Estimations of porosity and permeability from well logs are important yet difficult tasks encountered in geophysical formation evaluation and reservoir engineering. Motivated by recent results of artificial neural network (ANN) modelling offshore eastern Canada, we have developed neural nets for converting well logs in the North Sea to porosity and permeability. We use two separate back‐propagation ANNs (BP‐ANNs) to model porosity and permeability. The porosity ANN is a simple three‐layer network using sonic, density and resistivity logs for input. The permeability ANN is slightly more complex with four inputs (density, gamma ray, neutron porosity and sonic) and more neurons in the hidden layer to account for the increased complexity in the relationships. The networks, initially developed for basin‐scale problems, perform sufficiently accurately to meet normal requirements in reservoir engineering when applied to Jurassic reservoirs in the Viking Graben area. The mean difference between the predicted porosity and helium porosity from core plugs is less than 0.01 fractional units. For the permeability network a mean difference of approximately 400 mD is mainly due to minor core‐log depth mismatch in the heterogeneous parts of the reservoir and lack of adequate overburden corrections to the core permeability. A major advantage is that no a priori knowledge of the rock material and pore fluids is required. Real‐time conversion based on measurements while drilling (MWD) is thus an obvious application.

We use a poroelastic modeling algorithm to compute numerical experiments of wave propagation in White's partial saturation model. The results are then compared to the theoretical predictions. The model consists of a homogeneous sandstone saturated with brine and spherical gas pockets. White's theory predicts a relaxation mechanism, due to pressure equilibration, causing attenuation and velocity dispersion of the wavefield. We vary gas saturation either by increasing the radius of the gas pocket or by increasing the density of gas bubbles. Despite that the modeling is two dimensional and interaction between the gas pockets is neglected in White's model, the numerical results show the trends predicted by the theory. In particular, we observe a similar increase in velocity at high frequencies (and low permeabilities). Furthermore, the behavior of the attenuation peaks versus water saturation and frequency is similar to that of White's model. The modeling results show more dissipation and higher velocities than White's model due to multiple scattering and local fluid-flow effects. The conversion of fast P-wave energy into dissipating slow waves at the patches is the main mechanism of attenuation. Differential motion between the rock skeleton and the fluids is highly enhanced by the presence of fluid/fluid interfaces and pressure gradients generated through them.

Source rocks are described by a porous transversely isotropic medium composed of illite and organic matter (kerogen, oil, and gas). The bulk modulus of the oil/gas mixture is calculated by using a model of patchy saturation. Then, the moduli of the kerogen/fluid mixture are obtained with the Kuster and Toksöz model, assuming that oil is the inclusion in a kerogen matrix. To obtain the seismic velocities of the shale, we used Backus averaging and Gassmann equations generalized to the anisotropic case with a solid-pore infill. In the latter case, the dry-rock elastic constants are calculated with a generalization of Krief equations to the anisotropic case. We considered 11 samples of the Bakken-shale data set, with a kerogen pore infill. The Backus model provides lower and upper bounds of the velocities, whereas the Krief/Gassmann model provides a good match to the data. Alternatively, we obtain the dry-rock elastic moduli by using the inverse Gassmann equation, instead of using Krief equations. Four cases out of 11 yielded physically unstable results. We also considered samples of the North Sea Kimmeridge shale. In this case, Backus performed as well as the Krief/Gassmann model. If there is gas and oil in the shale, we found that the wave velocities are relatively constant when the amount of kerogen is kept constant. Varying kerogen content implies significant velocity changes versus fluid (oil) saturation.

We obtain the wave velocities and quality factors of clay‐bearing sandstones as a function of pore pressure, frequency and partial saturation. The model is based on a Biot‐type three‐phase theory that considers the coexistence of two solids (sand grains and clay particles) and a fluid mixture. Additional attenuation is described with the constant‐Q model and viscodynamic functions to model the high‐frequency behaviour. We apply a uniform gas/fluid mixing law that satisfies the Wood and Voigt averages at low and high frequencies, respectively. Pressure effects are accounted for by using an effective stress law. By fitting a permeability model of the Kozeny– Carman type to core data, the model is able to predict wave velocity and attenuation from seismic to ultrasonic frequencies, including the effects of partial saturation. Testing of the model with laboratory data shows good agreement between predictions and measurements.

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