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Development and application of a new theoretical model for additive impacts on mineral crystallization Zhaoyi (Joey) Dai, Fangfu Zhang, Narayan Bhandari, Guannan Deng, Amy T. Kan, Fei Yan, Gedeng Ruan, Zhang Zhang, Ya Liu, Alex Yi-Tsung Lu, and Mason Tomson Cryst. Growth Des., Just Accepted Manuscript • Publication Date (Web): 02 Jun 2017 Downloaded from http://pubs.acs.org on June 3, 2017

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Crystal Growth & Design

1

Development and application of a new theoretical model for additive impacts on

2

mineral crystallization

3 4

Zhaoyi (Joey) Dai1,2*, Fangfu Zhang1, Narayan Bhandari1, Guannan Deng1,2, Amy T.

5

Kan1,2, Fei Yan1, Gedeng Ruan1, Zhang Zhang1,2, Ya Liu1,2, Alex Yi-Tsung Lu1,2, Mason

6

Tomson1,2

7 8

1

9

Houston, TX 77005, US

Department of Civil and Environmental Engineering, Rice University, 6100 Main Street,

10

2

11

Treatment

Nanosystems Engineering Research Center for Nanotechnology-Enabled Water

12 13

* Corresponding Author contact information:

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E-mail address: [email protected]

15

Tel: (713)348-2149

16 17

ACS Paragon Plus Environment


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Abstract

19 20

Additives play an important role in crystallization controls in both natural and industrial

21

processes. Due to the lack of theoretical understanding of how additives work, the use and

22

design of additives in various disciplines are mostly conducted empirically. This study has

23

developed a new theoretical model to predict the additive impacts on crystallization based

24

on the classical nucleation theory and regular solution theory. The new model assumes that

25

additives can impact the nucleus partial molar volume and the apparent saturation status of

26

the crystallization minerals. These two impacts were parameterized to be proportional to

27

additive concentrations and vary with inhibitors. As a practical example, this new model

28

has been used to predict barite induction times without inhibitors from 4 to 250 oC and in

29

the presence of eight different scale inhibitors from 4 to 90 oC. The predicted induction

30

times showed close agreement with the experimental data published previously or

31

produced in this study. Such agreement indicates that this new theoretical model can be

32

widely adopted in various disciplines to evaluate mineral formation kinetics, elucidate

33

mechanisms of additive impacts, predict minimum effective dosage (MED) of additives,

34

and guide the design of new additives, to mention a few.

35 36

Keywords

37

crystallization; scale inhibition; membrane fouling; phosphonate; carboxylate; sulfonate

38


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39


Introduction

40 41

Mineral crystallization is an important reaction that occurs in various industrial processes,

42

including water treatment

43

exchange processes 8, and oil and gas productions 9. In many cases, mineral crystallization

44

can lead to detrimental impacts. For example, mineral scale formation can cause excessive

45

energy consumption, flow rate reduction, and economic losses in water treatment processes

46

via forming in the heat exchange units 2 or at the membrane surface 10-12; barite, one of the

47

most common scale minerals in the oil and gas industry, can cause enormous economic

48

loss through pipeline blockage, formation damage, or equipment malfunction 9. To avoid

49

such losses, various types of chemical additives have been added as scale inhibitors to

50

delay or prevent mineral scale formation. For example, scale inhibitor addition has been

51

used as one of the most economical and efficient scale control methods 13, 14. However, due

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to the lack of theoretical understanding of how additives impact the crystallization process,

53

additive usages for such crystallization process controls are mainly conducted in an

54

empirical manner

55

basis for better crystallization process controls using various additives in a quantitative way.

15-17

1-3

, drug purification

4-6

, CO2 geological sequestration 7, heat

. Therefore, a mechanistic model is desired to provide theoretical

56 57

In the past decades, many mechanisms have been proposed to explain the inhibition

58

mechanisms of additives in the crystallization process. Most of these mechanisms can be

59

categorized into two groups: surface adsorption and structure interference. By adsorbing

60

onto and deactivating the kink sites, the additives (or scale inhibitors) are believed to slow

61

down crystal growth through the Burton-Cabrera-Frank (BCF) spiral growth mechanism



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62

18-20

. This surface adsorption mechanism has been confirmed by experimental observations

63

21-23

. For example, Liu and Nancollas (1975) studied the barite seeded growth and

64

dissolution in the presence of N, N, N', N triethylenediaminetetra (methylene phosphonic

65

acid) (TENTMP), sodium tetrarnetaphosphate, and sodium tripolyphosphate at 25 oC. They

