Evaluation of the Different Compatibility Indices to Model and Predict Oil Colloidal Stability and Its Relation to Crude Oil Desalting

: Thirty crude oils, belonging to light, medium, heavy, and extra heavy, light sulfur, and high sulfur have been characterized and compatibility indices deﬁned. Nine crude oil compatibility indices have been employed to evaluate the compatibility of crude blends from the thirty individual crude oils. Intercriteria analysis revealed the relations between the different compatibility indices, and the different petroleum properties. Tetra-plot was employed to model crude blend compatibility. The ratio of solubility blending number to insolubility number was found to best describe the desalting efﬁciency, and therefore could be considered as the compatible index that best models the crude oil blend compatibility. Density of crude oil and the n-heptane dilution test seem to be sufﬁcient to model, and predict the compatibility of crude blends.


Introduction
The cost of crude accounts for between 80 and 90-95% of the total running costs of refineries, and therefore is the single most important determinant for the profitability of an oil company [1][2][3]. Therefore, refiners seek ways to process cheaper petroleum crudes, while minimizing the risk of equipment failure and unplanned shut down [4]. The cheaper crude oils, also called "opportunity crudes" are usually heavier with a higher concentration of compounds containing heteroatoms such as sulfur, nitrogen, oxygen, and metals [4][5][6][7]. Typically, in a refinery a blend of crude oils is processed rather than a single crude oil to ensure that an optimum product mix can be obtained at minimum costs. Refining margins can be improved by co-processing heavy crude oils with light crude oils [8]. Unfortunately, the co-processing heavy with light crude oils is frequently connected with incompatibility issues [9][10][11][12]. This can explain why the crude oil incompatibility has been a subject of numerous investigations [13][14][15][16][17][18][19][20][21][22]. Different methods have been developed, tested, and proposed to assess crude oil incompatibility [8,[10][11][12]. Some of these methods employ sophisticated equipment and procedures, which, unfortunately, are unavailable in refineries for regular monitoring of the optimal crude oil blending and are suitable for blends of two crude oils. For each additional crude oil added to a blend, the number of lab tests required to ascertain the range of incompatibility goes up exponentially making the determination of crude oil compatibility intractable in laboratory testing [42]. On another hand, some authors [8,34,39,44] reported that different procedures may qualify certain crude oil blend as compatible or incompatible depending on the used crude oil properties and laboratory conditions. In this study, we characterized thirty crude oils from all over the world, twenty two of which were processed in the Lukoil Neftohim Burgas (LNB) refinery. Nine crude oil compatibility indices, easy to apply in refineries, were employed to assess the colloidal stability and the affinity to form precipitation during blending. Then these indices were contrasted with the performance of LNB crude desalting units during processing different crude blends to discriminate those indices which are best linked to the desalting efficiency. Desalting efficiency is related to crude compatibility, lowering it when crude blend is incompatible [14]. Poor desalting was reported in our previous studies to lead to upset and emergency shutdown of one of the LNB middle distillate hydrotreaters [17,49] due to excessive fouling with ammonium chloride settled down in the hydrotreater water coolers.
Crude compatibility is still an ill-defined area in terms of its measurement and evaluation [38]. Most studies relate crude incompatibility to a higher fouling rate [2, 15,16,18,21,22,27]. Little is published about the relationship of crude incompatibility to desalting efficiency. Moreover, there is a lack of reports indicating the dependence of crude desalting efficiency on the compatibility indices employed to characterize crude compatibility. That was the reason why we performed this study with the aim to discuss the relations between crude oil compatibility indices and desalting efficiency. Additionally, we investigated the relationships between petroleum characterization parameters and the compatibility indices.

Crude Oil Characterization
Thirty crude oils originating from Russia, Azerbaijan, Kazakhstan, Turkmenistan, Libya, Egypt, USA, Venezuela, Equatorial Guinea, Saudi Arabia, Kuwait, Greece, Albania, Italy, Tunisia, and others were investigated in this work. These thirty crude oils include light low sulfur, light sulfur, intermediate low sulfur, intermediate sulfur, intermediate high sulfur, heavy high sulfur, and extra heavy high sulfur crudes. Twenty-two of them were processed in the LNB refinery, and eight of them were considered for possible processing in the refinery.
