SPE 164712

Modified Black Oil PVT Properties Correlations for Volatile Oil and Gas Condensate Reservoirs Ibrahim S. Nassar, GUPCO, Ahmed H. El-Banbi, and Mohamed H. Sayyouh, Cairo University

Copyright 2013, Society of Petroleum Engineers This paper was prepared for presentation at the North Africa Technical Conference & Exhibition held in Cairo, Egypt, 1517 April 2013. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

This work presents new Modified Black Oil (MBO) PVT properties (Rs, Rv, Bo, and Bg) correlations for volatile oil and gas condensate reservoir fluids. These new correlations do not require the use of fluid samples or EOS calculations. The correlations have the advantage of taking into consideration the effect of surface separator configuration (two and three stages) and conditions (separators pressures and temperatures).

The correlations were developed using fourteen actual reservoir fluid samples (7 gas condensates, 3 near critical fluids, and 4 volatile oils) spanning a wide range of fluid behavior and characteristics. Whitson and Torp method was used to generate Modified Black Oil (MBO) PVT properties that were used as a data set for correlations development.

The MBO PVT properties data points were generated by extracting the PVT properties of each sample using commercial PVT software program at twelve different separator conditions spanning a wide range of surface separator configuration and conditions to generate twelve curves for each sample. A statistical approach using a statistical software program (SPSS) was used to develop the new correlations models.

The results of the new models show reasonable agreement between Modified Black Oil PVT properties generated from the new correlations and the MBO properties extracted using Whitson and Torp method. The average absolute error in the correlations was 8.5% for volatile oils and 17.5% for gas condensates.

These correlations were also validated by comparing the results of modified black oil simulation using MBO PVT properties generated from these correlations to the results of full equation of state (EOS) compositional simulation. Also, the generalized material balance equation (GMBE) was used to calculate the initial oil/gas in place (IOIP/GIIP) for many simulated cases using PVT data generated from the new correlations and data generated from EOS models. The advantage of the new correlations comes from being the first in the industry (to the best of our knowledge) that explicitly take into consideration the effects of surface separators configurations (two or three stages) and conditions. Also, all input parameters in the correlations are readily available from field production data. These correlations do not require elaborate calculation procedures or PVT reports. Introduction

It was clear since 1920's that the engineering of oil reservoirs require the knowledge of how much gas was dissolved in the oil at reservoir conditions and how much the oil would shrink and gas would expand when it was brought to surface. Three properties (Rs, Bo, and Bg) serve these purposes and constitute the traditional (conventional) black oil PVT formulation7. However, it has been known for many years that volatile oil and gas condensate reservoirs cannot be modeled accurately with conventional black oil technique but require Modified Black Oil (MBO) approach. The MBO approach assumes that the stock tank liquid can exist in both liquid and gas phases in reservoir condition.

Gas condensate and volatile oil petroleum reservoir fluids are simulated frequently with fully compositional models but can also be efficiently modeled with a Modified Black Oil (MBO) approach15. A few authors have addressed the question of how to best generate the MBO PVT properties including the new function, condensate gas ratio (Rv) which represents the vaporized oil in gas.

2 SPE 164712

Whitson and Torp3 in 1983 used data derived from CVD experiments to calculate modified black oil PVT properties for volatile oil and gas condensate reservoirs. Perhaps the most useful application of CVD data is the calculation of liquid composition, which together with measured vapor composition yield high pressure K-values. At each depletion step, individual phase compositions (measured or calculated) are flashed using a set of appropriate K-values (ex.: Standings K-values Correlation) through a multistage separator simulator representing field conditions to calculate MBO PVT properties (Bo, Bg, Rs, Rv).

Coats4 in 1985 developed a different approach from Whitson and Torp to calculate the modified black oil PVT properties for gas condensate reservoirs only. In his approach, oil-gas ratio (Rv) is obtained by flashing the equilibrium gas at each stage through the specified surface separator configuration while the remaining parameters are calculated using a material balance procedure.

McVay2 in 1994 extended Coats work to include volatile oil reservoirs. He modified Coats procedure in a completely analogues manner to generate MBO PVT properties for volatile oil reservoirs.

Walsh and Towler5 in 1994 suggested a simple method to compute the black oil PVT properties of gas condensate reservoirs. The authors used the data available from standard CVD experiments and developed an algorithm to compute the black-oil PVT properties of gas condensate without the requirement of K-value model or equation of state (EOS) calculations. The method is rigorous, direct and simple and is ideally suited for spreadsheet applications. However, it depends on how many pressure steps are taken in the CVD laboratory experiments.

