Effect of extended heavier hydrocarbon fraction (Cn+) composition on optimum surface separation pressure and temperature

Hydrocarbon fluids are made up of defined components which include N2, CO2, H2S, C1, C2, C3, iC4, iC5, and C6  and undefined components known as heavier fractions (Cn+) which include paraffinic, naftenic and aromatic compounds. The hydrocarbons are separated on the surface before they are sent to the market. There are several factors affecting the hydrocarbons surface separation condition which include; pressure, temperature, gas liquid flow rates, surging or slugging tendencies of the feed stream, presence of impurities such as paraffin and sands. This work is limited to the study of the effects of pressure and temperature. To obtain stabilized hydrocarbons phases optimum surface separation, pressure and temperature must be selected. Several empirical models have been developed to obtain optimum surface separation pressure and temperature. However, these models do not consider the full composition of the well stream, and the heavier fractions are most often treated as a single component. This paper presents the estimation of an optimum surface separation-pressure and temperature of crude oil  while including the complete composition of the well stream and extended composition of the heavier fraction. The optimum pressure was estimated through the fluid properties such as oil formation volume factor, gas oil ratio and API gravity.  Optimum pressure and temperature is the one that produces maximum liquid yield (by minimizing oil formation volume factor and gas oil ratio) of maximum quality (by maximizing API gravity).  The fluid properties were predicted by phase equilibrium calculations using Peng Robinson thermodyinamic Model. The optimum pressure was first estimated considering the heavier fraction as single component and second the heavier fraction was splitted in pseudo components, both including the full composition of the well stream. Ahmed splitting method was used to extend the heavier fraction compostion, Kesler and Lee’s correlation was apllied to assign critical properties of the pseudo components. The results indicate that it is possible to estimate more accurately the optimum separation pressure by extending a composition of heavier fraction and accurate values of fluid properties were obtained. 
 
 Key words: C7+ fraction, splitting scheme, equation of state, Peng-Robison thermodynamic model, optimum separator pressure.


INTRODUCTION
Hydrocarbon surface separation is an important operation in maximizing the oil and gas surface recovering. Studying factors that affect the surface separation of hydrocarbon fluids is an important contribution in petroleum industry. To obtain stabilized hydrocarbon phases, optimum surface separation pressure and temperature must be selected. Several empirical models have been developed to obtain optimum surface separation pressure and temperature. Al-Jawad and Hassan (2010a,b) developed a group of correlations for optimum separator pressure for volatile oils using the results of theoretical correlations. According to Ling et al. (2013), these correlations were based on data from over 6000 test runs with various independent variables. They also stated that the correlations were empirical and did not consider the full composition of the well stream but heavier fraction was included. Whinery and Campbell (1958) developed a correlation for determining the optimum second-stage separator pressure in a three-stage separation system. AL-Jawad (2010a), stated that their new method was simple and it eliminated the need for the flash vaporization calculations.
On the other hand, Ling et al. (2013) pointed out that the disadvantage of this new correlation was that the accuracy and reliability of the calculations could not be guaranteed because the temperature of the separator, the stock tank, compositions of butane and heavier components were not included. In addition, Bahadori et al. (2008) presented a methodology for optimizing separator pressures in crude oil production units. Despite that in this method, the heavier fraction composition was extended, Ling et al. (2013) also pointed out that the drawback of this method is that it requires tremendous number of trial separator and still may not be able to obtain precise optimum pressures. According to the above-mentioned literature, neither the effect of heavier fractions nor the full composition of the well stream have been taken into consideration and the heavier fractions most often are treated as a single component. That is the reason why the present study includes these parameters by splitting the heavier fraction in pseudo components using Ahmed"s splitting scheme. This study only compares to Al jawad and Hassan (2010)"s correlations, since it is the one that includes the heavier fraction composition; consequently other studies are discarded from the comparison.

