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Petroleum Geostatistics 2015
- Conference date: 07 Sep 2015 - 11 Sep 2015
- Location: Biarritz, France
- ISBN: 978-94-6282-158-3
- Published: 07 September 2015
1 - 20 of 77 results
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Keynote - From Big Data with no Geology, to Geology without Data, Quo Vadis?
By F. Alabert*The author will present a personal perspective of past, current and future trends in petroleum Geostatistics, from the double angle of his experience as Geostatistics specialist in the early 80’s, and of his various later assignments as reservoir and exploration engineer and manager. Early petroleum applications of Geostatistics mostly related to specific tasks around filtering and interpolation of geophysical data for mapping.
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Multiple-point Statistics Simulations Accounting for Block Data
Authors J. Straubhaar*, P. Renard and G. MariethozMultiple-point statistics methods allow to generate highly heterogeneous fields reproducing the spatial features within a given training image. Whereas punctual conditioning data can be handled straightforwardly, dealing with information defined at larger scales is challenging. Among multiple-point statistics techniques, the direct sampling method consists in successively simulating each node of the simulation domain by randomly searching in the training image for a compatible pattern with that retrieved in the simulation grid. In this work, we exploit the basic principle of the direct sampling to propose an extension of the method able to deal with block data, i.e. target mean values for given subsets of the simulation grid. The proposed method is able to account for overlapping block data of any geometry and of different sizes. The approach can be used in a range of applications, including for example downscaling. Examples are presented illustrating the simulation of log-permeability fields.
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Facies Simulation of Channel Bodies Using Multiple Point Geostatistics and Probability Perturbation - A Case Study
Authors S. Hashemi*, A. Javaherian, M. Ataee-pour and H. KhoshdelThrough recent years, multiple point geostatistics (MPS) has been greatly used in reservoir simulation workflows due to its excellent ability to reproduce complex geobodies in simulation results. In this study, one of the MPS algorithms was applied to an extremely channelized carbonate reservoir. Different sources of data were integrated into this simulation workflow through creating the training image, soft conditioning data, and hard conditioning data. At the final stage of the simulation workflow, an optimization procedure was used to fully preserve the continuity and geometry of the channel bodies in the simulation results. This optimization process, which is based on probability perturbation, tackles the optimization problem as an integration process. The Tau model is used to integrate probability function from which the initial facies model is sampled with additional data in probability form. The geometry and continuity of channels in the final optimized facies models was fully preserved as expected to be according to the available seismic data.
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A Flexible Markov Mesh Model for Facies Modelling
Authors X. Luo* and H. TjelmelandIn this presentation we consider the problem of estimating a prior model for spatial discrete variables from a training image. To be able to combine the estimated prior model with a likelihood for observed data, we argue that one needs to use a prior formulation where an explicit formula is available for the prior distribution. Moreover, we argue that to avoid overfitting it is essential to limit the number of parameters in the prior. We propose to formulate a prior within the class of Markov mesh models, for which formulas for the point mass function are available. We define a flexible prior model within the class of Markov mesh models, where we are able to limit the number of model parameters even with a reasonably large sequential neighbourhood by restricting interactions of very high orders to be zero. To fit the Markov mesh prior to a training image we adopt a Bayesian approach, in which we consider the training image as observed data. We fit the model parameters to the training image by simulating from the resulting posterior distribution, and for this we use Gibbs sampler algorithm. We demonstrate the qualities of our approach in simulation examples.
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Simultaneous Prediction of Geological Surfaces and Well Paths
Authors P. Dahle*, A. Almendral-Vasquez and P. AbrahamsenWe present a novel model for the true vertical depth (TVD) positioning error in horizontal wells. The model utilizes a non-stationary Gaussian process known as the integrated Ornstein-Uhlenbeck process. This process is continuous and exhibits the known systematic accumulation of vertical errors with increasing measured depth. The well corrections produced are smooth and maintain the underlying shape of the well path. The smoothness can be adjusted through a correlation range parameter. Using the geological constraints contained in the zonation, we can predict or simulate surface depths and well depths simultaneously. The size of the surface and well displacements are governed by the relative magnitude of the surface and well path TVD uncertainties. The resulting well paths and surfaces stay within their uncertainty envelopes and are consistent with the zonation. The surface/well relationships can be expressed as a highly dimensional truncated multivariate Gaussian distribution. We draw samples from this distribution using an efficient rejection sampling strategy that allows fields with hundreds of horizontal wells to be handled.
