nmr chalk powder

8/13/2019 NMR Chalk Powder

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Table of Contents

1 Introduction ............................................................................................................................................... 42 Theoretical Background ............................................................................................................................. 6

2.1 History of development & Applications in the oil industry ............................................................... 6

2.2 Nuclear magnetism: The magnetic nucleus ...................................................................................... 7

2.3 Precession .......................................................................................................................................... 8

2.4 Measuring magnetization ................................................................................................................ 10

2.5 T1 Longitudinal relaxation time..................................................................................................... 11

2.6 T2 and T 2* Transversal relaxation times ........................................................................................ 13

2.6.1 Hahns Sequence ..................................................................................................................... 16

2.6.2 CPMG Sequence ...................................................................................................................... 17

3 Materials and methods ........................................................................................................................... 19

3.1 Solids ................................................................................................................................................ 19

3.2 Solutions .......................................................................................................................................... 19

3.3 Assembly and preparation of the sample. ...................................................................................... 21

4 Design of the NMR experiment ............................................................................................................... 22

4.1.1 Recycle delay ........................................................................................................................... 22

4.1.2 Number of echoes and TAU..................................................................................................... 23

4.1.3 Number of Scans ...................................................................................................................... 26

5 The inverse problem ................................................................................................................................ 30

5.1 Regularization .................................................................................................................................. 31

5.1.1 Weight ..................................................................................................................................... 31

5.2 Pruning............................................................................................................................................. 34

6 Results ..................................................................................................................................................... 366.1 Calcium chloride brine: .................................................................................................................... 38

6.1.1 Surface area: 2m 2 .................................................................................................................... 38

6.1.2 Surface area: 5m 2 .................................................................................................................... 39

6.1.3 Surface area: 10m 2 .................................................................................................................. 40

6.1.4 T 2 Relaxation time (CaCl 2 brine)............................................................................................... 41

6.1.5 Surface relaxivity (CaCl 2 brine) ................................................................................................ 41

6.2 Magnesium chloride brine: ............................................................................................................. 42


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6.2.1 Surface area: 2m 2 .................................................................................................................... 42

6.2.2 Surface area: 5m 2 .................................................................................................................... 43

6.2.3 Surface area: 10m 2 .................................................................................................................. 44

6.2.4 T 2 Relaxation time (MgCl 2 brine) ............................................................................................. 45

6.2.5 Surface relaxivity (MgCl 2 brine) ............................................................................................... 45

6.3 Sodium chloride brine ..................................................................................................................... 46

6.3.1 Surface area: 2m 2 .................................................................................................................... 46

6.3.2 Surface area: 5m 2 .................................................................................................................... 47

6.3.3 Surface area: 10m 2 .................................................................................................................. 48

6.3.4 T 2 Relaxation time (NaCl brine) .............................................................................................. 49

6.3.5 Surface relaxivity (NaCl brine) ................................................................................................ 496.4 Sodium sulfate brine........................................................................................................................ 50

6.4.1 Surface area: 2m 2 .................................................................................................................... 50

6.4.2 Surface area: 5m 2 .................................................................................................................... 51

6.4.3 Surface area: 10m 2 .................................................................................................................. 52

6.4.4 T 2 Relaxation time (Na 2SO4 brine) .......................................................................................... 53

6.4.5 Surface relaxivity (Na 2SO4 brine) ............................................................................................ 53

6.5 Bound Fluid and porosity................................................................................................................. 54

6.5.1 De-ionized water vs. low concentration brines ....................................................................... 54

6.5.2 De-ionized water vs. medium concentration brines ............................................................... 55

6.5.3 De-ionized water vs. high concentration brines ...................................................................... 56

7 Discussion ................................................................................................................................................ 57

8 Further work ............................................................................................................................................ 59

9 Conclusion ............................................................................................................................................... 60

10 References ........................................................................................................................................... 61


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1 Introduction

Recently, a number of studies have been focusing in the relaxivity of water in contact with solid

surfaces(Foley et al. 1996; Hum & Kantzas 2006; Chen et al. 2006) and particularly the influence of

dissolved ions in bound water relaxivity (Alam et al. 2010; Katika et al. n.d.). These are:

-Sodium chloride;

-Magnesium chloride;

-Calcium chloride;

-Sodium sulfate.

These brines contain ions found in seawater (Na + Ca2+, Mg 2+, and SO 4 2) and are thought to have positively

influenced the oil recovery in the Ekofisk field by two mechanisms: One is the compaction of the reservoir

caused by a weakening of the chalk. The second is the increase of wettability of the chalk (previously

neutral to moderately water wet), which increases the oil recovery by spontaneous imbibition and viscous

displacement (Austad et al. 2008).

Wettability can be defined as the preferential attraction of a mineral surface towards a particular fluid(Alam et al. 2010), thus is believed that the smaller residual oil saturation linked to wettability alteration

would be connected to an increase in surface relaxivity of fluids at the chalk surface (Hum & Kantzas 2006;

Chen et al. 2006). This parameter accounts for the effectiveness of the surface in promoting spin-

relaxation, and is also considered to be a measure of the strength of interactions between uids and pore

walls (Howard 1998).


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Although NMR methods have gained popularity within the oil industry in recent years, end users are often

unaware of the (non-trivial) underlying principles of nuclear magnetic resonance and somehow

sophisticated data processing required for the generation of the tangible T 2 distribution data.

This report intends to shed light on background theory as well as methods and procedures in order to

extract the most of the Oxford Instruments GeoSpec 2/53 DRX-HF digital spectrometer owned by DTU and

investigate the influence of the aforementioned ions on fluid relaxivity at calcite surfaces. The work is set

towards investigating the optimal parameters to perform the NMR experiment and understanding how

they affect the end product, a probability distribution of relaxation times of the magnetic field in the

transverse plane. These parameters include number of scans collected, number of echoes recorded, Tau,

and Recycle delay time.

The Laplace Inversion that takes place after the experiment transforming the transverse magnetization

decay into a distribution of T 2 relaxation times (process known as echo-fit or mapping (Coates et al. 1999))

is also scrutinized. The inputs of the process are explained and a method is proposed to determine the

optimal weighting factor to perform the inversion.

To test the method proposed, a battery of tests was designed to measure the T 2 distributions and surface

relaxivity of the various saturated chalk samples to try to identify which ions plays a part in altering bound

water relaxivity when in contact with crushed chalk samples. The results of the tests are then discussed and

further work suggested.


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2 Theoretical Background

2.1 History of development & Applications in the oil industry

The interest in nuclear magnetic resonance measurements in the petroleum industry dates back to the

1950s, shortly after the phenomena itself was predicted by Gorter, in 1936 (Steinberg & Cohen 1984). A

decade later Felix Bloch and Edward Purcell, working independently, successfully demonstrated the

existence of NMR by inducing and measuring its effects in water and paraffin respectively. In recognition of

their efforts, they were awarded with the Nobel Laureate in Physics in the year of 1952.

The early developments, notably by California Research (Chevron), Magnolia (Mobil), Texaco,

Schlumberger, and Shell were aimed at characterizing reservoir rocks (porosity and permeability) and fluid

content at laboratory scale. Soon downhole logging tools which relied on the earths magnetic field for

nuclei polarization were developed, but due to a number of shortcomings (low reliability and operational

limitations, such as high power consumption and low signal-to-noise ratio) did not achieve a wide

acceptance in the petroleum industry (Dunn et al. 2002).

Development of NMR tools for the petroleum industry was halted until the early 90s, when NUMAR

introduced its MRIL logging service which could accurately predict reservoir permeability (Coates et al.

