Multicomponent multiphase flow in porous media with temperature variation or adsorption

In this work, we extend the analytical theory for gas injection to consider the effects of variable temperature or adsorption of components at rock surfaces. A set of hyperbolic partial differential equations is established that describes the mass conservation of individual components and conservation of overall energy in a one-dimension model. The set of equations is then transformed into an eigenvalue problem that can be solved using the method of characteristics approach, which yields continuous variation of compositions and temperatures. Discontinuous solutions can be solved from the conservation of mass and energy in an integral form. The final solution consists of segments of continuous variation and discontinuous solution that are assembled according to physical constraints such as velocity rule and entropy condition.; The solution method is applied to enhanced coal-bed methane recovery by gas injection, where we maintain the isothermal flow assumption and focus on the effect of adsorption. The adsorption behavior is approximated by an extended Langmuir isotherm. The solutions obtained show that separation of gas species occurs due to the difference in the affinity of the gas species to the coal bed surfaces, and that the coal bed sequesters CO₂, a major component of greenhouse gas, effectively.; The effect of temperature variation is studied in enhanced oil recovery by gas injection, where adsorption at rock surface is neglected. A careful examination of the solutions in binary systems reveals that for many cases the temperature fronts propagate slowly and separately from the composition fronts. The propagation of composition fronts is accompanied only by small temperature variation resulting from heat of condensation and vaporization. In this case, it is reasonable to assume isothermal flow at the downstream end. However, under certain conditions, the temperature fronts catch up to and interact with trailing composition fronts. The simultaneous propagation of temperature and composition fronts is examined in detail for this scenario.; A one-dimensional finite-difference scheme with single-point upstream weighting is used to confirm the analytical solutions, and satisfactory agreement is obtained. However, the analytical approach appears to be orders of magnitude faster, and is free of numerical dispersion.