1. Practical Scale Tendencies
Reaction kinetics as reported in the literature

2. Scale risks as defined by various operators
Scale Type
Risk
Scale Tendency
Scale Mass (mg/l)
Comments
Calcite
Low
1-3
<50
Moderate
5-15
50-250
Severe
>20
>250
FeCO3
1-5
<15
Found with CaCO3
15-50
BaSO4
<10
8-20
10-40
Rarely from self scaling
>30
>50
Generally due to mixing
SrSO4
Found with BaSO4
NaCl
>1
30,000
Precipitates immediately
Scale risks as defined by various operators

3. Factors governing Scale buildup & Risk
All scale prediction models are equilibrium- based
A separate model is needed to predict scale kinetics
Three mechanisms of scale buildup
Nucleation – (Homogeneous or heterogeneous)
Crystal growth (Primary or secondary)
Transport to surface (secondary)
Adhesion (Secondary)
Scale growth is limited by these mechanisms
Speciation Adsorption
Particle Dynamics
Factors governing Scale buildup & Risk

4. Scale buildup is prevented by
Threshold inhibition
prevent nucleation
Growth inhibition/Crystal Distortion
prevent stable growth and large crystals
Dispersion
prevent large crystal agglomeration
Scale buildup is prevented by

5. Scale Prediction-Scale Risk relationship
What are the fundamentals of nucleation, crystal growth, and adhesion
Crystal growth and nucleation: tracking precursors to polymorphs Patrick R. Unwin. Faraday Discuss., 2007,136, as per:

6. Scaling mechanisms Scale Mechanisms Control Chemicals Threshold scale
inhibitor
Nucleation
Crystal Growth
Modifier
Crystal Growth
Adhesion
Dispersants
Scaling mechanisms
Growth of ZnO Crystals with Branched Spindles and Prismatic Whiskers from Zn3(OH)2V2O7·H2O Nanosheets by a Hydrothermal Route. Hai-Sheng Qian, Shu-Hong Yu*, Jun-Yan Gong, Lin-Bao Luo, Lan-Lin Wen Crystal Growth Design 2005, 5(3),
Synthetic nanoparticles functionalized with biomimetic leukocyte membranes possess cell-like functions Alessandro Parodi, et. al. Nature Nanotechnology.  8,  61–68  (2013)  doi: /nnano
Polymer Directed Formation of Unusual CaCO3 Pancakes with Controlled Surface Structures Shao-Feng Chen, Shu-Hong Yu*, Tong-Xin Wang, Jun Jiang, H. Cölfen*, Bing Hu, B. Yu Adv. Mater. 2005, 17(12),  (Top 10 paper).

7. Nucleation – three types
Primary
Secondary (Crystal growth)
scale grows on existing crystals
Homogeneous
Heterogeneous
Nucleation in clean water
Scale grows on foreign particles, like dust
This occurs during production
Nucleation – three types

8. Primary-Homogeneous Nucleation
System is free of any solids
Solids (e.g., calcite) spontaneously form
The solid formed is pure.
No other materials present (e.g., sand, dust, clay, etc.)
Primary-Homogeneous Nucleation

9. Primary-Heterogeneous Nucleation
Primary Heterogeneous Reaction
The System contains an existing solid surface (e.g., clay, sand, pipe wall)
the scale molecules (e.g., CaCO30) adsorb to the surface
The surface lowers the energy barrier to aggregation
growth continues on the new surface
Lower S is needed to initiate scale
Primary-Heterogeneous Nucleation
S. Labille, A Neville, G Grapham, and L Boak An Assessment of Adhesion of Scale and Electrochemical Pretreament for the Prevention of Scale Depositionon Metal Surfaces. SPE

10. Secondary Nucleation The System already contains calcite
CaCO30 molecules adsorb to calcite surface and grow off it
The calcite surface lowers the energy barrier to reaction
Lower supersaturation is required to form scale
Secondary Nucleation

11. Experimental Data

12. Experimental measurements
Nucleation (primary)
Induction time (time before solids start to form)
particle size and distribution
crystal structure (what minerals form)
Crystal growth (secondary)
crystal size growth rate
concentration changes vs. time
Adhesion (particle transport)
Pressure buildup in a capillary
labs measure one or more of variables in an experiment
Experimental measurements

13. Dynamic tube-blocking studied
Dynamic tube-blocking studies is a common method to test for scale inhibitor performance