66

suggested that the growth rate delay and the initial surge of additive (i.e., inhibitor)

67

concentration in dissolution are due to the adsorption of inhibitor onto seed surface or

68

incorporation into the crystals 21. In addition to surface adsorption, structure interference

69

due to the formation of inhibitor-ion complex or clusters can also slow down the

70

crystallization process

71

nucleation clusters can influence the local structure of nucleated particles 23. The structure

72

distortion or inhibitor incorporation can lead to the increase of solubility and the decrease

73

of supersaturation, which finally slow down the crystallization rate

74

most of these studies failed to establish mechanistic models to describe these mechanisms

75

and quantify the impacts of additives. As a result, these mechanisms can hardly be used to

76

guide the usage of additives in practical applications.

24

. It is suggested that the complexation of inhibitors onto pre-

25, 26

. Unfortunately,

77 78

The induction time is defined as the time elapsed between the establishment of

79

supersaturation and the formation of detectable crystalline phases. This definition implies

80

the practical significance of induction time that it can correspond to the time when mineral

81

scale starts to cause problem. In practical applications, the induction time ( ti , s) has been

82

widely used to represent the kinetics of mineral crystallization 27-32. Some semi-empirical

83

models have been developed to predict the mineral induction times with or without the

84

presence of additives (e.g., scale inhibitors) 31, 33-36. These models assume that the addition


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of additives raise the activation energy of crystallization and increase the induction time

86

(ti). The change of the logarithm of induction time is assumed to be linearly proportional

87

to the concentration of inhibitors (i.e., log10  ti   log10 ti0  b  Cinhibitor ). The induction

88

times without inhibitors (i.e., ti0 ) and the inhibition efficiencies (i.e., b) can be fitted from

89

semi-empirical equations based on the induction times measured under different conditions

90

for different minerals and inhibitors. These models show good prediction capability and

91

have been widely adopted in oil and gas industry for mineral scale control. Unfortunately,

92

these models need more sufficient theoretical basis so that they can be extrapolated to other

93

types of scale inhibitors under other conditions, or be used to elucidate the mechanisms of

94

the inhibition process.

 

95 96

This study intends to develop a mechanistic model to quantify the additive impacts in the

97

crystallization process. Based on the classical nucleation theory (CNT) and regular solution

98

theory, this model quantified the additive impacts through the changes of molar volume

99

and Gibbs free energy. Using barite as an example, this model can accurately predict its

100

induction time without inhibitors from 4 to 250 oC and with the presence of eight different

101

scale inhibitors from 4 to 90 oC, which were measured in this study or previous research.

102

This study successfully bridged the experimental observations with theoretical

103

assumptions and showed a new way to illustrate the mechanisms of various additives to

104

control crystallization process.

105 106

Model development

107



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108

Using barite crystallization as an example, the crystallization process can be expressed as:

109

  BaSO4 Ba 2  SO42  

110

(1)

The Gibbs free energy change of this reaction ( Gr0 ) is: 0 0 0 Gr0  Gbarite  GBa , 2  G SO 2

111

(2)

4

112

where ∆G0 stands for the Gibbs free energy (J mol-1) of different species. The saturation

113

index (SI) of barium sulfate is defined as follows: 2

114

SI

barite

 log10

2

 Ba 2 [ Ba ] SO 2 [ SO4 ] 4

K sp , BaSO

,

(3)

4

115

where [·] and γ stand for the concentration (mol/kg H2O) and activity coefficients of

116

different species, respectively; Ksp is the mineral solubility product and equals to

117

exp  Gr0 / RT   mol/kg H2O  . Theoretically, SI should be zero when solids are at

118

equilibrium with the solution. If SI is larger than 0, the solution is over-saturated and has a

119

potential to precipitate, and vice versa. The SI values were calculated using software

120

ScaleSoftPitzer developed by Rice University 9, 37-41.

2

121 122

The induction time ( ti ) includes the relaxation stage (tr) for the achievement of quasi

123

steady-state distribution of molecular clusters, the nucleation stage(tn) for critical nuclei

124

formation in aqueous phase, and the very early crystal growth stage when the nuclei grow

125

from critical radius to a detectable size (tg) 31, 42-45. In low viscosity solutions, the relaxation

126

stage (tr) is believed to be much shorter than the nucleation stage (tn), and thus we have

127

ti  tr  tn  t g  tn  t g

45

.

