Abstract
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.
Highlights
Geochemical reactions can affect the permeability in a geothermal reservoir
Pore scale models incorporating mineral precipitation and dissolution have been studied earlier in, and the corresponding Darcy scale models have been investigated further in. These papers assume that the pore geometry is not changed by the chemical reactions, which is a valid assumption when the deposited or dissolved mineral layer is thin compared to the pore aperture
As will result from below, the evolution of S depends on unknowns of the model, leading to a porous medium where the size and geometry of the void space are in evolution
Summary
Geochemical reactions can affect the permeability in a geothermal reservoir. As the injected water and the in situ brine have different temperatures and chemical composition, reservoir rock properties can develop dynamically with time as the fluids flow through the reservoir. Pore scale models incorporating mineral precipitation and dissolution have been studied earlier in (van Duijn and Pop 2004; van Noorden et al 2007), and the corresponding Darcy scale models have been investigated further in (van Duijn and Knabner 1997; Knabner et al 1995) These papers assume that the pore geometry is not changed by the chemical reactions, which is a valid assumption when the deposited or dissolved mineral layer is thin compared to the pore aperture. Investigations honoring the porosity changes may be found in (Kumar et al 2011; van Noorden 2009a, b), where mineral precipitation and dissolution have been considered on either circular grains or in a thin strip In these papers, the position of the interface between grain and void space is tracked, giving a problem with a free boundary. The paper ends with a summary with some comments on applications and a presentation of a special case of the model equations in Sect. 4, together with some concluding remarks
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