day 2 - pcp system operating principle and step by-step design procedure

July 2010 G. Moricca 1

3 days course

Progressing Cavity Pump Systems

- day 2 -

PCP Operating Principle,

System Components and

Design Procedure

G. Moricca

[email protected]


Course agenda

Day 1

Overview of Artificial Lift Technology and

Introduction to PCP Systems

Day 2

PCP Operating Principle, System Components

and Design Procedure

Days 3

PCP System Installation, Start-up, Monitoring

and Troubleshooting

PCP System Operating Principle, System Components and Design Procedure

PCP Operating Principle

PCP System: Down-hole Components

PCP System: Surface Drive Equipments

PCP’s pump features:— Displacement— Flow rate— Head— Torque / Horsepower— Axial Load— Rod Effective Stress— Efficiency

Workshop Session: PCP pump displacement calculation

PCP Design Process Overview

PCP design step-by-step calculation procedure:— Minimum displacement required— Net lift— Pump Torque— Rod Torque : Resistive torque— Axial Load— Rod Effective Stress— Drive system

July 2010 3G. Moricca

Day 2 Course agenda


PCP

Operating

Principle

Main sources:

‒ Processing Cavity Pumping Systems. Petroleum Engineering Handbook vol. IV

‒ Processing Cavity Pumps, Downhole Pumps and Mudmotors. L. Nelik and J. Brennam. Gulf Publishing.


At the end of this section, you will be able to

understand:

● The operating principle of the PCP pump

● The different types of PCP pumps

● The main components PCP pump:

―stator

―Rotor

● Pump Geometry

PCP Operating Principle


Typical PCP system

● PCP’s are positive displacement pumps, which consist of two key parts, the stator and the rotor. The stator remains stationary and the rotor rotates.

● The PCP is described as a gear pump with a single helical rotor, which rotates inside a double internal helical elastomer lined stator.

● The stator is run into the well on the bottom of the production tubing, while the rotor is connected to the end of the rod string.

● The rotor turns eccentrically in the stator forming cavities from the intake, beginning of the flow, to the discharge at the end of the pump.

● The PCP delivers a constant flow that is proportional to the size of the cavity and rotational speed of the rotor.

● Rotation of the rod string at surface is powered by a hydraulic or direct drive system, which causes the rotor to spin within the fixed stator, resulting in fluid production at surface.

PCP System


5- You created Progressing Cavity Endless Pistons!

PCP System: Operating Principle

Progressing Cavity Pump Principle

1- Just imagine a piston.

2- Imagine multiple pistons behind each other.

3- Now we’ll make the wall thickness at zero

4- And change the piston shape slightly


How a Progressing Cavity Pump works

PCP System: Operating Principle

http://upload.wikimedia.org/wikipedia/commons/a/a5/Progressive_cavity_pump_animation.gif



PCP System-

Down-holecomponents

Main sources: Processing Cavity Pumping Systems. Petroleum Engineering Handbook vol. IV


Progressing Cavity Pumps

PCP consist of two

elements: the rotor

and stator.

Progressing cavity

pumps are a type of

rotary positive

displacement pump

designed to transfer

fluid through a

sequence of small

fixed shape cavities

as the helix shaped

rotor is rotated

within the stator.rotor

statorcavity

PCP System components


Stator

The stator consists of a steel tube, which encases an elastomer mould designed to achieve a specific geometric configuration.

The fabrication of the stator begins with machining a reusable metal core in the male configuration of the stator’s double internal helix.

The metal core is positioned in the center of the stator casing, which has been cleaned and coated internally with a metal bonding agent to the elastomer.

The stator is attached to the end of the tubing string and run into the well prior to the rotor or rods. An exception to this configuration is if an insert-able PCP system is used.



Elastomer

The elastomer is the heart of the PCP pump. Elastomerselection is a critical step in the PCP design as it influences pump run life and performance.

Proper selection requires good knowledge of the well’s operating conditions and fluid composition.

Elastomer compatibility tests maybe required to measure the effect of the wellbore fluid on the material. To do these tests, a sample of the elastomer is immersed into the wellbore fluid (oil or water).

The test will determine volume increases or decreases and hardness or softness changes of the elastomer. These tests are typically conducted at bottom-hole pressure and temperature, over a 72 to 240 hour period.



Elastomer

Most elastomers are primarily made up of nitrile, a copolymer of

butadiene and acrylonitrile.

The butadiene contributes to mechanical properties, such as

tear resistance.

Acrylonitrile contributes to chemical properties, such as the

resistance to aromatics.

Hydrogenated nitrile elastomer gives better H2S and temperature

resistance, as well as a fluorocarbon elastomer for greater

resistance to aromatics and H2S.

It is important to note that each manufacturer supplies its own

formulation of elastomers, references and descriptions.




The properties of pumped liquid determines which elastomer to select.

There are many different elastomers available.

According to the specific operational conditions, a proper elastomer as to be chosen to provide the longest wear possible for various applications.


Rotor

● The rotor is the moving (rotating) component of the PCP and is held from the surface by the drive string, which is typically a conventional or continuous sucker rod.

● The rotor has contact with the stator elastomeralong the seal line. The amount or degree of interference fit is critical to the efficiency and life expectancy of the pump.

● The rotor is machined to exacting tolerances and plated with chrome or chrome alternatives.

● The chrome provides a protective coating that minimizes abrasion, friction and corrosion damage.

