58 Geophysics in Geothermal Exploration Porosity can also be estimated by electrical measurement. Archie (1942) has shown empirically that for water-saturated permeable formations, the relation between the true formation resistivity, Rt, and the resistivity, Rw, of the water impregnating the formation is given by: R R F t w m = = −Φ (2.2) where F is the “resistivity formation factor”. Φ is proportional to the formation porosity and m is a “cementation factor”, that is a formation characteristic. The F value derived from the resistivity measurement, Rt, is unaffected by the mineralogical constituents of the formation matrix. Although the “cementation factor” value may vary between 1.3 and 3 according to the formation lithology, an approximate value equal to 2 is generally adopted. 2.1.2 Permeability Permeability describes the property of a porous rock regarding fluid flow through the pore space. It depends on the porosity, the pore space dimension, and geometry. In hydrogeology, the hydraulic permeability Kf has the dimension of a velocity (mostly given in cm/s) (Figure 2.2). In practice, the unit DARCY (d) is commonly used. 1 Darcy is the permeability of a material that permits a volume flow of 1 cm3/s through a section of 1 cm2 under a pressure gradient of 1 atm/cm of a fluid with a viscosity of 1 centipoise. One millidarcy, 1 md = 10–6cm/s. Permeability depends in a very complex way on the properties of the pore space. The dominant influences are: • Porosity: Permeability increases with increasing porosity, but this is strongly influenced by the rock type. • Pore size: Permeability increases with increasing grain size; this is the dominant parameter, especially for sedimentary rocks. • Pore shape and specific surface: Pore space geometry determines permeability and the capillary forces; these forces control the retention of water in the angles and capillaries between the grains. • Arrangement of pores • Permeability decreases with compaction and cementation. Morlier and Sarda (1971) have looked at ultra-sonic data (P-wave and S-wave velocities, frequencies, and attenuations) and petrophysical data (porosity, permeability, specific surface) of numerous core plugs of different rock types (sandstone, limestone, carbonate). Their laboratory experiments have led them to the following results: • When there is only one saturating fluid, the attenuation is an increasing function of frequency f and of the reverse of the kinematic viscosity (ρf /μ with ρf: fluid density, μ: fluid viscosity (centipoise)).
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