The crude oils were fractionated in a true boiling point (TBP) Euro Dist System from ROFA Deutschland GmbH, designed to perform according to ASTM D-2892 requirements. The atmospheric residue from the TBP column was fractionated in a Potstill Euro Dist System according to ASTM D-5236 requirements. The density of the crude oils and their fractions was measured in accordance with ASTM D 4052. Sulphur content of the crude oils and their fractions was determined in accordance with ASTM D D4294. Pour point was determined in accordance with requirements of ASTM D 5853. Water and sediment content analyses were performed according to the procedures described in ASTM D 4006 and ASTM D 473 respectively. Method ASTM D 445 was applied to measure the crude oil kinematic viscosity. Chloride content was determined by applying the standard method ASTM D 3230. Acid number of crude oils was measured by potentiometric titration in accordance with ASTM D 664. SARA (saturates, aromatics, resins, asphaltenes) analysis of the crude oils was done by employing liquid chromatography following the procedure described in [50]. The methods used to characterize vacuum residue applied in the LNB refinery are explained in detail in our earlier studies [51][52][53].
For the purposes of defining the compatibility indices, solvent power and critical solvent power according to the procedure described in [42], the investigated crude oils and their blends with n-heptane were characterized for their distillation properties according to ASTM D 7169 (HTSD). These distillation characteristics along with density were employed to estimate the characterization factor (Kw) as shown in Equation (1). Table 1 summarizes the properties of all crude oils investigated in the current study. The SARA analysis of the crude oils is shown in Table 2. Table 3 presents the properties of the crude oil fractions.

N-Heptane Dilution Test
The solutions of the selected crude oils and n-heptane were prepared at varying ratios between the crude oil and the normal paraffin. One sample tube contained 100 wt.% crude oil. The samples were thoroughly mixed and allowed to equilibrate and then centrifuged. The centrifuging process was carried out in a conventional centrifuge at 5000 rpm for 30 min. Supernatant oil liquid was removed from the centrifugal tube. The sediment was subsequently washed in n-heptane and dried. The drying process was carried out at 105 • C for 8 h. The recovered sediment was calculated in wt.% of the base of crude oil and plotted against the weight percent of n-heptane of the solution of the particular sample tube.

Crude oil Solvent Power and Critical Solvent Power
The solvent power of the crude oils was calculated as described in [42] and shown in Equation (2).
Kw-characterization factor of toluene = 10.15 [54]. The point of initial sediment precipitation, obtained from the n-heptane dilution test was used for determination of critical solvent power of the crude oil. Equation (2) is also used to estimate the critical solvent power. In that case, however, Kw, characterization factor of the blend crude oil of n-heptane at the point of initial sediment precipitation, is used.
The solvent power of the petroleum blends was calculated by the use of Equation (3): The petroleum blend is considered compatible when its solvent power is greater than the critical solvent power of the crude oil having the highest critical solvent power in the blend.

Compatibility Indices Based on Petroleum SARA Analysis Data
Colloidal instability index (CII) was calculated by using Equation (4) and the SARA data of the studied crude oils.
In addition, the stability criteria expressed as ratios Sat/Aro and Res/Asp were estimated too.

Oil Compatibility Model
Wiehe [26,27] first introduced the concept of oil compatibility model. It consists of defining the solubility and insolubility blending numbers and the ratio between them.
The ratio S BN /I N (solubility blending number/insolubility number) was estimated using the information obtained from the n-heptane dilution test [10] and employing Equation (5) [55].
where, Vh is the maximum volume of n-heptane (mL) at which the blend n-heptane-petroleum, where the crude oil volume is Voil (mL), does not form a precipitation of asphaltenes.
S BN was calculated using the crude oil solubility parameter and solubility parameter of n-heptane and toluene (Equation (6)). The solubility parameters (δ) for toluene and n-heptane were taken from literature [56] where δT = 18.3 MPa 0.5 and δH = 15.2 MPa 0.5 . Solubility parameter of the crude oil was calculated on the basis of the crude oil density and the correlation of Correra et al. [57] and shown as Equation (7).
