Calibrating the Todd and Longstaff Mixing Parameter Value for Miscible Finite-Sized Slug WAG Injection for Application on a Field Scale

The Todd and Langstaff (1972) mixing parameter (omega) is the most commonly used parameter in black oil reservoir simulators for modeling the effects of viscous fingering on a field scale, as their model is a useful alternative to compositional simulations. Todd and Longstaff (1972) recommended a choice for the value of omega to be 2/3 for secondary miscible gas injection to match the recovery of oil from Blackwell et al. (1959) experiments and omega to be 1/3 for secondary miscible gas injection on a field scale to account for field-scale heterogeneities. Blunt and Christie (1993) extended the model and showed that omega needs to be calibrated for simultaneous water alternating gas (SWAG) injection. They showed that the mixing parameter should be increased to 1 when modeling secondary miscible SWAG injection, and to 0.92 when modeling tertiary miscible SWAG injection. This work is a modification of Blunt and Christie's (1993) work to calibrate the value of omega for miscible finite-sized slug water alternating gas (FSS WAG) injection. In this paper we focus on the impact of WAG ratio, slug size, and type of recovery on the calibration of Todd and Longstaff's (1972) mixing parameter to highlight the importance of taking this parameter into account when simulating miscible FSS WAG injection using a black oil simulator. The value of omega was computed by matching the solvent concentration and the water saturation profiles from the 1D model against the 2D simulation. The results show that as the slug size increases, the value of omega decreases at different WAG ratios for both secondary and tertiary recovery. The application of the calibrated value of omega on a field scale showed that the value of omega had an impact on the oil recovery and on the total gas and water production, highlighting the importance of an appropriate mixing parameter selection.