Table of Contents

• Overview and History
• Overcoming the Obstacles
• Problems
• OLI Studio
• MSE Thermodynamic Framework
• OLI Flowsheet
• OLI Chemistry Wizard
• Conclusion

Overview and History

Prior to 1990, OLI software employed a foundational thermodynamic model to calculate equilibrium constants for aqueous electrolyte species. While this early approach was functional across a variety of systems, its predictive capabilities were inherently limited due to the model's simplified assumptions.

In 1990, OLI introduced a significant advancement by adopting a modified form of the Helgeson Equation of State, originally developed by Helgeson and later refined by Tanger¹. This formulation, widely recognized within the geochemical modeling community, offered a more robust and theoretically grounded framework for simulating high-temperature and high-pressure aqueous systems.

One of the key advantages of the Helgeson-Tanger model is its predictive power. By regressing a limited set of experimentally characterized salt systems, the model enables estimation of thermodynamic properties for a wide array of electrolyte species. These properties can then be used to calculate equilibrium constants over a broad range of temperatures and pressures, eliminating the need for direct solubility measurements in many cases.

However, the implementation posed challenges. A central requirement of the model is the accurate evaluation of the dielectric constant of water, which is sensitive to the presence of solutes and varies significantly with temperature and pressure. In the original implementation, these values were drawn from steam tables and recalculated dynamically within the code. This process, while accurate, resulted in slower computational performance due to the complexity of interpolating dielectric constants across varying conditions.

Overcoming the obstacles

Marshall Rafal, founder of OLI, recognized a key structural property of the Helgeson-Tanger equation of state: it is purely a function of temperature and pressure. Notably, it does not account for compositional effects, which are handled separately through the activity model. This distinction enabled a major optimization in the implementation of the equation.

Because the equation of state is independent of composition, its output could be pre-computed and expressed in a more computationally efficient form by fitting the outputs to polynomial expressions, significantly accelerating the calculation of equilibrium constants during simulations.

The resulting polynomial approximation took the following general form:

\[
\log K = a + \frac{b}{T} + cT + dT^2
\]

where:

• \(log K\) is the logarithm of the equilibrium constant,

• \(T\) is the temperature in Kelvin,

• and \(a\), \(b\), \(c\), and \(d\) are coefficients regressed from the original equation of state.

To capture the effect of pressure, each coefficient was itself fitted to a second-order polynomial function of pressure. For example, the coefficient \(a\) was defined as:

\[
a = a_1 + a_2 \cdot P + a_3 \cdot P^2
\]

where:

• \(P\) is the pressure in atmospheres,

• and \(a_1\)​, \(a_2\)​, and \(a_3\)​ are regression parameters.

This approach was applied systematically across the entire model: a unique set of polynomial equations was generated for every equilibrium expression. The result was a dramatic increase in computational efficiency, enabling faster simulations without sacrificing thermodynamic accuracy.

Problems

Polynomial regressions, while effective within calibrated datasets, tend to perform poorly when extrapolated beyond the original range of input variables. Recognizing this limitation, OLI has implemented constraints on both temperature and pressure to ensure the reliability and accuracy of calculated properties.

To enforce these safeguards, OLI Studio, OLI Chemistry Wizard, and OLI Flowsheet: ESP incorporate mechanisms that restrict the regressed range of the equation of state. These built-in boundaries help maintain thermodynamic consistency and prevent erroneous results under extreme or unvalidated conditions.

OLI Studio

AQ Thermodynamic Framework

In the Chemistry menu item, under Model Options...:

Select the T/P Span tab

In the AQ thermodynamic framework, users have the option to select between two methods for evaluating equilibrium expressions: K-fit Polynomials and Helgeson Direct.

• Use K-fit Polynomials: This is the default selection. It operates within a temperature range of 25 °C to 225 °C and a pressure range of 1 atm to 1500 atm. These bounds align with the regression limits of the AQ framework's dataset and are generally sufficient for most applications. Adjustments can be made to these ranges if a broader or narrower scope is required to improve coverage or precision; however, such changes may affect the accuracy of the underlying thermodynamic calculations.

• Use Helgeson Direct: This option is recommended when the most accurate representation of equilibrium expressions is required. It computes the state equation for each equilibrium explicitly, offering higher fidelity at the cost of increased computational demand. That said, with modern hardware, this performance trade-off is typically negligible.

It is important to note that the AQ framework’s data were originally regressed within the specified default limits. As such, modifications outside these bounds should be approached with caution to maintain data integrity.

Note: As of Version 12, the AQ thermodynamic framework is required for most corrosion rate calculations.

MSE Thermodynamic Framework

When using the MSE thermodynamic framework, you will notice that the T/P Span tab's options are disabled.

MSE always uses the Helgeson Direct method and cannot be changed.

OLI Flowsheet: ESP

The path to the polynomial function is slightly different in the OLI Flowsheet: ESP program. The user must select the Chemistry tab:

Like with OLI Studio, please look for the T/P Span tab.

The options here are the same as for OLI Studio.

OLI Chemistry Wizard

The OLI Chemistry Wizard does not support this ability to adjust the polynomial K-fit.

Conclusion

The introduction of the K-fit polynomial function marked a pivotal advancement in the evolution of OLI’s thermodynamic modeling capabilities. By transforming the Helgeson-Tanger equation of state into a pre-regressed polynomial form, OLI achieved a substantial gain in computational efficiency—enabling accurate, high-speed equilibrium calculations across a wide range of conditions. This innovation allowed complex models to be run more quickly without compromising the integrity of the underlying thermodynamics.

While the polynomial approach remains a cornerstone of legacy calculations, its use is now increasingly contextualized within the broader development of OLI’s software platform. With the MSE (Mixed-Solvent Electrolyte) framework emerging as the default standard for new projects, and always utilizing the Helgeson Direct method, the role of the K-fit function transitions from default engine to historical enabler—an engineering solution that bridged the gap between scientific theory and practical performance.

The K-fit polynomial function exemplifies OLI’s commitment to delivering scientifically grounded, computationally optimized tools. Its legacy underscores how deep domain expertise and innovation converge to solve critical modeling challenges—an ethos that continues to shape the design of our next-generation thermodynamic solutions.

Reference list:

1. Tanger, J. C., & Helgeson, H. C. (1988). Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures: Revised equations of state for the standard partial molal properties of ions and electrolytes. American Journal of Science, 288(1), 19–98.