Multiscale Modelling of Elastic Parameters

Abstract

Petrophysical properties in general and elasticity in particular have heterogeneous variations over many length scales. In a reservoir model, on which one for example can simulate fluid flow, seismic responses and resisitivity, it is necessary that the petrophysical parameters represent all these variations, even though the model is at a scale to coarse to capture all these properties in detail. Upscaling is a technique to bring information from one scale to a coarser in a consistent manner. Thus one upscaled model can be seen as homogeneous with a set of effective properties for its scale. For elastic properties, upscaling has traditionally been done by different volume weighted averaging methods like Voigt, Reuss or Backus averages which utilize limited or no information about the geology of the rock. The objective here is to do upscaling based on a technology where geological information is taken into account. This thesis considers different aspects governing elasticity upscaling in general and general geometry upscaling in particular. After the theory part it considers verification of the general geometry method and the implementation of this, projection of an elasticity tensor onto a certain symmetry and visualization of elastic moduli. Next the importance of including geological information is studied and upscaling is done on examples of realistic reservoir models. Finally elasticity upscaling utilized in a bottom-up approach to model 4D seismic is considered.