Boltzmann transformation of radial two-phase black oil model for tight oil reservoirs

Abstract Tight oil accumulates in impermeable reservoir rocks, often shale or tight sandstones. The flow behaviour of unconventional reservoirs is described by peculiar complexities such as the typical low permeability to viscosity ratio and dissolution some gases phase. Reservoir simulations that consider these negligible stand potential poorly characterizing dynamics. adoption similarity transformation effectively reduces associated with equations through spatial variable ( r ) temporal t ). Boltzmann $$\left(\xi =\dfrac{r}{\sqrt{t}}\right)$$ ξ = r t introduced facilitate reformulation transient two-phase phenomenon a radial geometry. technique converts Black model (thus highly nonlinear partial differential (PDEs)) ordinary (ODEs). resulting ODEs present reduced form on which solved finite difference approximations (the Implicit-Pressure-Explicit-Saturation (IMPES)) scheme. No loss vital characteristics was observed between transform model. Furthermore, approach facilitated determination pressure saturation unique functions variable. This derivation applied an infinitely acting where tends infinity $$\xi \rightarrow \infty$$ → ∞ Finally, this case study’s analytical solution formulated critical relations for fluid rate cumulative production, are useful single-phase analysis.