Paramétrisation 3D de l'espace en géologie sédimentaire : le modèle GeoChron

Reservoir modelling requires building a volumic mesh usually adapted to faults and horizons of the domain, on which petrophysical property models are computed. The common practice consists in using stratigraphic curvilinear grids formed of hexahedral cells whose indexes (i, j, k) constitute a sampling of a " 3D parametric function (u, v,t) where (u, v) correspond to the "paleo-geographic" coordinates tangent to the horizons and (t), viewed as an analog to the geological age of the terrains, is approximately orthogonal to the horizons. These grids are suited to the property-modelling geostatistical algorithms but their topological regularity induces errors or approximations in complex fault networks or folded environments. The GeoChron model corrects these drawbacks by clearly segragating the geometry of the domain of study (modelled by an unstructured tetrahedralised mesh), the link between this geometry and the geometry of the layers at the time or deposition (thanks to a 3D parametric function (u,v,t)) and the property model (computed in a regular fine-scaled grid). After exposing the mathematical framework of this model which emphasises the similarity with time stratigraphic (or Wheeler) diagrams used in sedimentology, we show two practical ways of building such a parameterisation and their implementation in the GOCAD geomodelling software. Then we show how the (t) component of the parametric function can be used to automatically compute a geometric estimate of the throw vector in any point of a fault surface. Finally, we present Borne applications concerning petrophysical property modelling, deformation estimation or seismic data integration.La modélisation des réservoirs pétroliers passe par une étape de construction d'une grille volumique généralement adaptée aux failles et aux horizons du domaine, sur laquelle les modèles de propriétés pétrophysiques sont calculés. On utilise pour cela des grilles curvilinéaires stratigraphiques formées de cellules hexaédriques dont les indices (i,,j, k) constituent un échantillonnage d'une fonction paramétrique 3D (u,v,t) où (u,v) correspondent aux coordonnées "paléogéographiques" tangentielles aux horizons et (t), considéré comme un analogue de l'age geologique des terrains, est approximativement orthogonal aux horizons. Ces grilles sont bien adaptées aux algorithmes géostatistiques de modélisation de propriétés mais leur régularité topologique entraîne des erreurs ou des approximations dans les domaines fortement faillés ou plissés. Le modèle GeoChron corrige ces défauts en séparant clairement la géométrie du domaine d'étude (représentée par un maillage tétraédrisé non structuré), la correspondance entre cette géométrie et la géométrie des couches au moment de leur formation (grâce à une fonction de paramétrisation 3D (u, v, t) ) et le modèle de propriété (calculé dans une grille régulière fine). Après avoir exposé le cadre mathématique de ce modèle qui met en valeur les similarités avec les diagrammes de time stratigraphy (ou de Wheeler) utilisés en sédimentologie, nous indiquons deux méthodes pratiques de construction d'une telle paramétrisation, implémentées dans le cadre du géomodeleur GOCAD. Puis nous montrons comment la composante (t) de la fonction de paramétrisation peut être utilisée pour calculer automatiquement en tout point d'une surface de faille une estimation géométrique du vecteur rejet. Enfin, nous présentons plusieurs applications possibles concernant la modélisation des propriétés pétrophysiques, l'estimation des déformations ou encore l'intégration des données sismiques

Paramétrisation 3D de l'espace en géologie sédimentaire (le modèle GeoChron)