All the methods for generating modified black oil PVT properties presented in the literature need a combination of lab

experiments (PVT reports) and elaborate calculation procedures. Recently, a new oil-gas ratio (Rv) correlation was developed by Abdel Fattah.9 This correlation doesnt require the use of fluid samples or elaborate EOS calculations. In practical use of this new correlation, difficulties were noticed from the use of the surface gas gravity parameter (it is assumed to be volumetric average between gas gravity in different separators, while gas gravity from low pressure separators may not be available in many field operations). Therefore, the surface gas gravity used by the correlation14 probably needs advanced knowledge in PVT to be calculated. Also, the effect of the surface separator configuration and conditions are not explicitly represented in the correlation. Separator conditions were implicitly represented in the specific gravity term. It was found that separator conditions would have significant impact on PVT properties for volatile oil and gas condensate reservoirs16.

In this work, we developed new MBO PVT correlations that combine the advantages of the previously published correlations9,14 and explicitly use separator configurations and conditions. Fluid Samples and EOS Modeling

Fourteen reservoir fluid samples are used in this study representing different fluid composition and phase behavior for the extraction of modified black oil (MBO) PVT properties (7 gas condensates, 3 near critical fluids, and 4 volatile oils).

Table 1 summarizes the major properties for the fluid samples including the fluid type, heptanes plus mole fraction (C7+), reservoir temperature, saturation pressure and initial gas oil ratio for each sample. Fig. 1 shows a graph for heptanes plus mole fraction (C7+) for each sample to illustrate that the samples span a large variation of fluids. We can see that a 12.5% C7+ can be considered as a distinguishing value between volatile oil and gas as proposed by McCain6.

Equation of State (EOS) models were created using commercial EOS PVT Software for each sample and tuned with the available lab experiments (Constant Composition Expansion, Differential Liberation, and Constant Volume Depletion). The EOS characterization was conducted following Coats and Smart14 procedure. The EOS Models were developed using the (PR EOS) or (SRK EOS). We first split the heptanes plus component and then we regressed on OMEGA A and OMEGA B parameters for the heavy pseudo-components and methane. Also, the Binary Interaction Coefficients (BICs) between methane and the heavy pseudo-components were used as regression parameters when needed. The regression is conducted by minimizing an objective function which quantifies the difference between the measured and calculated PVT properties. Tuned EOS Models were used generate MBO data set that we used to develop the correlations of this work. They were also used to output EOS parameters in compositional simulation format for validation purposes.

Figs.2 through 6 show the EOS results after tuning with the measured data from the available lab experiments for one of the samples (Volatile Oil 1) as an example. Fig.2 presents the phase envelop calculated from the tuned EOS for fluid VO1. Fig. 3 presents the match for Constant Composition Expansion experiment showing an excellent agreement between the relative volume values calculated from the tuned EOS model and the observed value from the constant composition expansion experiment. Figs. 4 through 6 present the match for the Constant Volume Depletion experiment observations (vapor z-factor, liquid dropout, and number of moles produced). EOS models for other fluid samples were developed in a similar way.

SPE 164712 3

Approach

Extracting the modified black oil (MBO) PVT properties for each sample from the tuned equation of state (EOS) using Whitson and Torp method generated at twelve different separator conditions was performed. The data set included 1,488 points for the 4 PVT curves from volatile oil samples, 1,212 points from near critical samples, and 2,280 points from the gas condensate samples.

A statistical software program (SPSS) was used to develop the new correlations models by fitting the data sets extracted above. In selecting the independent parameters for the 4 PVT properties curves, we selected parameters that are readily available and also have strong correlation with the dependent variables (Rs, Rv, Bo, and Bg). The new correlations do not require data from experimental fluid analysis (PVT reports), nor elaborate calculations with EOS models, and all the parameters are easily obtained from field production data.

After developing those correlations, we evaluated them by comparing the results of the modified black oil simulation using these PVT properties extracted from the new correlations to the results of full Equation of State (EOS) compositional simulation. Also, the generalized material balance equation was used to calculate the Initial Oil/Gas in Place (IOIP/GIIP). Models Construction Methodology

The first step in our work to develop the models was to select the independent parameters affecting the MBO properties which are (reservoir pressure, reservoir temperature, stock tank oil gravity, surface gas gravity, separator configuration, separator pressure and temperature, and saturation pressure), while the dependent parameters are the Modified Black Oil (MBO) PVT properties.

