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Fluid flow in PCP systems
In a PCP system, produced fluid flows from the pump to surface through the annular area between the rod string and tubing. High fluid viscosities, elevated flow rates, or restricted flow paths can result in large shear stresses developing in the fluid, which cause large frictional forces to act on the rod string. These effects can have the following implications on system loading:
- Fluid shear stresses produce flow losses along the tubing and across couplings, centralizers, and rod guides that contribute to increased pump pressure loading.
- Rotational frictional forces acting on the surfaces of the sucker rods, couplings, centralizers, and rod guides produce resistive rod string torque.
- Axial frictional forces acting on the rod-string body, couplings, centralizers, and rod guides and flow losses across couplings, centralizers, and rod guides produce upward forces that reduce rod-string tension.
Fluid-flow effects can range from having a minor to a dominant influence on PCP system design. This is illustrated in Fig. 1, which shows pressure losses for a range of flow rates and viscosities through a 100 m [328 ft] length of 76 mm [3.0 in.] Inside diameter (ID) tubing (typical of 89 mm [3.5 in.] tubing) without sucker rods present. Note that the pressure-drop values range from nearly zero to values that exceed the corresponding hydrostatic pressure. The change in slope in the curve of pressure loss vs. viscosity is a result of the transition from laminar to turbulent flow.
Unfortunately, depending on conditions, accurately quantifying fluid-flow effects can be extremely challenging. Difficulties arise when the calculations involve:
- Non-Newtonian fluid behavior
- Multiphase flow
- Complicated flow patterns around couplings and rod guides
Designers typically resort to an appropriate computer model to perform these calculations. It is beyond the scope of this chapter to describe in detail the methods or formulations typically used to quantify the fluid-flow parameters (e.g., pressure-loss profile along tubing, fluid-column density profile) used in the design of a PCP system. However, the following sections briefly overview the general approach used and outline some special considerations required in these assessments.
Single phase flow
When single-phase flow effects are assessed, the first step is to establish the type of flow regime. Normally, single-phase flow conditions can be classified as either:
- Laminar - smooth and steady and governed primarily by viscous forces (viscosity, velocity).
- Turbulent - fluctuating and agitated and depends mostly on inertial forces (density, velocity).
The type of flow regime is determined by calculating the Reynolds number for the flow conditions in question. Usually, the transition Reynolds number for annular pipe flow is assumed to be 2,100 for Newtonian fluids. Flow conditions with Reynolds numbers < 2,100 are considered laminar; conditions that have numbers > 2,100 are considered turbulent. The Reynolds number decreases as fluid viscosity increases or flow rate decreases. Thus, flow tends to be laminar in most heavy-oil applications.
Once the flow regime has been determined, appropriate annular pipe flow equations are used to evaluate the flow (pressure) losses within a surface-driven PCP system. These equations take into consideration:
- Fluid properties
- Flow rate
- Respective rod-string and tubing dimensions
In the case of standard rod strings, the reduced annular space associated with couplings, centralizers, and rod guides can lead to significant additional pressure losses, which should also be taken into consideration. In addition, the common flow-loss equations are typically based on a Newtonian fluid model in which the applied shear stress is proportional to the shear strain rate and the viscosity is the constant of proportionality (shear stress = viscosity × shear rate). However, most high-viscosity petroleum fluids (> 100 cp [100 mPa•s]) tend to be non-Newtonian, exhibiting pseudoplastic (shear thinning) behavior, which implies that the fluid effective viscosity decreases with increasing shear rate. Fluid viscosities typically are strongly influenced by temperature and variations in fluid composition (water cut, solution gas content). Therefore, it is very important to obtain representative fluid-property information for the application in question and to pay attention to the temperature and shear rates associated with fluid viscosity tests.
