Diffusion of CO2 at Reservoir Conditions: Models and Measurements

Abstract

Summary. Mathematical models are developed to describe the transport of dissolved CO2 in a liquid phase, and results of measurements of the diffusivity of CO2 in hydrocarbons and water at reservoir conditions are reported. The measurements were made with novel techniques based on the direct observation of the motion of an interface caused by the diffusion o CO2 through oil or oil shielded by water. Diffusion coefficients were determined by fitting the mathematical models to the observed motion of the interfaces. This method allows the measurement of diffusion coefficients without the need to determine phase compositions and is therefore suited to measurements at elevated pressures (reservoir conditions). Measured diffusion coefficients are reported for CO2 in pentane, decane, and hexadecane at 25deg.C [77deg.F] and pressures up to 6000 kPa [870 psia). Limited measurements of CO2 diffusion in Maljamar crude oil are also described. In addition, results of measurements for the diffusion of CO2 in water are presented. These are the first such measurements at high pressures (up to 6000 kPa 1870 psial). Correlations of diffusion pressures (up to 6000 kPa 1870 psial). Correlations of diffusion coefficients in liquids at atmospheric pressure are shown to give reasonable estimates of diffusion coefficients for CO2 in fluids at reservoir conditions. Finally, the measured diffusion coefficients and mathematical models are used to assess the impact of diffusive mixing on CO2 floods at various length scales to examine the relationship between laboratory-scale corefloods and field- scale displacements. Introduction Displacement efficiency in both secondary and tertiary CO2 floods depends on the development of favorable phase-behavior effects, resulting from mixing between CO2 and oil. Molecular diffusion is responsible for mixing at the pore level, and has been shown to be an important rate-controlling mechanism in CO2 flooding. The extent of the beneficial effects of phase behavior. therefore, depends on contact time, length of diffusion path, and rate of diffusion. In displacements where contact times are short (laboratory corefloods) or where diffusion paths are long (field-scale floods) and for systems where diffusion rates are low, nonequilibrium effects may reduce displacement efficiency. To determine the conditions for which nonequilibrium effects are important. and to scale laboratory corefloods to field conditions, estimates of diffusion path lengths and molecular diffusion coefficients are needed. Diffusion path lengths in real porous media have a wide range of values, which depend in a complex manner on such factors as pore-space geometry, microscopic and macroscopic pore-space geometry, microscopic and macroscopic heterogeneities, fluid physical properties, and rock wettability. Characteristic or "mean path lengths," however, may be estimated on the microscale from previously reported flow-visualization and fluid-distribution studies and on the macroscale from consideratio of reservoir heterogeneities and the effects of viscous fingering and gravity segregation. Comparatively few studies have been concerned with the measurement of molecular diffusion coefficients at reservoir conditions. Brow et al. measured the diffusivity of methane in crude oil from the Rangely field. CO2 at 18 000 kPa [2.600 psial and 70deg.C [160deg.F). They report a diffusion coefficient of 3.34 × 10 -9 M2iS 135.95 × 10–9 ft2/sec]. That value is similar in magnitude to those for methane in normal paraffin solvents measured at atmospheric pressure and temperatures in the range of 0 to 50deg.C 130 to 120deg.F) pressure and temperatures in the range of 0 to 50deg.C 130 to 120deg.F) reported by Hayduk and Buckley. Sigmund presents measurements of the diffusivity of methane in propane and butane for pressures in the range of 1500 to 20 000 kPa [220 to 2,900 psial and pressures in the range of 1500 to 20 000 kPa [220 to 2,900 psial and temperatures from 35 to 105deg.C 95 to 220deg.F]. The reported diffusion coefficients are in the range of 16 × 10 -') to 76 × 10-') m-/s [172x 10–9 18x 10–9 ft' /sec]. These are considerably higher than the diffusivities for methane in normal paraffins measured at atmospheric pressure Solvent viscosity for Sigmund's conditions, however, is considerably lower than that for the atmospheric pressure measurements, which show diffusivity to increase with pressure measurements, which show diffusivity to increase with decreasing solvent viscosity. Thus, the evidence available suggests that diffusivities for methane at reservoir conditions are not greatly different from those measured at atmospheric conditions, provided that solvent viscosities are similar. provided that solvent viscosities are similar. The only measurements reported for the diffusivity of CO2 in hydrocarbon solvents at elevated temperature and pressure (reservoir conditions) are those of Denoyelle and Bardon and de Boer et al. Denovelle and Bardon report diffusion coefficients of CO, in oil at reservoir conditions that are some 5 to 10 times higher than those measured at atmospheric conditions. They concluded that measurements of diffusivity at atmospheric conditions cannot be used as reasonable estimates of diffusivity at reservoir conditions. That conclusion is at variance with the work of de Boer et al., who observed that diffusion rates of CO, in crude oil at elevated pressures were consistent with calculated rates based on diffusion pressures were consistent with calculated rates based on diffusion coeficients measured at atmospheric conditions, provided that the system was clean and that there was no precipitation of asphaltenes. Asphaltenes were observed to form a highly resistive layer at the oil/water interface, which greatly reduced the mass transfer rate. Thus. uncertainty remains concerning the magnitude of diffusion coefficients at reservoir conditions and the relationship that these coefficients have to the corresponding measurements at atmospheric conditions. That relationship is important because diffusion coefficients at reservoir conditions are difficult to measure, and in contrast to the paucity of experimental data available for such conditions, a large body of data measured at atmospheric pressure exists for systems of interest to reservoir engineers. The purpose of this paper is to report measurements of diffusion coefficients for CO2 in hydrocarbons and water at reservoir conditions, and to establish their relationship to reported measurements of diffusivity at atmospheric conditions. The diffusivities of CO, in pentane, decane, hexadecane. Maljamar crude oil, and water were measured at-5deg.C 177deg.F] and pressures up to 6(M kPa 1870 psial. The measurements were made with novel techniques based on the direct observation of the motion of an interface caused by the diffusion of CO, into hydrocarbons and/or water. SPERE P. 93