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Pixel-based multiple-point statistical (MPS) modelling is an appealing geostatistical modelling technique as it easily honours well data and allows use of geologically-derived training images to reproduce the desired heterogeneity. A variety of different training image types are often proposed for use in MPS modelling, including object-based, surface-based and process-based models. The purpose of the training image is to provide a description of the geological heterogeneities including sand geometries, stacking patterns, facies distributions, depositional architecture and connectivity. It is, however, well known that pixel-based MPS modelling has difficulty reproducing facies connectivity, and this study investigates the performance of a widely-available industrial SNESIM algorithm at reproducing the connectivity in a geometrically-representative, idealized deep-water reservoir sequence, using different gridding strategies and training images. The findings indicate that irrespective of the sand connectivity represented in the training image, the MPS models have a percolation threshold that is the same as the well-established 27% percolation threshold of random object-based models. A more successful approach for generating poorly connected pixel-based MPS models at high net:gross ratios has been identified. In this workflow, a geometrical transformation is applied to the training image prior to modelling, and the inverse transformation is applied to the resultant MPS model. The transformation is controlled by a compression factor which defines how non-random the geological system is, in terms of its connectivity.

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Simple object- or pixel-based facies models use facies proportions as the constraining input parameter to be honored in the output model. The resultant interconnectivity of the facies bodies is an unconstrained output property of the modelling, and if the objects being modelled are geometrically representative in three dimensions, commonly-available methods will produce well-connected facies when the model net:gross ratio exceeds about 30%. Geological processes have more degrees of freedom, and facies in high net:gross natural systems often have much lower connectivity than can be achieved by object-based or common implementations of pixel-based forward modelling. The compression method decouples facies proportion from facies connectivity in the modelling process and allows systems to be generated in which both are defined independently at input. The two-step method first generates a model with the correct connectivity but incorrect facies proportions using a conventional method, and then applies a geometrical transform to scale the model to the correct facies proportions while retaining the connectivity of the original model. The method, and underlying parameters, are described and illustrated using examples representative of low and high connectivity geological systems.