1999). The technology has been improving continuously since then and NMR measurements have beensuccessfully deployed by the Oil majors to measure a wide range of parameters (Steinberg & Cohen 1984;

Coates et al. 1999; Bedford et al. 2000):

Mineralogy-independent porosity;

Water saturation and irreducible water saturation;

Permeability;

Hydrocarbon characterization;

Pore size distribution and geometry;

Residual oil estimation;

Mineralogy typing.


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2.2 Nuclear magnetism: The magnetic nucleus

The application of Nuclear Magnetic Resonance techniques requires the understanding of the nucleis

behaviour when subjected to an externally generated magnetic field. In order to achieve that, two inherent

characteristics belonging to nuclei must be introduced: nuclear magnetism and nuclear angular

momentum .

The first concept governing the behaviour of the nuclei in this field of study is angular momentum , or spin .

Protons and Neutrons have angular momentum. If the number of Protons and Neutrons in a nucleus is the

same, the spins cancel each other out and the net spin of the nucleus will be equal to zero. However, in an

unbalanced nucleus (where the number of protons differs from the number of neutrons) a resultant spin,

denoted by the letter J will be observed. Despite the name, spin in quantum physics is not the same as

the angular movement of a classical object, i.e. the spinning of a billiard ball. Elementary particles simply

have spin and it should be regarded as one of the fundamental characteristics of an elementary

particle along with charge, mass and magnetism (Levitt 2008).

Secondly, nuclei have magnetism and therefore can be modelled as a magnetic dipole, with north and

south poles. Much like a compass needle, nuclei tends to align with any external magnetic field when

subjected to it. The magnetic moment found in unbalanced nuclei is also referred to as the associated

magnetic field , since its existence depends on the charged particles in the nuclei and the angular

momentum .

Figure 1 - Magnetic and angular momentum of a hydrogen nucleus. Adapted from Coates et al. (1999)


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The angular moment and associated magnetic moment are intrinsic characteristics of each different

element. Since these two vectorial quantities are parallel to each other, they can be related by a constant,

which is called the gyromagnetic ratio :

=

(1)

Where

y=Gyromagnetic ratio;

= Magnetic moment;

J=Angular moment.

The gyromagnetic ratio y is therefore a measure of the strength of the nuclear magnetism (Coates et al.

1999). For the hydrogen nucleus, y=42.58MHz/Tesla.

2.3 Precession

The vectorial sum of these two forces acting on a nucleus and the torque imposed by an external magnetic

field B0 will generate a movement known as precession : Instead of simply aligning its own magnetic field

parallel to the external field, the nucleis field will precess around the lines of the field it was subjected to.

The angular velocity of this precession is governed by the gyromagnetic ratio , and the strength of the

external field B 0:

Figure 2 - Precession of a single spin. Adapted from Coates et al.(1999)


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In this case we are still interested in assessing the hydrogen nuclei, but since we know the strength of B 0 as

a function of distance from the tool surface, we can predict the Larmor frequency of the hydrogen nuclei as

a function of investigation depth. Hence we can focus our investigation to the desired distance from

the tools surface, avoiding the influence of the drilling fluid in the measurement by reading deep into the

formation.

2.4 Measuring magnetization

As stated previously, nuclei that have angular momentum and associated magnetic momentum such as

hydrogen will align with an external field when subjected to it. Counter intuitively though, not all nuclei

align parallel to the external field; some nuclei will assume the antiparallel orientation. This will lead to the

observation of two different quantum states: If the nucleus follows the orientation of the external field, it is

in the preferred, low-energy state. The nuclei which have their precessional axis aligned anti parallel to the

external field B 0 are in the high-energy state.

Figure 4 - Alignment of spins magnetic fields with B 0. Adapted from Coates et al. (1999)

When a large number of nuclei are subjected to a magnetic field though, most of them will orient parallel

to the external field (as mentioned previously, the low-energy state is preferred). The vectorial sum of the

individual nuclei magnetic fields is called bulk magnetization and denoted by M 0. The bulk magnetization of

a sample subjected to a B 0 field can be calculated by (Coates et al. 1999):


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0= 22( + 1 )3(4 2) 0 (3)Where:k = Boltzmanns constant;

T = absolute temperature (Kelvin);

h = Plancks constant;

I = the spin quantum number of the nucleus.

The equation above tells us that the resulting M 0 is directly proportional to the number of protons

subjected to the field (N), the spin number of the nuclei (which is element dependent) and to the

magnitude of the external field B 0 applied to the subject; being inversely proportional to the absolute

temperature.

2.5 T1 Longitudinal relaxation time

The alignment of the nucleis magnetic field to the external one is not immediate though. The resulting M 0

grows at an exponential rate, and its magnitude as a function of time is described by:

( ) = 0(1 1) (4)Where:

t = Time of exposure of nuclei to B 0;

Mz(t) = Magnitude of magnetization at time t projected on the z direction;M0 = Maximum nuclei associated magnetism achieved by the application of a given field.


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Figure 5 - Longitudinal relaxation: T 1. Adapted from Dunn et al. (2002)

The time T 1 is known as the longitudinal relaxation time . It represents the time elapsed between the

application of the external field B 0 and the moment when the net magnetization M z(t)reaches 63% of the

net magnetizations equilibrium value, M 0. At 3T1, 95% of M 0 is reached.

As seen from the picture above, the decay of the induced magnetic field M 0 when the external field (heredenoted by H) is turned off is governed by the same exponential decay. In this scenario, T 1 is interpreted as

the rate of relaxation of the protons. The interaction of the nuclear moment with the electric and magnetic

fields created by thermal motion in the lattice stimulate the transition between the magnetic energy levels

(during the relaxation, from low to high energy level), by absorbing energy to or from the surroundings

(Dunn et al. 2002). This process, called spin-lattice relaxation, eventually leads to thermal equilibrium

(M0=0).

T1 is an important parameter in NMR logging as it and indicates how effectively the energy of the spin

system is transferred to or from its surroundings (Dunn et al. 2002; Vevle 2011), reason it is also called

spin-lattice relaxation. T 1 can be used for instance, for differentiating between oil, water and gas in a

reservoir and for hydrocarbon characterization.


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2.6 T2 and T 2* Transversal relaxation times

So far, we learned that when hydrogen atoms are placed under the influence of a magnetic field, they will

tend to align with it (either parallel or anti-parallel to it), their axis precessing around the external fields

axis. This is only the first step though in the nuclear magnetic resonance measurement. In fact, at this stage

we merely aligned the magnetic moment of the nuclei with an external field, no resonance was observed.

Figure 6 - Nuclear magnetization M 0 aligned with external applied field B 0. Adapted from Coates et al.(1999)

It is important to remember that even though we are focusing our study on the hydrogen nuclei, all

elements present in the sample which have angular and magnetic moment will be aligned with the external

field, each one of them precessing at their specific Larmor frequency.

Resonance of the nuclei is achieved by placing an electric coil orthogonally to the main external field B 0 andapplying an alternating current to it. This will generate a radio frequency wave with the same frequency of

the AC current applied. This new orthogonal field will interact with the resulting nuclei field M 0, generating

a torque that will cause small variations in direction of the axis of the spinning nuclei and its magnetic field.

Resonance and the actual deflection, or tipping of the magnetic field though will be only achieved by the

nuclei that spin with the Larmor frequency equal to the frequency of the wave generated by the orthogonal

coil.


