On Approximation of Phase Equilibria of Multicomponent Hydrocarbon Mixtures and Prediction of Oil Displacement by Gas Injection

Abstract

Ab s tr act . This study is direct continuation of that presented in [1][2][3][4][5][6][7] . Further progress in using splitting of the problem of multicomponent two-phase flow into physicochemical and hydrodynamical parts is reported . First, conditions of phase equilibrium are expressed in terms of new variables, namely tie-live parameter and concentrat ion of a component . An effective procedure for such transformation is described . Next, it is shown, that for 1 D displacement the property of route invariante holds, n ame ly projection of t he so l ution into the ti e-live parameter space remains the same for d ifferent fluid-dynamical parameters, even in the case of composition-dependent density. It is demonstrated also, that the property holds approximately also for more general flows, including 2D flows in homogeneous and non-homogeneous reservoirs . Some examples are presented for oil disp lacement by inject i on of N2 or COZ -containing gas .1 . Alternative description of phase equilibria . It was shown previously, that the problem of oil by gas injection ("miscible gas flooding") in 1D statement can be splitted into two successively solved problems, namely a physicochemical and hydrodynamical ones, so that the physicochemical problem is expreseed entirely in terme of phase equilibria (see [1][2][3][4][5][6][7]) . A key element in such a splitting consists in transformation of the conditions of phase equilibria to new variables, namely concentration of a ("legding" component C, and a vector-parameter -y of tie lines .We consider a system of n components that may form a single-phase or two-phase mixture . Composition of a system is specified by the composition vector C = {Cl, . . . CnC } . We use molar concentrations Ci to characterize amount of given component in the mixture ; overall and partial molar densities are denoted by N and Ni, correspondingly. The concentrations satisfy the obvious relation C1+ . . .+Cn = 1 .(1 )Therefore, composition vector can be represented by a point within (n -1) -dimensional regular polyhedron of unit height (a triangle for n = 3, a tetrahedron for n = 4, etc) .The interior of the polyhedron is divided into single-phase and two-phase domains separated with a (nc -2) dimensional binodal surface, the locus of bubble-points and dew-points at given valnes of pressure and temperature . Thermodynamics implies that there is one-to-one correspondence between the sets of bubble points and due points . This correspondente is specified by the requirement that compositions corresponding to two respective points are in thermodynamic equilibrium . Let Cl and C9 be two such points . Then all compositions along the straightline segment 0 : B : C=SCI+(1-S)C9 ; 0<S<1 . (2 )correspond to two-phase mixtures of liquid volume fraction S of composition Cl and gas volume fraction (1 -S) of composition C9 ; we will refer to S as the "liquid phase saturation", or just "saturation" . The segment 0 is a tie-line .Equations (2) for S < 0, or S > 1, define tie-line extensions beyond the two-phase dom...

Multiscale Reconstruction Of Compositional Transport

“…As a consequence of the parameterization, the -1 conservation equations, that were formerly solved in each grid block, is reduced to 2 equations. It is worth noticing that the advanced framework used in solving the problem in tie-line space was built based on the ideas originated from the Method of Characteristics (MOC) based theory of gas injection process [13] & [27] and tie-line based parameterization technique proposed in [10] & [28].…”

“…ideology (based on the tie-line concept) was later implemented for a more general case [10] & [28], where the original compositional problem is projected onto a tie-line space, and later, the parameters pertaining to two-phase region of EoS-based system are determined using polynomial approximations.…”

An Extended Natural Variable Formulation for Compositional Simulation Based on Tie-Line Parameterization

“…One extra parameter, such as the liquid fraction or saturation, can be used to identify the particular position on the tie-line, or its extension. So, for a two-phase region, there is a complete correspondence between the tie-line-based variable set described in Entov et al (2001), Voskov and Tchelepi (2009a) and the natural variable set.…”

Analytical Modeling for Two-Phase EOR Processes: Splitting between Hydrodynamics and Thermodynamics

“…The exact solutions for the displacement of n-component ideal mixtures were obtained using the projection to an auxiliary system 21 . These solutions along with the definition of the reduced system were further used for injection of different gases into different oils [23][24][25] . The technique developed is valid just for the case of continuous gas injection and cannot be applied for non-self-similar slug problems.…”

“…The initial and boundary conditions (24), (25) and (26) The boundary condition (26) for slug injection gives the following value of potential ϕ:…”