Seismic reservoir characterization in offshore Nile Delta. Part I: comparing different methods to derive a reliable rock-physics model.

Seismic-reflection data are used in reservoir characterization not only for obtaining a geometric description of the main subsurface structures but also for estimating properties like lithologies and fluid contents of the target levels of interest. To this end, a rock-physics model (RPM) is incorporated into a seismic inversion scheme, such as amplitude versus angle (AVA) inversion (Grana and Della Rossa, 2011) or full-waveform inversion (Bacharach, 2006), to directly derive petrophysical rock properties from pre-stack seismic data. The outcomes of petrophysical-seismic inversion provide reservoir property maps to reservoir engineers for field appraisal, selection of optimal well location, and production enhancement (Bosh et al. 2010). A rock-physics model is a generic transformation (fRPM) that can be expressed as follow: The RPM relates rock properties (which typically are porosity - φ -, water saturation - Sw - , shale content - Sh -) and the depth (z), that can be easily related to the pressure conditions, to elastic attributes (such as P-wave and S-wave velocities - Vp, Vs - and density). A rock-physics model can be based on theoretical equations (Avseth et al. 2005), or on empirical set of equations derived from available information (e.g. well-log or core measurements) for the specific case of interest (Mazzotti and Zamboni, 2003). In the last case, either a linear or a non-linear model can be considered (Eberhart-Phillips et al. 1989). In case of a non-linear approach many methods can be used to derive such rock-physics model. Among the non-linear approaches neural networks (Saggaf et al. 2003) and stochastic optimizations (Aleardi, 2015) have received great attention. Anyway, independently from the method used, there is no doubt that the quality and the reliability of available well-log data and/or core measurements play an essential role in defining a solid RPM. The aim of this work is derive a reliable RPM to be used in conjunction with an AVA inversion for the characterization of a clastic reservoir located in offshore Nile delta. To derive the RPM both theoretical and empirical approaches are employed. For what concerns the empirical approaches we use both a linear and two non-linear methods to define different rock-physics models. The linear model is obtained by applying a multilinear stepwise regression, whereas neural networks and genetic algorithms are used to derive non-linear transformations from petrophysical to elastic properties. The main difference among neural networks and genetic algorithms is that the former is a gradient-based method while the latter is a global, stochastic, optimization method. We start by introducing the different methods used to derive the theoretical and the empirical rock-physics models. Then, the RPMs resulting from theoretical and empirical approaches are analyzed in detail to define the benefits and the limits of each method. Moreover, in the empirical approaches we focus our attention on discussing the differences between linear and non-linear methods for the specific case under examination and on analyzing the drawbacks that characterize the neural network technique. The simplicity and the reliability of the empirical rock-physics model derived by applying multilinear stepwise regression and the optimal prediction capability of the theoretical rock-physics model enable us to consider these two RPMs in the petrophysical AVA inversion that is discussed in the companion paper titled “Seismic reservoir characterization in offshore Nile Delta. Part II: Probabilistic petrophysical-seismic inversion”.