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Petroleum Geostatistics 2019
- Conference date: September 2-6, 2019
- Location: Florence, Italy
- Published: 02 September 2019
101 - 108 of 108 results
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The Posterior Population Expansion Ensemble Method to Invert Categorical Fields
Authors P. Renard, C. Jäggli, Y. Dagasan and J. StraubhaarSummaryThis paper introduces the Posterior Population Expansion (PoPEx) method. It is an ensemble based method that can be used to identify categorical parameter fields in a Bayesian perspective. The method generates iteratively an ensemble of categorical fields and evaluates their likelihood values. During this process, the relation between observed state variables and parameter values is derived from the ensemble and used to constrain the generation of the next categorical fields. The method is shown to be more efficient than more classical McMC approaches and to provide accurate uncertainty estimates. As the method still requires to compute the likelihood for a significant number of fields, we also explore how Generative Adversarial Networks could be used to accelerate PoPEx by predicting rapidly the misfit.
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A Bayesian Approach for Full-waveform Inversion Using Wide-aperture Seismic Data
Authors S.L. Da Silva, P. Carvalho, C.A. Da Costa, J. Araújo and G. CorsoSummaryFull-waveform inversion (FWI) is a powerful technique to obtain high-resolution velocity models, which is based on the wave equation. We investigate the frequency-domain FWI of wide-aperture data. We have used a Bayesian inversion framework with l-BGFS algorithm. For the prior information, we have used a spatial covariance operator based on information collected in two wells at the ends of the velocity model. The data uncertainties were estimated according to the distance source-receiver (offset) and the angular frequency to emphasizes the waves with a greater angular range (diving waves). Finally, we report a numerical example using the Marmousi model with a maximum offset of 16,960 meters to demonstrate the effectiveness of the proposed inversion methodology. The proposed strategy has been successful to obtain gas and oil cap structures in high-resolution.
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Joint Bayesian Spatial Inversion of Lithology/fluid Classes, Petrophysical Properties and Elastic Attributes
Authors T. Fjeldstad, D. Grana and H. OmreSummaryWe consider joint prediction of lithology/fluid classes, petrophysical properties and elastic attributes in a Bayesian spatial framework based on a set of geophysical observations. A probabilistic model accounting for both vertical and lateral spatial dependency is proposed based on a Markov random field prior model for the lithology/fluid classes. We discuss in specific the rock physics model for the elastic attributes, which is well-known to be multimodal and skewed due to the presence of different lithology/fluid classes and saturation effects of the subsurface. The posterior model is assessed by an efficient Markov chain Monte Carlo algorithm. The proposed workflow is demonstrated on a Norwegian Sea gas discovery, with realistic spatial continuity in the predictions.
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Markov Chain Monte Carlo Methods for High-dimensional Mixture Distributions
Authors L. Passos de Figueiredo, D. Grana, M. Roisenberg and B. RodriguesSummaryWe present a Markov chain Monte Carlo method for the computation of the posterior distribution of discrete and continuous properties in geophysical inverse problems. Mixture distributions, Gaussian or non-parametric, have been proposed to model the multimodal behaviour or subsurface properties. However, due to the spatial correlation of subsurface properties, the number of modes of the mixture distribution increases exponentially with the number of samples in the data vector. In this work, we propose a new Markov chain Monte Carlo method based on two steps. First, we update the configuration of the discrete property (for example, facies or rock types), then we update the configuration of the continuous properties (for example, elastic or petrophysical properties). The first step can be performed according to a jump move, where a new configuration is proposed, or a local move, where the configuration of the previous iteration is preserved. The second step is performed by sampling the new configuration of continuous properties either from the analytical expression of the Gaussian distribution of the continuous properties conditioned by the facies configuration in the Gaussian-linear case, or by numerically sampling from the non-parametric conditional distribution in the non-Gaussian and non-linear case. The methodology is demonstrated through the application to synthetic and real datasets.
