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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; 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.

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.

We propose a method to manage uncertainties about the layering of 3D reservoir models, using stochastic correlations of sedimentary units identified along wells, according to the sequence stratigraphy paradigm. A stratigraphic model represents the architecture of the stratigraphic succession of an area. Sequence stratigraphy is a common paradigm in reservoir studies to interpret and correlate local high resolution observations (outcrops, well logs and core samples) and more exhaustive but lower resolution data such as 3D seismic. The incompleteness of these data, their quantity and their varying quality, added to the fact that the processes that control the geometry and the conformability of the sequences are complex and poorly known, lead to uncertainties. The proposed method aims at building stratigraphic models honoring 1D interpretations along wells together with conceptual sequence stratigraphic rules formulated quantitatively as correlation costs. The algorithm chosen is a modified version of the Dynamic Time Warping algorithm. More than finding the best correlation using a set of rules, it handles different orders of sequences, takes in account the conformability of the horizons, and its output is a set of different possible correlations, allowing for generating alternative stratigraphic layerings. This methodology is demonstrated on the Teapot Reservoir, Wyoming.

On the basis of a field study, we discuss the need of a new paradigm for the construction of structural models. Indeed, within the traditional framework, building a 3D consistent fault network model consists in: first, picking faulting evidences on 3D seismic images and then, according to a priori concept derived from tectonic history, manually extrapolate in a consistent manner these evidences. The extrapolation step is actually the interpretation task that any structural geologist performs to build a 3D model from the observed evidences. However, such interpretations should not be considered as unique for uncertainty assessment and management. Therefore, we argue for the use of a stochastic system which will perform the extrapolation task (i.e. the construction of the 3D structural model). However, this computer method needs to be fed with similar geological knowledge as used in manual interpretation, such as structural style or interaction between faults of different tectonic origins. Integrating this conceptual information within a numerical system remains a key challenge.

To study the impact of subsurface uncertainties on oil recovery, it is common to build a large set of models which cover these uncertainties. Despite increase of computational capabilities, as models become more complex, it is not possible to perform full physic flow simulation for all the generated models. This is why stochastic reservoir model sets are often decimated to assess the impact of static uncertainties on dynamic reservoir performance. This contribution will focus on the use of proxy to perform this data set reduction. A lot of different proxies have been developed, from the simplest to the more complicated so it is difficult to choose the good one according to a particular goal. We present different criteria to compare the proxy quality and their helps to assess uncertainties on oil recovery. A first criterion will be based on the relation which may exists between the model distances computed on the proxy responses and those compute on flow responses. Another criterion is the speed factor and simplification provide by the proxy compared to the full physic simulator. These two criteria are very simple and can be applied in an early time to avoid deploying time consuming proxies which won’t provide accurate information. The last criterion presented here, is the confidence intervals which can be computed around probabilistic reservoir production forecasts computed on a small representative subset of model. Even if this criterion can be used only when the entire dataset has been simulated, it provides some quantification about a possible bias created by a proxy and the remaining uncertainties on oil recovery. We present here a comparison study between widely different proxy responses applied on a real dataset of that methodology. This will give us some keys to choose a proxy which is a good compromise between accuracy and easy to handle methodology.