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Collaborating Authors
Results
Sequential Bayesian Gaussian Mixture Linear Inversion of Seismic Data for Elastic and Reservoir Properties Estimation
Grana, Dario (Stanford University) | Mukerji, Tapan (Stanford University)
Summary We propose here a methodology to sequentially simulate elastic and reservoir properties, such as impedances, porosity, and facies, in order to obtain a set of reservoir models conditioned by seismic data. The sequential inversion approach provides multiple simulations obtained as solution of a Bayesian linear inverse problem where we assume that rock properties are distributed according to a Gaussian mixture model, i.e. a linear combination of Gaussian distributions. The weights of the Gaussian components are the probabilities of the facies. The main advantage of this approach is that the assumption of Gaussian mixture distribution of reservoir properties overcomes the common Gaussian assumption allowing the description of the multimodal behavior of the data. Furthermore the solution of the Bayesian Gaussian mixture linear inverse problem preserves analytical tractability. The linear inverse theory results valid in the Gaussian case have been extended to the multimodal case, by deriving the analytical expression of means, covariance matrices, and weights of the Gaussian mixture conditional distribution of the model. We describe here how to compute the analytical solution and implement a sequential approach in the simulation algorithm. We then apply the sequential Gaussian mixture linearized inversion to layer maps extracted from a 3D geophysical model of a clastic reservoir located in the North Sea. Impedances are first inverted from seismic data, then porosity and facies are simulated from impedance maps. This application provides a complete set of reservoir models with multimodal rock properties.
- Geology > Geological Subdiscipline > Geomechanics (0.70)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock (0.50)
Adaptive Spatial Resampling as a Markov Chain Monte Carlo Method for Stochastic Seismic Reservoir Characterization
Jeong, Cheolkyun (Stanford University) | Mukerji, Tapan (Stanford University) | Mariethoz, Gregoire (Stanford University)
Summary Seismic reservoir characterization aims to transform obtained seismic signatures into reservoir properties such as lithofacies and pore fluids. We propose a Markov chain Monte Carlo (McMC) workflow consistent with geology, well-logs, seismic data and rock-physics information. The workflow uses a multiple-point geostatistical method for generating realizations from the prior distribution and Adaptive Spatial Resampling (ASR) for sampling from the posterior distribution conditioned to seismic data. Sampling is a general approach for assessing important uncertainties. However, rejection sampling requires a large number of evaluations of forward model, and is not efficient for reservoir modeling. Metropolis sampling is able to perform a reasonably equivalent sampling by forming a Markov chain. The ASR algorithm perturbs realizations of a spatially dependent variable while preserving its spatial structure. The method is used as a transition kernel to produce a Markov chain of geostatistical realizations. These realizations are converted to predicted seismic data by forward modeling, to compute the likelihood. Depending on the acceptation/rejection criterion in the Markov process, it is possible to obtain a chain of realizations aimed either at characterizing the posterior distribution with Metropolis sampling or at calibrating a single realization until an optimum is reached. Thus the algorithm can be tuned to work either as an optimizer or as a sampler. The validity and applicability of the proposed method and sensitivity of different parameters is explored using synthetic seismic data.
Using Kernel Principal Component Analysis to Interpret Seismic Signatures of Thin Shaly-Sand Reservoirs
Dejtrakulwong, Piyapa (Stanford University) | Mukerji, Tapan (Stanford University) | Mavko, Gary (Stanford University)
Summary Characterizing thin shaly-sand reservoirs using seismic data can be challenging due to limited seismic resolution. This paper investigates seismic signatures of thin shaly-sand reservoirs with statistical attributes extracted using kernel principal component analysis (KPCA). We model sand-shale sequences as a first-order, discrete, 1-D Markov chain. Then we assign properties to the sand-shale layers using established rock-physics relations. From multiple realizations of synthetic seismograms, we extract statistical attributes using KPCA with Gaussian and polynomial kernels. Results show that these attributes can be used to differentiate sequences with different net-to-gross ratios or different water saturations. Thus a workflow similar to our synthetic study using KPCA can potentially be applied to real seismic data to characterize thin shaly-sand reservoirs.