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Time-lapse Fluid Prediction Using Selection Gaussian Prior Models in a Bayesian Framework
Authors O.B. Forberg, H. Omre and Ø. KjosnesSummaryManagement of oil reservoirs rely upon trustworthy information about their condition. We develop statistical methodology for reliable characterization of the porosity and fluid distribution in a reservoir based on time -lapse seismic AVO data. Of particular interest to us is characterization of the dynamic fluid filling, which is crucial for reservoir engineering management, including the design of efficient infill well drilling programs. The porosity is assumed to be time constant, while the water saturation is dynamic. The objective of the study is to characterize the reservoir at two timepoints given the seismic data. We approach the problem in a Bayesian spatial inversion setting. The solution is then defined by a posterior probability distribution. A prerequisite to obtain a solution as such is a suitable prior model for the reservoir characteristics and a seismic likelihood model for the seismic data, which both have to be specified. The seismic likelihood model is assumed to be Gauss-linear and relies upon known geophysical relations. Since the water saturation is bimodal within the reservoir, the fluid filling being either oil or water, specifying a prior model is challenging. We propose a solution using a selection Gaussian random field prior model.
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Comparison of Recursive Neural Network and Markov Chain Models in Facies Inversion
Authors E. Talarico, W. Leäo and D. GranaSummaryThe prediction of the spatial distribution of geological facies based on well log measurements and geophysical data is generally treated as a stochastic sampling or optimization problem. Approaches based on Hidden Markov Models provide satisfactory results in terms of data mismatch but the geological realism of the predicted facies model depends on the prior assumptions related to facies proportions and sequence patterns. We propose here an innovative approach based on Recursive Neural Network and we compare the results to the convolutional Hidden Markov Model approach based on first-order and higher-order Markov chains. An example of application is presented with a quantification of the accuracy of the modeling results and fitness of the probability estimates.
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Spatial Continuity and Simultaneous Seismic Inversion of Facies and Reservoir Properties Ready for Flow Simulation
By H. DebeyeSummaryGeostatistical simultaneous facies inversion based on the Bayesian inference method is presented. Recent debate on the topic has been focused on the one-step versus the two-step approach. Here we side-step this topic by investigating and discussing the trace-by-trace versus the spatial full 3D inversion method. Experiments are done to compare several variations of trace-by-trace with no lateral conditioning, trace-by-trace with lateral conditioning and full 3D methods with lateral conditioning. Conditioning is based on either exponential or Gaussian variograms. With several QCs it is shown that quality of results improves going from trace-by-trace to full 3D inversion. Likewise quality of results improves going from conditioning based on exponential variograms to conditioning based on Gaussian variograms. The full 3D method with lateral conditioning based on Gaussian variograms beats the other schemes with respect to the look and feel and statistics of the facies realizations.
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Ensemble Updating of Binary State Vectors by Maximising the Expected Number of Unchanged Components
Authors M.K. Loe and H. TjelmelandSummaryThe main challenge in ensemble-based filtering methods is the updating of a prior ensemble to a posterior ensemble. In the ensemble Kalman filter (EnKF) the update is constructed based on a linear-Gaussian model assumption. In the present study we consider how the underlying ideas of the EnKF can be transferred to a situation where the components of the state vector are binary variables. Based on a generalised view of the EnKF, we formulate a class of possible updating procedures. We adopt a hidden Markov model for the state and observation vectors, and define an optimal update by maximising the expected number of binary variables that remain unchanged. The performance of our approach is demonstrated in a simulation example inspired by the movement of oil and water in a petroleum reservoir. In particular we empirically compare our results with corresponding results when using a naive updating strategy where the posterior ensemble is sampled independently of the prior ensemble, and with the results from a computationally intensive, but Bayesian optimal updating procedure. Our filter performs much better than the naive approach, but of course not as good as the Bayesian optimal filter.
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