Document Type : Research Paper
Authors
 Shahriar Osfouri ^{} ^{1}
 Reza Azin ^{2}
 Hamid reza Amiri ^{3}
 Zahra Rezaei ^{4}
 Mahmoud Moshfeghian ^{5}
^{1} Associate Professor, Department of Chemical Engineering, Faculty of Petroleum, Gas, and Petrochemical Engineering, Persian Gulf University, Bushehr, Iran
^{2} Associate Professor, Department of Petroleum Engineering, Faculty of Petroleum, Gas, and Petrochemical Engineering, Persian Gulf University, Bushehr, Iran
^{3} M.S. Student, Department of Petroleum Engineering, Faculty of Petroleum, Gas, and Petrochemical Engineering, Persian Gulf University, Bushehr, Iran
^{4} M.S. Student, Department of Chemical Engineering, Faculty of Petroleum, Gas, and Petrochemical Engineering, Persian Gulf University, Bushehr, Iran
^{5} Professor, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran
Abstract
Gas condensate reservoirs are characterized by a distinctive retrograde behavior and potential for condensate drop out during production and sampling. Efficient modeling of gas condensate reservoir requires careful phase behavior studies of samples collected prior to and during the production life of reservoir. In this work, an integrated characterization and tuning algorithm is proposed to analyze the pressurevolumetemperature (PVT) behavior of gas condensate samples. Each characterization and tuning scenario is described by a “path” which specifies the class of fluid, splitting and lumping (if any), the type of correlation, and grouping strategy (static or dynamic). Different characterization approaches were tested for the effective description of heavy end. Meanwhile, dynamic and static strategies were implemented to tune the equation of state (EOS) through nonlinear regression. The optimum combination of characterization and tuning approach was explored for each sample by a rigorous analysis of the results. It was found out that the exponential distribution function gives the best performance for heavy end characterization in a dynamic tuning strategy. Also, analyses indicate that using higher single carbon number may not necessarily make EOS tuning more accurate. In addition, the optimum step is reached in either the third or fourth step for most cases in a dynamic tuning approach, and is sensitive neither to the characterization path nor to the selected end carbon number.
Keywords
Main Subjects
Gas condensate reservoirs contain hydrocarbon accumulates at a temperature between critical and cricondentherm points (Ahmed, 2007). These reservoirs are characterized by a distinctive retrograde behavior and potential to leave beyond heavy ends, known as condensates, in a reservoir during production and sampling (Fevang, 1995; Kool et al., 2001; McCain and Alexander, 1992; Schebetov et al., 2010). The proper and optimized development and modeling of gas condensate reservoirs require careful phase behavior studies of the samples collected prior to and during the production life of reservoir. Reservoir management strategies depend closely on the quality of samples, experiments conducted on them, and the pressurevolumetemperature (PVT) study performed based on these experiments. An integrated approach in sampling, PVT experiment, and phase behavior modeling is essential for a multiwell reservoir to achieve a robust reservoir fluid description. Due to complexities in their phase behavior and flow patterns, the development of gas condensate reservoirs can be associated with several uncertainties. Main PVT analyses for understanding the behavior of gas condensate systems include compositional analysis, constant volume depletion (CVD), and constant composition expansion (CCE) experiments (Ahmed, 1989, 2007; Pedersen et al., 1989; Whitson and Brule, 2000). Phase behavior modeling of hydrocarbon samples, including gas condensates, by using equations of state (EOS) has been a wellknown technique applied widely to predicting the PVT behavior of fluid during the production life of a reservoir. These EOS are useful tools for predicting properties such as dewpoint pressure, the density of liquid and vapor phases, liquid dropout across pressure decline, vaporliquid equilibrium (VLE) calculations etc. (Ahmed, 2007; ImoJack, 2010; Nasrifar et al., 2005; Nasrifar and Moshfeghian, 2002; Nazarzadeh and Moshfeghian, 2013; Whitson and Brule, 2000; Yarborough, 1979). Cubic EOS is widely applied to the phase behavior studies of gas condensate systems. A comprehensive classification of EOS are reviewed by Wei and Sadus (Wei and Sadus, 2000). Among the large family of cubic EOS, PengRobinson (PR) and SoaveRedlich Kwong (SRK) equations are the two equations of state most familiar to petroleum engineers (Ahmed, 1989, 2007; Nazarzadeh and Moshfeghian, 2013; Peng and Robinson, 1976; Soave, 1972; Whitson and Brule, 2000). Tuning of EOS parameters according to the measured data is a crucial step before applying it to VLE simulations and predicting thermodynamic and physical properties of each phase. Numerous studies have been reported for the tuning strategies of EOS to fit gas condensate data (Aguilar Zurita and McCain, 2002; Danesh, 1998; Hosein and Dawe, 2012; Merrill et al., 1994; Pedersen et al., 1988). Different tuning strategies are described in detail by Whitson (Whitson and Brule, 2000) and Danesh (Danesh, 1998). A tuning strategy coupled with Pedersen splitting method was recently used to tune Patel and Teja EOS (Patel and Teja, 1982) and to study the phase behavior of multiple samples taken from a retrograde gas condensate field (Mehrabian and Crespo, 2011). An important step in EOS modeling is the characterization of heavy end which may cause drastic effects on predictions if not properly conducted. This step involves splitting, lumping, and predicting the physical properties of pseudocomponents that provide the best description of heavy end according to reported experimental results (Ahmed, 1989; Danesh, 1998; Whitson, 1983; Whitson and Brule, 2000). Among different techniques employed to characterize plus fraction in gas condensate systems, exponential and gamma distribution functions are most widely used (AlMeshari et al., 2005; Moshfeghian et al., 2006; Pedersen et al., 1992; Pedersen et al., 1989; Shariati et al., 2001; Whitson et al., 1990). The lumped plus fraction may undergo successive splitting/lumping before EOS can predict dew point pressure within an acceptable range. An integrated characterization and tuning strategy with a focus on EOS parameters will result in a tuned EOS that can predict experimental data within an acceptable range (Danesh, 1998; Whitson and Brule, 2000). This integrated approach has been applied to PVT studies of gas condensate (AlMeshari et al., 2005; Hosein and Dawe, 2012; Hosein and Jagai, 2003; Merrill et al., 1994) and proved to yield better results.
The objectives of this paper are to present an integrated characterization and tuning algorithm and to apply it to PVT data samples collected from a supergiant multiwell gas condensate reservoir. In the following sections, the properties of the collected samples and measured quantities are presented first. Then, the methodology is proposed and discussed. After that, the proposed methodology is applied to samples, and the results are analyzed to explore the most efficient combination of characterization and tuning procedure for each sample.
2. Experimental data
The experimental data include three representative gas condensate samples which were prepared through screening of more than 80 comprehensive PVT reports collected during 20 years from exploration and production wells in a supergiant, multilayer, multiwell gas condensate field. The screening criteria considered factors such as quality control of well conditioning, separator, and PVT tests. This was accomplished by using drillstem test (DST) data and checking stability conditions in the first step, followed by quality checking of PVT data (Osfouri et al., 2014). Also, it was essential to check the quality of separator equilibrium conditions and to validate the consistency of the measured PVT data reported for recombined samples using standard techniques (Thomas et al., 2007; Whitson and Brule, 2000) before EOS tuning. This approach involves comparing the dew point pressure of separator gas with the bubble point pressure of separator liquid samples, using the HoffmanStanding (Hoffman et al., 1953) plot, comparing condensategas ratio (CGR) of the recombined fluid with that of the reservoir fluid, and performing material balance on the measured CVD data. Details of PVT quality control and sampling equilibrium conditions for the samples under study are discussed elsewhere (Osfouri et al., 2014). Although this approach is rather complicated and time consuming, it filters invalid data and focuses on valid data measured in equilibrium conditions for EOS tuning and determining representative fluid(s) in the reservoir. Table 1 summarizes the compositional analysis and plus fraction properties of three representative samples of the studied reservoir.
Table 1
Original composition (mol.%) of gas condensate samples and properties of plus fraction.
