A new method to estimate the partition of corrosion inhibitors

1.1 Additional considerations and partitioning coefficient calculation

The experimental procedure used in inhibitor tests is shown in Figure 1.

1. The partition tests are carried out with a known inhibitor concentration in a brine-oil mixture vol%. It is important to note that this concentration (C_i,M) considers the total volume of the initial mixture (V_M), stage 1.

2. When the brine-oil mixing process is carried out, the formation of a homogeneous phase is considered where the inhibitor is dispersed, stage 2.

3. After that, the separation of the two phases takes place, and the inhibitor would be expected to diffuse towards one of the phases; e.g., in the case of water-soluble inhibitors, the molecules will diffuse towards the water phase where a re-concentration phenomenon occurs (stage 3, Figure 1). The theoretical concentration of the inhibitor in the water phase (C_i,T) could be estimated considering its total dissolution.

4. The same considerations apply in the case of oil-soluble inhibitors.

The theoretical inhibitor concentration, C_i,T, can be determined from the following equation:

where C_f is the theoretical concentration of the inhibitor expected in the water phase (C_i,T), given by the following equation:

where C_i,M and V_M are the inhibitor’s concentration (mg L⁻¹) and the volume of the mixture (mL), respectively, and V_WP,M is the water phase volume used in the mixture (mL).

Thus, if the inhibitor’s concentration in the water phase (C_W) is quantified after the mixing process, it must be equal to the “theoretical” one; that is C_W = C_i,T and the partition coefficient or partitioning is 1 (P_CI = 1 or 100 %). Otherwise, the partitioning (P_CI) is lower than one and associated with the capacity of the inhibitor to dissolve in the water phase (C_W). Then, the partition coefficient is given by the following equation:

where C_W is the inhibitor’s concentration in the water phase, once the analysis has been performed, and C_i,T is the theoretical inhibitor’s concentration expected in the water phase volume used in the mix.

Thus, the partition of a beta-amino acid type corrosion inhibitor in its zwitterionic form (R12Na) was determined in mixtures of water-organic phases using ultraviolet–visible spectrophotometry. The volume ratio of water-organic phases, temperature and the inhibitor’s dosage were varied, using NACE 1D182 brine and kerosene as the water and organic phases, respectively. Our study included the analysis of other results reported on this topic in the literature.

3.1 Characterization by UV–vis spectrophotometry

The characterization of R12Na standards and the graph A versus [R12Na] obtained by the UV–vis technique is shown in Figure 2. A maximum absorption band for each standard is observed at 422 nm (λ), which is associated with a possible organic compound absorbed predominantly in the visible region (Doležal et al. 2011; Espinosa-Aguilar and De La Cruz-Morales 2015). This absorption band is associated with n → π* and π → π* transitions, likely due to the formation of complexes of the indicator with amino groups (Espinosa-Aguilar and De La Cruz-Morales 2015). Furthermore, a linear proportionality between the absorbance (A) and the concentration of the R12Na inhibitor is evident, recording a determination factor (R²) higher than 0.99, which supports the feasibility of the analytical method.

3.2 Determination of the partitioning coefficient

3.2.3 Experiment 3: inhibitor dosage effect

The theoretical inhibitor concentration expected in the water phase (Equation 2) at 20, 100, and 200 mg L⁻¹ in the mixture, was evaluated for each dosage.

Dosage 1: 20 mg L⁻¹ (ratio 80:20 vol%)

(8)Ci,T=Ci,M×VMVWP,M=(20 mg L−1)(100 mL)80 mL=25 mg L−1

Dosage 2: 100 mg L⁻¹ (ratio 80:20 vol%)

(9)Ci,T=Ci,M×VMVWP,M=(100 mg L−1)(100 mL)80 mL=125 mg L−1

Dosage 3: 200 mg L⁻¹ (ratio 80:20 vol%)

(10)Ci,T=Ci,M×VMVWP,M=(200 mg L−1)(100 mL)80 mL=250 mg L−1

Table 2 shows the partitioning results in the presence of 20, 100 and 200 mg L⁻¹ of R12Na, using a ratio of 80–20 vol% WP–OP and 60 °C. These results can be compared with that obtained for the 50 mg L⁻¹ dosage, the same water cut, and temperature (Table 1). It is important to note that results are in the same order of magnitude, obtaining partitioning values of 41.69 %, 43.86 %, and 44.04 % in the presence of 20, 50, and 100 mg L⁻¹ of inhibitor, respectively; indicating the partitioning coefficient does not depend on the inhibitor’s dosage up to concentrations of 100 mg L⁻¹. Conversely, the partitioning decreased for the 200 mg L⁻¹ dosage, which could be due, on the one hand, to the saturation of the water phase, whereas, on the other hand, to a decrease in the linearity of the plot A versus [R12Na], constructed using standards concentration from 5 to 500 mg L⁻¹, as shown in Figure 3; decreasing the R² factor and increasing the method error, as the inhibitor concentration is larger. It is noteworthy that the UV–vis spectrophotometry is conditioned by the Lambert–Beer law, which tends to not be valid at high concentrations, where absorptivity varies as a function of the aggregation of molecules in the solution and light scattering phenomena.

