Equations lead to asphaltene deposition predictions

Oct. 28, 2002
An evaluation found that when tuned, the Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) equations of state (EOS) can predict heavy oil densities and SARA fractions with only a smaller error.

An evaluation found that when tuned, the Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) equations of state (EOS) can predict heavy oil densities and SARA fractions with only a smaller error.

One needs to know these values in order to predict the likelihood of asphaltene deposition.

The evaluation tuned the SRK and PR equations of state with only one set of measured densities and then the equations were used for density predictions of four Western Canadian heavy oils and bitumens with no further fitting parameters. The calculations indicated that the tuned EOSs could be used to predict the densities of the SARA fractions of at least Western Canadian heavy oils and bitumens.

Without volume corrections, the evaluation found that the SRK and PR EOS could not predict the SARA fraction densities accurately. The SRK EOS with Peneloux correction, however predicted the densities with small error.

Heavy oil

The industry typically characterizes heavy oil and bitumen in terms of solubility classes. The most commonly used solubility classes of heavy oils and bitumens are the SARA fractions (saturates, aromatics, resins, and asphaltenes).

Of these fractions, the industry has the most interest in asphaltenes because these fractions can precipitate with changes in pressure, temperature, or composition.

Asphaltenes are defined formally as the crude oil fraction that precipitates upon addition of an n-alkane (usually n-pentane or n-heptane) but yet remains soluble in toluene.1

Asphaltenes can deposit in surface facilities and pipelines upon the addition of condensate diluent. Treatments to remove these deposits increase operating costs.

To prevent or mitigate asphaltene deposition, one needs to predict asphaltene precipitation. A good prediction of asphaltene precipitation by various models, however, requires accurate prediction of liquid molar volumes of the existing components in the system. In other words, molar volume or density prediction is the first step of asphaltene precipitation modeling.2

Some have proposed correlations for predicting the molar volumes of SARA fractions.2-5 The correlations, however, are empirical in nature and can involve large errors when extrapolated beyond the range of variables covered in the study.6

As an alternative, one can estimate molar volumes of the solubility classes with cubic equations of state (CEOS) such as the SRK EOS7 and the PR EOS.8 Unfortunately, these CEOS generally do not provide accurate predictions of the molar volumes of liquids and pseudo-pure compounds such as SARA fractions.

Peneloux developed a correction term for the SRK EOS to improve molar volume predictions.9 Akbarzadeh extended the Peneloux correction to SARA fractions and proposed new correlations for the calculation of SARA fraction critical properties and acentric factors.10

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They estimated the SARA fraction densities and solubility parameters with a modified SRK EOS and input the predicted values into a regular solution theory model for predicting the onset of asphaltene precipitation in various oils.10

Predicted densities

Equation 1 (see Equation box) is a typical form of a cubic equation of state. In this equation P is pressure, T is temperature, and V is molar volume. The parameters u1 and u2 are different constants for different equations of state. For the SRK EOS,7 u1 = 1 and u2 = 0. For the PR EOS,8 u1 = 2, and u2 = –1.

One estimates the SRK EOS parameters a and b for a given component from the critical properties and acentric factor, as shown by Equations 2 and 3.

The PR EOS parameters are estimated from Equations 4 and 5.

Both the SRK and PR EOS predict vapor pressure of pure compounds with comparable accuracy; however, neither accurately predicts liquid molar volume of heavy hydrocarbons without volume translation.

One obtains the Peneloux correction from Equation 6, where Equation 7 estimates the c. In Equation 7, ZRA is the Racket compressibility factor proposed by Spencer and Danner.11 It can be estimated from Equation 12, where ω is the Pitzer's acentric factor.

In the same way, one applies the Peneloux correction to the PR EOS.

One should note that Equation 7 is developed for the SRK EOS and a similar expression for the PR EOS is not provided.

Critical properties

For determining the EOS parameters for SARA fractions, one requires their critical properties and acentric factor. This evaluation used the correlation of Riazi and Al-Sahhaf10 15 to obtain the saturate critical properties and acentric factor.

Akbarzadeh developed Equations 9-11 for estimating the critical properties and acentric factors of aromatics, resins, and asphaltene monomers. In these equations M is the molar mass of the fraction in g/mol and Cf is a correction factor that accounts for structural effects.10

One can consider this factor as a fitting parameter for tuning the EOS. The values of Cf for each solubility class and each EOS were determined empirically.

Results

As discussed before, one requires a correction factor to calculate the acentric factors of the saturates and the other fractions (Equation 12). In this work, Cf is considered a tuning factor; that is, the calculated densities for the SARA fractions of only Athabasca bitumen are matched with the measured densities by changing Cf.

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Table 1 shows the SARA fractions for four different heavy oils, and Table 2 shows the values of Cf for each SARA fraction of Athabasca bitumen obtained by tuning the SRK EOS and PR EOS with the Peneloux correction.

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Note that changing Cf did not have much effect on the prediction ability of the SRK and PR EOS without volume translation. In other words, the SRK and PR EOS do not work well for heavy compounds such as SARA fractions without volume corrections.

Once the evaluation determined a value of Cf for each solubility class of only one bitumen sample, it used that value to predict the densities of the other crude oils and their SARA fractions.

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Table 3 compares the measured and predicted densities of saturate, aromatic, resin and asphaltene fractions of the four Western Canadian crude oils by different EOS. The results showed that the SRK and PR EOS without volume corrections could not predict the SARA densities accurately. The SRK and PR EOS with Peneloux correction predicted the densities with small error.

Both the SRK and PR EOS predict liquid densities well. For example, the value for the saturates %AAD is 0.51 with SRK and 1.02 with PR. In the case of resins, %AAD is 1.5 with SRK and 1.55 with PR.

