Evaluation of compositional models and PVT correlations for Iraqi light crude oils properties

Evaluation of common compositional models and pressure–volume–temperature (PVT) correlations are carried out against field data for light crude oil from north Iraqi reservoirs. The reported data and the evaluation are significant to the petroleum industry, as various international and local oil companies operate in this region. The comprehensive PVT program Multiflash™ 7.2 is utilized, employing the Peng–Robinson (PR) and Redlich–Kwong–Soave (RKS). The oil formation volume factor, bubble point pressure, solution gas–oil ratio (Rso), and saturated oil viscosity are chosen for this evaluation. The results demonstrate that the PR and RKS compositional models, with some adjustments, exhibit much higher accuracy as compared to PVT correlations. For example, the errors between the model's predictions and the field data for the Rso are 9% for PR ad 17% for the RKS model. In contrast, for the PVT correlations, much higher errors are obtained. The lowest errors (32%) are obtained with the Ikiensikimama and Ajienka, while above 90% errors (the highest) are reported by Petrosky and Farshad. This study will enable the petroleum industry to improve and optimize the production operations in north Iraq–Kurdistan region.


| INTRODUCTION
Predictions of the pressure-volume-temperature (PVT) parameters for production and reservoir engineering are essential for successful operations. These parameters can be measured directly in laboratory PVT cells, which are costly and timeconsuming. Alternatively, empirical correlations have been developed from field data, such as the "Black Oil" correlations. These correlations do not require the fluids' composition but are based on the specific gravities of the gas and the oil.
Clearly, the correlations do not address the "why" and "how" of the physical phenomena, and they are usually limited in their application and associated with high errors. To address these issues, several researchers introduced a "Compositional Model," which is more rigorous and based on the fluid composition and incorporates the physical phenomena, ensuring highly accurate results. The "Compositional Model" is usually associated with an "Equation of State" that relates the PVT relationship of produced fluids, thereby predicting their physical properties.
Northern Iraq reservoirs include light crudes. For this region, field data PVT properties are scarce. Also, there has been no systematic evaluation of PVT properties' predictive methods. These are essential for the design and performance of the production pipelines and facilities for Northern Iraq.
The present study addresses the above-mentioned significant gap in accurate predictions of the PVT properties for the Northern Iraq region light oil reservoirs, as follows. First, field data are collected from several reservoirs in this region. Next, available correlations and compositional models will be evaluated against the field data. Finally, recommendations about the predictive methods used by researchers and engineers operating in Northern Iraq are presented.