● For each rotation of the rotor, fluid will move one pitch length of the stator.

● A different type of rotor pitch determines the ideal usage for a particular application. For example, the aggressive pitch of the KUDU-60TP pump is ideal for large sand concentrations and the KUDU-80TP pump is for lower clearance applications.

Heavy Oil geometryversus Conventional

80TP: NO sand

60TP suitable for large sand concentration



Fluid rate


Geometry of the

Progressing Cavity Pump

The geometry of the rotor-stator

assembly is such that it achieves two

or more series of separated cavities.

When the rotor turns inside the stator,

the cavities move in a spiral from

one end of the stator to the other,

creating the pumping action.


PCP System Geometry


Single lobe pump

The most typical PCP for oil production is a pump with a 1:2 geometry (1 lobe-rotor, and 2 lobes-stator) also referred as single lobe pump.

PCP System Geometry


PCP’s Geometry

● The geometry of pump is generally defined by two numbers, the first

being the number of lobes of rotor, and the second being the number

of lobes of the stator.

● These two numbers define the rotor-stator lobe ratio or simply, lobe

ratio.

● The most common lobe ratio are: 1:2 3:4 5:6 7:8 9:10

● Because the number of rotor and stator lobes differ by one, a fluid-

filled cavity is formed between a rotor and a stator: this is a key to its

operating principle.

PCP System Geometry


PCP’s GeometryPump dimensions are identified using the following terminology:

Pr

Ps

E

2E

Ds

dr

Ds

E

The stator has the same internal

form and geometric

measurements as the rotor with

the exception that it has a double

180° shifted double thread and

twice the pitch.

dr

PCP System Geometry


Pitch length

The pitch length is defined as a

length of 360° rotation of a

crest trace of one of the helix

lobes, and is symbolized as: P

For a 1-2 lobe pump:Ps = 2Pr

For a multi-lobe pump:Ps = Pr x [(Lr + 1)/Lr]

where:Pr = pitch length of rotor, ftPs = pitch length of stator, ftLr = number of rotor lobes

PCP System Geometry


Cavity

●Cavities are lenticular ,spiral, separate

volumes created between the stator and

the rotor when they are assembled.

●Each cavity moves in spiral around the

axis of the stator, progressing from the

inlet to the outlet as a consequence of the

rotor rotation.

●The length of the cavity is alwaiys the

pitch length of stator.

●The number of cavities C is calculated as

follows:

C = Lr x [(Hs / Pr) -1]

where:Lr is the number of rotor lobesHs is the length of the stator

Pr is the length of the rotor pitch

PCP System Geometry

http://upload.wikimedia.org/wikipedia/commons/c/ce/Progressive_cavity_pump_cavities.png

http://upload.wikimedia.org/wikipedia/commons/c/ce/Progressive_cavity_pump_cavities.png


PSP pump configuration

PCP pumps are available in two

different configurations:

1.Tubular Pumps , or those ones

attached directly to tubing

string.

2.Insertable pumps , or the

arrangement that make it

possible to install and retrieve

the down hole PCP pump by the

sucker rod string.

In both models are suitable to

handle a wide range of liquids

efficiently, regardless their viscosity.

PCP System configuration


PCP System sizes


PSP’s main characteristics summary

●PCPs are particularly well suited to pumping the following types of fluid:―solids in suspension ―high viscosities―abrasive slurries ―solids, liquids, gas mixtures ―oil and water mixtures without emulsification

●PCP pressure limitation is a function of:―stator material―fluid properties (mainly viscosity)―interference fit between stator and rotor

●Total power system efficiency isusually higher for PCPs than otherforms of artificial lift system:

PCP System characteristics


PCP System-

Surface DriveEquipments



PCP Surface Drive System

Surface systemThe surface system includes:

1. Wellhead drive unit

2. Stuffing box

3. Power transmission

4. Prime mover

In addition, the surface system

may also includes:

5. Safety shutdown devices

6. Torque limiters

7. Recoil control devices

8. Electronic speed

controller (ESC)

9. Monitoring system


PCP Surface Drive Systems

A- Fixed speed drive:

Belt drive

B - Belt and gear

reducer drive

C - Variable speed

drive: mechanical

system

D - Variable frequency

drive system


Surface Drive System

The surface equipment used in a conventional surface-driven PCP system must perform the following functions:

1. Suspend the rod string and

carry the axial loads

2. Deliver the torque required at

the polished rod

3. Safely rotate the polished rod

at required speed

4. Provide for safe release of the

stored energy during shutdown

5. Prevent produced fluid from

escaping the system.



Vertical Drive Head

The Vertical Direct Drive is a cost effective and reliable way to transfer the power to the sucker rod string.

It compounds two types depending upon the way they are designed:

1. without any gear, or direct drive (DH/DS)

2. featuring built-in gear reducer (GH).



Vertical Drive Head – Direct Drive (DH/DS)

Vertical DH/DS types drives are normally selected where higher speeds are expected for the application, according to the pump displacement available in the field.

Usually it can be applied to speeds from110 rpm up to 450 rpm.

The speeds are achieved by changingthe set of sheaves and/or byusing variable frequency drive.

−Speed Range [rpm]: 110 to 450−Axial Load Capacity [kilo pounds]:

5; 20; 33; 37 and 50−Power Capacity Range [hp]: 3 to 200



Vertical Drive Head in the field



Vertical Drive Head – Built-in Gear Box

Vertical GH types drives are normally selected where lower speeds are expected for the application, particularly for high displacement PCP pumps.

