Carbonated water flooding (CWI) increases oil production due to favorable dissolution effects and viscosity reduction. Accurate modeling of CWI performance requires a simulator with the ability to capture the true physics of such process. In this study, compositional modeling coupled with surface complexation modeling (SCM) are done, allowing a unified study of the influence in oil recovery of reduction of salt concentration in water. The compositional model consists of the conservation equations of total carbon, hydrogen, oxygen, chloride and decane. The coefficients of such equations are obtained from the equilibrium partition of chemical species that are soluble both in oleic and the aqueous phases. SCM is done by using the PHREEQC program, which determines concentration of the master species. Estimation of the wettability as a function of the Total Bound Product (TBP) that takes into account the concentration of the complexes in the aqueous, oleic phases and in the rock walls is performed. We solve analytically and numerically these equations in 1 - D in order to elucidate the effects of the injection of low salinity carbonated water into a reservoir containing oil equilibrated with high salinity carbonated water.

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This paper is concerned with the study of the main wave interactions in a system of conservation laws in geochemical modeling. We study the modeling of the chemical complexes on the rock surface. The presence of stable surface complexes affects the relative permeability. We add terms representing surface complexes to the accumulation function in the model presented in [14]. This addition allows to take into account the interaction of ions with the rock surface in the modeling of the oil recovery by the injection of carbonated water. Compatibility hypotheses with the modeling are made on the coefficients of the system to obtain meaningful solutions. We developed a Riemann solver taking into account the complexity of the interactions and bifurcations of nonlinear waves. Such bifurcations occur at the inflection and resonance surfaces. We present the solution of a generalized eigenvalue problem in a (n+1)-dimensional case, which allows the construction of rarefaction curves. A method to find the discontinuous solutions is also presented. We find the solution path for some examples.

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This paper describes miscible displacement upon air injection in a porous medium saturated with oil corresponding to conditions of high-pressure air injection (HPAI). We assume that injection fluids and produced fluids are fully miscible with the oil at the prevailing high pressure. We use three pseudo-components, viz., oxygen, oil, and an inert component, which includes nitrogen, carbon dioxide, etc. To model the fingering instabilities, we follow a similar procedure as proposed by Koval (SPE J. 3(02):145–154, 1963) and include the reaction between oxygen and oil in the Koval model. The equations are solved numerically, using a finite element software package (COMSOL). The results show that a combustion wave is formed. We study the performance at low and high viscosities and show that the reaction improves the speed and degree of recovery at later times.

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We study systems of partial differential-algebraic equations (PDAEs) of first order. Classical solutions of the theory of hyperbolic partial differential equation such as discontinuities (shock and contact discontinuities), rarefactions and diffusive traveling waves are extended for variables living on a surface S, which is defined as solution of a set of algebraic equations. We propose here an alternative formulation to study numerically and theoretically the PDAEs by changing the algebraic conditions into partial differential equations with relaxation source terms (PDREs). The solution of such relaxed systems is proved to tend to the surface S, i.e., to satisfy the algebraic equations for long times. We formulate a unified numerical scheme for systems of PDAEs and PDREs. This scheme is naturally parallelizable and has faster convergence. We do not perform a rigorous analysis about the convergence or accuracy for the method, the evidence of its effectiveness is presented by means of simulations for physical and synthetical problems.

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We study nonlinear waves in two phase geochemical flow in one spatial dimension in porous media. We assume that each chemical species may flow in one or both phases with concentrations obeying thermodynamical equilibrium. We present a new methodology for reducing a number of equations applicable to injection problems for general systems of conservation laws in Geochemistry. This reduction is achieved by solving a nonlinear inverse problem. Nevertheless, we are able to perform a complete and explicit characteristic analysis, obtaining rarefaction and shock waves that are used to solve the representative Riemann problems, besides the main bifurcations structures appearing in the phase space are derived with explicit expressions. We illustrate the methodology by means of an example with four equations.

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Understanding the interplay of foam and non-aqueous phases in porous media is key to improving the design of foam for enhanced oil recovery and remediation of aquifers and soils. A widely used implicit-texture foam model predicts phenomena analogous to cusp catastrophe theory: the surface describing foam apparent viscosity as a function of fractional flows folds backwards on itself. Thus there are multiple steady states fitting the same injection condition J defined by the injected fractional flows. Numerical simulations suggest the stable injection state among multiple possible states but do not explain the reason.
We address the issue of multiple steady states from the perspective of wave propagation, using three-phase fractional-flow theory. The wave-curve method is applied to solve the two conservation equations for composition paths and wave speeds in 1D foam-oil flow. There is a composition path from each possible injection state J to the initial state I satisfying the conservation equations. The stable displacement is the one with wave speeds (characteristic velocities) all positive along the path from J to I. In all cases presented, two of the paths feature negative wave velocity at J; such a solution does not correspond to the physical injection conditions. A stable displacement is achieved by either the upper, strong-foam state or lower, collapsed-foam state, but never the intermediate, unstable state. Which state makes the displacement depends on the initial state of a reservoir. The dependence of the choice of the displacing state on initial state is captured by a boundary curve.@en

