Search

International audience; Time-lapse studies not only allow to monitor the reservoir but are also useful to access risk in the overburden. They usually assume that the velocity change during reservoir depletion is isotropic, but, from a geomechanical perspective, velocity changes have no reason to be isotropic. Numerous authors observe that the velocity changes in the overburden suggest rock damage such as crack opening which implies anisotropic elastic property changes. Rock damage depends on several geomechanical parameters such as the initial rock elastic properties, the in situ stress, the stress state change, the crack shapes and their orientations, etc. We show that retrieving an anisotropic time-lapse velocity change is possible using a pre-stack seismic tomographic approach. The anisotropic time-lapse velocity change is decomposed into a functions basis which respects the travel-time perturbation symmetries. The anisotropic time-lapse velocity change predicted by the rock physics models can be expressed in this general basis with some algebra. We apply the proposed tomographic inversion on a cross-section of a real reservoir and we relate the anisotropic time-lapse velocity change to horizontal crack distribution in the overburden. Results show a good qualitative consistency between the prediction of the rock physics model and the tomography results.

We have developed an implicit method to automatically generate several possible models of salt top surfaces with varying geometries and topologies. This method can be conditioned to available data such as well markers and seismic picks. Because seismic imaging of salt is prone to velocity uncertainty and Fresnel zone effects, the input of the method is a seismic image that is segmented into three regions: salt, sediments, and uncertain. The uncertain region contains the salt boundary, and all further computations focus within this zone. A monotonic scalar field, ranging from zero on the edge of the certain salt body to one on the maximal possible salt boundary, defines the cumulated probability for a point to be outside the salt body. A random scalar field, also bounded between zero and one, is then used as a threshold for the first scalar field. The salt boundary is implicitly defined by the zero isovalue of the difference between the two fields, and it can be further extracted using marching cubes. The random field parameters have a geometric and topological impact on the simulated salt volumes. They can be adapted to reproduce specific geological features, but their inference remains difficult. The application of the method for the reconstruction of diapir boundaries from a set of partly interpreted sections indicates that it is well-suited to honor numerous constraining data while proposing different possible structural scenarios in the uninterpreted parts.

International audience; In this paper, an implicit structural modeling method using locally defined moving least squares shape functions is proposed. The continuous bending energy is minimized to interpolate between data points and approximate geological structures. This method solves a sparse problem without relying on a complex mesh. Discontinuities such as faults and unconformities are handled with minor modifications of the method using meshless optic principles. The method is illustrated on a two-dimensional model with folds, faults and an unconformity. This model is then modified to show the ability of the method to handle sparsity, noise and different reliabilities in the data. Key parameters of the shape functions and the pertinence of the bending energy for structural modeling applications are discussed. The predefined values deduced from these studies for each parameter of the method can also be used to construct other models.

International audience; Incorporating prior geological knowledge in geophysical process models often meetspractical meshing challenges and raises the question of how much detail is to be includedin the geometric model. We introduce a strategy to automatically repair and simplifygeological maps, geological cross-sections and the associated meshes while preservingelementary consistency rules. To identify features breaking validity and/or the thinfeatures potentially problematic when generating a mesh, we associate an exclusion zonewith each model feature (horizon, fault). When these zones overlap, both the connectivityand the geometry of the geological layers are automatically modified. The output modelenforces specific practical quality criteria on the model topology and geometry thatfacilitates the generation of a mesh with lower bounds on minimum angles and minimumlocal entity sizes. Our strategy is demonstrated on an invalid geological cross-section froma real-case study in the Lorraine coal basin. We further explore the impacts of the modelmodifications on wave propagation simulation. We show that the differences on theseismograms due to model simplifications are relatively small if the magnitude ofsimplifications is adapted to the physical problem parameters.C 2018 Published by Elsevier Masson SAS on behalf of Acade´mie des sciences. This is anopen access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

International audience; The Earth below ground is the subject of interest for many geophysical as well as geological investigations. Even though most practitioners would agree that all available information should be used in such an investigation, it is common practice that only a part of geological and geophysical information is actually integrated in structural geological models. We believe that some reasons for this omission are (a) an incomplete picture of available geological modeling methods, and (b) the problem of the perceived static picture of an inflexible geological representation in an image or geological model.With this work, we aim to contribute to the problem of subsurface interface detection through (a) the review of state-of-the-art geological modeling methods that allow the consideration of multiple aspects of geological realism in the form of observations, information, and knowledge, cast in geometric representations of subsurface structures, and (b) concepts and methods to analyze, quantify, and communicate related uncertainties in these models. We introduce a formulation for geological model representation and interpolation and uncertainty analysis methods with the aim to clarify similarities and differences in the diverse set of approaches that developed in recent years.We hope that this chapter provides an entry point to recent developments in geological modeling methods, helps researchers in the field to better consider uncertainties, and supports the integration of geological observations and knowledge in geophysical interpretation, modeling and inverse approaches.