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To illustrate the concept of resonance in a simple way, we can use an example belonging to the two

dimensional plane. Imagine the movement of a pendulum, or a child in a swing: I we apply a periodic force

to the weight of the pendulum at twice the frequency of the swing (which might prove difficult); the

amplitude of the movement will not change. Well only cause small variations in the position of the

pendulum as a function of time. If we apply this torque in resonance with the natural frequency of the

pendulum though, well see that the amplitude of the movement is amplified, meaning that the system is

capable of receiving energy in that particular frequency.

The tipping of M 0 is analogue to the one described above: by the application of a second, oscillating

external field at the Larmor frequency of the nuclei, the nuclei that precess around the external field B 0 will

have its oscillating movement amplified by the resonating torque induced. The strength of the second field

B1 is much smaller than M 0, so the module of the magnetization depends solely on the main external field

B0.

Another important effect of the application of the RF wave is the synchronization of the spins: Not only will

they rotate at the same frequency; theyll be forced to stay in phase with each other.

The angle between the axis of the spins and B 0 will increase according to the following formula:

Where:

= tip angle (degrees);

B1 = Amplitude of oscillating field;

= time of over which B 1 is applied.

= 1 (5)

Figure 7 - 90 o tipping of M 0 to xy plane.Adapted from Dunn et al. (2002)


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Eventually, when reaches 90 o, M 0 will be found entirely on the xy plane. In NMR terminology, angular-

pulse terms such as a pulse (or 180 pulse) and a /2 pulse (or 90 pulse), refer to the oscillating

fields pulse that causes the magnetization M 0 to be tipped by 180 or 90 .

Once the application of B 1 ceases the spins magnetic axis will realign with the z axis, under the influence

of B0 returning the angle to its original value.

Concurrently, the transversal magnetization (The xy component of M 0) will start decaying. The decay in the

transverse plane is called free induction decay (FID) or T 2*. In an ideal situation where B 0 is perfectly

homogeneous and there is no interaction between the individual spins, T 2 and T 2* would be equal to T 1, but

experience tells us that this decay is very shorta few tens of microseconds.

This increased rate of the T 2* decay is explained by the loss of phase coherence between the spins, caused

by two distinct contributions. So far we considered B 0 to be homogeneous, which is in practice

unachievable. In fact, the slight distortions in the applied field B 0 will lead the spins to precess at marginally

different speeds according to equation 2. Because of the tremendous speed of the precession, a small

variation in the strength of the magnetic field will have a significant impact in the measurement of

transversal relaxation. Considering a magnetic field strength of 1 Tesla, a 0.0001% difference between two

regions of the static field causes the precession of two spins in these regions to be dephased by 180

(therefore cancelling teach others contribution to the module of M 0 in the xy plane) in about 10 ms (Dunn

et al. 2002; Vevle 2011).

Figure 8 - Free induction decay. Notice that M 0 is measured on the transversal plane from the main external field B 0. Adapted fromDunn et al. (2002)


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Figure 9 -The xy component of M 0 will decay with time and the z component will be restored. The amplitude decay in the

transverse plane is called free induction decay (FID) or T 2*. This decay is usually exponential and is very shorta few tens of s .

(Adapted from http://www.revisemri.com/questions/basicphysics/fid)

The second effect has to do dissipating of phase coherence trough the direct interaction between nuclei.

Each nuclear spin experiences not only the main applied magnetic field (partially shielded by the electron

cloud), but also local magnetic fields generated by other magnetic nuclei in the immediate environment.

These local fields are time-varying due to the relative motion in the liquid phase and will slightly distort the

main magnetic field B 0. This will lead to position and time dependent shifts in the Larmor frequency of the

spinning nuclei and will lead to further loss of phase coherence (Freeman 2004).

In order to neutralize the influence of dephasing caused by magnetic inhomogeneity in B 0 on the

measurement of transverse relaxation, a series of pulse sequences were designed to compensate for that

effect.

2.6.1 Hahns Sequence

We saw that immediately the tipping of M 0 on the xy plane, the spins of the nuclei will precess at different

speeds and the resulting loss of phase coherence quickly destroys the transverse signal. It is important to

notice though that the main cause of the inhomogeneity of B 0 is not time dependent: it simply arises from

the difficulty in generating an ideal homogeneous field, nevertheless B 0 is static.

Figure 10 Dephasing of magnetic resultant M 0 in the transversal plane. (Adapted drawing by AG Filler - copyright: GDFL

1.3/CCASA 3.0, image source: http://en.wikipedia.org/wiki/File:Spin_Echo_Diagram.jpg).


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Now, lets suppose that after an elapsed time , another orthogonal RF pulse is applied, this time tipping

the magnetization vector M 0 by 180o. Well observe that the spins that were rotating at a lower angular

velocity (or Larmor frequency) and were lagging behind will actually be in front of the faster spins now that

the direction of the rotation was reversed. After the chosen time has passed since the application of

the 180 o pulse, the spins will come in phase again, and a magnetization vector on the xy plane will

observable once more. This resurgence of the magnetization vector in xy is referred to as the spin echo or

Hahns echo. The discovery of the spin echo by Edward Hahn in 1950 may be regarded as the birth of

modern pulsed NMR (Levitt 2008).

Figure 11 Rephasing of M 0 in the transversal plane at 2 achieved by the application of an 180o pulse at time . (Adapted

drawing by AG Filler - copyright: GDFL 1.3/CCASA 3.0, image source: http://en.wikipedia.org/wiki/File:Spin_Echo_Diagram.jpg).

2.6.2 CPMG Sequence

The CPMG sequence, named after its inventors Carr, Purcell, Meiboom, and Gill is a development on the

Hahns sequence. While Hahn applied one 180 o pulse after a time elapsed and read the amplitude of

the transversal field at 2 (both times refer to the tipping of the magnetization), the CPMG sequence

repeats this 180 o pulse several times with intervals being always multiples of 2 . With the train of

echoes resulting from the CPMG sequence, we can infer the time constant at which the transverse

magnetization happens. The amplitude of the spin-echo train at time t, which is the amplitude of the

transverse magnetization M x(t), can be fitted to a sum of exponential curves (Coates et al. 1999):

( ) = ( 0 1) (6)


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Figure 12- Exponential decay curve (in blue) fitted to a spin-echo train. Adapted from Coates et al. (1999)

It is important to notice that only the dephasing effect provoked by the inhomogeneity of the field will be

cancelled. The amplitude of the echo of M 0 will be lower than the initial value of transverse magnetization

due to dephasing resulting from molecular interactions and diffusion.

The T2 decay from the formation contains most of the petrophysical information obtainable from NMR

logging and therefore is the prime objective of NMR logging measurements (Coates et al. 1999).


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3 Materials and methods

3.1 Solids

A total of 52 samples were prepared for the experimental procedure. The solids in the sample consisted of

crushed outcrop chalk samples corresponding to the surface area of 1m 2, 2m 2, 5m 2 and 10m 2. The surface

area for the chalk was calculated by weight, using the results from the BET test that indicated a specific

surface area of 1.6m 2/g:

( ) = ( 2)

(

2)

(7)

Table 1 Calculation of weight of crushed chalk used in samples

The outcrop chalk was collected in the Stevns Klint, outside Copenhagen, and its calcium carbonate content

was measured to be higher than 99% . The main intrusions found in this chalk consist of clay, namely iliteand smectite. Even though clay dominates measurements of the internal surface area of some soils and

rocks it appears not to play a major role in determining the surface-mediated NMR relaxation rates of rocks

(Foley et al. 1996). This fact was corroborated in the work of Alam et al. (2010), when even large surfaces of

kaolinite had little or no effect on relaxation profile of different solutions when added to them.

