Oil & Gas - Maximising Recovery Programme (formerly SHARP) IOR Views

Approaches

There are two principal approaches to probabilities – the frequentist approach that views probabilities as the limiting frequencies of multiple random experiments, and the Bayesian approach that views probability as the degree of belief in a position.  Since uncertainty in reservoir modelling is epistemic – that is it arises from a lack of knowledge of the single reservoir that nature has provided – we have to use a Bayesian approach. 

Bayes Theorem allows one to use measured or observed data about a complex system, to update our beliefs about the uncertainty that exists.  The framework is shown in Figure 1.  By sampling from distributions of our uncertain model parameters to produce an ensemble of model predictions we are able to compute the likelihood of each combination of model parameters. The likelihood, which comes from a probability model for errors in measurements and simulation, is used to determine the posterior probability (or probability including the observed production data) of each set of model parameters. 

Figure 1: Uncertainty Quantification Centre Bayesian Framework

The current active areas of research are described in the sections below.

Efficient Generation of History Matched Models

The goal here is to develop and test robust algorithms that generate high quality matches and yet efficiently explore parameter space.  This will result in an improvement in history matching efficiency.

Assessing Match Quality

Here, we examine how assessment of uncertainties in measured data affects uncertain forecasts as well as developing statistical models of simulation error.  Both of these aspects are necessary to achieve realistic uncertainty assessments.

Producing Uncertain Forecasts

Our goal is to produce accurate estimates of uncertainty in forecast behaviour.  This is not as straightforward as it sounds since the uncertainty depends on our prior assessment of uncertainties in input parameters, the choices we make in assessing the likelihood of any specific model, and the efficiency of sampling of parameter space.  We would also like to be in a position to automatically generate new history-matched models with appropriate probabilities as required (for example as new data arrives).

The techniques we develop have been tested on a number of synthetic models (because it is only through the use of synthetic models that the truth is known), and applied to a number of real field cases provided by the sponsoring companies of the Uncertainty Project.  We have been able to obtain multiple history matched models with parameter values that are well separated in parameter space for the two real field examples we are working on at present (a North Sea field and a West African field). 

A topic of particular interest at present is determining how the choice of sampling input parameters affects the computed uncertainty – a recent example has shown that it is possible to obtain two sets of equally valid matches in the history period whose uncertainty ranges differ significantly in the forecast period.

Figure 2:  Watercut History Match for Well A in Field X using Two Different Sampling Strategies

Figures 2 and 3 show history matches using a sampling strategy designed to locate multiple regions of good fitting models and a strategy designed to refine the fit to obtain a good history match.  The history match was set up to obtain matches to individual well rates. For Well A (Figure 2), there is some difference in uncertainty in forecast watercut between the two strategies, but probably not a large enough difference to be concerned about.  For Well B (Figure 3), however, there is a significant uncertainty in watercut development revealed by the more exploratory search.

Figure 3:  Watercut History Match for Well B in Field X using Two Different Sampling Strategies