A. A. Afanasyev

Simulation of the properties of a binary carbon dioxide-water mixture under sub- and supercritical conditions

A method for determining the multiphase thermodynamic equilibriums of a binary mixture expressed in pressure-enthalpy-mixture composition variables is suggested. The use of such variables, in contrast to the classical thermodynamic pressure-temperature-composition variables, makes it possible to determine not only the two-phase, but also three-phase states of a mixture. The method can be used to describe real properties of mixtures in a wide range of pressure and temperature values containing critical points; it can be helpful in modeling of the mixture flows in a porous medium. The suggested problem of calculating the multiphase equilibrium can be visually interpreted in terms of geometry by constructing a convex envelope for the thermodynamic potential of the mixture. This method is used to study the phase diagram of the carbon dioxide-water mixture.

Mathematical model of nonisothermal multiphase binary mixture flow through a porous medium

A model of nonisothermal binary mixture flow through a porous medium, applicable over a wide range of thermobaric conditions, including temperatures higher than the critical mixture temperature, is proposed. A nonclassical approach used for modeling the mixture properties makes it possible to uniformly describe its single-, two- and three-phase thermodynamic equilibria and the corresponding flows under sub- and supercritical thermodynamic conditions. The wide application of thermodynamic methods to determining the real mixture properties leads to a nonstandard mathematical model in which the conservation laws are closed with a conditional extremum problem, not finite or differential equations. A dispersion analysis of the model equations is performed and the characteristic velocities in zones of different mixture phase states are determined.

Investigation of the evolutionarity of discontinuities in binary mixture flows through a porous medium

The discontinuity surfaces (shock waves) that arise in nonisothermal carbon dioxide-water binary mixture flows through a porous medium are considered. In the plane of determining parameters the discontinuity adiabats are investigated and their evolutionarity diagrams are plotted. It is shown that one of the adiabat branches corresponds to the displacement fronts at which there are no temperature jumps and phase transitions and the other branch to temperature jumps and phase transition fronts. The adiabat branches may intersect at a point that corresponds to the Jouguet point for the parameters both ahead of and behind the finite-amplitude jump. It is shown that in the neighborhood of this double Jouguet point the adiabat behavior differs from the classical adiabat behavior at single Jouguet points.

On the formulation of problems of nonisothermal water and vapor flow through a high-permeability formation

The formulation of self-similar problems of single- and two-phase water and vapor flow through high-permeability rocks is considered in the case when heat conduction is unimportant. The properties of the corresponding system of conservation laws, which affect the relative position of the integral curves of the Riemann waves and the discontinuity adiabatic curves, are investigated. The problem of breakdown of an arbitrary discontinuity in a geothermal formation with supercritical water parameters is solved.

Investigation of hydrodynamic instability of CO2 injection into an aquifer

The two-dimensional problem of supercritical carbon dioxide injection into an aquifer is solved. Shocks and rarefaction waves propagating in a sequence from an injection well into the formation are described within the framework of a complete nonisothermal model of flows in a porous medium. In the approximation of isothermal immiscible water and carbon dioxide flow the hydrodynamic stability of the leading displacement front is investigated for various reservoir pressures and temperatures. The parameters of unstable fronts are determined using a sufficient instability condition formulated in analytic form. The approximate analytic results are supported by the direct numerical simulation of CO2 injection using the complete model in which thermal effects and phase transitions are taken into account.

Steady-state water and vapor flows in a porous medium

Stationary regimes of nonisothermal flow of a liquid and its vapor through a porous medium in the gravity field are investigated. Possible flow types are analyzed in the plane of the determining parameters. The analytical results obtained are used in discussing the possibility of finding the pressure and temperature in the interior of a geothermal system from the parameters of the liquid and vapor flow in its permeable surface formations.

Investigation of time-dependent two-dimensional displacement in a porous medium in the self-similar formulation of the problem

Two-dimensional flow through a porous medium when a gas is injected into a permeable aquifer of infinite extension is investigated. The self-similar asymptotic solutions which describe the early stage of the time-dependent two-dimensional process of gas spreading along the caprock over the aquifer are constructed. The asymptotics are constructed on the assumption of the considerable aquifer thickness when the processes in the neighborhood of the aquifer base have no effect on flow along the caprock. Two-dimensional wave patterns describing the gas saturation distribution are investigated by means of the direct numerical simulation. The dimensions of the gas accumulation region are estimated as functions of the similarity parameters.

Numerical simulation of formation of a concentrated brine lens subject to magma chamber degassing

The mathematical model of flow of a binary salt-water mixture through a porous medium in a wide range of pressure and temperature is developed taking different multiphase thermodynamic equilibria of the mixture into account. Formation of concentrated brine lenses above a degassing magma chamber is investigated within the framework of the model. The lenses are assumed to be coupled with generation of ore deposits. It is shown that the lens formation is caused by phase transitions of two different types undergoing at different depths in the magmatic fluid rising towards the surface. In the shallow zones salt precipitation on the skeleton of the porous medium in the form of a solid phase leads to clogging of pore space and reduction of the permeability. As a result, the magmatic fluid flow towards the surface is blocked and this facilitates the concentrated brine accumulation in a local zone.

Parametric investigation of a brine lens formation above degassing magma chamber

Formation of porphyry-type ore deposits is associated with degassing of crustal magma chambers. Saline, metalrich magmatic fluid penetrates into a shallow region saturated with cold meteoric water where the metals concentrate in brine lenses. The formation of the lenses and, thus, of the deposits occurs due to phase transitions [1]. The evaporation of H2O results in enrichment of residual fluid in NaCl. At a depth of 1–2 km precipitation of solid halite blocks the pore space and facilitates formation of concentrated brine lenses.

Magma degassing during eruption through water-saturated porous rocks

In the case of extrusive eruption, we consider the problem on magma degassing which rises in a volcano conduit crossing porous water-saturated rocks. We show that the intensity of outflow of volcanic gases into the rocks is comparable to the intensity of their transport with the rising magma. The magma degassing in the rocks substantially affects the eruption dynamics, in particular, the duration of the periods of eruptive activity.