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Modeling the Complex Stress Field - Incorporating Stochastic Models of Natural Fractures to Improve Completion Design in Unconventional Reservoirs
Authors Y. Aimene*, J. Yarus, R.M. Srivastava and Y. PandeyUnlike conventional reservoirs in which dual porosity/permeability is the primary rock property needed for fluid flow, unconventional reservoir permeability is created through hydraulic fracturing in which other key reservoir properties are needed. The success of a hydraulic fracturing job depends on the stress field around the wellbore. Unfortunately, the presence of faults and natural fractures creates a variability that could enhance the fracturing or prevent its success. Consequently, stress variability needs to be quantified to optimize the position of the fracture stages during hydraulic fracturing. This paper describes a combined use of geostatistical methods to simulate the distribution of the natural fractures and a geomechanical meshless material point method (MPM) method to account explicitly for their interaction with the regional stress. The geostatistical natural fracture network used as input in the MPM geomechanical tool enables the estimate of the complex stress field map. In resource plays such as the Eagle Ford, this can directly affect stimulation design around high density fractures. The combination of the new geostatistical natural fracture simulation method with the explicit representation of the simulated natural fractures in the MPM-based geomechanical approach is a powerful tool that could improve completion strategies in unconventional reservoirs.
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Explicit Fracture Network Modelling - From Multiple Point Statistics to Dynamic Simulation
Authors T. Chugunova*, V. Corpel and J.P. GomezThis paper addresses the problem of an explicit fractured media modelling on an operational case. On one side, realistic fracture models are mainly used for research purposes in order to better investigate the flow behaviour impacted by the complex multi-scale fracture network. Often, a very fine grid and a consequent computational time are needed. On the other side, an operational fractured reservoir is still generally modelled using an implicit fracture media representation. The upscaled petrophysical properties and dual media are defined in a coarse grid trying to limit the computational time of dynamic simulation. The challenge of this work is to demonstrate that an explicit fracture modelling is not reserved only for the research domain but can be applied to an operational case study. The static model is constructed using a Multiple Point Statistics (MPS) approach in order to represent complex patterns of fractures and faults interconnection while managing uncertainty on fractures location. A dynamic behaviour is simulated based on this realistic fracture reservoir representation. To stay parsimonious with regard to computational time, we use a volume displacement technique which allows keeping a simple medium assumption and optimal grid refinement.
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Bayesian Generalized Gaussian Inversion of Seismic Data
Authors K. Rimstad and H. Omre*Bayesian Gen-Gauss inversion is defined and it is demonstrated that it has great flexibility. The model is successfully used to invert seismic AVO data, and approximately 30% improvements in MSE of Bayesian Gauss inversion is obtained. The model extends easily to 3D, although the computational demands will increase considerably.
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Multiple-point Statistics and Bayesian Inverse Theory - Some Inspirations from Mean-field and Curie-weiss Theories
Authors J.S. Gunning and A. GunningFor petroleum geostatistics, modelling of rock facies is of leading order importance: they are the dominant predictor of flow, and the dominant control of remote sensed data. Stronger geological control is desirable, and this is effectively introduced via multipoint statistics (MPS). The obscure character of MPS algorithms has hitherto prevented their clean integration with Bayesian inverse theory. We show that expressing MPS priors in terms of Gibbs energies makes this possible, and meets the dual requirements of modelling low entropy images well, and allowing rapid probability recomputations under local perturbations. By their close relation to ``standard'' Markov random field models via mean-field theory, albeit with a complex graph, their parameter inference problems are rendered easier by some analogies with classical Curie-Weiss type models. The data assimilation problem leads to an NP-hard problem equivalent to constrained binary quadratic programming, even for simple priors. This gives access to newer discrete optimisation methods like semidefinite programming (SDP). These relaxations provide remarkably good lower bounds on the optimisation, and serve as helpful validation of direct heuristic methods like annealing. Some demonstration problems on seismic AVO inversion illustrate the Gibbsian MPS formulation and its successful optimisation via both SDP and annealing.