128


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The classical nucleation theory (CNT) is developed to represent the competition between

130

the decrease of bulk Gibbs free energy (i.e., related to SI) and the increase of surface energy

131

(i.e., related to σ and Vm) when nuclei form in the nucleation stage 30, 42. After nucleation

132

stage, nuclei continue to grow via various pathways

133

growth happens in the crystal growth stage, Söhnel and Mullin (1979, 1988) derived the

134

induction time without the presence of scale inhibitors based on CNT as follows 45, 46:

135

1/4 5/3  3   Vm ti     8/3 4  2   Av D ceq

1/4

45-47

. By assuming the polynuclei

  10SI /2   Vm2 3 Av  'Vm4/3 2 Av2/3  , (4) exp      SI /2 2  3 2 4( RT )2 (2.303  SI )   4( RT ) (2.303  SI )   (10  1)  1/4

136

where R is the ideal gas constant (8.31 J K-1 mol-1); T is temperature in Kelvin (K); Vm is

137

the molar volume of scale mineral (e.g., 5.21×10-5 m3/mol for barite); σ is the superficial

138

interfacial energy between mineral and solution (J m-2) changing with temperature (i.e.,

139

   298 K  aT T  298.15  , in which  298K is the superficial interfacial energy at 25 oC

140

and aT is the coefficient for temperature dependence); Av is the Avogadro constant (6.02

141

× 1023 mol-1); D is the effective diffusion coefficient (m2 s-1); ceq is the equilibrium

142

concentration of the lattice ions (mol/kg H2O); β and β’ are the shape factors (i.e., for

143

spheres, β = 16π/3 , β’ = π 30); SI is the saturation index defined in Equation (3).

144 145

Using barium sulfate as an example, the effect of added inhibitors, Inh, on the nucleation

146

process is modeled by assuming that a trace amount of inhibitor (r 2 and r < 0.001. The new model developed in this study is

336

the first theoretical model that can explain such observations.

34, 56, 57

. In Figure 6, it is also observed

337



log10(ti/s)

(a) BHPMP 8 7 6 5 4 3 2 1 0

This study_SI = 2.00, T = 296 K SI = 2.00_pred This study_SI = 2.54, T = 296 K SI = 2.54_pred This study_SI = 2.72, T = 296 K SI = 2.72_pred

0.00

1.00 2.00 3.00 Inhibitor Concentration (ppm)

338

(b) DTPMP 7 6 5

log10(ti/s)

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Page 20 of 34

This study_SI = 2.00, T = 298 K

4 SI = 2.00, T = 298 K_pred

3 2

This study_SI = 2.02, T = 343 K

1

SI = 2.02, T = 343 K_pred

0 0.00

0.50 1.00 1.50 2.00 Inhibitor Concentration (ppm)

339


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log10(ti/s)

(c) HDTMP 7 6 5 4 3 2 1 0

This study_SI = 2.00, T = 298 K SI = 2.00, T = 298 K_pred This study_SI = 2.02, T = 343 K SI = 2.02, T = 343 K_pred

0.00


340

(d) NTMP

log10(ti/s)

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7 6 5 4 3 2 1 0

This study_SI = 2.00, T = 298 K SI = 2.00, T = 298 K_pred This study_SI = 2.00, T = 340 K SI = 2.00, T = 340 K_pred This study_SI = 2.17, T = 298 K SI = 2.17, T = 298 K_pred

0.00 1.00 2.00 3.00 Inhibitor Concentration (ppm) 341 342

Figure 5. Barite induction time under various conditions in the presence of non-polymeric

343

phosphonate inhibitors: (a) BHPMP, (b) DTPMP, (c) HDTMP, and (d) NTMP. The

344

experimental measurements are represented as symbols, and the predictions by this study

345

are represented as lines.

346



(a) PPCA 5 This study_SI = 2.02, T = 340 K

log10(ti/s)

4 SI = 2.02, T = 340 K_pred

3

Xiao_SI = 2.81, T = 298 K

2

SI = 2.81, T = 298 K_pred

1

Xiao_SI = 2.93, T = 298 K

0.00


SI = 2.93, T = 298 K_pred

347

(b) PVS 5 4

log10(ti/s)

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Page 22 of 34

Yan_SI = 2.0, T = 343 K SI = 2.0, T = 343 K_pred

3

Yan_SI = 2.1, T = 298 K

SI = 2.1, T = 298 K_pred

2


1 0.00


348


Page 23 of 34

(c) CMI 5

log10(ti/s)

4 Yan_SI = 2.6, T = 277 K

3

SI = 2.6, T = 277 K_pred Yan_SI = 2.1, T = 298 K

2

SI = 2.1, T = 298 K_pred

1


0 0

1 2 3 Inhibitor Concentration (ppm)

4

349

(d) PMAC 4

This study_SI = 2.74, T = 277 K SI = 2.74, T = 277 K_pred

3

log10(ti/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


This study_SI =2.08, T = 298 K SI =2.08, T = 298 K_pred

2


1


0 0

2 4 Inhibitor Concentration (ppm)

6

350 351

Figure 6. Barite induction time under various conditions in the presence of polymeric

352

inhibitors: (a) PPCA, (b) PVS, (c) CMI, and (d) PMAC. The experimental measurements

353

are represented as symbols, and the predictions by this study are represented as lines.

