Uncertainty Quantification in Reservoir Prediction: Part 1—Model Realism in History Matching Using Geological Prior Definitions

Abstract

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

An Attempt to Boost Posterior Population Expansion Using Fast Machine Learning Algorithms

“…Due to the possibility of computing gradients in GAN models space, deterministic inversion using GANs is also possible but can be hindered by the non-linearities of the problem (Laloy et al, 2019 ). Simpler models, such as Support Vector Machines (SVM) were also used to construct informative geological prior to constrain sampling for realistic reservoir models (Arnold et al, 2019 ).…”

A Multi-Stencil Fast Marching Method with Path Correction for Efficient Reservoir Simulation and Automated History Matching

“…In consequence, geological models have inherent uncertainty, and the evaluation of uncertainty is crucial for production prediction as well as development optimization (Oliver et al, 2008). For scenarios where well testing or production data is available, automated history matching (AHM) can be adopted to reduce the uncertainty of geological models, and reservoir simulation typically needs to be conducted on a large number of realisations to explore how dynamic responses are affected by the change of model parameters (Oliver and Chen, 2011;Arnold et al, 2019;Demyanov et al, 2019;Zhang et al, 2021a). However, conventional reservoir simulation methods based on finite difference, finite volume or finite element methods (Zhang et al, 2018(Zhang et al, , 2021c are generally time-consuming for transient problems, and it can be prohibitively expensive to run simulations on all realisations in the process of AHM.…”

Combined inverse and forward numerical modelling for reconstruction of channel evolution and facies distributions in fluvial meander-belt deposits

“…In such cases, databases are commonly employed to provide information about the distributions of facies known from analogous modern rivers and outcropping successions (e.g., Colombera et al, 2012aColombera et al, , 2012bColombera et al, , 2013. Such databases are used to inform reservoir models that seek to depict the expected distribution of facies and elements within subsurface successions (Arnold et al, 2019).…”

“…For each reservoir, or sector thereof, the uncertainty relating to geological and petrophysical features is usually addressed by generating multiple equiprobable models built using stochastic modelling methods (Caumon, 2018). The approaches that are typically used to model the distributions of meander-belt facies associations in subsurface fluvial successions consist of general-purpose geostatistical modelling tools, such as those based on two-point statistics (e.g., sequential indicator simulations; Journel & Alabert, 1989;Deutsch & Journel, 1992) or on multi-point statistics (e.g., Srivastava, 1994;Strebelle, 2002;Straubhaar & Malinverni, 2014;Arnold et al, 2019;Calderon et al, 2019). However, pixel-based geostatistical methods commonly struggle to reproduce the geometry and connectivity of complex facies configurations in three dimensions (Renard et al, 2011;Rongier et al, 2016).…”

“…A solution to this is offered by inverse (i.e., reverse) stratigraphic modelling methods (e.g., ChaRMigS method of Parquer, et al, 2017), which honour observations of abandoned meanders by integrating them into a vector-based modelling structure that can be used to determine the temporal evolution of a river channel. In all cases, the question of uncertainty assessment remains central and calls for considering multiple realizations of reservoir geometry (Pyrcz et al, 2015;Caumon, 2018;Arnold et al, 2019). Overall, these rule-based approaches have been shown to be a promising way to address the shortcomings of pixel-based and object-based methods, in particular towards honouring all quantitative spatial observations while maintaining consistent relationships between the simulated architectural elements.…”