The built-in gear reducer provides a reduction speed ratio equals to 1:5.16

Usually it can be applied to speeds from 79 rpm up to 397 rpm and, similarly to DH types, the desired speeds can be achieved by changing the set of sheaves and/or the use of variable frequency drive.

− Speed Range [rpm]: 79 to 397− Axial Load Capacity [kilo pounds]: 5; 9; 20 and 33− Power Capacity Range [hp]: 5 to 100



Vertical Drive Head – Built-in Gear Box in the field



Right Angle Drive Head

Right Angle RH types drives feature a built-in 6.15 :1 ratio gear reducer and

are normally selected where lower speeds are expected for the application,

particularly for high displacement PCP pumps.

The geometry of the right angle drive head arrangement allows the alternative

use of gas engine and hydraulic prime movers. In case of using gas engine, a

proper set of sheaves and gas engine speed controller provide the target speed

for the application.

− Speed Range [rpm]: 80 to 200

− Axial Load Capacity [kilo pounds]: 33

− Power Capacity Range [hp]: 60

− Power Supply: Gas engine (~1800 rpm)



Right Angle Drive Head in the field


PCP System-

PCP’s pumpfeatures




At the end of this section, you will be able to understand

and calculate:

the PCP’s pump features:

―Displacement

―Flow rate

―Head

―Torque / Horsepower

―Axial Load

―Rod Effective Stress

―Efficiency

PCP System: PCP’s pump features



Pump

Displacement

As already mentioned,

pump dimensions are

identified using the

following terminology:

Pr

Ps

E

2E

Ds

dr

DsE


Nominal Pump Displacement

At any cross section of the pump, the area of fluid is equal to:

A = 4E x dR

And the volume (cubic inches per 1 revolution) of fluid per cavity is equal to:

V = A x Ps

Taking into account units (1 in3 = 1.031x10-4 bbl and 1RPM is equal to 1440

RPD, 1 in3 per rpm is equal to 1.03x10-4 x 1440 = 0.1485 bbl/day) the

theoretical pump displacement (single lobe pump) can be determined

from:

PD = 0.1485 x V

where PD is the pump displacement in bbl/day/rpm



Nominal Pump flow rate

●The theoretical pump flow rate (bbl/day) is:

Q = PD x ωwhere:

Q = Flow-rate (bpd)PD = Pump displacement (bpd/rpm)ω = Pump rotational speed (rpm)

●The calculated Q will differ from actual production rates at surface due to:―inefficiency (slip/leakage) in the PCP ―down-hole fluid volume will be higher than that at the surface (Bo effect).

●Volumetric efficiencies of 70 - 80% are typical.

●PCP manufacturers do not usually publish figures on the pump eccentricity, diameter of the rotor and stator pitch and so it is difficult to manually calculate pump rates.

●Instead manufacturers provide a pump curve and a value for displacement (bpd/rpm) and maximum pressure differential rating in terms of head or psi for a specific rotor elastomer.



Nominal Pump Head

The pump head is determined by:

1.The number of cavities formed between the rotor and the stator

2.The head developed into an elementary cavity, which depend on:

− The seal (or clearance) between rotor and stator: the diameter of the rotor is slightly

bigger than minor diameter of the stator.

− The pumped fluid characteristics: higher head are achieved with viscous fluid.

− Geometry of the pump: diameter and rotor pitch, eccentricity.

− The chemical composition of the elestomer.

− The mechanical characteristic of the elastomer.

− The thickness of the elastomer.

Pump head is defined by :

ΔP = (2np -1) δpwhere:

ΔP = pump head rating, psi

np = number of pitches of stator

δp = head rating developed into an elementary cavity, psi



Pump stages

One single PCP pump stage is equal to

one cavity length which is the stator pitch, Ps.

The number of stages or number of pitches of stator required to obtain

the required pump head can be obtained as following:

np = (ΔP/δp - 1) /2 where:

ΔP = required pump head rating, psi

δp = head rating developed into an elementary cavity, psi

As a rule of thumb, progressive cavity pumps are designed for

approximately 75 psi differential pressure per stage. Consequently, if

1000 psi differential pressure is required, and a pump having a stator pitch 2

ft long is used, the total length of the pump is approximately 30 ft.



Nominal Torque Load

Torque loads are a function of the:

― pump differential pressure

― pump internal friction

― a resistive torque of the fluid between the rod/couplings and tubing.

The total torque can be expressed as:

Ttotal = Tfriction + Thydraulic + Tresistive

where:

− Tfriction is the torque required to overcome the fit between the stator and

rotor and allow the pump to turn. The value is typically 65-100 lbs and is

known form experience rather than a direct calculation. In the case of a

swollen elastomer this value be much higher.

− Thydraulic is due to the work that the pump does.

− Tvesistive is the torque required to overcome friction of the rod string

rotating in the produced fluid.



Nominal Torque Load

Tfriction = 65 -100 ft-lbs (1 foot-pound force ≈ 1.3558 N-m)

Thydraulic = 0.0897 x PD x ΔP

where:

PD =Pump displacement (bpd/rpm);

ΔP = Pump differential pressure (psi)

Tresistive = (4.77 x 10-8 x IDtbg2 x Drod

2 x L x µ x ω)/(IDtbg2 x Drod

2 )

where:

IDtbg = Internal tubing diameter (inches)

Drod = Diameter of rod string

L = Total length of rod string

µ = Fluid viscosity (cP)

ω = RPM of pump (rpm)



Actual Torque Load

The actual torque load is function of the efficiency of the pump.