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Bayesian Gaussian Mixture Linear Inversion in Geophysical Inverse Problems
Authors D. Grana*, T. Fjeldstad and H. OmreWe present a Bayesian linear inversion based on Gaussian mixture models and its application to geophysical inverse problems. The proposed inverse method is based on a Bayesian approach where we assume a Gaussian mixture random field for the prior model and a Gaussian linear likelihood function. The model for the latent discrete variable is defined to be a stationary first-order Markov chain. Here, we propose an analytical solution of the posterior distribution of the inverse problem. A sampling algorithm can be used to simulate realizations from the posterior model. Two examples of applications using real data are presented. The first example is a rock physics inversion for the estimation of facies and porosity; the second example is a seismic inversion for the estimation of facies and P-impedance. For each example, we show a set of conditional simulations, and the corresponding maximum a posteriori and prediction intervals.
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M-Factorial Kriging - An Efficient Aid to Noisy Seismic Data Interpretation
Authors J.L. Piazza*, C. Magneron, T. Demongin and N.A. MüllerThe interpretation of 3D seismic data sets is often made difficult by the presence of various types of residual noise and amplitude attenuation effects. When subtle amplitude variations related to reservoir heterogeneities, fractures or fluid effects are investigated, these flaws may become penalizing in the framework of reservoir geophysics interpretation. Several geostatistical tools are proposed by different authors to complement seismic processing with the advantage of being optimized and applied in a focused subset of the 3D seismic data set. Among them, the M-Factorial Kriging technique is found to be very efficient in terms of quality of the results and turn-around times. In the case study presented in this paper, various M-Factorial Kriging models are combined in order to attenuate different components of noise and amplitude artefacts in the interest of a better structural and stratigraphic interpretation of a deeply buried clastic reservoir.
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Resolution of Reflection Seismic Data Revisited
Authors T.M. Hansen*, K. Mosegaard and A. ZuninoIt is commonly accepted that layers thinner than about 1/8 of the dominant wavelength cannot be resolved from reflection seismic normal incidence data. We demonstrate that there is in theory no limit the resolution of normal incidence reflection seismic data. The resolution of reflection seismic data is linked to the noise level, parameterization and a priori information.
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Convolved Hidden Markov Models for Well-log Inversion
Authors T. Fjeldstad* and H. OmreBayesian inversion of convolved data from discrete profiles, for example well-log data from lithofacies well profiles, is studied and found feasible to make. The projection approximation of the likelihood model provides reliable approximate posterior models, which can be used as proposal in an independent-proposal MCMC M-H algorithm, to generate realizations of lithofacies profiles from the correct posterior model.
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A Unified Framework for a Class of Ensemble Data Assimilation Algorithms in Reservoir History Matching Problems
By X. Luo*In recent years ensemble data assimilation (EnDA) algorithms, such as the ensemble Kalman filter, the ensemble smoother and their iterative counterparts have received considerable attention from researchers and practitioners in petroleum engineering, due to their relative simplicity in implementations, reasonable computational costs and reliable performance. The main goal of this paper is to extract some common structures among a class of EnDA algorithms, and establish a mathematical framework that can not only be used to analyze these existing methods in a unified way, but also entails new algorithm developments in the future. For illustration, in an example demonstrated in the paper, we transplant a deterministic inversion algorithm into the proposed framework, and derive from it an EnDA algorithm that has been applied to the Brugge field case study. The new EnDA algorithm tends to converge faster than the original inversion algorithm itself. In addition, instead of obtaining a single solution as the original inversion algorithm does, the new EnDA algorithm provides an ensemble of solutions that lays the ground for uncertainty quantification. On top of this example, we believe that one may also incorporate other deterministic inversion/optimization methods into the proposed framework and gain similar benefits.
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Consistent Joint Updates of Facies and Petrophysical Heterogeneities Using an Ensemble Based Assisted History Matching
Authors R.G. Hanea*, T. Ek and B. SebacherIn our opinion, there are two main approaches for parameterizing the uncertainties in the subsurface characterization which impacts the flow behavior of the reservoir (disregarding structural and faults uncertainties). The first one, is to update the petrophysical properties, permeability and porosity, directly. The second strategy is to consider the underlying trends (the rock itself) as uncertain. Consequently, the facies distribution is treated as an uncertain parameter. The next logical step is to update both the facies distribution and petrophysical properties simultaneously, without losing the consistency. This paper introduces a new methodology where we are able to consistently update the facies distributions, the petrophysical properties, whilst honoring the facies information from both well logs and seismic, without the need of an extra iteration process. The results presented are using a synthetic case, a replica of a real field case in the North Sea. We will compare the new methodology against the results obtained when only the facies distributions are updated using the APS methodology. We show that the new approach captures the general trend of the facies distributions, it is closer to the true permeability distribution and it has the same predictive power.