A question arises here about dependence of MBO properties on surface gas gravity term which was a point of confusion in the previous correlation.14 Therefore; in the development of the correlations of this work, we considered the surface gas gravity of first stage separator and second stage separator as independent model parameters. Surface gas gravity of the stock tank was not considered because it is usually not easily available in field operation.

The independent parameters with plotted with the dependent parameters to provide us with the initial guess for the model shape and a trial and error procedure was used to arrive at an appropriate model shape. Non-linear regression was then used to find the model constants that minimize the difference between observed data points (extracted from the EOS model) and the calculated points. For models validation, we drew cross-plots between observed and calculated values and calculated the least mean square error (R2) and the average absolute error given by the following equation:

Error

.................................................................................(1) Another step was performed to complete the work for the extraction of MBO PVT properties so those correlations can be

applied for any field case. Because saturation pressure may not be known in some cases, new saturation pressure correlations were developed. The saturation pressure correlations depend on the same parameters and the calculated saturation pressure will be used to divide the MBO curves to the saturated and the under-saturated parts. To account for the cases where saturation pressure may be available from other sources, all correlations were presented for two cases: (1) known saturation pressure, and (2) unknown saturation pressure. The following presents the new correlations models and their results. First, the saturation pressure correlations are presented followed by the saturated curve correlations for the 4 PVT parameters, and finally the under-saturated curves. Saturation Pressure Models

The most widely used correlations for saturation pressure are probably the ones by Standing6, Vasquez and Beggs17, and Al-Marhoun18. We tried to modify these correlations to account for three stage separation which is commonly used for volatile oils and gas condensates and found that the modified Al-Marhoun correlation gives the best results with our data base.

In the following, we present two correlations for saturation pressure: one for volatile oil and the other for gas condensate. Both correlations have the same form, but for volatile oil it will be function of initial producing solution gas-oil ratio (Rsi) while for gas condensate, it will be function of initial producing condensate-gas ratio (Rvi).

Volatile Oil Saturation Pressure (Bubble Point) Correlation:

4 SPE 164712

P A R X Y T .......................................(2) Gas Condensate Saturation Pressure (Dew Point) Correlation: P A R X Y T ......................................(3) Where, X and Y are given by:

X ..............................................................................................................................(4)Y ...............................................................................................................................(5)

The above correlation parameters are given in Tables 2 and 3 for two-stage and three-stage separation for volatile oils and

gas condensates, respectively. The average absolute error for the correlations is presented in Table 15. Saturated Curve Models

The following sections present the new correlations for the 4 PVT parameters (Rs, Rv, Bo, and Bg) for the saturated curves. Solution Gas-Oil Ratio Model

a) Known Saturation Pressure The final form of the modified correlation is:

R

....................................................................(6)

X ..............................................................................................................................(7)

Y .............................................................................................................................(8)

V STO ......................................................................................................................(9)

The correlation parameters have been computed by regression and are presented in Table 4 for gas condensate and volatile oil (for both two-stage and three-stage separators). The average absolute errors and the least mean square errors mentioned earlier are presented in Table 15.

b) Unknown Saturation Pressure The final form of the modified correlation is: R

.....................................................................(10)

X ..............................................................................................................................(11) Y ..............................................................................................................................(12)

SPE 164712 5

V T STO .........................................................................................................................(13)

The new correlation parameters are given in Table 5 for gas condensate and volatile oil for both two-stage and three-stage separators. The average absolute error for this correlation is presented along with other correlations in Table 15. Oil Formation Volume Factor Model

a) Known Saturation Pressure The final form of the correlation is:

B ^ ..........................................................(14)

X STO ....................................................................................................................(15)

Y STO .....................................................................................................................(16)

V T STO .....................................................................................................................(17) The oil formation volume factor correlation parameters (when saturation pressure is known) are given in Table 6 for gas

condensate and volatile oil for both two-stage and three-stage separators. The average absolute error for the correlation is given in Table 15.

b) Unknown Saturation Pressure The final form of the correlation is: B A P A 10^A X A Y EXPA V ..................(18)

X STO ....................................................................................................................(19)