14. Dynamic tube blocking studies

15. Generalized flow schematic
Cation solution
Pressure Measurement
Anion solution
Scale Inhibitor
Pressure Measurement
Generalized flow schematic

16. Experimental Results
B. Bazin, N. Kohler, A. Zaitoun, T. Johnson, and H. Raaijmakers A new class of green mineral scale inhibitors for squeeze treatments. SPE87453

17. Experimental results using Bellasol™ inhibitors

18. Static tests
Jar tests or light scatter tests

19. Example results from static jar test
Ba+2 after 12 hours
MAT
PPPC
VSCo
DETA
DTPA
Base
1.4
1.6
1.3
0.9
1.1
2.5 ppm
4.8
6.5
2.7
2.2
5.2
5 ppm
9.8
13.1
10.3
7.8
9.4
7.5 ppm
12.1
13.2
11.4
12.5
10 ppm 13
12.9
12.7
13.3
Example results from static jar test
(bottle image)

20. Example output from light scatter test
“Primary Nucleation” experiments, showing the impact of saturation ratio on the length of time elapsed before calcite start to form.
1 m NaCl brine
Saturation (1=equilibrium)
Example output from light scatter test
He et al., Inhibition of calcium carbonate precipitation in NaCl brines from 25 to 90 C. Applied Geochemistry

21. Crystallographic studies
U. Leeds scale growth and inhibition studies
T. Chen and A. Neville, K. Sorbie, and Z. Zhong Using synchroton radiation wide-angle X-ray scattering (WAXS) to study inhibition effect of DTPMP on CaCO3 scale formation. SPE100440

22. CaCO3 growth at 80C on a Si capillary cell
SPE100440

23. CaCO3 growth at 80C on a Si capillary cell
Crystal planes
with 2 theta angles
Calcite
C104 – 6.9o
C110 – 8.5o
C113 – 9.2o
C202 – 10.1o
No inhibitor
Aragonite
4ppm DTPMP
A111 – 6.2o
Vaterite
V110 – 5.9o
V112 – 6.5o
CaCO3 growth at 80C on a Si capillary cell
SPE100440

24. Plot Explanation - Crystal Projections
Calcite projection
Projection numbering
From google search calcite crystal projections
Plot Explanation - Crystal Projections

25. Viewed vs. time – no inhibitor
~16 minutes to 900 Cps intensity
Calcite
Vaterite
Aragonite
C104 – 6.9o
C110 – 8.5o
C113 – 9.2o
C202 – 10.1o
V110 – 5.9o
V112 – 6.5o
A111 – 6.2o
Viewed vs. time – no inhibitor
SPE100440

26. When viewed in time with inhibitor
~16 minutes to 100 Cps intensity
When viewed in time with inhibitor
SPE100440

27. What is learned in the experiment
Crystals precipitates and dissolve
Crystals do not adhere to surface
The more soluble crystals form first
The most stable solid eventually dominates
What is learned in the experiment
SPE100440

28. Kinetic models
How kinetics are predicted

29. Illustration of nucleation kinetics
Primary-homogeneous nucleation
Clun …
Ca+CO3=Clu1
Clu1+Ca=Clu1’
Clu1’+CO3=Clu2
Clu2+Ca=Clu2’
Clu2’’+CO3=Clu3 …
CO3
Clu3
Clu2’ Ca
Gactivation=energy required to form the cluster containing n components
CO3
G or System Energy
Clu2
Clu1
Clu1’ Ca
Greaction=energy released when the cluster contains z components
Critical nuclei radius*
Critical nuclei radius*
Cluz
Stable solid
Size (radius) of crystal cluster (nanometer scale)
Illustration of nucleation kinetics
Clu=cluster of molecules (e.g., CaCO30) forming the nuclei that turns into the precipitate.
Based on a diagram created by Prof. M. Tomson at Rice University (calcite scale handbook, reference needed)

30. Saturation and cluster size distribution
average cluster radius at a specific saturation ratio
critical radius
nucleation is spontaneous r*
Saturation and cluster size distribution
Nucleation induction times are based on the probability of forming a particle with a radius greater than the critical radius

