1. Scale Tendency Hand Calculations
Simplified models used to predict scale tendencies

2. Scale Tendency calculations in four steps
1) Write the reaction
𝑁𝑎𝐶𝑙 𝑠, ℎ𝑎𝑙𝑖𝑡𝑒 = 𝑁𝑎 + 𝑎𝑞 + 𝐶𝑙 − (𝑎𝑞)
2) Convert to an Equilibrium equation (shorthand form shown)
𝐾 𝑠𝑝 𝑁𝑎𝐶𝑙, ℎ𝑎𝑙𝑖𝑡𝑒 = 𝑎 𝑁𝑎 + ∗ 𝑎 𝐶𝑙 − 𝑁𝑎𝐶𝑙 (𝑠) = 𝑦 𝑁𝑎 + ∗ 𝑚 𝑁𝑎 + ∗ 𝛾 𝐶𝑙 − ∗ 𝑚 𝐶𝑙 − 𝑁𝑎𝐶𝑙 (𝑠)
3) Rearrange to test for solids
𝑆= 𝑦 𝑁𝑎 + ∗ 𝑚 𝑁𝑎 + ∗ 𝛾 𝐶𝑙 − ∗ 𝑚 𝐶𝑙 − 𝑁𝑎𝐶𝑙 𝑠 ∗ 𝐾 𝑠𝑝 𝑁𝑎𝐶𝑙, ℎ𝑎𝑙𝑖𝑡𝑒
1.0 by definition
4) Simplify
𝑆= 𝑦 𝑁𝑎 + ∗ 𝑚 𝑁𝑎 + ∗ 𝛾 𝐶𝑙 − ∗ 𝑚 𝐶𝑙 − 𝐾 𝑠𝑝 𝑁𝑎𝐶𝑙, ℎ𝑎𝑙𝑖𝑡𝑒
Scale Tendency calculations in four steps

3. Example: calculate SNaCl
measured
calculated
Na,ppm (mol/kg)
Cl, ppm (mol/kg)
Ksp C / P, atm)
Na
Cl
86,000 (3.74)
145,000 (4.09)
38.2 / 1)
0.84
(symmetry)
𝐾 𝑠𝑝 𝑁𝑎𝐶𝑙, ℎ𝑎𝑙𝑖𝑡𝑒 = 𝑎 𝑁𝑎 + ∗ 𝑎 𝐶𝑙 − 𝑁𝑎𝐶𝑙 (𝑠) = 𝑦 𝑁𝑎 + ∗ 𝑚 𝑁𝑎 + ∗ 𝛾 𝐶𝑙 − ∗ 𝑚 𝐶𝑙 − 𝑁𝑎𝐶𝑙 (𝑠)
Step 1) 2)
𝑆= 𝑚 𝑁𝑎 + ∗ 𝑚 𝐶𝑙 − ∗ 𝑦 𝑁𝑎 + ∗ 𝛾 𝐶𝑙 − 𝐾 𝑠𝑝 𝑁𝑎𝐶𝑙, ℎ𝑎𝑙𝑖𝑡𝑒
15.30∗0.71=10.86
Solve)
𝑆= 3.74∗4.09 ∗ 0.84∗ =0.28
Example: calculate SNaCl

4. Calculate SNaCl with and without activity coefficients
Na,ppm (mol/kg)
Cl, ppm (mol/kg)
Ksp
C / P, atm)
Na
Cl
87,250 (4.30)
134,549 (4.30)
35.8
0.74
147,250 (6.41)
225,414 (6.36)
36.5
1.11
10,800 (0.47)
19,850 (0.56)
41.3
0.69
S (w/o )
S (with )
0.52
0.28
1.12
1.37
0.006
0.003
(symmetry)
Calculate SNaCl with and without activity coefficients