Most annular flow correlations assume that the flow is through two concentric pipes. In a rod-string and tubing system, however, wellbore curvature and gravity will position the rod string against one side of the tubing in most situations. As a result, the flow pattern that develops may deviate from the concentric case. The effect of offsetting the rod string is to create a larger, unrestricted area for flow, thus reducing the magnitude of the fluid shear rates and pressure losses. The magnitude of this reduction depends on the amount that the rod string is offset from center (i.e., eccentricity) and the relative diameters of the tubing, rods, and couplings. Conservative reductions for laminar flow are 40% for coupling, centralizer, and rod-guide losses and 25% for rod-body losses. For turbulent flow, reductions of 10% for coupling, centralizer, and rod-guide losses and 5% for rod-body losses are reasonable.
The significance that flow losses have on system design depends on the application. In many instances, such as wells producing light oil or high-water-cut fluids at moderate rates, the flow losses are generally small, so they often are neglected in system design. However, in wells producing high-viscosity fluids, excessive flow losses may occur with certain rod-string and tubing combinations (i.e., large rods in small-diameter tubing). In such cases, flow losses are an extremely important consideration in system design that must be addressed through appropriate sizing of the rod-string and tubing components. For example, consider flow of a 2,500 cp [2500 mPa•s] fluid through a 760 m [2,493 ft] length of tubing with 25.4 mm [1 in.] rods and slimhole standard couplings. The corresponding flow losses are shown as a function of flow rate in Fig. 2 for 73 mm [2.875 in.] tubing (Case 1) and 88.9 mm [3.5 in.] tubing (Case 2). These flow losses have been “corrected” to account for non-concentric flow. The results show that excessive flow losses would render it impractical to use 73 mm [2.875 in.] tubing unless operating at very low flow rates (i.e., < 20 m 3 /d [126 B/D]). In contrast, use of 88.9 mm [3.5 in.] tubing leads to much lower flow losses because of the increased flow area. Fig. 2 also illustrates the effect that flow restrictions have on the magnitude of flow losses. With the 73 mm [2.875 in.] tubing, flow losses associated with the couplings comprised approximately 25% of the total losses even though the coupling flow length was a very small portion of the total rod length (10 of 760 m [33.3 of 2,493 ft]).
Multiphase flow can be defined as the simultaneous flow of two or more phases of fluid, normally liquid and gas. In an oil well producing gas-saturated liquids, when the pressure drops below the bubblepoint, gas will evolve, resulting in multiphase gas/liquid flow. As this gas/liquid mixture flows through the production system, the two phases may commingle in a variety of flow patterns. The particular pattern or “flow regime” that occurs has a significant effect on multiphase-flow behavior and pressure loss. Flow-regime maps facilitate the determination of flow patterns from gas and liquid flow rates, fluid properties, and wellbore inclinations. Fluid properties are usually obtained from empirical correlations. Depending on the particular flow regime, different multiphase-flow algorithms are used to calculate the hydrostatic and frictional pressure gradients. The hydrostatic gradient is determined from both gas and liquid densities and takes into account the different velocities of the different phases. The frictional gradient is calculated from friction factors based on two-phase fluid properties. Fig. 3 illustrates the procedure used for multiphase-flow calculations, which generally are too complex to perform manually.
Most common empirical correlations for fluid properties have been developed for lighter oils, and they may not apply to heavier crudes. In general, caution must be exercised when these empirical correlations are extrapolated out of the range for which they were developed. In addition, correlations developed for heavy oils from a particular field can differ considerably for heavy oils of the same API gravity in another region.
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- Dodge, D.W. and Metzner, A.B. 1959. Turbulent flow of non-newtonian systems. AIChE J. 5 (2): 189–204. http://dx.doi.org/10.1002/aic.690050214.
- Haci, M. and Cartalos, U. 1996. Fluid Flow in a Skewed Annulus. Journal of Energy Resource Technology 118 (2): 89-87. http://dx.doi.org/10.1115/1.2792710.
- Brill, J.P. and Mukherjee, H. 1999. Multiphase Flow in Wells, No. 17. Richardson, Texas: Monograph Series, SPE.
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