3D Multiple-Point Statistics for facies simulation using 2D and 1D conceptual models

Modeling geological reservoirs is a crucial step for understanding underground systems. Several activities such as oil and gas exploration, CO 2 sequestration, or geothermal energy production, need a realistic 3D characterization of reservoirs with uncertainty assessment. Multiple-Point Statistics (MPS) simulation is widely used for that task, because it allows for integrating complex conceptual models, honoring field data and taking into account for non stationarities in a stochastic framework. MPS methods require a training image (TI) from which the spatial arrangements are borrowed for the simulations. Therefore, 3D TIs are needed for 3D simulations in classical implementations. However, in practice, we often have access only to 2D or 1D informations from outcrops or boreholes in analog sites. Here, we propose a MPS technique allowing to generate 3D simulations based on 2D orthogonal TIs or on 2D and 1D orthogonal TIs. The algorithm consists in successively simulating sections and/or lines according to the orientation of the input 2D/1D TIs, until the 3D block is filled. Each section/line is simulated by using the TI(s) for the same orientation and by also taking into account for the spatial statistics in the transversal 2D or 1D section(s) provided by the corresponding TI(s). Therefore, the proposed method exploits as much as possible the input models. It is based on IMPALA, a parallel MPS algorithm for facies simulations, and, in addition to overcome the lack of 3D TIs in practical applications, the method is much faster than a classical 3D simulation based on a full 3D TI.