Y STO .....................................................................................................................(20) V T STO .........................................................................................................................(21)

Similarly, the new correlation parameters are given in Table 7 for gas condensate and volatile oil for both two-stage and three-stage separators. The average absolute error is presented in Table 15. Condensate-Gas Ratio Model

The initial condensate-gas ratio (Rvi) is one of the independent parameters that have a significant effect on the correlation

accuracy. However; in case of volatile oils, this parameter is not available from production data. For volatile oils, this

6 SPE 164712

parameter is not the reciprocal of the initial producing gas-oil ratio. It is actually the amount of oil (or condensate) vaporized in the gas coming out of the solution at surface separators. In black oil correlations, the parameter condensate-gas ratio is not defined as the gas associated with black oil is dry gas19. Therefore, a new correlation for initial condensate-gas ratio (Rvi) will need to be used first to compute a value we can use for other correlations in volatile oil cases. The form of the initial condensate-gas ratio, Rvi, correlation is:

R A EXPA X Y A STO A STO A A ................................................................................................................................................(22)

X SG P ...................................................................................................................(23)

Y SG P ....................................................................................................................(24)

The new correlation parameters are given in Table 8 for volatile oil only for two-stage and three-stage separators. For gas condensates, the initial Rvi value can be obtained from production data. Now for the rest of the correlations and for both fluid types (volatile oils and gas condensates) Rvi values will be available. For gas condensates, it will be available from production data while for volatile oils, it will be calculated from the new correlation. a) Known Saturation Pressure

The final form of the condensate-gas ration correlation is:R A P A P A EXPA X A Y EXPA V R ................................................................................................................................................(25)

X SG P ..................................................................................................................(26)

Y SG P ....................................................................................................................(27)

.....................................................................................................................(28)

During the regression process, we found that it was hard to obtain a good curve fit especially for the tail part of the curve in the condensate-gas ratio model. This was the main reason to explain the higher error percentage in this correlation for gas condensates than volatile oils. The new correlation parameters are given in Table 9 for gas condensate and volatile oil for both the two-stage and three-stage separators. The average absolute error is presented in Table 15.

b) Unknown Saturation Pressure

For the unknown saturation pressure case, the average absolute error percentage was about 16% for volatile oil and 25% for gas condensate. The new correlation parameters are given in Table 10 for gas condensate and volatile oil for both the two-stage and three-stage separators. The average absolute error is presented in Table 15.

SPE 164712 7

The final form of the Rv correlation is: R A P A P A EXPA X A Y EXPA V R ................................................................................................................................................(29)

X SG P ...................................................................................................................(30) Y SG P ...................................................................................................................(31)

..............................................................................................................................(32)

Gas Formation Volume Factor Model

a) Unknown Saturation Pressure

Knowing that the shape of gas formation volume factor, Bg, curve is monotonic increase below the saturation pressure and sudden increase to very high values at low pressures (approximately below 1000 psi), we first regressed against the entire curve followed by regression only against part of the curve at pressure greater than 1000 psi to improve the accuracy of the correlations. B A P EXPA X A Y EXPA V ........................(33)

X SG P ...................................................................................................................(34)

Y SG P ....................................................................................................................(35)

V STO T ........................................................................................................................(36) The new correlation parameters are given in Tables 11 and 12 for gas condensate and volatile oil for two-stage and three-

stage separators. The average absolute error is presented in Table 15. Table 11 is used if we want to calculate Bg values for high and low pressures. Table 12 is used if we would like to have better accuracy correlation for Bg in the high pressure range (P > 1000 psi). Under-Saturated Curve Models

The following equations are presented to show how the 4 MBO PVT properties (Rs, Rv, Bo, and Bg) can be calculated for both volatile oils and gas condensates above the saturation pressure. Solution Gas Oil Ratio Model

The same model for the saturated curve with the same correlation parameters will be used to calculate the solution gas oil

ratio at the saturation pressure for gas condensate fluids. For volatile oils, it can be obtained from production data as it is equal to the initial producing gas-oil ratio.

R R ...........................................................................................................................(37) The average absolute error is presented in Table 15 for both known and unknown Psat.

