Flow in Perforated Pipes: A Comparison of Models and Experiments
- Thomas Clemo (Boise State U.)
- Document ID
- Society of Petroleum Engineers
- SPE Production & Operations
- Publication Date
- May 2006
- Document Type
- Journal Paper
- 302 - 311
- 2006. Society of Petroleum Engineers
- 1.6.6 Directional Drilling, 4.1.5 Processing Equipment, 3.3.6 Integrated Modeling, 2.2.2 Perforating, 5.5 Reservoir Simulation, 4.1.2 Separation and Treating, 1.6 Drilling Operations, 2.3 Completion Monitoring Systems/Intelligent Wells
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- 668 since 2007
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A model of pressure losses in perforated pipes that includes the influence of inflow through the pipe walls compares favorably with past and recent experimental studies. The single-phase model was developed in 1987, but it is not generally known in the petroleum industry. This model is compared to three experiments: one using air and two using water. The model must be manipulated to conform with the way individual experimenters report their findings. In general there is good agreement. Where there is poor agreement, the cause may be experimental artifacts. A second model fails to match experimental results when the pipe geometry changes significantly.
With the advent of horizontal drilling technology, flow in long perforated pipes has become an important topic. Numerous investigations (Dikken 1990; Penmatcha et al. 1997; Ouyang et al. 1998; Tang et al. 2000; Wolfstiener et al. 2000; Valvatne et al. 2001; Ouyang and Aziz 2001) have shown that pressure losses in horizontal pipes and multiwell configurations significantly influence the distribution of flow to the pipes. More flow enters the heel than the toe of the pipe. While the influence of inflow through the pipe walls has been recognized as an important effect, wellbore flow models used in these studies either ignore the influence of perforations or use a flawed representation. Recent experimental investigations (Ihara et al. 1994; Kloster 1990; Su 1996; Yuan 1997; Yuan et al. 1999) of liquid flow in perforated pipes and channels allow models of the influence of inflow on pressure losses to be tested for a variety of pipe configurations. Agreement with experiments using air flow (Olson and Eckert 1966; Yuan and Finkelstein 1956) can provide a strong indication that a model developed with water is robust.
Numerous models of pressure losses within pipes with inflow exist. The three investigated here are Ouyang (1998), Yuan et al. (1999), and Siwon (1987). Only Siwon's model compares favorably with all the experiments described in this paper. I will concentrate on the comparison with Siwon's model, with some review of the predictions using Yuan et al. The model of Ouyang does not have the correct functional dependence. It is mentioned because it seems to be the most widely used.
While Siwon's model is consistent with the experiments conducted by Olson and Eckert (1966), Su (1996), and Yuan (1997), there are some data that do not agree with Siwon's model. In this situation it is important to keep as much transparency as possible so that readers can form their own opinions. The three experiments are quite different, which provides a wide basis for comparison. Unfortunately, the presentation of these data is also quite different. To preserve the transparency of the original data, the models have been manipulated to fit the original data presentation.
There are two basic conclusions: (1) Perforations cause an increase in head gradient with and without inflow through the perforations; and (2) Inflow causes larger head gradients than would occur without inflow, but ?15% less than would be expected, assuming a constant friction factor and considering only the momentum increase induced by increasing flows.
The development starts with the momentum-balance equation—the basis for understanding pressure losses in pipes. Three derivative forms of the balance equation corresponding to different ways of presenting the experimental data are presented. Next comes the model and experiments of Siwon, followed by the model of Yuan et al. Then, three experiments are described and compared to the models.
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Altshul, A. and Kishelev, P. 1975. Hydraulics and Aerodynamics. Secondedition. USSR: Stroisdat Publishing House.
Chen, N. 1979. An ExplicitEquation For Friction Factor In Pipe. Industrial and Engineering ChemistryFundamentals 18 (3): 296-297.
Clauser, F. 1956. The Turbulent Boundary Layer. Advances in AppliedMechanics 4:1.
Dikken, B.J. 1990. PressureDrop in Horizontal Wells and Its Effect on Production Performance. JPT 42(11): 1,426-1,433. SPE 19824.
