porosity deformation approach (PDA) for understanding and modeling stress-dependent changes of the elastic properties of sedimentary rocks. PDA separates the pore space into stiff and compliant parts. The load dependencies of the elastic properties have linear contributions due to the former and exponential contributions due to the latter. We evaluate data sets of elastic properties of two vertical transverse isotropic shale samples measured under uniaxial stress. Then we apply the PDA and our optimization algorithm to the measured data sets to model the stress dependency of the seismic velocities and validate the modeling with experimentally obtained results. We have developed for the first time the constant anellipticity approach (CAN), which estimates the off-axis velocity (in an inclined direction relative to the symmetry axis direction) as a function of stress. Measurements of off-axis velocities are often missing information, and CAN permits us to fill this gap. This provides further background for the reconstruction of the stress dependency of the compliance tensor from acoustic log data.

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Stochastic inversion of pressure and saturation changes from time-lapse AVO data

Geophysics ◽

10.1190/1.2235858 ◽

2006 ◽

Vol 71 (5) ◽

pp. C81-C92 ◽

Cited By ~ 17

Author(s):

Helene Hafslund Veire ◽

Hilde Grude Borgos ◽

Martin Landrø

Keyword(s):

Stochastic Model ◽

Seismic Data ◽

Synthetic Data ◽

Time Lapse ◽

Bayesian Framework ◽

Reservoir Modeling ◽

Data Set ◽

The North ◽

Fluid Saturation ◽

Likelihood Model

Effects of pressure and fluid saturation can have the same degree of impact on seismic amplitudes and differential traveltimes in the reservoir interval; thus, they are often inseparable by analysis of a single stacked seismic data set. In such cases, time-lapse AVO analysis offers an opportunity to discriminate between the two effects. We quantify the uncertainty in estimations to utilize information about pressure- and saturation-related changes in reservoir modeling and simulation. One way of analyzing uncertainties is to formulate the problem in a Bayesian framework. Here, the solution of the problem will be represented by a probability density function (PDF), providing estimations of uncertainties as well as direct estimations of the properties. A stochastic model for estimation of pressure and saturation changes from time-lapse seismic AVO data is investigated within a Bayesian framework. Well-known rock physical relationships are used to set up a prior stochastic model. PP reflection coefficient differences are used to establish a likelihood model for linking reservoir variables and time-lapse seismic data. The methodology incorporates correlation between different variables of the model as well as spatial dependencies for each of the variables. In addition, information about possible bottlenecks causing large uncertainties in the estimations can be identified through sensitivity analysis of the system. The method has been tested on 1D synthetic data and on field time-lapse seismic AVO data from the Gullfaks Field in the North Sea.

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