Gas Migration by Diffusion in Aquifer Storage
- Vijay Bagrodia (U. of Michigan) | Donald L. Katz (U. of Michigan)
- Document ID
- Society of Petroleum Engineers
- Journal of Petroleum Technology
- Publication Date
- February 1977
- Document Type
- Journal Paper
- 121 - 122
- 1977. Society of Petroleum Engineers
- 5.1.1 Exploration, Development, Structural Geology, 2.4.3 Sand/Solids Control, 4.6 Natural Gas, 3.2.4 Acidising
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In aquifer-storage reservoirs, natural gas, primarily methane, displaces water and forms a gas phase in contact with water-saturated porous media. Normally, such waters do not contain dissolved gas initially and the question arises as to how much gas would enter the water phase by diffusion over a period of time. Then, if there is phase by diffusion over a period of time. Then, if there is a hydraulic gradient across the storage field and water moves slowly, how much gas would be carried away from beneath the storage bubble?
Pandey et al. and Chou-Chen provided experimental data on diffusion rates of gases through water-saturated porous media. Their studies give representative values porous media. Their studies give representative values for the diffusion coefficient of methane related to porosity and permeability. Typical aquifer reservoir sands porosity and permeability. Typical aquifer reservoir sands might have 100-md permeability with a lower limit of 1 md and a higher limit of 1,000 md, and with porosities ranging from 12 to 20 percent. Using these reservoir properties, the diffusion coefficients are found from properties, the diffusion coefficients are found from Chou-Chen's correlation of diffusion with permeability.
A typical aquifer-storage reservoir has a gas phase above water-filled porous sand. This sand is assumed to be homogeneous and initially saturated with water that is free of methane. The natural gas is assumed to be pure methane. Formulas were set forth for finding the relative saturation of methane in the water as compared with saturated water at a pressure of 48.3 bar (700 psia) and a temperature of 25 deg. C (77 deg. F).
By taking a molar balance across an element of water-saturated sand at y ft below the gas-water interface and by applying Fick's law with the effective diffusivity coefficient, one can compute the accumulation of methane in the element with time using Eq. 1.
C = concentration of methane in water phase phi = porosity of the sand phi = porosity of the sand De = effective diffusivity coefficient y = depth below the interface, ft t = time, years.
This second-order differential equation can be solved with the help of the initial boundary conditions; that is, initially porous sand is saturated with water, free of methane. At the gas-water interface, water in porous media is saturated with methane. Integration of Eq. 1 gives (2)
where C is the concentration of methane in saturated water at 48.3 bar (700 psia) and 25 deg. C (77 deg. F).
Eq. 2 relates the relative concentration of methane in water to depth below the interface, time, effective diffusivity coefficient, and porosity.
Solutions were made for three cases of 1,100 and 1,000 md. The results of the integration for 100-md sand of 16-percent porosity are shown in Fig. 1.
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