5. Example: Calculate SCaCO3
Cation
Anion
ppm (mol/kg)
Act coef (25C, 1atm)
Na+
14,500 (0.63)
0.665
Cl-
22,510 (0.69)
0.681 K+
1,234 (0.032)
0.612
SO4-2
2,142 (0.022)
0.087
Ca+2
1,420 (0.035)
0.253
HCO3-
158 (4.0e-3)
0.555
Ba+2
2 (1.4e-5)
0.207
CO3-2
(1.18e-5)
0.093
𝑪𝒂𝑪 𝑶 𝟑 = 𝑪𝒂 +𝟐 + 𝑪 𝑶 𝟑 −𝟐
Step 1) …
𝑆= 𝛾 𝐶𝑎 +2 ∗ 𝑚 𝐶𝑎 +2 ∗ 𝛾 𝐶 𝑂 3 −2 ∗ 𝑚 𝐶 𝑂 3 −2 𝐾 𝑠𝑝, 𝐶𝑎𝐶 𝑂 3 (𝑐𝑎𝑙𝑐𝑖𝑡𝑒), (𝑇,𝑃)
Step 4)
Assemble necessary variables (from software or literature)
𝐾 𝑠𝑝, 𝐶𝑎𝐶 𝑂 3 , (25 𝐶,1 𝑏𝑎𝑟) =2.43 𝑒 −9
Plug in data and calculate
Answer: ST=3.99
Example: Calculate SCaCO3

6. Calculate T & P effects on Scale tendencies
CaSO4
BaSO4
CaCO3 Na Ca Ba Cl
SO4
CO3 C
Bar
Ksp  50 30
2.78E-05
1.99E-10
2.41E-09
0.647
0.216
0.185
0.664
0.135
0.083 80
150
1.30E-05
2.61E-10
1.63E-09
0.624
0.178
0.164
0.636
0.113
0.068
120
300
3.28E-06
2.37E-10
4.65E-10
0.589
0.134
0.137
0.596
0.082
0.049
140
460
1.61E-06
1.96E-10
2.35E-10
0.568
0.115
0.124
0.575
0.066
0.040
170
600
4.46E-07
1.37E-10
6.06E-11
0.535
0.088
0.104
0.538
0.045
0.028 T
P, bar
CaSO4
BaSO4
CaCO3 C
Bar S 50 30 80
150
120
300
140
460
170
600
Calculate T & P effects on Scale tendencies

7. Scale tendency models
Hand calculations that include methods to predict K and 

8. Scale Prediction models
CaCO3
BaSO4, CaSO4, SrSO4
Halides
Unique scales K 
Langlier Saturation Index 
Ryznar Stability index
Pukoris Scale Index
Stiff Davis
Oddo-Tomson
Computer Models (like OLI)
semi-empirical
Theoretical
Scale Prediction models

9. Example: Calculate SCaSO4
Cation
Anion
Ion
ppm (mol/kg) 
ion
Na+
14,500 (0.63)
0.665
Cl-
22,510 (0.69)
0.681 K+
1,234 (0.032)
0.612
SO4-2
2,142 (0.022)
0.087
Ca+2
1,420 (0.035)
0.253
HCO3-
158 (4.0e-3)
0.555
Ba+2
2 (1.4e-5)
0.207
CO3-2
(1.18e-5)
0.093
𝑪𝒂𝑺 𝑶 𝟒 = 𝑪𝒂 +𝟐 + 𝑺 𝑶 𝟒 −𝟐
Step 1) …
𝑆= 𝛾 𝐶𝑎 +2 ∗ 𝑚 𝐶𝑎 +2 ∗ 𝛾 𝑆 𝑂 4 −2 ∗ 𝑚 𝑆 𝑂 4 −2 𝐾 𝑠𝑝, 𝐶𝑎𝑆 𝑂 4 (𝑎𝑛ℎ𝑦𝑑𝑟𝑖𝑡𝑒), (𝑇,𝑃)
Step 4)
Assemble necessary variables (from software or literature)
𝐾 𝑠𝑝, 𝐶𝑎𝑆 𝑂 4 , (25 𝐶,1 𝑏𝑎𝑟) =4.40 𝑒 −5
Plug in data and calculate
Answer: ST=0.385
Example: Calculate SCaSO4

10. Langelier Saturation Index (CaCO3 only)
Well known, pre-computer method
Developed in 1936 to predict corrosion and CaCO3 scale in municipal water
Results (next slide)
LSI>0 Scale forms
LSI<0 Scale dissolves
Limits
6.5 – 9.0 pH
4000 mg/l TDS
95o C
𝐿𝑆𝐼= 𝑝𝐻 𝑚𝑒𝑎𝑠 − 𝑝𝐻 𝑠
pHmeas = measured pH
pHs = pH at saturated CaCO3
𝑝𝐻 𝑠 = 𝑝𝐾 𝐴2 − 𝑝𝐾 𝑠𝑝 − log 𝐶𝑎 +2 − log 𝐴𝑙𝑘
pK2 =HCO3  CO3 equilibrium const.
pKsp = Calcite solubility product const.
Ca+2 = Calcium conc. (mol/l)
Alk = Alkalinity conc. (mol/l as HCO3-)
Langelier Saturation Index (CaCO3 only)

