Difference between revisions of "Scaling Tendencies"

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===What is Scaling?===
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==What is Scaling?==
  
Scaling is the deposition of a mineral salt on processing equipment. Scaling is a result
+
Scaling is the deposition of a mineral salt on processing equipment. Scaling is a result of supersaturation of mineral ions in the process fluid. Through changes in temperature, or solvent evaporation or degasification, the concentration of salts may exceed the saturation, leading to a precipitation of solids (usually crystals).
of supersaturation of mineral ions in the process fluid. Through changes in temperature, or solvent evaporation or degasification, the concentration of salts may exceed the saturation, leading to a precipitation of solids (usually crystals).
+
  
'''Solubility Product Constant, K_sp'''
+
To understand Scaling, the Scaling Tendency and Scaling Index definitions are used. These definitions depended on the Solubility Product Constant, K<sub>sp</sub> and Ion Activity Product, IAP definitions.
The solubility of ionic compounds of salts and minerals in water are governed by a solubility equilibrium expression and a solubility product constant known as K_sp. It is important to note that the solubility product, K_sp is a function of both temperature and pressure. Consider the general dissolution reaction below (in aqueous solutions):
+
  
aA_((s))⇌bB_((aq))+dD_((aq))
 
  
With equilibrium constant K_sp defined as:
+
'''Solubility Product Constant, K<sub>sp</sub>'''
K_sp=〖(a〗_B )^b  ∙(a_D )^d
+
  
Where, a_B and a_D are the activities of the aqueous species. The activity of any species i is defined as the product of its concentration in molality by its corresponding activity coefficient:  
+
The solubility of ionic compounds of salts and minerals in water are governed by a solubility equilibrium expression and a solubility product constant known as K<sub>sp</sub>. It is important to note that the solubility product, K<sub>sp</sub> is a function of both temperature and pressure. Consider the general dissolution reaction below (in aqueous solutions):
  
a_i=m_i γ_i
+
aA<sub>(s)</sub>⇌bB<sub>(aq)</sub>+dD<sub>(aq)</sub>
  
'''Ion Activity Product, IAP'''
+
With equilibrium constant K<sub>sp</sub> defined as:
A real solution may not be in the state of equilibrium. This non-equilibrium state is described by the ion activity product (IAP). It has the same form as the equilibrium constant K_sp, but involves the actual activities of the species in solution.
+
IAP=(a_B )_actual^b∙ (a_D )_actual^d
+
  
==Scaling Tendency and Pre-scaling Tendency in OLI Software==
+
K<sub>sp</sub>=(''a''<sub>B</sub>)<sup>b</sup>∙(''a''<sub>D</sub>)<sup>d</sup>
  
 +
Where, ''a''<sub>B</sub> and ''a''<sub>D</sub> are the activities of the aqueous species. The activity of any species i is defined as the product of its concentration in molality by its corresponding activity coefficient:
  
 +
''a''<sub>i</sub>=m<sub>i</sub> γ<sub>i</sub>
  
=== Scaling Tendency (Reported in the software as Post-Scale)===
 
  
Scaling tendencies are essentially saturation ratios. When the scaling tendency for a species is 1.0, it indicates that its solid form is in equilibrium with water. A scaling tendency below 1.0 indicates sub-saturation and that the solid phase will not form.
+
'''Ion Activity Product, IAP'''
  
===What is a Scaling Tendency?===
+
A real solution may not be in the state of equilibrium. This non-equilibrium state is described by the ion activity product (IAP). It has the same form as the equilibrium constant K<sub>sp</sub>, but involves the actual activities of the species in solution.
 +
 +
IAP=(''a''<sub>B</sub>)<sup>b</sup><sub>actual</sub>∙(''a''<sub>D</sub>)<sup>d</sup><sub>actual</sub>
  
Scaling Tendency is defined as the ratio of the concentration of the ions of the salt of interest divided by the equilibrium constant of the same salt (K<sub>sp</sub>). For example for the following reaction
+
==Scaling Tendency and Scaling Index==
  
CaCO<sub>3(s)</sub> = Ca<sup>+2</sup> + CO<sub>3</sub><sup>-2</sup>
+
The Scaling Tendency (ST) is defined as the ratio of the Ion Activity Product (IAP) divided by the equilibrium constant (K<sub>sp</sub>).
  
