Characteristic time and length scales for subsurface mineralisation

Reactive flows in porous rocks may precipitate mineral products in the pore space. The aim of this study is to identify the time and length scales for such subsurface mineralisation processes. We introduce a first-order model describing the fate and transport of a reactive charge in a one-dimensional domain. In this model, the ability to deliver and mineralise the charge is controlled by the clogging of the pore space with the mineral product. Under the assumption that full clogging of the pores first occurs at the domain entrance, we determine a time scale for a mineralisation operation. We then show that, at this time scale, the maximum storage of minerals in the domain is approached when the reaction rate balances the transport rate (Damköhler number = 1). From this, we are able to explicitly identify a characteristic length scale for a mineralisation processes. Together, our findings provide useful starting points for understanding and optimising subsurface mineralisation operations.