Component 
Well name 

W_{1} 
W_{2} 
W_{3} 

N_{2} 
3.26 
3.51 
3.23 
CO_{2} 
1.91 
1.92 
1.96 
H_{2}S 
0.12 
0.12 
0.15 
C_{1} 
82.95 
82.79 
83.06 
C_{2} 
5.33 
5.35 
5.27 
C_{3} 
1.98 
2 
1.96 
iC_{4} 
0.42 
0.43 
0.42 
nC_{4} 
0.7 
0.72 
0.7 
iC_{5} 
0.31 
0.32 
0.31 
nC_{5} 
0.46 
0.29 
0.29 
C_{6} 
0.49 
0.39 
0.57 
C_{7} 
0.46 
0.48 
0.47 
C_{8} 
0.43 
0.45 
0.44 
C_{9} 
0.28 
0.29 
0.29 
C_{10} 
0.21 
0.22 
0.22 
C_{11} 
0.15 
0.15 
0.15 
C_{12+} 
0.54 
0.57 
0.51 
Total (mol.) 
100 
100 
100 
MW C_{12+} 
211.91 
214.89 
211.25 
C_{12+} relative density 
0.835 
0.837 
0.835 
Gas MW 
22.09 
22.12 
22.03 
Gas relative density 
0.763 
0.764 
0.761 
In addition to the analysis given in Table 1, each sample underwent extra compositional analysis with both C_{7+} and C_{20+} as the last heavy components. The wells were drilled in different blocks, and the distribution of hydrocarbon composition within the field may be detected by comparing the PVT data. The experimental data included reservoir fluid compositional analysis, a complete set of constant composition expansion (CCE), and constant volume depletion (CVD) tests along with the separator data for all the samples. According to the experimental data, the dew point pressure of this field was measured in the range of 32.20–34.14 MPa (46824950 psia). Tables A1 and A2 in Appendix summarize the measured PVT data used in this study. These data include vapor Zfactor, retrograde liquid relative volume, and cumulative produced moles of liquid dropout of CVD experiments as well as Zfactor, relative volume, and liquid dropout of CCE experiments. All the data were used in EOS tuning. Figure 1a shows a typical phase diagram for samples W_{1} and W_{2}, and liquid dropout versus pressure obtained from CCE test is displayed in Figure 1b; Figure 1C shows Zfactor (obtained from CCE test) versus pressure. According to Figure 1, these representative samples have different phase behaviors although their compositions seem similar as reported in Table 1. Moreover, the PVT reports indicate a 255 psia difference between the measured dew point pressures of these samples.
a) 
b) 


c) 

Figure 1
a) PT diagram, b) liquid drop out, and c) and Z factor of the CCE experiment for representative samples W_{1} (solid) and W_{2} (dashed).
3. Methodology
In this work, two EOS tuning strategies, named as static and dynamic strategies, were followed to find the best match between the experimental data and EOS predictions using the sum of squares of relative error as the objective function:
(1) 
where, and are calculated and measured quantities, including dewpoint pressure and all the measured properties of CVD and CCE tests. The objective function is minimized using LevenbergMarquardt algorithm (Edgar, 2001). In both proposed strategies, tuning of EOS is integrated with the characterization of plus fraction. Furthermore, to check the validity of the characterization method, the phase envelope of the samples were checked before and after the characterization of plus fraction. In static tuning, component grouping is fixed and remains unchanged throughout EOS tuning. On the other hand, dynamic tuning involves the modification of component grouping while EOS tuning is in progress. The former strategy focuses on EOS parameters only, while the latter combines EOS tuning with a dynamic component grouping. In this approach, the best distribution function, empirical correlations for estimating critical properties and acentric factor, and lumping procedure are determined in line with optimizing EOS parameters. To this end, the exponential (Pedersen et al. (1989)) and gamma (Whitson et al., 1990) distribution functions were used for describing the pseudocomponent single carbon number (SCN) group distributions. In addition, the correlations of LeeKesler (Lee and Kesler, 1975) and Twu (Twu, 1984) were used to predict the critical properties and acentric factor of SCN groups. Based on the selected strategy, different combinations of plus fraction splitting (if necessary), component lumping (if necessary), and empirical correlations may be applied for efficient PVT modeling. This will be described as different tuning “paths” as follows. In order to avoid more complexity in EOS modeling, the PengRobinson (PR) EOS was used throughout the rest of the study:
(2) 
where,
(3) 

(4) 

(5) 
and is a dimensionless parameter such that:
(6) 

(7) 
and of plus fraction are adjustable parameters of the objective function.