The actual pump performance are determined experimentally using a test bench.



Actual pump performance: test procedure

There are currently no accepted industry standards for conducting bench

tests, however the test procedure to determine the actual pump

performance can be outlined as following.

Test bench setup

1. The pump is installed horizontally on a test bench.

2. Rotation and power are provided to the rotor through a drive system.

3. Fluid is pumped through a close-loop system consisting of: pump, discharge

lines, fluid reservoir, filtering system, and intake lines.

4. Water with a small amount of oil added for lubrication is used as the test

fluid.

5. A choke on the discharge lines used to regulate the pump differential

pressure.



Actual pump performance: Test procedure

Test process

1. The test process normally consists of varying the discharge pressure

while operating the pump at constant speed.

2. Various test parameters are monitored and recorded.

3. The discharge pressure is usually set at zero at the start of the test and is

then sequentially increasing to the maximum test pressure that, in most

cases, matches or exceeds the rated pressure of the pump.

4. Depending on the manufacturer, this procedure is repeated at up to four

different speeds.

5. Some manufacturers also determine the maximum pressure that a pump

can withstand. This is done by completely restricting the pump discharge

and measuring the pressure under that condition.



Actual pump performance: Test procedure

Test report

1. The test report usually contains the following information:

― test speed,

― pump discharge pressures,

― temperatures, actual fluid rates,

― volumetric efficiencies,

― hydraulic pressures,

― torques.

2. The report should also include information on the pump components,

including:

― model number,

― rotor and stator serial numbers,

― dimensions,

― elastomer type,

― thread connections.



Volumetric Efficiency

The Volumetric Efficiency is calculated as the ratio of the measured fluid rate to the theoretical fluid rate.

Theoretical

fluid rate

(Q) is

determined

base on the

test speed

and nominal

displacement

of the pump

(pump

geometry).

E = (DS -dR)/2

L = PS x n

A = 4E x dR

V = A x Ps V = 4E x dR x PS

PD = 0.1485 x V PD = 0.148 x 4E x dR x PS

Q = PD x n x ω Q = 0.148 x 4E x dR x PS x n x ω

Q = 0.148 x 4E x dR x L x ω

E Pump eccentricity in

DS Major diametr of rotor in

dR Minor diametr of rotor in

A Cross section of the pump area in2

Ps Stator pitch in

PD Unitary Pump displacement bpd/rpm

n Number of stages nr

L Total stator length in

ω Pump rotational speed rpm

Q Pump flow-rate bpd



Volumetric Efficiency

At zero differential pressure it is expected that a PCP pump would operate at a

Volumetric Efficiency of 100 %.

This is the reason why the Actual Volumetric Efficiency starts from 100 %. It

can be read as a Normalized Nominal Volumetric Efficiency.

95.1% 0.951 94.0

89.4

Efficiency Vol. Nominal

ntDisplaceme Nominal

rate fluid Measured

Efficiency Vol. Nominal



Total Efficiency : is the ratio of the output fluid power (Ph) to the input (shaft) power (Ppmo).

Pump

speed

(ω)

Dif.tial

pressure

Fluid

rate

( Q )

Nominal

Vol.tric

Eff.ncy

( NVE )

Actual

Vol.tric

Eff.ncy

Fluid

power

( Ph )

Total

torque

(T)

Actual

Power

( Ppmo )

Total

Eff.ncy

rpm m mc/d % % kW N-m kW %100 0 89.4 95.1 100 0.00 180 1.88 0.0

100 200 87.6 93.2 98.0 1.99 414 4.33 45.9

100 300 86.0 91.5 96.2 2.93 478 5.00 58.5

100 400 85.5 91.0 95.6 3.88 558 5.84 66.5

100 500 78.7 83.7 88.0 4.47 659 6.90 64.8

100 600 74.4 79.1 83.2 5.07 794 8.31 61.0

100 700 64.3 68.4 71.9 5.11 893 9.35 54.7

100 750 57.4 61.1 64.2 4.89 980 10.26 47.6

100 800 51.7 55.0 57.8 4.70 1019 10.67 44.0

100 850 46.1 49.0 51.6 4.45 1072 11.22 39.6

ND Nominal displacement 94 mc/d @100 rpm

NVE Nominal volumetric displacement NVE = Fluid rate / Nominal displacement

Ph = Q ρ g h / 86.4 x 106 Ppmo = 1.047 x 10-2 T ω/ Ept

Ph = fluid power kW Ppmo = require prime-mover power kW

Q = fluid rate mc/d T = polished-red torque N-m

ρ = fluid density kg/mc ω = polishe-rod rotation rpm

g = gravity (9.81) m/sec2 Ept = power transmission eff.ncy 100%

h = differential head m



Volumetric & Total Efficiency

In general, volumetric efficiency decreases with increasing differential

pressure. This decrease is caused by the leakage of fluid across the

rotor/stator seal line from higher to lower pressure cavities.

Higher fluid viscosities

may contribute to

decrease slippage

rates and increased

volumetric efficiency.

0

20

40

60

80

100

120

0 200 400 600 800 1000

Eff

icie

ncy (

%)

Rated lift (m)

Pump Test Efficiency Chart

Nominal Vol. Eff. Actual Vol. Eff. Total Eff.



