Mathematical Model for Leakage-Free Tightness Tests with Power-Law Fluids in Long Lines

Tightness tests that check for system leakage consist of pressurizing a closed-end line to a specified value, shutting off the pump, and monitoring pressure over time. The current work presents a dimensionless mathematical model for simulating a leakage-free tightness test in long pipes operating with drilling fluids, such as choke and kill lines. The problem is considered to be isothermal and weakly compressible. The model comprises the one-dimension mass and momentum equations for transient flows, and the drilling fluid is modeled as a power law fluid. A dimensionless scale based on uniform pressurization time was proposed, and three governing dimensionless parameters were identified to affect the problem: the Joukowski-to-target pressure ratio, a dissipative parameter (the Joukowski pressure-to-viscous stress ratio), and the power law index. The three parameters directly influence the pressurization time, the stabilized pressure, and the pressure stabilization time. Two correlations to predict the maximum pressure drop after the pump shutdown were proposed, and the differences between the correlations and simulation values lie within 10% and 3%, respectively.