| Summary of PVT correlations
In the past seven decades, researchers tried to introduce various black oil correlations for some specific geological regions because of differences in reservoir fluid compositions. These correlations are essential procedures for predicting reservoir fluid properties from pressure, temperature, and oil and gas gravity data, as the PVT laboratory is costly, time-consuming, and not reliable Labedi, 1 Al-Marhoun, 2 and Mazandarani and Asghari. 3 In 1942, for United States crude oils, the first correlation was developed by Standing and Katz to estimate formation volume factor by using pressure, temperature, solution gas-oil ratio (Rso), and both oil and gas gravities. However, this correlation was complicated because it was graphical. 4 Later, in 1947, Standing developed another correlation for predicting formation volume factor using bubble point pressure (Pb) based on laboratory data for crude oil in California, known as the most famous correlation for predicting Rso and Pb in worldwide crude oils. 5 Later, in the 1980s, two different correlations for predicting gas-oil ratio using Pb and oil viscosity were developed by Vasquez and Beggsy 6 and Glaso. 7 This correlation used about 6000 data points, applicable within two different American Petroleum Institute (API) ranges below and above 30 API degrees 6 and Glaso. 7 Al-Marhoun 8 developed a correlation for predicting the physical properties of crude oils in the Middle East based on field data from 69 different reservoirs. That developed correlation was used to estimate the Rso and Pb.
In 1991, Kartoatmodjo and Schmidt 9 introduced a new correlation for four different regions based on 5392 data points collected from the literature. The first data group was from Southeast Asia, mainly Indonesia, the second group was from North America in offshore areas, and the two other groups were from the Middle East and Latin America.
Furthermore, 1 year later, Al-Marhoun 10 proposed another correlation for the estimation formation volume factor based on more than 700 different reservoirs from North USA and Middle East reservoirs, which can be applied either above or below saturation pressure.
Petrosky and Farshad 11 developed another correlation using 90 datasets based on Standing's correlation for Gulf of Mexico crude oils. Their correlation predicted Pb, formation volume factor, and the gas-oil ratio. In 2004, another correlation was developed by Dindoruk and Christman for the same crude oil, using more than 100 PVT reports from the Gulf of Mexico.
Moreover, El-Banbi et al. 12 developed a new correlation between gas condensates and volatile crude oils. The developed correlation used 13 fluid samples, of which eight were for gas condensate and five for volatile oil.
One year later, Hemmati and Kharrat 13 developed another correlation for Iranian crude oil for a wide range of API from 18.8 to 48.34. This was each of Pb, Rso, and oil formation volume factor (OFVF) at Pb.
There was no correlation available for Iraqi crude oil until 2012, but in 2012 Ahmedzeki 14 developed a new correlation based on 104 data points from a different region of Iraq which was developed only for estimating Pb. The model was built based on the application of the artificial neural network (ANN) to build this model.
For Middle-East crude oils, Karimnezhad et al., 15 also developed a new correlation for Pb based on about 429 laboratory PVT data points. Also, for heavy crude oils, both Riyahin et al., 16 and Torabi et al., 17 developed new correlations for both Iranian crude oils and Canadian oils. Also, Jarrahian et al., 18 developed another correlation for Pb, which was applied worldwide. In the same year, Mazandarani and Asghari 3 developed a new correlation using Iranian crude oil data from more than 30 Iranian oil fields. The correlation was evaluated against 207 PVT samples available in the literature.
Consequently, in 2016, another correlation was developed by Mahdiani and Kooti 19 to predict the OFVF using an ANN and four genetic programming models.
Later in 2020, Uzogor and Akinsete 20 developed a new correlation for Nigerian crude oils. The different API range between 21°and 45°shows the applicability and accuracy of this correlation for the specified region 20 The development of correlations for Nigerian crude oil was still ongoing in 2021; Chaharlangi et al. 33

| Summary compositional models
Reservoir fluid is a multicomponent mixture made up primarily of oil and gas. It can, on occasion, contain water and solids. Because of the significant impact interaction of such elements, determining their qualities takes time and effort. Because reservoir compositions change, applying equations that deal with many components to a specific reservoir is impossible. As a result, several equations of state (EOS) were developed to determine how one heptane group and a heavier component interacted to form a limiting pseudocomponent number.
This study employs, with software modifications, the Redlich-Kwong-Soave (RKS) 34 and Peng and Robinson 35 models.

| Redlich-Kwong-Soave (1972)
One of the simplest EOS models is the RKS model, a modified equation of Redlich and Kwong's 36 equation. His improvement leads to an improvement in reproducing saturation conditions of pure substances, which results in the development of mixtures. The final equation proposed by the RKS model is: where, a v b , , and defined in Appendix A1. The development was carried out by the RKS model was in a parameter a in different temperaturedependence, as given below: Where, a k T , , and ci i ci are defined in Appendix A1.

| Peng-Robinson 35
The Peng-Robinson equation know as a two-constant EOS, because express pressure as a sum of two terms, one is repulsion pressure (P R ) and other one is attraction pressure (P A ), as given below: After modification of Redlich-Kwong 36 and RKS 34 final cubic EOS proposed by Peng-Robison is: Based on pure component critical temperature and pressure, both a and b constants are derived. Also, another parameter, which Peng-Robinson develops, is an acentric factor. Details of the two main equations are given in Appendix A1. In 1978, the Peng-Robinson equation was modified based on binary interaction parameters. Because there should be some differences between heavy components and the lighter component, modification suggested that, for any mixture containing components with acentric factors greater than 0.49, the equation will give different results and must be treated with different EOS models. Ultimately, the reasons for selecting these two models are simplicity and applicability for different reservoir fluid multicomponents. Also, these two models are well defined in used software developed in 2021.

