Perpustakaan Digital ITB

One of the fundamental equations in reservoir engineering is the diffusivity equation. A core limitation of this formula is the assumption of a homogenous medium, which is a condition that real reservoirs rarely satisfy. Numerical simulation can model heterogeneity at fine scales, but at a high computational cost. Upscaling offers a compromise by replacing fine-scale heterogeneity with a single upscaled permeability, yet the reliability of this approximation is poorly quantified. This paper aims to implement a statistical approach to quantify the limits of permeability upscaling in steady-state radial flow, determining under what geological conditions a proxy analytical model remains sufficiently accurate and reliable. A 1D radial reservoir model (1000 ft) was constructed with log-normally distributed permeability using a spherical variogram model with standard deviation (?) and correlation length (a). A true numerical pressure profile was then calculated for every 1 ft. A corresponding pressure profile was also calculated analytically for every N number of blocks in the model using representative block permeability values, and its error was then compared to the previous profile. Monte Carlo simulation determined that the success rate of these cases achieving a match below 1% average error reduces drastically as standard deviation increases and correlation length decreases, with up to 500 blocks required to reliably achieve a good pressure profile match. Therefore, correlation length and standard deviation serve as functional indicators of reservoir heterogeneity as their values directly affect the reliability and accuracy of permeability upscaling.