International audience; In geology, implicit structural modelling constructs the geometry of geological structures (e.g. layers) by interpolating between sparse field data. A model is represented by a volumetric scalar field which is discontinuous on structural discontinuities such as faults or stratigraphic unconformities. The management of such discontinuities may involve boolean operations on several scalar fields or the creation of conformal meshes. Instead, we propose a ghost cell technique for the cartesian grid together with a set of relations between the ghost points, the regular nodes, and the discontinuities. Consequently, poor quality meshes are avoided and only the resolution of the grid has an impact on the solution. The modelling problem is posed as a least square’s minimization of a bending energy penalization on data mismatch functions and approximated by finite difference. As all relationships in the grid are implicitly defined, except close to the discontinuities, this algorithm is computationally efficient. We provide some benchmarks of the method on two-dimensional examples with folds, faults, and erosions.

International audience; RINGMesh is an open-source platform proposing a data model to support Shared Earth Modeling with unstructured meshes. This initiative is complementary to ontologic-based syntax and standard file formats. We provide features not only to share data and interpretation but also a concrete implementation framework to convert and manipulate models with the requirements needed by geomodelers, solvers and simulators. We advocate that this opens new perspectives for more efficient subsurface modeling workflows that harness uncertainties by confronting data, models and interpretations.

Summary We introduce a new method for implicit structural modeling. The method belongs to the Discrete Smooth Interpolation class of methods. We exploit the highly symmetric nature of Cartesian grids to propose new regularization operators that discretize very naturally on the Cartesian grid using finite differences: these operators do not have to be defined on boundary nodes, and their generalization to higher dimensions is straightforward. Numerical examples show that the proposed method is both robust and numerically efficient.

International audience; We introduce a method to process boundary defined geological models and ease their meshing. Our method detects and fixes geological model invalid features, (e.g. small gaps breaking model watertightness) and complex features (e.g. thin layers, unconformities and small fault throws) which constrain mesh element resolutions and angles making mesh generation challenging. These features are modeled by a graph that provides a formal framework to operate and correct the input model. The possible operations to fix the geometrical and topological issues are equivalent to graph elementary operations. Our method then first operates on the graph aiming at removing all the edges representing invalid features. The second step is to account for these topological changes in the geometrical model. The procedure is illustrated on an invalid 2D subsurface cross-section characterized by many small gaps and several intersections between the faults and the horizons.

International audience; Interpreting salt is a complex and time consuming task in seismic interpretation. Considerable progresses have been made recently by automatic methods which detect deterministic salt tops from the seismic image. However, uncertainties about salt exist, owing to intrinsic physical limitations of seismic imaging. Therefore, we propose a new workflow to generate several possible models of salt top surfaces with varying geometries and topologies. The method we propose is divided into three steps. We first segment the seismic volume into three regions: salt, sediments and uncertain, depending on the reliability of the automatic interpretation. We then compute a monotonic scalar field in the uncertain region, ranging from zero at the contact with salt to one at the contact with sediments. We finally generate a random field bounded between zero and one. The salt boundary is implicitly defined by the zero isovalue of the scalar field defined as the difference between the distance and the random fields. Applications of this workflow on a 2D seismic image and a 3D synthetic data set illustrate the potential of the method to efficiently address salt interpretation uncertainties.

International audience; Limited resolution and quality of seismic data and time requirements for seismic interpretation can prevent a precise description of the connections between faults. We have focused on the impact of the uncertainties related to the connectivity of en echelon fault arrays on fluid flow simulations. We used a set of 100 different stochastic models of the same en echelon fault array. These fault array models varied in the number of relay zones, relative position of fault segments, size of overlap zones, and number of relay faults. We automatically generated a flow model from each fault array model in four main steps: (1) stochastic computation of relay fault throw, (2) horizon building, (3) generation of a flow simulation grid, and (4) definition of the static and dynamic parameters. Flow simulations performed on these stochastic fault models with deterministic petrophysical parameters entailed significant variability of reservoir behavior, which cannot always discriminate between the types of fault segmentation. We observed that the simplest interpretation consisting of one fault yielded significantly biased water cut forecasts at production wells. This highlighted the importance of integrating fault connectivity uncertainty in reservoir behavior studies.

