Effect of combining rules on modeling of asphaltene precipitation

Abstract

Asphaltene deposition causes serious problems in the oil industry and reduces oil recovery. Deposition happens as a consequence of asphaltene precipitation which is a process as a result of a change in thermodynamic stability. Thus, prediction and preventing of the precipitation condition are the first step of preventing asphaltene precipitation and deposition. In this study, a thermodynamic model for asphaltene precipitation has been developed using Peng–Robinson (PR), Soave–Redlich–Kwong (SRK), and a new modification on SRK [modified-SRK equations of state (EOS)]. To modify EOS for non-pure sample (oil sample), van der Waals mixing rule with three types of combining rule containing conventional, Margules, and van Laar type was used. In addition, to verify the derived model, the experiments were conducted on a live oil sample to investigate the effect of pressure reduction and gas injection [nitrogen (0.1, 0.2, and 0.4 mol fraction) and first stage gas (0.2, 0.4 and 0.6 mol fraction)] on asphaltene precipitation. The results show that at low pressures (pressures below 5000 psia), nitrogen is not soluble in oil and the injection of nitrogen reduces asphaltene precipitation because of the liberation of the light component from crude oil; however, increasing the pressure (pressures above 6000 psia) increases the solubility of nitrogen and increases the asphaltene precipitation. For the first stage gas injection, asphaltene precipitation increases because of its high solubility in crude oil at any pressure. The amount of asphaltene precipitation due to first stage gas injection is higher than nitrogen injection except at nitrogen concentration and pressures near the bubble point (pressure of 7000 psia and nitrogen injection of 0.1 mol fraction). According to the modeling results, van Laar type combining rule in conjugated with modified-SRK-EOS predicts the amount of asphaltene precipitation very well at all situations of pressures and different gas injections, and has the least deviation from experimental data rather than the other two types of combining rules; and using mentioned combining formula, the RMSE value decreases to about 50% of the conventional combining rule. It is because of the accurate and distinct interaction parameters of each pair of components in van Laar equation.

Appendices

Appendix 1: Asphaltene molecular weight

Asphaltene is a self-association molecule that makes very hard to measuring the accurate molecular weight of it. However, there are many works done for measuring the molecular weight of asphaltene. The results of several important works done on this issue with different experimental methods are shown in Table 9 and Fig. 12.

Table 9 Reviews and experimental works for determination of asphaltene molecular weight

Fig. 12

Abundance of asphaltene molecular weight according to Table 9

Appendix 2: Binary interaction parameters

Equations of state need some binary interaction coefficients to be applicable for mixtures. In this section, binary interaction parameters for different combining rules and different EOS are presented.

• 1. One-binary interaction parameter (conventional combining rule).

  In this type of combining rule, one-binary interaction parameter is used for each pair of components (i.e., K_ij = K_ji).

  Binary interaction coefficients for common pairs of material containing light hydrocarbons for conventional combining rule are available in the literatures (Arya et al. 2017; Hustad et al. 2014). Binary interaction coefficients for asphaltene with other hydrocarbons are calculated according to experimental data available for upper onset pressure of reservoir oil (Hajizadeh et al. 2020) and are presented in Table 10.

  Table 10 Binary interaction parameter (K_ij)

• 2. Two-binary interaction parameters (Margules type and van Laar type combining rules).

  In this type of combining rules, two-binary interaction parameters are used for each pair of components (i.e., K_ij ≠ K_ji). For this type of combining rule, there is a semi-empirical correlation for binary interaction parameter as Eq. 16 (Fateen et al. 2013):

  $$K_{ij} = 1 - \frac{1}{2}\frac{{b_{j} }}{{b_{i} }} \sqrt {\frac{{a_{i} }}{{a_{j} }}} - \frac{1}{2}\frac{{b_{i} }}{{b_{j} }} \sqrt {\frac{{a_{j} }}{{a_{i} }}} + \frac{1}{2}\frac{{b_{j} RT}}{{\sqrt {a_{i} a_{j} } }} \frac{{\theta_{1} }}{{T_{{r_{i} }}^{{\theta_{2} }} P_{{r_{i} }}^{{\theta_{3} }} }}.$$

  (16)

  This equation is applicable for PR-EOS with adjustable parameters θ₁, θ₂, and θ₃ which, for some pair of species, are presented by Fateen et al. (2013) and for other species are adjusted in this study. These parameters are listed in Table 11.

  Table 11 θ₁, θ₂, and θ₃ for calculation of binary interaction parameter (K_ij) of PR-EOS (the parameters in the left side of diagonal line are for Margules and in the right side are for van Laar)

For calculation of binary interaction parameters for SRK-EOS and modified-SRK-EOS, we used the relation between the binary interaction parameter of PR- and SRK-EOS according to Eq. 17 (Jaubert and Privat 2010):

$$K_{ij}^{\text{SRK}} = \frac{{2\xi K_{ij}^{\text{PR}} \delta_{i}^{\text{PR}} \delta_{j}^{\text{PR}} + \xi (\delta_{i}^{\text{PR}} - \delta_{j}^{\text{PR}} )^{2} - (\delta_{i}^{\text{SRK}} - \delta_{j}^{\text{SRK}} )^{2} }}{{2\delta_{i}^{\text{SRK}} \delta_{j}^{\text{SRK}} }}$$

(17)

$$\delta_{i} = \frac{{\sqrt {a_{i} } }}{{b_{i} }}$$

(18)

$$\xi \propto \left( {\frac{1}{\varOmega }} \right).$$

(19)

The difference between binary interaction of SRK and modified-SRK-EOS is the amount of “$\delta_{\text{Asp}}$” parameter because of difference in “b” parameter of these two EOS, according to Table 1.

Also the amount of “ξ” in Jaubert and Privat (2010), assumed to be constant about 0.807341 for SRK-EOS, we changed it to ξ = 0.794 for modified-SRK-EOS according to Eq. (19).