Equation-of-state (EOS) compositional simulation is commonly used to model the interplay between phase behavior and fluid flow for various reservoir and surface processes. Because of its computational cost, however, there is a critical need for efficient phase-behavior calculations using an EOS. The objective of this research was to develop a proxy model for fugacity coefficient based on the Peng-Robinson EOS for rapid multiphase flash in compositional flow simulation. The proxy model as implemented in this research is to bypass the calculations of fugacity coefficients when the Peng-Robinson EOS has only one root, which is often the case at reservoir conditions.

The proxy fugacity model was trained by artificial neural networks (ANN) with over 30 million fugacity coefficients based on the Peng-Robinson EOS. It accurately predicts the Peng- Robinson fugacity coefficient by using four parameters: Am, Bm, Bi, and ΣxiAij. Since these scalar parameters are general, not specific to particular compositions, pressures, and temperatures, the proxy model is applicable to petroleum engineering applications as equally as the original Peng-Robinson EOS. The proxy model is applied to multiphase flash calculations (phase-split and stability), where the cubic equation solutions and fugacity coefficient calculations are bypassed when the Peng-Robinson EOS has one root. The original fugacity coefficient is analytically calculated when the EOS has more than one root, but this occurs only occasionally at reservoir conditions.

A case study shows the proxy fugacity model gave a speed-up factor of 3.4% in comparison to the conventional EOS calculation. Case studies also demonstrate accurate multiphase flash results (stability and phase split) and interchangeable proxy models for different fluid cases with different (numbers of) components. This is possible because it predicts the Peng-Robinson fugacity in the variable space that is not specific to composition, temperature, and pressure. For the same reason, non-zero binary iteration parameters do not impair the applicability, accuracy, robustness, and efficiency of the model. As the proxy models are specific to individual components, a combination of proxy models can be used to model for any mixture of components. Tuning of training hyperparameters and training data sampling method helped reduce the mean absolute percent error to less than 0.1% in the ANN modeling.

To the best of our knowledge, this is the first generalized proxy model of the Peng-Robinson fugacity that is applicable to any mixture. The proposed model retains the conventional flash iteration, the convergence robustness, and the option of manual parameter tuning for fluid characterization.

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