3.2 Solutions

The brines used to flood the solid samples consisted of calcium chloride, sodium chloride, magnesium

chloride and sodium sulfate solutions. The solutions were prepared using calcite equilibrated water and

had the same ionic strength [1.83mol dm -3]. These were labelled the high concentration solutions and

were then dissolved by 10 and 100 times, creating the medium and low concentration solutions

respectively.

Chalk1 2 5 10

Weight (g) 0.625 1.25 3.125 6.25

Specific Surface (m2)


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Tests were also performed using de-ionized water. For the equilibrated calcite solution (used to prepare

the high concentration samples) 24ppm of synthetic CaCl 2 [10 microns, 98%] were used. To achieve that

concentration, the solution remained on the stirrer until the calcite concentration indicated that it was

equilibrated (Katika et al. n.d.).

The amplitude of the spin-echo train is proportional to the number of hydrogen nuclei associated with the

fluids in the pores within the sensitive volume (Coates et al. 1999). It would be interesting to achieve

exactly the same amount of water in each sample then, since we would be able to compare not only the

relaxation time, but also the influence ions might have on the amplitude of the measured signal.

It was also noticed by Alam et al. (2010) that the cumulative amplitude of the T 2 distribution is an

indicative of the number of hydrogen atoms found in the solution. In fact, according to the manufacturer of

the NMR equipment, performing the integral of all the T 2s (area under the curve) gives us the total porosity

when compared to the signal from a known reference ((Oxford Instruments Magnetic Resonance) & (Green

Imaging Technologies) 2012), corroborating Alams findings since NMR porosity is based on the hydrogen

content of the porous medium.

The liquid parcel of the sample then was measured to have exactly the same amount of hydrogen atoms for

every test tube. This was achieved by calculating the density of each solution and making sure that the base

solution (water) content was the same for each sample, regardless of concentration of the brine or weight

of the specific salt.

Table 2 - Nomenclature of prepared samples

676.5 6765 67650 676.5 580 5800 1000.0 10000 100000 865.0 8650 865001 CaL01 CaM01 CaH01 MgL01 MgM01 MgH01 NaL01 NaM01 NaH01 SO4L01 SO4M01 SO4H012 CaL02 CaM02 CaH02 MgL02 MgM02 MgH02 NaL02 NaM02 NaH02 SO4L02 SO4M02 SO4H025 CaL05 CaM05 CaH05 MgL05 MgM05 MgH05 NaL05 NaM05 NaH05 SO4L05 SO4M05 SO4H05

10 CaL010 CaM010 CaH010 MgL010 MgM010 MgH010 NaL010 NaM010 NaH010 SO4L010 SO4M010 SO4H010

Na2SO4Samples nomenclature

Surfacearea (m)

Brine CaCl2concentration

MgCl2 NaCl


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3.3 Assembly and preparation of the sample.

To assemble the test material, a digital scale (model Toledo PR503 - readability: 0,001g, repeatability:

0.0005 g) was used to measure the weight that corresponded to the desired area of chalk and volume of

solution for each sample. The chalk was dried at a temperature of 60 oC to ensure no humidity was present

in the sample. Two ways of assembling the sample were tested: by adding the solution and later the solids

and the inverse. It was noticed that when the solution was added prior to the addition of the solid parcel

there was a larger number of bubbles contained within the sample, even after its mixing by ultrasonic

agitation. The second procedure (addition of solids and then solution to the test tube) was chosen.

After assembly the samples were agitated for two cycles of 15 min each on the ultrasonic shaker (Model

Elma Transsonic T-310, 30W, 35 kHz), sealed and kept inside a refrigerator for 3 days. Prior to the NMR test

sequence, the samples went through the agitator once more and left to rest until the chalk had completely

settled and sample was at room temperature, around 25 oC. They were then placed in the oven at a

temperature of 30 oC for one hour to reach the working temperature of the NMR hardware. Once in place,

the sample rested for 30 more minutes and finally the tests commenced.


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4 Design of the NMR experiment

Prior to the start of the battery of tests a comprehensive investigation was done to investigate the optimal

acquisition parameters for the tests. The research was focused on the following:

-RD (recycle delay);

-NECH (number of echoes);

-TAU = TE/2 (Time between 180 o pulses);

-NS (number of scans determine the number of acquisitions to be stacked).

Figure 13 CPMG sequences displaying tipping pulses, RD, TW and TE. Adapted from Coates et al. (1999)

4.1.1 Recycle delay

The recycle delay controls how long one scan of the acquisition will take, and therefor will dictate indirectly

for how long the system will be idle. A correct setting of RD is crucial to re-polarize the sample after the

echo train was acquired. The permanent field B 0 will re-establish the resultant nuclear magnetic field M 0

aligned with the z axis in the interval RD-(TE x NECH). If TW=RD-(TE x NECH)


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To select a RD time that allows for the stabilization of M(t) at is maximum value (M 0), the NMR equipment

was set for continuous acquisition (by entering GS on the acquisition command line of the software

RiNMR) and the calculated signal-to-noise-ratio was observed. The RD time is then slowly increased while

the acquisition is still running, causing the SNR to increase, since M(t) increases with time and the noise

level remains unchanged. When the SNR stabilizes (does not increase with an increase in RD), we have

reached the plateau in M(t).

Figure 14 Influence of choice of recycle delay on initial signal amplitude. Adapted from Coates et al. (1999)

4.1.2 Number of echoes and TAU

Looking at figure 6 we can see that the timespan of the acquisition phase is determined by the number of

echoes recorded (NECH) times the interval between the 180 o pulses (TE). Early inversion results showing

the T 2 distribution determined that the free fluid has a very long decay time, of around 3s, while the peak

related to the fluid bound to a mineral surface would lie around the time of 200ms.

The choice of the number of echoes was not a restraint in this case (a larger number of echoes would

increase the time for each experiment, which was not a concern), the focus was in selecting the TAU that

best described the sample. Generally in a NMR experiment, the TAU is set to a time as low as possible, in

order to represent the faster decays associated with small pore sizes (which is the case, for example, when

analysing shale). When testing the crushed chalk sample though, it was soon observed by analysing the T 2

relaxation distributions that the saturated crushed chalk sample could be properly described by relatively

large TAU spacings as seen on figure 15, and that the solutions output peak was consistent with a mono

exponential decay.


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After observing that our powder packs presented little variation in pore sizes (in opposition to a

heterogeneous core for instance) and the regime was surface-limited (as opposed to diffusion-limited), the

TAU that outputted the narrowest T 2 probability distribution peak for the bound water was chosen as the

most representative of the system. This corresponded to the TAU spacing of 200s and departing from this

value (either diminishing or increasing it) would generate a wider probability distribution of the T 2 peaks,

associated with lower signal-to-noise rations.

Figure 15 T 2 distribution for a de-ionized water saturated chalk with different TAU settings.

Determined in conjunction with the TAU parameter, the number of echoes (NECH) has to be large enough

so the whole decay in transverse magnetization is captured. The acquisition phase of the experiment itself

is dictated by the time between echoes (2xTAU) and the number of echoes recorded (NECH), so the

product of this two parameters should be a time longer than the relaxation of the transverse magnetic field

itself. The NECH value is set as a power of 2 (1024, 1048, 4096) and for the presented experiments was

fixed to 32.768 echoes.

