Wax Precipitation Modeling in VMGSim
Waxes are assumed to be formed by n-alkanes crystallizing from a hydrocarbon fluid to orthorhombic crystals in solid solutions . The crystallization and deposition of waxes during production and transport of both crudes and refined products are responsible for yearly losses of billions of dollars to the petroleum industry in prevention, maintenance and repair costs. Waxes cause reduction of production, well shut-in, plugging in pipelines and require man power and use of chemicals to fight the problem . The best way to deal with this problem would be to predict its occurrence to devise proper operational strategies. A reliable thermodynamic model, able to predict wax formation in a fluid at a given condition, using only information on the fluid composition would be a powerful tool to prevent wax formation.
One of the most rigorous (and popular) wax precipitation thermodynamic models is the one from Coutinho [2, 3, 4]. This model’s main features are:
- It represents wax as a solid solution. There are two versions of the model, the Wilson and UNIQUAC variants. The Wilson model approximates the wax as a single solid (amorphous) solution. This approach is relatively simple to apply and gives a good representation of the data, so it is recommended for general engineering use. The more complex UNIQUAC variant models the tendency of waxes to split into several separate solid solution phases.
- It gives good predictions of waxing behavior, wax appearance temperature and the amount of wax precipitated at different temperatures.
- It requires that the n-paraffins are explicitly present in the fluid model, as these are the wax forming components.
- In principle, the wax model can be used in conjunction with any conventional cubic equations of state.
The objective of this communication is to present the implementation of the wax phase modeling in VMGSim 10.0. Wilson’s version from Coutinho’s work was selected as the model to be implemented for the wax phase calculation. Coutinho’s model requires the characterization of the n-paraffins of the fluid and this information can be obtained using VMGSim’s PIONA Characterization technique. The implementation of the thermodynamic wax phase model was accompanied by the development of a Liquid-Wax PT flash to predict the wax precipitation and wax appearance temperatures.
Coutinho’s model has been implemented in VMGSim in a way that minimum or no tuning is required to match experimental data. Wax activity coefficient parameters were internally tuned to be compatible with the hydrocarbon group contribution-based interaction parameters for the Advanced Peng Robinson based property packages.
A detailed characterization of the studied waxy fluid and the right value of the onset wax phase fraction are the necessary requirements to produce accurate “out of the box” wax appearance temperatures and wax precipitation curves in VMGSim.
The Wax Precipitation model is available in the following Advanced Peng Robinson (APR)-based property packages: Advanced Peng Robinson, Advanced Peng Robinson for Natural Gas and Advanced Peng Robinson for Natural Gas 2.
Wax Phase Modeling - Coutinho's Wilson Model 
In Coutinho’s model , the fugacity of a n-paraffin in the solid solution at a pressure P can be expressed in terms of the liquid phase fugacity, pure component thermophysical properties and the activity coefficient at low pressure. The low-pressure activity coefficient, which takes into account the deviation from ideal behavior, is calculated using the predictive Wilson equation which provides a good description of the phase behavior of waxy solutions.
To apply Coutinho’s model calculations, it is necessary to define what components are present in the wax phase. The thermophysical properties used in the Wilson model, that can be found elsewhere [6, 7, 8], are valid for paraffins with carbon numbers above 8 and; based on different sources [5, 6, 8], the minimum paraffin carbon number that can be found in the wax phase varies from 8 to 20.
Based on the previous statements, in VMGSim, the wax phase will be formed only by paraffin compounds with carbon number greater or equal to 8.
Wax Phase Equilibrium
To apply the wax thermodynamic model, it is necessary to compute the equilibrium between wax and the fluid phases. By using Coutinho’s model  coupled with a cubic equation of state (Advanced Peng Robinson for instance) for the liquid and vapor phases, it is possible to compute the Gibbs energy of any phase. Equilibrium occurs for the phase distribution for which the Gibbs energy is at a minimum.
To solve this problem, a wax PT flash algorithm was added to VMGSim, the algorithm uses a phase -stability test and a phase split procedure to compute the final material balance. The stability test can determine if it is possible to split a new phase off from an existing phase. The phase split procedure finds the equilibrium point for a given set of coexisting phases by adjusting the phase fractions and compositions until the Gibbs energy is at a minimum.
