Profiling of Relaxation Time and Diffusivity Distributions using Low

Field NMR

Michael RauschhuberGeorge HirasakiApril 26, 2011

1

Motivation For NMR Profiling

• Current NMR Profiling typically relies on slice selection– multiple thin slices needed to generate a profile

• Saturation profiles can be determined only for air/water systems or D2O/oil systems.

• Goal: Generation of profiles for oil/water systems without the need for multiple slice experiments.

2

Imaging Gradients• Standard MRI technique to detect spatial

information from a desired sample.

• In a uniform magnetic field,

• In the presence of a linear magnetic field gradient gx,

• Precession frequency is linearly related to spatial position

02Β

π

γfL Sample

x-xL

f-fL

3

xgBxf x 02

xcenter

fL LxL xxgfxf 2

Image Construction

• Acquisition of the full echo is necessary for image construction.

• Application of a FFT reconstruction is performed in order to generate the 1-D profile.

• Finally, frequency can be converted to distance using the linear relationship between frequency and sample position.

6 6.5 7 7.5 8 8.5 9 9.5 10-1600

-1400

-1200

-1000

-800

-600

-400

-200

0

200

400

Sig

nal a

mpl

itude

(a.

u.)

time (msec)

Echo, g = 0.800 G cm-1, SI = 64, DW = 50 sec

0 500 1000 1500 2000 2500-3

-2

-1

0

1

2

3

Signal amplitude (a.u.)

h (c

m)

Water Profile, g = 0.800 G cm-1, SI = 64, DW = 50.0 sec

4

• By appropriately selecting TR and TE, spin density, T1-weighted, or T2-weighted images can be attained.

Image Contrast for a Single Echo• Technique used to differentiate fluids with different T1 or T2..

• For Single Spin Echo Imaging Sequence,

Method of Contrast

TE TR

Spin Density TE << TA < TB TA < TB <<TR

T1 Contrast TE << TA < TB TA < TR < TB

T2 Contrast TA < TE < TB TA < TB <<TRTA: relaxation time of fast relaxing componentTB: relaxation time of slow relaxing component

For T1 Contrast, selection of TR should allow for one fluid to be fully polarized while the other is only partially polarized. Similarly, for T2 contrast, the proper choice of TE should allow for greater relaxation of one fluid than the other.

210

expexp1T

T

T

T

M

M ER

5

Spin Density ImageLayered Water – Squalane (C-30 oil, = 22 cP) System

TA = T2,squalane = 125 msTB = T2,water = 2800 ms

TE = 8 ms TE << TA < TB TR = 15000 ms TA < TB <<TR

• Using a spin density image, the squalane and water layers cannot be differentiated from one another, because water and squalane have a similar Hydrogen Index.0 500 1000 1500 2000 2500

-3

-2

-1

0

1

2

3

Signal amplitude (a.u.)

h (c

m)

Spin Density Image of a Layered Water-Squalane Sample (TE = 8.00 msec, T

R = 15000 msec)

6

Water

Squalane

T1-Weighted ImageLayered Water – Squalane System

• Due to the selection of TR, the squalane layer is fully polarized between scans while the water is only partially polarized. Therefore, the squalane layer has a greater amplitude in the image.0 500 1000 1500 2000 2500

-3

-2

-1

0

1

2

3

Signal amplitude (a.u.)

h (c

m)

T1-Weighted Image of a Layered Water-Squalane Sample (T

E = 8.00 msec, T

R = 714 msec)

TA = T2,squalane = 125 msTB = T2,water = 2800 ms

TE = 8 ms TE << TA < TB TR = 714 ms TA < TR < TB

7

Water

Squalane

T2-Weighted Image Layered Water – Squalane System

• Due to the selection of TE, the squalane layer has undergone much more relaxation than the water layer. Therefore, the water layer has a greater amplitude in the image.

0 500 1000 1500 2000 2500-3

-2

-1

0

1

2

3

Signal amplitude (a.u.)

h (c

m)

T2-Weighted Image of a Layered Water-Squalane Sample (T

E = 140 msec, T

R = 15000 sec) TA = T2,squalane = 125 ms

TB = T2,water = 2800 ms

TE = 140 ms TA < TE < TB

TR = 15000 ms TA < TB <<TR

8

Water

Squalane

T2 Profiling• A CPMG-style imagining sequence, known as Rapid Acquisition

with Relaxation Enhancement (RARE), can be used to generate a collection of profiles with increasing T2 relaxation.

• Spatial distribution of T2 can be achieved by analyzing the decay of the acquired profiles.