The scaling tendency (ST) is:
 
  
ST = [Ca<sup>+2</sup>][CO<sub>3</sub><sup>-2</sup>]/K<sub>sp</sub>
+
'''Equation (1)'''  ST=IAP/K<sub>sp</sub>  
  
The three possible ST scenarios are the following:
 
  
    Scaling Tendency      Result
+
Scaling tendencies are essentially saturation ratios. Thus, if
    < 1.0           The solid is under-saturated and is not expected to form
+
    = 1.0           The solid is saturated and may or may not form
+
    > 1.0           The solid is over-saturated is expected to form
+
  
===Scale Index (Reported in the software as SI, Index)===
+
*ST < 1 Indicates sub-saturation, and the solid is not expected to form
 +
*ST = 1 Indicates saturation, and the solid is in equilibrium with water
 +
*ST > 1 Indicates supersaturation, and solids will form
  
Scale Index (SI) is the log value of the Scaling Tendency (ST):
 
  
SI = Log (ST)
+
'''Note:''' The Scaling Tendency (ST) is reported in the software as Post-Scale.
  
  
There are three scenarios for the Scale Index (also referred to as the Saturation Index)
+
The Scale Index (SI) (aka: Saturation Index in the literature), is given by the following relationship:
  
*SI = 0 IAP = Ksp → saturated (in equilibrium)
 
*SI < 0 IAP < Ksp → undersaturated
 
*SI > 0 IAP > Ksp → supersaturated
 
  
 +
'''Equation (2)'''    SI =log<sub>10</sub>(IAP/K<sub>sp</sub>)
  
===Pre-Scaling Tendency (Reported in the software as Pre-Scale)===
 
  
OLI software defines a Pre-Scaling tendency as the scaling tendency before solids precipitate. The Pre-scaling tendency is calculated the same as the Post-scaling tendency:
+
Thus, if
 +
*SI < 0 Indicates sub-saturation, and the solid is not expected to form
 +
*SI = 0 Indicates saturation, and the solid is in equilibrium with water
 +
*SI > 0 Indicates supersaturation, and solids will form
  
ST = IAP/K<sub>sp</sub>
 
  
 +
'''Note:''' The Scaling Index (SI) is reported in the software as SI, Index
  
 +
==Pre-Scaling Tendency and Scaling Index==
  
===Pre-Scaling Index (Reported in the software as SI, Index)===
 
  
 +
Pre-Scaling tendency is defined as the scaling tendency before any solids are formed (this can be seen as all the species suspended in solution). The same formulas for ST and SI are applied (Equations 1 and 2).
  
Pre-Scale Index (SI) is the log value of the Pre-Scaling Tendency (PST):
+
The Pre-Scaling tendency is reported in the software as Pre-Scale.
  
PSTI = Log (PST)
 
  
Note: Many industries, notably the up-stream oil & gas industry, use the pre-scaling tendency to make design decisions about adding anti-scaling and anti-fouling agents or if the asset is as risk.
+
'''Note:''' Many industries, notably the up-stream oil & gas industry, use the pre-scaling tendency to make design decisions about adding anti-scaling and anti-fouling agents or if the asset is as risk.
  
 
+
==Difference between Post-scale and Pre-scale==
===Difference between Post-scale and Pre-scale===
+
  
 
*Pre-Scale: The saturation ratio before solids precipitate.  
 
*Pre-Scale: The saturation ratio before solids precipitate.  
 
*Post-Scale: The saturation ratio AFTER solids precipitate (if solids are selected).  
 
*Post-Scale: The saturation ratio AFTER solids precipitate (if solids are selected).  
 
*S, ST – Saturation, Scale Tendency: The ratio of the concentration (activity) to its solubility (S=1).  
 