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Simulation of Conditional Spatial Fields Using Random Mixing
Authors S. Hörning*, A. Bardossy and S. TysonA new method for simulating conditional spatial fields is presented which improves on linear geotatistics currently used in commercial petroleum software. It preserves the continuity of extreme high and low value regions and provides an assessment of uncertainty based on the dependence of the magnitude of adjacent values. Moreover, this method includes flexibility to handle a variety of conditioning constraints, including non-linear constraints, integral equalities and inequalities
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Interactive Earth Modeling in Unconventional Reservoirs - Principles, Methods, and a Case Study from the Mississippian, Barnett Shale
Authors J. Yarus*, C. Rodriguez, J. Dahl, C. Davila and J. SpaidDespite the decreased activity in shale resource exploitation over the last six months, long-term projections remain more optimistic for a variety of reasons, including the geometrically increasing demand for energy, the need for energy independence, and the global environmental pressure for a greener energy-based economy. This presentation focuses on increasing drilling efficiency through geostatistical modeling technology and cites practical workflows and methods that have proven successful in shale development. As an example, recent drilling success in the Barnett shale is shown to be the result of stochastic modeling and the integration of key reservoir properties into a predictive “super-variable” or quality index. The result is a continuing reduction in the price per barrel of oil equivalent (BOE) toward sustainable economic levels, even in the current market. The case study presented can be extended to other shale plays and serves as an example of practicality and effectiveness using stochastic modeling methods to more precisely design well plans to intersect the top of objective target early remaining in the zone throughout, avoid geohazards, identify optimal drilling targets (sweet spots), and assist in economical completion practices.
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Kriging Unconventional Production Decline Rate from Geological and Completion Parameters
Authors O. Grujic* and J. CaersIn this extended abstract we propose novel kriging based technique for forecasting and uncertainty quantification in unconventional shale reservoirs. Our technique is data driven; we start from all available reservoir data including high dimensional sets of hydraulic fracturing and geological parameters, along with hydrocarbon production time series. We use functional data analysis to decompose production time series, into a low dimensional space of functional principal component scores. Which enabled us to transform the forecasting problem from complex rate vs. time into a simple regression problem of predicting functional principal component scores at new well locations. Prediction of functional principal component scores is accomplished with recently developed multivariate dice-kriging method. Entire technique is demonstrated on a real reservoir dataset containing 180 horizontal wells with 28 geological and fracturing parameters.
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Gridless Simulation for Assessment of Volumetric Uncertainty
More LessIt is possible to assess volumetric uncertainty using a gridless geostatistical simulation method that directly simulates the shape of contour lines of continuous variables, such as thickness, net-to-gross or porosity. This method is not as fast as global Monte Carlo methods, which can easily produce millions of realizations of global averages; but the number of realizations it can produce in a reasonable amount of time is considerably more than conventional geostatistical conditional simulation, which is typically limited to hundreds of realizations. It is an improvement on global Monte Carlo methods because it honours well data, and can incorporate soft or indirect information. It is an improvement on conventional conditional simulation because it more easily honour complex information on the geometry of the oil-water contact.
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Local Geostatistical Filtering Using Seismic Attributes
Authors R. Meunier*, H. Binet and L. PeignardFactorial kriging or kriging with filtering (Matheron, 1982) is used on post-stack or pre-stack seismic dataset to filter out unwanted components from the seismic signal. To account for non-stationarity that is often encountered within seismic data sets, kriging parameters can be locally set using Local Geo-Statistics (LGS) or M-GS (Moving-GeoStatistics) (Magneron, 2009). There are several approaches to compute the optimized parameters; local variogram parameters in adjacent areas, automatic cross-validation techniques and morphological analysis. The paper focuses on the latter approach. The idea is to determine some interesting characteristics of a seismic image that should then be transformed to local kriging parameters for the variogram model and the neighbourhood extension. Mathematical morphology techniques provide a set of tools to analyse the image, however they are not well known by geophysicists who are more familiar with seismic attributes. A seismic attribute is a quantity extracted or derived from seismic data that can be analysed in order to enhance information of a seismic image. The advantage of using seismic attributes is that they are available on common geophysical interpretation software packages. Surprisingly there is no much reference of the application of such attributes to derive the local parameters of the geostatistical filters.
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