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 Pre-scaling Tendency in OLI Software

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.

What is a Scaling Tendency?

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 (Ksp). For example for the following reaction

CaCO3(s) = Ca+2 + CO3-2

The scaling tendency (ST) is:

ST = [Ca+2][CO3-2]/Ksp

The three possible ST scenarios are the following:

    Scaling Tendency      Result
    < 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)

Scale Index (SI) is the log value of the Scaling Tendency (ST):

SI = Log (ST)


There are three scenarios for the Scale Index (also referred to as the Saturation Index)

  • SI = 0 IAP = Ksp → saturated (in equilibrium)
  • SI < 0 IAP < Ksp → undersaturated
  • SI > 0 IAP > Ksp → supersaturated


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