The method of characteristics, or fractional-flow theory, is extremely useful in understanding complex Enhanced Oil Recovery (EOR) processes and in calibrating simulators. One limitation has been its restriction to Newtonian rheology except in rectilinear flow. Its inability to deal with non-Newtonian rheology in polymer and foam EOR has been a serious limitation. We extend fractional flow methods for two-phase flow to non-Newtonian fluids in one-dimensional cylindrical flow, where rheology changes with distance from injection well. The fractional flow curve is then a function of position and we analyze the characteristic equations for two applications-polymer and foam floods. For polymer flooding, we present a semi-analytical solution for the changing fractional flow curve where characteristics and shocks collide. The semi-analytical solution is shown to give good agreement with the finite-difference simulation thus helping us understand the development and resolution of shocks. We discuss two separate cases of foam injection with or without preflush. We observe that the fractional flow solutions are more accurate than finite-difference simulations on a comparable grid and hence the method can be used to calibrate simulators. For SAG (alternating-slug) foam injection, characteristics and shocks collide, making the fractional-flow solution complex. Nonetheless, one can solve exactly for changing mobility near the well, to greater accuracy than with conventional simulation. The fractional-flow method extended to non-Newtonian flow can be useful both for its insights for scale-up of laboratory experiments and to calibrate computer simulators involving non-Newtonian EOR. It can also be an input to streamline simulations.
The disposal of acid gas (CO 2 /H 2 S mixtures) is a critical aspect in the production of hydrocarbons from sour gas fields. The increasing emphasis on CO 2 sequestration has also renewed interest in the disposal of flue gas mixtures (primarily containing CO 2 and H 2 S). A common strategy for safe disposal, in either case, is to inject the acid gas in aquifers close to production plants. These strategies rely on solubility calculations at different pressures and temperatures, governed by the field operating conditions. We present a comprehensive approach using Gibbs free energy minimization to calculate acid gas solubility in water at high temperatures (298−393 K) and pressures (0.1−80 MPa). The advantage of this approach is the flexibility to use different thermodynamic models for different phases. The proposed model uses the Peng−Robinson (PR) Equation of State (EOS) description for gas components while the liquid components are described using the ideal assumption for the temperature range 298−323 K and the Nonrandom Two-Liquid (NRTL) activity coefficient model at temperatures greater than 323 K. The model predictions compare well with experimental data for binary (CO 2 −H 2 O and H 2 S−H 2 O) and ternary mixtures (CO 2 − H 2 S−H 2 O). The model can also be easily extended to predict the solubility of any gas in water as well as brine containing ions to incorporate geochemical reactions.
Multicomponent cation exchange reactions have important applications in groundwater remediation, disposal of nuclear wastes as well as enhanced oil recovery. The hyperbolic theory of conservation laws can be used to explain the nature of displacements observed during flow with cation exchange reactions between flowing aqueous phase and stationary solid phase. Analytical solutions have been developed to predict the effluent profiles for a particular case of heterovalent cations (Na 1 , Ca 21 and Mg 21) and an anion (Cl 2 ) for any combination of constant injection and constant initial composition using this theory. We assume local equilibrium, neglect dispersion and model the displacement as a Riemann problem using mass action laws, the charge conservation equation and the cation exchange capacity equation. The theoretical predictions have been compared with experimental data available at two scales-the laboratory scale and the field scale. The theory agrees well with the experimental data at both scales. Analytical theory predictions show good agreement with numerical model, developed using finite differences.
Acid gases (CO 2 /H 2 S) injected in aquifers for continuous hydrocarbon production from sour gas fields (gas reserves with acid gas contaminants) can react with the ions present in the brine. The solubility predictions are then, quite different than those without reactions. Accurate solubility estimates in the presence of such reactions are integral towards developing an effective acid gas disposal strategy for continuous production from these fields. Also, the modeling of CO 2 injection in oil reservoirs entails complex interplay of flow, geochemical reactions and hydrocarbon phase behavior. The geochemical reactions affect the component mole numbers, which can change the number of hydrocarbon phases and/or affect the distribution of components in them. In this research, we propose the Gibbs free energy minimization algorithm that integrates geochemical reactions and phase behavior to find equilibrium compositions for these two applications. We use this algorithm to find equilibrium compositions for not just pure phase equilibrium (without reactions) but also phase and chemical equilibrium (with reactions).While the number and composition of the hydrocarbon phases may vary; we assume all the geochemical reactions are at equilibrium. In the first application, we use this algorithm to estimate solubility of acid gases (CO 2 and/or H 2 S) in pure water as well as CO 2 solubility in high salinity brine. The algorithm predicts the solubility for binary systems of CO 2 -H 2 O and H 2 S-H 2 O at high pressures and at temperatures upto 50C. The use of Pitzer's activity coefficient model for aqueous phase components also helps predict the solubility of CO 2 in high salinity brine. In the second application for hydrocarbons, we investigate the impact of geochemical reactions on the phase distribution of CH 4 -CO 2 -H 2 O mixture. We observe that the geochemical reactions do not change the equilibrium phase mole fractions at 50C in the pressure range 0.1-20 MPa.
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