Calibrating the Todd and Longstaff’s mixing parameter value for miscible finite sized slug WAG injection for application and optimisation on a field scale
Al-Haboobi, Zainab Imad Murtadha
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Water alternating gas (WAG) injection is a method of controlling the viscous fingering impact in a miscible gas injection to improve the volumetric sweep efficiency and to improve the oil recovery. Conventional reservoir simulation such as performed by a black oil simulator is too coarse to resolve the viscous fingering accurately at field scale. This is because the fingers are smaller than field scale grid blocks. Instead, empirical models are used to describe the fingers and to allow simulators to predict reliable recovery. Todd and Longstaff (1972) model is the most commonly used among different black oil reservoir simulators to model the effects of viscous fingering on a field scale. The reason for that is it requires the selection of a single parameter, namely the mixing parameter, w, the value of which 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 choice for the w value of ⅔ for secondary miscible gas injection to match the recovery of oil from Blackwell et al.'s (1959) experiments. They recommended w = ⅓ for field scale simulation to account for heterogeneities. Blunt and Christie (1993) showed that the mixing parameter needs to be calibrated for simultaneous water and gas (SWAG) injection. They calibrated the value of w as a function of the fractional flow of water injected and showed that the value has to be increase to 1 when modelling secondary SWAG injection and to 0.92 when modelling tertiary SWAG injection, however their work did not take into account the effect of miscible finite-sized slug WAG (FSS WAG) injection. The work in this thesis extends the work of Blunt and Christie (1993) to calibrate the value of w taking into account the WAG ratio and slug size in miscible FSS WAG injection for both secondary and tertiary recovery. The value of is iteratively determined for a set of WAG ratios, slug sizes, and types of recovery.