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Oil Formation Volume Factor Model

Under-saturated Bo is frequently calculated using oil compressibility. Several oil compressibility correlations are available (e.g. Standing, Vasquez and Beggs, and Laster) for black oil fluids. However, these correlations do not take into consideration the three-stage separators. The following correlation is presented for MBO fluids and it takes surface separator configurations and conditions into account. The new correlation form is: B A P A V A P A B A X A Y ...(38)

....................................................................................................................(39)

...................................................................................................................(40)

V T STO .........................................................................................................................(41)

The new correlation parameters are given in Table 13 for gas condensate and volatile oil for both two-stage and three-stage separators. The average absolute error is presented in Table 15.

Condensate Gas Ratio Model

The same model for the saturated curve with the same correlation parameters will be used to calculate the initial condensate-gas ratio (Rvi) at the saturation pressure for volatile oil. The new correlation for Rvi is just used as input for the saturated curve model. For gas condensates, initial condensate-gas ratio is obtained from production data. R R .............................................................................................................................(42) The average absolute error is presented in Table 15 for both known and un-known Psat. Gas Formation Volume Factor Model

The value of under-saturated gas formation volume factor, Bg, decreases with increasing pressure, regardless of whether the pressure is above saturation pressure or not. Therefore, the final form of the new correlation is the same as the saturated curve model. The average absolute error is presented in Table 15. For volatile oils, under-saturated gas formation volume factor is not defined and therefore, only gas condensate average absolute error is presented here.

Correlations Validation

The accuracies of the new correlations are evaluated firstly by cross plots between actual values and calculated values and secondly by calculating the average absolute error. Figs. 7 to 10 show example cross plots between observed and calculated values for the new correlations models.

For further validation and to estimate the effect of the correlation error on the results of the applications these correlations will be used for, two more procedures were used in validation:

1. The results of the Modified Black Oil simulation using PVT properties generated from the new correlations were compared to the results of full compositional Equation-of-State (EOS) simulation.

2. The Generalized Material Balance equation was used to calculate the Initial-Oil/Gas-In Place (IOIP/IGIP) for several simulated cases.

SPE 164712 9

In order to examine the effects of MBO PVT Properties, all other potential sources of differences between compositional and MBO simulation results should be eliminated. First, the same simulator was used for compositional and MBO simulation runs. Second, the same EOS models that were used for generating MBO PVT properties were also used for compositional simulation runs.

We used the generalized material balance equation (GMBE) in its straight line form to calculate the Initial-Oil/Gas In Place using the PVT properties calculated from the new correlations and these values were compared to those calculated from the compositional simulation models. The procedure to perform this comparison started by running hypothetical compositional simulation cases to predict reservoir performance for each of the fourteen reservoir fluid samples. These runs were also used in the simulation comparison between the MBO and compositional models. Then, the GMBE was used in its straight line form (graphically) to estimate initial oil in place, N, and initial gas in place, G, following Walshs approach. Fig. 11 shows an example of the results of GMBE as a straight line using PVT generated from the new correlations. Table 14 compares between the calculated Initial Oil/Gas In-Place using PVT extracted from the new correlations and compared with the values of the compositional simulation models. The table shows that the errors of material balance calculation using PVT from the new correlations range from minimum of 3% up to a maximum of 23%, which represent reasonable accuracy.

Finally, we compared the results of the Modified Black Oil simulation using PVT generated from these correlations to the results of Full Equation of State (EOS) compositional simulation. All simulation runs started from pressure greater than the saturation pressure and went to pressures significantly below the saturation pressure (no pressure maintenance) up to abandonment pressure of 500 psi. A commercial simulator program (ECLIPSE) was used for the simulation runs. Figs. 12 and 13 show example comparison results of compositional simulation and MBO simulation. These figures indicate a reasonable match between reservoir pressure and the producing gas oil ratio calculated from MBO simulation (using PVT properties calculated from the new correlations) and those calculated from the compositional simulation. Discussion

The importance of the new correlations comes from the fact that they can generate reasonably accurate PVT properties for

volatile oil and gas condensate fluids without the need for a laboratory report or elaborate EOS calculations. They also take into consideration the effect of surface separator conditions. Also, all parameters used in the correlations are readily available especially for the surface gas gravity term that was a point of confusion in previous MBO correlations9,17.