*S, ST – Saturation, Scale Tendency: The ratio of the concentration (activity) to its solubility (S=1).  
*SI – Scale Index: Log(S).  
+
*SI – Scale Index: Log(ST).  
  
  
 
+
'''Scaling Tendency''' is the saturation ratio after all potential solids come to equilibrium with water. This is the true equilibrium condition (time=∞). I
'''Scaling Tendency''' is the saturation ratio after all potential solids come to equilibrium with water. This is the true equilibrium condition (time=∞). In OLI Software the Scaling Tendencies are reported under the name of '''Post-Scaling'''.
+
  
 
'''Pre-scaling Tendency''' represents the condition before any solids are allowed to form. This is a non-equilibrium condition and can be viewed as the condition where time=0.
 
'''Pre-scaling Tendency''' represents the condition before any solids are allowed to form. This is a non-equilibrium condition and can be viewed as the condition where time=0.
  
 +
==Calculating Scaling Tendency: An Example==
  
===Calculating Scaling Tendency: An Example===
+
Below there is an example of how the software calculates the Scaling Tendency.
 
+
Below there is an example of how the software calculates the Scaling Tendency. Consider the dissolution of sodium bicarbonate:
+
 
+
NaHCO<sub>3(s)</sub> = Na<sup>+</sup> + HCO<sub>3</sub><sup>-</sup>
+
 
+
 
+
Scaling Tendency is defined as ST = IAP/K<sub>sp</sub>
+
 
+
 
+
Where '''IAP''' is the '''Ion Activity Product''', and is defined as the product of specific  ions (in this case the ions resulting from the dissociation of a particular solid); and '''K<sub>sp</sub>''' is the '''Solubility Product Constant'''  which gives the thermodynamic limit of ion availability.
+
 
+
 
+
Let’s consider a 1.0 molal NaHCO<sub>3</sub> solution. The IAP is calculated as follows:
+
 
+
IAP = [gamma<sub>Na<sup>+</sup></sub>]*[m<sub>Na<sup>+</sup></sub>]*[gamma<sub>HCO<sub>3</sub><sup>-</sup></sub>]*[m<sub>HCO<sub>3</sub><sup>-</sup></sub>]
+
 
+
 
+
Assuming Ideal Solution Activities:
+
 
+
 
+
gamma<sub>Na<sup>+</sup></sub> = 1.0
+
 
+
gamma<sub>HCO<sub>3</sub><sup>-</sup></sub> = 1.0
+
 
+
m<sub>Na<sup>+</sup></sub> = 1.0
+
 
+
m<sub>HCO<sub>3</sub><sup>-</sup></sub> = 1.0
+
 
+
 
+
Then,
+
 
+
IAP = (1.0)(1.0)(1.0)(1.0)
+
 
+
IAP = 1.0
+
 
+
 
+
Defining the Ksp
+
 
+
 
+
K<sub>sp</sub> = [gamma<sub>Na<sup>+</sup></sub>]*[m<sub>Na<sup>+</sup></sub>]*[gamma<sub>HCO<sub>3</sub><sup>-</sup></sub>]*[m<sub>HCO<sub>3</sub><sup>-</sup></sub>]
+
 
+
K<sub>sp</sub> = 0.403780
+
 
+
 
+
 
+
The Scaling Tendency is then the ratio of available ions to the thermodynamic limit:
+
 
+
 
+
ST = IAP/K<sub>sp</sub>
+
 
+
ST = 1.0/0.403780
+
 
+
ST = 2.48
+
 
+
 
+
Was assuming ideal conditions valid?? The actual species concentration and activity coefficients (calculated by the OLI software) are:
+
 
+
 
+
gamma<sub>Na<sup>+</sup></sub> = 0.598
+
 
+
gamma<sub>HCO<sub>3</sub><sup>-</sup></sub> = 0.596
+
 
+
m<sub>Na<sup>+</sup></sub> = 0.894
+
 
+
m<sub>HCO<sub>3</sub><sup>-</sup></sub> = 0.866
+
 
+
 
+
 
+
This results in a different IAP:
+
 
+
 
+
IAP= (0.598)(0.894)(0.596)(0.866)
+
 
+
IAP=0.276
+
 
+
 
+
The new Scaling Tendency is the following:
+
 
+
ST = IAP/K<sub>sp</sub>
+
 
+
ST = 0.276/0.40378
+
  
ST = 0.683
+
[[File:scaling tendency example.png]]
  
 
[[Category:Tips]]
 
[[Category:Tips]]

Revision as of 21:43, 13 February 2020

Contents

What is Scaling?

