Bayesian inversion of time‐lapse seismic data for the estimation of static reservoir properties and dynamic property changes

Grana, Dario; Mukerji, Tapan

doi:10.1111/1365-2478.12203

Cited by 46 publications

(14 citation statements)

References 46 publications

(97 reference statements)

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“…The same model can be used to predict the seismic data

d^{'}

for any repeated monitor seismic survey, measured at a different time than the baseline survey. Because the model is linear, the same convolutional model can be also applied to seismic data difference, if data are preliminary corrected for time shifts (as in Buland and EI Ouair ; Grana and Mukerji ). If we indicate the seismic amplitude differences (after time warping) with

Δ d = d^{'} - d

and we indicate the change in reflectivity with

Δ r_{p p}

, then the time‐lapse forward model can be written as

Δ d = W Δ {boldr}_{p p} + ε,

where the change of reflectivity

Δ r_{p p}

at a given travel‐time sample t :

\begin{matrix} true \\ right normalΔ r_{p p} ((), t, θ) & = & left \frac{1}{2} ((), 1 + ta n^{2} θ) \frac{\partial}{\partial t} \ln \frac{α^{'} ((), t)}{α ((), t)} - 4 \frac{{\overset{β}{true}}^{2}}{{\overset{α}{true}}^{2}} si n^{2} θ \frac{\partial}{\partial t} \ln \frac{β^{'} ((), t)}{β ((), t)} \\ left + \frac{1}{2} ((), 1 - 4 \frac{{\overset{β}{true}}^{2}}{{\overset{α}{true}}^{2}} si n^{2} θ) \frac{\partial}{\partial t} \ln \frac{ρ^{'} ((), t)}{ρ ((), t)}, \end{matrix}

…”

Section: Methodsmentioning

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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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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“…The same model can be used to predict the seismic data

d^{'}

Δ d = d^{'} - d

and we indicate the change in reflectivity with

Δ r_{p p}

, then the time‐lapse forward model can be written as

Δ d = W Δ {boldr}_{p p} + ε,

where the change of reflectivity

Δ r_{p p}

at a given travel‐time sample t :

\begin{matrix} true \\ right normalΔ r_{p p} ((), t, θ) & = & left \frac{1}{2} ((), 1 + ta n^{2} θ) \frac{\partial}{\partial t} \ln \frac{α^{'} ((), t)}{α ((), t)} - 4 \frac{{\overset{β}{true}}^{2}}{{\overset{α}{true}}^{2}} si n^{2} θ \frac{\partial}{\partial t} \ln \frac{β^{'} ((), t)}{β ((), t)} \\ left + \frac{1}{2} ((), 1 - 4 \frac{{\overset{β}{true}}^{2}}{{\overset{α}{true}}^{2}} si n^{2} θ) \frac{\partial}{\partial t} \ln \frac{ρ^{'} ((), t)}{ρ ((), t)}, \end{matrix}

…”

Section: Methodsmentioning

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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“…RPMs prescribe either analytical or empirically observed relations between rock elastic properties (e.g., velocity and impedance) and reservoir properties (e.g., fluid saturation and porosity). A large number of RPMs have been proposed in the literature (Mavko et al, 2009), which mainly differ in their underlying assumptions and the calculation of dry rock properties (Grana & Mukerji, 2015). In general, the modulus and elastic properties (such as AI) of the solid phase and dry rock and fluid phase may be calculated via the Voigt-Reuss-Hill model (Mavko et al, 2009), Wood's equation (Mavko et al, 2009), and the Hertz-Mindlin model (Dadashpour et al, 2007), for given reservoir parameters such as porosity, mineral content, and water saturation.…”

Section: Rpmmentioning

confidence: 99%

“…Tian and MacBeth (2015) proposed a Bayesian 4-D seismic inversion workflow for reservoir characterization by combining static loop and dynamic loop methods together, which not only reduces the nonuniqueness of the 4-D seismic inversion but also avoids the rescaling issues. Grana and Mukerji (2015) proposed to estimate the dynamic reservoir property changes and static reservoir properties by using Bayesian inversion of 4-D seismic data. Amini and MacBeth (2018) also used a Bayesian approach to resolve oil water contact and gas oil ratio using 4-D seismic data.…”

Section: Introductionmentioning

confidence: 99%

Inversion of Time‐Lapse Seismic Reservoir Monitoring Data Using CycleGAN: A Deep Learning‐Based Approach for Estimating Dynamic Reservoir Property Changes

