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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
41 - 60 of 77 results
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Can Geostatistical Models Represent Nature’s Variability? An Analysis Using Flume Experiments
Authors C. Scheidt*, A. Fernandes, C. Paola and J. CaersOne of the difficulties in multi-point geostatistics (MPS) is the definition of the training image (TI). In the context of uncertainty modeling, the construction of a set of TIs is desirable, but the number of TIs and the characteristics that should to be varied in the TI are not well understood. In this research, we explore the question of the definition of the TIs using tank experiments. A set of snapshots of delta deposits seen in the tank are used to explore the variability of the system over time and to see if MPS can reproduce the variability of the set of images using only a few, well-selected images that are taken as TI. Preliminary methodologies are explored to select representative images, where the variation of the deposits over time is studied. Our results show that MPS was able to reproduce the variability in the full set of images, hence the variability of the studied system. Analyzing the characteristics of the selected images is a first step forward in the attempt to define TIs. This study only present preliminary investigations and more general answers will be explored.
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Role of Geostatistical Techniques on the Evolution of 3D Reservoir Interpretation and Modelling Outcomes - An Example
Authors N. Orellana*, I. Yemez, J. Cavero, V. Singh and E. IzaguirreOne of the key challenges in 3D reservoir modeling is distributing the identified facies and their properties in defined 3D framework honoring geology and available data. Different geostatistical techniques are used for reservoir facies and properties distribution in the 3D reservoir models which have different inputs and assumptions. These techniques constrain 3D reservoir models to local data which should represent the geological knowledge and help in creating appropriate flow behaviours through dynamic simulation. However, these simulation results are highly dependent on the available input data, geomodeler’s knowledge and experience. To capture the geological model evolution from discovery to development phases and assess the influence of different simulation techniques (SIS, TGS, Object Based, Multipoint) on the reservoir facies and properties distribution a geological model was built for a clastic reservoir and updated as and when new data/information was available. The modeling results (Original hydrocarbon in-place & recoverable resources/reserves and production forecasts) show significant variations for different phases of the project. If enough data, appropriate data QC, geological rules, mapping principles and geostatistics are not properly applied to capture all possible range of parameters and geological scenarios in the 3D modeling process, the results will be highly uncertain and affect decisions.
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MPS Application in Carbonate Field and Joint Probability Updating of Trend and Depositional Scenario
Authors C. Corradi*, M. Bazzana, A. Da Pra, M. Pontiggia, J. Caers and C. ScheidtIn the late exploration to early appraisal phases of a reservoir, dynamic data are usually not available. Only information from seismic and a few wells is on hand for characterizing the reservoir. As a result, a high degree of uncertainty is present. A new workflow has been developed for a rapid model updating with well data, to produce more realistic uncertainty quantification. In this work, we present a specific methodology regarding the updating of probabilities of key uncertain parameters involved in the reservoir modelling, when new data becomes available. The main concept is to use a Bayesian framework to update prior probabilities of key geological parameters, in this case depositional scenario and spatial trend, when new data from drilling is obtained. The application of the workflow to a real carbonate field, characterized by a high degree of uncertainty, is presented. This method could give a huge improvement, especially for green fields with considerable uncertainty in the depositional system, proportion and trend. Furthermore, it could increase the overall efficiency by speeding up the process from geological modelling to reservoir dynamic modelling, without lost accuracy, especially regarding the uncertainty management.