Since the PCP is a

positive displacement

pump its rate

performance is not

substantially affected

by pressure across the

pump. However, with

increasing pump

differential the seal

between the individual

cavities is not adequate

and slippage of the

pumped fluid takes place

resulting in a drop in

pump efficiency. Pump

efficiency is a function of

the interference fit

between the rotor and

stator and the viscosity

of the fluid pumped.



Pump Torque

As discussed pressed previously, pump torque consists of a combination of hydraulic, friction, and viscous components. Viscous pump torque will be negligible for test conducted with water.

Hydraulic torque can be estimated accurately from pump displacement and differential pressure.

Thydraulic = 0.0897 x PD x ΔP

where:–PD =Pump displacement (bpd/rpm);–ΔP = Pump differential pressure (psi)

Therefore, friction torque can be estimated by subtracting hydraulic torque from the measured pump torque.

Friction torque tends to correspond closely to the rotor/stator fit.

Under down-hole operation conditions, because of the fluid environment and temperature, the friction torque could be substantially higher than the bench test value.



Rod Loading

In a PCP system, the rod-string must be

capable of carrying axial load and

transmitting torque between the surface

drive and the bottom-hole pump.

Therefore, rod-string design encompasses

an evaluation of the axial tension and torque

loading conditions for the full range of

anticipated operating conditions.



Axial Load and Torque

The axial load and torque at any location along a rod string is made up of several different components:

1. Pump hydraulic torque and pump axial load are applied to the rod string at the pump.

2. Resistive (viscosity) torque and rod weight are developed in a distributed manner along the length of the rod string.

In almost all cases, the rod string axial load and torque are maximum at the polished-rod connection at surface.



Axial Load

The axial forces in the rod can be calculated from:

Faxial = Frod + Fpumpwhere:

Frod = Pump depth (ft) x Unitary Rod weight (lb/ft)

and:

Fpump = (ΔP x Aeff) – (Pd x Arod)

where:


Pd = Pump discharge pressure (psi)

Arod = Area of rod string (in2)

Aeff = Effective area or fluid area (Astaor – Arotor)

For a single lobe pump:

Aeff = 8EDs + [(π Ds2/4) x 8Edr]

where:

E = Eccentricity of rotor (in)

Ds = Major diameter of rotor (in)

dr = Minor diameter of rotor (in)



Rod Effective Stress

The combined loading of torque and axial load on the rod string

can be accounted for using Von Mises stress equation.

Calculation the torque and axial loads are best performed using

software although there are a number of equations and tables that

can be used to estimate the forces and calculate the effective stress

on the rod.

In order to ensure a safety factor an effective stress of less that

70-80% of maximum is used.

inD

D

T

D

F totalaxial

diameter, string-rod theis where

1106.0106.1stress Effective

62

2

42

25



Drive systemThe required power output of the prime mover can be calculated from:

Hp = (1.904 x 10-2 x Trod x ω) / η

where:

Hp = required horsepower hp

Trod = Total calculated torque (ft-lbf)

ω = System rotation speed (rpm)

η = Efficiency of driver system (%)



Horsepower

The down-hole torque required to turn the pump is quoted by some

manufacturers in terms of Hp. The following equation can be used to covert

between torque and Hp for a given RPM:

Hp = (T x RPM) / 5252



WorkshopSession

-PCP pump

displacement calculation


Problem

Knowing the geometry parameters of a single lob PCP pump:

―Major diameter of the rotor = 4.388 in

―Minor diameter of the rotor = 3.087 in

―Rotor pitch length = 22.170 in

―Stator pitch length = 23.666 in

calculate the Pump displacement.......

Workshop sessionPCP’s pump features


PCP pump displacement

Workshop sessionPCP’s pump features

Data

Single lobe pump

DS Major diameter of the rotor 4.388 in

dR Minor diameter of the rotor 3.087 in

Pr Rotor pitch length 22.170 in

Ps Stator pitch length 26.666 in

Calculate

E Rotor eccentricity E = (DS -dR)/2 = 0.651 in

A Area fluid A = 4E x dR = 8.032 in2

V Volume per revolution V = A x Ps = 214.2 in3

PD Pump displacement PD = 0.1485 x V = 31.8 bbl/day/rpm

PCP Design Process Overview


Main source: Processing Cavity Pumping Systems. Petroleum Engineering Handbook vol. IV


PCP System design

This section outlines the PCP design process and the

selection criteria including:

1.Pump displacement

2.Pump pressure capability

3.Geometric design

4.Elastomer type

5.Rod coating characteristic.


PCP System design

PCP design process overview

As with other artificial-lift system, the design process is generally iterative, and individual parameters are often adjusted to achieve an optimal design for a particular application.

The design process includes:1. Information gathering for the application of interest (reservoir data, fluid

properties, production data, well record).

2. Well completion design for the anticipated/aspected fluid rates. This can be estimated by setting a dynamic fluid level and calculating production rates based on reservoir data and inflow performance relationship. As output, the optimised completion string (tubing size and rod-string configuration), pump-seating depth and production parameters (fluid rate, intake and discharge pressures, net lift, pump speed) will be obtained.

3. Selection of the PCP pump model capable of satisfying the desired pump displacement and lift requirement.

4. Evaluation of the rod loading, rod-string/tubing wear.

5. Selection of the surface equipments


PCP

process

design

flowchart

A design process flow chart outline the many factors and considerations that should be addressed in the selection of an effective overall system configuration and operating strategy.

