Rapid PVT Model Improvement Using Risk Analysis Technique in Gas Condensate Reservoirs

Seyyed Mahdia Motahhari¹, Amir Bagherian², Mohammad Amin Safarzadeh^3*

¹National Iranian Oil Company, Tehran, Iran.
²Iran Iranian Central Oil Fields Company, Tehran, Iran.
³University of Calgary, Calgary, Canada.

DOI: 10.4236/oalib.1112498                

Abstract

A realistic model of reservoir fluid samples is essential before conducting reservoir simulations, especially for gas condensate reservoirs. Errors in PVT modeling typically stem from three main sources: fluid sampling, fluid property measurement, and fluid model construction. This work presents a rapid method for constructing a more realistic PVT fluid model before tuning. Three fluid samples from different Iranian gas condensate reservoirs were selected to achieve this. A suitable equation of state (EOS) and appropriate correlations for key factors like critical pressure, temperature, acentric factor, and binary interaction coefficients were chosen using sensitivity and risk analysis techniques. The optimal default selection of a PVT model produces a representative model of the real fluid sample with minimal variation in variables when matching laboratory data. This approach is applicable to various PVT modeling packages. Before model optimization, a base model is selected based on literature and experience. The sensitivity and risk analysis technique uses the residual mean square (RMS) error as the objective function. The results of this work indicate that a significant number of models constructed using the derivative method had lower RMS errors compared to the base model. The risk analysis technique is shown to provide the best default selection for the PVT fluid model. While some approaches in the literature recommend using specific EOS and correlations for gas condensate samples, the results of this work show that the interaction effect of PVT model variables leads to the best combination of EOS and correlations for each PVT sample. This approach can be extended to improve the PVT modeling process.

Keywords

Gas Condensate Reservoir, Fluid Model, Risk Analysis, PVT Model, Residual Mean Square

1. Introduction

Gas condensate field development planning requires compositional simulation studies to appraise gas and condensate reserves, production methods, and surface facilities design [1] [2]. Determining PVT properties is crucial for all reservoirs but plays an especially vital role in gas-condensate reservoirs. For instance, condensate/gas ratio plays a major role in estimates for the sales potential of both gas and liquid. In fact, it is central to our understanding of gas condensate reservoirs. EOS-based fluid modeling involves several critical steps, including optimal component selection by means of C₇₊ characterization, incorporating robust phase equilibrium calculations and solution techniques to ensure convergence, and a rigorous regression method to tune the model to laboratory data [3] [4]. Incorrect default PVT model suggestions prior to tuning, the last step can be time-consuming and often frustrating. The tuning or regression of the EOS parameters should be performed if the EOS model does not match fluid properties from experimental data. Tuning requires trial and error in setting regression parameters and data weight factors [5]. To construct a tuned model, various PVT software products have been developed [6]. Choosing default equations and correlations before tuning is the common step of all software packages. Afterward, automatic or manual adjustments of EOS parameters can be performed [7].

The choice of which model to use as a default before manual or automatic tuning depends on fluid type and condition. Research to date has focused on suggesting correlations for special conditions rather than offering a unique method. Some approaches recommend using specific EOS and the correlations for gas condensate samples. For example, the Modified Redlich-Kwong-Soave may be better for fluids such as black, low and medium volatility oils and lean gases far from the critical point. The Peng-Robinson EOS is preferred for highly volatile oils or liquid-rich gas condensates nearer the critical point. It may be necessary to use more than one model. For instance, the Modified Redlich-Kwong-Soave EOS generally gives poor density predictions. Sometimes, the Benedict-Webb-Rubin-Starling equation is used to calculate densities [8]. These findings might have been much more convincing if they resulted from a unique approach.

