Simplified and 3D models have been studied to predict the performance of progressing cavity pumps (PCPs). Simplified models were mainly made for metallic stator PCP performance. Their purpose was to represent the relationship between pump flow rate and differential pressure. Previous studies proposed to solve the system of mass conservation equations. In these studies, the geometry of the gap area was not clearly represented by neglecting the curvatures of stator and rotor. In addition, only frictional loss was considered, but local loss by gradual contraction or expansion of the gap area was not considered.
In this study, we present a new analytical approach considering curvature and local loss. The depth of the gap area and local loss could be calculated analytically by a middle streamline and a curvature. On the basis of periodicity of distribution of cavities, simplified calculation for a slippage was possible without a system of mass conservation equations. Therefore, this model represents clearer geometry and a more simplified approach. The results show that this model shortens the calculating time and facilitates programing; in addition, the model validation is good in matching with experimental data.