Annular labyrinth seals are designed as tortuous paths that force a working fluid to expand and contract repeatedly through small clearances between high and low pressure stages of turbomachinery. The resulting expansion and recirculation reduces kinetic energy of the flow and minimizes leakage rate between regions of high and low pressure through the seal. Most current seal geometries are selected based on what has worked in the past, or by incremental improvements on existing designs. In the present research, a balance drum used in a multistage centrifugal pump was chosen as a starting point. A design of experiments (DOEs) study was performed to investigate the influence of groove scale on leakage rate across the seal for a fixed pressure differential. The computational fluid dynamics (CFD) model of the selected labyrinth seal has an upstream region leading to 20 evenly spaced semicircular grooves along a 267 mm seal length, with a clearance region of 0.305 mm. The seal geometry was specified by a set of five variables. The variables allow for variation in scale of the semicircular grooves within a pattern of five independently scaled grooves repeated four times along the seal length. The seal was constructed with a parameterized CFD model in ansys-CFX as a 5 deg sector of the full 3D seal. A noncentral composite designed experiment was performed to investigate the effects of five parameters on leakage rate in the system. This study demonstrates a practical approach for investigating the effects of various geometric factors on leakage rate for balance drum seals. The empirical ten-parameter linear regression model fitted to the results of the experimental design yields suggested groove radii that could be applied to improve performance of future seals.