Modeling of Experiments on Water Vaporization for Gas Injection Using Traveling Waves
- Elizabeth Zuluaga (Chevron Corp.) | Larry W. Lake (U. of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2008
- Document Type
- Journal Paper
- 248 - 256
- 2008. Society of Petroleum Engineers
- 5.3.2 Multiphase Flow, 1.8 Formation Damage, 4.3.4 Scale, 4.1.2 Separation and Treating, 3.3.6 Integrated Modeling, 5.4.6 Thermal Methods, 5.2.2 Fluid Modeling, Equations of State, 4.6 Natural Gas, 5.8.8 Gas-condensate reservoirs, 5.5 Reservoir Simulation, 4.1.5 Processing Equipment, 1.6.9 Coring, Fishing, 5.5.8 History Matching, 5.3.1 Flow in Porous Media, 5.4.2 Gas Injection Methods
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Dry gas injected into wells will vaporize water from near the wellbore. The vaporization starts from the well and proceeds outward. Gas flowing to producers is in equilibrium with the reservoir brine, but water will be vaporized because the pressure drop that occurs toward the wellbore increases the ability of the gas to contain water. Thus, there are different mechanisms for injection and production.
For both gas injection and gas production, vaporization concentrates solids in the brine that will precipitate into the formation when sufficiently concentrated. This paper reports on a combined experimental and theoretical analysis on the vaporization portion of this problem for dry gas injection.
Experiments have been performed previously to determine the rate of water vaporization from Berea core samples at uniform initial water saturation (Zuluaga and Monsalve 2003). These experiments were performed by injecting dry methane into core samples that contained immobile water to represent water vaporization in a gas injector.
Effluent water concentration curves showed two vaporization periods: a constant rate period and a falling rate period. The existence of a constant rate period means that the mass transfer within the core is occurring at conditions of local equilibrium. We interpret the falling rate period as the result of a moving capillary transition zone in which the amount of water vaporized decreases slowly because of capillary pressure effects. The falling rate period is the consequence of capillary imbibition of a wetting phase at very small saturation.
We interpret the vaporization results with two traveling wave solutions. The first, which can be solved analytically, assumes that the capillary diffusion coefficient, D, and the volume fraction of water in the gaseous phase, Cwg , are constant. For this case, the results of the traveling wave solution are matched to the results of laboratory experiments by adjusting D. The second traveling-wave solution must be solved through numerical integration. In this case, the relative permeability scaling exponent is adjusted to match the laboratory experiments. The fitting provides insights into the nature of wetting phase flow at small saturation. Lastly, the experimental and mathematical procedure discussed in this paper is certainly a new method to obtain relative permeability exponents for the wetting phase at very low values of wetting-phase saturation (down to theoretically zero values).
Dodson and Standing (1944) performed the first experimental study to determine the amount of water vaporized at different pressures and temperatures using PVT cells. They found that the rate of water vaporization increases with temperature and decreases with pressure and solids content in the water.
Bette and Heinemann (1989) confirmed vaporization in cores taken from gas injectors in the Arun field. The water content in these cores was very small; in some cases the cores were completely dry.
Kamath and Laroche (2000) and Mahadevan and Sharma (2005) performed experiments in permeable media that were initially fully saturated with brine. When gas was used as a displacing fluid, there were two flow regimes: a displacement regimen followed by a vaporization regimen. Using gas as both a displacing agent and a drying agent makes the study of the vaporization alone difficult.
Zuluaga and Monsalve (2003) performed vaporization experiments in permeable media at outlet pressures ranging from 1,000 to 2,000 psig and temperatures from 194 to 212°F. The experiments were not displacements, the initial water saturation being set as a nonflowing saturation by a porous plate method.
Fig. 1 shows the rate of water production for an experiment performed at 1,500 psig outlet pressure and 194°F. The experiments were perfomed by measuring the accumulated mass of water as it exited the medium and as it was sorbed on a silica substrate. The rate shown in Fig. 1 was obtained by differentiating the cumulative data with respect to time. Two vaporization periods occur: a constant rate period and a falling rate period. These two periods of water vaporization have been extensively reported for drying of solids (ceramic, wood) in the chemical engineering literature (Allerton 1949; Perry and Green 1984; Mujumdar 1987). Our goal is to understand and quantify this behavior.
There has been little modeling of water vaporization for flow through permeable media. Most approaches have been based on modifications of existing compositional simulators by incorporating water as a component in the equation of state (Bette and Heinemman 1989; Kurihara et al. 2000). The effect of salinity has been included either with salinity-dependent solubility tables (Morin and Montel 1995) or by adding salt as a component in an equation of state (Lee and Lin 1999). Some have modified material balance equations to account for water vaporization (Humphreys 1991).
This study formulates and obtains solutions to the conservational laws describing water vaporization. We study the vaporization for gas injectors as a traveling wave in which capillary imbibition occurs. The solution obtained allows predictions of remaining water saturation with distance and time during both the constant and the falling rate periods (Zuluaga 2005).
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