Modeling and validation of pressure propagation in drilling fluids pumped into a closed well

This study presents a mathematical model to simulate the pressure propagation that takes place when a drilling fluid is pressurized within a closed pipe-annular geometry. The model assumes that fluid motion is one-dimensional and weakly compressible and the system is considered isothermal. The model comprises the continuity and momentum balance equations, which are iteratively solved by the method of characteristics. The proposed model can be applied to both Newtonian and Bingham fluids. The viscous effect is considered in the model using the friction factor approach. Pressure values obtained from the model are compared to experimental data from Oliveira et al. (2012b) for a Newtonian (water) and two drilling fluids. Not only the magnitudes but also the oscillation frequencies of the measured and computed values show a qualitatively fair agreement for both kinds of fluid. Both measured and computed values show that pressure is not fully transmitted in drilling fluids. Three dimensionless numbers are identified as the model governing parameters. A model sensitivity analysis shows that pressure propagation can be enhanced by combining the governing parameters.