Assessment of different approaches to rock-physics modeling: A case study from offshore Nile Delta

The estimation of a reliable rock-physics model (RPM) plays a crucial role in reservoir characterization studies. We assess different methods in deriving a reliable RPM that will be used in conjunction with amplitude-versus-angle inversion for the characterization of a clastic reservoir located in offshore Nile Delta. The reservoir zone is located in gas-saturated sand channels surrounded by shale sequences within a depth interval ranging between 2.3 and 2.7 km. One theoretical and three empirical approaches to derive a RPM are analyzed: The theoretical RPM is established using the well-known rock-physics equations valid for granular materials, whereas the empirical RPMs are derived using one multilinear stepwise regression and two nonlinear regression procedures based on neural networks (NNs) and genetic algorithms (GAs). A proper calibration and validation of the derived RPMs is conducted by using the extensive log suite of four existing wells drilled over an area of 100 km2. For the investigated reservoir interval and for the encasing shales, all the analyzed methods give a final RPM that is able to reliably predict the elastic attributes (P-wave velocity, S-wave velocity, and density) from the petrophysical properties of interest (porosity, water saturation, and shaliness). Among the empirical approaches, the RPM predicted by the multilinear regression is characterized by a prediction capability very similar to the RPMs predicted by the nonlinear GA method, thus demonstrating that in the investigated zone, the relation linking the petrophysical properties to the elastic attributes can be conveniently described by a multilinear model. Differently, the NN method seems to be affected by the overfitting problem that produces a RPM with a lower prediction capability than the RPMs estimated by the other methods. The theoretical method yields predictions of elastic properties very similar to those produced by multilinear regression.