International audience; In this paper we demonstrate how recent geomodelling techniques can be combined and used to build a 3D geological model on a real case study: the former coal mine of Merlebach (France), that is targeted to be exploited for low-temperature geothermal energy production. From geological maps, cross-sections, borehole and mine exploitation data, we build a 3D model in which are identified the rocks and infrastructures having significantly different permeabilities. First, a structural model of the main geological interfaces in our area of interest (2 horizons and 13 faults) is built with classical geomodelling techniques. Then, we propose to model by surfaces the 71 irregularly stacked, very close and very thin, subvertical coal beds. To ease their construction, we use an implicit method which represents 3D surfaces as isovalues of a scalar field defined in a 3D tetrahedral grid of the area. The corresponding triangulated surfaces are remeshed with a recently proposed method based on Voronoi diagrams so that the exploited parts of the coal beds, now filled by sand, can be computed. The 3D surface-based geological model, in which infrastructures can be inserted as piecewise lines, can be volumetrically meshed. It is available for download as supplemental material, as well as a volumetric grid.

International audience; Geologists and geophysicists often approach the study of the Earth using different and complementary perspectives. To simplify, geologists like to define and study objects and make hypotheses about their origin, whereas geo-physicists often see the earth as a large, mostly unknown multivariate parameter field controlling complex physical processes. This paper discusses about some strategies to combine both approaches. In particular, I review some practical and theoretical frameworks associating petrophysical heterogeneities to the geometry and the history of geological objects. These frameworks open interesting perspectives to define prior parameter space in geophysical inverse problems, which can be consequential in under-constrained cases.

International audience; Fault-related displacements impact oil and gas flow predictions at reservoir scales. In this contribution, we integrate a quantitative description of fault-related deformation directly embedded into the structural mod-eling workflow. Consistent fault displacements are produced by using numerical fault operators that deform horizons in accordance with theoretical isolated fault displacement models to generate kinematically consistent structural models. We compare structural modeling approaches based on such fault operators with those relying on interpolation. Several synthetic cross-sections are generated from a reference high-resolution structural model of the Santos Basin, Brazil. Models are reconstructed from this 2D synthetic sparse dataset using both methods. Their ability to produce consistent structural models is assessed by comparing reconstructed and reference models. On this example, kinematic modeling improves the quality of automatically generated models when only few and poor quality observations are available, thus reducing the time needed for structural validation.

International audience; We discuss the sampling and the volumetric impact of stratigraphic correlation uncertainties in basins and reservoirs. From an input set of wells, we evaluate the probability for two stratigraphic units to be associated using an analog stratigraphic model. In the presence of multiple wells, this method sequentially updates a stratigraphic column defining the stratigraphic layering for each possible set of realizations. The resulting correlations are then used to create stratigraphic grids in three dimensions. We apply this method on a set of synthetic wells sampling a forward stratigraphic model built with Dionisos. To perform cross-validation of the method, we introduce a distance comparing the relative geological time of two models for each geographic position, and we compare the models in terms of volumes. Results show the ability of the method to automatically generate stratigraphic correlation scenarios, and also highlight some challenges when sampling stratigraphic uncertainties from multiple wells.

International audience

International audience; We propose a method to automatically generate a 3D sealed geological model from a set of disconnected surfaces. Our method also permits to remove small features (e.g. thin layers) of the model. To remove the gaps and other inconsistencies between the input surfaces and to build watertight volumes, we propose a two step approach. First we recover the model topology and then we modify its geometry. The topology recovery of the geological model detects the geological model inconsistencies and small features. Relying on tolerances, it allows geometrical displacement of model entities while preventing the output model to be too far away from the input surfaces. The second step modifies the geometry of the model in accordance with its newly defined topology. The output model is sealed and is an adequate input for volumetric discretization, then flow and geomechanical modeling. Our method is illustrated on a synthetic model containing delicate features characteristic of geological structural models such as non manifold features.

International audience; Channelized systems form complex sedimentary reservoirs. Their modeling calls for using conditioning data when possible. A reverse migration simulation fitting to observed data has been proposed. It permits to reconstruct the channelized paleo-system and to better understand reservoir architecture. Ancient oxbow lakes are precious witnesses of the evolution of the system. However, the global chronology of their abandonment can be hard to deduce from subsurface data. Most of the time only local relative chronologies are accessible for close oxbow lakes. The knowledge of oxbow lakes global relative abandonment ages is of first importance for the reconstruction of the paleo-system. We propose a few criteria based on the geometry of the system to facilitate the extraction of local chronologies. From these local analyses, deduction of the global chronology is possible thanks to a stochastic ordering method.