Below, figures 16 and 17 presents the output from a test performed with the suggested parameters: By

choosing sensible values for TAU and NECH, the whole transverse relaxation interval is recorded (figure 16)


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Contrasting with the first scenario, in figures 18 and 19 the time set for the acquisition (2xTAUxNECH) is not

long enough to record the whole decay of the transverse magnetization curve (notice that on figure 18 the

y axis still marks 45000 counts by the end of acquisition). The resulting inversion (figure 20) fails to depict

the sample tested.

Figure 19 The resulting inversion is compromised since the measurement time was shorter than the relaxation time itself.

(Capture from Distribution window from Resonance Instruments Ltd. WinDXP, ver. 1.8.1.0)

4.1.3 Number of Scans

Number of scans (NS) refers to the number of times the CPMG sequence will be repeated within an

experiment. The waves from successive scans are then stacked, increasing the signal from the sample

(coherent amplitudes) while keeping the noise at low levels (non-coherent amplitudes).

While most of the literature on the topic of NMR T 2 relaxation experiments set a constant value for the

number of scans taken (Alam et al. 2010; Foley et al. 1996; Hum & Kantzas 2006), it was decided to aim for

a constant signal-to-noise ratio for the results presented. When performing distributed exponential

analysis, it is more important to acquire data to a specified signal to noise ratio than to a fixed number of

scans in order to make a consistent comparison between data sets ((Oxford Instruments Molecular

Biotools), 2006a). In order to understand the correlation between the number of scans and the resulting

signal-to-noise ratio an experiment proposed by Dr. Alexander Sagidullin (NMR Specialist at Oxford

Instruments) was setup. It consisted of the following steps:


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1. A NMR tube filled with the porous material up to a height of 50mm (correspondent to the active

measurement area of the NMR equipment where B 0 is homogeneous) was prepared and saturated with

de-ionized water. The sample was agitated in the ultrasonic shaker for 2 periods of 15 minutes and

conditioned in the oven for one hour at 30 oC. Before the test, the sample was left to rest in the NMR

machine for 30 minutes.

3. CPMG parameters were adjusted to the test conditions (P90 and P180, TAU, NECH, dwell time, receiver

gain), making sure at least 15 to 25% of the data acquired represented noise.

4. The test was run with the sample in place and several different numbers of scans (4, 8, 16, 32 and 64).

For each test, the amplitude of the signal was recorded. In between the tests with the sample, tests with

the same NS were recorded without the sample in place in order to assess the magnitude of the noise.

5. To get the signal-to-noise ratio for each number of scans (NS), the ratio Signal/Noise was calculated.

This is achieve by measuring the amplitude of the signal of the test performed with the sample (Signal) and

the amplitude of the test performed without the sample (Noise) on the software RINMR by typing SIZE on

the process command line.

6. By plotting the results as NS vs. SNR, we encounter proportionality between number of scans and SNR in

the format . , where the parameter 'a' is characteristic of the hardware and will be constant for

all samples. This value was found to be equal to 0.5 as seen on figure 20.

Figure 20 Plot of Signal-to-noise ratio as function of number of scans.


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To predict NS for a particular sample, an initial SNR(NS) is needed, achieved by running a pre-test with a

limited number of scans, for instance NS=4, by repeating steps 4 and 5. The values are then entered in the

formula:

= ( )( )0.5 2 (8)

Where:

SNR(x) = Signal-to-noise ratio desired;

x = Number of scans needed to achieve the desired signal-to-noise ratio (SNR(x));

SNR(y) = Signal-to-noise ratio calculated from a pre-test of the sample (usually with limited number of

scans);

y = Number of scans of the pre-test.

In order to appreciate the impact the signal-to-noise ratio will have on the version results, two samples

were tested. Each of these samples went through four tests, using different number of scans, leading to

results portraying different SNR levels:

Figure 21 - Sample "a": 1m2 of chalk in 10ml of de-ionized water.


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Figure 22 - Sample "b": test tube filled with chalk fully saturated in de-ionized water

It is clearly observable from figures 21 and 22 that a lower signal-to-noise ratio leads to an artificial

broadening of the T 2 distribution, fact also highlighted by Foley et al. (1996) in his work.


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5 The inverse problem

On the previous item of this report, design of the NMR experiment, we saw that the final product of the

NMR measurement is usually not the transversal relaxation curve itself. The T 2 decay, which is modelled as

a sum of several exponential functions (equation 6), is in a way a measurement derived from a physical

system that we are trying to describe. The physical quantity sought after in our case is the relaxivity for

each hydrogen nucleus contained in the sample, directly linked to their relaxation times. The equation 9

describes continuous distribution of exponentials for a CPMG experiment ((Oxford Instruments Molecular

Biotools) 2006a).

= /=1 (9)And to determine the amplitudes f j (which represents the T 2 distribution) from the amplitudes g 1 (the NMR

data), we should attempt to minimize the following function ((Oxford Instruments Molecular Biotools)

2006a):

( / )2=1 (10)

Which describes the difference or error between the measured and the fitted data.

The conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-

posed problem though. An ill-posed problem is one in which at least one of the following conditions apply

(Saunders et al. 2013):

- It does not have a solution;

- The solution is not unique;

- A small perturbation of the problem may cause a large change in the solution.


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5.1 Regularization

According to Mosegaard (2012), the NMR inverse problem can be considered ill-posed or mixed-

determined, since it is characterized by innitely many (usually) inexact solutions. This occurs because

the minimization algorithm does not discern between noise and actual data that represents the system and

therefore tries to fit the noise in the solution function. When dealing with this kind of problem, it is

common to place some kind of physical constraint on the solution based on a priori knowledge about

the nature of the system we are trying to describe (Dunn et al. 2002). One such constraint is the belief

that the function f j (that describes the system) should be reasonably smooth. In order to achieve a

smooth and well-posed solution, a linear combination of functions in the form 2=1 is added toequation 10 in a process known as regularization ((Oxford Instruments Molecular Biotools) 2006a):

( / )2+ 2=1=1 (11)Here, the first term is the so- called mist between the observed data gi and the computed data, and is a

weighting factor determining the relative balance between the mist and the squared model norm (the

second term) (Mosegaard 2012). If is small, minimization of the data t will have rst priority. A too small

value of though may induce the generation of spurious peaks in the T 2 distribution, since the function

would be reduced to Equation 10, which is the original ill-posed problem. The other case, where is too

large, minimization of the misfit term will be the priority and the data we are trying to fit will be lost. This

would translate as a flatter distribution in T 2, artificially broadening the relaxation times ((Oxford

Instruments Molecular Biotools) 2006a).

5.1.1 Weight

As mentioned previously, the correct choice of the regularization weight is indispensable in order to obtain

a T2 distribution that represents the physical system it represents. On a simple system as the one studied, a

homogeneous powder pack saturated in de-ionized water or brine, the expected output of the inversion

would be two independent relaxation peaks. One peak would display the water bound to the solid powder

with a faster relaxation and the free fluid would be portrayed at the end of the scale, as seen on the works

of Chen et al. (2006) and Foley et al. (1996). On figures 23, 24 and 25, we can see examples on how the

weight affects the result of the inversion:


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Example A: Besides the two expected peaks representing the bound and free fluid we can clearly

see inversion artefacts as highlighted on the figure.

Figure 23 Example A: CaM10 weight 0.01 (Capture from Distribution window from Resonance Instruments Ltd. WinDXP,

ver. 1.8.1.0)

Example B: By choosing =0.5 the peaks to the left of the bound fluid are smoothened out, as

noise generating the artefacts was suppressed by the weighing factor.

Figure 24 Example B: CaM10 weight 0.5 (Capture from Distribution window from Resonance Instruments Ltd. WinDXP, ver.

