Improving the Single Component Peng-Robinson Z-Factor Approach for Inerts

EDITED 20-05-2024 - Significant improvements to fit quality with the inclusion of temperature dependant BIP's has been made since the article was first written below. To find the latest work - including plots and maps showing residuals - can be found on the GitHub site

--- Original article below for posterity ---

Following feedback from Curtis Whitson and Simon Tortike on my single component Peng Robinson Z-Factor calculation method, I explored the potential of extending the approach to explicitly incorporate inerts. This was driven by two main considerations: First, the accuracy of my original single-component model was inherently limited by the choice of critical pressure and temperature correlation. Second, as we increasingly encounter scenarios such as CCUS with high inert concentrations, a simplified yet accurate approach is needed to handle up to 100% inerts — beyond the applicable range for approaches such as Wichert & Aziz.

Methodology

Step 1: I gathered 68,668 density data points from the NIST database for pure vapor and supercritical states of CO2, H2S, and N2, across temperatures of 50-300°F and pressures of 14.7-15,000 psia. These densities were then converted into Z-Factors.

Step 2: I applied regression analysis to these data points using a Peng-Robinson equation of state (EOS), modifying the Volume Shift for CO2, N2, and H2S, and adjusting the OmegaA and OmegaB parameters for CO2. CO2 was the most challenging to model accurately, yet the approach achieved better than 1% average error and maintained less than 5% error for 99% of the data points, except near the critical point.

Step 3: I digitized 1,052 Z-factor measurements from 88 samples detailed in Wichert’s 1970 thesis, which covered mixtures containing 0 - 54.5% CO2, 0 - 73.9% H2S, and 0 - 25.2% N2. I then developed a four-component Peng-Robinson model and modified the coefficients of the Sutton critical property correlation for the hydrocarbon gas and adjusted the binary interaction coefficients between all four components. This optimization was performed with a Python-driven workflow, minimizing the overall root mean square error by systematically regressing the Sutton coefficients with Python (outer loop) and the binary interaction parameters with PhazeComp (inner loop).

Results

While the Peng Robinson formulation is made a bit more complex due to 4 components vs 1, as well as inclusion of binary interaction coefficients, it still requires no iteration and so remains computationally efficient and robust, continuing to tick the boxes I was going after. Match qualities remain good - as detailed below - up to and including 100% pure inert compositions.

Cross plots below detail the pure component inert matches, along with the Wichert Z-Factor matches.

Additional Resources

All the datasets used for these regressions have been uploaded for public access. To replicate these findings, you will need to download and install Aaron Zicks’ PhazeComp software, which will run these models with the free functionality. I encourage those interested in deepening their understanding of EOS modelling to invest time in mastering this software.

Access the 4-Component Peng-Robinson Z-Factor Model on GitHub