This study presents the derivation and the numerical solution of composite models in which both the rod string and the fluid dynamics are coupled so as to accurately account for the effects of viscous friction in sucker-rod pumped wells.; A viscous damped hyperbolic first order partial differential equation is coupled to the time derivative of Hooke's law to model the rod string motion and Navier Stokes equations are used to model the fluid dynamics in the rod-tubing annulus. A set of four equations comprise the composite model from which four sub-models for different flow scenarios are considered. The equations are solved numerically by a shock capturing algorithm known as the MacCormack Explicit Scheme which is a two-step predictor-corrector scheme and is second order accuracy in time and space.; Five example problems covering various pump setting depths, fluid properties and surface pumping unit kinematics are presented to study the effects of certain important variables. From the analyses of the results of these example problems it is concluded that (1) while the effects of fluid dynamics may appear masked in shallow to medium depth sucker-rod pumped wells, they can not be ignored in deeper wells where large discrepancies occur in the prediction of system parameters, (2) the load range decreases moderately as viscosity increases and the predicted polished rod horsepower does not change significantly over the range of viscosities studied in shallow to medium depth sucker-rod pumped wells, (3) the presence of small quantities of the gas phase in the fluid column reduces system peak torque and precipitate the need for smaller counterbalance weights and (4) the influence of two-phase gas-liquid flow in the rod-tubing annulus on system design parameters declines with increasing pump setting depth. The results are compared against other design models appearing in the literature.
展开▼