At each step, the designer selects certain operating parameters or specific equipment components and must then asses the impacts of these decisions on system performance.


PCP System design


1. The first step in the design process is to gather information for the application of interest:— Past experiences— Fluid properties— Production (actual or expected)— Well records— Reservoir data.

2. Next, it is necessary to determine the anticipated fluid rate.

3. Initial values must then be set for the:— Wellbore geometry— Pump-setting location— Dynamic fluid level— Tubing size— Rod-string configuration

If the design is for an existing well, some of these parameters may already be constrained.


PCP System design


4. Once these equipment and operating parameters are established, flow losses can be calculated.

5. If the floe losses are unacceptably high, they can be reduced by:— increasing the tubing size— reducing the rod-string, or— decreasing the fluid rate.

6. Next, initial values for pump intake and discharge pressure, net lift, pump speed, and pump displacement can be set.

7. Initial values must then be set for the:— Wellbore geometry— Pump-setting location— Dynamic fluid level— Tubing size— Rod-string configuration

If the design is for an existing well, some of these parameters may already be constrained.


PCP System design

PCP pump selection

The pump selection include:

1. Pump displacement

2. Pump pressure capability

3. Geometric design

4. Elastomer type

5. Rod coating characteristic.

PCP System design


PCP displacement

It is typical to select pumps with a design flow rate that is somewhat higher than the expected fluid rate to reflect pumps inefficiencies during production operations.

Fluid slippage, inflow problems, and gas interference all contribute to reduced pump volumetric efficiency.

The design fluid rate and prescribed pump rotational speed define the minimum required pump displacement as:

efficiency pump c volumetri theis

rpm speed, rotational pump theis

bpd nt,displaceme pump required theis

bpd/rpm nt,displaceme pump required minimum theis

:where

min

min

E

Q

PD

E

QPD

req

req

PCP System design


PCP displacement

Initially, an optimal pump speed should be assumed on the basis of the

intended application conditions, with the primary considerations being the

viscosity of the produced fluids and tubing-wear potential.

In general, there has been a trend recently toward higher speeds because new

pump models and better sizing practices have been developed.

PCP System design


PCP pressure capability

The net pump lift requirement determines the minimum required pressure capability of the pump.

In determining the net lift value for pump selection, the full service life conditions should be considered.

Net lift is defined as the difference between discharge and intake pressures of the PCP pump under the expected operating conditions:

and...........

psi pressure, intake pump theis

psi pressure, discharge pump theis

psi pressure, requiredlift net theis

:where

int

int

P

P

P

PPP

dsc

lift

dsclift

PCP System design


PCP pressure capabilityThe pump intake pressure can be expressed as:

and the pump discharge pressure, as:

psi pressure,column -liquidannular theis

psi pressure,column -gasannular theis

psi pressure, head-casing theis

psi pressure, intake pump theis :where

int

int

anl

ang

ch

clcgch

P

P

P

P

PPPP

psi pressure, frictional tubing theis

psi pressure,column -liquid tubing theis

psi pressure, head- tubing theis

psi pressure, discharge pump theis :where

fr

tl

th

dsc

frtlthdsc

P

P

P

P

PPPP

PCP System design


Once the minimum pump displacement and

net lift requirement are established, these

values can be used to determine the range of

the pump models that will satisfy the

requirements of a particular application.

If there is no pump that satisfy a particular

set of requirements, then the system design

or operating conditions must be changed.

PCP System design


Torque requirement

Rotation of the rotor withinthe stator forces the fluidto move up the fromcavity to cavity.

A series of dynamicinterference seals separatethe cavities and providea differential pressure capacity.

The energy required to turn the rotor and move the fluid against this pressure gradient is provided in the form of torque.

Pump torque is composed of friction, hydraulic and viscous component.

PCP System design




Torque requirement

As already anticipated, the total torque can be expressed as:

Ttotal = Tfriction + Thydraulic + Tresistive

where:

−Tfriction is the torque required to overcome the fit between the

stator and rotor and allow the pump to turn. The value is typically 65-

100 lbs and is known form experience rather than a direct calculation. In

the case of a swollen elastomer this value be much higher.

−Thydraulic is due to the work that the pump does.

−Tresistive is the torque required to overcome friction of the rod string

rotating in the produced fluid.

and...........

PCP System design


Nominal Torque Load

Tf = 65 -100 ft-lbf (1 foot-pound force ≈ 1.3558 N-m)

Th = 0.0897 x PD x ΔP

where:

Thdr = Hydraulic Torque (ft-lbf)

PD = Pump displacement (bpd/rpm)

ΔP = Pump differential pressure, or lift pressure (psi)

Tr = (4.77 x 10-8 x IDtbg2 x Drod


2 )

where: Tr = Resistive torque (ft-lbf)






PCP System design


Actual Torque Load

The actual torque load that satisfy a particular set of requirements of a particular

application, can be found on the down-hole pump performance specification provided

by manufacturers, generally available at one speed (usually at 100 rpm).

PCP System design


Actual Torque Load

Having in mind that the pump performance specifications are

generated using water (with a small amount of oil added for

lubrication) as test fluid, running the rotor at constant rate (typically

at 100 rpm), it is essential to make a proper allowance (in the pump

selection process) for the torque requirements associated with:

1. pump friction torque, and

2. viscous pump torque, especially in the case of highly viscous

fluid,

to ensure that the power limitations and load capacities of the

surface-drive system and rod string are not exceeded.