Scaling is the deposition of a mineral salt on processing equipment. Scaling is a result of supersaturation of mineral ions in the process fluid. Through changes in temperature, or solvent evaporation or degasification, the concentration of salts may exceed the saturation, leading to a precipitation of solids (usually crystals).

To understand Scaling, the Scaling Tendency and Scaling Index definitions are used. These definitions depended on the Solubility Product Constant, Ksp and Ion Activity Product, IAP definitions.


Solubility Product Constant, Ksp

The solubility of ionic compounds of salts and minerals in water are governed by a solubility equilibrium expression and a solubility product constant known as Ksp. It is important to note that the solubility product, Ksp is a function of both temperature and pressure. Consider the general dissolution reaction below (in aqueous solutions):

aA(s)⇌bB(aq)+dD(aq)

With equilibrium constant Ksp defined as:

Ksp=(aB)b∙(aD)d

Where, aB and aD are the activities of the aqueous species. The activity of any species i is defined as the product of its concentration in molality by its corresponding activity coefficient:

ai=mi γi


Ion Activity Product, IAP

A real solution may not be in the state of equilibrium. This non-equilibrium state is described by the ion activity product (IAP). It has the same form as the equilibrium constant Ksp, but involves the actual activities of the species in solution.

IAP=(aB)bactual∙(aD)dactual

Scaling Tendency and Scaling Index

The Scaling Tendency (ST) is defined as the ratio of the Ion Activity Product (IAP) divided by the equilibrium constant (Ksp).


Equation (1) ST=IAP/Ksp


Scaling tendencies are essentially saturation ratios. Thus, if

  • ST < 1 Indicates sub-saturation, and the solid is not expected to form
  • ST = 1 Indicates saturation, and the solid is in equilibrium with water
  • ST > 1 Indicates supersaturation, and solids will form


Note: The Scaling Tendency (ST) is reported in the software as Post-Scale.


The Scale Index (SI) (aka: Saturation Index in the literature), is given by the following relationship:


Equation (2) SI =log10(IAP/Ksp)


Thus, if

  • SI < 0 Indicates sub-saturation, and the solid is not expected to form
  • SI = 0 Indicates saturation, and the solid is in equilibrium with water
  • SI > 0 Indicates supersaturation, and solids will form


Note: The Scaling Index (SI) is reported in the software as SI, Index

Pre-Scaling Tendency and Scaling Index

Pre-Scaling tendency is defined as the scaling tendency before any solids are formed (this can be seen as all the species suspended in solution). The same formulas for ST and SI are applied (Equations 1 and 2).

The Pre-Scaling tendency is reported in the software as Pre-Scale.


Note: Many industries, notably the up-stream oil & gas industry, use the pre-scaling tendency to make design decisions about adding anti-scaling and anti-fouling agents or if the asset is as risk.

Difference between Post-scale and Pre-scale

  • Pre-Scale: The saturation ratio before solids precipitate.
  • Post-Scale: The saturation ratio AFTER solids precipitate (if solids are selected).
  • S, ST – Saturation, Scale Tendency: The ratio of the concentration (activity) to its solubility (S=1).
  • SI – Scale Index: Log(ST).


Scaling Tendency is the saturation ratio after all potential solids come to equilibrium with water. This is the true equilibrium condition (time=∞). I

Pre-scaling Tendency represents the condition before any solids are allowed to form. This is a non-equilibrium condition and can be viewed as the condition where time=0.

Calculating Scaling Tendency: An Example

Below there is an example of how the software calculates the Scaling Tendency.

Scaling tendency example.png