Faculté des sciences

Probability aggregaton methods and multiple-point statistics for 3D modeling of aquifer heterogeneity from 2D training images

Comunian, Alessandro ; Renard, Philippe (Dir.) ; Straubhaar, Julien (Codir.)

Thèse de doctorat : Université de Neuchâtel, 2011 ; 2187.

Multiple-point statistics (MPS) is a rising method for the characterization of heterogeneity. Its strength and its Achilles' heel lie in the training image, which is the conceptual model of geological heterogeneity on which MPS simulations are based. Indeed, on one side the use of the training image allows great flexibility when for example for bi-dimensional (2D) simulation a training image can... Plus

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    Summary
    Multiple-point statistics (MPS) is a rising method for the characterization of heterogeneity. Its strength and its Achilles' heel lie in the training image, which is the conceptual model of geological heterogeneity on which MPS simulations are based. Indeed, on one side the use of the training image allows great flexibility when for example for bi-dimensional (2D) simulation a training image can be provided by a photo-mosaic of an outcrop or by a sketch drawn by a geologist. On the other side, in three-dimensions (3D) a training image is rarely available.

    When the information provided by a 3D image is not accessible, then one must somehow use probabilistic information which comes from lower dimen- sion sources, like for example 2D training images. If different 2D sources of information are available, one possibility is to aggregate the corresponding probability information. This problem is very general and several methods exist. Two main categories of methods are distinguished: those based on the sum (convex) and those based on the multiplication (non-convex). When the weighting factors can be determined from some training data, the best reliabilities are obtained with the Beta-transformed linear pool and the Bor- diey's formula. Instead, when training data are not accessible, reasonably reliable results can be obtained with the Bordley's formula and with the Markovian-type categorical prediction.

    One convex method and one non-convex method are tested for the ag- gregation of information coming from 2D training images. For the tests, one 3D image of a micro-computed tomography of a sandstone and one 3D realization of a fluvio-glacial environment are used as references. Two di- mensional slices of the reference 3D images are used as training images for providing the information to be aggregated with the methods cited above, but also for the simulation with two novel method proposed here. One of this methods is baaed on sequential 2D simulations conditioned by the data computed during the previous simulation steps (method s2Dcd). With this last method it is possible to obtain , without the use of a 3D training im- age, 3D simulations which can be considered close to the reference images according to most comparison criteria considered. Moreover, while the re- sults obtained with the method s2Dcd are close to the results obtained with a MPS simulation which make use of a 3D training image, the CPU time required by s2Dcd is from two to four orders of magnitude smaller than with a traditional 3D simulation. This computational efficiency is a step forward for the introduction of MPS in frameworks which require a great number of realizations in a reasonably restricted amount of time, like for example Monte Carlo methods or stochastic inverse problems.

    Other techniques exists to deal with the simulation in 3D when a 3D training image is not available. One of this techniques, developed in this thesis' framework, is applied for the simulation of the image of the fluvio- glacial aquifer analog used as reference for the tests depicted above. It is a hierarchical technique: six parallel outcrops mapped during a quarry excava- tion serve to recognize geological features at different scales and on different depositional layers. Once the complexity of the observed heterogeneity is simplified, object based techniques are used to simulate 3D training images containing simple shapes. Maps of the orientation of the main geological structures are created by interpolating orientations derived from morpholog- ical analysis. All these information are then included in a MPS simulation framework. The geological heterogeneity reproduced using this technique is realistic and can provide an high-resolution benchmark for fluid flow and transport problems.

    In summary, this thesis demonstrates that is is possible to apply MPS methods obtaining credible results from a geological point of view even in absence of a 3D training image.