Estimating permeability from grain‐size distributions or from well logs is attractive but difficult. In this paper we present a new, generally applicable, and relatively inexpensive approach which yields permeability information on the scale of core samples and boreholes. The approach is theoretically based on a fractal model for the internal structure of a porous medium. It yields a general and petrophysically justified relation linking porosity to permeability, which may be calculated either from porosity or from the pore‐radius distribution. This general relation can be tuned to the entire spectrum of sandstones, ranging from clean to shaly. The resulting expressions for the different rock types are calibrated to a comprehensive data set of petrophysical and petrographical rock properties measured on 640 sandstone core samples of the Rotliegend Series (Lower Permian) in northeastern Germany. With few modifications, this new straightforward and petrophysically motivated approach can also be applied to metamorphic and igneous rocks. Permeability calculated with this procedure from industry porosity logs compares very well with permeability measured on sedimentary and metamorphic rock samples.

SUMMARY Based on self organized growth, a self‐similar geometrical model of rock materials is established. The structural mode of the internal surface is carried over to the three‐dimensional structure of the pore space and solid phase, which can be described as a fractal network. It is characterized by the fractal dimension of surface, which can be measured by physical and stereological methods. From this, the fractal behaviour of other geometrical properties, relevant for physical processes, such as porosity, number of solid connections, tortuosity and constrictivity of the capillary system and of the solid phase can be derived.

Permeability is one of the key rock properties for the management of hydrocarbon and geothermal reservoirs as well as for aquifers. The fundamental equation for estimating permeability is the Kozeny-Carman equation. It is based on a capillary bundle model and relates permeability to porosity, tortuosity and an effective hydraulic pore radius which is defined by this equation. Whereas in clean sands the effective pore radius can be replaced by the specific surface or by the grain radius in a simple way, the resulting equations for permeability cannot be applied to consolidated rocks. Based on a fractal model for porous media, equations were therefore developed which adjust the measure of the specific surface and of the grain radius to the resolution length appropriate for the hydraulic process. These equations are calibrated by a large data set for permeability, formation factor, and porosity determined on sedimentary rocks. This fractal model yields tortuosity and effective pore radius as functions of porosity as well as a general permeability-porosity relationship, the coefficients of which are characteristic for different rock types. It can be applied to interpret the diagenetic evolution of the pore space of sedimentary rocks due to mechanical and chemical compaction with respect to porosity and permeability.

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Numerical simulation of reactive transport was validated in a core flooding experiment simulating conditions in a managed geothermal reservoir. Permeability was measured along a sandstone core prepared with anhydrite and subjected to a temperature gradient. Anhydrite was dissolved and precipitated in the cold upstream and hot downstream regions of the core, respectively. The numerical code SHEMAT was used to simulate coupled transport and chemical reactions at the temperature front (http://www.rwth-aachen.de/geop/shemat/). It comprises an extended version of the geochemical speciation code PHRQPITZ for calculating chemical reactions in brines of low‐high ionic strength and temperatures of 0–150°C. Permeability is updated to porosity via a novel, calibrated power‐law based on a fractal pore‐space model resulting in a large exponent of 11.3. Simulation results agree well with measured permeability. This both validates the model and demonstrates that the fractal relationship is crucial for a successful simulation of this type of reactive transport.

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