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 models. This paper also demonstrates how to handle modelling approaches where geological parameters and geostatistical reservoir model parameters are not the same, such as measured channel dimensions versus affinity parameter ranges of a multi-point statistics model. This can be solved using a multilayer perceptron technique to move from one parameter space to another and maintain realism. The overall workflow was implemented on three case studies, which refer to different depositional environments and geological modelling techniques, and demonstrated the ability to reduce the volume of parameter space, thereby increasing the history-matching efficiency and robustness of the quantified uncertainty.
Highlights
The main problem in forecasting reservoir behaviour is the lack of information available to populate any reservoir model of a heterogeneous geological system away from the wellbores
This paper demonstrates how to handle modelling approaches where geological parameters and geostatistical reservoir model parameters are not the same, such as measured channel dimensions versus affinity parameter ranges of a multipoint statistics model
A good analogy to the problems faced in creating reservoir models was supplied by Christie et al (2005), who likened forecasting reservoir production to drawing a street map and predicting traffic flows based on what you see from several street corners in thick fog
Summary
The main problem in forecasting reservoir behaviour is the lack of information available to populate any reservoir model of a heterogeneous geological system away from the wellbores. Bayesian uncertainty quantification is a commonly used approach in reservoir engineering, where the model mismatch to some data (e.g. production data) is used to estimate the likelihood and, based on some assumption of the prior, infer the posterior. Bayes’ theorem is a statistical method that allows one to update the estimates of probability given an initial set of prior beliefs and some new data This can be applied to the problem of predicting reservoir model parameters by updating the parameter probabilities based on field observations such as oil/water production rates. Most companies keep the history-matching workflow under the control of only the reservoir engineer Parameters such as skin, productivity index, relative permeability and porosity/permeability multipliers are typically applied to tune the geological uncertainties, these change the continuity and structure of the geological model which was built to represent the likely correlation structure of the reservoir, potentially in ways that are not geologically possible. The section describes the importance of applying geological priors to quantifying reservoir uncertainty
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