3.1. Static tuning strategy
Based on the available data, three composition classes, named as Class A, Class B, and Class C, were defined, for which characterization and EOS tuning was carried out using the static tuning strategy:
Class A: in this class, the original composition up to C_{12+} was considered in the PVT calculations. Any composition beyond C_{12} was lumped into a C_{12+ }pseudocomponent, and its critical properties were calculated using empirical correlations. No further grouping was made on the composition. The tuning of EOS was performed by focusing on the critical properties of plus fraction and EOS parameters (Ω_{a }and Ω_{b}) for certain components.
Classes B and C: these classes focus on the lumped composition of the samples shown in Tables 2 and 3 respectively. The components used in grouping are different between classes B and C. For class B, the last component was split into C_{12} and C_{13+}, followed by lumping C_{12} with C_{7}C_{11} pseudocomponents. On the other hand, no splitting was made on the components in class C, and grouping approach was different from that used in class B. Procedures for calculating the critical properties of the lumped components and EOS tuning were similar for all the classes.
Table 2
Composition (mol.%) of the lumped samples (Class B).
Component or group 
W_{1} 
W_{2} 
W_{3} 
N_{2}C_{1} 
86.21 
86.30 
86.30 
H_{2}S 
0.12 
0.12 
0.15 
CO_{2} 
1.91 
1.92 
1.96 
C_{2}C_{3} 
7.31 
7.35 
7.23 
iC_{4} to C_{6} 
2.38 
2.15 
2.29 
C_{7} to C_{12} 
1.70 
1.77 
1.73 
C_{13+} 
0.37 
0.39 
0.35 
Properties of C_{13+} MW: Relative density 
228.92 0.842 
225.94 0.843 
225.28 0.843 
Table 3
Composition (mol.%) of the lumped samples (Class C).
Component or group 
W_{1} 
W_{2} 
W_{3} 
N_{2}C_{1} 
86.21 
86.30 
86.29 
H_{2}SCO_{2} 
2.03 
2.04 
2.11 
C_{2}C_{3} 
7.31 
7.35 
7.23 
iC_{4} to nC_{5} 
1.89 
1.76 
1.72 
C_{6} to C_{8} 
1.38 
1.32 
1.48 
C_{9}C_{11} 
0.64 
0.66 
0.66 
C_{12+} 
0.54 
0.57 
0.51 
Properties of C_{12+} MW: Relative density 
211.25 0.835 
219.91 0.835 
214.89 0.837 
3.2. Dynamic tuning strategy
In this strategy, the single carbon number (SCN) of the plus fraction component is fixed and compared with fluid composition to decide if any further splitting is necessary. If required, splitting will be performed by either exponential or Gamma distribution functions, followed by estimating the critical properties and the acentric factor of the pseudocomponents. The calculations are continued through simultaneous component regrouping and EOS tuning by the fivestep procedure as described in Whitson (Whitson and Brule, 2000) until the best match between the measured and predicted experiments is obtained. In addition, the phase diagram of the regrouped composition at each stage must be compared with that of the original fluid.
A flow chart and summary of these strategies is shown in Figure 2. In this figure, the dynamic and static strategies are denoted by D and S symbols respectively. Additionally, each strategy is described by a “path” which specifies the class of fluid or the SCN of plus fraction, splitting and lumping (if any), and the type of empirical correlation. For the dynamic strategy, the grouping step is also included. For class B, splitting C_{12+} to C_{12} and C_{13+} was conducted by either exponential (Ex) or Gamma (Ga) distribution functions. For example, the path named as SBGAL refers to a case in the static strategy in which grouping class B with gamma distribution function and LeeKesler’s (Lee and Kesler, 1975) correlation is studied. The abbreviation “NO” in classes A and C indicates that no splitting was made on them and both are run with composition up to C_{12+}. In the dynamic strategy, for example, D7EXL1 refers to a case in which C_{7+} is split by exponential distribution function, and LeeKesler’s (Lee and Kesler, 1975) correlation is used to characterize SCN and lumped groups. The last number (1 in this example) refers to the grouping step of Whitson’s procedure (Whitson and Brule, 2000).
Figure 2
A schematic of characterization and tuning approach proposed for this study (Legends: Ex: exponential distribution function; Ga: Gamma distribution function; D: dynamic tuning; S: static tuning; LK: LeeKesler’s correlation; T: Twu’s correlation).