This work explains a procedure to predict Cu potentials in the ore-Kupferschiefer using structural surface-restoration and logistic regression (LR) analysis. The predictor in the assessments are established from the restored horizon that contains the ore-series. Applying flexural-slip to unfold/unfault the 3D model of the Fore-Sudetic Monocline, we obtained curvature for each restored time. We found that curvature represents one of the main structural features related to the Cu mineralization. Maximum curvature corresponds to high internal deformation in the restored layers, evidencing faulting and damaged areas in the 3D model. Thus, curvature may highlight fault systems that drove fluid circulation from the basement and host the early mineralization stages. In the Cu potential modeling, curvature, distance to the Fore-Sudetic Block and depth of restored Zechstein at Cretaceous time are used as predictors and proven Cu-potential areas as targets. Then, we applied LR analysis establishing the separating function between mineralized and non-mineralized locations. The LR models show positive correspondence between predicted probabilities of Cu-potentials and curvature estimated on the surface depicting the mineralized layer. Nevertheless, predicted probabilities are particularly higher using curvatures obtained from Late Paleozoic and Late Triassic restorations.

International audience; The logic of sedimentary channelized systems is only partly preserved in the depositional record. We propose a new method to reconstruct 3D channelized systems from incomplete observations made on surface or subsurface images that integrates the uncertainty on meander abandonment chronology. Starting with the youngest channel path observed and the abandoned loops in the meander belt, the method generates local relative chronologies using cross-cutting analysis. It thus proposes a possible global chronology of channel meander abandonments by going back in time while updating the system configuration. This global chronology is obtained through a stochastic procedure that orders the youngest abandoned meanders with regard to their position and orientation relative to the current channel path. Ordered abandoned meanders are then integrated in the main channel path during the reverse migration process so that the global stochastic ordering is made at each time step of the migration algorithm consistently with the updated channel belt. The proposed approach is parameterized by the spatio-temporal density of meander cutoff along the channel belt, which can be inferred from analog databases. The application of our tool on a seismic stratal slice of the Mc-Murray Formation in Canada provides various possible global chronologies of the abandoned meanders. We analyze the variability of these chronologies and highlight its impact on the various possible subsurface 3D global archi-tectures of the paleo-system and on the associated subsurface heterogeneity.

Stochastic simulation of fracture systems is an interesting approach to build a set of dense and complex networks. However, discrete fracture models made of planar fractures generally fail to reproduce the complexity of natural networks, both in terms of geometry and connectivity. In this study a pseudo-genetic method is developed to generate stochastic fracture models that are consistent with patterns observed on outcrops and fracture growth principles. The main idea is to simulate evolving fracture networks through geometric proxies by iteratively growing 3D fractures. The algorithm defines heuristic rules in order to mimic the mechanics of fracture initiation, propagation, interaction and termination. The growth process enhances the production of linking structure and impacts the connectivity of fracture networks. A sensitivity study is performed on synthetic examples. The method produces unbiased fracture dip and strike statistics and qualitatively reproduces the fracture density map. The fracture length distribution law is underestimated because of the early stop in fracture growth after intersection. Highlights? We propose a stochastic fracture simulation method mimicking mechanical behavior. ? Non-stationary information can be integrated in the simulation. ? Resulting fractures are better connected than in classical planar networks.

Remote sensing data provide significant information to constrain the geometry of geological structures at depth. However, the use of intraformational geomorphologic features such as flatirons and incised valleys often calls for tedious user interaction during 3-D model building. We propose a new method to generate 3-D models of stratigraphic formations, based primarily on remote sensing images and digital elevation models. This method is based on interpretations of the main relief markers and interpolation of a stratigraphic property on a tetahedral mesh covering the domain of study. The tetrahedral mesh provides a convenient way to integrate available data during the interpolation while accounting for discontinuities such as faults. Interpretive expert input may be provided through constrained interactive editing on arbitrary cross-sections, and additional surface or subsurface data may also be integrated in the modeling. We demonstrate this global workflow on a structurally complex basin in the Sierra Madre Oriental, Northeastern Mexico.

International audience; A recent method for modeling folds uses a fold frame with coordinates based on the structural geology of folds: fold axis direction, fold axial surface and extension direction. The fold geometry can be characterised by rotating the fold frame by the pitch of the fold axis in the axial surface and the angle between the folded foliation and the axial surface. These rotation angles can be expressed as 1D functions of the fold frame coordinates. In this contribution we present methods for extracting and automatically modeling the fold geometries from structural data. The fold rotation angles used for characterising the fold geometry can be calculated locally from structural observations. The fold rotation angles incorporate the structural geology of the fold and allow for individual structural measurements to be viewed in the context of the folded structure. To filter out the effects of later folding the fold rotation angles are plotted against the coordinates of the fold frame. Using these plots the geometry of the folds can be interpolated directly from structural data where we use a combination of radial basis function and harmonic analysis to interpolate and extrapolate the fold geometry. This contribution addresses a major limitation in existing methods where the fold geometry was not constrained from structural data. We present two case studies: a proof of concept synthetic model of a non-cylindrical fold and an outcrop of an asymmetrical fold within the Lachlan Fold belt at Cape Conran, Victoria, Australia.

