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Petroleum Geostatistics 2019
- Conference date: September 2-6, 2019
- Location: Florence, Italy
- Published: 02 September 2019
61 - 80 of 108 results
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Characterizing Connectivity in Heterogeneous Porous Media Using Graph Laplacians
Authors E. Nesvold and T. MukerjiSummaryIt is desirable to be able to generate and compare grid-free representations of geological structure at multiple scales without having to create a detailed earth model. Graphs are a natural framework both as spatially explicit models of structure and for characterization of connectivity properties. Here, we use the fast marching method and spectral clustering to map point clouds over permeability cubes and discrete geology bodies as graphs at the desired scale. We also show how the spectral properties of these graphs, i.e. the eigenvalue distribution of the graph Laplacian, can be used to characterize connectivity structure and to compute distributions for different types of geology. Possible applications are sensitivity analysis of geomodeling input parameters, Bayesian graph representations of geology and flow simulation over the resulting graphs.
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Direct Geostatistical Simulation on Unstructured Grids I: Recent Improvements for Additive Variables
More LessSummaryThis paper presents an upgraded workflow to address direct geostatistical simulations on unstructured grids. Comparing to previous approaches, this algorithm is based on a recently proposed spectral decomposition applicable to a wide class of variograms and allowing for non-stationarity. The method is encapsulated in a workflow dedicated to unstructured grids including facies modeling and hydrocarbon in place computations. The proposed methodology is able to treat any kind of grid; it takes into account the support effect and it decreases drastically the computation time compared to previous approaches based on Sequential Gaussian Simulations. The method is illustrated on a synthetic example and some results on a true case study are also provided.
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Direct Geostatistical Simulation on Unstructured Grids II: A Proposal for Non-additive Variables
Authors P. Mourlanette, P. Biver, P. Renard and B. NoetingerSummaryFor non-additive variables such as permeability, no simple solution is available for direct geostatistical simulation on unstructured grids. The standard approach uses a regular grid whose cell size is constant and should correspond to the measurement scale. The permeability is simulated on that grid with any standard geostatistical simulation technique. In a second step, the permeability is upscaled on the coarser unstructured grid. To minimize the loss of time and memory involved in this method, we propose a new workflow to directly simulate permeability on unstructured grids. The method is based on the use of the power averaging law and a local estimation of its exponent for each cell of the unstructured grid. A surface of response for the exponent is built using experimental design and a set of numerical upscaling experiments. It allows estimating rapidly the local exponents as a function of the cell dimensions and geostatistical parameters. In each cell, permeability is simulated on random points using spectral turning bands and the values are averaged using power law and the local exponents. We present the results of our method on a few synthetic cases and discuss the different benchmark available.
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Topologically Constrained Boolean Discrete Fracture Network Models
By T. ManzocchiSummaryRandom Boolean Discrete Fracture Network Models cannot reproduce the topological or clustering characteristics of natural fracture systems. Line placement rules have been developed for 2D Boolean fracture models allowing creation of models with widely varying topology, connectivity and clustering for a given fracture intensity and length distribution. Topology is defined by the relative proportions of I-, Y- and X-nodes present. Connectivity is characterised by the proximity of the system to its percolation threshold. Clustering is defined by the coefficient of variation of spacing between fractures measured on a scan-line. A set of numerical experiments has been run to determine the critical connectivity of 2D isotropic fracture systems as a function of fracture length distribution and topology. Differences in fracture clustering emerge from the models. Results indicate that determination of fracture intensity, topology and clustering may be sufficient to determine macroscopic fracture system connectivity irrespective of the fracture length distribution.
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Quantifying Uncertainty of Fracture Intensity in Reservoirs
More LessSummaryModelling fracture intensity at the reservoir scale is challenging due to the scarcity of spatially exhaustive data and the sampling bias caused by the small support size of wellbore image logs. Multiple attempts have aimed at accounting for this sampling bias, but most have treated the fracture intensity measured from well logs as hard data that needs to be honoured during geostatistical modelling. In this paper, we demonstrate that there may be large uncertainties associated with upscaling well log derived fracture intensities to the reservoir scale, and then provide a mechanism for quantifying this uncertainty and provide a workflow for propagating it through the reservoir modelling process. Specifically, we use Bayesian inference from data collected empirically from a set of fit-for-purpose prior fracture networks. We then develop a workflow to model the reservoir fracture intensity uncertainty away from the wells, while integrating non-linear multivariate secondary data. 3D models of probability density function of reservoir fracture intensity are thus obtained for the entire reservoir, which can then be used to generate different scenarios of discrete fracture networks. Models created with this approach are compared between different simulation methods, demonstrating the value of accounting for non-linearity in secondary data.