La modélisation des réservoirs pétroliers passe par une étape de construction d'une grille volumique généralement adaptée aux failles et aux horizons du domaine, sur laquelle les modèles de propriétés pétrophysiques sont calculés. On utilise pour cela des grilles curvilinéaires stratigraphiques formées de cellules hexaédriques dont les indices (i,,j, k) constituent un échantillonnage d'une fonction paramétrique 3D (u,v,t) où (u,v) correspondent aux coordonnées "paléogéographiques" tangentielles aux horizons et (t), considéré comme un analogue de l'age geologique des terrains, est approximativement orthogonal aux horizons. Ces grilles sont bien adaptées aux algorithmes géostatistiques de modélisation de propriétés mais leur régularité topologique entraîne des erreurs ou des approximations dans les domaines fortement faillés ou plissés. Le modèle GeoChron corrige ces défauts en séparant clairement la géométrie du domaine d'étude (représentée par un maillage tétraédrisé non structuré), la correspondance entre cette géométrie et la géométrie des couches au moment de leur formation (grâce à une fonction de paramétrisation 3D (u, v, t) ) et le modèle de propriété (calculé dans une grille régulière fine). Après avoir exposé le cadre mathématique de ce modèle qui met en valeur les similarités avec les diagrammes de time stratigraphy (ou de Wheeler) utilisés en sédimentologie, nous indiquons deux méthodes pratiques de construction d'une telle paramétrisation, implémentées dans le cadre du géomodeleur GOCAD. Puis nous montrons comment la composante (t) de la fonction de paramétrisation peut être utilisée pour calculer automatiquement en tout point d'une surface de faille une estimation géométrique du vecteur rejet. Enfin, nous présentons plusieurs applications possibles concernant la modélisation des propriétés pétrophysiques, l'estimation des déformations ou encore l'intégration des données sismiques.Reservoir modelling requires building a volumic mesh usually adapted to faults and horizons of the domain, on which petrophysical property models are computed. The common practice consists in using stratigraphic curvilinear grids formed of hexahedral cells whose indexes (i, j, k) constitute a sampling of a " 3D parametric function (u, v,t) where (u, v) correspond to the "paleo-geographic" coordinates tangent to the horizons and (t), viewed as an analog to the geological age of the terrains, is approximately orthogonal to the horizons. These grids are suited to the property-modelling geostatistical algorithms but their topological regularity induces errors or approximations in complex fault networks or folded environments. The GeoChron model corrects these drawbacks by clearly segragating the geometry of the domain of study (modelled by an unstructured tetrahedralised mesh), the link between this geometry and the geometry of the layers at the time or deposition (thanks to a 3D parametric function (u,v,t)) and the property model (computed in a regular fine-scaled grid). After exposing the mathematical framework of this model which emphasises the similarity with time stratigraphic (or Wheeler) diagrams used in sedimentology, we show two practical ways of building such a parameterisation and their implementation in the GOCAD geomodelling software. Then we show how the (t) component of the parametric function can be used to automatically compute a geometric estimate of the throw vector in any point of a fault surface. Finally, we present Borne applications concerning petrophysical property modelling, deformation estimation or seismic data integration.NANCY-INPL-Bib. électronique (545479901) / SudocSudocFranceF

In vitro analysis of patellar kinematics: validation of an opto-electronic cinematic analysis protocol

Opto-electronic cinematic analysis has already proven useful in the investigation of patients with a knee replacement; however, neither patellar tracking nor the various positional parameters relevant to instability such as patellar tilt and/or patellar shift have ever been specifically evaluated using this type of system. The aim of this research was to validate the relevance of this type of cinematic analysis in order to use it in the evaluation of the main factors underlying patellar instability. Six fresh-frozen anatomical specimens were studied. The data were acquired using the Motion Analysis system. Statistical analysis reveals a good reproducibility of measurements. Our protocol based on an opto-electronic acquisition system has an accuracy of 0.23 mm for shift and of 0.4 for rotation, which is calculated by integrating the various experimental parameters and instrumental features specific to the Motion Analysis system. The results are consistent with published results which further attests to the validity and the efficacy of the protocol and encourages us that this protocol is suitable for the in vitro study of patellar kinematics

Study of patellar kinematics after reconstruction of the medial patellofemoral ligament