1.8.1.0).


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Is important to point out though that the peak referring to the free fluid, to the right on the plot, was

broadened and had its amplitude diminished. The T 2 distribution is actually a probability distribution and

we can affirm that the increase in made the data linked to the free fluid relaxation less certain. Since our

focus is on the study of variations in bound fluid though, this was considered the optimal inversion result.

Example C: By performing the inversion with =5, we can observe that part of the signal is

suppressed and both peaks (bound and free fluid) are smoothened out and merged. By

inadvertently applying a too high weight, important nuances in data are overseen.

Figure 25 - Example C: CaM10 weight 5 (Capture from Distribution window from Resonance Instruments Ltd. WinDXP, ver.

1.8.1.0).

The software used to perform the inversion, WinDXP, is able to calculate automatically the regularization

factor based on a calculated signal-to-noise ratio. However, for high signal-to-noise ratios the weight

determined by the software might be too small, leading to the generation of spurious peaks in the T 2

distribution (Oxford Instruments Molecular Biotools) 2006a). In order to select a sensible value for the

weight used in the inversion, the criteria suggested by the software manual was followed: the weight is set

to a high value (the adopted was set to 5), and slowly decrease until an appropriate value is obtained,

meaning the result of the inversion can appropriately describe the physical system contained in the sample.


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5.2 Pruning

Calculating the inverse problem has an extremely high computational cost due to the large amounts of data

handled (an N by N matrix, where N is equal to the number of data points acquired) and number of

iterations performed. The software used for the inversion, WinDXP (distributional exponential analysis),

prunes the data acquired, to a maximum of 512 points, thus handling a 512x512 matrix.

The pruning function can select individual data points (discarding the rest of the data) or select an average

of all the data point contained in an interval. The spacing in between the point selected can be either linear

or logarithmic (figures 26 and 27 respectively):

Figure 26 - Linear pruning interval - a single point per interval is sent to the inversion routine.

Figure 27 - Logarithmic pruning interval - a single point per interval is sent to the inversion routine. Data in the beginning of

interval is more densely represented.


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In order to minimize the influence of noise in the signal, the option that promotes averaging within an

interval was chosen. The interval was set to logarithmic since the interval of most interest of the data

acquired lies in the early stages of the decay (which describes the decay linked to the fluid bound to the

mineral surface).


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6 Results

The results from the tests performed in the form of the T 2 relaxation distributions are presented in thissection. T 2_peak for different salinities and specific surfaces were calculated for each sample and compared

against the T 2_peak of a common standard (crushed chalk saturated in water). In this way, we can compare

the effectiveness of each brine (and concentration) in promoting changes in the solid-fluid interface.

A plot with the bound fluid for each sample (varying with specific surface and concentration) is also

presented. The samples were acquired with different number of scans (in order to attain similar signal-to-

noise ratios), so the amplitudes of the peaks in the T 2 distribution and the area below the curves varied

between samples (they are both directly proportional to the number of scans stacked in the acquisition

phase). It was mentioned previously though that the amplitude of the spin-echo train and the area below

the T 2 distribution curve is proportional to the number of hydrogen nuclei in a sample ( Materials and

Methods Solutions ). Since the samples were prepared to have exactly the same amount of water (and

therefore hydrogen nuclei), we were able to normalize the integral of the T 2 distribution and directly

compare the values corresponding to the bound and free fluid for different samples.

In order to assess relaxivity in the tested samples, the general relaxivity formula was used (Equation 12).

The last term of the equation, linked to relaxation by diffusion was assumed negligible. Isolating the

relaxivity term, we have Equation 13.

1

2, =1

2, ++( )2

12

(12)

= 12,

12, , (13)Where:

= Relaxivity ( m/s);

V = Pore volume (m 3);

S = Surface area (calculated by BET m 2);


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T2,bound and T 2, bulk = Time of peaks associated with bound and free fluid in the T 2 relaxation distribution.

The pore volume was calculated by measuring the height of the chalk powder column in the container and

calculating the volume it ocupated. The volume of the grain was calculated by dividing the measuredweight of each sample by the known density of calcite, 2.71g/cm 3.

The parameters used for the NMR acquisition and inversion of the raw data, which are in fact the main

focus of this report are presented in the tables below:

Table 3 - Optimized acquisition parameters

Table 4 - Optimized inversion parameters

TAU SNR* Recycle Delay NECH(s) n/a (s) n/a200 300 30 32768

Acquisition parameters

mode averaging number of points set manually valuelog yes 511 yes 0.5

Pruning

Inversion parameters

Weight

*Number of scans were changed accordingly to fit condition SNR=300


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6.1 Calcium chloride brine:

6.1.1 Surface area: 2m 2

Figure 28 T 2 relaxation distribution. CaCl 2 brine, 2m2 specific surface.

Table 5 Shift in T 2_peak and T 2_bulk for low, medium and high brine concentrations compared to a standard. CaCl 2 brine, 2m2

specific surface.

Sample DW02measured measured % change measured % change measured % change

Surface area (m) 2 2 0.00% 2 0.00% 2 0.00%concentration (ppm) n/a 676.5 n/a 6765.0 n/a 67650.0 n/a

T2_peak (s) 2.83E+05 3.18E+05 12.17% 3.04E+05 7.41% 2.32E+05 -18.05%T2_bulk (s) 3.72E+06 3.95E+06 6.32% 3.57E+06 -3.93% 3.39E+06 -8.85%

CaL02 CaM02 CaH02


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specific surface.



T2_peak (s) 3.31E+05 2.83E+05 -14.54% 2.88E+05 -13.07% 2.78E+05 -16.04%T2_bulk (s) 3.82E+06 3.88E+06 1.52% 3.62E+06 -5.24% 3.20E+06 -16.19%

CaL05 CaM05 CaH05


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specific surface.

Sample DW010

measured measured % change measured % change measured % changeSurface area (m) 10 10 0.00% 10 0.00% 10 0.00%

concentration (ppm) n/a 676.5 n/a 6765.0 n/a 67650.0 n/aT2_peak (s) 3.15E+05 2.82E+05 -10.57% 2.97E+05 -5.72% 2.65E+05 -16.07%T2_bulk (s) 3.69E+06 3.86E+06 4.57% 3.58E+06 -2.89% 3.02E+06 -18.18%

CaL010 CaM010 CaH010


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6.1.4 T2 Relaxation time (CaCl 2 brine)

Figure 31 - T 2 Bound fluid peak times vs. brine concentration CaCl 2.

6.1.5 Surface relaxivity (CaCl 2 brine)

Figure 32 Calculated relaxivity vs. brine concentration CaCl 2.


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Figure 34 T 2 relaxation distribution. MgCl 2 brine, 5m2 specific surface.

Table 9 Shift in T 2_peak and T 2_bulk for low, medium and high brine concentrations compared to a standard. MgCl 2 brine, 5m2

specific surface.

Sample DW05

measured measured % change measured % change measured % changeSurface area (m) 5 5 0.00% 5 0.00% 5 0.00%concentration (ppm) n/a 580.0 n/a 5800.0 n/a 58000.0 n/a

T2_peak (s) 3.31E+05 2.34E+05 -29.39% 2.05E+05 -38.09% 1.92E+05 -41.83%T2_bulk (s) 3.82E+06 3.62E+06 -5.17% 3.61E+06 -5.62% 3.46E+06 -9.32%

MgL05 MgM05 MgH05


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Figure 35 T 2 relaxation distribution. MgCl 2 brine, 10m2 specific surface.