Al-Jawad and Hassan correlation
AL-Jawad and Hassan (2010) developed a correlation for estimating optimum separation pressure for heavy oils separation, one for high pressure separator in case for two stage and two for the first and second separators for three-stage separation system. In these correlations the optimum pressures have been correlated with mole percent of methane and hexane plus in the well stream, temperature of the separator and the optimum pressure of the previous separator. These equations represent unique correlations because they are using methane and hexanes plus mole percents.
The correlation coefficient A of these equations equal to 0.96. Table 1 presents the values of the constants "a' of the correlations for this system. Barrufet (1998c) defined oil mixture as composed of defined and undefined components known as heavier fraction or C n+ fraction. Pedersen and Christensen (2015) stated that defined components of oil mixture are N 2 , CO 2 , H 2 S, C 1 , C 2 , C 3 , iC 4 , iC 5 , and C 6 while  referred that undefined components will typically contain Paraffinic, Naphthenic, and Aromatic compounds. Barrufet (1998b) also mentioned that the defined components can be quantitatively identified using chromatographic analysis, while Ahmed referred that due to the limitation of laboratory separation techniques in analyzing and characterizing the undefined components of hydrocarbon fluids these components are traditionally lumped together and categorized as the plus fraction (C n+ ). Pedersen and Christensen (2015) also revealed that to perform a phase equilibrium analyses on hydrocarbon systems the physical properties for cubic equation of state (EOS) are critical pressure (P c ), critical temperature (T C ) and acentric factors (ω) of each component contained in the mixture. These properties have been measured and compiled for defined components. Whitson (1982) and Sancet (2007) referred that undefined components are difficult components to be properly characterized in terms of their critical properties and acentric factors. Therefore, in this paper the phase equilibrium calculations are performed with splitted heavier fraction and assigned critical properties and acentric factor in each pseudo component.  defined splitting schemes as the procedures of dividing the heavier fraction into hydrocarbons groups with single carbon number (C 7, C 8, C 9, etc) described by the same physical properties used for pure components. Imo-Jack et al. (2012) stated that heavier fraction in reservoir fluids contains different components which are impossible to identify by chemical separation techniques. Even if it was possible to identify them, it would not be possible to measure the critical properties and other EOS parameters for fluids heavier than C 20+ . Stamaki (2001) mentioned that this problem is solved practically by making approximate characterization of the heavier compounds with experimental and mathematical methods. According to , several authors have proposed different splitting methods for extending the molar distribution behavior of C 7+. Imo-Jack et al. also referred that these models are based on the assumption that there is a continuous relationship between composition and molecular weight of the pseudo components. Ahmed (2007a) and Riazi (1997) described the three main steps required for characterization of heavy end fractions:

Splitting schemes
(i). Splitting the heavier fraction into single carbon number, with known (molar and mass) amounts and molecular weights, (ii). Assigning boiling point, molecular weight and specific gravity to each fraction, (iii). Estimating critical properties of each fraction.
Ahmed described three important requirements to be satisfied when applying any of the proposed splitting models which are presented in Equations 3 to 5. The sum of the mole fraction of the individual pseudo components is equal to the mole fraction of C 7+, as expressed in Equation 3. (4) The sum of the product of the mole fraction and molecular weight divided by the specific gravity of each individual component is equal to that of C 7+ as expressed in Equation 5. Several splitting schemes have been proposed, these schemes are used to predict the compositional distribution of the heavy plus fraction.

Ahmed's splitting method
Ahmed devised a simplified method for splitting the C 7+ fraction into pseudo components. The method originated from studying the molar behavior of 34 condensate and crude oil systems through detailed laboratory compositional analysis of the heavy fractions. The splitting scheme is based on calculating the mole fraction, n Z at progressively higher number of carbon atoms. The extraction process continues until the sum of the mole fraction of the pseudo components are the same as the total mole fraction of the heptanes plus   Where n is the number of carbon atoms and S is the coefficient of the equation with the values given in Table  1.
In this splitting method a set of physical properties proposed by Katz and Firoozabadi ( n M ), specific gravity and critical properties for the petroleum fraction 6 C through 45 C are used. After extending the compostion of heavier fractions in pseudo components, critical properties and acentric factors must be assigned for the last fraction  n C . In this paper Kesler and Lee"s correlation was used to estimate these properties.

