Tubing Performance Relation (TPR)

James A. Craig

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.

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 21 1 2 2

1 22 2 lc c c c

P v P vg gZ Z W E

g g g g

1

lE

0W 2

2 lc c

vP gZ E

g g

2

sin2c c c

dP g v dv f v

dL g g dL g d

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 PerformanceWellbore Flow PerformanceOutflow Performance Relation

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.

Pressure Loss Estimation in Fluid Types

Single-Phase Liquid FlowThis 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 FlowFor dry gas wells there are several correlations to calculate pressure drop in single-phase gas flow. They include:Average temperature and compressibility methodOriginal Cullendar and Smith methodModified Cullendar and Smith method

A simplified method by Katz et al (1959) assumes an average temperature and average compressibility over the flow length

0.55 2 2

200,0001

Sin wh

g Sg M

SD P e Pq

TZLf e

0.0375 gLSTZ

2

3.712log

/Mf D

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

Multiphase FlowPressure 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)

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.

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.”

References