The low error suggests that one can use the tuned EOS to predict the densities of the SARA fractions of at least Western Canadian heavy oils and bitumens.

One requires mixing rules to calculate the properties of oils from their solubility classes (SARA fractions). This evaluation estimated crude oil density from the following well-known mixing rule from Equation 12, where wi is the mass fraction of the constituent i in the bitumen.11

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Table 4 shows the measured and calculated densities of the four bitumens and heavy oils.

According to this table, %AAD was 0.73 with the SRK EOS and 1.18 with the PR EOS.

References

  1. Wiehe, L.A., and Liang, K.S., "Asphaltenes, Resins, and Other Petroleum Macromolecules," Fluid Phase Equilibrium, No. 117, 1996, p. 201.
  2. Ferworn, K.A., Thermodynamic and Kinetic Modeling of Asphaltene Precipitation from Heavy Oils and Bitumens, PhD. Thesis, University of Calgary, 1995.
  3. Yarranton, H.W., and Masliyah, J.H., "Molar Mass Distribution and Solubility Modeling of Asphaltenes," AIChE J., No. 42, 1996, pp. 3533-43.
  4. Mannistu, K.D., Yarranton, H.W., and Masliyah, J.H., "Solubility Modeling of Asphaltenes in Organic Solvents," Energy & Fuels, No. 11, 1997, pp. 615-22.
  5. Pedersen, K.S., Skovberg, P., and Ronningsen, H.P., "Wax Precipitation from North Sea Crude Oils: 4. Thermodynamic Modeling," Energy & Fuels, No. 5, 1991, pp. 924-32.
  6. Kokal, S.L., and Sayegh, S.G., "Gas-Saturated Bitumen Density Predictions Using the Volume Translated Peng-Robinson Equation of State," J. Can. Pet. Tech., No. 29, 1990, pp. 77-82.
  7. Soave, G., "Equilibrium Constants from a Modified Redlich-Kwong Equation of State," Chem. Eng. Sci., No. 27, 1972, pp. 1197-1203.
  8. Peng, D.Y., and Robinson, D.B., "A New Two Constant Equation of State," Ind. and Eng. Chem. Fundamentals, No. 15, 1976, pp. 59-64.
  9. Peneloux, A., Rauzy, E., and Freeze, R., "A Consistent Correction for Redlich-Kwong-Soave Volumes," Fluid Phase Equilibrium, No. 8, 1982, pp. 7-23.
  10. Akbarzadeh, K., Ayatollahi, S., Moshfeghian, M., Alboudwarej, H. and Yarranton, H.W., "Estimation of the SARA fraction properties using the SRK EOS," CIPC Paper No. 2001-122, Canadian International Petroleum Conference, Calgary, June 12-14, 2001.
  11. Spencer, C.F., and Danner, R.P., "Improved Equation for Prediction of Saturated Liquid Density," J. Chem. Eng. Data, No. 17, 1972, pp. 236-41.
  12. Reid, R.C., Prausnitz, J.M., and Poling, B.E., The Properties of Gases & Liquids, 4th Edition., McGraw-Hill, New York, 1989.
  1. Sy-Siong-Kiao, R., Caruthers, J.M., and Chao, K.C., "Polymer Chain-of-Rotators Equation of State," Ind. Eng. Chem. Res., No. 35, 1996, pp. 1446-55.
  2. Akbarzadeh, K., and Moshfeghian, M., "Application of the Polymer Chain-of-Rotator (PCOR) Equation of State and its Extension to Polymer Blends," Fluid Phase Equilibrium, No. 187-188, 2001, pp. 347-61.
  3. Riazi, M.R., and Al-Sahhaf, T.A., "Physical Properties of Heavy Petroleum Fractions and Crude Oils," Fluid Phase Equilibrium, No. 117, 1996, pp. 217-24.

The authors

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Kamran Akbarzadeh is a research associate in the chemical and petroleum engineering department at the University of Calgary. His current work centers on the experimental investigation and modeling of asphaltene precipitation in heavy oils and bitumens. Akbarzadeh has a BS in chemical engineering from Shiraz University, Iran, an MS in chemical engineering from AmirKabir University of Technology, Tehran, and a PhD in chemical engineering from Shiraz University.

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Shahaboddin Ayatollahi is an assistant professor of chemical engineering at Shiraz University, Iran. He is currently the head of the Shiraz University computer center and specializes in enhanced oil recovery. Ayatollahi has a BS and an MS in chemical engineering from Shiraz University, and a PhD in chemical engineering from the University of Waterloo, Canada.

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Khashayar Nasrifar is a thermodynamist and currently working with the Institute of Petroleum Engineering, University of Tehran. Nasrifar has a BS, an MS, and a PhD in chemical engineering from Shiraz University.

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Harvey Yarranton is an associate professor of chemical and petroleum engineering at the University of Calgary. He previously worked for Dome Petroleum Ltd. and Amoco Canada Ltd. in reservoir, production, and operations engineering. His research interests are in thermodynamics, transport of hydrocarbons, and treatment of water-in-oil emulsions. Yarranton has a BS and PhD in chemical engineering from the University of Alberta. He is a member of CIM, SPE, CSChE, and AIChE.

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Mahmood Moshfeghian is currently working in the chemical engineering department of the University of Qatar in Doha and remains a professor of chemical engineering at Shiraz University, Iran. Moshfeghian has a BS, an MS, and a PhD in chemical engineering from Oklahoma State University. He is a member of the Iranian academy of sciences, Iranian Petroleum Institute, and Iranian Association of Chemical Engineers.