## Introduction

What is the difference between a scaling tendency and a pre-scaling tendency?

Many users are confused by what OLI means by a scaling tendency and a pre-scaling tendency (also known as a pScale). OLI uses the scaling tendency (hereafter known as ST) to indicate how much mass needs to be moved between phases. The pScale is used only as an indication of the amount of scale that will form.

## What is a scaling tendency (ST)?

Lets consider the dissolution of a solid such as calcium carbonate. The equilibrium expression will look like this:

CaCO_{3(s)} = Ca^{2+} + CO_{3}^{2-}

We will define the solubility product as:

K_{SP} = (a_{Ca2+})(a_{CO3(2-)})

Where "a" is the activity of the species and has the form:

a_{i} = γ_{i}[i]

We now define the scaling tendency for calcium carbonate as:

ST = γ_{Ca2+}[Ca^{2+}]γ_{CO3(2-)}[CO_{3}^{2-}]/K_{SP}

Scaling Tendency | Result |
---|---|

< 1.0 | The solid is under-saturated and is not expected to form |

= 1.0 | The solid is saturated and is expected to form |

> 1.0 | The solid is over-saturated and may or may not form. |

Why may a solid have a value greater than 1.0 for a Scaling Tendency? You may have deselected the solid for consideration but the ions in solution are greater than the solubility product. Or the temperature of the calculation has exceeded the temperature range for the solid. See TRANGE for an explanation.

## What does OLI actually use Scaling Tendencies (ST) for?

We use the ST for each solid to determine how much mass will move between the liquid phase and the solid phase. To make this explanation a bit clearer we will consider what we are doing with calcium carbonate. The software first determines the mole flow of each inflow entering into the solver calculation. The software makes no assumptions about phases at this time (solid, liquid or vapor). The software understands that the user has allowed CaCO3 to form as a solid but the software has not made any initial estimates about how much solid will be present, if any.

The solver must eventually solve a series of equations and unknowns. To do this we must provide an initial value for each unknown. We have a small program called the initializer algorithm which makes an attempt to determine some solution chemistry – an estimate really. The solver does by assuming activity coefficients of 1.0 for most species.

This will calculate a scaling tendency for the allowed solids and a vapor tendency and 2nd liquid tendency as well. It may be possible that the newly created scaling tendency is larger than 1.0. The initializer algorithym has overestimated the amount of ions and has returned a value greater than 1.0 for the scaling tendency.

The solver then adjusts the mass-balances between phases, in this case moving both Calcium and Carbonate ions from the liquid phase to the solid phase and then recalculate the scaling tendency. This repeats until there is no change in the scaling tendencies.

When the iterations have completed, we will have solids with scaling tendencies less than 1.0 (under-saturated), 1.0 which means they form or greater than 1.0 which means the solids are excluded because of model choices or the above mentioned TRANGE.

## What is a pre-scaling tendency?

We discussed why we use scaling tendencies in the preceding section. To reiterate, we initially make an estimate of what the unknown variables will be in our equation matrix. We initially assume that no solids are present. During the convergence run we will obtain our first set of scaling tendencies. These scaling tendencies are what we call the pre-scaling tendencies (pScale). It is important to know that the solver has not fully converged the equations at this point and the pScale value has some assumptions built into it.

- The pScale value is not from a fully converged solution. The activity model may still have some uncertainty to it.
- Since no solids were initially assumed to be present in the calculation, each pScale is independent of all other solids. Some solids may have common ions (such as the carbonates). Each solid carbonate, for example, will have the full concentration of ions available for the pScale value. This makes each pScale value independent of other solids. This will not be true with the actual scaling tendency.
- Effects of TRANGE are not considered with pScale. If the solid is outside the regressed temperature range the pScale value may be too high (or to small).