Bayesian uncertainty quantification of reservoir prediction is a significant area of ongoing research, with the major effort focussed on estimating the likelihood. However, the prior definition, which is equally as important in the Bayesian context and is related to the uncertainty in reservoir model description, has received less attention. This paper discusses methods for incorporating the prior definition into assisted history-matching workflows and demonstrates the impact of non-geologically plausible prior definitions on the posterior inference. This is the first of two papers to deal with the importance of an appropriate prior definition of the model parameter space, and it covers the key issue in updating the geological model-how to preserve geological realism in models that are produced by a geostatistical algorithm rather than manually by a geologist. To preserve realism, geologically consistent priors need to be included in the history-matching workflows, therefore the technical challenge lies in defining the space of all possibilities according to the current state of knowledge. This paper describes several workflows for Bayesian uncertainty quantification that build realistic prior descriptions of geological parameters for history matching using support vector regression and support vector classification. In the examples presented, it is used to build a prior description of channel dimensions, which is then used to history-match the parameters of both fluvial and deep-water reservoir geostatistical B Vasily Demyanov

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Models used for reservoir prediction are subject to various types of uncertainty, and interpretational uncertainty is one of the most difficult to quantify due to the subjective nature of creating different scenarios of the geology and due to the difficultly of propagating these scenarios into uncertainty quantification workflows. Non-uniqueness in geological interpretation often leads to different ways to define the model. Uncertainty in the model definition is related to the equations that are used to describe the modelled reality. Therefore, it is quite challenging to quantify uncertainty between different model definitions, because they may include completely different model parameters. This paper is a continuation of work to capture geological uncertainties in history matching and presents a workflow to handle uncertainty in the geological scenario (i.e. the conceptual geological model) to quantify its impact on the reservoir forecasting and uncertainty quantification. The workflow is based on inferring uncertainty from multiple calibrated models, which are solutions of an inverse problem, using adaptive stochastic sampling and Bayesian inference. The inverse problem is solved by sampling a combined space of geological model parameters and a space of reservoir model descriptions, which represents uncertainty across different modelling concepts based on multiple geological interpretations. The workflow includes building a metric space for reservoir model descriptions using multi-dimensional scaling and Geosci (2019) 51:241-264 classifying the metric space with support vector machines. The proposed workflow is applied to a synthetic reservoir model example to history match it to the known truth case reservoir response. The reservoir model was designed using a multi-point statistics algorithm with multiple training images as alternative geological interpretations. A comparison was made between predictions based on multiple reservoir descriptions and those of a single one, revealing improved performance in uncertainty quantification when using multiple training images.

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