Recent software developments in PVT have heightened the need for a unique method to initialize model tuning. In this paper, we propose a much more systematic approach to identify the best equation of state (EOS) and correlations for constructing an appropriate representative model (default model) with minimal variable variation, ultimately improving the process of tuning to laboratory data. The primary purpose of this research is to enhance the accuracy and efficiency of PVT modeling by optimizing parameter selection and providing a clear framework for model initialization, thereby facilitating better predictions and insights into reservoir behavior.

2. Problem Definition

The main objective of this paper is to determine the best default selection of PVT fluid model before utilization of tuning process (Figures 1 (a)-(c)). Generally, to match the observed data, two steps should be taken. First, robust equations and correlations are selected as a default (physical part). Most of the existing software packages offer unique correlations for any kind of PVT data. Second, based on suggested equations, the tuning process is conducted. As shown in Figure 1(c), using an improper default model leads to a severe and time-consuming tuning process.

Figure 1. Relative contribution of default model selection process (blue) and regression (orange) process to match observed data.

Throughout the life of a hydrocarbon reservoir, from discovery to abandonment, a great number of decisions depend on incomplete and uncertain information [9]. The novelty of the study is choosing the best default composed of correlations for different PVT parameters based on PVT samples to mitigate uncertainty. Then, PVT equation of state, critical properties, acentric factor and binary interaction coefficients are introduced as uncertain parameters to construct default PVT model considering PVT sample. Combination of all PVT correlations to select the best PVT default is not reasonable due to vast run and consequently, it is a time-consuming process. So, it is necessary to propose a novel workflow in which the PVT default will be chosen rapidly by minimum run for each PVT sample.

3. Proposed Workflow

PVT modeling of conventional default (software suggestion) is performed as a base run. Next, sensitivity analysis to distinguish the most effective parameters on residual mean square (RMS) is implemented. The sensitivities are then used to modify the unknown model parameters to correlate the predicted data. On completion of PVT correlation combination step, the process of default model specification and parameter estimation was carried out. The workflow was tested in three PVT models of gas condensate. Proposed workflow is shown in Figure 2.

Figure 2. Proposed algorithm for determination of default PVT model before tuning.

3.1. Conventional Default PVT Modeling

All the available software packages offer default equations and parameters based on literature and developer’s viewpoints. As mentioned before, some approaches in literature recommend using specific EOS and correlations for specified fluid type. Although these suggestions may be appropriate in some cases, it is not possible to consider them as a general rule.

3.2. Sensitivity Analysis

Sensitivity analyses are performed to evaluate the gradients of the error functions with respect to the model parameters used in the analysis. It quantifies the uncertainty in a model’s estimates by analyzing variations in the model’s parameters. Thus, sensitivity analyses can be used to reduce time of analysis. Efficient parameter selection is crucial for reducing computational costs while ensuring accurate results because it minimizes the dimensionality of the model, enhances the convergence of numerical algorithms, and optimizes resource usage. By focusing on the most influential parameters through sensitivity analysis, we can streamline computations and improve model performance.

3.3. Risk Analysis

Petroleum industry is a classic case of decision-making under uncertainty; it provides an ideal setting for the investigation of risk corporate behavior and its effects on the firm’s performance [10]. The decision tree analysis technique for making decisions in the presence of uncertainty can be applied to many different project management situations. A decision tree is a decision support tool used in operational research. It helps with decision-making regarding strategies and managing conditional probabilities. Decision trees are a part of the decision theory approach widely used by decision makers while dealing with few possible solutions. Decision trees are diagrams that can be used to represent decision problems so that their structure is made clearer.

Figure 3 shows a decision tree to calculate RMS for Peng Robinson EOS. Unlike decision tables, decision trees can represent problems with sequential decision-making, where decisions must be made at different stages in the problem. Decision trees constitute a potent and important tool for modeling and optimization of probabilistic multistage decision-making problems.

4. Result

The proposed workflow was applied to three gas condensate PVT models. Table 1 compares the composition of three Iranian gas condensates. After implementation

Figure 3. Decision tree for calculation of RMS for Peng Robinson equation of state.

