Upscaling of Non-isothermal Reactive Porous Media Flow with Changing Porosity

Abstract

Upscaling of non-isothermal reactive porous media flow with changing porosityBringedal, C.; Berre, I.; Pop, I.S.; Radu, A.F. Published in: Transport in Porous Media DOI:10.1007/s11242-015-0530-9Published: 01/09/2016 Document VersionAccepted manuscript including changes made at the peer-review stage Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Link to publication• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract Motivated by rock-fluid interactions occurring in a geothermal reservoir, we present a two-dimensional pore scale model of a periodic porous medium consisting of void space and grains, with fluid flow through the void space. The ions in the fluid are allowed to precipitate onto the grains, while minerals in the grains are allowed to dissolve into the fluid, and we take into account the possible change in pore geometry that these two processes cause, resulting in a problem with a free boundary at the pore scale. We include temperature dependence and possible effects of the temperature both in fluid properties and in the mineral precipitation and dissolution reactions. For the pore scale model equations, we perform a formal homogenization procedure to obtain upscaled equations. A pore scale model consisting of circular grains is presented as a special case of the porous medium.

Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow

“…Later this model was formulated for a periodic porous medium and upscaled to Darcy scale by Bringedal et al (2016). The freely moving interface between the mineral layer and the void space is modeled through a level set function at the pore scale.…”

“…The authors derive two-dimensional effective equations honoring the pore scale dependence through cell problems. The geometry is the same as considered by van Noorden (2009a), where Bringedal et al (2016) also include heat transport as well as temperature effects in the fluid flow and in the chemical reactions.…”

“…For geothermal systems, modeling the temperature dependences and heat transport correctly is crucial. We will build upon the upscaled model derived in (Bringedal et al 2016) by solving the cell problems and investigate the behavior of the resulting effective properties. Further, to test the model we consider an idealized case study where clogging occurs.…”

“…Further, to test the model we consider an idealized case study where clogging occurs. The model by Bringedal et al (2016) does not allow phase change, but we mention that Duval et al (2004) upscaled decoupled two-phase flow with phase change using volume averaging.…”

“…We investigate changes of the effective properties for a two-dimensional periodic porous medium as the grain geometry changes. We consider specific grain shapes and study the evolution by solving the cell problems numerically for an upscaled model derived in Bringedal et al (2016). In particular, we focus on the limit behavior near clogging.…”