4. Results and discussion
The proposed methodology described in the previous section was applied to three representative gas condensate samples having a valid measured PVT data. Based on this methodology, a sensitivity analysis was carried out on samples by varying some considerable variables such as the type of strategies, distribution functions, empirical correlations, and grouping method on EOS tuning. The abbreviations for each tuning path were described previously. Figure 3 shows the effect of all variables on average absolute deviation of P^{dew} predictions for sample W_{1} by tuned EOS in a dynamic approach. By setting the maximum allowable AAD% for P^{dew} prediction equal to 1%, the simulation paths resulting in an AAD% ≤ 1% may be regarded as acceptable.
Figure 3
Average absolute deviation of P^{dew} predictions using tuned EOS for sample W_{1} in the dynamic strategy.
Similar sensitivity analysis was made on other properties by setting a maximum allowable deviation for each subobjective function. For example, Figures 4 and 5 show the effect of all the parameters on average absolute deviation of cumulative produce moles (CPM) and liquid dropout predictions for the same sample in the dynamic approach respectively.
Figure 4
Average absolute deviation of CPM predictions using tuned EOS for sample W_{1} in the dynamic strategy.
Figure 5
Average absolute deviation of liquid drop out predictions using tuned EOS for sample W_{1} in the dynamic strategy.
The maximum allowable tolerance was set to 5% and 20% for these properties; it was also set on 2% and 3% for oil relative volume and gas compressibility factor respectively. If the accuracy of the predicted property by a specific “path” falls within the defined tolerance, the path will be assigned “1”; otherwise, it will be assigned “0” to indicate that selected grouping and tuning “path” fails to predict the property correctly. The proposed “path” would succeed if only predictions fall within the acceptable range for all the five properties.
Table 4 summarizes the results of the EOS tuning sensitivity analysis of sample W_{1}. According to this table, there are eight acceptable “paths” for efficient fluid characterization and EOS tuning in this case. These paths include D7EXL2, D7EXL3, D7EXL4, D7EXT3, D7EXT4, D7GAL3, D7GAL4, and D12EXL3. All other possibilities fail to predict the fluid behavior correctly. Tables 5 and 6 summarize the results of samples W_{2} and W_{3}, indicating that there are five and fourteen acceptable “paths” for these wells respectively.
Table 4
Results of the dynamic tuning strategy of sample W_{1}.
Path 
P^{dew} 
Relative volume 
CPM 
Liquid drop out 
Z 
Result 
D7EXL1 
0 
0 
1 
1 
0 
0 
D7EXL2 
1 
1 
1 
1 
1 
1 
D7EXL3 
1 
1 
1 
1 
1 
1 
D7EXL4 
1 
1 
1 
1 
1 
1 
D7EXL5 
0 
0 
0 
1 
1 
0 
D7EXT1 
0 
0 
0 
1 
1 
0 
D7EXT2 
0 
0 
0 
1 
1 
0 
D7EXT3 
1 
1 
1 
1 
1 
1 
D7EXT4 
1 
1 
1 
1 
1 
1 
D7EXT5 
0 
0 
0 
1 
1 
0 
D7GAL1 
0 
0 
1 
1 
1 
0 
D7GAL2 
0 
0 
0 
1 
1 
0 
D7GAL3 
1 
1 
1 
1 
1 
1 
D7GAL4 
1 
1 
1 
1 
1 
1 
D7GAL5 
0 
0 
0 
1 
1 
0 
D7GAT1 
0 
0 
1 
1 
1 
0 
D7GAT2 
0 
0 
0 
0 
1 
0 
D7GAT3 
0 
0 
0 
1 
1 
0 
D7GAT4 
0 
0 
0 
1 
0 
0 
D7GAT5 
0 
0 
0 
1 
1 
0 
D12EXL1 
0 
0 
1 
1 
0 
0 
D12EXL2 
0 
0 
0 
1 
1 
0 
D12EXL3 
1 
1 
1 
1 
1 
1 
D12EXL4 
0 
1 
1 
1 
1 
0 
D12EXL5 
0 
0 
0 
1 
1 
0 
D12EXT1 
0 
0 
1 
1 
1 
0 
D12EXT2 
0 
1 
1 
1 
1 
0 
D12EXT3 
0 
1 
1 
1 
1 
0 
D12EXT4 
0 
0 
1 
1 
1 
0 
D12EXT5 
0 
0 
0 
1 
1 
0 
D12GAL1 
0 
0 
1 
1 
0 
0 
D12GAL2 
0 
0 
0 
0 
1 
0 
D12GAL3 
0 
0 
0 
0 
1 
0 
D12GAL4 
1 
1 
1 
1 
0 
0 
D12GAL5 
0 
0 
0 
1 
1 
0 
D12GAT1 
0 
0 
0 
1 
1 
0 
D12GAT2 
0 
0 
0 
0 
1 
0 
D12GAT3 
1 
1 
0 
1 
1 
0 
D12GAT4 
1 
1 
1 
1 
0 
0 
D12GAT5 
0 
0 
0 
1 
1 
0 
D20NoL1 
0 
1 
1 
1 
0 
0 
D20NoL2 
0 
0 
0 
0 
1 
0 
D20NoL3 
0 
0 
0 
0 
1 
0 
D20NoL4 
0 
1 
1 
1 
0 
0 
D20NoL5 
0 
0 
0 
1 
1 
0 
Table 5
Results of the dynamic tuning strategy of sample W_{2}.