Table 1. Compositions of three Iranian gas condensate samples.

Sample one
Component	Mole Fraction
H2S	0.0394
N2	0.1086
CO2	0.0238
C1	0.6643
C2	0.0650
C3	0.0281
IC4	0.0052
NC4	0.0103
IC5	0.0032
NC5	0.0034
C6	0.0057
C7	0.0086
C8	0.0090
C9	0.0068
C10	0.0045
C11	0.0020
C12+	0.0121
Sample two
Component	Mole Fraction
N2	0.02104
CO2	0.00179
C1	0.82174
C2	0.06308
C3	0.03438
IC4	0.00536
NC4	0.01309
IC5	0.00439
NC5	0.00454
C6	0.00587
C7	0.00461
C8	0.00399
C9	0.00350
C10	0.00240
C11	0.00212
C12	0.00137
C13	0.00127
C14	0.00103
C15	0.00087
C16+	0.00356
Sample three
Component	Mole Fraction
CO2	0.0217
N2	0.0034
H2S	0.0000
C1	0.7064
C2	0.1076
C3	0.0494
NC4	0.0302
NC5	0.0135
C6	0.0090
C7+	0.0588

of sensitivity analysis and combination of uncertain parameters for each sample, the best default correlation was selected. In the following, the results of three samples are explained.

4.1. Fluid Sample One

Table 2 shows the results obtained from the sensitivity analysis. As it can be seen, change of EOS has the most effect on RMS for this sample. Figure 4 is used to determine the most effective parameter for Sample 1. ZJ, RK and PR3 EOS, Crit. Prop.-RD, Crit. Pro.-RD and C, Acentric Prop.-T and E have the minimum RMS in their category.

Table 2. Sensitivity analysis of Sample one.

Sample one
	EOS	Critical Properties	Acentric Factor	BIC	RMS	Rang Variation
Default	PR3	LK	LK	KF	0.485260422	0
EOS-PR	PR	LK	LK	KF	0.534117582	0.212438491
EOS-SRK	SRK	LK	LK	KF	0.697698914
EOS-RK	RK	LK	LK	KF	0.524950261
EOS-ZJ	ZJ	LK	LK	KF	0.366278359
EOS-SRK3	SRK3	LK	LK	KF	0.619860615
EOS-SW	SW	LK	LK	KF	0.490236014
Crit. Pro.-C	PR3	C	LK	KF	0.434776005	0.04532993
Crit. Prop.-RD	PR3	RD	LK	KF	0.389446076
Crit. Prop.-W	PR3	W	LK	KF	0.492002072
Crit. Prop.-P	PR3	P	LK	KF	0.539034893
Acentric Prop.-E	PR3	LK	E	KF	0.442734145	0.03183171
Acentric Prop.-T	PR3	LK	T	KF	0.410902436
Acentric Prop.-P	PR3	LK	P	KF	0.673873215
BIC-CP	PR3	LK	LK	CP	0.437909819	−0.04735060

Figure 4. Determination of sensitive parameters for Sample one.

Three EOS and two other correlations (Critical Properties, Acentric Factor, and BIC) were selected for the rapid construction of the PVT model, respectively (Table 3).

24 runs (combination of effective parameters) were done and the best model with minimum RMS was selected as a default model. To verify the method, all 280 (7 × 5 × 4 × 2) runs were also performed.

Figure 5 depicts the cumulative distribution function for Sample 1. Since the vertical axis is probability, it must fall between zero and one. It increases from zero to one as we go from left to right on the horizontal axis. Intuitively, it is the “area so far” function of the probability distribution.

Table 3. Selection of effective correlation for Sample one.

Correlation	Parameter 1	Parameter 2	Parameter 3
EOS	ZJ	PR3	RK
Critical Properties	RD	C	-
Acentric Factor	T	E	-
BIC	CP	KF	-

Figure 5. PVT default model position compared with other PVT models (Sample one).

