Baysian Uncertainty Analysis for Oil Reservoir Modelling and Field Development

Complex geologies and limits on data collection result in large uncertainties in the modelling of oil reservoirs. The current industry approach continues to make large approximations in both the modelling and uncertainty quantification. Bayesian statistics can provide a coherent encompassing mathematical structure incorporating many data types with explicit representation of all major sources of uncertainty. A complex geological model based on initial data is created and then converted to a coarser reservoir model involving fairly simplistic depiction of uncertainty (commonly using multipliers on large blocks of the assumed geology). Subsequent data such as production output is used to infer aspects of the approximate reservoir model, but is not pushed back to the original geology model. Challenges include handling complex data forms, computationally expensive and high-dimensional models, and complex representations of uncertainty. We will address these using Bayesian emulation methodology described below. An emulator is an approximate representation of a complex physical model with known accuracy, often several orders of magnitude faster to evaluate, and hence can facilitate previously intractable calculations. Another objective is to make robust decisions for an oil field development plan. Solving this full decision problem requires infeasibly many simulations to examine many possible futures and potential choices, combined with careful representation of the company's utility function and associated uncertainties.

Roxar (iCASE sponsor) has made initial progress by bringing these diverse aspects from different scientific fields (geology, reservoir engineering, decision theory) into a single calculation within their ENABLE workflow. Important and related challenges remain and include:
a) Currently some aspects of geological model uncertainty are described by a stochastic simulator. This passes into the reservoir simulator requiring the emulation of a stochastic model and a more detailed treatment of structural uncertainty.
b) Addressing the full decision theory problem which accounts for uncertain futures is infeasible with modern computing power. Robust decisions rely critically on realistic uncertainty statements about future predictions.

The two issues are inherently linked. A suitably advanced solution to problem a) is required to make problem b) meaningful and relevant. Any approximations employed in a) are only reasonable if it can be shown that they do not impact upon the results of b) where the models are used for decision making.

iCASE studentship part a) proposal:
Develop Bayesian emulation methodology for stochastic simulators applicable to stochastic geology models and combine with advanced representations of structural uncertainty to capture the uncertainties missed in the model parameterisation. A coherent Bayesian framework allowing 'Big Loop' learning can be used to link the geological and reservoir models.

iCASE studentship part b) proposal:
Solve the decision theory problem by adapting the strategy of Williamson et al who propose emulating the decision and utility structure. This allows vast numbers of evaluations over many possible futures, necessary for the full Bayesian decision theoretic calculations.

Novelty of the research proposed:
The representation of the above problem within an overarching Bayesian model accounting for all uncertainties which allows 'Big Loop' learning would represent a substantial advancement in the field and provide tangible commercial results.

New aspects include:
a) Emulation of stochastic models
b) Model discrepancy
c) High dimensional input and outputs
d) Decision theory for oil field management

The novelty of the proposed research lies within each of a) - d) but also their integration into one unified calculation. Each will be demonstrated for simple simulated models and then used to analyse a small subset of tasks for a realistic oil