Global upscaling of secondary and tertiary displacements
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Fluids injected during secondary and tertiary floods often leave parts of the reservoir unswept mostly because of large heterogeneity and mobility ratio. Several applications require an analytical scheme that could predict production with as few parameters possible. We develop such an analytical model of volumetric sweep that aims to apply an extension of Koval’s theory where flow is assumed to be segregated under vertical equilibrium conditions for secondary and tertiary displacements. The unified theory for vertical equilibrium (viscous and dispersive) is also derived as a precursor to model development. The original Koval factor is applicable for upscaling secondary miscible floods. The new analytical model for secondary and tertiary floods is applied to provide quick estimates of oil recovery of miscible as well as immiscible displacements, which is then calibrated against field data. The model parameters, Koval factor, sweep efficiency and pore volume, estimated after history matching could be used to make reservoir management decisions. The model is very simple; history matching can be done in a spreadsheet. Single-front, gravity-free, displacements can be modeled using Koval factors. Two-front, gravity-free, displacements can also be modeled using Koval-type factors for both the fronts. These Koval-type factors, coupled with laboratory scale relative permeabilities, allows for scaling the displacement to a larger reservoir system. The new method incorporates by-passed pore volume as a parameter, a difference between this work and that of Molleai, along with Koval factors and local front velocities. For two front displacements, it also accounts for the interaction between the fronts which honors correct mass conservation, another difference with the work of Molleai. The results from new models for secondary and tertiary displacements were verified by comparing them against numerical simulations. The application was also demonstrated on actual field examples. Current techniques for reservoir surveillance rely on numerical models. The parameters on which these numerical models depend on are very large in number, introducing large uncertainty. This technique provides a way to predict performance without the use of computationally expensive fine scale simulation models, which could be used for reservoir management while reducing the uncertainty.