We consider a model for precipitation and dissolution in a porous medium, where ions transported by a fluid through the pores can precipitate at the pore walls and form mineral. Also, the mineral can dissolve and become part of the fluid as ions. These processes lead to changes in the flow domain, which are not known a priori but depend on the concentration of the ions dissolved in the fluid. Such a system can be formulated through conservation equations for mass, momentum, and solute in a domain that evolves in time. In this case the fluid and mineral phases are separated by a sharp interface, which also evolves. We consider an alternative approach by introducing a phase field variable, which has a smooth, diffuse transition of nonzero width between the fluid and mineral phases. The evolution of the phase field variable is determined through the Allen--Cahn equation. We show that as the width of the diffuse transition zone approaches zero, the sharp-interface formulation is recovered. When we consider a periodically perforated domain mimicking a porous medium, the phase field formulation is upscaled to Darcy scale by homogenization. Then, the average of the phase field variable represents the porosity. Through cell problems, the effective diffusion and permeability matrices are dependent on the phase field variable. We consider numerical examples to show the behavior of the phase field formulation. We show the effect of flow on the mineral dissolution, and we address the effect of the width of the diffuse interface in the cell problems for both a perforated porous medium and a thin strip.

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.

The Atlantic meridional overturning circulation and associated poleward heat transport are balanced by northern heat loss to the atmosphere and corresponding water-mass transformation. The circulation of northward-flowing Atlantic Water at the surface and returning overflow water at depth is particularly manifested—and observed—at the Greenland–Scotland Ridge where the water masses are guided through narrow straits. There is, however, a rich variability in the exchange of water masses across the ridge on all time scales. Focusing on seasonal and interannual time scales, and particularly the gateways of the Denmark Strait and between the Faroe Islands and Shetland, we specifically assess to what extent the exchanges of water masses across the Greenland–Scotland Ridge relate to wind forcing. On seasonal time scales, the variance explained of the observed exchanges can largely be related to large-scale wind patterns, and a conceptual model shows how this wind forcing can manifest via a barotropic, cyclonic circulation. On interannual time scales, the wind stress impact is less direct as baroclinic mechanisms gain importance and observations indicate a shift in the overflows from being more barotropically to more baroclinically forced during the observation period. Overall, the observed Greenland–Scotland Ridge exchanges reflect a horizontal (cyclonic) circulation on seasonal time scales, while the interannual variability more represents an overturning circulation.

a b s t r a c tMotivated by porosity changes due to chemical reactions caused by injection of cold water in a geothermal reservoir, we propose a two-dimensional pore scale model of a thin strip. The pore scale model includes fluid flow, heat transport and reactive transport where changes in aperture is taken into account. The thin strip consists of void space and grains, where ions are transported in the fluid in the void space. At the interface between void and grain, ions are allowed to precipitate and become part of the grain, or conversely, minerals in the grain can dissolve and become part of the fluid flow, and we honor the possible change in aperture these two processes cause. We include temperature dependence and possible effects of the temperature in both fluid properties and in the mineral precipitation and dissolution reactions. For the pore scale model equations, we investigate the limit as the width of the thin strip approaches zero, deriving upscaled one-dimensional effective equations.