Ihara, M., Kikuyama, K., and Mizuguchi, K. 1994. Flow in Horizontal Wellbores WithInflux Through Porous Walls. Paper SPE 28485 presented at the SPE AnnualTechnical Conference and Exhibition, New Orleans, 25-28 September.
Kloster, J. 1990. Experimental Research On Flow Resistance In PerforatedPipe. MS thesis, Norwegian Inst. of Technology, Trondhiem, Norway.
Olson, R. and Eckert, E. 1966. Experimental Studies of Turbulent Flow in APorous Circular Tube With Uniform Fluid Injection Through The Tube Wall. J. ofApplied Mechanics 33:7-17.
Ouyang, L.-B. 1998. Single Phase and Multiphase Fluid Flow in HorizontalWells, PhD dissertation, Stanford U., Palo Alto, California.
Ouyang, L.B. and Aziz, K. 1996.Steady-State Gas Flow InPipes. Petroleum Science and Engineering 14:137-158.
Ouyang, L.B. and Aziz, K. 2001. A General Single-PhaseWellbore/Reservoir Coupling Model For Multilateral Wells. SPEREE 14 (4):327-335.SPE 72467.
Ouyang, L.-B., Arbabi, S., and Aziz, K. 1998. General Wellbore Flow Model forHorizontal, Vertical, and Slanted Well Completions. SPEJ13 (2):124-133. SPE 36608.
Parker, J., Boggs, J., and Blick, E. 1969. Introduction to Fluid Mechanicsand Heat Transfer, page 232. Reading, Massachusetts: Addison-Wesley.
Penmatcha, V., Arbabi, S., and Aziz, K. 1997. Effects of Pressure Drop inHorizontal Wells and Optimum Well Length. Paper SPE 37494 presented at theSPE Production Operations Symposium, Oklahoma City, Oklahoma, 9-11 March.
Siwon, Z. 1987. Solutions for Lateral Inflow in Perforated Conduits. J. ofHydraulic Engineering 113 (9): 1,117-1,132.
Streeter, V.L. 1950. Steady Flow in Pipes and Conduits. EngineeringHydraulics. Chap. VI. H. Rouse (ed.), page 398. NYC:John Wiley & Sons.
Su, Z. 1996. Pressure Drop in Perforated Pipes For Horizontal Wells. PhDdissertation, Norwegian U. of Science and Technology, Trondheim, Norway.
Su, Z. and Gudmundsson, J. 1998. Perforation Inflow Reduces FrictionalPressure Loss in Horizontal Wellbores. Petroleum Science & Engineering19:223-232.
Tang, Y., Ozkan, E., Kelhar, M., Sarica, C., and Yildiz, T. 2000. Performance of Horizontal WellsCompleted with Slotted Liners and Perforations. Paper SPE/CIM 65516presented at the 2000 SPE/CIM International Conference on Horizontal WellTechnology, Calgary, 6-8 November.
Valvatne, P.H., Durlofsky, L.J., and Aziz, K.: 2001. Semi-Analytical Modeling of ThePerformance of Intelligent Well Completions. Paper SPE 66368 presented atthe SPE Reservoir Simulation Symposium, Houston, 11-14 February.
Wolfsteiner, C., Durlofsky, L.J., and Aziz, K. 2000. Efficient Estimation of the Effectsof Wellbore Hydraulics and Reservoir Heterogeneity on the Productivity ofNon-Conventional Wells. Paper SPE 59399 presented at the SPE Asia PacificConference on Integrated Modelling for Asset Management, Yokohama, Japan, 25-26April.
Yuan, H. 1997. Investigation of Single-Phase Liquid Flow Behavior inHorizontal Wells, PhD dissertation, U. of Tulsa, Tulsa.
Yuan, H.J., Sarica, C., and Brill, J.P. 1999. Effect of Perforation Density onSingle-Phase Liquid Flow Behavior in Horizontal Wells. SPEPF 14 (3):203-209. SPE 57395.
Yuan, S. and Finkelstein, A. 1956. Laminar Pipe Flow With Injection andSuction Through A Porous Wall. Trans., ASME:719.