Boltzmann transformation of radial two‑phase black oil model for tight oil reservoirs
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Date
2022-07
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Springer
Abstract
unconventional reservoirs is described by peculiar complexities such as the typical low permeability to viscosity ratio and
the dissolution of some gases in the oil phase. Reservoir simulations that consider these complexities negligible stand the
potential of poorly characterizing the reservoir flow dynamics. The adoption of similarity transformation effectively reduces
the complexities associated with the flow equations through spatial variable (r) and temporal variable (t). The Boltzmann
variable =r√t is introduced to facilitate the reformulation of transient two-phase flow phenomenon in a radial geometry.
The technique converts the two-phase Black oil model (thus highly nonlinear partial differential equations (PDEs)) to ordinary
differential equations (ODEs). The resulting ODEs present a reduced form on the flow model which is solved by finite difference
approximations (the Implicit-Pressure-Explicit-Saturation (IMPES)) scheme. No loss of vital flow characteristics
was observed between the Black oil model and the similarity transform flow model. Furthermore, the similarity approach
facilitated the determination of pressure and saturation equations as unique functions of the Boltzmann variable. This derivation
is applied to an infinitely acting reservoir where the Boltzmann variable tends to infinity ( → ∞ ). Finally, this case
study’s analytical solution formulated critical relations for fluid flow rate and cumulative production, which are useful for
single-phase flow analysis.
Description
This article is published by Springer 2022 and is also available at https://doi.org/10.1007/s13202-022-01528-8
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Citation
Journal of Petroleum Exploration and Production Technology (2022) 12:3409–3424