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 A

B

d C

e

Rotor Center Rotor Axis A’

B’ C’

AA’

BB’

CC’

A PCP Stator Ps

A S

B

A C

S’

D

d 4e

A

B

C

D

A Rotor in Stator

+

4e

+ +

Rotor Cross Center Rotor Axis Stator Center Line

Basic Correlations Cross-sectional areas of the rotor and the stator

A rotor

1 = πd 2 4

Astator

1 2 = πd + 4ed 4

Fluid flow area at any place

A f = 4ed

Basic Correlations … Cavity moving speed along stator center line

v = nPs n Ps -

rotational speed length of a cavity is the pitch length of the stator

Flow rate in a PCP

qt = A f v = 4ednPs

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

qa = qt − qs = 4ednPs − qs Volumetric efficiency of a PCP

qa qs = 1− Ev = qt qt

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

qtl = n

Qt

qtl = nQ t qtl – Total flow rate at pump intake Qt – Theoretical displacement per revolution

Production Rate Design

qa = nQt − qs Where:

Qs qs n qa

-

Theoretical displacement

-

slip rate

-

rotational speed

-

actual flow rate

Rotational Speed Design q Flow Capacity, B/D

Speed n1 = 200 RPM Qtn1/n0

Speed n0 = 100 RPM Qt

Slip

Lift Capacity, ft

H

Rotational Speed Design … d

pwh

Pump Depth

0 qd

q

pi A pwf

B

pd p

Rotational Speed Design 100(qa + qs ) n= Qt

q = C0 + C1H + C2 H 2 + C3 H 3 + C4 H 4 + C5 H 5

2 3 4 5 = − + + + + qs (C1 H C2 H C3 H C 4 H C5 H )

Rotational Speed Design … q Flow Capacity, B/D

Qtn A

qa

Qt

100 RPM qs

Ha

Lift Capacity, ft

H

Production Rate Design … Algorithm to Solve Total Flow Rate: •

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.

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.

Production Rate Design …

Head, ft

H

n0 =100 RPM

2n0

n

Ha

3n0

Well System Curve

S

Qt

qa qt

Flow Rate, B/D

q

Production Rate Design … p

Pressure,psia

pwf Outflow Δpi Inflow

qi Flow Rate, B/D

q

Viscosity Effect - on slip Viscosity effect on slip

qs _ µ qs-µ qs µ-

= -

32

µ

qs

Slip of viscous fluid Slip of water Viscous fluid viscosity in SSU

qa = nQt − q s _ µ

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 qsµ(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 …

Ps

ls

π(d+4e)

Viscosity Effect - Cavity Filling … Ac

t

w

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

ls 1 µ (nQt − q s _ µ ) pin = 3 8.04 E 6 dt Where:

l s = ( Ps2 + (π (d + 4e)) 2 )1 / 2 4ePs t= πl s

Viscosity Effect - Cavity Filling … Critical Speed for Fluid Completely Filling the cavity 3

8.04 E 6dt pin + q s _ µ ) / Qt n=( ls µ

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.