11. LSI Derivation (to show equilibrium equation)
Start with this
𝑝𝐻 𝑠 = 𝑝𝐾 2 − 𝑝𝐾 𝑠𝑝 − log 𝐶𝑎 +2 − log 𝐴𝑙𝑘
𝑝𝐾 𝑠𝑝 = 𝑝𝐾 2 −𝑝𝐻 𝑠 − log 𝐶𝑎 +2 − log 𝐴𝑙𝑘
Rearrange
−log 𝐾 𝑠𝑝 = −log 𝐾 2 + log 𝐻 𝑠 − log 𝐶𝑎 +2 − log 𝐴𝑙𝑘
Convert p to -log
Multiply by -1
log 𝐾 𝑠𝑝 = log 𝐾 2 − log 𝐻 𝑠 + log 𝐶𝑎 log 𝐴𝑙𝑘
𝐾 𝑠𝑝 = 𝐾 2 ∗ 𝐶𝑎 +2 ∗ 𝐻𝐶𝑂 3 − 𝐻 +
Take the exponent
𝐶𝑂 3 −2 = 𝐾 2 ∗ 𝐻𝐶𝑂 3 − 𝐻 +
Insert CO3 equation
End with Solubility
𝐾 𝑠𝑝 = 𝐶𝑎 +2 ∗ 𝐶𝑂 3 −2
LSI Derivation (to show equilibrium equation)

12. Interpreting LSI Results
Scaling and Corrosion Tendency
Treatment +4
Severe Scale Forming
Required +3
Significant Scale Forming
Recommended
+2.0
Moderate Scale-forming
Suggested
+0.5
Slightly scaling and noncorrosive
Balanced but corrosion possible
No Treatment
-0.5
Slightly corrosive and non-scaling -1
Mild Corrosion
-2.0
Moderate Corrosion -3
Severe Corrosion
Interpreting LSI Results

13. Calculate LSI for the following water
Measured data
Constants and pH
Ion
mg/l
mol/l
Na+
23,000
1.0
Ca+2
400
0.01
Cl-
35,500
Alk
610
25C
100C
pK2
10.33
10.09
pKsp
8.62
9.28 pH
7.54
7.47
Results
𝐿𝑆𝐼=𝑝𝐻− 𝑝𝐾 2 − 𝑝𝐾 𝑠𝑝 − log 𝐶𝑎 +2 − log 𝐴𝑙𝑘
25C
100C
LSI
OLI(ScaleTend)
6.8 35
𝐿𝑆𝐼 25𝐶 =7.54− −8.62 − log − log =1.83
𝐿𝑆𝐼 100𝐶 =7.47− −9.25 − log − log =2.63
Calculate LSI for the following water

14. LSI on the web These website contain an LSI calculator
LSI on the web
These website contain an LSI calculator

15. Ryznar Stability Index
Ryznar (1942) refined LSI to distinguish waters with same LSI but different Ca/Alk ratios
A ionic strength term is added to include salinity effects
Primarily for corrosion, semi-quantitative for scale
RSI is inverted: low values indicate scaling. High values indicate corrosion
𝑅𝑆𝐼=2 𝑝𝐻 𝑠 − 𝑝𝐻 𝑚𝑒𝑎𝑠
Where:
𝑝𝐻 𝑠 = 𝑝𝐾 2 − 𝑝𝐾 𝑠𝑝 − log 𝐶𝑎 +2 − log 𝐴𝑙𝑘 +𝐼′
and:
𝐼′= 2.5 𝐼 𝐼 +5.5𝐼
and:
𝐼= 1 2 𝑖 𝑚 𝑖 𝑧 𝑖 2
pK2 and pKs are same as Langelier constants
I=ionic strength
M=concentration (mol/kg)
z=ion charge
Ryznar Stability Index

16. Interpreting RSI Results
Scaling and Corrosion Tendency
Heavy Scale
Light Scale
Little Scale or Corrosion
Some Corrosion
Heavy Corrosion
9.0+
Corrosion Intolerable
Interpreting RSI Results