Solubility blending number of the petroleum blends is the volumetric average for those oils [47] and was estimated by applying Equation (8). Table 4 summarizes all the compatibility indices employed in this work for all the studied crude oils.

Relations between Compatibility Indices and Crude Oil Properties
The experimental strategy presented in the current study to determine the compatibility indices was accomplished in three stages explained below: (1) Preparing mixtures of crude oil with n-heptane at different ratios; (2) determination of the onset of asphaltene precipitation; (3) estimation of compatibility indices. Crude oils, investigated in this study, exhibited different behaviors during the dilution with n-heptane. Figure 1 presents three typical graphs of relation of recovered sediment to the n-heptane content in the crude oil-n-heptane mixture. Most crude oils have behavior similar to that shown in Figure 1a. Recovered sediment starts to increase rapidly at a given n-heptane concentration for each oil sample and this threshold is called initial sediment precipitation. As explained before the initial sediment precipitation is used to estimate the crude oil solvent power and critical solvent power by the use of Equations (1) and (2). Most of the studied crude oils had solvent power below 60 and they could be classified as cyclohexane equivalent [28]. Crude oil with solvent power of zero is equivalent to n-heptane, and a crude oil with a solvent power of one hundred is equivalent to toluene [42]. Some of the light crude oils with solvent power less than 44 and characterization factor Kw in the range 11.8-12.2 showed behavior similar to that presented in Figure 1b,c. These light crude oils can be considered as self-incompatible or near-incompatible [27]. Recovered sediment can decrease or remain unchanged with increasing the quantity of n-heptane in the blend crude oil-n-heptane. In our study crude oils with low asphaltene and high paraffinic content such as CPC, Kuwait M, Azeri light demonstrated the behavior shown in Figure 1b,c during the nheptane dilution process. It is well-known that the sediment recovered during the crude oil centrifuging process can be classified as inorganic and organic. Inorganic sediment is represented by suspended impurities, such as sand, dirt, clay, or rust coming from the crude oil production process [13,55]. Organic sediments include asphaltenes, and high molecular waxes [13,55,58]. Sediment decreasing during the n-heptane dilution process of Kuwait M crude oil might be a result of the mutual dissolving of waxes and asphaltenes. Waxes can improve dissolution of asphaltenes because of the interaction between side alkyl chains in asphaltenes and waxes [55,[58][59][60][61][62]. The dissolution of the solids is accelerated because of increasing volume of alkyl layers surrounding the asphaltenes polyaromatic cores [60]. That is why, the proper determination of flocculation point of the mentioned above light paraffinic low asphaltenes crude oils is very difficult and even impossible. Their solubility power is close to that of the n-heptane. Additional in-depth study is required to generate correct results for the compatibility indices based on the n-heptane dilution test [10,26].
bility indices was accomplished in three stages explained below: (1) Preparing mixtures of crude oil with n-heptane at different ratios; (2) determination of the onset of asphaltene precipitation; (3) estimation of compatibility indices. Crude oils, investigated in this study, exhibited different behaviors during the dilution with n-heptane. Figure 1 presents three typical graphs of relation of recovered sediment to the n-heptane content in the crude oiln-heptane mixture. Most crude oils have behavior similar to that shown in Figure 1a. Recovered sediment starts to increase rapidly at a given n-heptane concentration for each oil sample and this threshold is called initial sediment precipitation. As explained before the initial sediment precipitation is used to estimate the crude oil solvent power and critical solvent power by the use of Equations (1) and (2). Most of the studied crude oils had solvent power below 60 and they could be classified as cyclohexane equivalent [28]. Crude oil with solvent power of zero is equivalent to n-heptane, and a crude oil with a solvent power of one hundred is equivalent to toluene [42]. Some of the light crude oils with solvent power less than 44 and characterization factor Kw in the range 11.8-12.2 showed behavior similar to that presented in Figure 1b,c. These light crude oils can be considered as self-incompatible or near-incompatible [27]. Recovered sediment can decrease or remain unchanged with increasing the quantity of n-heptane in the blend crude oil-n-heptane. In our study crude oils