The numerical model ARMOS, which simulates areal flow of water and light hydrocarbon in an unconiined aquifer, isdescribed. Based on the assumption of local vertical equilibrium, area! flow equations for water and hydrocarbon are derived which exhibit reduced dimensionality and nonlinearity. A finite‐element method is used to solve the water and oil equations using an efficient semidecoupled approach. Input required by the model includes area! boundaries, elevations of the aquifer lower boundary, and initial water and hydrocarbon levels in monitoring wells. Soil and fluid properties include hydrocarbon density, viscosity and surface tension, saturated hydraulic conductivity, van Genuchten air‐water capillary pressure curve parameters, and the maximum residual hydrocarbon saturations in the saturated and unsaturated zones. Fluid heads or fluxes may be specified on the domain perimeter and pumping rates are prescribed at recovery wells. The water pumping rate is automatically limited when drawdown reaches a pump‐off set point (or the screen bottom), and hydrocarbon recovery is limited when well hydrocarbon thickness becomes zero. Model output includes water and hydrocarbon levels in monitoring wells, cumulative product recovery, and free and residual hydrocarbon volumes in the soil. A hypothetical problem involving optimization of free product recovery and a field application of the model to a large pipeline leak are described.

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Production Co.V."'. Kremesec "'r., SPE, Amoco Production Co. Summary. A series of gravity-assisted vertical core displacements of contact-miscible and multiple-contact-miscible C0 2 /recombined-crude-oil systems was conducted and simulated. Gravity-assisted displacements offer the advantages of eliminating gravity tongues and stabilizing viscous fingers. Although the process has been used successfully in the field, a mechanistic laboratory and modeling study of gravity-assistedmultiple-contact-miscible CO 2 flooding has not been described previously.The results from this experimental and computer modeling study elucidate the complex mechanisms acting in gravity-assisted CO 2 flooding. Component transfer, as occurs in multiple-contact-miscible processes, can strongly affect flood-front stability. In general, better performance is obtained from vertically downward displacements than from comparable displacements in horizontal cores. Miscibility develops at the same pressure in vertical floods and in a much shorter core length. It was further demonstrated that displacement efficiency increases at conditions where mixing of CO 2 and oil is minimized. Excellent simulation of experimental recoveries and rates were obtained with a compositional simulator in a one-dimensional (1D) mode.

A simple conceptual model is presented that leads to a quantitative description of the behavior of light non–aqueous phase liquid (LNAPL) in fine‐grained soil (FGS). The occurrence of large (15 feet) (4.6 m) LNAPL accumulations in observation wells in FGS and of LNAPL located below the water table is explained by macropore theory and capillarity of the FGS. Using soil capillary data, fluid property data, and a simple spreadsheet model, the LNAPL saturation in a soil profile and LNAPL recovery were predicted for a field study site. The predicted LNAPL distribution, saturation, and recovery matched the field observations and actual LNAPL recovery. Measured LNAPL saturations were <2%, while model‐predicted values were <3%. The model predicted recovery of ∼530 gallons (2009 L). After 1.5 years of continuous operation, a three‐phase, high‐vacuum extraction system recovered 150 gallons (568 L) of LNAPL. Application of a model that assumes homogeneity of the soil that is heterogeneous at a small scale may seem to be a misapplication; however, conceptualizing the model domain at a sufficiently large scale (3 to 6 feet; 0.9 to 1.8 m) allows for the FGS to be viewed as a homogeneous medium with small effective porosity.

This paper describes experimental and theoretical studies of cation exchange in porous media with micellar fluids formulated using a broad-equivalent-weight (BEW) sulfonate. The sulfonates can be described as composed of two pseudocomponents a quasi-monosulfonate (the oil-moving pseudo components a quasi-monosulfonate (the oil-moving component) and a quasi-disulfonate (the sulfonate-solubilizing component). With this description and a mass-action model for cation exchange between the micelles, clays, and solution, a match between computer model predictions and results of laboratory single-phase flow tests in Berea sandstone was carried out. The assumptions required are reviewed and independent experimental results presented. With these assumptions and parameter values determined from the Berea history match, satisfactory predictions of divalent cation concentrations in field core experiments have been made. The good predictive capability of this model allows initial screening and development of micellar formulations for specific reservoir applications to be conducted at appropriate hardness levels. Introduction It is well known that the oil recovery performance of a micellar fluid is strongly affected by salinity and hardness (calcium and magnesium divalent cations). This is because they have strong effects on the phase behavior and interfacial tension (IFT) of the surfactant/oil/brine system. It is also well known that the hardness and salinity of the micellar fluid can change significantly as a result of cation exchange and dissolution as the micellar fluid propagates through the reservoir. Since a knowledge of the in-situ levels of salinity and hardness is of primary importance in the screening and development of micellar fluids for field applications, an adequate prediction is necessary. Cation exchange between a brine and the clays within a reservoir rock occurs if the injected fluids have a salinity and hardness different from that of the in-place fluids. Smith, Griffith, and Hill and Lake have studied this problem and have shown the significance of the cation-exchange capacity (CEC) of the clays and the selectivity of the cation species with the clays. The clay selectivity is a measure of the preference of the clay for monovalent vs. divalent cations; for a given brine, smaller values indicate a higher fraction of the clays complexed by the divalent cations. Further, Hill and Lake concluded that the law of mass action is the best model with which to describe the process. Smith, and Hill and Lake, also showed that calcium and magnesium ions have the same selectivity with the clays vs. sodium, and hence they can be treated as a single ionic species. Hill and Lake extended their study to systems containing surfactants. They found that cation exchange in the presence of a surfactant system was complicated by interaction between surfactant and divalent cations. To describe the levels of hardness measured in the presence of surfactant micelles, they postulated the formation of a divalent-cation/surfactant complex and modeled the phenomenon with a mass-action isotherm. Gupta provided phenomenon with a mass-action isotherm. Gupta provided additional data supporting the formation of such a complex. Hirasaki and Lawson proposed a Donnan equilibrium model to describe the association of sodium and calcium with the micelles, and they estimated selectivity values from the resulting expressions. Hirasaki has incorporated a mass-action model, surfactant adsorption, and electroneutrality conditions with the mass balances neglecting dispersion to obtain a description of cation exchange during single-phase-flow in porous media. He has solved the system of equations using a method-of-characteristics approach and has been able to describe the experiments of Hill and Lake and Gupta showing good agreement between experiment and theory. The model is limited to one surfactant species and two cations-one monovalent and one divalent. The surfactant system used by Gupta closely conforms to these limitations. The micellar system used by Hill and Lake, however, was composed of two petroleum sulfonates and sodium alkyl ethoxysulfate (Neodol 25–3S). Nevertheless, Hirasaki assumed the surfactant mixture to be acting as a single surfactant species. This paper deals with the cation exchange that occurs during the propagation of a micellar system containing BEW sulfonate. The objective is to history-match limited tests in Berea cores and then to use the understanding gained and parameter values obtained to predict hardness concentrations in field cores over a wide range of micellar compositions. To correlate the Berea data and to extrapolate to other conditions, the approach of Hirasaki is desirable because of its simplicity. However, the complex composition of the BEW sulfonate micellar system, as well as a desire to include an adsorption isotherm and dispersion-important for small slug processes-precluded the straightforward use of the equations and the solution that he put forward. SPEJ P. 580