Zhi

Sun

2020

JGR Solid Earth

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Carbon capture and storage is being pursued globally as a geoengineering measure for reducing the emission of anthropogenic CO2 into the atmosphere. Comprehensive monitoring, verification, and accounting programs must be established for demonstrating the safe storage of injected CO 2. One of the most commonly deployed monitoring techniques is time‐lapse seismic reservoir monitoring (also known as 4‐D seismic), which involves comparing 3‐D seismic survey data taken at the same study site but over different times. Analyses of 4‐D seismic data volumes can help improve the quality of storage reservoir characterization, track the movement of injected CO 2 plume, and identify potential CO 2 spillover/leakage from the storage reservoirblue. However, the derivation of high‐resolution CO 2 saturation maps from 4‐D seismic data is a highly nonlinear and ill‐posed inverse problem, often requiring significant computational effort. In this research, we apply a physics‐based deep learning method to facilitate the solution of both the forward and inverse problems in seismic inversion while honoring physical constraints. A cycle generative adversarial neural network (CycleGAN) model is trained to learn the bidirectional functional mappings between the reservoir dynamic property changes and seismic attribute changes, such that both forward and inverse solutions can be obtained efficiently from the trained model. We show that our CycleGAN‐based approach not only improves the reliability of 4‐D seismic inversion but also expedites the quantitative interpretation. Our deep learning‐based workflow is generic and can be readily used for reservoir characterization and reservoir model updates involving the use of 4‐D seismic data.

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“…Many different methods have been developed to invert for rock properties from seismic data constrained by borehole data. Since various seismic measurements such as seismic amplitudes and velocities are directly affected by the elastic properties of rocks, several deterministic and probabilistic methods have been developed to invert seismic data for the elastic properties of rocks (Buland & Omre, 2003;Bosch et al 2010;Grana & Mukerji, 2015). Some methods have also been developed that aim to invert seismic data for petrophysical rock properties, exploiting implicit and empirical correlations between the petrophysical and elastic properties of rocks (Bachrach, 2006;Grana & Della Rossa, 2010;Shahraeeni & Curtis, 2011;Shahraeeni et al 2012).…”

Section: Introductionmentioning

confidence: 99%

Variational Bayesian inversion (VBI) of quasi-localized seismic attributes for the spatial distribution of geological facies

Nawaz

Curtis

2018

Geophysical Journal International

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We introduce a new Bayesian inversion method that estimates the spatial distribution of geological facies from attributes of seismic data, by showing how the usual probabilistic inverse problem can be solved using an optimization framework while still providing full probabilistic results. Our mathematical model consists of seismic attributes as observed data, which are assumed to have been generated by the geological facies. The method infers the post-inversion (posterior) probability density of the facies plus some other unknown model parameters, from both the seismic attributes and geological prior information. Most previous research in this domain is based on the localized likelihoods assumption, whereby the seismic attributes at a location are assumed to depend on the facies only at that location. Such an assumption is unrealistic because of imperfect seismic data acquisition and processing, and fundamental limitations of seismic imaging methods. In this paper, we relax this assumption: we allow probabilistic dependence between seismic attributes at a location and the facies in any neighbourhood of that location through a spatial filter. We term such likelihoods quasi-localized. Exact Bayesian inference is impractical because it requires normalization of the posterior distribution which is intractable for large models and must be approximated. Stochastic sampling (e.g., by using Markov chain Monte-Carlo-McMC) is the most commonly used approximate inference method but it is computationally expensive and detection of its convergence is often subjective and unreliable. We use the variational Bayes method which is a more efficient alternative that offers reliable detection of convergence. It achieves this by replacing the intractable posterior distribution by a tractable approximation. Inference can then be performed using the approximate distribution in an optimization framework, thus circumventing the need for sampling, while still providing probabilistic results. We show in a noisy synthetic example that the new method recovered the coefficients of the spatial filter with reasonable accuracy, and recovered the correct facies distribution. We also show that our method is robust against weak prior information and non-localized likelihoods, and that it outperforms previous methods which require likelihoods to be localized. Our method is computationally efficient, and is expected to be applicable to 3D models of realistic size on modern computers without incurring any significant computational limitations.

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Bayesian inversion of time‐lapse seismic data for the estimation of static reservoir properties and dynamic property changes

Cited by 46 publications

References 46 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

Inversion of Time‐Lapse Seismic Reservoir Monitoring Data Using CycleGAN: A Deep Learning‐Based Approach for Estimating Dynamic Reservoir Property Changes

Variational Bayesian inversion (VBI) of quasi-localized seismic attributes for the spatial distribution of geological facies

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