It has been shown experimentally in the literature that for clayey formations, oil with polar components and an aqueous phase with divalent ions, a secondary waterflood with low salinity water composition improves oil recovery by some 5–20%. Our focus is on a less well known mechanism, i.e. low salinity enhanced solvent (e.g. carbonated water) recovery, as low salinity enhances the aqueous solubility of carbon dioxide. Indeed, after injection the latter is transferred from the aqueous to oleic phase thus decreasing the oil concentration in the oleic phase and diluting the residual oil. To study this mechanism we formulate the conservation equations of total hydrogen, oxygen, chloride and decane. Therefore, we solve analytically and numerically these equations in 1−D in order to elucidate the effects of the injection of low salinity carbonated water into a reservoir containing oil equilibrated with high salinity carbonated water. We use PHREEQC (acronym of pH-REdox-Equilibrium C-program) to obtain the accurate equilibrium partition of neutral species that are soluble both in the oleic and the aqueous phase by application of the Krichevsky-Ilinskaya extension of Henry's law for solubility of gases in liquids. Using Gibbs phase rule it can be shown that the phase behavior only depends on the pH and the chloride concentration. The above mentioned equilibrium relations use Pitzer's activity coefficients to extend the validity up to 6M. We obtain the saturation, composition and the total Darcy velocity profiles. The significant new insight obtained is that by changing only the salinity in carbonated waterflooding the oil recovery can be enhanced.

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In this work, we introduce a formalism for two-phase geochemical flow. Here, we admit that the chemical species flow in both phases. Moreover, we consider chemical interaction and chemical equilibrium laws for which it is possible to obtain algebraic relationships between the chemical species. In this work, we consider that we have only one free chemical species, i.e., by using equilibrium laws, we admit that all chemical species can be written as function of only one, which we denote as y. We present a formalism for this kind of flow, moreover, we obtain the eigenvalues, eigenvectors, and bifurcations structures. We also show the structure of integral and Hugoniot curves in the saturation versus chemical species plane.@en

We develop a Riemann solver for transport problems including geochemistry related to oil recovery. The example considered here concerns one-dimensional incompressible flow in porous media and the transport for several chemical components, namely H₂O, H⁺, OH⁻, CO₂, (Formula presented.), (Formula presented.), and decane; they are in chemical equilibrium in the aqueous and oleic phases, leading to mass transfer of CO₂ between the oleic and aqueous phases. In our ionic model, we employ equations with zero diffusion coefficients. We do so because it is well known that for upscaled equations, the convection terms dominate the diffusion terms. The Riemann solution for this model can therefore be applied for upscaled transport processes in enhanced oil recovery involving geochemical aspects. In our example, we formulate the conservation equations of hydrogen, oxygen, hydrogen, and decane, in which we substitute regression expressions that are obtained by geochemical software. This can be readily done because Gibbs phase rule together with charge balance shows that all compositions can be rewritten in terms of a single composition, which we choose to be the hydrogen ion concentration (pH). In our example, we use the initial and boundary conditions for the carbonated aqueous phase injection in an oil reservoir containing connate water with some carbon dioxide. We compare the Riemann solution with a numerical solution, which includes capillary and diffusion effects. The significant new contribution is the effective Riemann solver we developed to obtain solutions for oil recovery problems including geochemistry and a variable total Darcy velocity, a situation in which fractional flow theory does not readily apply. We thus obtain an accurate solution for a carbonated waterflood, which elucidates some mechanisms of low salinity carbonated waterflooding.

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We develop a Riemann solver for transport problems related to oil recovery. We consider one dimensional incompressible flow in porous media involving several chemical components, namely $H_2O$, $H^+$, $OH^-$, $CO_2$, $CO_3^{2-}$, $HCO_3^-$ and decane, which are in chemical equilibrium in aqueous and oleic phases. As there is mass transfer between phases and the partial molar volume differs between aqueous and oleic phases leading to a variable total Darcy velocity, fractional flow theory does not easily apply. Recall that for upscaled equations the convection terms completely dominate the diffusion terms; this is why our basic model considers the limit of zero diffusion coefficients. The Riemann solution for this model can therefore be applied for upscaled transport processes in enhanced oil recovery involving geochemical aspects. We formulate three conservation equations, in which we substitute regression expressions that are obtained by geochemical software (PHREEQC). Gibbs phase rule together with charge balance shows that compositions can be rewritten in terms of the pH only. We use the initial and boundary conditions for carbonated aqueous phase injection in an oil reservoir containing connate water with some carbon dioxide. We compare the Riemann solution with a numerical solution, which includes capillary and diffusion effects. The structure of the Riemann solution for constant oil viscosity, from left (upstream) to right (downstream), consists of two rarefaction waves connected by a chemical shock; the latter is continued with a constant state and finally a fast Buckley-Leverett saturation shock. In the first rarefaction wave only the saturation changes, while in the second one both saturation and composition change. The connection point between the rarefaction waves can be constructed from a curve of states where the two characteristic velocities coincide. The significant new contribution is the effective Riemann solver we developed to obtain solutions for oil recovery problems including geochemistry and a space dependent total Darcy velocity. @en