Prediction of Turbulent Friction in Rod-Pumped Wells
- Jun Xu (U. of Tulsa) | S.A. Shirazi (U. of Tulsa) | D.R. Doty (U. of Tulsa) | M.G. Prado (U. of Tulsa) | R.N. Blais (U. of Tulsa)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2000
- Document Type
- Journal Paper
- 182 - 189
- 2000. Society of Petroleum Engineers
- 2.4.3 Sand/Solids Control, 4.1.2 Separation and Treating, 3.1.1 Beam and related pumping techniques, 4.2.3 Materials and Corrosion, 3.1.2 Electric Submersible Pumps, 4.11.1 Corrosion Research, 3.1 Artificial Lift Systems, 5.3.2 Multiphase Flow, 4.1.5 Processing Equipment
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Frictional forces acting on a rod caused by a rod reciprocating in flowing fluid significantly affect the prediction and diagnosis of rod pumping system performance. Available studies of the flow in the tubing combined with moving rods and couplings are limited to laminar flow. The flow is more likely to be turbulent, however, for liquids with low viscosity and for regions near the rod couplings. Therefore in the current study, turbulent flow in the annular region between the stationary tubing wall and the moving rod/coupling is considered.
Computational fluid dynamics (CFD) is used to simulate turbulent flow in the annular region with moving rods and couplings. Also, a simplified model using a mixing-length method is developed that is more computationally efficient than the CFD code. The CFD code that uses the standard k-? model is used to predict turbulent friction factors in the annulus with the moving rods and couplings. The simplified model is developed to predict turbulent friction factors in the annulus with the moving rods. The results from these models are compared with each other and to the available data published. The friction factors between the rod/coupling and fluid can be represented by four parameters: the rod to tubing radius ratio, the coupling to tubing radius ratio, the fluid Reynolds number, and the relative rod velocity.
Rod pumping systems have historically been among the most popular and effective methods of artificial lift for oil reservoirs. Since the late 1950's, a substantial effort has been made to develop dynamic mathematical models that can be used to predict the performance of rod pumping systems.1,2 Previous efforts,1,2 however, have been limited to the dynamics of the rod and fluid. The dynamics of the flow have either been limited to laminar flow, or have been determined strictly by guesswork. Byrd and Hale3 made a related study of the rod coupling piston effect on the load of a rod pumped well. Lea4 solved the viscous-flow equation of motion in the pump-plunger/barrel, rod/tubing, and coupling/tubing annuli, and calculated the pressure and shear-stress distribution on a rod pumping system. However, turbulent viscous friction and Coulomb friction were ignored in all previous studies.
Under certain pumping conditions and for low viscosity fluids, the flow in the annulus between the tubing and the rod can be turbulent (especially for those portions of the pumping cycle where the rod velocity is the largest). Also, the couplings distributed along the rod string can readily induce turbulence. Experimental evidence and theoretical analysis both show that the turbulent viscous friction associated with the rods and couplings can be several times higher than laminar friction.5 Thus, there is a need for models to account for turbulent friction in the design and simulation of a sucker rod pumping system.
In the present work, CFD is used to analyze turbulent flow in the annulus between the tubing and the rod. The method is used to predict friction factors for the rod, tubing, and coupling. In addition, a simplified model is developed that can be used to predict the friction factors for the rod and the tubing.
A schematic diagram of the annular region between the stationary tubing and the moving rod and couplings is illustrated in Fig. 1. The rod and couplings travel either upward or downward, while fluid flows primarily upward. Therefore, the flow in the annulus can be complicated and transient in nature. The CFD model, described below, is general and can be used to predict the transient hydrodynamic behavior of the flow field. However, the computation can be very time consuming with the current capabilities of available computers. Therefore, a few simplifying assumptions are used to develop an efficient solution method to analyze the flow. For example, the flow is assumed to be either moving upward or downward at a constant speed. This assumption simplifies the CFD method considerably, allowing a simplified model to be developed.
The CFD method is used to validate the proposed simplified model. The CFD method is also used to evaluate rod coupling effects for cases with complicated geometry where the analytical method would be extremely hard to implement. Because experimental data related to this problem are limited and available only for such special cases, for example, stationary rods, the use of CFD tools can provide reliable analysis at a much lower cost.
Both the comprehensive CFD and the simplified methods are described below.
Comprehensive CFD Method.
A commercially available CFD code called CFX™ is used in the present study. The CFD code solves the governing flow equations in a specified domain. The flow in the annulus is turbulent, so a turbulent flow model is required to predict the flow field. There are several turbulence models available in CFX,6 including the standard k-? model, the low-Reynolds-number k -? model, the RNG k-? model, and the Reynolds stress model. In the present work the so-called standard k-? model and a low-Reynolds-number version of the k-? model are used to solve for the turbulent or eddy viscosity. The standard k-? turbulent model, which uses turbulent kinetic energy k and its dissipation rate ?, is relatively efficient and has been used to solve many engineering problems with complex geometries. Both k-? turbulence models can be used to predict turbulent flow within the annular region around the complex geometry of the moving rods and couplings. The low-Reynolds-number k-? turbulence model requires more grid points and is computationally much less efficient than the so-called standard k-? turbulence model. Therefore, the low-Reynolds-number model is used in this study only to check the accuracy of the standard k-? model results.
The CFD code can generate numerical solutions for a vast variety of fluid flow problems. Care should be taken in using the CFD code to insure good numerical convergence and grid-independent solutions. Effective simulating criteria were obtained by comparing simulation predictions against a substantial body of experimental data gathered from the existing literature for such similar flows as pipe flow and annular flow with both stationary walls, and from trial and error.7
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