Summary In immiscible three-phase flow, the lead oil bank can split into two, a Buckley-Leverett shock wave followed by a new type of shock wave. Such a nonclassical "transitional" shock wave is common in three-phase flow. Its sensitivity to diffusion implies that capillary pressure must be modeled correctly to calculate the flow. In particular, transitional shock waves arise in water-alternating-gas (WAG) flow. They can be calculated by semi-analytic methods, which are helpful in the design of effective WAG recovery strategies.
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Marchesin et al. (2001) studied this question.
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