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Correlation Analysis of Fracture Intensity Descriptors with Different Dimensionality in a Geomechanics-constrained 3D Fracture Network
Authors W. Zhu, B. Yalcin, S. Khirevich and T. PatzekSummary3D intensity parameters of fracture networks cannot be measured directly and are usually correlated with the lower dimensionality intensity parameters, such as P21, P10. A comprehensive correlation analysis between lower dimensionality measures, P10, P20, P21, I2D (total number of intersections per unit area) and higher dimensionality ones, P30, P32, I3D (total number of intersections per unit volume) are investigated. We also correlate small cube samples and underlying fracture networks that represent cores or tunnels. The fracture networks are constrained by geomechanics principles and outcrop data to make them geologically meaningful. We show that orientation of fracture samples impacts correlations between the 2D and 3D parameters and samples parallel to the principal stresses yield better correlations. 3D intensity parameters, P30, I3D, and P32 can be predicted from 2D or small cube samples. However, 1D intensity P10 doesn’t have a strong correlation with 3D intensity parameters. The size of cube samples should be larger than 10 percent of the original size to capture main structural information. Furthermore, the minimum number of samples to reach a good correlation from 2D and cube samples are 20 and 60 respectively.
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Upscaling of Plastic Geomechanical Properties to Reproduce Anisotropic Failure in Heterogeneous Continua
Authors B. Zhang, R. Chalaturnyk and J. BoisvertSummaryThe importance of geomechanical simulation is well documented for projects associated with significant pressure and temperature changes. Deformations and failure zones in reservoirs will impact fluid flow, caprock integrity, and well integrity. However, geological modelling cell sizes are typically at the centimetre scale in order to incorporate geological features resulting in models with millions of cells which are computationally expensive for current reservoir-geomechanical simulations. One option to overcome these computational challenges is to properly upscale geomechanical properties and simulate at a larger scale with fewer gridblocks. While many current upscaling techniques normally assume failure criteria for each upscaled cell, anisotropic failure response caused by sub-grid heterogeneity are significant complicating factors for heterogeneous continua. A local numerical upscaling technique is proposed to obtain the anisotropic failure criteria for heterogeneous continua. The implemetation of it in a highly heterogeneous IHS system shows a large difference in M-C failure envelopes in different directions caused by different failure modes. With the optimum loading rate selected for the local triaxial tests based on a sensitivity analysis, the proposed techinique can be efficiently applied in large-scale models and determine anisotropic strength parameters which can reproduce the change of shear strength at different stress state.
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A Flexible Markov Mesh Prior for Lithology/fluid Class Prediction
Authors H. Tjelmeland, X. Luo and T. FjeldstadSummaryWe consider the problem of predicting the spatial distribution of lithology/fluid classes from observed seismic data. We formulate the problem in a Bayesian setting and argue that the best choice of prior for this problem is a Markov mesh model. To obtain a flexible prior we formulate a general class of Markov mesh models and a corresponding hyper-prior for the model parameters of the Markov mesh model. We discuss three different strategies for how to combine the hierarchical Markov mesh prior, a training image and a likelihood model for the observed seismic data, to obtain predictions of the lithology/fluid classes. We present results from a case study for a seismic section from a North Sea reservoir. In particular the results show larger connectivity in the lithology/fluid classes when using our flexible Markov mesh prior, compared to what one gets with a simpler, manually specified Markov random field prior.
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A Workflow for Generating Hierarchical Reservoir Geomodels Conditioned to Well Data with Realistic Sand Connectivity
Authors D.A. Walsh and T. ManzocchiSummaryConventional geostatistical modelling methods are unable to reproduce the low connectivity typical of deep marine turbidite reservoirs at high net:gross ratios, because the connectivity of these geomodels is inevitably controlled by their net:gross ratio. Previous studies have developed modelling methods that can honour independently both the low connectivity and high net:gross ratios of these systems at different hierarchical scales, however they are unable to honour available well data. We present a new workflow for building reservoir geomodels conditioned to well data, with realistic levels of sand connectivity and hierarchical stacking.
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K-fold Cross-validation of Multiple-point Statistical Simulations
Authors P. Juda, P. Renard and J. StraubhaarSummaryIn reservoir models, the choice of spatial interpolation or stochastic simulation methods for subsurface properties is crucial when dealing with heterogeneous media. Multiple-point statistics (MPS) algorithms allow to simulate complex structures but they are controlled by hyper-parameters whose identification can be tedious. Furthermore, many different geostatistical methods and models are available. In this work, we present an application of K-fold cross-validation for the selection of a spatial simulation method. The proposed technique allows to rank models based on their predictive accuracy and is completely generic: it can handle categorical and continuous variables, as well as compare MPS algorithms to variogram-based, or object based models. It can be used for the selection of any type of parameters, including the choice of the training image. We demonstrate the performance of the method on a synthetic test case used previously for benchmarking training image selection techniques and on a real field application including non-stationarity.