Table 2:

Partitioning results for the R12Na inhibitor in water phase (brine), water cut 80 vol%, 60 °C and varying the inhibitor dosage.

	20 mg L−1			100 mg L−1			200 mg L−1
A	0.0139	0.0121	0.0108	0.0676	0.0653	0.0620	0.0703	0.0682	0.0658
C W, mg L−1	11.80	10.29	9.17	57.27	55.33	52.56	59.58	57.81	55.76
C i,T, mg L−1	25.0			125.0			250.0
P CI	0.4722	0.4117	0.3668	0.4582	0.4426	0.4205	0.2383	0.2312	0.2231
% PCI	47.22	41.17	36.68	45.82	44.26	42.05	23.83	23.12	22.31
% PCI avg.		41.69			44.04			23.09

Figure 3:

A versus [R12Na] from 5 to 500 mg L⁻¹ of the R12Na inhibitor.

3.3 Inhibitor partitioning analysis of results reported in the literature

Based on the above assumptions, different partition studies reported in the literature were analyzed (Joosten et al. 2000; Xiong et al. 2016). In the first work, two partitioning tests at room temperature, using brine, and a condensate of the Britannia field were performed (Joosten et al. 2000). Centrifuge tubes of 50 mL were used and volumes of gaseous condensate and brine were added by varying the percentage of water from 5 to 20 vol% (test 1), and in the presence of 0–400 mg L⁻¹ of inhibitor named 22C (test 2). Mixtures in the presence of inhibitor were reversed 50 times mixing both phases and inhibitor dispersion; they immediately were subjected to centrifugation to separate the water phase and perform the analysis, using the gas chromatography coupled to mass spectrometry (GC–MS).

In the study described by (Joosten et al. 2000) (Figure 1, test 1), the results of water (C_W) and condensate (C_O) concentrations, as well as the partitioning of the inhibitor, considering the ratio of inhibitor concentrations in water–oil phases (C_W/C_O), varying the percentage of water up to 20 % are reported; while in Figure 2 (test 2), the results of C_W, C_O, and the C_W/C_O ratio for mixtures 80:20 vol% brine-condensate, containing 100, 200, and 400 mg L⁻¹ of inhibitor are depicted. In the first graph (Joosten et al. 2000), a decrease in C_W and C_O is observed from 2,500 to 250 mg L⁻¹ and from 25 to 14 mg L⁻¹, respectively. In the case of the partition given by the C_W/C_O ratio, the same trend is observed varying from 150 to 30 approximately. This behavior is similar in the presence of different inhibitor concentrations (Figure 2, test 2), reaching partition values (C_W/C_O) of ∼0.5. According to these results, it is suggested that the solubility of the inhibitor decreases in the water phase, as the percentage of brine is larger; however, these partition results are atypical, since the inhibitor concentration in the water phase (C_W, test 1) reaches values up to two-orders of magnitude higher for the 50 mg L⁻¹ dosage. These results can be explained taking into account a re-concentration of the inhibitor in the water phase. Thus, in both experiments it is required to calculate the theoretical inhibitor concentration expected in water phase (C_i,T, Equation (2)).

In the first test, the inhibitor concentrations in water (C_W, graphs 1 and 2) were reported for different vol% (1.0, 2.5, 5.0, 10, and 20) in the presence of 50 mg L⁻¹ or ppm of inhibitor; then, the volume of water is different and C_i,T can be determined according to the following equation:

where X, is the volume of water phase in the mixture (0.5, 1.25, 2.5, 5.0, and 10.0 mL).

In the second test, the volume of water phase (V_WP,_M) is 40 mL (80 vol% of brine) in the presence of different inhibitor concentrations; thus, the concentration is calculated using the following equation:

where X is the inhibitor’s concentration (100, 200, and 400 mg L⁻¹ or ppm).

The inhibitor concentrations in the water phase (C_W), taken from graphs 1 and 2 (Joosten et al. 2000), and C_i,T and P_CI determined by Equations (2) and (3) for the different analyzed cases are shown in Table 3. As mentioned before, as the volume of water used in the mixtures decreased it an increase in the C_i,T is expected; in Table 3 this concentration is determined to vary from 5,000 to 250 mg L⁻¹ for water cuts from 1 to 20 vol% (test 1); for the different inhibitor concentrations (test 2), these values varied from 125 to 500 mg L⁻¹. It is important to note that Figure 1 is reported on a logarithmic scale by (Joosten et al. 2000); thus, the C_W values reported in Table 3 and partition results could be slightly different; however, despite the results, they are reasonable and in the same order of magnitude.