Surface separation conditions
Separators are used to separate oil, water and to remove material such as entrained solid impurities from the crude oil production (Chilingar, 1969). Ling et al. (2013) explained that the separator working principle is based on the three hydrocarbon phases: vapor, liquid-oil and liquidwater with different densities, which allow them to separate when moving. Gas will be on top, water on the bottom, and oil in the middle. Each condition of pressure and temperature at which hydrocarbon phases are separated is called a stage of separation. There are different number of stage used in petroleum industry to separate oil and gas. Ling et al. (2013) also referred that the simplest system is two-stage separation consisting of one separator and one stock tank. It is most applicable for low-API-gravity oils, low gas/oil ratios (GORs), low flowing pressures. The three-stage separation illustrated in Figure  The four-stage separation is designed for high-API gravity oils, high GOR, and high flowing pressures. Fourstage separation is also applicable when high flowing pressure gas is needed for market or for pressure maintenance. There are several factors affecting the separation of hydrocarbon fluids, such as: temperature, pressure, gas liquid flow rates, surging or slugging tendencies of the feed streams, presence of impurities (paraffin, sand). This paper will focus on pressure and temperature effect.Furthermore, Ahmed also referred that if the separator pressure is high, large amounts of light components will remain in the liquid phase at the separator and will be lost along with other valuable components to the gas phase at the stock tank. However, on the other hand, if the pressure is too low, large amounts of light components will be separated from liquids and they will attract substantial quantities of intermediates and heavier components. Therefore optimum surface separation pressure is required. Adewumi (2017) stated that optimum separator pressure is the one that produces the maximum liquid yield (at minimum gas/oil ratio and formation volume factor) of maximum quality (by maximizing stock tank API gravity) as shown in Figure 2. Table 2 shows the typical inicial values of gas oil ratio, formation volume factor and API gravity for different reservoirs fluids.

Equation of state (EOS)
An equation of state (EOS) is used to predict the pressure, volume and temperature behavior of gas and  The specific gravity of C7+ is 0.86. crude oil fluid. Ramdharee and Muzenda (2013) mentioned that there are many families of EOS, suitable for different purposes and substances. In petroleum engineering the most commonly used EOS are cubic polynomials. Barrufet (1998a) stated that cubic EOSs are the simplest polynomials that can provide an adequate description of both: liquid and gas properties. They can describe the state of pure fluids and mixtures (single or multiphase) and their properties. Funjinaga and Raijo (1999) stated that cubic equations are explicit in pressure and can be written as the sum of "b' term indicating repulsion forces and 'a' term indicating attraction forces. One of the most used EOS in petroleum engineering is the Peng-Robinson EOS (1975). The Peng Robinson is three-parameter corresponding sates model which is expressed as: Where "a' is the attraction parameter and "b' is the repulsion parameter defined by Equations 11 and 12 respectively: Equation 10 can be expressed as a cubic polynomial in compressibility factor (Z) as: When working with mixtures the same expressions in Equation 10 applies except that (aα) and (b) are evaluated for a mixture using a set of mixing rules. The most commonly used mixing rules are: Quadratic mixing rule for "a" : Linear mixing rule for "b": The cubic expression for a mixture is then evaluated using Equation 18 Where "m' refers to mixture

PVT data
This study was conduted based on the data presented by Bahadori (2008). According to Bahadori, this data were collected from Pazann-Asmari, black oil Reservoir-India and is presented in Table  2. The reservoir pressure is 3700 (psig), bottom hole temperature is 208 F and molecular weight of C7+ = 236. The specific gravity of C7+ is 0.86.
In this study the optimum pressure was estimated based on the fluid properties such as oil formation volume factor, gas oil ratio and API gravity. These properties were estimated through phase equilibrium calculations using Peng Ronbison thermodynamic Model. The optimum pressure is the one that provide maximum API gravity , minimum oil formation volume factor and gas oil ratio. The optimum pressure was estimated considering the system as three stage, where second stage was optimization stage.
The heavier fraction was splitted in pseudocomponents using Ahmed splitting method. To perfom phase equilibrium calcualtions critical properties and acentric factors must be assigned to the heavier fractions and pseudocomponents. Kesler and Lee"s correlation was used to assign these properties. The summary of this methodology is presented in Figure 3. The phase equilibrium calculations were conducted through VBA program, and the programing procedures are indicated in Figure 4.

