An inverse-source problem for maximization of pore-fluid oscillation within poroelastic formations

Handle URI:
http://hdl.handle.net/10754/623514
Title:
An inverse-source problem for maximization of pore-fluid oscillation within poroelastic formations
Authors:
Jeong, C.; Kallivokas, L. F.
Abstract:
This paper discusses a mathematical and numerical modeling approach for identification of an unknown optimal loading time signal of a wave source, atop the ground surface, that can maximize the relative wave motion of a single-phase pore fluid within fluid-saturated porous permeable (poroelastic) rock formations, surrounded by non-permeable semi-infinite elastic solid rock formations, in a one-dimensional setting. The motivation stems from a set of field observations, following seismic events and vibrational tests, suggesting that shaking an oil reservoir is likely to improve oil production rates. This maximization problem is cast into an inverse-source problem, seeking an optimal loading signal that minimizes an objective functional – the reciprocal of kinetic energy in terms of relative pore-fluid wave motion within target poroelastic layers. We use the finite element method to obtain the solution of the governing wave physics of a multi-layered system, where the wave equations for the target poroelastic layers and the elastic wave equation for the surrounding non-permeable layers are coupled with each other. We use a partial-differential-equation-constrained-optimization framework (a state-adjoint-control problem approach) to tackle the minimization problem. The numerical results show that the numerical optimizer recovers optimal loading signals, whose dominant frequencies correspond to amplification frequencies, which can also be obtained by a frequency sweep, leading to larger amplitudes of relative pore-fluid wave motion within the target hydrocarbon formation than other signals.
Citation:
Jeong C, Kallivokas LF (2016) An inverse-source problem for maximization of pore-fluid oscillation within poroelastic formations. Inverse Problems in Science and Engineering 25: 832–863. Available: http://dx.doi.org/10.1080/17415977.2016.1201663.
Publisher:
Informa UK Limited
Journal:
Inverse Problems in Science and Engineering
Issue Date:
4-Jul-2016
DOI:
10.1080/17415977.2016.1201663
Type:
Article
ISSN:
1741-5977; 1741-5985
Sponsors:
This work was partially supported by an Academic Excellence Alliance grant between King Abdullah University of Science and Technology (KAUST) and the University of Texas at Austin and by the Society of Petroleum Engineers STAR Fellowship and the William S. Livingston Fellowship at the University of Texas at Austin awarded to the first author.
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Full metadata record

DC FieldValue Language
dc.contributor.authorJeong, C.en
dc.contributor.authorKallivokas, L. F.en
dc.date.accessioned2017-05-15T10:35:05Z-
dc.date.available2017-05-15T10:35:05Z-
dc.date.issued2016-07-04en
dc.identifier.citationJeong C, Kallivokas LF (2016) An inverse-source problem for maximization of pore-fluid oscillation within poroelastic formations. Inverse Problems in Science and Engineering 25: 832–863. Available: http://dx.doi.org/10.1080/17415977.2016.1201663.en
dc.identifier.issn1741-5977en
dc.identifier.issn1741-5985en
dc.identifier.doi10.1080/17415977.2016.1201663en
dc.identifier.urihttp://hdl.handle.net/10754/623514-
dc.description.abstractThis paper discusses a mathematical and numerical modeling approach for identification of an unknown optimal loading time signal of a wave source, atop the ground surface, that can maximize the relative wave motion of a single-phase pore fluid within fluid-saturated porous permeable (poroelastic) rock formations, surrounded by non-permeable semi-infinite elastic solid rock formations, in a one-dimensional setting. The motivation stems from a set of field observations, following seismic events and vibrational tests, suggesting that shaking an oil reservoir is likely to improve oil production rates. This maximization problem is cast into an inverse-source problem, seeking an optimal loading signal that minimizes an objective functional – the reciprocal of kinetic energy in terms of relative pore-fluid wave motion within target poroelastic layers. We use the finite element method to obtain the solution of the governing wave physics of a multi-layered system, where the wave equations for the target poroelastic layers and the elastic wave equation for the surrounding non-permeable layers are coupled with each other. We use a partial-differential-equation-constrained-optimization framework (a state-adjoint-control problem approach) to tackle the minimization problem. The numerical results show that the numerical optimizer recovers optimal loading signals, whose dominant frequencies correspond to amplification frequencies, which can also be obtained by a frequency sweep, leading to larger amplitudes of relative pore-fluid wave motion within the target hydrocarbon formation than other signals.en
dc.description.sponsorshipThis work was partially supported by an Academic Excellence Alliance grant between King Abdullah University of Science and Technology (KAUST) and the University of Texas at Austin and by the Society of Petroleum Engineers STAR Fellowship and the William S. Livingston Fellowship at the University of Texas at Austin awarded to the first author.en
dc.publisherInforma UK Limiteden
dc.subjectamplification frequenciesen
dc.subjectinverse-source problemen
dc.subjectPDE-constrained optimizationen
dc.subjectpore-fluid flow hysteresis modelen
dc.subjectpore-fluid oscillationen
dc.subjectporoelastic solidsen
dc.subjectWave-based enhanced oil recoveryen
dc.titleAn inverse-source problem for maximization of pore-fluid oscillation within poroelastic formationsen
dc.typeArticleen
dc.identifier.journalInverse Problems in Science and Engineeringen
dc.contributor.institutionDepartment of Civil Engineering, The Catholic University of America, Washington, DC, USAen
dc.contributor.institutionDepartment of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, Austin, TX, USAen
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