Chapter 4 Models of Electromagnetic Induction in the Earth

Abstract

The presence of fluids in the pore space of rocks causes wave attenuation and dispersion by the mechanism broadly known as wave-induced fluid flow (WIFF). WIFF occurs as a seismic wave that creates pressure gradients within the fluid phase, and the resulting oscillatory movement of the fluid relative to the solid is accompanied with internal friction until the fluid pressure is equilibrated. If two immiscible pore fluids with substantially different bulk moduli – such as water and gas – form patches, significant wave attenuation, and dispersion result. Their frequency dependence is controlled by the size, shape, and spatial distribution of fluid patches. We focus on the so-called mesoscopic patches referring to a length scale much larger than typical pore size and yet much smaller than the seismic wavelength.To decode WIFF effects in the laboratory setting, we interpret experimental results of ultrasonic signatures of sandstone and limestone core samples during water injection. Therein, the progress of water saturation is monitored via computed tomography (CT). Depending on the injection rate and overall saturation characteristic, water-patch distributions at the millimeter scale are observed. We also monitor saturation-induced acoustic changes using ultrasonic transducers. From these wave field recordings, we infer P-wave velocity and attenuation as a function of saturation. We show that the observed acoustic signatures can be modeled using random patchy saturation models based on Biot’s theory of poroelasticity.To understand implications of WIFF at the sonic frequency band, we analyze time-lapse well log data from the CO2 geosequestration site in Nagaoka, Japan. We retrieve a P-wave velocity–saturation relation (VSR) that can be explained in terms of WIFF at millimeter-scale fluid patches. Thus, mesoscopic heterogeneity can be responsible for attenuation and dispersion in the well logging frequency band. To study the implications on seismic signatures, we construct a modeling scenario inspired by the CO2 storage project at the Sleipner field, Norway. Through a numerical upscaling technique, we demonstrate that WIFF in the presence of centimeter-scale fluid patches may produce noticeable kinematic changes and amplitude distortions in seismic data at reservoir scale.