Baysian Uncertainty Analysis for Oil Reservoir Modelling and Field Development
Lead Research Organisation:
Durham University
Department Name: Mathematical Sciences
Abstract
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
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
People |
ORCID iD |
Ian Vernon (Primary Supervisor) | |
Jonathan Owen (Student) |
Description | Ongoing development of a Bayesian statistical framework for providing robust decision support where complex and computationally expensive simulators are used to represent a real physical system. An iterative decision support algorithm is formulated which utilises structured Bayesian emulators as statistical approximations to the computationally expensive computer simulators. These permit the efficient exploration of the decision parameter space and hence are able to identify a robust class of decisions, avoiding non-robust decisions that often arise in an optimisation procedure. Bayesian emulation techniques have also been developed which can exploit known behaviour in simulator output to achieve increasingly accurate results compared to existing emulation methodology. Both forms of emulator may be incorporated into a hierarchical framework that links multiple emulators (for different quantities) over multiple levels obtaining more accurate results with a smaller uncertainty. The process also incorporates techniques for performing an uncertainty quantification of all major sources of uncertainty which are appropriate to providing decision support. |
Exploitation Route | Complex and computationally expensive computer simulators with high-dimensional input parameter space and large numbers of outputs are increasingly being used across many scientific disciplines, government and industry to improve the understanding of the behaviour of physical systems and to guide future decisions. The structured Bayesian emulators yield greater accuracy in the predictions versus current methodology whilst maintaining the ability to explore all of the input parameter space. The iterative decision support algorithm provides a class of robust decisions which allows the decision makers to assess the implications of their choices. Techniques for incorporating structured uncertainties into the analysis improve the robustness of decisions whilst identifying how the end user may reduce their uncertainty. |
Sectors | Agriculture, Food and Drink,Chemicals,Energy,Environment,Financial Services, and Management Consultancy,Healthcare,Government, Democracy and Justice,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology,Transport |
Title | Algorithm for constructing designs for non-hypercube parameter spaces incorporating prior knowledge |
Description | Technique for constructing a design for sampling from non-hypercube input parameter spaces for computer simulators whilst incorporating prior knowledge of regions in which samples are most desired. |
Type Of Material | Computer model/algorithm |
Year Produced | 2019 |
Provided To Others? | No |
Impact | Ability to construct designs for computer simulators which are not of the standard hypercube shape. Inclusion of prior knowledge and information of where samples should be taken in the design process. |
Title | Bayesian emulation techniques for handling partial boundaries in parameter space |
Description | Bayesian emulation techniques to handle partial boundaries in the input parameter space. |
Type Of Material | Computer model/algorithm |
Year Produced | 2019 |
Provided To Others? | No |
Impact | Accurate Bayesian emulation in situations where partial boundaries occur in the input parameter space such as is the case in the OLYMPUS petroleum reservoir model from the ISAPP TNO OLYMPUS Field Development Optimisation challenge. |
Title | Hierarchical emulation framework linking structured emulators for computer model ensembles |
Description | Hierarchical emulation framework for computer model ensemble mean. For each individual computer model within an ensemble, this framework includes multiple (structured) emulators for various outputs of the model which are linked to obtain an emulator for an output of interest. The final level of the hierarchical framework connects these emulators for each individual computer model's output to obtain an emulator for the computer model ensemble mean of this output. |
Type Of Material | Computer model/algorithm |
Year Produced | 2020 |
Provided To Others? | No |
Impact | Exploitation of structure within individual simulator outputs to construct increasingly accurate emulators with reduced uncertainty of other simulation output for an individual ensemble member, as well as for the ensemble mean. |
Title | Iterative decision support algorithm |
Description | Iterative decision support algorithm which incorporates appropriate structured uncertainties and uses Bayesian emulators for computationally expensive computer simulators to provide decision support. |
Type Of Material | Computer model/algorithm |
Year Produced | 2018 |
Provided To Others? | No |
Impact | Reduction in the number of simulations required. Ability to incorporate all major sources of uncertainty. Algorithm yields a robust class of decisions as opposed to a single potentially non-robust decision. |
Title | Statistical computer model efficient ensemble subsampling technique |
Description | Application of statistical technique to the problem of computer model efficient ensemble subsampling. Predictions of the mean output over all models in the ensemble, whilst providing a quantification of the uncertainty due to using a subset. |
Type Of Material | Data analysis technique |
Year Produced | 2018 |
Provided To Others? | No |
Impact | Reduction in computation time due to using fewer computer models evaluations, permitting greater exploration of the input parameter space. Ability to predict the mean output if all models in the ensemble were used, whilst providing a quantification of the uncertainty due to using a subset of the models. |
Title | Structured Bayesian emulators using known computer simulator behaviour |
Description | Construction of structured Bayesian emulators which incorporate known behaviour of computer simulators. |
Type Of Material | Computer model/algorithm |
Year Produced | 2019 |
Provided To Others? | No |
Impact | Bayesian emulators for computer simulators which have an increased accuracy and reduced uncertainty. |
Title | Uncertainty quantification techniques for optimisation and decision support |
Description | Techniques for performing an uncertainty quantification using computer simulators for the purpose of optimisation or decision support which eliminate linear changes in a utility function that have no effect on the location in parameter space of the optimal setting. |
Type Of Material | Computer model/algorithm |
Year Produced | 2019 |
Provided To Others? | No |
Impact | Reduction in the uncertainty used when performing optimisation or providing decision support to that which is relevant, hence smaller sets of decision parameter settings may be achieved whilst maintaining robustness. |
Description | Collaboration with Prof Jonathan Carter, Coventry University |
Organisation | Coventry University |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | Development of novel Bayesian emulation techniques to handle partial fault boundaries, as observed in petroleum reservoirs and applied to the ISAPP TNO OLYMPUS Field Development Optimisation Challenge for well placement. Development and implementation of an iterative decision theoretic framework for performing petroleum reservoir well placement optimisation. |
Collaborator Contribution | Knowledge of the petroleum industry and well placement. Setting up and performing simulations for petroleum reservoir well placement. |
Impact | Development of novel Bayesian emulation techniques to handle partial fault boundaries. Development and implementation of an iterative decision theoretic framework for well placement optimisation. Multi-disciplinary: Bayesian statistics and petroleum reservoir engineering. |
Start Year | 2018 |
Description | Internship at Emerson July - August 2017 |
Organisation | Roxar AS |
Country | Norway |
Sector | Private |
PI Contribution | Investigations into the ISAPP TNO OLYMPUS Field Development Optimisation Challenge including an application of statistical techniques. Comparison of open source and commercial petroleum reservoir simulation software. |
Collaborator Contribution | Provision of petroleum engineering knowledge and insights into the OLYMPUS petroleum reservoir model. |
Impact | Statistical techniques are evidently useful in the analysis of the TNO OLYMPUS Field Development Optimisation Challenge. Open source software performs well compared to the equivalent commerical petroleum reservoir simulation software. Multi-disciplinary: Bayesian statistics and petroleum reservoir engineering. |
Start Year | 2017 |