31. Generalized Model for Nucleation
Energy gained from creating the bonds
Work needed to create the surface
Where:
Gf = Free energy of formation of the new crystal (J)
r = radius of the new scale cluster (cm)
V = molecular volume (cm3)
 = surface tension of cluster (erg/cm2)
a/ao = saturation condition (scaling tendency)
k = Boltzmann’s constant (1.303e-19 J/K)
Generalized Model for Nucleation
Gibbs-Thomson equation (Gibbs-Kelvin)

32. Induction time and saturation using log-scale
Primary-homogeneous nucleation
1hr
1min
1 m NaCl brine
Induction time and saturation using log-scale
He et al., Inhibition of calcium carbonate precipitation in NaCl brines from 25 to 90 C. Applied Geochemistry

33. Induction time model Primary-homogeneous nucleation
log 𝑡 𝑜, 𝐶𝑎𝑙𝑐𝑖𝑡𝑒 (𝑠𝑒𝑐𝑜𝑛𝑑𝑠)=4.22− 13.8 log⁡(𝑆) − 𝑇(𝐶𝑒𝑙𝑐𝑖𝑢𝑠) log⁡(𝑆)∗𝑇
Curve fitting of the induction time. The process variable are the measured temperature and supersaturation
Induction time model
He et al., Inhibition of calcium carbonate precipitation in NaCl brines from 25 to 90 C. Applied Geochemistry

34. Effects of adding ATMP inhibitor
Primary-homogeneous nucleation
ATMP, ppm
0.01
0.025
0.037
0.05
0.075
Effects of adding ATMP inhibitor

35. Secondary Nucleation & Crystal Growth

36. Current theory postulate that inhibitors adsorb on growth sites slowing growth
Adsorb to high-energy kink sites and prevent further crystal growth
Interacts with critical nuclei (6-8 molecules grouped together) and prevents them from growing to a stable crystal
Edges
Kinks
Good growth area
Excellent growth area
Poor growth area
Sides
Corners
Mechanisms

37. Secondary Nucleation-Crystal Growth curves
Seeded growth of BaSO4 with and without inhibitor
long-term growth conforms to:
ks=rate constant
function of surface area and activity of seed crystal
C=measured conc
C0=equilibrium conc
Inhibitor retards growth
𝒅𝑪 𝒅𝒕 =𝒌𝒔 𝑪− 𝑪 𝟎 𝟐
Secondary Nucleation-Crystal Growth curves
R.M.S. Wat, K.S. Sorbie, A.C. Todd, P. Chen, and P. Jiang Kinetics of BaSO4 Crystal Growth and Effect in Formation Damage. SPE23814

38. General crystal growth model for Secondary Nucleation
Solid surfaces or particles (e.g., walls, sand grains) increase nucleation rate because it decreases activation energy
𝑩= 𝒅𝑵 𝒅𝒕 = 𝒌 𝒔 𝒄− 𝒄 ∗ 𝒏
B = is the number of nuclei formed per unit volume per unit time.
N = is the number of nuclei per unit volume.
ks  = is rate constant
c = solute concentration
c* = solute concentration at saturation
n = empirical exponent
General crystal growth model for Secondary Nucleation

39. Primary-heterogeneous nucleation
Secondary nucleation is influenced by particle shear and collision
Fluid shears a Crystal, sweeping away growing nuclei that become new crystals
Crystals collide creating further growth
𝑩= 𝒅𝑵 𝒅𝒕 = 𝒌 𝟏 𝑴 𝑻 𝒋 𝒄− 𝒄 ∗ 𝒃
B = is the number of nuclei formed per unit volume per unit time.
k1 = rate constant
MT = suspension density
j = empirical exponent
b = empirical exponent
Secondary Nucleation

40. Practical Nucleation issues
Homogeneous nucleation does not exist during production
Studied in basic research laboratory to understand reaction mechanisms
Heterogeneous nucleation occurs during production
Studied in applied technology laboratories to evaluate product performance
Field performance and Case studies describe results
Technique in commercial processes
sugar, salts, fertilizers, etc.
designed to fix crystal size and distribution
Practical Nucleation issues

41. Controlling factors in nucleation and crystal growth

42. Increase Mg:Ca ratio slows down nucleation rates

43. We do not use the G-T equation
We don’t care about the Gibbs-Thomson equation because it includes many assumptions it also assumes primary homogeneous nucleation
It does explain the factors that control nucleation
We do not use the G-T equation

44. Transport to surface and adhesion
Diffusion or dispersion of crystallites or precipitating species to the static surface
Electrostatic and chemical bonding to surface
Transport to surface and adhesion

