(191e) 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).