Advection of methane in the hydrate zone: model,analysis and examples |
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Authors: | Malgorzata Peszynska Ralph E. Showalter Justin T. Webster |
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Affiliation: | 1. Department of Mathematics, Oregon State University, Corvallis, USA;2. Department of Mathematics, North Carolina State University, Raleigh, USA;3. College of Charleston, Charleston, USA |
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Abstract: | A two‐phase two‐component model is formulated for the advective–diffusive transport of methane in liquid phase through sediment with the accompanying formation and dissolution of methane hydrate. This free‐boundary problem has a unique generalized solution in L1; the proof combines analysis of the stationary semilinear elliptic Dirichlet problem with the nonlinear semigroup theory in Banach space for an m‐accretive multi‐valued operator. Additional estimates of maximum principle type are obtained, and these permit appropriate maximal extensions of the phase‐change relations. An example with pure advection indicates the limitations of these estimates and of the model developed here. We also consider and analyze the coupled pressure equation that determines the advective flux in the transport model. Copyright © 2015 John Wiley & Sons, Ltd. |
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Keywords: | monotone evolution equations compositional flow model methane hydrates general porous medium equation phase change constraints |
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