Monitoring Multiphase Flow via Earth’s

Field Nuclear Magnetic Resonance

Keelan O’Neill University of Western Australia

School of Mechanical and Chemical Engineering

SUT Subsea Controls Down Under 20th October 2016

Fluid Science & Resources

www.fsr.ecm.uwa.edu.au/

Motivation for research

2

The future of oil and gas production

• Development of deeper offshore fields

and marginal fields

• Increased produced water

• Increased subsea processing

Production hub

Satellite field wells

Subsea manifolds

Satellite field wells

Atkinson, I., et al., A New Horizon in Multiphase Flow

Measurement. Oilfield Review, 2004. 16(4): p. 52-63

Subsea production arrangement

Objectives of flow metering

• Measurement of phase fractions

• Measurement of phase velocities

• Flow regime identification

J. Yoder, The many phases of multiphase flowmeters,

Pipeline & Gas Journal, 240 (2013) 40-41

0

100

200

300

400

500

2011 2012 2013 2014 2015 2016

Tota

l sh

ipm

en

ts (

$U

S m

illio

n)

Year

World Multiphase flow meter market

14% growth

Commercial magnetic resonance flowmeter: M-Phase 5000

Multiphase flow meter technologies

3

Advantages of nuclear magnetic resonance

• Non-invasive measurement

• Non-radioactive technology

• Flow regime independent

Common measurement principles

• Gamma ray attenuation

• Electrical impedance measurement

• Ultrasonic measurement systems

Superficial Gas Velocity, USG [m/s]

Su

perf

icia

l L

iqu

id V

elo

cit

y,

US

L [m

/s]

Flow

direction

Upstream transducer

Downstream transducer

Ultrasonic

emission Flow

Gamma-ray

source

Detector

Collimator

Nuclear magnetic resonance

4

Ultra-low field Low field High field

Summary of nuclear magnetic resonance (NMR)

magnetic field strengths

50 µT 50 mT 7 T

Earth’s field

NMR

Well-logging

tool

Magnetic resonance

imaging

Chemical

spectroscopy

Nuclear magnetic resonance

5

tdelay ta

90o RF pulse

Free induction decay

Pulse and Collect Experiment

Basic classical mechanics description

1. Align nuclei (1H atoms) with

magnetic field (polarisation)

B0

M

X

Z

Y

3. Observe the

magnetisation relax

2. Apply radio

frequency pulse

Radio frequency

pulse

The Earth’s field NMR flow meter

6

Pre-polarising

magnet EFNMR

detection coil Flow

direction

Faraday

cage Key system features

• Detected in the Earth’s

magnetic field

• Time of flight measurement

• Remote detection system

EFNMR: Earth’s field nuclear

magnetic resonance

Independent

flowrate

measurement

1. Polarisation

B0

M

X

Z

Y

2. Excitation

Radio frequency

pulse

3. Detection

Model for NMR signal

7

LP

𝐒(𝑣, 𝑡𝑎) = 𝑆0 1 − 𝑒− 𝜏𝑃𝑇1 𝑒

− 𝜏𝑃𝐷𝑇1 1 −

𝑡𝑑𝑒𝑙𝑎𝑦 + 𝑡𝑎

𝜏𝐷𝑒− 𝑡𝑑𝑒𝑙𝑎𝑦+𝑡𝑎

𝑇2∗

τ𝐷 = 𝐿𝐷𝑣

τ𝑃𝐷 = 𝐿𝑃𝐷𝑣

τ𝑃𝐷 = 𝐿𝑃𝐷𝑣

Halbach

array

EFNMR

Detection

Flow

LD

Polarisation Intermediate decay Detection

tdelay ta

90o RF pulse

Free induction decay

Parameters L: length τ: residence time v: velocity S0: initial magnetization T1: spin-lattice relaxation T2

*: observed spin-spin relaxation

LPD

Pulse and Collect Sequence

Tikhonov Regularisation

8

Real image Reconstructed image Image with noise

M. Bertero and P. Boccacci, Introduction to inverse problems in imaging. 1998, CRC Press.

Pipe velocity distribution

r

z

The inverse problem

Model

transfer

matrix

NMR Signal

Velocity probability

distribution

A × P 𝑣 = S P(𝑣) = A−1 × S

Tikhonov regularisation

• Least squares fitting

method

• Allows complex models to

be fit to experimental data

Single phase velocity analysis

9

0

1

2

3

4

5

6

0 0.5 1 1.5 2P

(v)

