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**Thore, Pierre (25)**- Vincent, Gilles (1)
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**File Type**

Mazuyer, Antoine (Universite de Lorraine- GeoRessources) | Giot, Richard (Universite de Lorraine- GeoRessources) | Cupillard, Paul (Universite de Lorraine- GeoRessources) | Conin, Marianne (Universite de Lorraine- GeoRessources) | Thore, Pierre (Total SA)

**Abstract**

The aim of this study is to estimate the initial stress in reservoirs before production using 3D calibrated geomechanical models. We propose an inverse method for estimating stress. Wellbore data can be integrated in a Mechanical Earth Model in order to estimate stresses nearby wells. It yields a first rough estimation in the whole reservoir by a simple interpolation which is not in equilibrium with the external forces and boundary conditions. From this rough stress field, the inversion aims at finding a physically acceptable stress state (i.e.: in equilibrium with the external forces and boundary conditions) that fit the local stresses wells. The forward problem is ensured by a Finite Element Analysis which is able to take into account structures such as faults, which have a significant influence on the stress magnitude and orientation. Inverse loop stops when the stress computed near wells matches the one estimated using borehole data. The uncertainties on the boundary conditions, elastic parameters and the first stress estimation are taken into account with a stochastic approach. In this study, faults are built with a volumetric representation of the core and damage zone by introducing elastic parameters variations within. This representation is possible because only small deformations are expected.

**Introduction**

Subsoil raw materials exploitation generally induces stress changes. For instance, depletion disturbs the mechanical equilibrium, yielding a stress change in the reservoir and in the overlying geological layers (the overburden). It could have dramatic consequences such as borehole instability (Zoback et al., 2003) and fault reactivation, which can lead to unexpected oil and gas leaks or migration (Wiprut and Zoback, 2002).

Stress estimation is important during field exploitation to avoid these problems and to anticipate measures to stabilize wells using different drilling and casing techniques (Wilson et at., 1999). Depletion can be monitored and it is possible to estimate the relative stress change during the exploitation. The goal of this paper is to introduce a new approach to estimate the absolute stress in the reservoir and the overburden before exploitation.

Artificial Intelligence, boundary, boundary condition, damage zone, elastic parameter, equilibrium, fault core, finite element analysis, Finland Johansson, in-situ rock stress, international symposium, inverse, inverse problem, machine learning, mechanical parameter, model space, Reservoir Characterization, reservoir geomechanics, stress estimation, Upstream Oil & Gas, Wellbore Design, wellbore integrity

SPE Disciplines:

**Summary**

We have performed a set of inversions on a thinly bedded clastic reservoir from the West of Shetland. The inversion techniques comprise a data-driven deterministic inversion (contractor), a data-driven stochastic inversion (contractor), a model-driven deterministic inversion (proprietary), and a model-driven stochastic inversion (proprietary). The variability between the results obtained from these different inversion techniques is far greater than the variability between the realizations obtained from a single stochastic inversion. This shows that the main uncertainty associated with the seismic inversion is the parameterization of the inversion itself.

annual meeting, Artificial Intelligence, deterministic inversion, information, inversion, inversion technique, Inversion Uncertainty, low frequency, propagation, real data, realization, Reservoir Characterization, resolution, seg houston 2013, seismic inversion, seismic inversion uncertainty, shale, stochastic inversion, Upstream Oil & Gas

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

Asnaashari, Amir (Université Joseph Fourier Grenoble) | Brossier, Romain (Université Joseph Fourier Grenoble) | Garambois, Stéphane (Université Joseph Fourier Grenoble) | Virieux, Jean (Université Joseph Fourier Grenoble) | Audebert, François (TOTAL E&P) | Thore, Pierre (TOTAL E&P)

Full Waveform Inversion (FWI) is an appealing technique for time-lapse imaging, especially when the prior model information is included into the workflow. After baseline reconstruction, several strategies such as: differential, parallel difference, and sequential difference can be used to assess the physical parameter changes. Using the synthetic Marmousi data-sets, we study which strategy could be more robust and give more accurate time-lapse velocity changes in the presence of noise. We illustrate that the sequential difference method, starting from a reconstructed baseline model and inverting the monitor data-set, can give a better result in the case of random ambient noise. However, the differential approach could also be interesting if the time-lapse response can be preserved from the noise level.

application, Artificial Intelligence, baseline, baseline model, difference method, differential, differential data, FWI, information, inversion, noise, noisy, optimization problem, parallel difference, reconstruction, regularized fwi, Reservoir Characterization, robustness, sequential difference, time-lapse imaging, Upstream Oil & Gas, weighting

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

Technology: Information Technology > Artificial Intelligence > Representation & Reasoning > Optimization (0.46)

Summary I compare different sets of solutions obtained with three stochastic algorithms to a highly multimodal inverse problem: the seismic to well tying of Time-Lapse Data. The problem is to find the perturbations of velocity and density in a layered model which explain the differences between the base and the monitor surveys. Several almost equivalent solutions exist especially if the thicknesses of the layers are thin. To explore the solution space I used three stochastic based optimizers: Simulated Annealing, Genetic Algorithms and Covariance Matrix Adaptation Evolution Strategy. In this paper, I compare the results obtained by the different algorithms not only in terms of speed and fitness but also in the way they offer the widest range of acceptable realizations.

algorithm, annual meeting, Artificial Intelligence, base trace, CMAE, cost function, different stochastic algorithm, equation, evolution strategy, evolutionary algorithm, Hansen, information, inversion, machine learning, monitor trace, multimodal problem, realization, reflectivity, Reservoir Characterization, SEG, stochastic algorithm, travel time, Upstream Oil & Gas

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

Technology:

