The Rock Physics Handbook

Mavko, Gary; Mukerji, Tapan; Dvorkin, Jack

doi:10.1017/9781108333016

Cited by 659 publications

(612 citation statements)

References 670 publications

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“…Rock physics models aim to predict the elastic response of saturated porous rocks. Most of the available models, such as empirical relations, granular media models and inclusion models, are derived for reservoir conditions in which the rock and fluid parameters are known (Mavko et al 2009). If the fluid volumes change, the elastic properties change as well.…”

Section: Literature Reviewmentioning

confidence: 99%

“…from 35 to 40 MPa): indeed, many of the physical models proposed for the pressure effect assume exponential trends. In mixtures of gas and water, a small amount of gas (such as 5% of gas) in a brine-saturated rock causes a large drop in P-wave velocity, whereas an increase in gas from 5% to 100% causes a small change in P-wave velocity: indeed, the bulk modulus of a mixture of gas and water is often computed using Reuss harmonic relation (Mavko et al 2009).…”

Section: Proposed Formulationmentioning

confidence: 99%

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Rock physics modelling and inversion for saturation‐pressure changes in time‐lapse seismic studies

Lang

Grana

2019

Geophysical Prospecting

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Time‐lapse seismic data are generally used to monitor the changes in dynamic reservoir properties such as fluid saturation and pore or effective pressure. Changes in saturation and pressure due to hydrocarbon production usually cause changes in the seismic velocities and as a consequence changes in seismic amplitudes and travel times. This work proposes a new rock physics model to describe the relation between saturation‐pressure changes and seismic changes and a probabilistic workflow to quantify the changes in saturation and pressure from time‐lapse seismic changes. In the first part of this work, we propose a new quadratic approximation of the rock physics model. The novelty of the proposed formulation is that the coefficients of the model parameters (i.e. the saturation‐pressure changes) are functions of the porosity, initial saturation and initial pressure. The improvements in the results of the forward model are shown through some illustrative examples. In the second part of the work, we present a Bayesian inversion approach for saturation‐pressure 4D inversion in which we adopt the new formulation of the rock physics approximation. The inversion results are validated using synthetic pseudo‐logs and a 3D reservoir model for CO2 sequestration.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Proposed Formulationmentioning

confidence: 99%

Rock physics modelling and inversion for saturation‐pressure changes in time‐lapse seismic studies

Lang

Grana

2019

Geophysical Prospecting

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“…To answer this question, let us also assume that, because the porosity and the dry-frame and mineral moduli are the same in all layers, they also can be used for the entire package treated as a homogeneous body. Gassmann's (1951) equation reads (e.g., Mavko et al 2009), as follows:…”

Section: Analytical Solutionmentioning

confidence: 99%

“…where K w is the bulk modulus of water and K g is that of gas. If, instead of the exact Gassmann's (1951) equation 6, we use the V p -only fluid substitution approximation (Mavko et al 2009), as follows:…”

Section: Analytical Solutionmentioning

confidence: 99%

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Effective bulk modulus of the pore fluid at patchy saturation

Wollner

Dvorkin

2018

Geophysical Prospecting

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We explore a package of parallel porous layers, each filled with a different fluid. Assume that this package is sampled by an elastic wave with the wavelength much larger than the thickness of an individual layer. Also assume that the layers are hydraulically isolated from each other, meaning that the diffusion length is smaller than that of the individual layer. This assumption is relevant to a patchy saturation scenario. Suppose that we wish to conduct the fluid substitution operation on this package treated as a single porous elastic body. What is the effective bulk modulus of the pore fluid to be used in this operation that will result in the same elastic modulus as computed by Backus averaging the individual moduli of the layers? We address this question analytically by assuming that the porosity, dry frame, and the mineral matrix properties of the individual layers are the same for all layers. The only difference between the layers is the pore fluid. We find that the resulting effective bulk modulus of the fluid thus derived falls between the arithmetic and harmonic averages of the fluid bulk moduli in the layers. It can be approximated by a linear combination of these two bounds where the weights are 0.50 and 0.50 or 0.75 for the arithmetic average and 0.25 for the harmonic average, depending on the elastic moduli of the dry frame, the mineral, and the pore fluids. This solution also provides a relation between the effective bulk modulus of the pore fluid in the system under examination and water saturation to be used in the fluid substitution operation at a coarse spatial scale.

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Seismic Attenuation and Stiffness Modulus Dispersion in Porous Rocks Containing Stochastic Fracture Networks

et al. 2018

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Understanding seismic attenuation and modulus dispersion mechanisms in fractured rocks can result in significant advances for the indirect characterization of such environments. In this paper, we study attenuation and modulus dispersion of seismic waves caused by fluid pressure diffusion (FPD) in stochastic 2‐D fracture networks, allowing for a state‐of‐the‐art representation of natural fracture networks by a power law length distribution. To this end, we apply numerical upscaling experiments consisting of compression and shear tests to our samples of fractured rocks. The resulting P and S wave attenuation and modulus dispersion behavior is analyzed with respect to the density, the length distribution, and the connectivity of the fractures. We focus our analysis on two manifestations of FPD arising in fractured rocks, namely, fracture‐to‐background FPD at lower frequencies and fracture‐to‐fracture FPD at higher frequencies. Our results indicate that FPD is sensitive not only to the fracture density but also to the geometrical characteristics of the fracture length distributions. In particular, our study suggests that information about the local connectivity of a fracture network could be retrieved from seismic data. Conversely, information about the global connectivity, which is directly linked to the effective hydraulic conductivity of the probed volume, remains rather difficult to infer.

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The Rock Physics Handbook

Cited by 659 publications

References 670 publications

Rock physics modelling and inversion for saturation‐pressure changes in time‐lapse seismic studies

Rock physics modelling and inversion for saturation‐pressure changes in time‐lapse seismic studies

Effective bulk modulus of the pore fluid at patchy saturation

Seismic Attenuation and Stiffness Modulus Dispersion in Porous Rocks Containing Stochastic Fracture Networks

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