Path 
P^{dew} 
Relative volume 
CPM 
Liquid drop out 
Z 
Result 
D7EXL1 
0 
1 
1 
1 
1 
0 
D7EXL2 
0 
1 
1 
1 
1 
0 
D7EXL3 
1 
1 
1 
1 
1 
1 
D7EXL4 
1 
1 
1 
1 
1 
1 
D7EXL5 
0 
1 
0 
1 
1 
0 
D7EXT1 
0 
1 
1 
1 
1 
0 
D7EXT2 
0 
0 
0 
1 
1 
0 
D7EXT3 
0 
1 
0 
1 
1 
0 
D7EXT4 
1 
1 
1 
1 
1 
1 
D7EXT5 
0 
1 
0 
1 
1 
0 
D7GAL1 
0 
1 
1 
1 
1 
0 
D7GAL2 
0 
0 
0 
1 
1 
0 
D7GAL3 
0 
1 
1 
1 
1 
0 
D7GAL4 
0 
1 
1 
1 
1 
0 
D7GAL5 
0 
1 
0 
1 
1 
0 
D7GAT1 
0 
1 
1 
1 
1 
0 
D7GAT2 
0 
0 
0 
0 
1 
0 
D7GAT3 
0 
0 
0 
1 
1 
0 
D7GAT4 
0 
1 
1 
1 
1 
0 
D7GAT5 
0 
1 
0 
1 
1 
0 
D12EXL1 
0 
1 
1 
1 
1 
0 
D12EXL2 
0 
1 
0 
1 
1 
0 
D12EXL3 
1 
1 
1 
1 
1 
1 
D12EXL4 
0 
1 
1 
1 
1 
0 
D12EXL5 
0 
1 
0 
1 
1 
0 
D12EXT1 
0 
1 
1 
1 
1 
0 
D12EXT2 
0 
1 
1 
1 
1 
0 
D12EXT3 
0 
1 
1 
1 
1 
0 
D12EXT4 
0 
1 
1 
1 
1 
0 
D12EXT5 
0 
0 
0 
1 
1 
0 
D12GAL1 
0 
1 
1 
1 
0 
0 
D12GAL2 
0 
0 
0 
0 
1 
0 
D12GAL3 
0 
0 
0 
0 
1 
0 
D12GAL4 
1 
1 
1 
1 
0 
0 
D12GAL5 
0 
1 
0 
1 
1 
0 
D12GAT1 
0 
1 
1 
1 
0 
0 
D12GAT2 
0 
1 
0 
1 
1 
0 
D12GAT3 
1 
1 
1 
1 
1 
1 
D12GAT4 
0 
1 
1 
1 
1 
0 
D12GAT5 
0 
1 
0 
1 
1 
0 
D20NoL1 
0 
1 
1 
1 
0 
0 
D20NoL2 
0 
0 
0 
0 
1 
0 
D20NoL3 
0 
0 
0 
0 
1 
0 
D20NoL4 
0 
1 
1 
1 
0 
0 
D20NoL5 
0 
1 
0 
1 
1 
0 
Table 6
Results of the dynamic tuning strategy of sample W_{3}.