Velocity [m/s]

0.18 m/s

0.35 m/s

0.53 m/s

0.71 m/s

0.88 m/s

1.06 m/s

0

5

10

15

20

25

30

0 0.1 0.2 0.3 0.4 0.5 0.6

NM

R S

ign

al [μ

V]

Time since pulse [s]

0.18 m/s

0.35 m/s

0.53 m/s

0.71 m/s

0.88 m/s

1.06 m/s

Expt.

data

Model

fit

Experimental NMR signals fit using

regularisation

Corresponding velocity probability

distributions

Experimental conditions

Single phase water flows at 4 – 52 L/min (0.08 – 1.15 m/s)

Velocity comparison

10

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Pre

dic

ted

me

an

ve

loc

ity f

rom

NM

R

an

aly

sis

[m

/s]

Measured mean velocity from in-line rotameter [m/s]

-5.0%

-2.5%

0.0%

2.5%

5.0%

0 0.2 0.4 0.6 0.8 1 1.2

NM

R p

red

icte

d v

elo

cit

y d

evia

tio

n

Measured mean velocity from in-line rotameter [m/s]

Comparison of measured mean

velocities

Mean absolute error = 1.9 %

Deviation plot

NMR measurement

section

Independent rotameter

measurement (Uncertainty of ± 5%)

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2N

MR

pre

dic

ted

ve

loc

itie

s [

m/s

]

Rotameter measured velocities [m/s]

Two pipe analysis

11

Experimental conditions • Overall flow rates:

15 – 50 L/min

• Separation distance (LPD):

0.68, 0.78. 0.88 and 0.98 m

Velocity (pipe

A) ~ 33% of

velocity (pipe B)

Flow Pipe A

Pipe B

Halbach array

EFNMR detection

coil

0

1

2

3

4

0 0.4 0.8 1.2 1.6

P(v

)

Velocity [m/s]

30 l/min

40 l/min

50 l/min

LPD

Two pipe system velocity probability

distributions

Comparison of measured mean

velocities

B 0.68 m

0.78 m

0.88 m

0.98 m

Pipe

A

LP

D

Gas/liquid analysis

12

Flow regime identification

0

20

40

60

80

0 10 20 30 40 50

NM

R S

ign

al [µ

V]

Time [s]

Stratifiedflow

Slug flow

Video analysis Video analysis

region

EFNMR

Detection

Coil

Halbach

Array

ID:

31 mm

Liq

uid

Ho

ldu

p

Time [s]

USL = 0.13 m/s

USG = 0.88 m/s

Velocity and holdup determination

13

0

2

4

6

8

0 0.1 0.2 0.3 0.4

NM

R s

ign

al [µ

V]

Time since pulse [s]

Experimental data

Model fit

0

1

2

3

4

0 0.25 0.5 0.75 1

P(v

)

Velocity [m/s]

Processed signal & model fit Velocity probability

distribution

0

0.25

0.5

0.75

1

0 10 20 30 40

Ve

loci

ty [

m/s

]

Overall time [s]

𝑥𝐿 = 𝑆0,2𝑃𝑆0,𝐹𝑢𝑙𝑙

𝑆 0,2𝑃

𝑆 0,𝐹𝑢𝑙𝑙

Liquid holdup

determination

0

0.25

0.5

0.75

1

0 10 20 30 40Li

qu

id H

old

up

Overall time [s]

Stratifiedflow

Slugflow

0.00

0.25

0.50

0.75

1.00

0 10 20 30 40 50 60

Liq

uid

Ho

ldu

p

Video holdup

NMR holdup

0.00

0.25

0.50

0.75

1.00

0 10 20 30 40 50 60

Liq

uid

Ho

ldu

p

Experimental Time [s]

