A finite element code for modelling tracer transport in a non-isothermal two-phase flow system for CO2 geological storage characterization

This paper presents a new finite element method (FEM) code for modeling tracer transport in a non-isothermal two-phase flow system. The main intended application is simulation of the movement of so-called novel tracers for the purpose of characterization of geologically stored CO2 and its phase partitioning and migration in deep saline formations. The governing equations are based on the conservation of mass and energy. Among the phenomena accounted for are liquid-phase flow, gas flow, heat transport and the movement of the novel tracers. The movement of tracers includes diffusion and the advection associated with the gas and liquid flow. The temperature, gas pressure, suction, concentration of tracer in liquid phase and concentration of tracer in gas phase are chosen as the five primary variables. Parameters such as the density, viscosity, thermal expansion coefficient are expressed in terms of the primary variables. The governing equations are discretized in space using the Galerkin finite element formulation, and are discretized in time by one-dimensional finite difference scheme. This leads to an ill-conditioned FEM equation that has many small entries along the diagonal of the non-symmetric coefficient matrix. In order to deal with the problem of non-symmetric ill-conditioned matrix equation, special techniques are introduced . Firstly, only nonzero elements of the matrix need to be stored. Secondly, it is avoided to directly solve the whole large matrix. Thirdly, a strategy has been used to keep the diversity of solution methods in the calculation process. Additionally, an efficient adaptive mesh technique is included in the code in order to track the wetting front. The code has been validated against several classical analytical solutions, and will be applied for simulating the CO2 injection experiment to be carried out at the Heletz site, Israel, as part of the EU FP7 project MUSTANG.