Position of conventional default (red point) is shown in Figure 5. Applying the proposed workflow and using effective parameters (Table 3) decreases the default model RMS significantly (blue point).

All models existing between these two points are constructed by correlations and parameters, which were picked out from sensitivity analysis. Using sensitivity analysis, the optimal model before conducting tuning was achieved quickly.

4.2. Fluid Sample Two

Table 4 shows RMS and its variation range as a result of sensitivity analysis. For Sample 2, PR3, SW EOS, Critical Prop-RD and W, C, Acentric Prop.-E and T have minimum RMS in their category. Three and two effective EOS, and other correlations (Critical Properties, Acentric Factor and BIC) were selected to rapid construction of PVT model, respectively (see Table 5 and Figure 6).

24 runs (combination of effective parameters) were done and the best model with

Table 4. Sensitivity analysis of Sample 2.

Sample two
	EOS	Critical Properties	Acentric Factor	BIC	RMS	Rang Variation
Default	PR3	LK	LK	KF	0.245514451	0
EOS-PR	PR	LK	LK	KF	0.247671454	0.032740995
EOS-SRK	SRK	LK	LK	KF	0.278255446
EOS-RK	RK	LK	LK	KF	0.570884529
EOS-ZJ	ZJ	LK	LK	KF	0.431359348
EOS-SRK3	SRK3	LK	LK	KF	0.257132594
EOS-SW	SW	LK	LK	KF	0.24633074
Crit. Pro.-C	PR3	C	LK	KF	0.28813747	0.036101523
Crit. Prop.-RD	PR3	RD	LK	KF	0.252035947
Crit. Prop.-W	PR3	W	LK	KF	0.217270362
Crit. Prop.-P	PR3	P	LK	KF	1.008775396
Acentric Prop.-E	PR3	LK	E	KF	0.271869996	0.026355544
Acentric Prop.-T	PR3	LK	T	KF	0.245514452
Acentric Prop.-P	PR3	LK	P	KF	6.162041322
BIC-CP	PR3	LK	LK	CP	0.240113473	−0.00540097

Figure 6. Determination of sensitive parameters for Sample two.

Table 5. Selection of effective correlation for Sample two.

Correlation	Parameter 1	Parameter 2	Parameter 3
EOS	PR3	SW	PR
Critical Properties	RD	W	-
Acentric Factor	E	T	-
BIC	CP	KF	-

Figure 7. PVT default model position compared with other PVT models (Sample two).

minimum RMS was selected as a default model. In order to compare the result of sensitivity analysis, all 280 (7 × 5 × 4 × 2) runs were performed (see Figure 7).

For this sample, applying the proposed workflow and using effective parameters (Table 4) decreases default RMS. Similar to Sample 1, all models existing between these two points are constructed by correlations and parameters, which are picked out from sensitivity analysis for Sample 2.

4.3. Fluid Sample Three

Table 6 shows RMS and its variation range as a result of sensitivity analysis. SW and PR EOS, Critical Prop.-C and KL, Acentric Prop.-T and E have the minimum RMS in their category. Three and two effective EOS, and other correlations (Critical Properties, Acentric Factor and BIC) were selected to rapid construction of PVT model (Table 7).

24 runs (combination of effective parameters) were done and the best model with minimum RMS was selected as a default model. In order to compare the result of sensitivity analysis, all 280 (7 × 5 × 4 × 2) runs were performed (see Figure 8 and Figure 9).

Using effective parameters decreases default RMS significantly (Table 6). Similar to previous samples, all models existing between these two points are constructed

Table 6. Sensitivity analysis of Sample three.