17.
Ryznar on the Web

18. Puckorius Scaling Index (PSI)
Based on water buffering capacity and the maximum quantity of precipitate that can form
𝑃𝑆𝐼=2 𝑝𝐻 𝑆 − 𝑝𝐻 𝑒𝑞
Where:
&
𝑝𝐻 𝑠 =9.3+𝐴+𝐵−𝐶−𝐷
𝑝𝐻 𝑒𝑞 =1.465∗ log 10 𝐴𝑙𝑘 +4.54
and:
𝐴= log 𝑇𝐷𝑆 −1 10
𝐵=−13.12∗ log 𝑇 𝐾
𝐷= log 𝐴𝑙𝑘 𝑎𝑠 𝐶𝑎𝐶𝑂3
𝐶= log 𝐶𝑎 +2 𝑎𝑠𝐶𝑎𝐶𝑂3 −0.4
𝐴𝑙𝑘 = 𝐻𝐶𝑂 ∗ 𝐶𝑂 3 + 𝑂𝐻
Puckorius Scaling Index (PSI)

19. Stiff Davis Index 𝑆𝑆𝐼=𝑝𝐻+ log 𝐶𝑎 +2 + log 𝐴𝑙𝑘 −𝐾
Stiff and Davis (1952) refined LSI to correct for high salinity of oilfield waters
All the corrections are contained within a Temperature / Salinity plot
𝑆𝑆𝐼=𝑝𝐻+ log 𝐶𝑎 log 𝐴𝑙𝑘 −𝐾
Stiff Davis Index

20. Salinity Plot for Stiff-Davis4
3.5
0oC 3
30oC
50oC
2.5
60oC
70oC K 2
80oC
1.5
90oC
100oC 1
0.5
0.4
0.8
1.2
1.6 2
2.4
2.8
3.2
3.6 4
Molar Ionic Strength
Salinity Plot for Stiff-Davis

21. Calculate SSI for the same water
Measured data
Constants and pH
Ion
mg/l
mol/l
mz2
Na+
23,000
1.0 1
Ca+2
400
0.01
0.04
Cl-
35,500
Alk
610
25C
100C
pK2
10.33
10.09
pKsp
8.62
9.28 pH
7.54
7.47
𝜇= =1.025
Results
𝑆𝑆𝐼=𝑝𝐻+ log 𝐶𝑎 log 𝐴𝑙𝑘 −𝐾
𝑆𝑆𝐼 25𝐶 =7.54−2−2−3.3=0.24
𝑆𝑆𝐼 100𝐶 =7.47−2−2−1.4=2.07
25C
100C
Stiff Davis
OLI(ScaleTend)
6.8 35
Calculate SSI for the same water

22. Oddo-Tomson Indices Initially developed in 1980’s
Available for CaCO3, CaSO4, BaSO4, and SrSO4
Includes gas phase for calcite scale
based on English units; F and psia
Oddo-Tomson was a significant advancement over previous indices. Operators and service companies created spreadsheets with this model. Many are still in use.
Oddo-Tomson Indices
Equations for Calculating CaCO3 scaling with a gas phase present.

23. 𝑆𝐼= log 𝐶𝑎 +2 𝐻𝐶𝑂 3 − 2 𝑃 𝑦𝑔 𝐶𝑂2 ∅𝑔 𝐶𝑂2 +5.85+𝐴−𝐵+𝐶
𝐴= ∗𝑇−1.64∗ 10 −6 ∗𝑇 2
𝐵=5.27𝑥 10 −5 ∗𝑃
𝐶=1.431∗𝐼𝑆−3.334∗ 𝐼𝑆
Oddo-Tomson – CaCO3
T in Fahrenheit, P in psia, I in mg/l TDS/58400
J.E. Oddo, J.P. Smith, and M.B. Tomson Analysis of and solutions to the CaCO3 and CaSO4 problems in West Indonesia. SPE22782.

