Liquid Inventory and Conditional Persistence of Finite Slugs Through Smooth Wellbore Inclination Transitions: A Mass-Conservative Reduced-Order Analysis

The evolution of a finite liquid slug through a changing wellbore inclination depends on both liquid exchange and the distribution of liquid within the slug. A mass-conservative specified-exchange reduced-order model is developed to distinguish these effects during a smooth transition from horizontal flow to a 2° upward inclination. Front pickup responds to the prescribed local inclination stimulus, whereas rear shedding follows a finite spatial adaptation law. An analytical inventory solution is derived and used to evaluate 24 controlled cases spanning three transition lengths, four incident slug lengths, and two exchange closures. For an incident length of eight diameters, Closure A produces downstream lengths of 10.344–12.674 diameters. Under Closure B, the corresponding lengths decrease from 4.309 diameters to complete inventory depletion. The conditional incident-length boundaries are 3.598, 5.948, and 10.826 diameters at a station 100 diameters beyond the transition. Conservative sectional-holdup reconstructions and independent numerical integration check the liquid balance and analytical solution. The analysis quantifies how exchange adaptation, observation distance and holdup variation shape liquid inventory and occupied length. Closure-space, center-speed and display-resolution tests further quantify the sensitivity of the predictions to the selected model assumptions. The parameter sets are illustrative and have not been physically calibrated or independently validated; the reported boundaries describe inventory depletion under the specified closures.