Table 10 Shift in T 2_peak and T 2_bulk for low, medium and high brine concentrations compared to a standard. MgCl 2 brine, 10m2

specific surface.

Sample DW010


T2_peak (s) 3.15E+05 2.31E+05 -26.63% 1.98E+05 -37.24% 1.82E+05 -42.17%T2_bulk (s) 3.69E+06 3.75E+06 1.50% 3.48E+06 -5.72% 3.58E+06 -3.07%

MgL010 MgM010 MgH010


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6.2.4 T2 Relaxation time (MgCl 2 brine)

Figure 36 - T 2 Bound fluid peak times vs. brine concentration MgCl 2.

6.2.5 Surface relaxivity (MgCl 2 brine)

Figure 37 Calculated relaxivity vs. brine concentration MgCl 2.


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6.3 Sodium chloride brine


Figure 38 T 2 relaxation distribution. NaCl brine, 2m2 specific surface.

Table 11 Shift in T 2_peak and T 2_bulk for low, medium and high brine concentrations compared to a standard. NaCl brine, 2m2

specific surface.



T2_peak (s) 2.83E+05 2.65E+05 -6.31% 2.55E+05 -10.13% 2.42E+05 -14.58%T2_bulk (s) 3.72E+06 3.74E+06 0.58% 3.84E+06 3.27% 3.98E+06 6.97%

NaL02 NaM02 NaH02


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specific surface.

Sample DW05


T2_peak (s) 3.31E+05 2.92E+05 -11.87% 2.93E+05 -11.35% 2.83E+05 -14.47%T2_bulk (s) 3.82E+06 3.78E+06 -1.14% 3.88E+06 1.42% 4.00E+06 4.71%

NaL05 NaM05 NaH05


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specific surface.

Sample DW010



NaL010 NaM010 NaH010


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6.3.4 T2 Relaxation time (NaCl brine)

Figure 41- T 2 Bound fluid peak times vs. brine concentration NaCl.

6.3.5 Surface relaxivity (NaCl brine)

Figure 42 Calculated relaxivity vs. brine concentration NaCl.


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6.4 Sodium sulfate brine


Figure 43 T 2 relaxation distribution. Na 2SO4 brine, 2m2 specific surface.

Table 14 Shift in T 2_peak and T 2_bulk for low, medium and high brine concentrations compared to a standard. Na 2SO4 brine, 2m2

specific surface.



T2_peak (s) 2.83E+05 3.01E+05 6.24% 2.84E+05 0.10% 2.61E+05 -7.91%T2_bulk (s) 3.72E+06 3.98E+06 6.97% 3.84E+06 3.33% 3.42E+06 -7.90%

SO4L02 SO4M02 SO4H02


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specific surface.

Sample DW05

measured measured % change measured % change measured % changeSurface area (m) 5 5 0.00% 5 0.00% 5 0.00%

concentration (ppm) n/a 865.0 n/a 8650.0 n/a 86500.0 n/aT2_peak (s) 3.31E+05 3.01E+05 -8.87% 3.22E+05 -2.52% 3.21E+05 -3.08%T2_bulk (s) 3.82E+06 4.07E+06 6.53% 3.92E+06 2.72% 3.87E+06 1.21%

SO4L05 SO4M05 SO4H05


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specific surface.




SO4L010 SO4M010 SO4H010


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6.4.4 T2 Relaxation time (Na 2SO4 brine)

Figure 46- T 2 Bound fluid peak times vs. brine concentration Na 2SO4.

6.4.5 Surface relaxivity (Na 2SO4 brine)

Figure 47 Calculated relaxivity vs. brine concentration Na 2SO4.


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6.5 Bound Fluid and porosity6.5.1 De-ionized water vs. low concentration brines

6.5.1.1 Bound fluid

Figure 48 Calculated bound fluid vs. Surface area. Low concentration brines

6.5.1.2 Porosity

Figure 49 Calculated porosity vs. Surface area. Low concentration brines


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6.5.2 De-ionized water vs. medium concentration brines

6.5.2.1 Bound fluid

Figure 50 Calculated bound fluid vs. Surface area. Medium concentration brines

6.5.2.2 Porosity

Figure 51 - Calculated porosity vs. Surface area. Medium concentration brines


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6.5.3 De-ionized water vs. high concentration brines

6.5.3.1 Bound fluid

Figure 52 Calculated bound fluid vs. Surface area. High concentration brines

6.5.3.2 Porosity

Figure 53 Calculated porosity vs. Surface area. High concentration brines


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7 Discussion

In this work the influence of different parameters programmed in the CPMG sequence used to record

nuclear transversal magnetic relaxation has been investigated. Based on the understanding of the physicalunderlying principles of the NMR experiment a range of values for TAU, numbers of echoes, recycle delay

and number of scans were tested and outputs analysed. As a result, a set of optimized parameters and

methods to investigate T 2 relaxation times in crushed chalk samples saturated with different brines were

proposed: While a combination of TAU of 200s and NECH of 32k proved optimal for the tests

performed, simple routines were designed to assess the optimal recycle delay and number of scans

required for each sample.

The influence of signal-to-noise ratio on the Laplace inversion results from raw data was demonstrated and

highlighted the (often overseen) importance of acquiring data to the same SNR in order to make different

datasets comparable. The procedure described on the section Materials and methods Solutions ensures

the viability of normalizing T 2 distribution data acquired with different number of scans stacked. This was

achieved by keeping the amount of hydrogen equal between different samples.

The Laplace Inversion that takes place after the experiment transforming the transverse magnetization

decay into a distribution of T 2 relaxation times was also scrutinized. The pruning of the data prior to the

inversion was explained as well as the options linked to the process. The nature of the inverse problem was

discussed briefly and the need for the regularization of the object function that calculates the difference

(or error) between the data acquired and the function that describes the physical model explained. The

influence of the weight given to the smoothing factor during the inversion process was demonstrated and

a method to manually determine the weight proposed. Even though this proved simple for the samples

studied, the determination of the weight might pose a challenge for more complex systems, such as a

heterogeneous core with a wide pore size distribution. The rigorous treatment given to the raw data was

extended to the inversion process and all the inversions computed in the last part of the report, Results ,

were done with the same weight (therefore the exact same function) to ensure comparability of the

processed data.

The processed data was plotted according to different brine concentrations and water for each specific

surface, of 2, 5 and 10m 2. The signal derived from the bound water in samples containing 1m 2 of crushed

chalk proved to be too small to be coherent in a comparison of different samples and thus was not

presented on the plots.


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As seen on the plots and tables comparing peaks in the T 2 relaxation distribution, all brines influenced the

relaxation times in bound water to some degree. However none of the others brines was as influential as

the magnesium chloride brine, which was effective even at a very low concentration. These smaller

relaxation times translated in a lower amount of adsorbed fluid when calculating the bound water by

integrating the peak in T 2 distribution associated with it. The impact of the brines on the amount of bound

fluid was so striking that it was decided to double check this effect using a different perspective

measuring how the brines influenced porosity. A clear correlation between the presence of brines and their

concentration and the reduction of the samples porosities was perceived, and again the highest difference

recorded was for the magnesium chloride brine.

Austad and peers at the University of Stavanger pointed out that the possible substitution between Mg 2+

and Ca 2+ could occur at the chalk surface and change the wettability of the rock, which would impact the

relaxivity of the fluid in contact with the solid surface (Puntervold & Austad 2008; Shariatpanahi et al. 2010;

Strand et al. 2006; Zhang et al. 2007). However this substitution was observed to be highly dependent on

the temperature of the environment, and would be deemed insignificant below 90 o C (while our tests were

performed at 30 o C).

