Interfaces between the solid matrix and the void space characterize the hydraulic properties of a porous medium. 5 and 6 we summarize the lessons learned and give recommendations.Ģ.1 Scales of Consideration for Porous Media Processes 3 by their targeted use, the form of the relation, and any special features. 4, we compare the relations presented in Sect. After that, we discuss the variety of published porosity–permeability relations grouped by the approach used to derive the relations, focusing mainly on (bio-)geochemically altered porous media and less on other geometry-modifying processes or the task of estimating permeability from porosity in general. Further, we present an overview of the (bio-)geochemical processes changing the pore structure and morphology, and thus changes to the porosity and permeability. 2 a thorough definition of the scales of consideration we introduce the REV scale, upon which the porosity–permeability relations are valid, and we introduce the parameters porosity and permeability. The manuscript is organized as follows: We first provide in Sect. The objective of this paper is to review the existing porosity–permeability relation concepts, to summarize their typical features, and to conclude with some recommendations focusing on systems with (bio-)geochemical pore space alterations. To integrate the alterations in the pore structure and morphology, a commonly employed method relates changes in the permeability to another effective REV-scale parameter, the porosity. The concept of using permeability avoids the need for a detailed description of the fluid–solid interface at the expense of losing information regarding pore-scale details. The permeability of a porous medium is one of these parameters and is used by modelers to represent the resistance to fluid flow in the porous medium on the scale of a representative elementary volume (REV), where an averaging concept is applied such that the individual pore geometry does not need to be resolved. On top of that, effective (upscaled) parameters on larger scales require less pore geometry data, which is hard or, usually, impossible to collect in practical applications. Therefore, it is often appropriate, and required for the sake of computational feasibility, that the impacts of such morphology changes to the flow field be described by effective hydraulic properties. While changes in the pore surface properties, and thus the pore’s void space geometry, occur on the pore scale or even on the molecular scale, the scales of the application or of the engineering problem are typically much larger. Examples of such transforming processes are chemical reactions or microbiological activities. Alterations in the pore surface structure or the pore morphology can occur through a whole variety of processes coupled to and interacting with the flow of fluids. Usually, this flow occurs in the fluid-filled void space bounded by an impermeable solid matrix. It shows the variety of existing approaches and concludes with their essential features.įlow through porous media can be described and analyzed on different spatial scales. This review first defines the scale on which porosity–permeability relations are typically used and aims at explaining why these relations are not unique. Other exceptions are relations that consider a critical porosity at which the porous medium becomes impermeable this is often used when modeling the effect of mineral precipitation. Exceptions to this general trend are only few of the porosity–permeability relations developed for biomass clogging these consider a residual permeability even when the pore space is completely filled with biomass. However, many of these relations do not lead to fundamentally different predictions of permeability alteration when compared to a simple power-law relation with a suitable exponent. Some authors use exponential or simplified Kozeny–Carman relations. To predict the reduction in permeability due to biomass growth, many different and often rather complex relations have been developed and published by a variety of authors. Commonly applied porosity–permeability relations in simulation models on the REV scale use a power-law relation, often with slight modifications, to describe such features they are often used for modeling the effects of mineral precipitation and/or dissolution on permeability. An understanding of the pore structure morphology and the changes to flow parameters during these processes is critical when modeling reactive transport. Reactive transport processes in a porous medium will often both cause changes to the pore structure, via precipitation and dissolution of biomass or minerals, and be affected by these changes, via changes to the material’s porosity and permeability.
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