Calculation of Water Displacement by Gas in Development of Aquifer Storage
Authors: Coats K.H. , Richardson J.G. 
Published: December 2007

Abstract
During the initial growth of a gas bubble in an aquifer storage reservoir the injected gas tends to override the water. The resulting low displacement efficiency and big rate of gas travel down-structure make it difficult to maintain water-free production. This paper illustrates the use of two-dimensional, two-phase calculations to simulate this gas-water displacement. Calculations were performed for a stratified aquifer and for several homogeneous sands differing in permeability, porosity and thickness. Results are discussed and compared with performance predictions obtained from the simpler Buckley-Leverett and Dietz formulas. This comparison indicates the necessity for the two-dimensional calculations in realistically simulating the gravity override of the water by injected gas.

Introduction
In recent years natural gas has been stored near markets in aquifers where insufficient storage capacity is available in depleted fields. Operators of these aquifer storage reservoirs have encountered technical problems relating to the gas-water displacement accompanying initial growth of these gas bubble. Injected gas tends to override the water, with a resultant low displacement efficiency and high rate of gas travel down-structure toward spill points. Low displacement efficiency makes if difficult to sustain water-free gas production. Sometimes the fingering of gas down-structure may be so pronounced that the injection rate must be severely curtailed, which excessively lengthens the time required for bubble growth. This paper is concerned with estimating - for given aquifer characteristics and fluid properties the displacement efficiency, rate of gas movement down-structure and rate of gravity drainage of water behind the gas front. Several published articles relate to simulative capability necessary to handle this problem. The Dietz formulae and Buckley-Leverett method have some applicability to the problem. Woods and Comer reported one - dimensional, radial calculations which accounted for the two-phase flow of gas and water. Most recent research directed toward understanding aquifer behavior in relation to gas storage has concentrated on single-phase flow in aquifer. Douglas, Peaceman and Rachfords presented a method for calculating multidimensional two-phase flow in reservoirs; their method has been applied in work reported by Nielsen and Tek, Blair and Peaceman and Goddin. Refs. 5 and 7 show comparisons between experimental data and calculations similar to those employed here.
One purpose of this paper is to illustrate the use of two-dimensional, two-phase flow calculations in simulating the difficult problem of water displacement by gas in a vertical cross-section. The pronounced fluid density and viscosity, differences combine with the disparity in horizontal and vertical dimensions of the cross-section to pose one of the more difficult problems in reservoir simulation. The calculations described account for capillary and gravity forces, relative permeability and reservoir heterogeneity. An example reservoir is described and calculated results are presented for a variety of injection rates and values of permeability, reservoir thickness and dip angle. A second purpose is to compare the two-dimensional calculations with results obtained from the Buckley-Leverett and Dietz formulas. For this reason most calculations were performed for a simplified example reservoir to which the latter techniques night reasonably be applied However, the computer program employed applies equally well to cases involving arbitrary spatial variations of permeability porosity, reservoir thickness and dip angle.
SPEJ
P. 105ˆ