RF

Gradient

Signal

…

…g1 g2 g2

1

1 2 2

Restriction: 21g1 = 2g2

TR >>TE

…

9

T2 ProfilesSample: Water, g1 = g2 = 0.800 G cm-1

, 1 = 1.30 msec,

= 3.00 msec, DW = 40.0 sec, SI = 64

10

Yates Core Sample (D)

Sample: Yates D, g1 = g2 = 0.800 G cm-1, 1 = 1.30 msec,

= 3.00 msec, DW = 80.0 sec, SI = 3211

Texas Cream Limestone (TCL 80)

Sample: TCL 80, g1 = g2 = 0.800 G cm-1, 1 = 1.30 msec,

= 3.00 msec, DW = 80.0 sec, SI = 3212

NMR D-T2 Profiling

• T2 can be spatially resolved using the RARE pulse sequence.

• By incorporating diffusion gradient pulses, NMR imaging techniques allow for the measurement of fluid self-diffusion coefficients.

• Simultaneous spatial resolution of D and T2 will allow for the determination of saturation profiles even when oil and water phase exhibit overlapping T2 distributions.

13

D-T2 Profiling Pulse Sequence

RF

Gradient

Signal

1

’

2

gD

gD gD

gD gF

2

gF

2

gF

L L S

1

33

L L

x2

x2

x2

y2

S S

y yy y y

Prephasing Gradient

Diffusion Gradients

Readout Gradient

14

Saturation Profiles

oil

ioili

iwateri

oil

ioili

o

HI

TDfTDf

HI

TDf

S

2,

2,

2,

,,

,

• Saturation profiles can be determined for samples exhibiting overlapping T2 peaks for water and oil by utilizing the difference in diffusivity to distinguish their signals.

• D-T2 maps were acquired in 3 cm segments and then were stacked together creating a composite image for the entire 1 ft. sand column.

• Dwell Time (DW) was selected based on the detection length of the probe to prevent aliasing 15

Sandpack Experiments

• Sandpack (U.S. Silica 20/40)– Porosity = 0.36– Permeability = 80 Darcy

• Initial Waterflood• Oilflood

– Detection of Capillary End Effect

• 0.3 PV Waterflood• 0.6 PV Waterflood

16

Water Saturated SandPack

17

100

101

102

103

104

0

5

10

15

20

25

T2 (msec)

h (

cm

)

10-8

10-7

10-6

10-5

10-4

10-3

10-2

0

5

10

15

20

25

D (cm2 sec-1)

h (

cm

)

0 0.050

5

10

15

20

25

So

h (

cm)

So,avg

= 0.000 0.001

Oil SaturationProfile AverageMass Balance

Saturation Profile of a water saturated sandpack

S0,mass = 0.00

S0,prof = 0.00

Identification of Capillary end effect

18

Saturation Profile of oilflood. Capillary end effect can be identified at the top (outflow)end of the profile.

S0,mass = 0.87

S0,prof = 0.86

Capillary end effect number

NC,end = 0.81

Oil Flood

19Saturation Profile of oilflood. Increasing inject rate from 5 ft day to 40 ft day helped inremoving the end effect

S0,mass = 0.88

S0,prof = 0.94

Capillary end effect number

NC,end = 0.10

0.3 PV Waterflood

20

S0,mass = 0.63

S0,prof = 0.62

Saturation Profile of a sandpack after 0.3 PV waterflood.

Mobility Ratio

M = 1.2

Gravity NumberNGrav = 0.93

0.6 PV Waterflood

21Saturation Profile of a sandpack after 0.6 PV waterflood.

S0,mass = 0.36

S0,prof = 0.35

Mobility Ratio

M = 1.2

Gravity NumberNGrav = 0.93

Summary of Sandpack Saturation Profiles

• Displacement of oil by water can by visualized through the generation of NMR saturation profiles.

• After 0.3 PV waterflood, the water front advanced near the center of the column

• After 0.6PV waterflood, breakthrough of water occurred, and the saturation profile confirms that the oil saturation near the outlet is below the initial oil saturation.

22

Conclusions• Two NMR profiling pulse sequences have been designed and

implemented for the measurement of T2 and D-T2 in a low-field spectrometer.

• 1-D NMR profiling allows for the detection of spatially varying properties, such as saturation and porosity, within a sample.

• D-T2 profiling allows for the detection of two NMR sensitive phase when they possess a significant contrast in viscosities.

• NMR determined saturation profiles extracted from D-T2 profiling results yielded profiles with averages very close to the average saturations determined via mass balance at various stages within the flooding process.

23

Questions?

24

Backup Slides

T2 Profiling

25

Backup Slides

Selection of Imaging Parameters

26

Parameter Selection• Experimental parameters, such as sample size, gradient

strength and duration, and the number and spacing of the acquired data points, must be selected to ensure that useful information can be extracted from the profiles

• Attenuation due to diffusion is dependent on the product of gradient strength (g) and duration (). Therefore, g and should be selected in order to reduce the amount of the relaxation due to diffusion

• The dwell time (DW), or spacing between acquired data points, determines the image length, and the number of data points collected per echo (SI) sets the number of points resolved over that distance.