with low asphaltene and high paraffinic content such as CPC, Kuwait M, Azeri light demonstrated the behavior shown in Figure 1b,c during the n-heptane dilution process. It is well-known that the sediment recovered during the crude oil centrifuging process can be classified as inorganic and organic. Inorganic sediment is represented by suspended impurities, such as sand, dirt, clay, or rust coming from the crude oil production process [13,55]. Organic sediments include asphaltenes, and high molecular waxes [13,55,58]. Sediment decreasing during the n-heptane dilution process of Kuwait M crude oil might be a result of the mutual dissolving of waxes and asphaltenes. Waxes can improve dissolution of asphaltenes because of the interaction between side alkyl chains in asphaltenes and waxes [55,[58][59][60][61][62]. The dissolution of the solids is accelerated because of increasing volume of alkyl layers surrounding the asphaltenes polyaromatic cores [60]. That is why, the proper determination of flocculation point of the mentioned above light paraffinic low asphaltenes crude oils is very difficult and even impossible. Their solubility power is close to that of the n-heptane. Additional in-depth study is required to generate correct results for the compatibility indices based on the n-heptane dilution test [10,26]. The relations between different crude oil properties and measured compatibility indices shown in Tables 1-4 were examined by using the intercriteria analysis (ICrA). The ICrA approach is specifically designed for datasets comprising evaluations, or measurements of multiple objects against multiple criteria. In the initial formulation of the method, the aim was to detect statistically meaningful relations between the criteria, in order to eliminate future evaluations/measurements against some of the criteria, which exhibit high enough correlations with others. The reader can find more information concerning the application of ICrA in our recent studies and the references there [17,63]. ICrA defines the relations between the studied criteria (parameters) in terms of intuitionistic fuzzy pairs µ, ν [17,63]. Depending on the values of µ and ν seen in pair, positive consonance, negative consonance, and dissonance between any pair of criteria (parameters) can be defined.  [17,63]. Table 5 presents the µ values of ICrA of the different compatibility indices summarized in Table 4. It is evident from the data in Table 5 that the solvent power of the crude oil weakly positively correlates (µ = 0.81) with the solubility parameter and solubility blending number. The solubility blending number negatively weakly correlates with CII and ratio Sat/Aro (µ = 0.20 and µ = 0.16 respectively).   (Figure 2a). The relation between S BN and CII can be described by a power function (Figure 2a) with a squared correlation coefficient of R 2 = 0.978. The relation between solubility parameter and Sat/Aro ratio can be also described by a power function with a squared correlation coefficient R 2 = 0.938. The compatibility indices solubility parameter, S BN and solvent power correlate with density [28,46]. The content of saturates and aromatics in the crude oil and its fractions also correlates with density [63]. Therefore, the presence of a statistically meaningful relation between solubility blending number, for example, and the indices determined based on SARA analysis data can be expected. Indeed, this is confirmed by the data shown in Figure 2b,c.
The ICrA examination of the data in Table 6 revealed that the solvent power had a weak statistically meaningful relation with the density, sulfur and asphaltene content in the crude oil. Figure 3 depicts the relations between solvent power and crude oil density (a) and sulfur content (b). The asphaltene content in the crude oil was also found to relate to the solvent and critical solvent power (Figure 4). The C 5 asphaltene content was found to have a bigger impact on the solvent power than the C 7 asphaltene content. In general, the heavy crude oils, which have higher contents of sulfur, polar aromatics, and asphaltenes exhibit higher solubility power because the polar aromatic compounds (resins) in the crude oil are stabilizing agents that prevent the asphaltene precipitation [64]. Respectively, the crude oils, which have higher saturate (low density) and lower asphaltene contents, can be colloidal instable and they are more susceptible to cause sediment deposition during the petroleum exploration and processing [65]. Green color means statistically meaningful positive relation; Red color implies statistically meaningful negative relation. The intensity of the color designates the strength of the relation. The higher the color intensity, the higher the strength of the relation is. Yellow color denotes dissonance.