International audience; Volumetric restoration can provide crucial insights into the structural evolution of three-dimensional (3-D) petroleum systems. A major limitation to its widespread application is the need to include complex architectures and realistic mechanics such as flexural slip. We apply an implicit approach that allows for, including unconformities, thin and/or pinched-out layers in the models but that cannot explicitly localize slip along horizons. To take advantage of this approach while accounting for flexural slip in 3-D restoration, we investigate new geomechanical properties. We consider flexural slip folding as a result of stacked rigid and thin weak layers, which can be modeled using transversely isotropic properties. We compare restorations of an anticline using transversely isotropic properties, isotropic properties, and a stack of rigid isotropic layers with nonfrictional slip between the layers. Our results show that transversely isotropic properties reasonably approximate flexural slip folding. We use these new tools to model the evolution of a complex system located in the Niger Delta toe. The system includes a detachment fold, a fault-bend fold, and a structural wedge formed in series. Growth stratigraphy and erosional surfaces delimit the kinematics of deformation. Regional erosive surfaces, 3-D gradients of fault slip, and vertical variations in mechanical strength motivated the use of our new restoration techniques. Restoring two growth units results not only in reinforcing the interpretation that the area is behaving as a deforming thrust sheet at critical taper, but also in highlighting coeval activity on both the hinterland structures and the toe of the thrust belt.

International audience

We have developed a 3D modeling strategy of the encased minibasin of Inceyol in Sivas (Turkey). The challenge lies in the combination of sparse outcrop data and the complex interpretive geometry of geologic structures that come from salt tectonics. We have succeeded in modeling the convoluted salt surface using an explicit indirect surface patch construction method followed by a manual mesh improvement. Then, we modeled the minibasin sediments with an implicit approach. The result highlighted the remarkable geometry of the convoluted salt horizon and its associated minibasin by extending in 3D the geologist’s interpretive 2D sections. This case study proved that building complex geometries is feasible with the existing tools and a good expertise in the various geomodeling techniques. Our work also underlined the need for new methods to ease the modeling of such tectonic features from sparse data. We have developed a 3D view of the model thanks to WebGL technology, as well as downloadable data to constitute a reference case study.

International audience; Due to the limited resolution of seismic reflection data in imaging near vertical structures, structural models can have significant uncertainties related to fault geometries and position. These uncertainties can be reduced by performing a history matching analysis on a large number of structural models generated stochastically. This work investigates about the integration of vertical seismic profiling data as another way to constrain and reduce such uncertainties. Because travel-times are not sufficiently sensitive to fault geometry perturbations and because we cannot model amplitudes accurately, we rely on phase distortion of seismograms as they propagate through the faulted models. To extract instantaneous phase information from seismograms, we used the empirical mode decomposition algorithm. This approach offers several advantageous properties compared to computing the instantaneous phase by analytic signal transformation. An instantaneous phase misfit was then defined as the L2 norm of two instantaneous phase functions. A numerical experiment was carried out in which 60 fault networks were generated stochastically from a single 3D interpretation of multiple cross sections; the 60 models were then ranked from the most similar up to the most dissimilar from a randomly chosen reference model. Results show that the proposed misfit can successfully constrain fault geometry

International audience; Conditioning a forward stratigraphic model to seismic or well data is still a challenge. So, such model cannot usually be used to run static or dynamic reservoir studies. In common methodologies, training images are built from FSM and used with Multiple Point Statistics methods to integrate the information in static geocellular models. Similarly, we present a method that uses a FSM as training model to generate 3D stratigraphic correlations of a set of units identified along wells. The wells are correlated iteratively, each new well being correlated to the result of the previous correlation. This ensures to take the 3D disposition of the wells into account. When the probability of association of the units is computed, we use the Dynamic Time Warping algorithm to build a consistent stratigraphic correlation. First results on synthetic data are presented, using a forward model built with the Sedsim algorithm and three wells.

