ИСТИНА

Multiphase flows in porous media with a transition between sub- and supercritical thermodynamic conditions occur in many natural and technological processes (e.g. in deep regions of geothermal reservoirs where temperature reaches critical point of water or in gas-condensate fields where subject to critical conditions retrograde condensation occurs and even in underground carbon dioxide sequestration processes at high formation pressure). Simulation of these processes is complicated due to degeneration of conservation laws under critical conditions and requires non-classical mathematical models and methods. A new mathematical model is proposed for efficient simulation of binary mixture flows in a wide range of pressures and temperatures that includes critical conditions. The distinctive feature of the model lies in the methodology for mixture properties determination. Transport equations and Darcy law are solved together with calculation of the entropy maximum that is reached in thermodynamic equilibrium and determines mixture composition. To define and solve the problem only one function - mixture thermodynamic potential - is required. Such approach allows determination not only single-phase states and two-phase states of liquid-gas type as in classical models but also two-phase states of liquid-liquid type and three-phase states. The proposed mixture model was implemented in MUFITS (Multiphase Filtration Transport Simulator) code for hydrodynamic simulations. As opposed to classical approaches pressure, enthalpy and composition variables together with fully implicit method and cascade procedure are used. The code is capable of unstructured grids, heterogeneous porous media, relative permeability and capillary pressure dependence on temperature and pressure, multiphase diffusion, optional number of sink and sources, etc. There is an additional module for mixture properties specification. The starting point for the simulation is a cubic equation of state that is used for mixture thermodynamic potential - entropy - calculation in pressure, enthalpy and composition variables. A polynomial spline is implemented to save the potential for subsequent hydrodynamic simulations. At this stage the majority of complicated thermodynamic procedures are performed prior to hydrodynamic that results in sufficient acceleration of calculations. The code was used for analysis of multiphase water-carbon dioxide mixture flows in porous media. Using the developed methodology the mixture phase diagram was calculated both below and above critical point of water. A zone of three-phase state conditions was detected where the mixture splits in three phases: liquid water and liquefied and gaseous carbon dioxide. The mixture flows subjected to formation of the three-phase flow region were investigated. The work is supported by Grant of the President of the Russian Federation (575.2010.1, 4810.2010.1).