The issues of leakage with respect to the clearance between the pump plunger outer diameter and the pump barrel inner diameter and other operation conditions have been revisited in this paper. Both Poiseuille flow rate due to the pressure difference and Couette flow rate due to the plunger motion have been considered. The purpose of this study is to better understand the nature of the leakage with respect to pressure difference, eccentricity, and motion related to the plunger of typical sucker rod pump systems. More specifically, based on the newly derived relaxation time scales for transient solutions of the governing Navier–Stokes equations, the quasi-static nature of relevant measurement techniques is confirmed for the current production systems. This key observation is also demonstrated with a computational model using the experimentally measured pressure difference and the plunger movement.

The issues of leakage with respect to the clearance between the pump plunger outer surface and the pump barrel inner surface and other operational conditions have been revisited in this paper. Both Poiseuille flow rate due to the pressure difference and Couette flow rate due to the plunger motion have been considered. The purpose of this study is to explore the possibility of representing the entire downhole pump system with a simple viscoelastic model. We have explored both Kelvin and Maxwell viscoelastic models along with the dynamic behaviors of a mass point attached to the viscoelastic model. By using the time-dependent polished rod force measured with a dynamometer as the input to the viscoelastic models, we have obtained the displacement responses, which match closely with the actual measurements in experiments and operations. Further study and experiments have been planned and partially implemented in the McCoy School of Engineering at Midwestern State University, a member of the Texas Tech University System.

In this paper, the entire downhole fluid-sucker rod-pump system is replaced with a viscoelastic vibration model, namely a third-order differential equation with an inhomogeneous forcing term. Both Kelvin’s and Maxwell’s viscoelastic models can be implemented along with the dynamic behaviors of a mass point attached to the viscoelastic model. By employing the time-dependent polished rod force measured with a dynamometer as the input to the viscoelastic dynamic model, we have obtained the displacement responses, which match closely with the experimental measurements in actual operations, through an iterative process. The key discovery of this work is the feasibility of the so-called inverse optimization procedure, which can be utilized to identify the equivalent scaling factor and viscoelastic system parameters. The proposed Newton–Raphson iterative method, with some terms in the Jacobian matrix expressed with averaged rates of changes based on perturbations of up to two independent parameters, provides a feasible tool for optimization issues related to complex engineering problems with mere information of input and output data from either experiments or comprehensive simulations. The same inverse optimization procedure is also implemented to model the entire fluid delivery system of a very viscous non-Newtonian polymer modeled as a first-order ordinary differential equation (ODE) system similar to the transient entrance developing flow. The convergent parameter reproduces transient solutions that match very well with those from fully fledged computational fluid dynamics models with the required inlet volume flow rate and outlet pressure conditions.

In this paper, the entire downhole fluid sucker rod pump system is replaced with a viscoelastic vibration model, namely a third-order differential equation with an inhomogeneous forcing term. Both Kelvin and Maxwell viscoelastic models can be implemented along with the dynamic behaviors of a mass point attached to the viscoelastic model. By employing the time-dependent polished rod force measured with a dynamometer as the input to the viscoelastic dynamic model, we have obtained the displacement responses, which match closely with the experimental measurements in actual operations, through an iterative process. The key discovery of this work is the feasibility of the so-called inverse optimization procedure which can be utilized to identify the equivalent scaling factor and viscoelastic system parameters. The proposed Newton-Raphson iterative method with some terms in the Jacobian matrix expressed with averaged rates of changes based on perturbations of up to two independent parameters provides a feasible tool for optimization issues related to complex engineering problems with mere information of input and output data from either experiments or comprehensive simulations. The same inverse optimization procedure is also implemented to model the entire fluid delivery system of a very viscous non-Newtonian polymer modeled as a first-order ordinary differential system similar to the transient entrance developing flow. The convergent parameter reproduces transient solutions which match very well with those from full-fledged computational fluid dynamics models with the required inlet volume flow rate and the outlet pressure conditions.