Application of variance-based sensitivity analysis in modeling oil well productivity and injectivity

Abstract

Well intervention performed on oil or gas well often involves the injection of different stimulating fluids or chemical solutions that aims to increase the production rate. The main objective of this paper is to identify the effect of uncertainty in different variables and parameters used to quantify well productivity and injectivity. Monte Carlo simulation technique is used to develop probabilistic models for radial Darcy's inflow on the one hand and near wellbore water-based chemical injection on the other hand. The probabilistic model is based on assigning probability density function for all variables and parameters used in the governing formulas. Variance-based sensitivity analysis (VBSA) was performed to quantify the contribution and the correlation between different model's inputs and outputs. Results indicate that some rough assumptions for about 60% of injectivity model's parameters and factors, i.e., value with considerable error/uncertainty, can still result in output with small standard deviation in comparison with other parameters. In Darcy's law, the uncertainty in reservoir pressure value affects the calculated flow rate two times higher than the effect of the formation of permeability or produced fluid viscosity. At low drawdown condition, about 50% of Darcy's flow variance is caused by the uncertainty in reservoir pressure input value. Throughout VBSA, it is also found that data accuracy of variables and parameters used in the injectivity model is not of importance as for formation permeability, injected fluid viscosity, pressure, and temperature of the injected fluid. Application of this methodology will focus on the cost of information needed by the decision makers and will save a lot of efforts and resources needed to apply confirmation tests or to validate different data sets.

Kriging-Based Design for Robust High-Performance Control Systems

“…In what follows, a Kriging surrogate modelbased design procedure is presented to identify uncertain variables that provoke high variability in the system performance in order to improve the robustness of an HPCS. Note that other established techniques to perform sensitivity analysis of engineered systems exist in literature (Saltelli 2002), including Bayesian (Capellari et al 2016), polynomial chaos-expansion (Sudret 2008;Blatman and Sudret 2010), and Monte Carlo (Zio and Pedroni 2012; Ahmed et al 2019) approaches. In this study, the surrogate model-based procedure presented in (Micheli et al 2020b) has been selected to build on findings that Kriging was a computationally fast, accurate and promising tool enabling the robust design of HPCS under uncertainty.…”