PCP System design


PCPDesign

-step-by-step

calculation procedure

Main source: Processing Cavity Pumping Systems. Petroleum Engineering Handbook vol. IV


PCP System design

This section outlines the step-by step calculation

procedure for the PCP system design.

At the end of this section, you will be able to calculate:

― Minimum displacement required

― Pump intake pressure

― Pump discharge pressure

― Net lift

― Pump Torque

― Rod Torque

― Axial Load

― Rod Effective Stress

― Required power for the Drive system


Problem

Statement

− A vertical well is expected to produce 629 bpd of 12 °API (61.429 lb/ft3) oil

and no water, gas, or sand.

− The well is cased with 7 in OD casing perforated at 3281 ft from surface.

− At the desired flow rate, the fluid level is expected to be 1968 ft from the

surface.

− The casing is vented to atmosphere, while the flow-line pressure is 218 psi.

− The oil viscosity is 1000 cP.

Design a PCP system to produce this well with the following constrain:

− The pump should be set below the perforations at 3312 ft

− Its speed should not exceed 250 rpm

− The pump should not loaded above its rated pressure

− The rod stress should be < 80% of yield (API Grade D rods = 586 MPa =

85000 psi)

PCP System design


The following pumps are available:

Assume that any of these pumps will operate at 85% volumetric efficiency

under down-hole conditions and that the friction torque will be 20% of the

hydraulic torque at the pump’s rated pressure.

Pump A Pump B Pump C Pump D Pump E

PD Displacement bpd/rpm 0.944 1.887 2.831 4.403 6.290

E Pump eccentricity in 0.236 0.256 0.335 0.276 0.453

ω Pump rot, @ Qreq rpm 157 85 74 39 45

P Pressure rating psi 1740 1740 2611 2176 1740

DS Major diameter in 1.969 2.126 2.047 2.283 2.913

dR Minor diameter in 1.496 1.614 1.378 1.732 2.008

OD Tubing OD in 3.500 3.740 4.252 4.500 4.500

ID Tubing ID in 2.867 2.990 3.480 3.920 3.920

L Pump length ft 13.12 14.76 26.24 39.36 32.8

PCP System design


Solution

1. Minimum displacement required

The minimum displacement required to achieve the desired flow rate without

exceeding the specified maximum pump speed will be:

The pump displacement must be > 2.114 bpd/rpm. This eliminate pump A and

B from further consideration.

2. Net liftNext step is to determine the net lift that is the difference between

discharge and intake pressures of the PCP pump under the expected

operating conditions:

and........

bpd/rpm 14.20.85350

629 min

E

QPD

req

intPPP dsclift

PCP System design


The Pump intake pressure will be:

―Casing-head pressure was defined to be atmospheric pressure, or 0 psi gauge pressure.

―The gas and liquid hydrostatic pressure can be calculated from the gas and liquid density and the column heights.

―The pump intake is 3312 ft from surface, and the fluid level is 1968 ft from surface.

―This means that there is 1968 ft of gas column and 1344 ft of liquid column.

psi pressure,column -liquidannular theis

psi pressure,column -gasannular theis

psi pressure, head-casing theis

:where

int

anl

ang

ch

clcgch

P

P

P

PPPP

PCP System design


―If the average gas density is estimated to be 0.05 lb/ft3 the gas hydrostatic pressure will be:

Gas gradient = Gas density/144 = (0.05 lb/ft3) / (144 in2/ft2) =0.00035 psi/ft

Pang = Gas gradient x Gas column = 0.00035 x 1968 = 0.68 psi

―The liquid hydrostatic pressure will be:

Liquid gradient =Liquid density/144 = (61.429 lb/ft3) / (144 in2/ft2) =0.4266 psi/ft

Panl = Liquid gradient x Liquid column = 0.4266 x 1344 = 573 psi

The pump intake pressure will be:

spi 574 573 0.68 0 int clcgch PPPP

PCP System design


―The pump discharge pressure will be:

―The tubing head pressure (Pth) is given as: 218 psi.

―The tubing liquid pressure (Ptl) will depend on the location of the top of the pump.

The pump is seated at 3313 ft (intake depth), but the three pumps alternatives have different lengths, so the top will be at a different location in each case.

Also, the flow loss will depend on the selection of tubing and rods.

The solution process will be iterative.

psi pressure, frictional tubing theis

psi pressure,column -liquid tubing theis

psi pressure, head- tubing theis

psi pressure, discharge pump theis :where

fr

tl

th

dsc

frtlthdsc

P

P

P

P

PPPP

PCP System design


If the pump length is 26.24 ft, the top of the pump will be at 3287.39 ft and

the tubing liquid pressure (Ptl) will be:

Liquid gradient =Liquid density/144 =

(61.429 lb/ft3)/(144 in2/ft2) = 0.4266 psi/ft

Ptl = Liquid gradient x Liquid column =

0.4266 x 3287.39 = 1402 psi

―Tubing friction pressure (Pfr)

The tubing friction pressure (with a tubing 3.5 in OD - 2.867 in ID,

and a rod 1.0 in), was estimated as 880 psi

PCP System design


The pump discharge pressure will be:

The net lift pressure will be:

The pump is required to work against a differentia pressure of 1929 psi.

