Design of PCP Wells

Design of Progressive Cavity Pump Wells

Desheng Zhou, SPE, H. Jasmine Yuan, SPE,

IHS INC.

Introduction• About PCP

– Special type of rotary positive displacement pump

– Flow through the pump is almost axial

• Advantages of PCPs– Lower investment – Broader applications to fluid mixtures – Less maintenance– Higher efficiency

Introduction …• PCPs in Petroleum Industry

– Single lobe pump– Non-pulsating smooth flow– Fluid viscosity will not degrade pump head– Normally no scale deposition– Low inertia of rotating parts

• Previous studies focused on– Working mechanism– Pumping behavior

Introduction …

• Purpose of this study– Design of PCP in production

system• Rotational speed design• Production rate design• Fluid viscosity effect

A PCP Rotor

e

A

A’

B

B’

C

C’

AA’ BB’ CC’

d

Rotor CenterRotor Axis

A PCP Stator

S S’

Ps

AB

CD

A

A B C D

4ed

A Rotor in Stator

Rotor Cross Center+

++ Rotor Axis

Stator Center Line4e

Basic CorrelationsCross-sectional areas of the rotor and the stator

Fluid flow area at any place

2

41 dArotor π=

eddAstator 441 2 += π

edAf 4=

Basic Correlations …Cavity moving speed along stator center line

n - rotational speedPs - length of a cavity is the pitch length of the stator

Flow rate in a PCP

snPv =

sft ednPvAq 4==

Basic Correlations …Taking into account of the slip rate, actual discharge rate

Volumetric efficiency of a PCP

sssta qednPqqq −=−= 4

t

s

t

av q

qqqE −== 1

Basic PCP Design

qtl – Total flow rate at pump intakeQt – Theoretical displacement per revolution

Correlation to calculate required rotational speed and total flow rate at pump intake

t

tlQ

qn =

ttl nQq =

Production Rate Design

Where:

Qs - Theoretical displacementqs - slip raten - rotational speedqa - actual flow rate

sta qnQq −=

Rotational Speed Design

H

q

Lift Capacity, ft

Flow

Cap

acity

, B/D

Speed n0 = 100 RPM

Speed n1 = 200 RPM

SlipQt

Qtn1/n0

Rotational Speed Design …

q

p

d

Pump Depth

qdpwf

pi pd

pwh

0A B

Rotational Speed Design

t

sa

Qqqn )(100 +

=

55

44

33

2210 HCHCHCHCHCCq +++++=

)( 55

44

33

221 HCHCHCHCHCqs ++++−=

Rotational Speed Design …

H

q

Lift Capacity, ft

Flow

Cap

acity

, B/D

100 RPMQt

qa

qs

Ha

A

Qtn

Production Rate Design …

• Assume the initial slip qs(1) is zero.

• Use Eq. 9 to calculate the total flow rate qa(1) at the PCP's intake for a given rotational speed n and theoretical flow rate Qt at 100 RPM.

• Use the calculated total flow rate qa(1) to calculate the inflow from reservoir to the pump intake and the outflow from wellhead to pump discharge. The outflow is in the annular between sucker rods and tubing for wellhead driving or in tubing for bottom driving. The flow rate for the inflow is the sum of the qa(1) and the separated gas at pump intake.

Algorithm to Solve Total Flow Rate:

Production Rate Design …• Obtain the differential pressure across the pump

from the calculated inflow and outflow pressure profile, and change the differential pressure to head H(1) by using the average fluid density through the pump.

• Check the required head H(1) with the lift capacity of the pump. If the head is greater than the lift capacity, stop the calculation. A longer PCP should be selected and start from step one. Otherwise,

• Calculate the volumetric slip rate qs(2) at the head H(1) from pump performance curves.

• Use the slip qs(2) and repeat the process from step two until the difference of qs(n)-qs(n-1) is less than an acceptable value.


q

H

Flow Rate, B/D

Hea

d, ft

S

n0 =100 RPM 2n0 3n0n Well System Curve

Qt qtqa

Ha


q

p

Flow Rate, B/D

Pres

sure

,psi

a

qi

pwf

Inflow

Outflow

Δpi

Viscosity Effect - on slip

Viscosity effect on slip

qs-µ - Slip of viscous fluid

qs - Slip of water

µ - Viscous fluid viscosity in SSU

ss qqµµ32

_ =

µ_sta qnQq −=

Viscosity Effect - on slip …• Obtain pump’s theoretical capacity

Qt at zero head

• For a series of given heads, H(1), H(2), and H(i), obtain corresponding flow rates q(1), q(2), and q(i)

• Calculate the volumetric slips of water by qs(i) = Qt – q(i) at any head H(i).

Viscosity Effect - on slip …• Calculate in-situ fluid viscosity of the

fluid, µ.

• Calculate the corrected slip rates qs-

µ(i) for the fluid.

• Calculate corrected flow rates, qc(i) = Qt

– qs-µ(i).

• Construct the corrected performance curve using H(i) and qc(i).

Viscosity Effect - Cavity Filling …

π(d+4e)

Psls


t

w

Ac

Viscosity Effect - Cavity FillingCritical Pump Intake Pressure for Fluid Filling the Cavity (Newtonian Fluid)

Where:

)(604.8

1_3 µµ st

sin qnQ

dtl

Ep −=

s

s

ss

lePt

edPl

π

π4

)))4((( 2/122

=

++=


Critical Speed for Fluid Completely Filling the cavity

tss

in Qql

pdtEn /)604.8( _

3

µµ+=

Conclusions• Algorithms and procedures to design pump

rotational speed and production rate from well inflow and outflow performances are presented.

• A method to account for the effect of viscosity on pump volumetric slip is proposed.

• Simplified models to calculate the critical pump intake pressures are developed for both Newtonian and non-Newtonian fluids.

Design of PCP Wells

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