Background: Medial patellofemoral ligament reconstruction is currently the technique of choice for the treatment of patellar instability. But what should be the most appropriate graft tension for optimal restoration of patellofemoral kinematics? Methods: Six freshly frozen cadaveric knees were studied, the three bone segments were respectively equipped with opto-reflective markers. The acquisitions were made using the Motion Analysis System®. Six successive acquisitions were performed for each knee under different levels of graft tension. Findings: With an intact medial patellofemoral ligament, the medial patellar tilt increased up to a mean value of 2.02° (SD 3.1), the medial patellar translation gradually increased up to a mean value of 3.3 mm (SD 2.25) with a slight lateral rotation over the first 30° of knee flexion with a maximum mean value of 1.22° (SD 0.8) at 20° of knee flexion. Reconstruction of the medial patellofemoral ligament was performed using different levels of tension applied to the graft. Only 10 N of graft tension could restore normal patellar tilt, lateral shift and rotation, with results approximating those measured on healthy knee. Interpretation: This study confirms the role of the medial patellofemoral ligament in providing adequate patellar stability during the first 30° of knee flexion. According to our findings, a 10 N tension applied to the graft appears sufficient to ensure proper control of patellar tracking whereas 20, 30 and 40 N of tension are excessive tension values inducing a major overcorrection in all studied parameters. Medial patello-femoral ligament reconstruction Patellar tilt - Patellar rotation - Patellar translation - Patellar instabilit

Geochron: a framework to estimate fracturation of deformed sedimentary layers

International audienceA full-3D balanced restoration technique is used to estimate the fracturation of adeformed sedimentary layer using a Geochron parametric representation of the ante-deformedgeological structure. The displacements and the strains which have affected the geological formationare computed assuming small deformations and using the elastic solid theory of continuous media. Insimple cases such as thin plates, this new approach is in agreement with results predicted by thetheory. Strain tensor invariants (dilatation coefficient, principal strains, etc.) coupled with mechanicalproperties of rock types are used to characterize the distribution of fracture orientations. It also givesuseful strain parameters that can be related to the observed faults. This general theoretical frameworkprovides solutions to complex problems such as the determination of strains resulting from tectonicevents and for predicting faulted zones in reservoirs. The method is applied on the Split MountainAnticline Case Study (Utah, USA), a natural outcropped clastic reservoir. Observed fractures on thefield are in good agreement with the ones predicted from the proposed restoration methodology. Thefinal goal of this research is to improve oil and gas recovery in fractured reservoirs by a betterestimation of the permeability tensor

The role of the medial ligamentous structures on patellar tracking during knee flexion

The influence of the medial patellar ligamentous structures on patellar tracking has rarely been studied. Thus the main purpose of this cadaveric biomechanical study was to determine the influence of the medial patellofemoral (MPFL), medial patellomeniscal (MPML) and medial patellotibial (MPTL) ligaments on the three-dimensional patellar tracking during knee flexion. This study was conducted using a validated cadaveric optoelectronic protocol for analysis of patellar kinematics. Methods For each cadaveric knee study, four successive acquisitions were performed; first was studied patellar tracking in healthy knees, then the junction between MPFL and vastus medialis obliquus (VMO) was sectioned, the MPFL was released at its patellar attachment and finally was released the insertion of the MPML and MPTL. Results In this study, the MPFL accounts for 50-60% of the medial stabilization forces of the lateral patellar shift during patellar engagement in the femoral trochlea. This work confirm and clarify the role of the MPFL as the primary stabilizer of the patella during the initial 30° of knee flexion. Moreover, this study shows no significant results regarding the stabilizing action of the VMO on the patella during knee flexion. Conclusion This in vitro study, conducted with an experimental protocol previously validated in the literature, helps quantify the actions of the MPFL, the VMO, and the MPML/MPTL respectively, and identify areas of joint motion where these structures have the most significant influence. This confirms the importance of reconstruction in the treatment of chronic patellar instability. During its reconstruction, care should be taken to adjust the MPFL balance during the initial 20°-30° of flexion