In some cases, for light crude oils with SBN/IN ratio below 1.4 and solvent power below 44, which are considered to pertain to the group of incompatible and near-incompatible crude oils (for example El Boury, CPC, and Azeri Light), the estimated solvent power values by Equation (9) were out of the regression standard error (5.7%), but in the range of The following expression of the relation between solvent power and crude oil properties has been established (Equation (9)) by performing a multiple linear regression: Sp = 34.76553 + 1.21187 × C5Asp + 0.10604 × Vis + 2.28072 × S R = 0.93 (coefficient of multiple correlation), standard error = 5.7% (9) In some cases, for light crude oils with S BN /I N ratio below 1.4 and solvent power below 44, which are considered to pertain to the group of incompatible and near-incompatible crude oils (for example El Boury, CPC, and Azeri Light), the estimated solvent power values by Equation (9) were out of the regression standard error (5.7%), but in the range of uncertainty of the method for solvent power determination (5-15%), as reported in [42] ( Figure 5a). crude oil compatibility evaluation [26]. The ratio between the solubility blending number and insolubility number was established as a reliable indicator that can determine the compatibility of the crude oils [27]. Figure 7 describes the SBN/IN ratios of the investigated crude oils. As can be seen from the data in Figure 7 three zones can be defined: incompatible zone SBN/IN < 1, near-incompatible zone 1 < SBN/IN < 1.4, and compatible zone SBN/IN > 1.4. It is evident from these data that both light and heavy crude oils pertain to the selfincompatible zone and near-incompatible zone, implying that all types of crude oil could belong to the group of the self-incompatible and near-incompatible oils. For this data set, no statistically meaningful relation was found between the insolubility number and any crude oil property. By performing a multiple linear regression, the following expression relating the critical solvent power to the C 5 asphaltene content, density of crude oil, and Conradson carbon content of the vacuum residue was developed.
Sp critical = 14.01745 + 1.127921 × C5Asp + 0.273233 × CCRvr + 11.65823 × D R = 0.85 (coefficient of multiple correlation), standard error = 5.8% The standard error of Equation (10) is in the range of uncertainty of the method for critical solvent power determination (5-15%) reported in [42] (Figure 5b). The laboratory experiments in LNB established that the typical error for solvent and critical solvent power determination did not exceed 10%.
The regression Equation (9) suggests that the crude oils which have higher C 5asphaltene content, higher viscosity, and higher sulfur content are stronger solvents. On the other hand, regression Equation (10) implies that the higher C 5 -asphaltene content crude oils are more difficult to dissolve and will require a stronger solvent to keep the asphaltenes in solution and prevent their precipitation. These findings are in line with those reported in our earlier study [17] showing that the higher asphaltene content crudes require blending with crude oils whose vacuum residue has a higher Conradson carbon content, and the petroleum has a higher density.
Similar to solvent power the S BN has a statistically meaningful relation with the crude oil density, sulfur, and C 5 asphaltene content (Figure 6). High sulfur crude oils with high content of C 5 and C 7 asphaltenes are characterized by a higher solubility blending number. It is well-known that solubility-blending number cannot be a self-sufficient parameter for crude oil compatibility evaluation [26]. The ratio between the solubility blending number and insolubility number was established as a reliable indicator that can determine the compatibility of the crude oils [27]. Figure 7 describes the S BN /I N ratios of the investigated crude oils. As can be seen from the data in Figure 7 three zones can be defined: incompatible zone S BN /I N < 1, near-incompatible zone 1 < S BN /I N < 1.4, and compatible zone S BN /I N > 1.4. It is evident from these data that both light and heavy crude oils pertain to the self-incompatible zone and near-incompatible zone, implying that all types of crude oil could belong to the group of the self-incompatible and near-incompatible oils. For this data set, no statistically meaningful relation was found between the insolubility number and any crude oil property.