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Keynote - Geologically Consistent History Matching Using the Ensemble based Methods
By Y. Chen*The ensemble-based data assimilation methods have shown great potential for automatic history matching after being introduced to petroleum industry a decade ago. Over the decade, this family of methods has evolved from the initial method known as the ensemble Kalman filter to the iterative ensemble smoother (perhaps the most promising one to date for history matching). The updating scheme of the ensemble-based methods relies on the covariance, which is ideal for model parameters that are typically assumed Gaussian, i.e. log transformed horizontal permeability (log-permx) and porosity for a given facies type. The geological models for most reservoirs now typically have multiple facies types, each with distinct petrophysical properties. In this case, the joint distribution of log-permx over the entire grid is no longer multi-variant Gaussian. If the gridblock log-permx is directly updated in the ensemble-based methods, facies boundaries are smeared out, and often the updated log-permx shows values that are outside of the normal range. In order to maintain geological realism of updated models and increase their predictability, different transformation and parameterization methods have been used with the ensemble-based data assimilation methods to account for the presence of multiple facies types in the model. In this talk, I will review these methods with examples and discuss the advantage and limitation of each method.
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Bayesian Inversion of Time-lapse Seismic Data Using Bimodal Prior Models
Authors I. Amaliksen* and H. OmreThe objective is to make inference about reservoir properties from seismic reflection data. The inversion problem is cast in a Bayesian framework, and bi-modal prior models are defined in order to honor the bi-modal behavior of the saturation variable. By using a Gauss-linear likelihood model the explicit expressions for the posterior models are obtained by the convenient properties of the family of Gaussian distributions. The posterior models define computationally efficient inversion methods that can be used to make predictions of the reservoir variables while providing an uncertainty assessment. The inversion methodologies are tested on synthetic seismic data with respect to porosity and water saturation at two time steps. Encouraging results are obtained under realistic signal-noise ratios.
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Fast Model Update Coupled to an Ensemble based Closed Loop Reservoir Management
Authors J.A. Skjervheim, R.G. Hanea* and G. EvensenAn integrated approach to reservoir modeling is required if the geomodel is included in the conditioning process, and a fast, consistent and automated model chain workflow from structural modeling to flow simulation needs to be established. In this paper we demonstrate the integrated workflow, named Fast Model Update (FMU), on a real field application and how FMU can be coupled to a closed-loop reservoir management process. An automated modeling process allows for working with multiple realizations and to perform combined static and dynamic uncertainty studies, where geological uncertainties are consistently propagated all the way to simulation. The use of multiple realizations allows for the use of statistical “ensemble methods” for big-loop model conditioning, where any uncertain parameter that is input to the model workflow can be updated (e.g., channel direction, facies probability, seismic velocity model, structural surfaces). Working with multiple model realizations in FMU, allows for robust reservoir management and well planning, where the geological uncertainty is taken into account. Decisions can be made and wells can be drilled, at a reduced risk by using a better representation of all uncertainties
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Quantifying the Uncertainty in the Facies Probability Cubes Using an Ensemble Kalman Filter Methodology
Authors B. Sebacher*, R.G. Hanea and T. EkThe work presented here introduces a new framework in the plurigaussian simulation context, which takes into account the uncertainty in the prior probability cubes. At the end of the assimilation process, we are able to offer besides an update of the facies fields, an update of the facies probability cubes. In order to achieve that, we extend the adaptive plurigaussian simulation methodology to work with multiple realizations of facies probability cubes and afterwards condition the facies fields to the production data. We generate an ensemble of facies fields by means of an ensemble of pairs of Gaussian fields. Each pair of Gaussian fields simulates a facies field from a different family of probability cubes. In the pluri-Gaussian methodology, the Gaussian fields represent the parameterization of the facies fields and are the parameters updated by the AHM process. The updated facies fields are generated with the updated values of the Gaussian fields. In addition, we are using the updated values of the Gaussian fields for reconstruction of the updated facies probability cubes. In our example, the ensemble of the prior facies probability cubes is created by perturbing a single realization with noise that is in correlation with a given prior uncertainty.
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Framework for Seismic Inversion of Full Waveform Data Using Sequential Filtering
Authors M. Gineste* and J. EidsvikSubsurface velocity inversion using full waveform modelling continues to be a challenging problem. Instead of approaching it as a deterministic optimization problem, it is here formulated in a probabilistic framework as a filtering problem, using shot data sequentially to update the estimation procedure. Such an approach has the potential of being more robust to e.g. noise and starting guess, but comes at the cost of more forward model evaluations. We present a small-sized synthetic example of using a sequential filtering method known as the Ensemble Kalman Filter for seismic velocity inversion and conclude with an outline of direction for further investigations.