24. 𝑆 𝑂 4 −2 = 𝐶 𝑆𝑂4 − 𝐶 𝑀𝑔 − 10 𝑝𝐾 ′ + 𝐶 𝑆𝑂4 − 𝐶 𝑀𝑔 − 10 𝑝𝐾 ′ 2 +4∗ 10 𝑝𝐾 ′ 𝐶 𝑆𝑂4 1/2 2
𝑝𝐾 ′ = 𝑒 −3 𝑇−1.2 𝑒 −6 𝑇 𝑒 −5 𝑃−2.38 𝐼 𝐼−1.3 𝑒 −3 𝐼 𝑇
𝑆𝐼 𝐶𝑎𝑆𝑂4, 𝑔𝑦𝑝𝑠𝑢𝑚 = log 𝐶 𝐶𝑎 𝑆 𝑂 4 − 𝑒 −3 𝑇+2.5 𝑒 −6 𝑇 2 −5.9 𝑒 −5 𝑃−1.13 𝐼 𝐼−2 𝑒 −3 𝐼 𝑇
𝑆𝐼 𝐶𝑎𝑆𝑂4, 𝑎𝑛ℎ𝑦𝑑𝑟𝑖𝑡𝑒 = log 𝐶 𝐶𝑎 𝑆 𝑂 4 − 𝑒 −3 𝑇+0.97 𝑒 −6 𝑇 2 −3.07 𝑒 −5 𝑃−1.09 𝐼 𝐼−3.3 𝑒 −3 𝐼 𝑇
Oddo-Tomson CaSO4
T in Fahrenheit, P in psia, I in mg/l TDS/58400
J.E. Oddo, J.P. Smith, and M.B. Tomson Analysis of and solutions to the CaCO3 and CaSO4 problems in West Indonesia. SPE22782.

25. Oddo-Tomson SrSO4 & BaSO4
𝑆 𝑂 4 −2 = 𝐶 𝑆𝑂4 − 𝐶 𝑀𝑔 − 𝐶 𝐶𝑎 − 10 𝑝𝐾 ′ 𝐶 𝑆𝑂4 − 𝐶 𝑀𝑔 − 𝐶 𝐶𝑎 − 10 𝑝𝐾 ′ ∗ 10 𝑝𝐾 ′ 𝐶 𝑆𝑂4 1/2 2
𝑆𝐼 𝑆𝑟𝑆𝑂4, 𝑐𝑒𝑙𝑒𝑠𝑡𝑖𝑡𝑒 = log 𝐶 𝑆𝑟 𝑆 𝑂 4 − 𝑒 −3 𝑇+6.4 𝑒 −6 𝑇 2 −4.6 𝑒 −5 𝑃−1.89 𝐼 𝐼−1.9 𝑒 −3 𝐼 𝑇
𝑆𝐼 𝑆𝑟𝑆𝑂4, 𝑏𝑎𝑟𝑖𝑡𝑒 = log 𝐶 𝐵𝑎 𝑆 𝑂 4 − 𝑒 −3 𝑇+11.4 𝑒 −6 𝑇 2 −4.8 𝑒 −5 𝑃−2.62 𝐼 𝐼−2.0 𝑒 −3 𝐼 𝑇
Oddo-Tomson SrSO4 & BaSO4
T in Fahrenheit, P in psia, I in mg/l TDS/58400
J.E. Oddo, J.P. Smith, and M.B. Tomson Analysis of and solutions to the CaCO3 and CaSO4 problems in West Indonesia. SPE22782.

26. Screenshot of the Oddo-Tomson paper

27. Screenshot of the Oddo-Tomson paper

28. Screenshot of the Oddo-Tomson paper

29. Larson-Skold Index epm=equivalents per million
Based on mild steel corrosion in Great Lakes water
Ratio of epm SO42- and Cl- to epm HCO3-+CO3-2
X< SO42- and Cl- will not interfere with film formation
0.8<X< SO42- and Cl- may interfere with film formation. Higher corrosion rates anticipated
X>1.2 - high local corrosion rates expected
Larson-Skold Index
epm=equivalents per million

30. Common Commercial Programs
Multi Scale (Expro Petrotech)
ScaleSoftPitz (Rice University)
Downhole SAT (French Creek Software)
ScaleChem (OLI Systems)
Common Commercial Programs

31. Equilibrium and steady- state
Equation of state *
Chemical Speciation*
Activity coefficient *
Phase equilibrium
Mass balance
Charge balance
Energy balance
Process simulation
non-Equilibrium and transient
Mass transfer
Phase velocity
Nucleation kinetics
Precipitation kinetics
Scale inhibition
Scale adhesion
Commercial Software Contain some-many of the following equations/models
* - minimum required for accurate oilfield scale prediction

32. Summary Many scale prediction tools available All have some value
All based on fundamental equilibrium equations
Each have adjustments for temperature and salinity
All have some value
Low cost
Easy to use
Can calculate complex systems
Can model mixing and inhibition
Summary