Scaling Tendencies

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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).

Solubility Product Constant, K_sp 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: 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:

a_i=m_i γ_i

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 K_sp, but involves the actual activities of the species in solution. IAP=(a_B )_actual^b∙ (a_D )_actual^d

Scaling Tendency and Scaling Index

Scaling Tendency (Reported in the OLI software as Post-Scale)

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

ST=IAP/K_sp

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:

SI =log_10⁡(IAP/K_sp ) 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 (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:

ST = IAP/Ksp


Pre-Scaling Index (Reported in the software as SI, Index)

Pre-Scale Index (SI) is the log value of the Pre-Scaling Tendency (PST):

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.


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(S).


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.


Calculating Scaling Tendency: An Example

Below there is an example of how the software calculates the Scaling Tendency. Consider the dissolution of sodium bicarbonate:

NaHCO3(s) = Na+ + HCO3-


Scaling Tendency is defined as ST = IAP/Ksp


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 Ksp is the Solubility Product Constant which gives the thermodynamic limit of ion availability.


Let’s consider a 1.0 molal NaHCO3 solution. The IAP is calculated as follows:

IAP = [gammaNa+]*[mNa+]*[gammaHCO3-]*[mHCO3-]


Assuming Ideal Solution Activities:


gammaNa+ = 1.0

gammaHCO3- = 1.0

mNa+ = 1.0

mHCO3- = 1.0


Then,

IAP = (1.0)(1.0)(1.0)(1.0)

IAP = 1.0


Defining the Ksp


Ksp = [gammaNa+]*[mNa+]*[gammaHCO3-]*[mHCO3-]

Ksp = 0.403780


The Scaling Tendency is then the ratio of available ions to the thermodynamic limit:


ST = IAP/Ksp

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:


gammaNa+ = 0.598

gammaHCO3- = 0.596

mNa+ = 0.894

mHCO3- = 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/Ksp

ST = 0.276/0.40378

ST = 0.683