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Integration of Seismic and Well Data to Characterize Facies Variation in a Carbonate Reservoir - The Tau Model Revisited
Authors M. Elahi Naraghi and S. Srinivasan*In this paper, we present a novel method of data integration based on the permanence of ratio hypothesis. In order to model the conditional probability, it would be convenient if the information from each data source can be assessed independently in order to find P(A|B) and P(A|C), and then these joint probabilities are merged to calculate P(A|B,C) accounting for the redundancy between different data sources. We propose a methodology for calculating the redundancy between different sources of information. Our formulation is based on the information from each data modeled using a mixture of Gaussian assumption indicative of the multiple facies or categories of rock properties observed in the reservoir. We implemented the proposed methodology to characterize a carbonate reservior in the Gulf of Mexico. The available data sets were drill cutting data, core data, well log measurements and 3D seismic volume. We used core data to calibrate log measurements to lithofacies. Then, we merged the probability maps of lithofacies using permanence of ratio hypothesis and generated multiple realization by Monte-Carlo sampling from the probability maps. The modeling resulted in identification of reservoir regions that have higher proportion of dolomitized grainstones that might be suitable drilling targets.
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An Approximate Bayesian Inversion Framework based on Local-gaussian Likelihoods
Authors M. Jullum* and O. KolbjørnsenWe derive a Bayesian statistical procedure for inversion of geophysical data to rock properties. The procedure is for simplicity presented in the seismic AVO setting where rock properties influence the data through elastic parameters. The framework may however easily be extended. The procedure combines sampling based techniques and a compound Gaussian approximation to assess local approximations to marginal posterior distributions of rock properties, which the inversion is based on. The framework offers a range of approximations where inversion speed and accuracy may be balanced. The approach is also well suited for parallelisation, making it attractive for large inversion problems. We apply the procedure to a 4D CO2 monitoring case with focus on predicting saturation content. Promising results are obtained for both synthetic and real data. Finally we compare our method with regular linear Gaussian inversion for density prediction, where our method gives an improved fit.
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Forecasting Production Decline Rate in Unconventional Resources by Kriging of Functional Data
Authors A. Menafoglio, O. Grujic* and J. CaersThe world, in particularly, the USA has seen an explosion in development of unconventional shale resources. In these reservoirs drilling and production occurs at development times orders of magnitude shorter than in conventional resources. As a result, decisions about where to drill and how to complete wells (hydro fracturing) need to be made in almost real-time, rendering the more traditional modelling approaches of geostatistics and flow modelling impractical. In this abstract, we present a novel approach of using the existing production data in a shale play to interpolate production decline rates for newly proposed wells. We develop these methods using novel techniques in statistical modelling based on the kriging of functional data and compare a variety of methods applied to the Barnett shale reservoir. Our Barnett dataset comes form publicly available databases (such as drillinginfo.com), and we considered a period of first 60 months of production in our study. Production profiles and well locations from 456 wells in our dataset were used for training purposes, with an aim to forecast remaining 456 wells that were not used for training (test set).
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A Functional Data Analysis Approach to Surrogate Modelling in Reservoir and Geomechanics
Authors E. Della Rossa* and F. BottazziGenerally computational costs of reservoir and geomechanical models can be particularly high, making uncertainty evaluation and risk assessment difficult to perform. To overcome this problem, several approximation methodologies based on surrogate modelling have been developed and are commonly adopted. On the other side, Functional Data Analysis is a well-established technique in statistics but its application in reservoir uncertainty evaluation is less common. We present here a functional data analysis technique for reservoir and geomechanical models. The proposed approach, combines surrogate modelling and Functional Data Analysis to build, for a definite set of input values in the uncertainty space, a functional interpolation whose objects are functions representing the output variables in a full range of times or in a given time-space domain of interest. The methodology is particularly suited for geomechanical uncertainty assessment where the output variables are characterized by a relatively smooth behaviour and the computational cost for a direct Monte Carlo approach is very high. The methodology is first illustrated with a geomechanical uncertainty characterization problem and then through a real reservoir application. In low-dimensional uncertainty characterization studies, the proposed method makes possible to perform reliable time-space dependent risk assessment with a very limited computational cost.