Sample three
	EOS	Critical Properties	Acentric Factor	BIC	RMS	Rang Variation
Default	PR3	LK	LK	KF	0.258440063	0
EOS-PR	PR	LK	LK	KF	0.169953169	−0.0222629
EOS-SRK	SRK	LK	LK	KF	0.236177159
EOS-RK	RK	LK	LK	KF	0.47925448
EOS-ZJ	ZJ	LK	LK	KF	0.400339469
EOS-SRK3	SRK3	LK	LK	KF	0.212809663
EOS-SW	SW	LK	LK	KF	0.160523622
Crit. Pro.-C	PR3	C	LK	KF	0.203013414	0.071120675
Crit. Prop.-RD	PR3	RD	LK	KF	0.28154613
Crit. Prop.-W	PR3	W	LK	KF	0.260023063
Crit. Prop.-P	PR3	P	LK	KF	0.274134089
Acentric Prop.-E	PR3	LK	E	KF	0.269581614	0.133589516
Acentric Prop.-T	PR3	LK	T	KF	0.272864826
Acentric Prop.-P	PR3	LK	P	KF	0.40317113
BIC-CP	PR3	LK	LK	CP	0.163876217	−0.09456385

Table 7. Selection of effective correlation for Sample three

Correlation	Parameter 1	Parameter 2	Parameter 3
EOS	SW	PR	SRK3
Critical Properties	C	KL	-
Acentric Factor	T	E	-
BIC	CP	KF	-

by correlations and parameters which were picked out from sensitivity analysis.

The results from the three gas condensate reservoirs confirm that applying the proposed methodology can significantly reduce the number of simulation runs—by more than 10 times.

5. Discussion

The results of the sensitivity analysis indicate that the equations of state (EOS) have a significant impact on the accuracy of PVT modeling for gas condensates. Sample one showed that the PR3 and ZJ EOS provided lower RMS values, indicating better performance. This highlights the importance of selecting the

Figure 8. Determination of sensitive parameters for Sample three.

Figure 9. PVT default model position compared with other PVT models (Sample three).

appropriate EOS based on the fluid’s characteristics.

In Sample two, the PR3 and SW EOS also performed well, confirming the trend observed in Sample one. The significant variation in RMS values based on critical properties and acentric factors suggests that these parameters should be carefully selected to enhance model accuracy.

Sample three’s results reaffirm the necessity of a systematic approach to sensitivity analysis, with the SW EOS providing the best fit. The combination of effective parameters identified through this analysis can lead to more reliable PVT models, reducing the need for extensive simulation runs.

Overall, the proposed workflow demonstrates a robust methodology for rapid PVT model construction. The significant reduction in RMS across samples illustrates its effectiveness in optimizing gas condensate modeling.

6. Conclusions

This study developed and implemented a novel workflow to efficiently select the best default PVT model before tuning, addressing the challenges posed by high-resolution compositional models. In cases where large numbers of components, such as detailed hydrocarbon fractions or non-hydrocarbon gases, need to be modeled, the computational cost can become prohibitive. Instead of using all available PVT correlations, which would require extensive computational resources, the proposed method significantly reduces the number of runs by focusing on the most relevant parameters for each PVT sample.

By applying sensitivity and risk analysis techniques, the workflow identifies the optimal default model with minimal computational effort, even when dealing with complex, multi-component fluid compositions. The results demonstrate that this approach reduces the number of simulation runs by a factor of 10 while maintaining accuracy in model selection. Furthermore, the analysis reveals that relying solely on generic correlations from existing literature can lead to improper default model choices, particularly in cases of high-resolution compositions. This highlights the necessity of adapted workflows for accurate PVT model selection.

Beyond PVT modeling, this methodology can be extended to other areas, such as reservoir simulation models, well modeling, and production forecasting, where efficient parameter selection is critical to reducing computational costs while ensuring accurate results. The approach offers a practical solution for streamlining the modeling process in various aspects of reservoir engineering, particularly in complex and time-consuming scenarios.

Conflicts of Interest

The authors declare no conflicts of interest.

Conflicts of Interest

The authors declare no conflicts of interest.

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