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Multiple-point Statistics Based on Gaussian Pyramids of the Training Image
Authors J. Straubhaar, P. Renard and T. ChugunovaSummaryIn this work, we present a new multiple-point statistics (MPS) method combining the direct sampling algorithm and the use of multiple-resolution representations of the training image (TI) through Gaussian pyramids. First, the pyramid is built by applying convolution with a Gaussian-like kernel, which provides versions of the TI at lower resolutions. Then, successive MPS simulations are performed within a pyramid: 1) a simulation is done in the lowest resolution level, 2) the result is used to condition a simulation in the next (finer) level, and 3) this last step is repeated until the initial resolution is simulated. This technique allows to guide the MPS simualtions and to obtain results that better reproduce the spatial statistics of the TI, compared to the results of MPS without pyramids.
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Successful Reconstruction of the Fluvial Conceptual Model on Gullfaks Sør with Object Modelling
Authors M.L. Vevle, I. Aarnes, K. Solheimsnes, C.G. Knudsen, R. Hauge and A. SkorstadSummaryWe show that object models are able to handle real world data complexity by applying a recently published object model to a North Sea reservoir. The reservoir used is the Statfjord formation of Gullfaks Sør, which has rich alluvial-fluvial sandstone deposits. For this reservoir, object modelling of channel objects and crevasse splays is preferred as it provides better geometric control of the channels and crevasses than indicator/data-driven models. However, earlier object models have had problems with conditioning to the amount of well data here. With this new approach, we can condition perfectly on well data, while also reducing the run time compared to previous models. The article addresses the improvements of the well conditioning which is central as it enhances the possibilities of doing automatic modelling of multiple realizations without any subjective modifications by the field geologists around wells. The improvements implicate that the necessary manual time for the geologists to create a good model can be reduced, which again implicates both cost-saving and a more robust automatable model. Our results demonstrate that object models have a vital role to play even in the current data-driven market of our industry.
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Using Geological Process Modeling to Enhance Lithofacies Distribution in a 3-D Model: An Example
Authors D. Otoo and D. HodgettsSummaryA major challenge in reservoir modeling is the accurate representation of lithofacies in a defined framework to honor geologic knowledge and available subsurface data. Considering the impact of lithofacies distribution on reservoir petrophysics, a two-stage methodology was applied to enhance lithofacies characterization in the Hugin formation, Volve field. The approach applies the Truncated Gaussian Simulation method that relies on sediment patterns and variograms, derived from geological process simulations. The methodology involves: (1) application of the geological process modeling (Petrel-GPMTM) software to reproduce stratigraphic models of the shallow-marine to marginal-marine Hugin formation (2) define lithofacies distribution in GPM outputs by using the property calculator tool in PetrelTM. Resultant lithofacies trends and variograms are applied to constrain facies modeling. Data includes: seismic data and 24 complete suites of well logs. The Hugin formation consists of a complex mix of wave and riverine sediment deposits within a period of transgression of the Viking Graben. Twenty depositional models were reproduced using different geological process scenarios. GPM-based facies models show an improvement in lithofacies representation, evident in the geologically realistic distribution of lithofacies in inter-well volumes, leading to the conclusion that a robust stratigraphic model provides an important stratigraphic framework for modeling facies heterogeneities.
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Random Walk for Simulation of Geobodies: A New Process-like Methodology for Reservoir Modelling
By G. MassonnatSummaryA new approach for modelling geobodies in clastic reservoirs has been developed using a random walk approach. It allows generating very realistic images of geology in the 3D space, with the preservation of sediment continuity along the sedimentation profile. The method is based on the simulation of sediment transportation path through the computation of trajectories. These ones are then dressed with parametric surfaces for generating the geobodies in the gridded reservoir model. The workflow includes: 1) the computation of the transportation flow for generating stream lines; 2) the simulation of sediment trajectories guided by the stream lines; 3) the dressing of the trajectories according to the location in the 3D space. The method enables an easy conditioning to well static hard data, but also an unusual conditioning on various dynamic and seismic information and data.
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Improving Geological Robustness into Iterative Geostatistical Seismic Inversion
Authors P. Pereira, I. Calçôa, L. Azevedo, R. Nunes and A. SoaresSummaryIn geostatistical seismic inversion methods the model perturbation and update is performed by stochastic sequential simulation and co-simulation algorithms in a regular Cartesian grid and using a global variogram model to describe the spatial continuity pattern of the subsurface petro-elastic property. These approaches do not capture heterogeneous small-scale features being hard to be reproduced when dealing to highly non-stationary geological environments. This work integrates local anisotropy steering volumes to describe local anisotropies within iterative geostatistical seismic inversion methods. The incorporation of local structural and spatial information allow to obtain more consistent spatial distribution of rock properties while avoids any transformation of inversion grid during simulation process by traditional geostatistical simulation techniques. The proposed methodology of this work was successfully applied to synthetic and real application examples.