Video holdup

NMR holdup

Holdup analysis comparison

14

Liquid: 4 L/min

Gas: 40 L/min

Liquid: 8 L/min

Gas: 40 L/min

Liquid: 12 L/min

Gas: 20 L/min

Higher frequency

slug flow

Low frequency

slug flow

Stratified flow

0.00

0.25

0.50

0.75

1.00

0 10 20 30 40 50 60

Liq

uid

Ho

ldu

p

Video holdupNMR holdup

Background stratified

under-prediction

• Gas bubbles

• Meniscus

• Increased relaxation

Slug unit

Background stratified

component

Partial slug capture

• Slug residence

time ~0.2 s

• Scan time ~0.7 s

• Slug not fully

captured

0

0.1

0.2

0.3

0.4

0 0.1 0.2 0.3 0.4

NM

R p

red

icte

d s

up

erf

icia

l velo

cit

y [

m/s

]

Rotameter measured superficial velocity [m/s]

10 L/min

20 L/min

40 L/min

Gas Flow rate

Two phase velocity analysis

15

0

0.25

0.5

0.75

1

0 10 20 30 40

Ve

loci

ty [

m/s

]

Overall time [s]

0

0.25

0.5

0.75

1

0 10 20 30 40

Liq

uid

Ho

ldu

p

Overall time [s]

𝑈𝑆𝐿 = 𝑥𝑖𝑣𝑖𝑁𝑖=1

𝑁

0.01

0.1

1

0 0.1 0.2 0.3N

MR

ve

loc

ity s

tan

da

rd d

evia

tio

n

[m/s

] Rotameter measured superficial velocity [m/s]

10 L/min

20 L/min

40 L/min

Gas Flow rate

Stratified Flow

Slug Flow

Conclusions

• Can accurately measure and model the FID

signal of a moving fluid through the flow

metering system

16

• Can determine the velocity probability

distribution of liquid moving in the system

via Tikhonov regularisation

• Able estimate the liquid velocity and holdup

over time for stratified and slug flow

0

1

2

3

4

5

0 0.5 1 1.5 2

P(v

)

Velocity [m/s]

0.22 m/s

0.66 m/s

1.10 m/s

0

0.25

0.5

0.75

1

0 10 20 30 40 50

Ve

loci

ty [

m/s

]

Overall time [s]

Stratified flow

Slug flow

Future work

• Analyse fluid flow in further

air/water flow regimes

17

Superficial Gas Velocity, USG [m/s]

Su

perf

icia

l L

iqu

id V

elo

cit

y,

US

L [m

/s]

• Fully develop analysis techniques

to be able to interpret three phase

flow (oil/gas/water)

• Apply dynamic nuclear

polarisation for signal

enhancement

Hogendoorn, J., et al., Magnetic resonance multiphase flowmeter: measuring principle

and multiple test results, in Upstream Production Measurement. 2015: Houston.

Gas

Oil

Water

• Incorporate oil into flow

metering system

Acknowledgements

Supervisors

Michael Johns, Einar Fridjonsson and Paul Stanwix

Final Year Project Students Adeline Klotz and Jason Collis

18

Thank you for your attention!

Questions?

Tikhonov regularisation

19

The inverse problem;

Model

transfer

matrix

NMR

Signal

Velocity

probability

distribution

Pipe velocity distribution

r

z

Residual norm Second

moment of P(v)

Generalised cross validation

method is used to optimise the

smoothing parameter (λ)

min ( A × 𝑃 𝑣 − 𝑆 2 + λ 𝑃 𝑣 2)

A × 𝑃 𝑣 = 𝑆 𝑃(𝑣) = A−1 × 𝑆

0

2

4

6

8

0 0.5 1 1.5

P(v

) Velocity [m/s]

λ = 1×10-3

λ = 75 (optimal)

λ = 1×104

Apply Tikhonov regularisation;

Comparison to a theoretical model

Theoretical turbulent power law distributions

𝑈 𝑟 = 𝑉𝑀𝑛 + 1

𝑛1 −

𝑟

𝑅

1𝑛

20

0

2

4

6

8

0 0.2 0.4 0.6 0.8 1

P(v

)

Velocity [m/s]

n = 4

n = 5.37

n = 7

Experimental

Experimental and theoretical distributions at v = 0.44 m/s

𝑛 = 𝑓 𝑅𝑒

𝑛 0.44𝑚

𝑠= 5.37

(Zagarola et al. 1997)