Hysteretic Aspects of CO2 Sequestration Modelling

The multiphase nature of the flow in porous media is characterized by hysteretic effects on the macroscopic level. These effects have a significant influence on the behavior of the whole system and therefore have to be taken into account. The aim of this subproject is to develop and implement models describing the hysteresis in the context of the CO2 sequestration process.The hysteresis relation of our primary interest is the relation between the capillary pressures and the saturations of the phases. As a basic flow model we use the model developed by the subproject Hoffmann based on Darcy’s law. We extend then this model by introducing a hysteresis operator relating the capillary pressures and the saturations. In the first year, we have studied existing models and approaches to the modeling of hysteretic behavior of capillary pressure versus saturations. Also, existing investigations of the effect of accounting for hysteretic models on the resulting behavior of flows were evaluated, and a model of the so-called play hysteretic operator relating capillary pressures and the saturations was implemented. In the second year, we extended a Darcy’s law based multi-phase flow model developed in the subproject Hoffmann by introducing a play hysteresis operator. Different types of finite elements were tested for solving hyperbolic and elliptic parts of the model. In particular, mass conservation equations were effectively solved with discontinuous Galerkin elements, whereas elliptic equations for the pressure were solved with conventional conformal finite elements. A detailed analysis of the numerical model demonstrated a number of severe difficulties mostly caused by the hysteretic dependence of the capillary pressure on the saturation and by the non-smoothness of the saturation itself. In order to obtain a stable behavior, we have tried several approaches involving different regularization techniques and finite element types. Finally, we have managed to obtain a stable convergence of the algorithm in the case of affine meshes. In the third year, we implemented another approach based on the solving of a convection-diffusion equation for the saturation. The presence of a diffusive term makes the numerical behavior more stable. On the other hand, such an equation is strongly non-linear. In order to handle it, we have developed an algorithm based on the Newton-Raphson method. Besides, we have implemented the Preisach operator for the hysteretic relation. This operator reflects the physical phenomena more appropriate than the play operator. At the same time, it causes less difficulties for the numerical convergence. This