27

Sample Size

An FID of water, with a sample height of 0.5 cm, was performed at incremental locations within the probe to determine the sweet spot.

•Sample should be located within the sweet spot of the NMR and centered about fL. Our MARAN has sweet spot of about 5 cm, so a sample with a height of 4 cm is used.

28

Effect of Diffusion

2

21

21

22

0

exp3

1212exp

T

tnngD

M

tM

For g1 = g2 = g and 21 = 2,

where n is the echo number 29

Effect of Diffusion• Due to the presence of several gradient

pulses, attenuation due to diffusion can be significant. As the product of gradient strength (g) and duration (1) is increased, the effect of diffusion becomes more pronounced.

For g1 = g2 = g and 21 = 2,

ngTDT

T,

311

1

121

222

2

#2

where T2# is the apparent spin-spin

relaxation time measured via RARE

• Excessive attenuation due to diffusion is not desirable.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

g (G cm-1)

T2#/T

2

1 = 0.25 msec

1 = 0.50 msec

1 = 0.75 msec

1 = 1.00 msec

1 = 1.25 msec

1 = 1.50 msec

1 = 1.75 msec

1 = 2.00 msec

D = 2.62*10-9 m2 sec-1

T2 = 2500 msec

hs = 4.0 cm

h = 1.0 cm

30

Minimum Gradient Strength

• Attenuation due to diffusion is dependent on the product of g and 1. Therefore, weak gradients can be used to minimize this effect.

• The gradient strength (g) deviates from the expected behavior at very low values. The lowest reliable gradient for the Maran-M was selected to be g = 0.8 G cm-1 which corresponds to the lowest gradient with less than 5% deviation between observed and predicted values. 31

Maximum Gradient Strength

• The application of larger imaging gradients results in a larger range of frequencies encoded by the imaging pulses.

• Profile rounding can occur when the range of encoded frequencies, Δf, takes up a large portion of the probe’s bandwidth.

• The maximum gradient strength should be selected to prevent significant rounding of the profile due to bandwidth limitations.

32

Dwell Time (DW)

• Dwell Time (DW) refers to the spacing between data points and sets the range of frequencies to be resolved by the measurement. DW must be selected in order to prevent aliasing of the signal using the Nyquist Criterion.

33

Number of Acquisition Points (SI)

• The number of acquisition points (SI) corresponds to the number of data points collected per echo as well as the number of points across the profile. Selection of SI and DW determine the profile’s resolution

• If data is acquired during the entire duration of the readout pulse, SI can be represented as

34

Selection Criteria

• Based on the sample size, the minimum T2 to be measured, and a selected value of T2

#/T2 , a g and 1 pair can be chosen.• The largest possible 1 will allow for the longest echo train and

subsequently, the broadest resolution of relaxation times.

T2#/T2 = 0.95

Resulting g and 1 pair:

g = 0.80 G cm-1

1 = 1.43 msec

35

Selection Criteria (cont’d).

• Once a g and 1 pair has been choose, DW and SI can be selected.

• Data must be acquired under the readout gradient. If we require data collection to last as long as possible, DW to be less than DWmax, and SI = 2n, then DW and SI can be determined.

DW = 44 msec SI = 64

36

Reducing Phase Sensitivity• Prepare magnetization with diffusion weighting first (Norris et al., 1992).

• Introduce /2 pulse during formation of first echo to remove out of phase signal (Alsop, 1997).

RF

Gradient

Signal

1

’

2

gD

gD gD

gD gF

2

gF

2

gF

L L S

1

33

L L

x2

x2

x2

y2

S S

y yy y y

Prephasing Gradient

Diffusion Gradients

Readout Gradient

37

Unipolar vs. Bipolar

Unipolar

Bipolar

38

1st Experiment 4th Experiment

Reducing Phase Sensitivity• Prepare magnetization with diffusion weighting first (Norris et al., 1992).

• Introduce /2 pulse during formation of first echo to remove out of phase signal (Alsop, 1997).

RF

Gradient

Signal

1

’

2

gD

gD gD

gD gF

2

gF

2

gF

L L S

1

33

L L

x2

x2

x2

y2

S S

y yy y y

Prephasing Gradient

Diffusion Gradients

Readout Gradient

39

Reducing Phase SensitivityPrior to Modification After Modification

40Squalane, g = 2.5 G cm-1, = 6 msec, h = 1.38 cm

Gradient Pre-pulses

• Gradient pre-pulses allow for the consistent application of gradient pulses during the NMR experiment by warming up the gradient coils

• Pre-pulses also add additional stability to the gradient waveform by balancing the effect of eddy currents on the system’s magnetization throughout the duration of the pulse sequence