Only pump C an D have a pressure rating exceeding this value.

Also, note that pump E cannot be used with this tubing (ID = 2.867 in) because

the major rotor diameter (2.913 in) is larger than the drift diameter of the

tubing.

However, if a larger tubing size that would accommodate the large rotor diameter

were used, the flow losses would be reduced, possibly to the point that the

pressure rating of pump E would not be exceeded. Therefore, the pump E will

continue to be considered a potential candidate.

psi 2500 880 1402 218

frtlthdsc PPPP

psi 1926 574 2500

int

PPP dsclift

PCP System design


3. Pump Torque

The torque in the pump is given by:

where:

− Th is due to the work that the pump does.

− Tf is the torque required to overcome the fit between the stator and

rotor and allow the pump to turn.

Pump C

Data: PD = 2.831 bpd/rpm and Prating = 2611 psi

Torque:

2.008970

08970

PDP.T

PDP.T

TTT

ratingf

lifth

fht

mN 843 lbfft 622 133 489

mN 180 lbfft 1332.83126112.00.0897 2.008970

mN 663 lbfft 4892.83119260.0897 08970

fht

ratingf

lifth

TTT

PDP.T

PDP.T

PCP System design


Pump D

Data: PD = 4403 bpd/rpm and Prating = 2176 psi

Torque:

Pump E

Data: PD = 6290 bpd/rpm and Prating = 1740 psi

Torque:

Pumps Torque:

― Pump C: Tt = 622 ft-lbf = 843 N-m

― Pump D: Tt = 932 ft-lbf = 1264 N-m

― Pump E: Tt = 1283 ft-lbf = 1740 N-m

mN 1264 lbfft 932 172 761

mN 233 lbfft 172440326112.00.0897 2.008970

mN 1031 lbfft 761440319260.0897 08970

fht

ratingf

lifth

TTT

PDP.T

PDP.T

mN 1740 lbfft 1283 196 1087

mN 266 lbfft 196629017402.00.0897 2.008970

mN 1473 lbfft 1087629019260.0897 08970

fht

ratingf

lifth

TTT

PDP.T

PDP.T

PCP System design


4. Rod Torque : Resistive torque

The resistive torque (Tr) is the torque required to overcome friction of the

rod string rotating in the produced fluid and is defined as:

Tr = (4.77 x 10-8 x IDtbg2 x Drod


2 )

where: Tr = Resistive torque (ft-lbf)






The resistive torques for each of these pumps can be calculated at the speed

at which they would run to produce the require amount of oil (Qreq =

629 bpd).

Pump’s rod torque:

― Pump C: Tr = 51 ft-lbf = 69 N-m

― Pump D: Tr = 33 ft-lbf = 44 N-m

― Pump E: Tr = 23 ft-lbf = 31 N-m

PCP System design


5. Axial Load

The axial forces in the rod can be calculated from:

Faxial = Frod + Fpumpwhere:

Frod = Pump depth (ft) x Unitary Rod weight (lb/ft)

and:

Fpump = (ΔP x Aeff) – (Pd x Arod)

where:


Pd = Pump discharge pressure (psi)

Arod = Area of rod string (in2)

Aeff = Effective area or fluid area (Astaor – Arotor)

For a single lobe pump:

Aeff = 8EDs + [(π Ds2/4) x 8Edr]

where:

E = Eccentricity of rotor (in)

Ds = Major diameter of rotor (in)

dr = Minor diameter of rotor (in)

PCP System design


At a discharge pressure of 2500 psi and intake pressure of 574 psi, the axial

load at the pump is as follows:

― Pump C: Faxial = 17378 lbf = 77.3 kN

― Pump D: Faxial = 18974 lbf = 84.4 kN

― Pump E: Faxial = 27899 lbf = 124.1 kN

The combined loading of torque and axial load on the rod string (Total or

Effective stress) can be accounted for using Von Mises equation……..

PCP System design


6. Rod Effective Stress

The Effective stress will be:

inD

ft-lbf T

lbfF

psi

D

T

D

F

total

axial

totalaxial

diameter, rod theis

load, tota theis

forces, axial theare

stress, Effective theis

: where

10001106.0106.1

stress Effective62

2

42

25

PCP System design


The combined loading of torque and axial load (Effective Stress) according

to Von Mises stress equation will be:

― Yield for Grade D rods = 586 MPa = 85000 psi

― The rod stress exceed the yield capacity if pump D or E are used.

― Pump C is adequate for this specific situation.

Pump C Pump D Pump E

D Rod diameter in 1 1 1

Faxl Axial forces lbf 17378 18974 27899

Ttot Total load ft-lbf 673 965 1306

σ Effective stress psi 76281 107426 146049

σ Effective stress Mpa 526 741 1007

PCP System design


7. Drive system

The required power output of the prime mover can be calculated from:

Hp = (1.904 x 10-2 x Trod x ω) / η

where:

Hp = required horsepower hp

Trod = Total calculated torque (ft-lbf)

ω = System rotation speed (rpm)

η = Efficiency of driver system (%)

Hp = (1.904 x 10-2 x 673 x 74) / 90 = 10.5 hp

PCP System design

2nd day PCP

course end

Thanks for

the attention

July 2010G. Moricca 102

PCP for high temperature (350°C/660°F),

high gas content (90%) and high fluid

pressure processing (260bar/3770psi).

G. Moricca

[email protected]