- Objective
- What is a scaling tendency?
- Difference between Post-scale and Pre-scale Tendencies
- Calculating Scaling Tendency: An Example
- What is a pre-scaling tendency?

# Objective

Welcome to OLI ScaleChem! We are excited to introduce you to a crucial concept for assessing scaling risks in your simulations: pre-scaling tendency. This innovative metric provides a quick reference for the likelihood of solid phase formation under given simulation conditions despite being an artificial value not strictly grounded in thermodynamics.

# What is a scaling tendency?

Before diving into pre-scaling and post-scaling tendencies, one must grasp the concept of thermodynamic scaling tendencies. Scaling refers to the deposition of mineral salts on processing equipment, which occurs when mineral ions in the process fluid become supersaturated. Factors like temperature changes, solvent evaporation, or degasification can lead to salt concentrations exceeding saturation, resulting in solid precipitation, typically as crystals.

Two key definitions are used to quantify scaling: Scaling Tendency and Scaling Index. These depend on the Solubility Product Constant (Ksp) and Ion Activity Product (IAP).

## Solubility Product Constant, K_{sp}

The solubility of salts and minerals in water is determined by a **solubility equilibrium expression** and a **solubility product constant, Ksp,** which varies with temperature and pressure. Consider the dissolution reaction:

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 and its corresponding activity coefficient:

*a*_{i}=m_{i} γ_{i}

## Ion Activity Product, IAP

A solution may not be in equilibrium, and this **non-equilibrium state** is described by the Ion Activity Product (IAP), which has the same form as Ksp but involves the **actual activities** of the species in solution:

IAP=(*a*_{B})^{b}_{actual}∙(*a*_{D})^{d}_{actual}

## 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 (K_{sp}).

**Equation (1)** ST=IAP/K_{sp}

Scaling tendencies are essentially saturation ratios. Thus:

- ST < 1 Indicates sub-saturation, and the solid is not expected to form
- ST = 1 Indicates saturation and the solid is in equilibrium with the 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 =log_{10}(IAP/K_{sp})

Thus:

- 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

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

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

# Difference between Post-scale and Pre-scale Tendencies

- 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 concentration (activity) ratio 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=∞).

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

# Calculating Scaling Tendency: An Example

Below is an example of how the software calculates the Scaling Tendency, using the AQ thermodynamic framework.

# What is a pre-scaling tendency?

*A more detailed answer*

OLI defines a Pre-Scaling tendency as the scaling tendency before any solids have been formed. Many industries, notably the upstream oil and gas industry, use the pre-scaling tendency to make design decisions about adding anti-scaling and anti-fouling agents or whether the asset is at risk.

The normal convergence path for any OLI equilibrium calculation is the following:

- Perform an initial estimate of all variables.
- Save ion activities for pre-scale calculations.
- Converge the equation set and check for phase changes.
- Adjust component mass for phase changes.
- Re-converge and test for further phase changes.
- Conclude the calculation if no phase changes occur.
- Finalize post-scaling tendencies, transport properties, and additional thermodynamic calculations.
- Generate the report.

## Estimated v. Rigorous Pre-scaling tendencies

OLI employs two methods for determining the pre-scaling tendencies: estimated and rigorous. Both methods are discussed next.

### Estimated Pre-Scales

Estimated pre-scaling tendencies are obtained before final convergence, providing a faster method that is generally accurate. For example, in OLI Studio, activating pre-scaling calculations involves selecting the Pre-Scaling Tendencies option and running the simulation. The estimated pre-scale value for CaCO3 (Calcite) might be 160.853, compared to a post-scale value 1.0, indicating solid formation.

We have an example created in version 12.0, which can be found at the bottom of the article.

Let's look at an example.

We have created a simple case in MSE.

While not representative of a true case in the upstream oil and gas industry, it shows some common components.

We now need to activate the Pre-scaling calculation (different OLI programs do this step in different ways; we are using OLI Studio as an example).

Use the **Specs** button to find the calculation option

Check the Pre-Scaling Tendencies box and then the Estimated button.

We will run this case and look at the output.

Look at the pre-scaling tendencies for CaCO3(Calcite). This value is 160.853. If you look at the Scaling Tendencies (also known as the post-scaling tendencies), the value for the same species is 1.0, which means the solid has formed.

### Rigorous Pre-Scales

Rigorous pre-scaling calculations ensure more accurate results, especially for models with common ions like CaCO3 and MgCO3 or soluble species like Na2CO3. This method involves:

- Performing an initial estimate.
- Converging the equation set and checking for phase changes.
- Adjusting component mass and re-converging as needed.
- Eliminating solids mathematically and re-converging.
- Storing scaling tendencies as pre-scaling tendencies.

In version 12.0 of OLI Engine, rigorous pre-scaling is automated. For example, with rigorous pre-scaling activated, the pre-scaling tendency for CaCO3 might be 160.959, compared to the estimated value of 160.853.

The overall calculation path is similar to the previously described path but it has one major change:

- Performing an initial estimate.
- Converging the equation set and checking for phase changes.
- Adjusting component mass and re-converging as needed.
- Eliminating solids mathematically and re-converging.
- Storing scaling tendencies as pre-scaling tendencies.

In the past, if you wanted to have rigorous pre-scaling tendencies, you had to recreate the chemistry model without any solids and then re-calculate the equation set. This manual step is now automatically done for you internally.

Here is an example: we are using the same input stream, but we are activating the rigorous pre-scaling option. Use the Specs button to select Rigorous.

Run the calculation

Look the pre-scaling tendencies for CaCO_{3}(Calcite). This value is 160.959 If you look at the Scaling Tendencies (this is also known as the post-scaling tendencies) the value for the same species is 1.0 which means the solid has formed. The calculation time is 0.196 seconds.

### Differences

While the differences between estimated and rigorous pre-scaling tendencies are usually small, they can be significant in larger models. For instance, the difference for CaCO3 in our example is minor, but the rigorous approach ensures more accurate and reliable results for complex systems.

We hope this guide helps you understand and utilize pre-scaling tendencies in OLI ScaleChem effectively. For further details, examples, or assistance, feel free to reach out to our support team. Happy scaling!