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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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

It has been shown in the literature that a secondary low salinity waterflood can improve the oil recovery by 5-20%. A possible mechanism is that the low salinity causes desorption of organic material, which may increase water-wetness and lead to more favorable relative permeability behavior. A less well-known mechanism is enhanced solvent (e.g., carbonated water) recovery as low salinity enhances the aqueous solubility of neutral components, which after injection will be transferred from the aqueous phase to oleic phase thus decreasing the oil concentration in the oleic phase and diluting the residual oil. By way of example we consider a low salinity carbonated waterflood into a reservoir containing oil equilibrated with high salinity carbonated water. For a given pH, the CO2 equilibrium concentration in low salinity injection water is higher than in the high salinity initial water. PHREEQC, a geochemical aqueous equilibrium programme, can be extended to obtain the accurate partition coefficient of neutral species that are soluble both in the oleic and the aqueous phase. For this we use the Krichevsky-Ilinskaya extension of Henry’s law for solubility of gases in liquids. Gibbs phase rule shows that the phase behavior only depends on the pH and the chloride concentration. In PHREEQC, we use Pitzer’s activity coefficients to extend the validity up to 6M. The output of PHREEQC can only be successfully incorporated in multiphase flow simulation programmes, e.g. COMSOL(TM), after applying a smoothing procedure for which we choose symbolic regression (EUREQA(TM)). An optimal formulation avoids spurious broadening of the concentration profiles in contact “discontinuities”. We obtain the saturation, composition and the total Darcy velocity profiles. The significant new insight is that by changing the salinity at constant pH the oil recovery by carbonated water flooding can be enhanced. This insight can be applied to optimize enhanced oil recovery with a low salinity waterflood. @en