Abstract
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 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.
Highlights
Geological uncertainties can be quantified in producing assets by a Bayesian process of first history matching (HM) geological parameters of the reservoir to production data using a least-squares misfit objective function, using a Markov chain Monte Carlo (MCMC)-based post-processor to estimate the Bayesian credible intervals
The workflow demonstrates how reservoir models based on multiple training images can be updated through history matching while ensuring that the resulting history-matched models are geologically realistic and consistent with a priori geological knowledge
Uncertainty quantification based on multiple training images demonstrated that adaptive stochastic sampling is capable of providing a close match to the observed production whilst maintaining geologically realistic model parameter relationships for a range of geological scenarios
Summary
Geological uncertainties can be quantified in producing assets by a Bayesian process of first history matching (HM) geological parameters of the reservoir to production data using a least-squares misfit objective function, using a Markov chain Monte Carlo (MCMC)-based post-processor to estimate the Bayesian credible intervals. There may be a number of modelling methods that are possible [e.g. the reservoir facies could be modelled using an object modelling method, a variogram-based geostatistical method such as sequential indicator simulations (SIS), multi-point statistics or a sedimentary process model] and many different data that can be applied in different ways Parameterisation This is the collection of Model parameters, and their related prior probabilities, chosen to represent the uncertainty of a reservoir. A complete space of all possible reservoir descriptions would encompass the true prior uncertainty for the reservoir, and sampling this space with adequate realisations would allow us to predict the Bayesian posterior probability accurately This reality is hard to accomplish, as demonstrated by the case study in Arnold et al (2012), where a small set of uncertain Scenarios (81) made matching all these possibilities to the production data all but impossible to achieve practically.
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