354



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355

Equation (4) was derived based on CNT and reflects the competition between the decrease

356

of Gibbs free energy and the increase of surface energy due to crystallization. Our new

357

model uses only two parameters (i.e., aG and aV) to represent the relative impacts of the

358

additives on these two counterparts, respectively. If the additives (e.g., inhibitors) lead to

359

a more significant increase in the molar volume than the decrease of Gibbs free energy, the

360

crystal (e.g., barite) nucleus is harder to form and thus the induction time will be longer. It

361

means that the aG and aV values represent the relative impacts on the two parameters that

362

control the competition between surface energy and bulk Gibbs free energy. Putting in

363

another way, it is the aG and aV values acting together, instead of individually, that can

364

reflect the effects of inhibitors due to different inhibition mechanisms, including adsorption,

365

structure interference, and kink site deactivation, to mention a few.

366 367

The individual parameters for each scale inhibitor per functional unit are listed in Table 3.

368

The relative impacts of each inhibitor per functional unit on Gibbs free energy (i.e., aG in

369

Equation (9)) and on molar volume (i.e., aV in Equation (13)) are listed in column 3 and

370

4, respectively. Using NTMP as an example, when the molar ratio r is 0.001, the relative

371

change of Gibbs free energy is 0.001 × 3 × 7.7 = 2.3% and the relative change of molar

372

volume is 0.001 × 3 × 57.2 = 11.4%. The four non-polymeric phosphonate inhibitors (listed

373

in Row 2 to 5 in Table 3) have similar aG , aV , and 1  aG  / 1  aV  ratios in terms of one

374

phosphonate functional group monomer, except for NTMP which has smaller aV and large

375

1  aG  / 1  aV  ratio. This result also indicates that the phosphonate groups are the main

376

functional groups and have similar crystallization inhibition efficiency in different


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377

inhibitors. This observation agreed with Flory (1953) that the reactivity of the functional

378

groups in large molecules can behave independently from each other

379

polymeric scale inhibitor containing phosphonate functional groups is used for barite scale

380

inhibition, its monomer impacts on the Gibbs free energy and molar volume of barite

381

crystallization can be estimated to be the average aG and aV values of the four

382

phosphonate inhibitors, respectively (i.e. aG = 7.32, aV = 82.93). For example, HEDP (i.e.,

383

1-Hydroxy Ethylidene-1,1-Diphosphonic Acid) is another widely used non-polymeric

384

phosphonate scale inhibitor

385

molecular weight of 206. The impacts of HEDP on Gibbs free energy and molar volume

386

can be estimated as aG  2aG = 14.65 and aV  2aV = 165.87, respectively, for the whole

387

HEDP molecule. Figure 7 shows the barite induction times in the presence of HEDP

388

predicted by our new model using the estimated aG and aV values for HEDP. The close

389

match with the measured induction times confirms the proposed similarities among the

390

non-polymeric phosphonate inhibitors. It also indicates that the inhibition kinetics of a new

391

non-polymeric phosphonate scale inhibitor can be estimated based on its number of

392

phosphonate groups it contains.

59

58

. If another non-

. HEDP contains two phosphonate groups and has a

393 394

Table 3. Column 2 shows the molecular weight (MW) containing one functional group.

395

Columns 3 to 4 show the fitted two individual parameters of each inhibitor correpsonding

396

to the MW per functional unit for barite. Column 5 shows the ratio of 1  aG  / 1  aV  . MW per functional

aG

Inhibitor

aV

unit


1  aG  / 1  aV 


BHPMP

137

7.8

107.6

0.081

DTPMP

115

6.5

79.5

0.093

HDTMP

123

7.4

87.4

0.095

NTMP

100

7.7

57.2

0.149

PPCA

74.5

10.4

37.6

0.294

CMI

274

68.8

279.2

0.249

PMAC

58

15.3

88.3

0.183

PVS

107

51.2

172.0

0.302

397

HEDP Predicted log10(ti/s)

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Page 26 of 34

8 7 6 5 4 3 2 1 0

This study_SI = 2.02, T = 340 K SI = 2.02, T = 340 K_pred This study_SI = 2.00, T = 298 K SI = 2.00, T = 298 K_pred

0.00


398 399

Figure 7. Barite induction time under various conditions in the presence of HEDP. The

400

experimental measurements are represented as symbols, and the predictions by this study

401

are represented as lines.

