Water alternating gas (WAG) injection is a method of controlling the viscous fingering impact in a miscible flooding processes to improve the volumetric sweep efficiency. The WAG technique is a mix of two conventional techniques: gas injection to improve the microscopic displacement efficiency and water flooding to improve the sweep efficiency. Overall, WAG improves the oil recovery.
Conventional reservoir simulation is too coarse to resolve fingers accurately at field scale. This is because the fingers maybe smaller than field scale grid blocks. Instead, empirical models are used to describe the fingers and to allow simulators to predict realistic recovery.
Effective parameter models such as Todd and Longstaff (1972) are used to model the effects of viscous fingering in field scale. This model is the most commonly used among different reservoir simulators, because it requires the selection of a mixing parameter, ω, whose value includes all of the factors affecting fingering. Additionally, it incorporates a method to calculate the effective viscosity when mixing occurs between oil and gas phases.
Todd and Longstaff (1972) recommended a mixing parameter ω = 2/3 for miscible injection to match the recovery of oil from Blackwell et al.'s (1959) experiments. They recommended ω = 1/3 - 2/3 to account for field scale heterogeneities.
Blunt and Christie (1993) showed that the mixing parameter, ω, needs to be calibrated for WAG injection. They calibrated the value of the mixing parameter, ω, as a function of the fractional flow of injected water. These equations are self-consistent, modified from the effective Todd and Longstaff mobility ratio and have been precisely solved in one dimension to account for fingering in three component systems. But their work was limited to simultaneous injection of water and gas.
In this paper we examine how calibration of ω varies with finite slug size for different WAG ratios using a 1D model. The results show that as the slug size increases, the value of mixing parameter ω, decreases. The value of mixing parameter ω is computed to match the concentration and saturation profiles from 2D simulation.