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Gradient Pore Pressure Modelling with Uncertain Well Data
Authors R. Nunes, P. Correia, A. Soares*, J.F.C.L. Costa, L.E.S. Varella, G. S. Neto, M. B. Silka, B.V. Barreto, T.C.F. Ramos and M. DominguesAbnormal pore pressures can result in drilling problems such as borehole instability, stuck pipe, circulation loss, kicks, and blowouts. Gradient pore pressure prediction is of great importance for risk evaluation and for planning new wells in early stages of development and production of oil reservoirs. In this paper, a stochastic simulation with point distributions method is presented to integrate uncertain data in pore pressure cube characterization. The method consists in the use of direct sequential simulation with point distributions. Wells data, in this case, are considered “soft” data, of which uncertainty is quantified by local probability distribution functions or a set of values. A case study using a real dataset is also presented to illustrate the results.
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Quantifying Uncertainty in Pore Pressure Estimation Using Bayesian Networks, with Application to Use of an Offset Well
Authors R.H. Oughton*, D.A. Wooff, R.W. Hobbs, S.A. O'Connor and R.E. SwarbrickPore pressure estimation is a crucial yet difficult problem in the oil industry. If unexpected overpressure is encountered while drilling it can result in costly challenges and leaked hydrocarbons. Prediction methods often use empirical porosity-based methods such as the Eaton ratio method, requiring an idealised normal compaction trend and using a single wireline log as a proxy for porosity. Such methods do not account for the complex and multivariate nature of the system, or for the many sources of uncertainty. We propose a Bayesian network approach for modelling pore pressure, using conditional probability distributions to capture the joint behaviour of the quantities in the system (such as pressures, porosity, lithology, wireline logs). These distributions allow the inclusion of expert scientific information, for example a compaction model relating porosity to vertical effective stress and lithology is central to the model. The probability distribution for each quantity is updated in light of data, producing a prediction with uncertainty that takes into account the whole system, knowledge and data. Our method can be applied to a setting where an offset well is used to learn about the compaction behaviour of the planned well, and we demonstrate this with two wells from the Magnolia field.
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Lateral Continuity of Stochastic Shale Barriers
Authors S. Lajevardi* and C.V. DeutschCharacterizing shale barriers in oilsands reservoirs is of critical importance for recovery predictions. High net to gross reservoirs contain small shale intervals that impede vertical drainage and have a large impact on recovery. The information on reservoir and shale interval thicknesses collected from vertical delineation wells provide only limited information about the horizontal extent and connectivity of these intervals. The main challenge is that often, such flow barriers cannot be correctly characterized due to the large spacing of delineation wells; the shales are laterally too small to be correlated between wells. Stochastic shales' characteristics are a strong function of their depositional environment (Harris, 1975). Over the past few decades, a significant amount of stratigraphic literature on the nature and character of mud beds in fluvial and tidal settings has been published (Galloway and Hobday, 1996; Miall, 1996). However, the detailed geometry and structure of remnant shales in dominantly sandy sediments is not well documented which motivates studies such as this. This paper proposes a novel methodology based on an inverse modeling scheme to estimate the lateral extent of shales independent of the gridding system. The paper includes a description of the methodology and a case study with implementation details and validation steps.