402


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403

It also deserves notice that the 1  aG  / 1  aV  ratios of all phosphonate inhibitors are

404

smaller than those of the polymeric inhibitors containing sulfonate or carboxylate

405

functional groups, which indicates that non-polymeric phosphonate scale inhibitors are

406

generally more effective than the polymeric inhibitors under most of these conditions. Such

407

comparison agreed with the experimental observations mentioned above. The large

408

deviations among the aG and aV values of the four polymeric scale inhibitors may be due

409

to the different functional groups they have. It will be valuable to further analyze such

410

differences in future research.

411 412

Conclusions

413 414

This study has developed a novel theoretical model to study the kinetics and mechanism

415

of mineral crystallization with or without the presence of additives. This model adopts the

416

CNT to calculate the induction time without the presence of additives with three

417

undetermined parameters (i.e.,  , aT , D ). The additives were assumed to exert impacts on

418

the molar volume and Gibbs free energy of the nucleus formation. These two impacts were

419

quantified to be proportional to the concentration of additives using the regular solution

420

theory with two parameters (i.e., aG , aV ). Their values represent the relative impacts on

421

the competition between the increase of surface energy and the decrease of Gibbs free

422

energy during the crystallization process.

423 424

This model was used to predict the induction times of barite with or without the presence

425

of eight different scale inhibitors from 4 to 90 oC. The close match between the measured



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Page 28 of 34

426

and predicted induction times show the correctness of this model. The four non-polymeric

427

phosphonate inhibitors show similar aG , aV , and 1  aG  / 1  aV  values, which

428

indicates that these phosphonate inhibitors have similar inhibition efficiency per

429

phosphonate functional group monomer. Among the eight scale inhibitors, the non-

430

polymeric phosphonate inhibitors have smaller

431

polymeric inhibitors. It suggests that the phosphonate inhibitors have more efficient scale

432

inhibition efficiencies, which agrees with experimental observations.

1  aG  / 1  aV 

ratios than other

433 434

In the future, more minerals and additives can be included into this model. It will also be

435

of great value to correlate the two parameters, aG and aV , with additive properties, for

436

example, molecular weight, gyration radius, functional group positions. With the guidance

437

of such a unified theoretical model, the usage and design of various additives for mineral

438

crystallization control in various disciplines will be more efficient.

439 440

Associated Content

441

Supporting Information. The details of the experimental conditions and the derivations of

442

the linear relationship between the logarithm of induction time and inhibitor concentrations

443

at constant temperature and saturation index are included in the supporting information.

444 445

Acknowledgements

446 447

The authors would like to acknowledge the financial support by a consortium of companies

448

including Baker Hughes, BWA, Chevron, ConocoPhillips, Dow, EOG, ExxonMobil,


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449

FLOTEK, GE, Hess Italmatch, JACAM, Kemira, Kinder Morgan, Lubrizol, Nalco

450

Champion, OASIS, OXY, RSI, Saudi Aramco, Schlumberger, Shell, SNF, Statoil, and

451

Total. This work was supported by the NSF Nanosystems Engineering Research Center for

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Nanotechnology-Enabled Water Treatment (ERC-1449500). The authors also want to

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thank Dr. Linda Driskill for her careful edits and revisions.



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For Table of Contents Use Only Development and application of a new theoretical model for additive impacts on mineral crystallization

Zhaoyi (Joey) Dai1,2*, Fangfu Zhang1, Narayan Bhandari1, Guannan Deng1,2, Amy T. Kan1,2, Fei Yan1, Gedeng Ruan1, Zhang Zhang1,2, Ya Liu1,2, Alex Yi-Tsung Lu1,2, Mason Tomson1,2

1

Department of Civil and Environmental Engineering, Rice University, 6100 Main Street,

Houston, TX 77005, US 2

Nanosystems Engineering Research Center for Nanotechnology-Enabled Water

Treatment

* Corresponding Author contact information: E-mail address: [email protected] Tel: (713)348-2149

Synopsis: Additives can impact the nucleus partial molar volume and the apparent saturation status of the crystallization minerals. These two impacts were parameterized to be proportional to additive concentrations and vary with inhibitors.



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Page 34 of 34

Inh

+

r  Inh BaSO4   Ba 2  SO42   BaSO4  Inhr


Development and Application of a New Theoretical ... - ACS Publications

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