Relation between Compatibility Indices and Crude Desalting Efficiency
Our previous study showed that the crude oil desalting efficiency is very important for the performance of the downstream units [49]. The desalting efficiency is defined as shown in Equation (11): Poor crude oil desalting entails upsets and increased corrosion in downstream units

Relation between Compatibility Indices and Crude Desalting Efficiency
Our previous study showed that the crude oil desalting efficiency is very important for the performance of the downstream units [49]. The desalting efficiency is defined as shown in Equation (11): Poor crude oil desalting entails upsets and increased corrosion in downstream units [49]. During processing different crude oil blends a variation of desalting efficiency between 70 and 96% was registered. All the studied compatibility indices in this work were examined for their relation to the desalting efficiency. Only the solvent power and the S BN /I N ratio were found to have a statistically meaningful relation with the desalting efficiency as shown in Figure 8. As evident from the data in Figure 8 the ratio S BN /I N is strongly related to the desalting efficiency than the solvent power. The crude oil blend with solvent power above 49 have a lower desalting efficiency. The solvent power of the crude oil is connected with its density and Kw-factor (Table 5). When the density of crude oil blend increases (respectively solvent power), the difference between the densities of petroleum blend and water decreases and water salinity diminishes. A crude oil with 0.898 specific gravity with produced water salinity of 25% has a density difference about five times as high as that of a crude oil with 0.973 specific gravity with produced water salinity of 3% at 40 • C [66]. The extra-heavy crude oils and bitumen, heavier than water are diluted to a dilbit of 0.97 specific gravity; the dilbit becomes lighter than the water phase, and the water salinity is 0%, typically [67]. Thus, for desalting and dehydration of heavier crude oil blends, the desalter will require more stringent operating conditions (temperate, type of chemical additives, wash water ratio, or settling time) [68] and design due to lower salinity in the diluted produced water in the desalter. During processing of near-incompatible crude oil blends (ratio SBN/IN < 1.4) a lower desalting efficiency was registered. Figure 8b depicts the relation between ratio SBN/IN and desalting efficiency, which is described by a second-order polynomial with R 2 = 0.9527. The insolubility number measures the degree of insolubility of the asphaltenes, and the solubility blending number measures the solvency of the oil for asphaltenes. The criterion of crude oil blend compatibility is SBNmix > INmax, that is the solubility blending number of the mixture of oils must be higher than the insolubility number of any oil in the mixture [26]. The higher the SBNmix the better its stability. On the other hand, the SBN is related to the asphaltene content in the crude oil ( Figure 6). It is well-known that asphaltenes in the crude oil, as a surface-active substance, cause the formation of higher stability oil/water emulsions [14]. The asphaltenes hinder separation of oil and water phases during the desalting and dewatering because the asphaltene molecules easily gather at the oil/water interface and undergo self-association, hence forming a rigid film at the oil/water interface [14]. Moreover, solids such as high molecular paraffin and clay are adsorbed and the mechanical strength of the interfacial film becomes more rigid than ever [69]. When the crude During processing of near-incompatible crude oil blends (ratio S BN /I N < 1.4) a lower desalting efficiency was registered. Figure 8b depicts the relation between ratio S BN /I N and desalting efficiency, which is described by a second-order polynomial with R 2 = 0.9527. The insolubility number measures the degree of insolubility of the asphaltenes, and the solubility blending number measures the solvency of the oil for asphaltenes. The criterion of crude oil blend compatibility is S BNmix > I Nmax , that is the solubility blending number of the mixture of oils must be higher than the insolubility number of any oil in the mixture [26]. The higher the S BNmix the better its stability. On the other hand, the S BN is related to the asphaltene content in the crude oil ( Figure 6). It is well-known that asphaltenes in the crude oil, as a surface-active substance, cause the formation of higher stability oil/water emulsions [14]. The asphaltenes hinder separation of oil and water phases during the desalting and dewatering because the asphaltene molecules easily gather at the oil/water interface and undergo self-association, hence forming a rigid film at the oil/water interface [14]. Moreover, solids such as high molecular paraffin and clay are adsorbed and the mechanical strength of the interfacial film becomes more rigid than ever [69]. When the crude blend is incompatible or near-incompatible and the asphaltenes are instable, the process of self-association at the oil/water interface may be accelerated resulting in the formation of a rigid film that deteriorates the desalting and dewatering efficiency.
