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)
kinetic energy correction,
no work done by or on the fluid,
1 1 2 2
c c c c
P v P vg g
Z Z W E
g g g g
2c c c
dP g v dv f v
dL g g dL g d
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
IPR & TPR curves can be combined
to find the Stabilized Flow Rate
(Point of Natural Flow).
The tubing shoe reaches the
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 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
A simplified method by Katz et al (1959) assumes an
average temperature and average compressibility over the
5 2 2
SD P e P
0.0375 g L
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
vertical depth, ft
Moody friction factor
absolute pipe roughness (0.0006 in. for most commercial pipe)
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)
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
These curves are developed for series of gas-liquid ratios
(GLR’s) and provide estimates of pressure as a function of
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.”