Summary We present an analysis of the Kurtosis method used to estimate the phase of the wavelet without well log information. The kurtosis is a high order statistics which preserves the phase information. This paper aims to test the reliability of the Kurtosis method based on synthetic and real seismic data. We have addressed in our tests a number of factors (e.g. Our observations on the real data examples show that the phase estimated by this technique is influenced by the geology.

estimation, frequency, frequency band, frequency bandwidth, kurtosis, kurtosis method, kurtosis-based wavelet estimation, Noise level, phase estimation, reflectivity, reflectivity series, reliability, Reservoir Characterization, seismic data, trapezoid frequency, Upstream Oil & Gas, wavelet, wavelet estimation, wavelet frequency, wavelet phase

Summary The approach presented here is a fast track method for extracting 4D signal in complex media. It is based on a transformation which maps the data from the real space to a pseudo 1D space where the current 4D inversion techniques are still valid.

We present a new technique for inverting 4D seismic data constrained by dynamics and geology. The inversion is first performed at well positions where all the constraints are set and afterwards extended to the full 3D dataset. The geological and dynamical constraints are set in the model definition i.e. a layered description of the geology (with permeable and non permeable layers) which may be different at each well. This information is then propagated concurrently from each well to the whole dataset. The way the inversion is posed prevents from side lobes effect and enables to discriminate density and velocity effects (P in the case of post-stack data and P&S in the case of prestack). The more reliable information is the P velocity since it affects both reflectivity and travel time.

algorithm, approach, change, definition, dynamical information, function, inversion, layer, model, production, propagation, Reservoir Characterization, reservoir description and dynamics, reservoir grid, SEG SEG San Antonio, seismic processing and interpretation, solution, trace, Upstream Oil & Gas, variation, well

Asnaashari, Amir (Université Joseph Fourier & CNRS) | Brossier, Romain (Université Joseph Fourier & CNRS) | Garambois, Stéphane (Université Joseph Fourier & CNRS) | Audebert, François (TOTAL E&P) | Thore, Pierre (TOTAL E&P) | Virieux, Jean (TOTAL E&P)

accuracy, application, Artificial Intelligence, baseline, baseline model, differential, differential fwi, differential inversion, differential waveform inversion, FWI, inversion, procedure, receiver, reference model, Reservoir Characterization, sensitivity, sensitivity analysis, standard fwi, time-lapse image, Upstream Oil & Gas, Waveform Inversion

In this work we studied and developed an efficient method to handle the wave simulation in presence of topography based on curvilinear finite difference. Foremost, we derived the modified equations and the free surface condition on the continuous problem. We used afterwards optimized stencils and optimized selective filters adapted from aeroacoustics. The use of conventional grid allowed us to directly extend the non-centered stencils at the boundaries developed by Berland et al. (2007) to our problem in curvilinear coordinates.

With the increasing scarcity of oil, the oil exploration industry explores ever more complex and challenging geological features. The complexity can arise because of complex geological structures (salt ridges, weathered zones, foothills for e.g.). In the particular context of foothills, specific elastic wave propagation phenomena arise from the the presence of topography; scattering of waves on the topography; site effects caused by interferences that cause amplification of the wave amplitude; complicated propagation of ground-roll, including mode conversions between surface and volume waves. On the mathematical side, finite elements and finite volume methods are the most suitable approaches to handle accurately the free surface condition in presence of a general topography. For instance, Marfurt (1984) used a finite element scheme. More recently, Komatitsch and Vilotte (1998) introduced a spectral element scheme as a computionnaly efficient way of tackling this problem. However, when dealing with operational needs that require extensive means of computations, such as seismic feasability studies, the finite difference method is the most appropriate (Regone, 2007). To overcome the staircase approximation of the free surface, Hestholm and Ruud (1994) adapted the finite difference method to curvilinear coordinates, as initially introduced by Fornberg (1988).

General equations In a foothills context, only the top edge of the geological model is curved. Therefore, we consider a transformation that map only the free surface topography. We assume that (z0(x), x 2 [0,xmax]) is the equation of the topography, so that |z0(x)| remains smaller than the maximum depth H of the geological model. We introduce the coordinate transform that we use in this work as initially introduced by Fornberg (1988).

Space differencing We developed a new scheme for curvilinear finite difference based on conventional grid. While the staggered and the rotated staggered grids are the most used for Cartesian finite difference, their application is no more adapted in our problem. In the following we explain the major reasons that motivate this choice. Hestholm and Ruud (1994) extended the Cartesian staggered grid formulation to curvilinear coordinates. They further used optimized finite difference operators in order to reduce numerical dispersion. However the application of the staggered grid requires an extensive mean of computations. This prohibitive cost is mainly due to the computation of the spatial vertical derivatives and the interpolation operator needed to achieve the calculation at the desired point. Moreover, the use of an interpolation operator can decrease the overall accuracy of the scheme as quoted by Magnier et al. (1994).

computational, Computational physics, elastic wave, elastic wave equation, geophysical journal international, geophysics, method, modeling, presence, Reservoir Characterization, reservoir description and dynamics, SEG Denver, seismic processing and interpretation, seismic wave propagation, Simulation, surface topography, topography, Upstream Oil & Gas

Klokov, Alexander (OPERA) | Baina, Reda (OPERA) | Landa, Evgeny (OPERA) | Thore, Pierre (Total) | Tarrass, Issam (Total)

apex, CIG, diffraction, diffraction component, diffraction imaging, diffraction model, domain, energy, fracture, Landa, migration, model, radon, reflection, Reservoir Characterization, reservoir description and dynamics, Scatterer, SEG SEG Denver, seismic processing and interpretation, separation, Upstream Oil & Gas

Thank you!