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Stochastic Modelling of Patterns Using Graph Cuts
Authors X. Li* and G. MariethozMultiple-point geostatistics (MPS) algorithms are very computationally demanding, which can limit their application in certain applications. Texture synthesis methods used in computer graphics involve concepts of training images which are similar as in MPS. Some very computationally efficient texture synthesis algorithms are able to produce geostatistical models that are comparable in quality with state-of-the-art MPS methods, while presenting computational advantages. In this paper we introduce a patch-based method based on graph cuts. It is a general tool which allowing to optimally cut patches incorporating information from previous parches using a max-flow algorithm. The cutting algorithm is based on the representation of a patch as a graph, and guarantees that the cut is optimal between more than two patches. By recording the errors of previous cuts and iteratively replacing patches areas of high error, the simulation is continuously improved and the training image texture is reproduced without noise or artifacts.
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Geological Metric Space Description by SVM Classification - Turbidite Reservoir Case Study with Multiple Training Images
Authors A. Kuznetsova*, V. Demyanov and M. ChristieThis paper shows the challenges related to handling multiple training images for reservoir prediction. We have identified two of the main challenges in handling multiple geological scenarios by creating a lower dimensional representation of the ensemble of model realizations: (i) how to relate geological knowledge to the metric space; and (ii) how to navigate in the metric space to facilitate in model update. In this work we demonstrate how to solve the classification problem in the metric space accounting for geological knowledge from a variety of prior geological concepts. In this paper we established geological relations in the metric space by making the links to the space of geologically interpretable parameters. These results would allow us to enhance geological realism of the new models obtained through the update process in the metric space.
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Integration of Multi-scale Uncertainty Assessment into Geostatistical Seismic Inversion
Authors L. Azevedo*, V. Demyanov and A. SoaresTraditional geostatistical seismic inversion approaches are able to account for the uncertainty related with the stochastic simulation algorithms that are used as part of the inverse methodology for the model perturbation. However, they assume stationarity and no uncertainty related with large scale geological parameters represented for example by the spatial continuity pattern and the prior probability distribution of the property to invert as estimated from well-log data. We propose a multi-scale uncertainty assessment for traditional iterative geostatistical seismic methodologies by integrating stochastic adaptive sampling and Bayesian inference to tune the variogram ranges and the prior probability distribution of the property to invert within the inverse workflow. The application of the proposed methodology to a challenging synthetic dataset showed a good convergence of the inverted seismic towards the recorded one while the local and global uncertainty were jointly assessed.
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Geobodies Stochastic Analysis for Geological Model Parameter Inference
Authors J.M. Chautru, R. Meunier*, H. Binet and M. BourgesIt is sometimes difficult to infer the input parameters of a geological model. For example, when variogram based simulation methods like SIS, Truncated Gaussian or Truncated Pluri-Gaussian facies simulation methods are used, inferring the facies horizontal variogram range may be very difficult in heterogeneous contexts, due to interwell spacing. This paper presents an indirect method for inferring input parameters, based on geobodies characteristics analysis, which can be used in such difficult cases. The method also allows selecting realizations of a geological model which have properties that are critical in flow simulations. The method is using dynamic synthesis results and production data to help validating the model parameters.
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First Arrival Travel Time Tomography - Bayesian Approach
Authors J. Belhadj*, T. Romary, A. Gesret and M. NobleFirst arrival time tomography aims at determining the propagation velocity of seismic waves from experimental measurements of their first arrival time. This problem is usually ill-posed and is classically tackled by considering various iterative linearised approaches. However, these methods can yield wrong seismic velocity for highly nonlinear cases and they fail to estimate the uncertainties associated to the model. In our study, we rely on a Bayesian approach coupled with an interacting Markov chain-Monte Carlo (MCMC) algorithm to estimate the wave velocity and the associated uncertainties. The main difficulty associated to this approach is that traditional MCMC algorithms can be inefficient when multimodal probability distributions or complex velocity models involving a great number of parameters come into play. Therefore, a first step toward an efficient implementation of the Bayesian approach is to properly parametrize the model to reduce its dimension and to select adequate prior distribution for the parameters. In this paper, we present a ten layers probabilistic model for the velocity, that we illustrate on tomography results.
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