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# Tubing Performance Relation (TPR)

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• @mohamed khamis Q increases while pwf " Bottomhole Flowing Pressure " decreases,this happen when drawdown increases between reservoir pressure and Flowing pressure at the bottom of a well

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• in slide 16 -how q increases with increasing BHFP

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• Mr. Craig, thank you very much for these slides on Well Performance. The slide did helm me to clear out some misunderstanding of this topic. If possible, could you please post slides on Completion casing design calculations.

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### Tubing Performance Relation (TPR)

1. 1. James A. Craig
2. 2.  The pressure drop required to lift reservoir fluids to the surface at a given rate is one of the major factors affecting Well Deliverability.  Up to 80% of the total pressure loss may occur.  Part of the loss in the tubing includes completion equipment, e.g. profile nipples, sliding sleeves, subsurface flow-control devices, etc.  Additionally, tubing string may be composed of multiple tubing diameters.
3. 3.  The pressure drop is a function of the mechanical configuration of the wellbore, the properties of the fluids, and the production rates.  Determination of this pressure drop is based on the mechanical energy equation for flow between two points in a system:  = Irreversible energy losses (viscous & friction)  Practically:  kinetic energy correction,  no work done by or on the fluid, 2 2 1 1 2 2 1 2 2 2 l c c c c P v P vg g Z Z W E g g g g            1  lE 0W   2 2 l c c vP g Z E g g      2 sin 2c c c dP g v dv f v dL g g dL g d      
4. 4.  Procedure:  We either fix the wellhead or bottomhole flowing pressure at a given rate.  The pressure drop along the tubing can be calculated by charts or correlations.  The resulting flowing pressure at the other end of the tubing can then be determined.  The resulting relationship between bottomhole flowing pressure and production rate is called Tubing Performance Relationship (TPR), and it is valid only for the specified wellhead pressure.  Other names include:  Vertical Lift Performance  Wellbore Flow Performance  Outflow Performance Relation
5. 5.  IPR & TPR curves can be combined to find the Stabilized Flow Rate (Point of Natural Flow).  The tubing shoe reaches the perforation depth.  Wellbore flowing pressure and tubing intake pressure are considered at the same depth.  At a specific rate when these two pressures are equal, the flow system is in equilibrium and flow is stable.
6. 6.  Pressure Loss Estimation in Fluid Types  Single-Phase Liquid Flow This type of fluid flow is generally of minor interest to the petroleum engineer, except for the cases of water supply or injection wells.  Single-Phase Vapour Flow For dry gas wells there are several correlations to calculate pressure drop in single-phase gas flow. They include:  Average temperature and compressibility method  Original Cullendar and Smith method  Modified Cullendar and Smith method
7. 7.  A simplified method by Katz et al (1959) assumes an average temperature and average compressibility over the flow length     0.5 5 2 2 200,000 1 S in wh g S g M SD P e P q TZLf e        0.0375 g L S TZ     2 3.71 2log / Mf D             
8. 8. o gas flow rate, scf/d tubing ID, in. flowing tubing intake pressure, psia flowing wellhead pressure, psia gas gravity (air = 1) average temperature, R average gas compressibilty f g in wh g q D P P T Z         actor vertical depth, ft Moody friction factor absolute pipe roughness (0.0006 in. for most commercial pipe) M L f    
9. 9.  Multiphase Flow Pressure drop in multiphase flow is more complex than that of a single-phase flow because parameters such as velocity, friction factor, density, and the fraction of vapour to liquid change as the fluid flows to the surface. Pressure drop can be determined either by correlations or by gradient curves. Some of the correlations are:  Duns and Ros (1963)  Dukler (1964)  Orkiszewski (1967)  Hageborn and Brown (1965)  Beggs and Brill (1973)  Mukherjee and Brill (1985)
10. 10.  Application of multiphase flow correlations requires an iterative, trial-and-error solution to account for changes in flow parameters as a function of pressure.  The calculation is intensive and is best accomplished with computer programs.  Gradient curves (also called Pressure-traverse curves) are developed as alternatives to the correlations. They are computer generated.  These curves are developed for series of gas-liquid ratios (GLR’s) and provide estimates of pressure as a function of depth.  Recent developed curves are based on the flow regime correlations, and not on field data as was originally done.
11. 11.  Joe Dunn Clegg (Editor): “Petroleum Engineering Handbook, Vol. IV – Production Operations Engineering,” Society of Petroleum Engineers, 2007.  Michael Golan and Curtis H. Whitson: “Well Performance,” Tapir Edition, 1996.  William Lyons: “Working Guide to Petroleum and Natural Gas Production Engineering,” Elsevier Inc., First Edition, 2010.  Schlumberger: “Well Performance Manual.”