In Table 3, for water cuts from 1 to 20 vol%, the partitioning results ranged from 0.57 to 0.81 (test 1); this variation is due, to a great extent, to the C_W data taken from graph 1 reported by (Joosten et al. 2000). Likewise, the partition results of the 22C inhibitor varied from 0.6 to 0.65 (test 2), which are consistent with those calculated at lower percentages of water with an average partition result of 0.63. Thus, it could be established that the 22C inhibitor is partially soluble in the water phase in agreement with its classification.

In the second work (Xiong et al. 2016), the partitioning of corrosion inhibitors (oil- and water-soluble) is analyzed, varying pH, water cut and temperature, using mixtures of synthetic brine and field oils. The mixing volume was 1 L (V_M), using oils with different viscosities: oil 1 (400 cps), oil 2 (3 cps) and oil 3 (1 cps). The corrosion inhibitors (CI) evaluated were CI A (oil soluble), CI B (water soluble), and CI C (water soluble) and their quantification is carried out with test kits using methyl orange and the UV–vis technique. More details of these tests are described in Table 4, taken from the literature (Xiong et al. 2016).

The theoretical concentration of the inhibitor C_i,T (Equation 2) and their partitioning (Equation 3) are determined for a 50 vol% brine-oil mixture, 50 mg L⁻¹ CI A (C_i,M), using three different field oils listed in Table 5. An increase in the solubility of the inhibitor in the water phase (C_W) and partitioning (P_CI) can be observed as the viscosity of the crude oil decreases, obtaining values from 0.02 to 0.2. However, these partition results in brine are low and consistent with the oil-soluble inhibitor classification. According to these results, at least 0.8 or 80 % of the inhibitor is soluble in the oil phase.

Likewise, C_i,T and P_CI results varying the vol% of the brine-oil mixture in the presence of 50 mg L⁻¹ CI A (C_i,M), using field oil 2 are shown in Table 6. An increase in the partition of the inhibitor in the water phase from 0.002 to 0.21 is observed, as the water cut increases from 10 to 75 vol%; indicating that 79 % of the inhibitor is found in the oil phase even for a 75 vol% of water cut and larger than 90 % for a 50 vol% water cut. These results are similar to those reported in Table 5, since it is the same oil-soluble inhibitor.

When the partition tests are performed varying the pH of the brine-oil mixture 50 vol%, in the presence of 50 mg L⁻¹ of CI B (C_i,M), using field oil 2, the obtained C_i,T and P_CI results are presented in Table 7. In this test, the inhibitor used is water soluble, and an increase in its solubility is expected; however, the results are the opposite. The maximum partition is 0.2 (20 %) obtained at pH 4, for pHs 5, 6, and 7, the results are 0.12, 0.04, and 0.03, respectively. This variation in the partitioning with the pH could be explained as dependent on its molecular structure and functional groups; nevertheless, the inhibitor used is unknown. According to these results and those reported in Tables 5 and 6, it is presumed that this inhibitor is also soluble in the oil phase.

In Table 8, C_i,T and P_CI results varying the test temperature of the brine-oil mixture 50 vol%, in the presence of 50 mg L⁻¹ CI C (C_i,M), using the field oil 2, are shown. Likewise, the inhibitor used is soluble in the water phase, however, the partition results are low varying from 0.12 and 0.10. Thus, it is plausible to consider that this inhibitor is also soluble in the oil phase. Finally, partition results varying the inhibitor dosage (C_i,M) using 50 vol% brine-oil mixture and field oil 2 are listed in Table 9. As in experiments 5 and 6, this inhibitor is water soluble and an increase in C_w and P_CI would be expected for higher concentrations of the inhibitor; however, these results are lower varying from 0.125 to 0.158, indicating that this inhibitor is also soluble in the oil phase; this assumption is consistent with the partition results shown in Table 6.

From these results, it can be established that the inhibitor partitioning calculation, considering a reconcentration phenomenon, seems to be consistent with the type of inhibitor used in the different brine-oil mixtures. Thus, it can explain the high concentrations of inhibitor determined in water samples (C_W) from pipelines, reaching concentrations above 100 mg L⁻¹ when the water content is less than 10 vol% and using the UV–vis spectrophotometry; conversely, lower concentrations (C_W) are reported for the same inhibitor dosage for water cuts above 75 vol%. Finally, the partitioning coefficient is different for each inhibitor, and depending on its application, it can vary significantly; however, its value must be known or determined with an appropriate technique to know the concentration of the dosed inhibitor and to establish suitable criteria for corrosion control.