Difference between revisions of "Scaling Tendencies"

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==What is Scaling?==
  
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===OLI Tips #39 What is a Scaling Tendency?===
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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).
  
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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.
  
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A scaling tendency is the ratio of the real-solution solubility product to the thermodynamic limit based on the thermodynamic equilibrium constant.
 
  
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For the usage of the term in the software, it is defined as
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'''Solubility Product Constant, K<sub>sp</sub>'''
  
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Definition for Pre-Scaling tendencies: They are scaling tendencies of a solid before we permit any other solid phases to appear, i.e. before we allow solids to form. This measure acts as if other solids do not exist. The common ion effect is not considered while these tendencies are calculated.
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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):
  
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Post –Scaling tendencies: Effect of common ions is considered. These tendencies are calculated after solids are formed. Technically the scaling tendencies which you see in the plot in analyzers are these post scaling tendencies.
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aA<sub>(s)</sub>⇌bB<sub>(aq)</sub>+dD<sub>(aq)</sub>
  
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Pre-scaling tendency is the same formula except for a situation when solids are not allowed to form. The mass transfer between LIQ phase to SOL is not considered while calculating these values. That is the only way to predict 'pre-scaling' tendencies.
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With equilibrium constant K<sub>sp</sub> defined as:
  
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K<sub>sp</sub>=(''a''<sub>B</sub>)<sup>b</sup>∙(''a''<sub>D</sub>)<sup>d</sup>
  
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For Example, Consider this dissolution
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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:
  
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NaHCO3(s) = Na+ + HCO3-
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''a''<sub>i</sub>=m<sub>i</sub> γ<sub>i</sub>
  
  
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The Ion Activity Product (IAP) is defined as the product of specific  ions (in this case the ions resulting from the dissociation of a particular solid).
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'''Ion Activity Product, IAP'''
  
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Let’s consider a 1.0 molal NaHCO3 solution:
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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.
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IAP=(''a''<sub>B</sub>)<sup>b</sup><sub>actual</sub>∙(''a''<sub>D</sub>)<sup>d</sup><sub>actual</sub>
  
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IAP = NamNaHCO3mHCO3
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==Scaling Tendency and Scaling Index==
  
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Assuming Ideal Solution Activities
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The Scaling Tendency (ST) is defined as the ratio of the Ion Activity Product (IAP) divided by the equilibrium constant (K<sub>sp</sub>).  
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Na = 1.0 HCO3 = 1.0
 
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mna = 1.0 mHCO3 = 1.0
 
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IAP = (1.0)(1.0)(1.0)(1.0)
 
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IAP = 1.0
 
  
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The Solubility Product (KSP) is the thermodynamic limit of ion availability
 
  
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Ksp = NamNaHCO3mHCO3
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'''Equation (1)'''  ST=IAP/K<sub>sp</sub>
  
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KSP = 0.403780
 
  
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The Scaling Tendency is then the ratio of available ions to the thermodynamic limit.
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Scaling tendencies are essentially saturation ratios. Thus, if
  
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ST = IAP/KSP
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*ST < 1 Indicates sub-saturation, and the solid is not expected to form
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ST = 1.0/0.403780
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*ST = 1 Indicates saturation, and the solid is in equilibrium with water
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ST = 2.48
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*ST > 1 Indicates supersaturation, and solids will form
  
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Was assuming ideal conditions valid??
 
  
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The actual species concentration and activity coefficients are:
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'''Note:''' The Scaling Tendency (ST) is reported in the software as Post-Scale.  
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Na = 0.598 HCO3 = 0.596
 
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mna = 0.894 mHCO3 = 0.866
 
  
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This results in a different IAP
 
  
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IAP= (0.598)(0.894)(0.596)(0.866)
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The Scale Index (SI) (aka: Saturation Index in the literature), is given by the following relationship:
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IAP=0.276
 
  
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The new Scaling Tendency is therefore:
 
  
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ST = IAP/Ksp
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'''Equation (2)'''    SI =log<sub>10</sub>(IAP/K<sub>sp</sub>)
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ST = 0.276/0.40378
 
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ST = 0.683
 
  
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Why are the concentrations not equal to 1.0? Speciation and chemical equilibria tend to form complexes which provide a “Sink” for carbonate species. In this example:
 
  
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CO2o = 0.016 molal
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Thus, if
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NaHCO3o = 0.101 molal
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*SI < 0 Indicates sub-saturation, and the solid is not expected to form
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CO32- = 0.012 molal
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*SI = 0 Indicates saturation, and the solid is in equilibrium with water
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NaCO3- = 0.004 molal
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*SI > 0 Indicates supersaturation, and solids will form
  
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What does the Scaling Tendency Mean?
 
  
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If ST < 1, then the solid is under-saturated
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'''Note:''' The Scaling Index (SI) is reported in the software as SI, Index
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If ST > 1, then the solid is super-saturated
 
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If ST = 1, then the solid is at saturation
 
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Scaling Index = Log (ST)
 
  
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The post-scaling tendency can go over 1.0 in special cases. If you have disabled a solid from forming (via the Menu Item: Chemistry: Model Options: Phases Tab) then it is possible to have a scaling tendency greater than 1.0. Also if the temperature is above a solid’s Temperature Range (TRANGE) then it can also be above 1.0. Please refer to the TRANGE support tip.
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==Pre-Scaling Tendency and Scaling Index==
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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).
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The Pre-Scaling tendency is reported in the software as Pre-Scale.
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'''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.
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==Difference between Post-scale and Pre-scale==
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*Pre-Scale: The saturation ratio before solids precipitate.
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*Post-Scale: The saturation ratio AFTER solids precipitate (if solids are selected).
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*S, ST – Saturation, Scale Tendency: The ratio of the concentration (activity) to its solubility (S=1).  
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*SI – Scale Index: Log(ST).  
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'''Scaling Tendency''' is the saturation ratio after all potential solids come to equilibrium with water. This is the true equilibrium condition (time=∞). I
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'''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.
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==Calculating Scaling Tendency: An Example==
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Below there is an example of how the software calculates the Scaling Tendency - using the AQ thermodynamic framework-
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[[File:scaling tendency example.png]]
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[[Category:Tips]]
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[[Category:Thermodynamics]]
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[[Category: Scaling and solid formations]]
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[[Category: Former Tips]]

Latest revision as of 11:58, 6 March 2020

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 - using the AQ thermodynamic framework-

Scaling tendency example.png

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