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A Hybrid Optimization Method for Solving Bayesian Inverse Problems under Uncertainty.

Zhang K, Wang Z, Zhang L, Yao J, Yan X - PLoS ONE (2015)

Bottom Line: The goal of history matching is to identify the minimum value of an objective function that expresses the misfit between the predicted and measured data of a reservoir.The optimization is constrained by a linear equation that contains the reservoir parameters.We reformulate the reservoir model's parameters and dynamic data by operating the objective function, the approximate gradient of which can guarantee convergence.

View Article: PubMed Central - PubMed

Affiliation: China University of Petroleum, 66 Changjiang West Road, Qingdao, Shandong, 266555, China.

ABSTRACT
In this paper, we investigate the application of a new method, the Finite Difference and Stochastic Gradient (Hybrid method), for history matching in reservoir models. History matching is one of the processes of solving an inverse problem by calibrating reservoir models to dynamic behaviour of the reservoir in which an objective function is formulated based on a Bayesian approach for optimization. The goal of history matching is to identify the minimum value of an objective function that expresses the misfit between the predicted and measured data of a reservoir. To address the optimization problem, we present a novel application using a combination of the stochastic gradient and finite difference methods for solving inverse problems. The optimization is constrained by a linear equation that contains the reservoir parameters. We reformulate the reservoir model's parameters and dynamic data by operating the objective function, the approximate gradient of which can guarantee convergence. At each iteration step, we obtain the relatively 'important' elements of the gradient, which are subsequently substituted by the values from the Finite Difference method through comparing the magnitude of the components of the stochastic gradient, which forms a new gradient, and we subsequently iterate with the new gradient. Through the application of the Hybrid method, we efficiently and accurately optimize the objective function. We present a number numerical simulations in this paper that show that the method is accurate and computationally efficient.

No MeSH data available.


The different log-permeability distribution.A:The initial permeability field; B:the real permeability field.
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pone.0132418.g010: The different log-permeability distribution.A:The initial permeability field; B:the real permeability field.

Mentions: Now, we analyze the optimization result of the production data by using both algorithms. Fig 9 shows the rate of water production of well Pro-4. The observed data varies greatly with the increase of time. We can obtain the simulation result that the stratigraphic parameters can be inversed by Eq 14. From Fig 10, we can realize that the matching curve from using Algorithm III is much closer to the observed data than that obtained by using Algorithm II.


A Hybrid Optimization Method for Solving Bayesian Inverse Problems under Uncertainty.

Zhang K, Wang Z, Zhang L, Yao J, Yan X - PLoS ONE (2015)

The different log-permeability distribution.A:The initial permeability field; B:the real permeability field.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4529104&req=5

pone.0132418.g010: The different log-permeability distribution.A:The initial permeability field; B:the real permeability field.
Mentions: Now, we analyze the optimization result of the production data by using both algorithms. Fig 9 shows the rate of water production of well Pro-4. The observed data varies greatly with the increase of time. We can obtain the simulation result that the stratigraphic parameters can be inversed by Eq 14. From Fig 10, we can realize that the matching curve from using Algorithm III is much closer to the observed data than that obtained by using Algorithm II.

Bottom Line: The goal of history matching is to identify the minimum value of an objective function that expresses the misfit between the predicted and measured data of a reservoir.The optimization is constrained by a linear equation that contains the reservoir parameters.We reformulate the reservoir model's parameters and dynamic data by operating the objective function, the approximate gradient of which can guarantee convergence.

View Article: PubMed Central - PubMed

Affiliation: China University of Petroleum, 66 Changjiang West Road, Qingdao, Shandong, 266555, China.

ABSTRACT
In this paper, we investigate the application of a new method, the Finite Difference and Stochastic Gradient (Hybrid method), for history matching in reservoir models. History matching is one of the processes of solving an inverse problem by calibrating reservoir models to dynamic behaviour of the reservoir in which an objective function is formulated based on a Bayesian approach for optimization. The goal of history matching is to identify the minimum value of an objective function that expresses the misfit between the predicted and measured data of a reservoir. To address the optimization problem, we present a novel application using a combination of the stochastic gradient and finite difference methods for solving inverse problems. The optimization is constrained by a linear equation that contains the reservoir parameters. We reformulate the reservoir model's parameters and dynamic data by operating the objective function, the approximate gradient of which can guarantee convergence. At each iteration step, we obtain the relatively 'important' elements of the gradient, which are subsequently substituted by the values from the Finite Difference method through comparing the magnitude of the components of the stochastic gradient, which forms a new gradient, and we subsequently iterate with the new gradient. Through the application of the Hybrid method, we efficiently and accurately optimize the objective function. We present a number numerical simulations in this paper that show that the method is accurate and computationally efficient.

No MeSH data available.