Path 
P^{dew} 
Relative volume 
CPM 
Liquid drop out 
Z 
Result 
D7EXL1 
1 
1 
1 
1 
1 
1 
D7EXL2 
0 
1 
1 
1 
1 
0 
D7EXL3 
1 
1 
1 
1 
1 
1 
D7EXL4 
1 
1 
1 
1 
1 
1 
D7EXL5 
0 
1 
1 
1 
1 
0 
D7EXT1 
1 
0 
1 
1 
1 
0 
D7EXT2 
0 
0 
0 
1 
1 
0 
D7EXT3 
0 
1 
0 
1 
1 
0 
D7EXT4 
1 
1 
1 
1 
1 
1 
D7EXT5 
0 
1 
0 
1 
1 
0 
D7GAL1 
0 
1 
1 
1 
1 
0 
D7GAL2 
0 
0 
0 
1 
1 
0 
D7GAL3 
1 
1 
1 
1 
1 
1 
D7GAL4 
1 
1 
1 
1 
1 
1 
D7GAL5 
0 
0 
1 
1 
1 
0 
D7GAT1 
0 
0 
1 
1 
1 
0 
D7GAT2 
0 
0 
0 
0 
1 
0 
D7GAT3 
0 
0 
0 
1 
1 
0 
D7GAT4 
1 
1 
1 
1 
1 
1 
D7GAT5 
0 
0 
1 
1 
1 
0 
D12EXL1 
1 
0 
1 
1 
0 
0 
D12EXL2 
1 
1 
1 
1 
1 
1 
D12EXL3 
1 
1 
1 
1 
1 
1 
D12EXL4 
1 
1 
1 
1 
1 
1 
D12EXL5 
0 
0 
1 
1 
1 
0 
D12EXT1 
1 
0 
1 
1 
1 
0 
D12EXT2 
0 
0 
1 
1 
1 
0 
D12EXT3 
1 
1 
1 
1 
1 
1 
D12EXT4 
1 
1 
1 
1 
1 
1 
D12EXT5 
0 
0 
1 
1 
1 
0 
D12GAL1 
1 
0 
1 
1 
0 
0 
D12GAL2 
0 
0 
0 
1 
1 
0 
D12GAL3 
0 
0 
0 
1 
1 
0 
D12GAL4 
1 
1 
1 
1 
0 
0 
D12GAL5 
0 
0 
1 
1 
1 
0 
D12GAT1 
1 
0 
1 
1 
0 
0 
D12GAT2 
1 
1 
0 
1 
1 
0 
D12GAT3 
1 
1 
1 
1 
1 
1 
D12GAT4 
1 
1 
1 
1 
1 
1 
D12GAT5 
0 
0 
1 
1 
1 
0 
D20NoL1 
1 
1 
1 
1 
0 
0 
D20NoL2 
0 
0 
0 
0 
1 
0 
D20NoL3 
0 
0 
0 
1 
1 
0 
D20NoL4 
1 
1 
1 
1 
0 
0 
D20NoL5 
0 
0 
1 
1 
1 
0 
Figure 6 shows the frequency plot for SCN, distribution function, empirical correlations, and grouping step which describe the most accurate paths in the dynamic tuning strategy. Based on this sensitivity analysis, a combination of SCN= 7 for plus fraction, exponential distribution function, LeeKesler’s (Lee and Kesler, 1975) correlation for estimating critical properties, and the third or the fourth step in grouping (Whitson and Brule, 2000) would result in the best EOS tuning and fluid property prediction. Also, this figure shows that increasing the SCN of plus fraction and grouping steps does not necessarily result in better outputs with higher accuracy.
Figure 6
Frequency plot for SCN, distribution function, empirical correlations, and grouping step of the most accurate paths in the dynamic strategy.
The results of employing the static tuning strategy are summarized in Tables 79 for wells W_{1}, W_{2}, and W_{3} respectively. Moreover, a typical phase envelop checking is illustrated in Figure 7. As it can be seen, the phase envelops before and after characterizationtuning procedure are the same. This approach is simpler to use as the fluid composition is fixed and there are less possible combinations to study. Comparing the static and dynamic tuning strategies suggest that the dynamic strategy offer better results if there is no constraint on the fluid composition. In the cases where fluid composition is to be set a priori, the static strategy may be applied. Furthermore, the increased number of fluid characterization and EOS tuning steps is associated with the larger number of optimization parameters for minimizing the objective function. As a result, the overall number of computation steps is higher in the dynamic tuning strategy compared to the static strategy.