45. Proposed nucleation equation
Kan, A., G. Fu, C. Fan, and M. Tomson Quantitative evaluation of calcium sulfate precipitation kinetics in the presence and absence of scale inhibitors. SPE121563

46. Generalized Model for Nucleation
𝑱=𝑨 𝒆 𝟏𝟔 𝑽 𝟐 𝝅 𝜸 𝟑 𝟑 𝒌𝑻 ln 𝑎 𝑎 𝑜 𝟐 𝒌𝑻 =𝒇𝒍𝒖𝒙 𝒐𝒇 𝒏𝒖𝒄𝒍𝒆𝒂𝒕𝒊𝒏𝒈 𝒄𝒍𝒖𝒔𝒕𝒆𝒓𝒔
Where:
Gf = Free energy of formation of the new crystal (J)
r = radius of the new scale cluster (cm)
V = molecular volume (cm3)
= surface tension of cluster (erg/cm2)
a/ao = saturation condition (scaling tendency)
k= Boltzmann’s constant (1.303e-19 J/K)
A= Comstant
Generalized Model for Nucleation

47. How then do we control scale

48. Burton-Cabrera -Frank (BCF) surface diffusion model describing crystal growth
A crystal face grows via progression of equidistant steps originating at a dislocation source
Step 1 – a solvated growth unit (6-coordinated) arrives at a crystal surface and adsorbs
Step 2 – a) Surface migration occurs followed by a desorption back into solution, or b) a step is reached
Step 3 – Incorporation into the crystal lattice at a kink site 2 3 1
Crystal Growth

49. Energy cost or gained released at each step2 3 1
∆Gdissolv
Energy needed to move cluster
∆Gk
∆Gs-diff
Energy released when bonded
Cluster reaches Kink (3)
Cluster reaches edge (2)
Cluster on surface (1)
Cluster in water
Energy cost or gained released at each step

50. Entry into kink site requires inhibitor desorption
New pseudo-kink sites are created and growth units accept impurity as its neighbor
Adsorbed inhibitors act as barriers to growth unit diffusion 3 2 1 SI SI SI SI
∆Gdissolv
Cluster reaches Kink (3)
Cluster reaches edge (2)
Cluster on surface (1)
∆Gk
∆Gs-diff
Cluster in water
Energy needed to move cluster
Energy released when bonded
Effects of inhibitor on Energy cost
Effect of inhibitors

51. Nucleation Inhibition
Current theory postulate that inhibitors poison the nuclei
Nucleus Formation begins as two ion pairs combine… O O
Critical Nucleus OH CH P 2 OH N O CH 2 CH P 2 O P O O O O
Nucleation Inhibition
One phopshonate molecule can inhibit 5,000 to 10,000 scalant molecules

52. Worthless trivia:
Carboxymethyl cellulose is added to ice cream to keep ice crystals from forming

53. FIGURE 5 - Assessment of the growth rate of the three different polymorphs formed on a metallic substrate at 80°C with no inhibitor and with 4ppm of PPCA
CaCO3 growth on SS-316
From: Martinod, A, A Neville, K Sorbie, & Z Zhong (2008) Assessment of CaCO3 inhibition by the use of SXRD on a a metallic substrate. Corrosion No

54. Gypsum nucleation kinetics
1 day
1hr
1min
Gypsum nucleation kinetics
He, S.L, J. Oddo, and M . Tomson., Nucleation and inhibition of calcium sulfate dihydrate in NaCl solutions up to 6m and 90 C . JCIF 162(2) 297.

55. SrSO4 nucleation kinetics
1 day
1hr
1 min
SrSO4 nucleation kinetics

56. Compare NaCl, gypsum, SrSO4,CaCO3, & BaSO4 induction times
1 day
BaSO4
1hr
SrSO4
25C/1mIS
1 min
NaCl
CaSO4.2H2O
Compare NaCl, gypsum, SrSO4,CaCO3, & BaSO4 induction times
Data extracted from papers described in this presentation

57. Compare NaCl, gypsum, SrSO4,CaCO3, & BaSO4 induction times
1 day
BaSO4
1hr
1 min
Compare NaCl, gypsum, SrSO4,CaCO3, & BaSO4 induction times
Data extracted from papers described in this presentation

