The Use of the Least-Squares Probabilistic-Collocation Method in Decision Making in the Presence of Uncertainty for Chemical-Enhanced-Oil-Recovery Processes
- Ali M. Alkhatib (Saudi Aramco) | Peter R. King (Imperial College London)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- August 2015
- Document Type
- Journal Paper
- 747 - 766
- 2015.Society of Petroleum Engineers
- uncertainty quantification, chemical EOR, decision making, least-squares Monte Carlo Method, probabilistic collocation method
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- 252 since 2007
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The least-squares Monte Carlo method (LSM) is a decision-evaluation method that can capture the value of flexibility of a process. This method was shown to provide us with some insight into the effect of uncertainty on decision making and to help us capture the upside potential or mitigate the downside effects for chemical enhanced-oil-recovery (EOR) process. The method is a stochastic approximate dynamic programming approach to decision making. It is modeled after a forward simulation coupled with a recursive algorithm, which produces the near-optimal policy. It relies on Monte Carlo simulation to produce convergent results. This incurs a significant computational requirement when using this method to evaluate decisions for reservoir-engineering problems because this requires running many reservoir simulations.
The objective of this study was to enhance the performance of the LSM by improving the sampling method used to generate the technical uncertainties used in producing the production profiles and to extend its application to different chemical EOR processes. The probabilistic-collocation method has been proved to be a robust and efficient uncertainty-quantification method. It approximates the random input distributions by use of polynomial-chaos expansions and produces a proxy polynomial for the output parameter requiring a limited number of model responses that is conditional on the number of random inputs and the order of the approximation desired. The resulting proxy can then be used to generate the different statistical moments with negligible computational requirement. By use of the sampling methods of the probabilistic-collocation method to approximate the sampling of the technical uncertainties, it is possible to significantly reduce the computational requirement of running the decision-evaluation method. This is known as the least-squares probabilistic-collocation method (LSPCM).
Both methods were demonstrated on a chemical EOR problem by use of a number of stylized reservoir models. The technical uncertainties considered were the residual oil saturation to chemical flooding, surfactant and polymer adsorption, and the viscosity multiplier of the polymer. The economic uncertainties considered were the oil price and the surfactant and polymer price. Both methods were applied by use of three reservoir case studies: a simple homogeneous model, the PUNQ-S3 (2010) model, and a modified portion of the SPE10 model (Christie and Blunt 2001). The results show that the use of the sampling techniques of the probabilistic-collocation method produced relatively accurate responses compared with the original method. For instance, it was possible to produce the same output for the modified SPE10 model by use of the second-order quadrature nodes--81 realizations--rather than the 103 realizations used for the LSM, thus achieving an order-of-magnitude reduction in computational time.
The scalability limits of both methods and the different possible enhancements to practically adapt the LSPCM to more-realistic and more-complex reservoir models were discussed. The application was extended to other chemical EOR processes, such as alkaline/surfactant/polymer flooding and polymer flooding, and to more-complex decision problems. The results show that the use of the LSPCM produced accurate results compared with the LSM.
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