International audience; This paper focuses on fault-related uncertainties in the subsurface, which can significantly affect the numerical simulation of physical processes. Our goal is to use dynamic data and process-based simulation to update structural uncertainty in a Bayesian inverse approach. We propose a stochastic fault model where the number and features of faults are made variable. In particular, this model samples uncertainties about connectivity between the faults. The stochastic three dimensional fault model is integrated within a stochastic inversion scheme in order to reduce uncertainties about fault characteristics and fault zone layout, by minimizing the mismatch between observed and simulated data.The stochastic fault model uses a priori information such as fault orientation, location, size and sinuosity, to sample both geometrical and topological uncertainties with realistic fault descriptions. Each fault object is parameterized by the random vector used to simulate fault features. Then, during inversion, the random vector of the current model is stochastically perturbed, producing a new parameter vector used as input by the stochastic fault model to produce a new model. Even if the topology varies from one model to another, the algorithm produces correlated models so that their flow responses evolve quite smoothly.The methodology is applicable in general and illustrated on a synthetic two-phase flow example. A first set of models is generated to sample the prior uncertainty space. Then models minimizing reference water-saturation data misfit are used as seeds to generate continuous Monte Carlo Markov Chains (MCMC) of models with discrete states. Posterior models reduce uncertainties about fault position, while the topology varies from one model to another. A second example highlights the interest of the parameterization when interpreted data are available, by perturbing geological scenarios and falsifying those that do not match two-phase flow observations.

International audience; The stochastic stratigraphic well correlation method considers the stratigraphic correlation of well data as a set of possible models to sample and manage uncertainty in subsurface studies. This method addresses the incompleteness of typical subsurface data such as limited seismic resolution, seismic blindness due to the lack of impedance contrast between distinct stratigraphic formations, borehole preferential location. The stochastic stratigraphic well correlation method is applied to the Malampaya buildup (a well documented offshore gas field located NorthWest of the Palawan Island, Philippines), aged upper Eocene to lower Miocene, and developed on the crest of a tilt-block. Among the available data, ten wells, seven of which are cored, have been drilled and a high resolution 3D seismic survey was acquired by Shell Philippines in 2002.

International audience; 3D Structural modeling is a major instrument in geosciences, e.g. for the assessment of groundwater and energy resources or nuclear waste underground storage. Fault net- work modeling is a particularly crucial step during this task, for faults compartmentalize rock units and play a key role in subsurface flow, whether faults are sealing barriers or drains. Whereas most structural uncertainty modeling techniques only allow for geometrical changes and keep the topology fixed, we propose a new method for creating realistic stochastic fault networks with different topologies. The idea is to combine an implicit representation of geological surfaces which provides new perspectives for handling topological changes with a stochastic binary tree to represent the spatial regions. Each node of the tree is a fault, separating the space in two fault blocks. Changes in this binary tree modify the fault relations and therefore the topology of the model.

The modeling of subsurface geometry and properties is a key element to understand Earth processes and manage natural hazards and resources. In this paper, we suggest this field should evolve beyond pure data fitting approaches by integrating geological concepts to constrain interpretations or test their consistency. This process necessarily calls for adding the time dimension to 3D modeling, both at the geological and human time scales. Also, instead of striving for one single best model, it is appropriate to generate several possible subsurface models in order to convey a quantitative sense of uncertainty. Depending on the modeling objective (e.g., quantification of natural resources, production forecast), this population of models can be ranked. Inverse theory then provides a framework to validate (or rather invalidate) models which are not compatible with certain types of observations. We review recent methods to better achieve both stochastic and time-varying geomodeling and advocate that the application of inversion should rely not only on random field models, but also on geological concepts and parameters.

International audience; Building a 3D geological model from field and subsurface data is a typical task in geological studies involving natural resource evaluation and hazard assessment. However, there is quite often a gap between research papers presenting case studies or specific innovations in 3D modeling and the objectives of a typical class in 3D structural modeling, as more and more is implemented at universities. In this paper, we present general procedures and guidelines to effectively build a structural model made of faults and horizons from typical sparse data. Then we describe a typical 3D structural modeling workflow based on triangulated surfaces. Our goal is not to replace software user guides, but to provide key concepts, principles, and procedures to be applied during geomodeling tasks, with a specific focus on quality control.

This paper develops a novel response surface method for characterizing the flow and its uncertainty in hydrocarbon reservoirs. Usually, due to computational requirement, the number of flow simulations that can be carried out is limited, which (1) leads to an under sampling of the uncertain space and (2) does not allow to capture curvatures and non-linearities in the reservoir flow behavior in face of uncertain parameters. The proposed method combines conventional flow simulation results with secondary information provided by fast alternatives such as connectivity measurements, single phase tracer or streamline simulation to overcome this sampling problem. Two response surface interpolation algorithms are investigated: discrete smooth interpolation and kriging with an external drift. Both (1) are independent of any predefined regression model, (2) can model complex response surfaces and (3) are able to integrate a secondary “soft” information. Cross validation is then carried out to evaluate the response surface reliability and the contribution of alternative simulation data. A modified version of the SPE 10th benchmark model is used to compare this methodology with standard ones. Results show: (1) the developed approach generates more accurate response surface than conventional techniques and (2) the cost of the method in time is clearly affordable compared to the gain in accuracy which allows a better appraisal of uncertainty on the reservoir flow response.