RESULTS AND DISCUSSION
The heavier fraction was extended in 2, 3 and 4 pseudo components and the results of the new composition are presented in Tables 3 to 5. The maximum API gravity, minimum Bosb and Rssb was found at T = 70°F. Tables 3 to 5 present the results of extended heavier fraction, assigned critical properties, acentric factors in each new component. The last fraction is always a heavier fraction (C n+ ), which are C 9+, C 10+, C 11+. All the splitting constraints presented in Equation 5 to 7 were satisfied. From Table 6 is observed that if the temperature increases, the fluid properties changes, where API gravity decrease, Bosb and Rssb increase. The optimum temperature used for pressure estimation for single and extended heavier fraction is 70°F. From Figures 5 to 7 Figure 4. Optimum pressure estimation procedure.
fraction, when compared to API for extended C 7+ fraction, these results were compared to initial stock tank liquid gravity API, presented in Table 7, where for crude oil the values are less than 45.
In the Table 7 is observed that API gravity values obtained using heavier fraction as single component are high compared to API gravity values for extended fraction in both methods, and keep decreasing as the number of pseudo components increases. The fluid properties predicted using the proposed methods are high when compared to properties obtained using empirical correlation. The optimum pressure predicted by the proposed method is greater compared to pressures obtained using empirical model. This shows the impact of using the full composition of the well stream and extended heavier fraction.

If
Step 2: Flash Calculations Step 3: Evaluate Mixing Rules Step 4: Calculate compressibility factors Step 5: Calculate coeficients to fugacities calculations Step 6: Evaluate Fugacities Step 7: Calculate New Kvalues Step 8: Calculate the Error Step 9: Calculate densities Step 10: Calculate fluid properties Estimate Optimum pressure  T  P  P  P  R  P  T  Z   o  c  c  i   ,  ,  ,  ,  ,  ,  , ,   Repeat Step 1 to 10. Choose:  Table 7 indicates that when the number of pseudo components increases API gravity decrease with tendency to theoretical API as presented in Table  7. This is also observed in oil formation volume factor where Figures 8 to 10 shows that increasing the number of pseudo components the oil formation volume factor increase, with tendency of predicting volatile oil when compared to theoretical expected properties as presented in Table 8, with values more than 2 bbl\STB. This observation is also valid to gas oil ratio where Figures 11 to 13 show an increase when the heavier fraction is splitted into more components, and value are less than 1750 scf\STB for crude oil as presented in Table 8. So this indicates the effect of extending the heavier fractions to more components than using as single component. The optimum second stage for single heavier fraction is presented in the Figures 14 to 20, where for maximum in API gravity, minimum in Bosb and Rssb, the optimum pressure is found at 174 psia. Similar optimum pressures estimation were made for extended heavier fraction in 2, 3 and 4 pseudo components and the results are presented in Table 7. In Table 7 is observed that the optimum pressure obtained using the heavier fraction as single component as greater compared to pressures obtained with extended fraction and keeps decreasing as fraction is continuously extended.

Conclusion
In this study, it is concluded that extended composition of C 7+ fraction affects the optimum surface separator pressure of the fluid stream. Both method showed that splitting the composition of the C 7+ fraction in pseudo components results in different estimated fluid properties when compared with properties estimated assuming the C 7+ as single component. An increment in the number of pseudo components the optimum second stage pressure changes because of changes in the fluid properties. Where accurate results are obtained when the heavier fraction is splitted in several pseudo components. Both methods showed that with an increment in second stage 50 J. Petroleum Gas Eng.    temperature, the API gravity decrease, oil formation volume factor and solution gas oil ratio increase.

RECOMMENDATIONS
Present study was limited to one type of reservoir fluid exposed to only a single separator test therefore more    (McCain, 1994).*For engineering purposes. Table 9. Al-Jawad and Hassan correlation constants "a" for equations 1 and 2.  splitting scheme was the only method applied to extend the composition of the heavier fraction. We suggest performing more studies where fluid properties are obtained through laboratory PVT tests. In present  research, these properties were obtained from standard PVT experiments which are conducted through phase equilibrium simulations. It is recommended that Figure 19. Optimum second stage pressure estimation from Bosb and API for C7+ splitted in 4 pseudo components.