The algorithm allows the possibility of any combination of the following phases: vapor, hydrocarbon liquid and wax. If water is present, an aqueous liquid phase can also be formed.
Wax Appearance Temperature (WAT)
The Wax Appearance Temperature refers to the onset temperature at which the precipitation of wax is observed. WAT is the most difficult point to measure in a wax precipitation curve, as it is theoretically the point where the first infinitesimally small amount of wax is formed.
In practice, it is only possible to detect a finite amount of wax; different experimental methods differ in their ability to detect small amounts of wax. For instance, to calculate the WAT in calorimetry based experiments some authors recommend to use a phase fraction of around 0.3 wt% . Coutinho et al.  matched WAT values from three different experimental sources (cross-polar microscopy, laser based solids detection system and field data) used on the same oil, in order to match the data, they had to use three different values for the wax onset fraction which varied from 0.19 to more than 1 wt%.
It is difficult to find a good default for the onset phase fraction, in VMGSim it was decided to use a value of 1.0 E-04 for the onset mole phase fraction which is roughly equivalent to 0.1 wt%. The onset mole phase fraction was left as an input from the user so it can be adjusted to match a specific experimental WAT value.
The WAT calculation is done through an iteration algorithm that performs a series of PT flash calculations at a constant pressure until the calculated temperature produces the desired onset wax phase fraction. This temperature is reported as the WAT.
Wax envelopes and precipitation curves can also be obtained in VMGSim; wax envelopes are essentially a series of WAT points calculated at different pressures using the same Wax Phase Fraction criterion; wax precipitation curves are a series of wax mole phase fraction at different temperatures and constant pressure.
In order to use the wax thermodynamic model for the calculation of WAT, wax envelopes or wax precipitation curves, the composition of the oil must be defined. The composition of a waxy oil is usually characterized by a laboratory test from which ideally the following two distributions can be obtained :
- The Single Carbon Number distribution: also, known as the Carbon Number analysis, this distribution represents the amount of material, which includes all the n-paraffins, iso-paraffins, olefins, naphthenes and aromatics, present in a carbon number fraction.
- The n-Paraffin distribution: this one represents the mass fraction of the Cn+ n-paraffins present in the feed. The n-paraffin distribution is not a standardized test and it is not always available, instead, the Wax Content (UOP 46-85 essay ) of the oil can be used for characterization.
In order to characterize waxy oils in VMGSim one can take advantage of VMGSim’s PIONA characterization, since this type of procedure already defines the oils in terms of chemical families, including n-paraffins. Once a PIONA slate has been created in VMGSim, the waxy oil can be characterized through the Oil Source unit operation using one of the following three procedures:
1. n-Paraffin Distribution
To use the n-paraffin distribution, the Carbon Number Analysis option from the Oil Source must be activated. In the Carbon Number Analysis tab, the single carbon number distribution is entered as usual, to enter the n-Paraffins distribution a toggle must be activated. Once it is activated the user will decide if the n-paraffins distribution will be entered as the total n-paraffin content per carbon number (in the same basis as the Cn Analysis) or as a fraction of the Carbon number content (also in the same basis as the Cn Analysis):
The n-paraffin distribution is entered in the column to the right of the Cn Distribution. Then, the characterization procedure is followed as usual by adding experimental variables and regressing the parameters of the unit operation.
2. Wax Content
The UOP 46-85 essay provides an estimate of the total wax content in the C20+ fraction of a crude oil.
This property is present inside the Wax Tab, to use this property in the Oil Source unit operation, the user must define the wax content in mass basis and the calculated amount of C20+ n-Paraffins will be adjusted to this number.
If the n-paraffin distribution has been defined in the Cn Analysis tab the Wax Content is calculated from this input and cannot be specified. If neither n-paraffin distribution nor the wax content is available, the value is calculated based on VMG's internal correlations for n-Paraffins distributions.
3. Internal Distributions
When the previous two values are missing, then the n-paraffin distribution will be obtained from the Oil Source internal correlations. The distribution will depend on the experimental variables added to the unit operation like molecular weight, density, PIONA distribution, etc.
