Modeling of viscous instabilities and channeling requires models at centimeter or millimeter scale establishes a need for an upscaling scheme that could predict production with as few parameters possible. We develop such an analytical model of volumetric sweep that aims to decouple heterogeneity from the mobility ratios for tertiary miscible displacements. The developed analytical model is solved by applying method of characteristics. The application is to provide quick estimates of oil recovery of displacements, as well as to provide scale up information for larger simulations. The original Koval work also provides a means of estimating oil recovery for miscible floods but it works if a single front displacement is assumed. This could be a limitation for tertiary floods where an oil bank forms and displacement has two fronts (Figure 1). This work also accounts for the interactions between these two fronts as they move in the reservoir, unlike previous work (Mollaei, 2011). This work could further be extended to tertiary polymer and ASP floods where similar oil bank forms at pixel scale for prediction of oil recovery.
For fields with large heterogeneity, which have severe channeling, the oil cut is small, the production history takes a long time to complete, and ultimate recovery is reached very slowly. Two-front, gravity-free, displacements can be modeled using the new model based on Koval's theory. This model captures the aspects such as oil cut reaching a peak and then falling off with very high ultimate recovery times for tertiary miscible floods.
Current techniques for upscaling displacement rely on empirical models. The parameters on which these empirical methods depend cannot be easily correlated to the parameters (heterogeneity, mobility ratio and dispersivity) that govern flow at the fine scale. This technique provides a way to predict performance without the use of computationally expensive fine scale simulation models.