Predicting the Phase Equilibria of Synthetic Petroleum Fluids with the PPR78 Approach

Today, the synthesis design and optimization of the processes are carried out with the help of process simulators (ProSim, PRO/II, ASPEN, …). It is however well known that the accuracy of the simulated results mainly depends on the quality of the thermodynamic model. In most cases, the phase behavior of multi-component systems for which nearly no data are available has to be known. The phase behavior can obviously be measured, but measurements are very time consuming. This is why modern process design requires models capable of (i) predicting the equilibrium properties without the preliminary use of experimental data (ii) yielding accurate results in both the sub-critical and critical regions. Simultaneous fulfillment of these requirements is a very difficult and challenging task for a thermodynamic model. Dealing with petroleum fluids, many difficulties appear. Indeed, such mixtures contain a huge number of various compounds, such as paraffins, naphthenes, aromatics, gases (CO₂, H₂S, N₂, …), mercaptans and so on. A proper representation involves to accurately quantifying the interactions between each pair of molecules, which is obviously becoming increasingly difficult if not impossible as the number of molecules is growing. To avoid such a fastidious work, an alternative solution lies in using a predictive model, able to estimate the interactions from mere knowledge of the structure of molecules within the petroleum blend. To build such a model, we have combined at constant packing fraction the 1978 version of the Peng-Robinson (PR) equation of state (EoS) and a Van Laar-type g^E function. The binary interaction parameters of the g^E model are calculated by a group contribution method (GCM) in order to make the model predictive. As explained in this study, this approach may equivalently be seen as a GCM to estimate the temperature-dependent k_ij of the widely used PR EoS working with classical mixing rules (linear on b and quadratic on a). This model has been called PPR78 (predictive, 1978 PR EoS). A cubic EoS has been chosen because in process design, due to their low complexity and their high accuracy for non-polar compounds, such EoS allow for fast screening of a large number of design alternatives and pre-selection of the most favorable candidate structures. A GCM has been chosen to estimate the binary interaction parameters because we were aware that the group contribution concept could be useful to model complex processes like those involving supercritical fluids and because the number of binary systems for which phase equilibrium data are available is at most several thousands while the number of the compounds used now by industry is estimated at around 100,000. It is thus necessary to be able to predict the binary interactions from the mere knowledge of the molecular structure. In product design, the availability of reliable methods for equilibrium property prediction is also important because fast screening of alternative chemical structures allows for reaching the specification requirements of the market before the competition, thus saving time, money and expert knowledge.

 

For the time being, fifteen groups are defined: CH₃, CH₂, CH, C, CH₄ (methane), C₂H₆ (ethane), CH_aro, C_aro, C_{fused aromatic rings}, CH_2,cyclic, CH_cyclic or C_cyclic, CO₂, N₂, H₂S and SH. It is thus today possible to estimate the Van Laar parameters (E_ij) or the k_ij (involved with the classical Van der Waals's mixing rules) for any mixture containing alkanes, aromatics, naphthenes, CO₂, N₂, H₂S and mercaptans whatever the temperature. In this study, the capability of this approach to predict the phase behavior of synthetic petroleum fluids is exhibited. We thus can say that this study is the culmination of the project development of the predictive PPR78 model. We are indeed convinced that a model must always be tested on mixtures of industrial interest. This is the reason why, we selected in the open literature, hundreds of mixtures for which fluid-fluid equilibrium data were reported. A large diversity of petroleum fluids (natural gases, gas condensates and crude oils) containing from three to several dozens of components was considered. The properties of petroleum fluids, including classical bubble point or dew point pressures but also complex gas injection experiments like swelling test or slim tube test were predicted with the PPR78 model. In most cases, good and even very good agreement is achieved for phase equilibrium properties when compared to experimental data.

 

In conclusion, the PPR78 model is a simple, accurate, flexible and reliable thermodynamic model, appropriate for the prediction of the phase behavior of multicomponent systems. This is why it is today routinely used in petroleum companies like TOTAL and integrated in commercial simulators of industrial processes like PROSIM (the PPR78 model will be available in PRO/II in a few months).