Analytical approach to formulate dissolution in inhomogeneous temperature fields
29/11/2014 00:12
The dissolution of supercritical CO2 in interstitial water is one of the most crucial research topics in CCS. Various phase field models based on free energies are often used to study the dynamics on the assumption of constant temperature and no heat transfer. However, the phenomena involved in the inhomogeneous temperature and the heat transfer is considered important for CCS because the gas CO2 at near the critical point has very large thermal conductivity.
We propose a new method based on the variational principle. The dynamics of a fluid can be divided into the kinetic part and thermodynamics part. The kinetic part is characterized by the conservation laws for mass, energy, momentum, and angular momentum. On the other hand, the thermodynamics is described by the equation of the entropy in the form as
Here ρ is total mass density, s is specific entropy, J is entropy flux, and Θ > 0 is a dissipative function. This equation connects the kinematics and thermodynamics. We give a Lagrangian density by the kinetic energy density minus the internal energy density, and an action by integrating it over space and time. The realized dynamics minimizes the action subject to the constraint (1). Noether’s theorem states that each of the conservation laws is associated with each corresponding symmetry. For example, the conservation laws for energy, momentum, and angular momentum are related to the translation symmetries in time and space, and rotational symmetry, respectively. We fix the dissipative function Θ to satisfy these conservation laws. While, we determine the entropy flux J so as to erase surface terms without fixing boundary conditions. We find that the interface energy effects on the dissolution of CO2 in inhomogeneous temperature, significantly.
Recent achievement:
H. Fukagawa and T. Tsuji, A formulation for dissolution in inhomogeneous temperature field, Proceedings of International Symposium on Earth Science and Technology, 2014.
H. Fukagawa, C. Liu, T. Tsuji, A variation formulation for dissipateive fluids in inhomogeneous temperature, submitted to Physical Review E.
preprint https://arxiv.org/abs/1411.6760