Low-Rank Kalman Filtering in Subsurface Contaminant Transport Models

Handle URI:
http://hdl.handle.net/10754/134735
Title:
Low-Rank Kalman Filtering in Subsurface Contaminant Transport Models
Authors:
El Gharamti, Mohamad ( 0000-0002-7229-8366 )
Abstract:
Understanding the geology and the hydrology of the subsurface is important to model the fluid flow and the behavior of the contaminant. It is essential to have an accurate knowledge of the movement of the contaminants in the porous media in order to track them and later extract them from the aquifer. A two-dimensional flow model is studied and then applied on a linear contaminant transport model in the same porous medium. Because of possible different sources of uncertainties, the deterministic model by itself cannot give exact estimations for the future contaminant state. Incorporating observations in the model can guide it to the true state. This is usually done using the Kalman filter (KF) when the system is linear and the extended Kalman filter (EKF) when the system is nonlinear. To overcome the high computational cost required by the KF, we use the singular evolutive Kalman filter (SEKF) and the singular evolutive extended Kalman filter (SEEKF) approximations of the KF operating with low-rank covariance matrices. The SEKF can be implemented on large dimensional contaminant problems while the usage of the KF is not possible. Experimental results show that with perfect and imperfect models, the low rank filters can provide as much accurate estimates as the full KF but at much less computational cost. Localization can help the filter analysis as long as there are enough neighborhood data to the point being analyzed. Estimating the permeabilities of the aquifer is successfully tackled using both the EKF and the SEEKF.
Advisors:
Hoteit, Ibrahim ( 0000-0002-3751-4393 )
Committee Member:
Stenchikov, Georgiy ( 0000-0001-9033-4925 ) ; Sun, Shuyu ( 0000-0002-3078-864X )
KAUST Department:
Physical Sciences and Engineering (PSE) Division
Program:
Earth Sciences and Engineering
Issue Date:
Dec-2010
Type:
Thesis
Appears in Collections:
Theses; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.advisorHoteit, Ibrahimen
dc.contributor.authorEl Gharamti, Mohamaden
dc.date.accessioned2011-06-28T07:53:14Z-
dc.date.available2011-06-28T07:53:14Z-
dc.date.issued2010-12en
dc.identifier.urihttp://hdl.handle.net/10754/134735en
dc.description.abstractUnderstanding the geology and the hydrology of the subsurface is important to model the fluid flow and the behavior of the contaminant. It is essential to have an accurate knowledge of the movement of the contaminants in the porous media in order to track them and later extract them from the aquifer. A two-dimensional flow model is studied and then applied on a linear contaminant transport model in the same porous medium. Because of possible different sources of uncertainties, the deterministic model by itself cannot give exact estimations for the future contaminant state. Incorporating observations in the model can guide it to the true state. This is usually done using the Kalman filter (KF) when the system is linear and the extended Kalman filter (EKF) when the system is nonlinear. To overcome the high computational cost required by the KF, we use the singular evolutive Kalman filter (SEKF) and the singular evolutive extended Kalman filter (SEEKF) approximations of the KF operating with low-rank covariance matrices. The SEKF can be implemented on large dimensional contaminant problems while the usage of the KF is not possible. Experimental results show that with perfect and imperfect models, the low rank filters can provide as much accurate estimates as the full KF but at much less computational cost. Localization can help the filter analysis as long as there are enough neighborhood data to the point being analyzed. Estimating the permeabilities of the aquifer is successfully tackled using both the EKF and the SEEKF.en
dc.language.isoenen
dc.subjectKalman Filteringen
dc.subjectSubsurface Contaminant Transport Modelen
dc.titleLow-Rank Kalman Filtering in Subsurface Contaminant Transport Modelsen
dc.typeThesisen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberStenchikov, Georgiyen
dc.contributor.committeememberSun, Shuyuen
thesis.degree.disciplineEarth Sciences and Engineeringen
thesis.degree.nameMaster of Scienceen
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