This paper proposes a novel history-matching method where reservoir structure is inverted from dynamic fluid flow response. The proposed workflow consists of searching for models that match production history from a large set of prior structural model realizations. This prior set represents the reservoir structural uncertainty because of interpretation uncertainty on seismic sections. To make such a search effective, we introduce a parameter space defined with a “similarity distance” for accommodating this large set of realizations. The inverse solutions are found using a stochastic search method. Realistic reservoir examples are presented to prove the applicability of the proposed method.

International audience; In this paper, we aim at providing a flexible and compact volumetric object model capable of representing many sedimentary structures at different scales. Geo-bodies are defined by a boundary representation; each bounding surface is constructed as a parametric deformable surface. We propose a three-dimensional sedimentary object with a compact parametrization which allows for representing various geometries and provides a curvilinear framework for modeling internal heterogeneities. This representation is based on Non Uniform Rational B-Splines (NURBS) smoothly interpolate between a set of points. The three-dimensional models of geobodies are generated using a small number of parameters, and hence can be easily modified. This can be done by a point and click user interactions for manual editing or by a Monte-Carlo sampling for stochastic simulation. Each elementary shape is controlled by deformation rules and has connection constraints with associated objects, in order to maintain the geometry and the consistency through editing. The boundary representations of the different sedimentary structures are used to construct hexahedral conformal grids in order to perform petrophysical property simulations following the particular three-dimensional parametric space of each object. Finally these properties can be upscaled, according to erosion rules, to a global grid that represents the global depositional environment.

This paper proposes to improve the natural fracture network characterisation by analysis microseismic data. We use a 3D Hough transform to build fracture orientation and density maps describing discontinuities that cannot be described by other measurements. The stochastic Discrete fracture simulator combines geostatistical and pseudo-genetic approaches to generate models that honour both measures from field characterisation and hierarchical organisation that result from the fracturing process itself. We suggest that using realistic fracture network characterisation and introducing mechanical concepts in the DFN simulation process affect connectivity of DFNs, hence is essential for predictivity of reservoir flow models.

International audience; Three-dimensional structural modeling is gaining importance for a broad range of quantitative geoscientific applications. However, existing approaches are still limited by the type of structural data they are able to use and by their lack of structural meaning. Most techniques heavily rely on spatial data for modeling folded layers, but are unable to completely use cleavage and lineation information for constraining the shape of modeled folds. This lack of structural control is generally compensated by expert knowledge introduced in the form of additional interpretive data such as cross-sections and maps. With this approach, folds are explicitly designed by the user instead of being derived from data. This makes the resulting structures subjective and deterministic. This paper introduces a numerical framework for modeling folds and associated foliations from typical field data. In this framework, a parametric description of fold geometry is incorporated into the interpolation algorithm. This way the folded geometry is implicitly derived from observed data, while being controlled through structural parameters such as fold wavelength, amplitude and tightness. A fold coordinate system is used to support the numerical description of fold geometry and to modify the behavior of classical structural interpolators. This fold frame is constructed from fold-related structural elements such as axial foliations, intersection lineations, and vergence. Poly-deformed terranes are progressively modeled by successively modeling each folding event going backward through time. The proposed framework introduces a new modeling paradigm, which enables the building of three-dimensional geological models of complex poly-deformed terranes. It follows a process based on the structural geologist approach and is able to produce geomodels that honor both structural data and geological knowledge.

International audience

International audience; This paper introduces a stochastic structural modelling method that honours interpretations of both faults and stratigraphic horizons on maps and cross-sections in conjunction with prior information, such as fault orientation and statistical size-displacement relationships. The generated stochastic models sample not only geometric uncertainty but also topological uncertainty about the fault network. Faults are simulated sequentially; at each step, fault traces are randomly chosen to constrain a fault surface in order to obtain consistent fault geometry and displacement profile. For each simulated fault network, stratigraphic modelling is performed to honour interpreted horizons using an implicit approach. Geometrical uncertainty on stratigraphic horizons can then be simulated by adding a correlated random noise to the stratigraphic scalar field. This strategy automatically maintains the continuity between faults and horizons. The method is applied to a Middle East field where stochastic structural models are generated from interpreted two-dimensional (2D) seismic lines, first by representing only stratigraphic uncertainty and then by adding uncertainty about the fault network. These two scenarios are compared in terms of gross rock volume (GRV) uncertainty and show a significant increase in GRV uncertainty when fault uncertainties are considered. This underlines the key role of faults in resource estimation uncertainties and advocates a more systematic fault uncertainty consideration in subsurface studies, especially in settings in which the data are sparse.