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The Data Integration Approach for Prospecting Missed Intervals. An Example Based on Gazprom Neft Assets
Authors E. Akhmetvaliev, A. Belanozhka, M. Pilipenko and K. KyzymaSummaryBesides the attempts to find solutions how to obtain “good” new data, there are many attempts to find solutions how to re-interpret old data. In Gazprom Neft, there are many activities on creating new log data interpretation methods, on implementation of the neural network and machine learning methods. It is crucial for fields with thousands of wells. Yet these modern methods have their own limitations related to data variability and specifics. Thus, there are many cases when we need to focus on integration of all old and sometimes “bad” data for solving the relevant production tasks especially when the well number is not too big.
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Automated Facies Classification for Seismic Inversion
Authors R. Beloborodov, J. Gunning, M. Pervukhina, I. Emelyanova, M.B. Clennell and J. HauserSummaryWe introduce an algorithm for simultaneous facies classification and fitting of rock physics models from multivariate well log data. Special features of the methodology are designed to render it resilient to data outliers. The algorithm is a robustified and globalized variety of the expectation-maximization algorithm, using reweighted robust nonlinear regression steps for the maximisation step, and heavy-tailed distributional models for the expectation step. Facies classifications are natural byproducts of the expectation step, and optimised rock physics models are produced by the maximisation step. The practical advantages of the approach are illustrated using data from the Satyr-5 well, located in the Northern Carnarvon Basin, North West Shelf of Australia. Outputs of the algorithm include facies labels and free parameters in the corresponding rock-physics models, which can be easily interpreted and directly used in downstream workflows such as facies-based seismic inversion.
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Integration of Production Optimization Strategy in Reservoir Petrophysical Models
Authors K. Al-Mala Khudhur, O. Fabusuyi, L. Azevedo and A. SoaresSummaryGeostatistical methods for reservoir characterization aims at obtaining petrophysical models conditioned to different direct and indirect data. For example geophysical data, such as seismic and electromagnetic data, through geostatistical inversion algorithms, well log data using stochastic simulations and production data by geostatistical history matching processes. The objective of the proposed methodology of this study, is to generate numerical models of a reservoir petrophysical properties, conditioned to a production strategy obtained with a closed loop optimization technique. In a first step of the proposed methodology a best production strategy, L0, is obtained by closed loop optimization using Particle Swarm Optimization. In a second step, one intends characterizing the spatial dispersion of parameters Z(x), conditioned to L0, by using an iterative procedure based on stochastic simulations of Z(x). In this way one succeed to obtain a geological consistent solution of petrophysical properties Z(x), which are conditioned to the chosen production strategy L0, while optimizing the spatial patterns characteristics of Z(x) like connectivity of sand bodies.
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Optimization of the Development of the Yurubcheno-Tokhomsky Field Based on the Conceptual Geological Model
By N. KutukovaSummaryThe article describes an approach of forecasting areas of high quality or poro-perm properties of carbonate reservoirs based on the integration of multi-scale geological and geophysical information from core to special seismic data processing. Conceptual geological model is the result of an integrated approach of studying core, seismic data and analysis of well productivity. The presented integrated approach is shown on the example of a unique field of Yurubcheno-Tokhomskoe, located in Eastern Siberia. A conceptual model of the Riphean natural reservoir based on the results of a comprehensive core study, seismic data and analysis of well productivity is presented. The integration of multi-scale studies allowed to create and to develop the basic principles for constructing a model of the Riphean natural oil-reservoir, to create forecast maps. Currently production drilling planning is based on the presented conceptual model.
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Conditioning the Probability Field of Facies to Facies Observations Using a Regularized Element-free Galerkin (EFG) Method
Authors B. Sebacher, R. Hanea and S. MarzavanSummaryIn this paper, we present a methodology to condition the prior probability field of the facies to the facies observations collected at the well locations. The prior probability field of the facies usually comes from seismic inversion and the facies observations are the result of the examination of the cores extracted at the well locations. Consequently, the prior probability field is not directly conditioned to facies observations. The presented methodology relies on a regularized form of the element-free Galerkin (EFG) method. The regularization has been introduced in order to account for the prior, whereas the EFG is an interpolation technique with a moving least squares criterion. The methodology presented here consistently updates the prior probability field of facies with the facies data collected at some locations in the reservoir domain. We present two case studies: one in which hard facies data are considered and a second where hard and soft facies observations are involved in the conditioning.
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