A blend of 50.5 wt.% Urals, 20 wt.% CPC, 24.5 wt.% Arabian medium, and 5 wt.%. Prinos (S BN /I N = 1.1, Sp = 42.9, Sp critical = 32.1) was processed in the LNB refinery. The blend was determined as near-incompatible because the difference between Sp and Sp critical was in the limits of 10% error and the ratio S BN /I N was below 1.4. A very low desalting efficiency (70 ÷ 75%) was observed in the crude oil desalting unit.
The solvent compatibility indices and critical solvent power and solubility blending number and insolubility number determined on the base of the n-heptane dilution test and employment of Equations (2), (3), and (5)- (8) have been used to model the compatibility of a four-component crude oil blend. Tetra-Plot was used for representation of the compatibility of the four-component crude oil blend by using Equations (2) and (3) (solvent power and critical solvent power) and the procedure described in [70]. Figure 9 presents the obtained tetra-plot of crude oil blend Urals, CPC, Prinos, and Arabian medium crude oils by the use. Critical zone of mixing separates the zones of compatibility (in green) and incompatibility (in red) of the four-component blend. The critical curves of three-component blends are depicted. The critical point of two-component blend is also shown in Figure 9. It can be seen from these data that some of the critical points do not lie on the critical zone or curves. Two-component blend CPC/Urals is incompatible in the ratio 65% wt./35% wt., but the addition of a third crude oil, as Arabian medium for example, can improve the stability of the petroleum blend and make it compatible.  Figure 10 indicates the tetra-plot of crude oil blend Urals, CPC, Prinos, and Arabian medium crude oils by using the data for solubility blending number and insolubility number. The data in Figure 10 do not significantly differ from the data in Figure 9. However, the use of solubility blending number and insolubility number predicts a lower space of incompatibility ( Figure 10) than that employing solvent power and critical solvent power  number. The data in Figure 10 do not significantly differ from the data in Figure 9. However, the use of solubility blending number and insolubility number predicts a lower space of incompatibility ( Figure 10) than that employing solvent power and critical solvent power ( Figure 9). This implies that the compatibility indices of solvent power and critical solvent power are more conservative and predict the incompatibility regions with lower degree of freedom concerning the variation in concentration of the four investigated crude oils for that case. Nevertheless, the compatibility indices of solubility blending number and insolubility number are better related to the desalting efficiency, supposing that they could be the more appropriate indices to assess crude blend compatibility reflecting the commercial field performance.

Conclusions
Nine crude oil compatibility indices were studied to evaluate the compatibility of crude blends from thirty individual crude oils. These crude oils belong to light, medium, heavy, and extra heavy, light sulfur, and high sulfur types. The compatibility indices, solvent power, solvent blending number determined on the base of the n-heptane dilution test were found to correlate with the petroleum density. The compatibility indices based on petroleum SARA analysis data, colloidal instability index, saturates/aromatics, and others also correlate with density. The solubility blending number and solvent power increase with augmentation of contents of asphaltenes and sulfur. The critical solvent power enhances with the magnification of crude oil density, content of crude oil asphaltenes, and vacuum residue Conradson carbon content. The desalting efficiency deteriorates when crude blends with lower ratio of solubility blending number to insolubility number and higher solvent power are processed. The ratio of solubility blending number to insolubility number was found to best describe the desalting efficiency, and therefore could be considered as the compatible index that best models the crude oil blend compatibility.

Conclusions
Nine crude oil compatibility indices were studied to evaluate the compatibility of crude blends from thirty individual crude oils. These crude oils belong to light, medium, heavy, and extra heavy, light sulfur, and high sulfur types. The compatibility indices, solvent power, solvent blending number determined on the base of the n-heptane dilution test were found to correlate with the petroleum density. The compatibility indices based on petroleum SARA analysis data, colloidal instability index, saturates/aromatics, and others also correlate with density. The solubility blending number and solvent power increase with augmentation of contents of asphaltenes and sulfur. The critical solvent power enhances with the magnification of crude oil density, content of crude oil asphaltenes, and vacuum residue Conradson carbon content. The desalting efficiency deteriorates when crude blends with lower ratio of solubility blending number to insolubility number and higher solvent power are processed. The ratio of solubility blending number to insolubility number was found to best describe the desalting efficiency, and therefore could be considered as the compatible index that best models the crude oil blend compatibility.