58. NaCl Kinetics S=1.148 S=1.199* ~10 minutes ~5 minutes
* Data from Figure 4 inserted onto image of Figure 3
NaCl Kinetics
From Chen, T, Montgomerie, H, Chen, P, Jackson, T, and Vikane, O Understanding te mechanisms off halite inhibition and evaluation of halite scale inhibitor by static and dynamic tests. SPE

59. CaSO4 scale risk plot

61. Four Regions of Saturation Values (calcite)
S>200, scale cannot be prevented with existing technology
S=150
(SI=2.3)
Region 3
10<S<150, scale can be delayed till the brine exits the process. About 1 mg/l of active inhibitor is sufficient to inhibit scale in this region
S= 10
(SI=1)
Region 2
1<S<10, scale occurs if other scale is present, but will not form on clean surfaces. Brines can be produced for long periods without risk
S=1
(SI=0)
Region 1
Below S=1 scale is sub saturated and will dissolve existing solids. Brines with S<1 are often corrosive to mild steel
S<1
(SI<0)
Time
Adapted from Tomson, M.B., and J.E. Oddo Calcite Scale Handbook, Measurement, Prediction, and control. Gas research Institute, Chicago, IL.
Four Regions of Saturation Values (calcite)

62. Scale buildup Nucleation Crystal Growth Transport Adherence
Mixed phases
Scale buildup
Scale buildup is sequential

63. Crystal Growth

64. Example real time image
Example real time image

65. Scale buildup prediction
Predictive models for scale buildup are unavailable
The uncertainty in identifying scale location is too great to develop a consistent model
Tomson (1996) developed a model to predict tube fouling as a result of CaCO3 scaling
Where:
S = Slope of calcium concentration versus distance up the pipe (general range between (mg/l)/ft)
Q = Brine flow (bbl/month)
R = pipe radius (generally 2.5 in)
Km = CaCO3 Mass transport constant (10-3 works well for most cases)
x = pipe length (generally 3,000 to 10,000 ft)
Scale buildup prediction

66. Scale Buildup – Flux Example Result
Example scale buildup plot using Tomson’s flux model for Calcute
Above 2000 BWPD, it will take 2 to 8 months to produce a scale 3/8” thick or ~50% tubing constriction (2 ½” ID)
Model has not been tested against known well production
10,000 ft
8,000 ft
6,000 ft
4,000 ft
2,000 ft
Scale Buildup – Flux Example Result
S=0.02 mg/l/ft, r=1.25 in, km=0.001 cm/s,

67. Buildup of suspended particles onto wall
Electrostatic attraction between surface and particle
Sedimentation (gravity effects)
Shear effects of fluid (dispersion)
Brownian motion (random movement)
Inertial forces (elbow, choke)
Eddy diffusion (turbulence movement)
𝑩𝒖𝒊𝒍𝒅𝒖𝒑=𝑷𝒂𝒓𝒕𝒊𝒄𝒍𝒆 𝒇𝒍𝒖𝒙 𝒕𝒐 𝒔𝒖𝒓𝒇𝒂𝒄𝒆 𝒈 𝒎 𝟐 𝒔 ∗𝑭𝒓𝒂𝒄𝒕𝒊𝒐𝒏 𝒕𝒉𝒂𝒕 𝒔𝒕𝒊𝒄𝒌𝒔
Buildup of suspended particles onto wall
I.R. Collins A new model for mineral scale adhesion. SPE Oilfield scale symposium, Jan Aberdeen Scotland

68. Electrostatic attraction is important when the distance is less than 1m
Important only when particle is adjacent to wall
Eddies generally keep material in suspension
Gravity is important in horizontal pipes
What it probably isn’t

69. CaCO3 nucleation kinetics, NTNU (Norway)
Primary-homogeneous nucleation
CaCO3 nucleation kinetics, NTNU (Norway)
1Ostvold, T. and P. Randhol Kinetics of CaCo3 scale formation. The influence of temperature, supersaturation, and ionic composition.

70. Calcite nucleation kinetics (comparing three experiments)
Primary-homogeneous nucleation
1 day
1hr
1min
Calcite nucleation kinetics (comparing three experiments)
Data from IFE (date) – citation name not shown here – request information

71. Calcite nucleation kinetics (additional results)
Data from IFE (date) – citation name not shown here – request information

72. Gypsum nucleation kinetics in pure water

73. Barite nucleation kinetics
1 day
1hr
1 min
Barite nucleation kinetics
SPE – barite nucleation