Figure 7
Phase envelops for well W_{1} (Path: BGaT) before () and after (·) characterizationtuning procedure.
Table 7
Results of the static tuning strategy of well W_{1}.
Path 
P^{dew} 
Relative volume 
CPM 
Liquid drop out 
Z 
Result 
ANoL 
0 
0 
1 
1 
1 
0 
ANoT 
0 
0 
0 
1 
1 
0 
BEXL 
0 
0 
1 
1 
1 
0 
BEXT 
0 
0 
0 
1 
1 
0 
BGAL 
0 
0 
1 
1 
1 
0 
BGAT 
1 
1 
1 
1 
1 
1 
CNoL 
0 
0 
1 
1 
1 
0 
CNoT 
0 
0 
1 
1 
1 
0 
Table 8
Results of the static tuning strategy of well W_{2}.
Path 
P^{dew} 
Relative volume 
CPM 
Liquid drop out 
Z 
Result 
ANoL 
0 
0 
0 
1 
1 
0 
ANoT 
1 
1 
1 
1 
1 
1 
BEXL 
0 
0 
1 
1 
1 
0 
BEXT 
0 
0 
1 
1 
1 
0 
BGAL 
0 
0 
1 
1 
1 
0 
BGAT 
0 
0 
1 
1 
1 
0 
CNoL 
0 
0 
1 
1 
1 
0 
CNoT 
0 
0 
1 
1 
1 
0 
Table 9
Results of the static tuning strategy of well W_{3}.
Path 
P^{dew} 
Relative volume 
CPM 
Liquid drop out 
Z 
Result 
ANoL 
0 
0 
0 
1 
1 
0 
ANoT 
0 
0 
1 
1 
1 
0 
BEXL 
0 
0 
1 
1 
1 
0 
BEXT 
1 
1 
1 
1 
1 
1 
BGAL 
1 
1 
1 
1 
1 
1 
BGAT 
1 
1 
1 
1 
1 
1 
CNoL 
0 
1 
1 
1 
1 
0 
CNoT 
0 
0 
1 
1 
1 
0 
5. Conclusions
The proposed algorithm showed that both fluid characterization and EOS tuning have a significant impact on the fluid phase behavior model, and when they are used simultaneously, the most acceptable results, or more precisely paths, can be achieved. When there is flexibility in final grouping of the fluid components, the dynamic approach is more effective than the other approaches. Since the dynamic approach examines all the factors and available levels on the objective function, achieving the global minimum of the nonlinear objective function is more probable compared to the static approach. The application of the proposed integrated fluid characterization and EOS tuning algorithm to the selected gas condensate samples showed that the SCN= 7 for plus fraction combined with exponential distribution function, LeeKesler’s correlation, and the third or fourthstep of the sevenstep Whitson’s grouping method can increase the accuracy of fluid model for the studied field. According to the proposed algorithm, the static approach may be successfully applied to systems with an interest in the special combination of component grouping such as the compositional gradient of certain components and wax or asphaltene deposition. This technique can also give accurate results with a local minimum of the objective function. The static approach requires less processing time as it has less computation steps compared to the dynamic technique.
Nomenclatures
CCE 
: Constant composition expansion 
CGR 
: Condensate gas ratio 
CPM 
: Cumulative produce moles (moles) 
CVD 
: Constant volume depletion 
D 
: Dynamic 
DST 
: Drillstem test 
EOS 
: Equation of state 
Exp. 
: Exponential function 
Ga 
: Gamma function 
MW 
: Molecular weight (gr/mole) 
P 
: Pressure (psia) 
RLD 
: Relative liquid dropout 
RV 
: Relative volume 
S 
: Static 
SCN 
: Single carbon number 
T 
: Temperature (°F) 
Greek Letters 

k 
: Dimension less parameter in Equation 7 
w 
: Acentric factor 
, 
: Adjustable parameters in equations 4 and 5 
Superscripts 

cal 
: Calculated 
dew 
: Dew point 
exp 
: Experimental 
Subscript 

c 
: Critical 