An efficient optimisation technique using adaptive spectral high-dimensional model representation: Application to CO2 sequestration strategies

Kurt R. Petvipusit, Ahmed H. Elsheikh, Peter R. King, Martin J. Blunt

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)


The successful operation of CO<inf>2</inf> sequestration relies on designing optimal injection strategies that maximise economic performance while guaranteeing long-term storage security. Solving this optimisation problem is computationally demanding. Hence, we propose an efficient surrogate-assisted optimisation technique with three novel aspects: (1) it relies on an ANOVA-like decomposition termed High- Dimensional Model Representation; (2) component-wise interactions are approximated with adaptive sparse grid interpolation; and (3) the surrogate is adaptively partitioned closer to the optimal solution within the optimisation iteration. A High-Dimensional Model Representation (HDMR) represents the model output as a hierarchical sum of component functions with different input variables. This structure enables us to select influential lower-order functions that impact the model output for efficient reduced-order representation of the model. In this work, we build the surrogate based on the HDMR expansion and make use of Sobol indices to adaptively select the significant terms. Then, the selected lower-order terms are approximated by using the Adaptive Sparse Grid Interpolation (ASGI) approach. Once the HDMR is built, a global optimizer is run to decide: 1) the domain shrinking criteria; and 2) the centre point for the next HDMR building. Therefore, this proposed technique is called a walking Cut-AHDMR as it shrinks the search domain while balancing the trade-off between exploration and exploitation of the optimisation algorithm. The proposed technique is evaluated on a benchmark function and on the PUNQ-S3 reservoir model. Based on our numerical results, the walking Cut-AHDMR is a promising approach: not only does it require substantially fewer forward runs in building the surrogate of high dimension but it also effectively guides the search towards the optimal solution. The proposed method provides an efficient tool to find optimal injection schedules that maximise economic values of CO<inf>2</inf> injection in deep saline aquifers.

Original languageEnglish
Title of host publicationSociety of Petroleum Engineers - SPE Reservoir Simulation Symposium 2015
PublisherSociety of Petroleum Engineers
Number of pages20
ISBN (Electronic)9781613993521
ISBN (Print)9781510800618
Publication statusPublished - 2015
EventSPE Reservoir Simulation Symposium 2015 - Houston, TX, United States
Duration: 23 Feb 201525 Feb 2015


ConferenceSPE Reservoir Simulation Symposium 2015
Country/TerritoryUnited States
CityHouston, TX

ASJC Scopus subject areas

  • Modelling and Simulation
  • Geochemistry and Petrology
  • Energy Engineering and Power Technology
  • Geotechnical Engineering and Engineering Geology


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