Wax Precipitation Calculations in VMGSim
Wax precipitation calculations can be found in four different unit operations from VMGSim:
Oil Source Unit Operation
The wax calculations can be found in the Wax tab from this unit operation. This tab is enabled when the Wax Precipitation box from the Summary tab is checked, this option is only available when the Application type is Oil / Refinery or Tight Fluids.
Traditional wax precipitation calculations like Wax Appearance Temperature (WAT), Wax Envelope and Wax Precipitation Curve (WPC) are included here.
Envelope Unit Operation
The Wax envelope can also be obtained in this unit operation, to enable the calculation, the Wax box at the bottom of the unit operation must be activated.
Pipe Segment Unit Operation
Wax calculations are available inside the Solids Formation tab from the Profiles tab. This tab shows the WAT plot across the pipe segment as well as warnings regarding the appearance or not of wax at the pipe conditions. The Solids Formation information can also be seen using phase envelopes that can include the Wax phase.
Special Properties Unit Operation
The WAT calculation is located in the Refinery tab from this unit operation.
The following example will go through the creation of a VMGSim case to compare its results against literature data from Daridon et al. .
The fluids of interest in this case are two condensate gases (CGA and CGB) coming from wells from a North Sea field . The composition, determined by gas chromatography, and properties of the fluids are shown in the next table .
Examination of the previous data reveals that both fluids are formed of more than 87 mol% of light components (N2, CO2, and hydrocarbons up to C4) whereas the C11+ fraction represents less than 5 mol% of the fluids. This quantity of heavy component, of which one-third is n-paraffins, is not negligible in comparison to the medium molecular components (C5 to C8) which act as a solvent for the waxes. Exploitation of such fluids, therefore, requires particular care because when gas-phase separation occurs and flashes off the liquid, the proportion of n-paraffins in condensate may become significant and a wax phase may appear.
The Wax Appearance Temperatures (WAT) of the fluids were measured directly by visualization of the wax crystal appearance using an all-around visibility setup.
Daridon et al.  also presented the vapor-liquid equilibrium (VLE) of the system, they were obtained through a PVT analysis apparatus.
The selected property package employed to simulate this example was Advanced Peng-Robinson, in order to take advantage of the improved vapor-liquid equilibrium predictions, the new hydrocarbon group contribution based interaction parameters for the Advanced Peng Robinson equation of state were used (version 2.0). This new set of interaction parameters can be selected from the Settings tab inside the Thermo form.
The VMGSim version used to build the case was 10.0.87. This case used the VMG unit set.
To characterize the fluid, the following pure components were added to a VMGSim case: N2, CO2, C1, C2, C3, iC4, C4, iC5 and C5; then, a PIONA slate was built based on the properties shown in the next figure.
To characterize the first fluid (CGA) an Oil Source unit operation was added to the case and the Carbon Number Analysis, the C11+ molecular weight and one saturation point from the previous tables (352.37 K, 34630 kPa) were used as the experimental values. The saturation point is necessary in order to have a good representation of the system’s VLE.
Note that the n-paraffin distribution from C6 to C10 is missing in the compositional analysis, so these values are kept empty, only the C11+ n-paraffin content is added.
Once the experimental variables are entered, the Oil Source unit operation is run, the data is regressed and the results from the following figure are obtained.
To calculate the WAT, check the Wax Precipitation box from the Summary tab, this will open the Wax tab.
In the Wax tab, check the Wax Appearance Temperature (WAT) box from the Wax Precipitation Calculations frame, this will enable the WAT frame where the Wax Phase Frac Criterion and the Pressure must be entered. The default value for the Wax Phase Frac Criterion is 1.0 E-04. To obtain the WAT value the pressure of interest must be specified, for this example, 38000 kPa (38 MPa) was used.
As it can be seen, in the previous figure the calculated WAT for this fluid at 38,000 kPa is 292.2 K this is around 7 K higher than the experimental value of 285.55 K. Since the experimental procedure to obtain the WAT is based on a visualization scheme, we don’t know what was the actual phase fraction used in the experiment. Therefore, we can vary this phase fraction to see if we obtain a closer value. A quick inspection showed that 2.2 E-04 produces a WAT of 285.4 K, essentially identical to the measured WAT.
To compare the rest of the WAT values from the experimental data, a Case Study based on the pressure and WAT values (using 2.2 E-04 as the Wax Phase fraction criterion) from the Oil Source unit operation was done. The results are shown in the next figure and the comparison between experimental and calculated data are shown in the table below.