| Data description and adjustment
From five separate oil reservoirs in various provinces throughout the North of Iraq-Kurdistan region, 7 PVT reports, approximately 60 data points, were gathered. Some samples were collected on the surface and recombined to the reservoir condition to accurately represent the in situ condition. This paper evaluated the most popular black oil correlations and compositional models to estimate fluid properties. Table 2 shows a range of PVT data points used in this study.

| Compositional fluid packages modeling
As described before, RKS 34 and Peng-Robinson 35 are two models selected to be compared with selected PVT correlations. The comprehensive PVT and physical properties data set are modeled in Multiflash™ 7.2 software provided by A Yokogawa KBC company.
In the software, the Peng-Robinson 35 model is defined as the primary model (PR78) and (PRA) as its advanced model. Also, the RKS 34 model is defined as a primary model (RKS) and (RKSA) as its advanced model, as shown in Figure 1.

| RESULTS AND DISCUSSION
In Microsoft Excel, selected PVT correlations are programmed. The necessary input data for each crude oil property was also introduced. This section is divided into four parts to show the best analysis of results for each OFVF, Pb, Rso, and crude oil viscosity.
As a result, statistical results of PVT correlations and compositional models are used, such as absolute average error (AAE) percentage, standard deviation (SD), R-square (R 2 ), and root mean square error. Appendix A2 contains the mathematical expressions for all statistical parameters. Table 3 shows the selection of eight PVT correlations in spreadsheet form and five compositional models. All correlations and EOS models showed the best fit compared to the given data. The resulting range for OFVF varies from: 1.0 to 2.362 bbL/STB, which depends on API degree, Rso, and mixture compositions.

| Bubble point pressure
As shown in Table 4, the range of Pb varies from 4525 to 173 psi. Seven PVT black oil correlations and five compositional models are selected to predict Pb. As a result, the following points observe:  Figure 2A, B. On the other side, as shown in Figure 2C, D for the same samples, the compositional models can be used in both pressure conditions above and below the bubble point pressure.

| Solution gas-oil ratio
Twelve PVT correlations were compared with five compositional models in this section, as shown in Table 5. As a result, the following statements were recorded: 1. As shown in Figure 3A results at pressures below Pb, which are 4525 and 919 psi, respectively. However, at higher pressures, precisely at or above the Pb, the prediction of Rso PVT correlations fails on the one hand. 2. On the other hand, to evaluate compositional models with measured Rso, all selected compositional models were examined, as shown in Figure 3C,D for S1RE-14&12 and 33188-MB samples, respectively. It clearly stated that all chosen compositional models are the best and most accurate in predicting Rso below and above Pb.
Finally, in Figures B3 and B4, the statistical results to clarify the comparison accuracy of PVT correlations and compositional models are presented.

| Saturated crude oil viscosity (μ s.o )
In general, different correlations exist for predicting all types of crude oil viscosities, but only for saturated oil viscosity, most common correlations are chosen and tabulated in Table 6. According to the findings: 1. All PVT correlations have a high degree of error compared to compositional models, with tolerance ranging from 37% in Labedi's (1992) correlation to 72% in Naseri et al. 26 Also, Figure 4A,B for S1RE-14&12 and 33188-MB crude oil samples graphically illustrated results, respectively. 2. Compositional models, on the other hand, outperform measured viscosity in PVT reports in terms of accuracy, as shown in Figure 4C,D, which depict a graphical comparison of the predicted value in compositional models. However, compositional models have errors in predicting viscosity at surface pressures. That is due to increased gas liberation, which is related to the gas compositions at these points.
Lastly, in Figures B5 and B6 show an objectional description of all statistical outcomes, including AAE, SDs, R 2 , and RMSE.     Labedi's (1992) correlation to 72% in Naseri et al. 26 The compositional models show less error in the 10%-11% range.
In general, the compositional models are recommended for predicting light oil reservoir PVT properties in the absence of a PVT laboratory to be used in petroleum industry applications.

ACKNOWLEDGMENTS
The authors are grateful to the Petroleum Engineering Department-Faculty of Engineering at Koya University for providing field data used in this study, and to the Yokogawa Company (KBC) for providing a license of the Multiflash TM 7.2 software.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.