Jun Xu (Doctor of Philosophy in Petroleum Engineering)
A Comprehensive Model for Combined Rod and Fluid Dynamics in Vertical and Deviated Rod-Pumped Wells
(154 pp. Chapter VII)
Directed by Dr. Zelimir Schmidt and Dr. Dale Doty
(354 words)
This study presents the modeling of a sucker rod pumping system in a vertical and deviated well. It focuses on the derivations and numerical solutions of a new set of comprehensive models, which incorporate rod motion and fluid flow through the annulus between the rod and tubing. Also included is model validation against the updated dynamometer database.
It is emphasized that previous efforts on the dynamics of the sucker rod pumping well system have been either limited to the vertical well assumption, or do not consider the dynamics and properties of the fluid in the pumped well. Turbulent viscous friction and Coulomb friction have been ignored in previous studies. The new comprehensive model allows appropriate consideration of the viscous friction between rod/coupling and fluid, both in laminar and turbulent flow, rod to tubing drag (Coulomb friction), and the effect of well deviation on the sucker rod pumping system.
The mathematical model for a deviated well is developed using the principles of virtual work. A set of partial differential equations, and their associate boundary conditions, have been derived to describe the dynamic performance of the system, including all the available components and most inflow conditions in the downhole. Because we are only concerned about the rod performance in the longitudinal direction, a
set of coupled governing equations has been segregated into separated ones simply by ignoring the lateral deformation. The effect of lateral deformation on the longitudinal dynamics is evaluated by introducing effective longitudinal stiffness, and by the Garlakin method. In the deviated model, not only viscous friction, but also the Coulomb friction and well deviation are included. The viscous friction factor, for flow in the annulus with moving rod, is developed by the computational fluid dynamics and is correlated into equations, using the curve fitting method for practical purposes. An explicit formulationof the Coulomb friction is derived, after simplifying the lateral equations. The model equations are solved by the numerical method and verified against many actual measurements from an up-to-date database. This dissertation gives numerous examples to demonstrate the applications of the new technique for the design, prediction and optimization of the sucker rod pumped wells.
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