41

Echo Shape in the Absence of Pre-pulses

• Examination of the echo data for the experiment shows that at low g values an echo with a single peak forms while the use of high g values results in echoes with two distinct peaks

• Formation of dual peaks is indicative of a sequence in which the gradients prior to refocusing are not properly balanced by the gradients after refocusing. In other words, the magnitude and duration of the first set of bipolar pulses is not equivalent to the second set even though their parameters are identical

Two PeaksOne Peak

Low g High g

42

Effect of Pre-Pulses on Profile Shape0 Pre-pulses

1 Pre-pulses

5 Pre-pulses

9 Pre-pulses

7 Pre-pulses

3 Pre-pulses

• Profiles of first echo at g = 19.4, 27.2, 32.2, 38.0, and 45.0 G cm-1 for sandpack at initial oil saturation (SMY, water). The number of gradient pre-pulses varied between 0 and 9.

• Profiles generated using too few pre-pulses demonstrate large variations and often times overlap with one another. As the number of pre-pulses was increased, the profiles start to flatten out and separate .

43

Effect of Pre-Pulses on Echo Shape

• In the absence of gradient pre-pulses, two peaks were noted in the echo. This resulted in the large fluctuations in profile amplitude.

• Gradient pre-pulses prevent the echo from forming two distinct peaks. This results in the profiles beginning to flatten out and separate.

Two Peaks One Peak

0 Pre-pulses 9 Pre-pulses

44

Impact of Pre-pulses on the D-T2 Profile

• In the absence of gradient pre-pulses, poorly shaped profiles manifest themselves as valleys in each region of interest in the intensity of the D data

• Incorporating an adequate number of pre-pulses into the D-T2 profiling pulse sequences removes these valleys noted in projected D data.0 Pre-pulses

9 Pre-pulses

45

Gradient-RF Pulse Spacing

• If the spacing between RF and gradient pulses is less than the gradient fall time, then the two will overlap causing degradation of the NMR signal.

• A series of FID experiments preceded by a gradient pulse can be used to examine the impact of RF-gradient spacing.

• As the time between RF and gradient pulses increases, the FID decays more slowly indicating less impact of the gradient on the RF pulse.

FID performed after application of gradient pulse (g = 20.0 G cm-1 , = 5.0 msec).

RF

Gradient

Signal

gD

1

x2

3

46

• FID results indicate that a spacing of 10

to 15 msec is needed to prevent the gradient from interacting with the RF.

• With a gradient-RF spacing of 10 msec for the D-T2 profiling experiment, a large portion of the oil signal will be lost due to relaxation before the collection of the first echo.

• In an effort to balance the NMR signal quality with the NMR signal strength, it is desired to collect the first echo before t = T2,logmean of the crude oil. Subsequently, gradient-RF spacing in the D-T2 profiling sequence was set to 5 msec.

• Even at sub-optimum gradient-RF spacing, improvements are noted in the profile shape.

Profile of 1st echo from D-T2 profiling sequence with g =19.4 G cm-1. Gradient-RF spacing is increased from 1.0 msec to 5.0 msec, and rounding behavior noted in profile is alleviated

Selecting a Gradient-RF Pulse Spacing

47

Impact of Gradient-RF Pulse Spacing on Saturation Profiles

1 msec 5 msec

Consistent dip in saturation profile at the bottom of each measurement region when an insufficient gradient-RF spacing is applied

Increasing the RF-gradient spacing helps to remove dips in the saturation profile.

48

Backup Slides

Data Processing: Rotating FFT Data to Generate a Meaningful Profile

49

Profile Rotation

• FFT reconstruction of echo data yields both real and imaginary contribution to the profile.

• FFT data for all echoes at a given height/frequency is rotated in order to generate 1-D profile. 50

Backup Slides

Selecting gradient strengths for D-T2 profiling

51

Diffusion Gradients• Using the attenuation equation for D-T2

profiling sequence and selected ’ and 1 values, estimates of expected signal can be generated.

• With water and SMY, two distinct diffusion attenuation regimes are noted due to their different diffusivities.

• Data points can be spaced over the water- and oil-sensitive regions, and the impact on the spacing and number of gradient strengths determined.

52

Even Spacing w.r.t g2

• As the number of gradient values used is reduced, the resulting saturation profile becomes noisier and underestimates the actual saturation.

• The use of 10 to 12 gradient strengths yields a saturation profile that is in good agreement with the full set (25 points).

53

An equal number of points were spaced across the water and oil sensitive ranges.

Geometric Spacing• A list of at least 8 gradient

strengths with geometric spacing yields a good saturation profile.

• However, geometric spacing yields poor results when measuring high oil saturation.

• Using either even spacing with respect to g2 or geometric spacing, the length of this list can be greatly reduced

54

An equal number of points were spaced across the water and oil sensitive ranges.