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Sandstone (1.00)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Mudrock > Shale (0.95)
- Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management > Open hole/cased hole log analysis (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management > Core analysis (1.00)
Sensitivity Study of Rock Physics Parameters for Modeling Time-Lapse Seismic Signature of Norne Field
Suman, Amit (Stanford University) | Mukerji, Tapan (Stanford University)
Summary Time lapse seismic modeling is an important step in joint inversion of time lapse seismic and production data of a field. Rock physics analysis is the basis for modeling the time-lapse seismic. However joint inversion of both types of data for estimation of reservoir parameters is highly non-linear and complex with uncertainties at each step of the process. So it is essential, before proceeding with large scale history matching, to investigate sensitive rock physics parameters in modeling time lapse seismic signature of a field. The rock physics analysis includes facies classification based on the well log data and generation of initial 3D seismic velocity-porosity cube. Then Gassmann's equation is used to generate time-lapse seismic by taking in to account the changes in the saturation and pressure of the reservoir. In this study we have used the data set of Norne field. At first facies are classified based on the well log data. Then we investigate sensitive parameters in the Gassmann's equation to generate the initial seismic velocities. The investigated parameters include mineral properties, water salinity, pore-pressure and gas-oil ratio (GOR). Next we investigate parameter sensitivity for time-lapse seismic modeling of Norne field. The investigated rock physics parameters are clay content, cement, pore-pressure and mixing. This sensitivity analysis helps to select important parameters for seismic history matching.
- Europe > Norway > Norwegian Sea (1.00)
- North America > United States > Kansas > Butler County (0.24)
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Tofte Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Not Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Ile Formation (0.99)
- (4 more...)
- Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Four-dimensional and four-component seismic (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management > Seismic (four dimensional) monitoring (1.00)
Exact and Approximate Solid Substitution Transforms
Saxena, Nishank (Stanford University) | Mavko, Gary (Stanford University) | Mukerji, Tapan (Stanford University)
Summary Using volume averaging we generalize Gassmann’s (1951) isotropic equation for fluid-filled porous media to solid-filled porous media with disconnected pores. This exact equation can be used as an analog of Gassmann's fluid substitution transform for solid-filled porous media, since it predicts the change in effective moduli upon solid substitution, depending only on porosity, elastic stiffness of frame and pore-solids, and initial effective stiffness. This solid substitution transform is exact if induced pore-stress field during a specific experiment is homogeneous. For all other cases, this equation is just an approximation, and has also been suggested by Ciz and Shapiro (2007). We note that this approximation does not always fall within rigorous solid substitution bounds, but under specified conditions, it is a strict bound on solid substitution. We therefore discuss the factors which govern the accuracy and applicability of this approximation. We also present a general solid substitution approximation which requires, in addition to porosity, at least one of the following: ultrasonic fluid filled un-drained modulus, saturated modulus with a hypothetical solid or crack porosity.
Stochastic inversion of facies from seismic data based on sequential simulations and probability perturbation method
Grana, Dario (Stanford University) | Mukerji, Tapan (Stanford University) | Dvorkin, Jack (Stanford University) | Mavko, Gary (Stanford University)
ABSTRACT We presented a new methodology for seismic reservoir characterization that combined advanced geostatistical methods with traditional geophysical models to provide fine-scale reservoir models of facies and reservoir properties, such as porosity and net-to-gross. The methodology we proposed was a stochastic inversion where we simultaneously obtained earth models of facies, rock properties, and elastic attributes. It is based on an iterative process where we generated a set of models of reservoir properties by using sequential simulations, calculated the corresponding elastic attributes through rock-physics relations, computed synthetic seismograms and, finally, compared these synthetic results with the real seismic amplitudes. The optimization is a stochastic technique, the probability perturbation method, that perturbs the probability distribution of the initial realization and allows obtaining a facies model consistent with all available data through a relatively small number of iterations. The probability perturbation approach uses the Tau model probabillistic method, which provides an analytical representation to combine single probabilistic information into a joint conditional probability. The advantages of probability perturbation method are that it transforms a 3D multiparameter optimization problem into a set of 1D optimization problems and it allowed us to include several probabilistic information through the Tau model. The method was tested on a synthetic case where we generated a set of pseudologs and the corresponding synthetic seismograms. We then applied the method to a real well profile, and finally extended it to a 2D seismic section. The application to the real reservoir study included data from three wells and partially stacked near and far seismic sections, and provided as a main result the set of optimized models of facies, and of the relevant petrophysical properties, to be the initial static reservoir models for fluid flow reservoir simulations.