3D-Parameterization of the 3D Geological Space – The GeoChron Model

International audienceOne of the key points in reservoir modeling is the building of a complex 3D-mesh, which mustintegrate various constraints: respecting the geometry of the fault network, taking into accountstratigraphic knowledge, computing petrophysical properties by geostatistical methods, allowingupscaling and/or flow simulation… The building of this mesh relies on the use of a parametriccoordinate system (u,v,t) such that (u,v) corresponds to “horizontal” curvilinear coordinatestangent to the horizons while (t) corresponds to the “vertical” curvilinear axis approximatelyorthogonal to the horizons. So far, common practice consists in covering the geological domainwith a “regular structured stratigraphic grid” with hexahedral cells and then to use the (i,j,k)indexes of the nodes of these cells as a sampling of the (u,v,t) coordinates. This kind ofstructured mesh is necessary to geostatistics, and to a lesser point flow simulation, which relyheavily on the implicit structure of the mesh to define neighborhoods and relationships betweencells. However, such a regular grid may lead to errors or approximation, for example whentrying to model complex faults networks or heavily folded horizons in such a way that edges'cells never cross these structural surfaces. In this article, we propose a completely new approachbased on the recently introduced “GeoChron” model where the (u,v,t) parameterization of thegeological space is computed independently of any stratigraphic grid. This approach allows aconsistent 3D-parameterization to be built whatever the complexity of the fault network, usingonly a tetrahedral mesh respecting the faults. Stratigraphic data, such as unconformity orsedimentation styles, can be taken into account in the construction of such a parameterization.The main benefit of such a parameterization of the 3D geological space is to allow past, presentand future geostatistical methods to be implemented in the (u,v,t) parametric space without usingany stratigraphic grid. As a consequence, it is then possible to populate polyhedral grids with thepetrophysical properties computed in the parametric space

Adaptive multi-scale ensemble-based history matching of seismic-derived models

International audienceWe present a new history matching approach designed for highly detailed seismic derived prior models. An ensemble-based optimization method is used to integrate production data and quantify associated uncertainties. An adaptive multi-scale wavelet parameterization is applied to stabilize the inversion and preserve the compatibility of history matched models with seismic data by first modifying a few low frequency parameters and then progressively allowing more important updates on a limited number of sensitive parameters of higher resolution. We show numerically that this adaptive multi-scale method avoids unnecessary updates and reduces noise, which are typically observed in standard ensemble-based methods when using a small ensemble. The new method is validated using a synthetic example. We observe that the final realizations better preserve the spatial distribution of the prior models, are less noisy and also fit the production data better than the realizations updated using a standard grid-blockmethod

Adaptive multi-scale ensemble-based history matching of seismic-derived models

International audienceWe present a new history matching approach designed for highly detailed seismic derived prior models. An ensemble-based optimization method is used to integrate production data and quantify associated uncertainties. An adaptive multi-scale wavelet parameterization is applied to stabilize the inversion and preserve the compatibility of history matched models with seismic data by first modifying a few low frequency parameters and then progressively allowing more important updates on a limited number of sensitive parameters of higher resolution. We show numerically that this adaptive multi-scale method avoids unnecessary updates and reduces noise, which are typically observed in standard ensemble-based methods when using a small ensemble. The new method is validated using a synthetic example. We observe that the final realizations better preserve the spatial distribution of the prior models, are less noisy and also fit the production data better than the realizations updated using a standard grid-blockmethod

Characterizing Fractured Reservoirs Using Structural Attributes

International audienceA new full-3D balanced restoration technique for geological structures is used to estimate the strain tensor and to define fractured zones applying failure criteria. This approach based on the elastic solid theory of continuous media gives the tensor of deformations. In simple cases such as thin plates this new approach is in agreement with results predicted by the theory. Strain tensor invariants (dilatation coefficient principal strains etc.) coupled with mechanical properties of rock types are used to characterize the distribution of fracture orientations. The method is applied on the Split Mountain