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A Nonlinear Conservation Law Modelin...

Brown, Elisabeth Mary Margaret.

A Nonlinear Conservation Law Modeling Carbon Sequestration.

Record Type:	Electronic resources : Monograph/item
Title/Author:	A Nonlinear Conservation Law Modeling Carbon Sequestration.
Author:	Brown, Elisabeth Mary Margaret.
Published:	Ann Arbor : ProQuest Dissertations & Theses, 2017
Description:	138 p.
Notes:	Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
Contained By:	Dissertation Abstracts International78-10B(E).
Subject:	Applied mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10610679
ISBN:	9781369855623

A Nonlinear Conservation Law Modeling Carbon Sequestration.
Brown, Elisabeth Mary Margaret.

A Nonlinear Conservation Law Modeling Carbon Sequestration. - Ann Arbor : ProQuest Dissertations & Theses, 2017 - 138 p.

Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.

Thesis (Ph.D.)--North Carolina State University, 2017.

A quasi-linear hyperbolic partial differential equation with a discontinuous flux models geologic carbon dioxide (CO2) migration and storage through residual trapping [17]. Dual flux curves emerge in this model, giving rise to flux discontinuities. One flux describes the invasion of the plume into pore space, and the other captures the flow as the plume drains and leaves CO2 bubbles behind, which are then trapped by brine in the pore space between rock grains. Flux functions with discontinuities in space have been previously studied; however, the flux in this model depends on how the plume height changes in time, a different kind of discontinuity that introduces new patterns. A striking feature of this simple model is that, because of its dual flux curves, solutions of the conservation law can include the prediction that the entire CO2 plume is deposited as bubbles in a finite time.

ISBN: 9781369855623Subjects--Topical Terms:

377601
Applied mathematics.

A Nonlinear Conservation Law Modeling Carbon Sequestration.
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100 1 $a Brown, Elisabeth Mary Margaret. $3 795421
245 1 2 $a A Nonlinear Conservation Law Modeling Carbon Sequestration.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2017
300 $a 138 p.
500 $a Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
502 $a Thesis (Ph.D.)--North Carolina State University, 2017.
520 $a A quasi-linear hyperbolic partial differential equation with a discontinuous flux models geologic carbon dioxide (CO2) migration and storage through residual trapping [17]. Dual flux curves emerge in this model, giving rise to flux discontinuities. One flux describes the invasion of the plume into pore space, and the other captures the flow as the plume drains and leaves CO2 bubbles behind, which are then trapped by brine in the pore space between rock grains. Flux functions with discontinuities in space have been previously studied; however, the flux in this model depends on how the plume height changes in time, a different kind of discontinuity that introduces new patterns. A striking feature of this simple model is that, because of its dual flux curves, solutions of the conservation law can include the prediction that the entire CO2 plume is deposited as bubbles in a finite time.
520 $a The model is explored in more detail, and some mathematical issues are resolved. We describe the construction of fundamental wave solutions of the equation, namely shock waves and rarefaction fans. To establish the admissibility of shock waves, we introduce the notion of cross-hatch characteristics to address the ambiguity of characteristic speeds in regions of the characteristic plane where the solution is constant. Detailed analytic solutions of wave interactions resulting from the dual flux model include some properties that do not occur in conventional scalar conservation laws. Some wave interactions yield novel phenomena due to the dual flux, such as shock-rarefaction interactions that would persist for all time with a single flux, here are completed in finite time.
520 $a The existence of an entropy solution of the Cauchy problem for any initial CO2 plume is established using wave-front tracking. To prove this theorem, we construct piecewise constant approximate solutions of the Cauchy problem using expansion shocks in place of rarefaction waves. In order to establish that a subsequence of approximate solutions converges to an entropy solution of the Cauchy problem, we have to account for the dual fluxes carefully.
590 $a School code: 0155.
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710 2 $a North Carolina State University. $b Applied Mathematics. $3 795422
773 0 $t Dissertation Abstracts International $g 78-10B(E).
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792 $a 2017
793 $a English
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