The answer for this apparent contradiction may have been demonstrated in another experiment executed

by Zhang et al. (2007) which showed the competitive nature of the ions Ca2+

and Mg2+

regarding adsorptionby chalk. It proved that at room temperature, the affinity of Ca 2+ towards the chalk surface at room

temperature is a factor of 3.4 times stronger than for Mg 2+, and magnesium adsorption would be hindered

by the presence of calcium ions (both ions were present in the brine to the same molar strength). In the

experiment executed for this report, the magnesium chloride brines had virtually no calcium ions. It is

possible that without their competition, magnesium ions could have substituted the calcium in the surface

of the chalk, forming magnesium carbonate or dolomite. This discussion though is beyond the scope of this

work and would be more fruitfully tackled on a project of its own.


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8 Further work

The completion of this project brought a better understanding of the NMR experiment in itself, the

mathematical tools used during the inversion process and a new methodology to ensure a more rigorous

treatment of the data, ensuring comparability between different datasets. The data from the experiments

measuring the influence of ions commonly found in seawater on solid-fluid interface as observed by NMR

transverse relaxation revealed that changes in relaxation times could be recorded even for very low brine

concentrations. Particularly, the effect of magnesium in measured T 2_peak of the bound water was not

entirely anticipated. While the report leaves a few unanswered questions, it opens up possibilities for

future research on the area, which could be roughly divided into two main areas:

Mathematical treatment of the inverse problem

Development of a procedure to determine the weight of the smoothing factor during the inversion

procedure, particularly important for complex samples;

Assessment of inversion quality and determination of the parcel of the T 2 peaks width are due to

sample characteristics (such as varying pore sizes within) and the parcel induced by a low SNR or

inadequate weight of the smoothing factor during inversion.

Impact of saline brines on Chalk samples

Assure repeatability of the experiments and coherence of the data by assembling more than one

sample per test;

Perform a dedicated test to measure the impact of the different brines on porosity of a loosely

packed saturated chalk powder. Since the height of the column of chalk within the NMR test tube

was small (varying between 4mm to 18mm for specific surfaces of 2m 2 and 10m 2 respectively) it sat

on the beginning of the scale, thus amounting to a high uncertainty on the measurement. A long

and thin test tube would better serve the purpose.

Tie the changes in relaxation times associated with the addition of different brines to the crushed

chalk to a measurable physical parameter, such as final oil recovery by imbibition of brines in oil

saturated cores and modification of wettability in new and aged chalk cores.


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10 References

(Oxford Instruments Magnetic Resonance) & (Green Imaging Technologies), 2012. NMR and Core Analysis.

(Oxford Instruments Molecular Biotools), 2006a. RI WinDXP User Manual ,

(Oxford Instruments Molecular Biotools), 2006b. User Manual - RINMR Software for NMR research and

applications ,

Alam, M.M., Katika, K. & Fabricius, I.L., 2010. Effect of dissolved ions on bound water on water wet mineral

surfaces as indicated by NMR transverse relaxation time ( T 2 ) Effect of dissolved ions on wettability. ,

pp.9093.

Austad, T. et al., 2008. Seawater in Chalk : An EOR and Compaction Fluid. , (August), pp.4 6.

Bedford, J. et al., 2000. Trends in NMR Logging. Oilfied Review, Schlumberger , 12(3), pp.219.

Chen, J., Hirasaki, G.J. & Flaum, M., 2006. NMR wettability indices: Effect of OBM on wettability and NMR

responses. Journal of Petroleum Science and Engineering , 52(1-4), pp.161171. Available at:

http://linkinghub.elsevier.com/retrieve/pii/S0920410506000647 [Accessed November 14, 2013].

Coates, G.R., Xiao, L. & Prammer, M.G., 1999. NMR logging: principles and applications , Halliburton Energy

Services. Available at: http://books.google.dk/books?id=vptTAAAAMAAJ.

Dunn, K.-J., Bergman, D.J. & Latorraca, G.A., 2002. Nuclear magnetic re sonance : petrophysical and logging

applications , Pergamon.

Foley, I., Farooqui, S. & Kleinberg, R., 1996. Effect of Paramagnetic Ions on NMR Relaxation of Fluids at Solid

Surfaces. Journal of magnetic resonance. Series A , 123(1), pp.95104. Available at:

http://www.ncbi.nlm.nih.gov/pubmed/8980068.

Freeman, R., 2004. Magnetic resonance in chemistry and medicine , Oxford: Oxford University Press.

Howard, J.J., 1998. QUANTITATIVE ESTIMATES OF POROUS MEDIA WETTABILITY FROM PROTON NMR

MEASUREMENTS. , 16(98), pp.529533.


62/63

62

Hum, F.M. & Kantzas, A., 2006. Using Low-Field NMR to Determine Wettability of , and Monitor Fluid

Uptake in , Coated and Uncoated Sands. , 45(7).

Katika, K., Alam, M.M. & Fabricius, I.L., Nuclear magnetic resonance and sound velocity measurements ofchalk saturated with magnesium rich brine.

Levitt, M.H., 2008. Spin dynamics : basics of nuclear magnetic resonance.

Mosegaard, K., 2012. Scientific Computing in Geoscience and Astrophysics - Linear Least Squares.

Puntervold, T. & Austad, T., 2008. Injection of seawater and mixtures with produced water into North Sea

chalk formation: Impact of fluidrock interactions on wettability and scale formation. Journal of

Petroleum Science and Engineering , 63(1-4), pp.2333. Available at:

http://linkinghub.elsevier.com/retrieve/pii/S0920410508000636 [Accessed December 3, 2013].

Saunders, M. et al., 2013. Laplace inversion of low-resolution NMR relaxometry data using sparse

representation methods. Concepts in Magnetic Resonance Part A: Bridging Education and Research ,

42(3), pp.7288.

Shariatpanahi, S.F., Strand, S. & Austad, T., 2010. Evaluation of Water-Based Enhanced Oil Recovery (EOR)

by Wettability Alteration in a Low-Permeable Fractured Limestone Oil Reservoir. Energy & Fuels ,

24(11), pp.59976008. Available at: http://pubs.acs.org/doi/abs/10.1021/ef100837v [Accessed

December 3, 2013].

Steinberg, E.. & Cohen, A.B., 1984. Nuclear Magnetic Resonance Imaging Technology: a Clinical Industrial

and Policy Analysis. Washington, DC: US Congress Office of Technology Assessment. , (September).

Strand, S., Hgnesen, E.J. & Austad, T., 2006. Wettability alteration of carbonatesEffects of potential

determining ions (Ca2+ and SO42) and temperature. Colloids and Surfaces A: Physicochemical and

Engineering Aspects , 275(1-3), pp.110. Available at:

http://linkinghub.elsevier.com/retrieve/pii/S092777570500796X [Accessed November 7, 2013].

Vevle, J., 2011. NMR measurements of wettability alternation in Berea Sandstone . University of Bergen.

Zhang, P., Tweheyo, M.T. & Austad, T., 2007. Wettability alteration and improved oil recovery by

spontaneous imbibition of seawater into chalk: Impact of the potential determining ions Ca2+, Mg2+,


63/63

and SO42. Colloids and Surfaces A: Physicochemical and Engineering Aspects , 301(1-3), pp.199208.

Available at: http://linkinghub.elsevier.com/retrieve/pii/S0927775706009915 [Accessed December 2,

2013].

nmr chalk powder

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