57 2. Surface geophysical methods Rock physics modeling is the process of quantitatively describing the relationship between the physical properties of rocks (such as porosity, mineral composition, and fluid saturation) and their geophysical properties (such as elastic wave velocities, and electrical conductivity). The ultimate objective is to interpret subsurface geology, reservoir characteristics, and fluid content from geophysical measurements. Rock physics modeling can involve theoretical models based on physical laws combined with numerical simulations or empirical relationships derived from laboratory measurements or field data. The estimation of physical parameters such as seismic velocities and attenuation or resistivity obtained by geophysical methods associated with experimental relationships established from laboratory experiments allows the estimate of porosity or permeability distributions in geological formations. 2.1.1 Porosity Porosity Φ is defined as the ratio of the volume of pore space to the total or bulk volume of the rock. Porosity is expressed as a decimal fraction or a percentage (%). Porosity is the result of various geological, physical, and chemical processes, and is generated during the genesis of the rock as “primary porosity”, and/or during the geological history of the rock as “secondary porosity” (tectonic processes (fractures), chemical processes, dissolution). Total porosity is the sum of the primary and the secondary porosity. The main factors, which influence primary porosity, are: • Grain and pore geometrical properties (arrangement and shape of the rock grains, grain size distribution), • Diagenetic processes, amount of cement, • Depth and pressure (which also influences secondary porosity) Theoretically, porosity for given packing is independent of grain size. However, porosity shows a tendency to increase with the change from spherical or well-rounded grains to angular particles. Decrease of porosity primarily results from packing and cementation for sands and sandstone, and from compaction for clays and shale. This reflects a general tendency of decreasing porosity with increasing depth. Effective porosity is the porosity that is available for free fluids; it excludes all nonconnected porosity. Effective porosity could be much lower than the total porosity when the pores are not connected or when the pores are so small that fluids cannot circulate. For a clean formation, if the matrix and fluid velocities are known, porosity can be computed from the acoustic Vp velocities by using the formula given by Wyllie et al. (1956) expressed in velocities. It is given by the following equation: Φ= − − v v v v v v ma p ma f f p (2.1) with Vma the matrix velocity, Vf the fluid velocity.
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