- Europe (0.69)
- North America > United States > California (0.28)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Mudrock > Shale (0.70)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Optimization (1.00)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Uncertainty > Bayesian Inference (0.66)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Directed Networks > Bayesian Learning (0.66)
- North America > United States > Texas (0.30)
- North America > United States > Colorado (0.30)
- North America > United States > California (0.29)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Sandstone (0.31)
- Geophysics > Borehole Geophysics (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling (0.48)
Quantitative log interpretation and uncertainty propagation of petrophysical properties and facies classification from rock-physics modeling and formation evaluation analysis
Grana, Dario (Stanford University) | Pirrone, Marco (Eni E&P) | Mukerji, Tapan (Stanford University)
ABSTRACT Formation evaluation analysis, rock-physics models, and log-facies classification are powerful tools to link the physical properties measured at wells with petrophysical, elastic, and seismic properties. However, this link can be affected by several sources of uncertainty. We proposed a complete statistical workflow for obtaining petrophysical properties at the well location and the corresponding log-facies classification. This methodology is based on traditional formation evaluation models and cluster analysis techniques, but it introduces a full Monte Carlo approach to account for uncertainty evaluation. The workflow includes rock-physics models in log-facies classification to preserve the link between petrophysical properties, elastic properties, and facies. The use of rock-physics model predictions guarantees obtaining a consistent set of well-log data that can be used both to calibrate the usual physical models used in seismic reservoir characterization and to condition reservoir models. The final output is the set of petrophysical curves with the associated uncertainty, the profile of the facies probabilities, and the entropy, or degree of confusion, related to the most probable facies profile. The full statistical approach allows us to propagate the uncertainty from data measured at the well location to the estimated petrophysical curves and facies profiles. We applied the proposed methodology to two different well-log studies to determine its applicability, the advantages of the new integrated approach, and the value of uncertainty analysis.
- Europe (0.94)
- North America > United States > California (0.28)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock (0.95)
- Geophysics > Borehole Geophysics (1.00)
- Geophysics > Seismic Surveying > Seismic Interpretation (0.88)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling (0.67)
- Information Technology > Data Science (1.00)
- Information Technology > Artificial Intelligence > Representation & Reasoning (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning > Clustering (0.68)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Undirected Networks > Markov Models (0.46)
Sensitivity Analysis for Joint Inversion of Production and Time-lapse Seismic Data of Norne Field
Suman, Amit (Stanford University) | Mukerji, Tapan (Stanford University)
Abstract Dynamic data, including production and time lapse seismic can be used in history matching process for better description of the reservoir and thus for better reservoir forecasting. However joint inversion of time lapse seismic and production data is complex and challenging with uncertainties at each step of the process. So it is essential, before proceeding with large scale history matching, to investigate parameter sensitivity for both types of data. In this study the data set of Norne field is used to find out which reservoir rock and fluid parameters have the most impact on time lapse seismic and production data at this field. The result of this study will be used in history matching of time lapse seismic and production data of Norne field.
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Tofte Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Not Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > PL 128 > Block 6608/10 > Norne Field > Ile Formation (0.99)
- (5 more...)
- Reservoir Description and Dynamics > Reservoir Simulation > History matching (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Four-dimensional and four-component seismic (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management > Seismic (four dimensional) monitoring (1.00)