International audience; Ensemble-based optimization methods are often efficiently applied to history-matching problems. Although satisfactory matches can be obtained, the updated realizations, affected by spurious correlations, generally fail to preserve prior information when using a small ensemble, even when localization is applied. In this work, we propose a multi-scale approach based on grid-adaptive second-generation wavelets. These wavelets can be applied on irregular reservoir grids of any dimensions containing dead or flat cells. The proposed method starts by modifying a few low frequency parameters (coarse scales) and then progressively allows more important updates on a limited number of sensitive parameters of higher resolution (fine scales). The Levenberg-Marquardt ensemble randomized maximum likelihood (LM-enRML) is used as optimization method with a new space-frequency distance-based localization of the Kalman gain, specifically designed for the multi-scale scheme. The algorithm is evaluated on two test cases. The first test is a 2D synthetic case in which several inversions are run using independent ensembles. The second test is the Brugge benchmark case with 10 years of history. The efficiency and quality of results of the multi-scale approach are compared with the grid-block-based LM-enRML with distance-based localization. We observe that the final realizations better preserve the spatial contrasts of the prior models and are less noisy than the realizations updated using a standard grid-block method, while matching the production data equally well.

Accurate modelling of all scales of heterogeneities is necessary for a precise flow modelling inside clastic reservoir. We propose to simulate small scale heterogeneties that can be deposed at the interface between sedimentary structures (e.g. between accretion figure in channel point bars). The geometries of the considered sedimentary structures are modelled as boundary representation using the Non-Uniform Rational B-Spline (NURBS) mathematical formulation. This representation of various sedimentary objects (channel, point bar, clinoform, lobe and levee) provides a curvilinear framework for petrophysical properties simulations. The spatial distribution of petrophysical properties such as permeabilities has been simulated using unconditional Sequential Gaussian Simulations (SGS). An upscaling is then performed in order to integrate the surface properties into flow simulation grid. Nevertheless, these features are often very thin and local and cannot be upscaled to a complete reservoir grid cell. Thus, these interface small-scale disparities are considered as transmissibility multipliers applied to the faces of the grid’s cells. Moreover erosion due to the deposit of other geobodies can modify the repartition of surface heterogeneities. Thus, order of deposit and erosion between objects are taken into account through all these procedures.

International audience; The characterization of sedimentary structures is an important step in constructing quantitative models of sedimentary deposits from digital images, such as 3D seismic data, satellite images, or digital outcrops. However, the interpretation of these structures generally consists of tedious line pickings followed by surface modeling to define geobodies. Automatic geobody extraction is an alternative, but it is sensitive to image noise, and it does not account for prior sedimentary knowledge. We decided to combine minimal picking by an interpreter with object-guided image processing and optimization to achieve fast and semiautomatic geobody interpretation. Our approach used a realistic volumetric geobody representation based on nonuniform rational basis splines, which can easily be deformed by the interpreter and numerical optimization. Custom edge detection guided by some initial rough interpretations was performed to strengthen the most relevant edges in the picture. Automatic optimization was then computed to fit the initial geobody to these highlighted edges. This approach was applied on satellite pictures showing alluvial channels, and some preliminary results on 3D seismic time slices were also presented. The interpreted channels were then used in a retrodeformation process to automatically reconstruct the point bars. This semiautomatic method opens new perspectives to help interpreters rapidly come up with 3D models of sedimentary structures from subsurface and analog surface data sets.

The reliable modeling of three-dimensional complex geological structures can have a major impact on forecasting and managing natural resources and on predicting seismic and geomechanical hazards. However, the qualification of a model as structurally complex is often qualitative and subjective making the comparison of the capabilities and performances of various geomodeling methods or software difficult. In this paper, we consider the notion of structural complexity from a geometrical point of view and argue that it can be characterized using general metrics computed on three-dimensional sealed structural models. We propose global and local measures of the connectivity and of the geometry of the model components and show how they permit to classify nine 3D synthetic structural models. Depending on the complexity elements favored, the classification varies. The models we introduce could be used as benchmark models for geomodeling algorithms. HighlightsWe describe complicated geometrical configurations in structural models.Nine benchmark 3D structural models for geomodeling methods are proposed.We propose four measures to compare geometry and connectivity of structural models.Several classifications of the proposed benchmark models are given.