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):
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:
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).
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
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:
The new Scaling Tendency is the following:
ST = IAP/Ksp
ST = 0.276/0.40378
ST = 0.683