The previous table shows the close agreement between experimental and calculated results. The average absolute error was 0.17% with a maximum deviation of 1.81 K.
The Vapor-Liquid equilibrium was also matched because an experimental saturation point was added to the oil characterization, if this was not done the VLE behavior would have been different and this would have affected the WAT calculations. Wax and VLE equilibrium results can be obtained using an Envelope unit operation connected to the Oil Source. To obtain the whole results range the Envelope settings were changed as seen in the next figures.
The next plot shows the comparison of VMGSim results against the Wax and Vapor-Liquid equilibrium curves, as it can be seen results are virtually identical.
The previous procedure can be repeated for the second fluid from the paper (CGB) . The characterization results are shown in the next figure.
To calculate the WAT values of this oil a WAT Phase criteria of 3.1 E-05 was used and the following results were obtained from a Case Study.
The next plot shows results comparison for both gas condensates, again close agreement between experimental and VMGSim results were found respect to the CGB fluid. In the case of the WAT calculations, the average absolute error was 0.61% with a maximum deviation of 4.98 K. The VLE of the CGB fluid was also matched, as it can be in the following figure that shows wax and VLE equilibria for both gas condensate fluids.
It is important to note that in this example the wax and vapor-liquid envelopes of two different oils were matched within the same VMGSim case with the same component slate. Also, no tuning was required to obtain the results, the only requisite was a detailed characterization of the fluids that included the paraffin distribution, physical properties and one saturation point.
Herbert Loria, Ph.D., P.Eng., VMG Calgary
Please contact your local VMG office for more information.
 Chevallier, V., Briard, A.J., Petitjean, D., Hubert, N., Bouroukba, M., Dirand, M., "Influence of the Distribution General Shape of n-Alkane Molar Concentrations on the Structural State of Multi-Alkane Mixtures" Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals, vol. 350, no. 1, 2000.
 Coutinho, J.A.P., Pauly, J. and Daridon, J.L., "A Thermodynamic Model to Predict Wax Formation in Petroleum Fluids" Brazilian Journal of Chemical Engineering, vol. 18, no. 4, pp. 411-422, 2001.
 Won, K.W., " Thermodynamics for Solid Solution-Liquid-Vapor Equilibria: Wax Phase Formation from Heavy Hydrocarbon Mixtures" Fluid Phase Equilibria, vol. 30, pp. 265-279, 1986.
 Erickson, D.D., Niesen, V.G., Brown, T.S., "Thermodynamic Measurement and Prediction of Paraffin Precipitation in Crude Oil" in SPE Annual Technical Conference and Exhibition, 3-6 October, Houston, TX, 1993
 Sansot, J.M., Pauly, J., Daridon, J.L., Coutinho, J.A.P., "Modeling High-Pressure Wax Formation in Petroleum Fluids" AIChE Journal, vol. 51, no. 7, pp. 2089-2097, 2005.
 Coutinho, J.A.P., Pauly, J., Daridon, J.L., "Modelling Phase Equilibria in Systems with Organic Solid Solutions" in Computer Aided Property Estimation for Process/Product Design, Amsterdam, Elsevier, 2004, pp. 229-250.
 Coutinho, J.A.P, Daridon, J.L., "Low-Pressure Modeling of Wax Formation in Crude Oils" Energy & Fuels, vol. 15, pp. 1454-1460, 2001.
 Coutinho, J.A.P., Edmonds, B., Moorwood, T., Szczepanski, R., Zhang, X., "Reliable Wax Predictions for Flow Assurance" Society of Petroleum Engineers, vol. SPE 78324, 2002.
 Huang, Z., Zheng, S., Fogler, H.S., Wax Deposition, Experimental Characterizations, Theoretical Model, and Field Practices, Boca Raton, FL: CRC Press, 2015.
 Universal Oil Products, "Paraffin Wax Content of Petroleum Oils and Asphalts" Honeywell, 1985.
 Daridon, J.L., Pauly, J., Coutinho, J.A.P., Montel, F., "Solid-Liquid-Vapor Phase Boundary of a North Sea Waxy Crude: Measurement and Modeling" Energy & Fuels, vol. 15, pp. 730-735, 2001.