The developed correlations are expected to have wide application in MBO simulations and volatile oil and gas condensate material balance applications. To highlight the new MBO PVT correlations applicability, we compared the results from the new correlations to the results of one of the most widely used black oil correlations (Standing correlation)16. The results from Abdel Fattah9,17 correlations were also compared with the new work. We will consider here the MBO PVT properties extracted with Whitson and Torp1 method as reference for comparison. Two samples (one volatile oil and one gas condensate) were used for full comparison between the new correlations, Abdel Fattahs correlations, and Standing correlations. The two selected samples were not used in developing the new correlations to present unbiased testing. Two sets of figures (Figs. 14-17 for the new gas condensate sample and Figs. 18-21 for the new volatile oil sample) show the comparison between the MBO PVT properties calculated by the new correlation, Abdel Fattahs, and Standing versus the values extracted from the EOS model. The figures show that the new correlations perform much better than the other correlations especially the one by Standing (which was developed for black-oil fluids).

All volatile oil samples from this work were then used in similar comparison and the error was calculated for the new correlations, Abdel Fattahs, and Standing. Table 16 provides the average absolute error for all the 4 MBO PVT functions computed with all correlations. The error was calculated referenced to the Whitson and Torp MBO PVT properties calculation method. Both the comparison figures and summary table show the superior behavior of the new correlations. One should also notice that the common black-oil PVT correlations will usually perform badly in volatile oil and gas condensate fluids. Also, the condensate-gas function (Rv) is not defined for commonly used black-oil PVT correlations. Conclusions Fluid samples representing different fluid composition and ranging from volatile oils to near critical fluids and up to gas condensates were characterized using a commercial EOS PVT software program and new MBO PVT properties (Bo, Rs, Bg and Rv) correlations were developed. Based on work presented in this paper, the following conclusions were made: 1. The new MBO PVT properties correlations do not require lab experiments or EOS model and they take into consideration

the surface separator configuration and conditions. Separate models were developed for volatile oil and gas condensate fluids.

2. The obtained results show reasonable agreement between MBO PVT properties generated from the new correlations and those extracted using Whitson and Torp (W&T) method. The average absolute error is 8.5% for volatile oils and 17.5% for gas condensates.

3. Application of the new correlations in material balance and reservoir simulation was performed for both validation and for

10 SPE 164712

estimation of error in case of applying those new correlations. The error in calculating the initial fluid in place using the GMBE ranges from 3% to 23%. Reasonable agreement between MBO simulation using PVT from the new correlations and fully compositional simulation was also obtained.

4. For volatile oil fluids, the new correlations are significantly more accurate than commonly used black-oil PVT correlations. Acknowledgement

The authors would like to express their gratitude to both Cairo University and GUPCO for making the programs used in this research work available. Nomenclature BIC = Binary Interaction Coefficient Bg = gas formation volume factor, bbl/SCF Bgi = initial gas formation volume factor, bbl/SCF Bo = oil formation volume factor, bbl/STB Boi = initial oil formation volume factor, bbl/STB Bosat = Oil formation volume factor at saturation pressure, bbl/STB CCE = constant composition expansion test C7+ = Heptanes plus components CGR = condensate yield, STB/MMscf, equal to Rv at CVD = constant volume depletion test DL = differential liberation test EOS = Equation Of State GIIP = original gas in-place OGIP, SCF GC = Gas Condensate GMBE = General Material balance Equation IOIP = Initial oil in place, STB MBE = Material Balance Equation MBO = Modified Black Oil PVT = Pressure Volume - Temperature PR = Peng-Robison Psat = Saturation Pressure Psep1 = Separator Pressure at first stage separator, psi Psep2 = Separator Pressure at second stage separator, psi Rs = solution gas-oil ratio, scf/STB Rsi = solution gas-oil ratio at initial pressure, scf/STB Rv = vaporized oil-gas ratio, STB/MMscf Rvi = vaporized oil-gas ratio at initial pressure, STB/MMscf STO = Stock Tank Oil Gravity, Fraction SG1 = Gas gravity at first stage separator, Fraction SG2 = Gas gravity at second stage separator, Fraction Tr = Reservoir Temperature, F VO = Volatile Oil References 1. Whitson, C.H. and Trop, S.B.: Evaluating Constant Volume Depletion Data, Paper SPE 10067, SPE, Richardson, TX.

USA, 1983. 2. Schilthuis, R.J.: Active Oil and Reservoir Energy, Trans. AIME 1936, 148, pp. 33-52. 3. Walsh, M.P.: A Generalized Approach to Reservoir Material Balance Calculations, paper presented at the International

Technical Conference of Petroleum Society of CIM, Calgary, Canada, JCPT, May 9-13, 1994.

SPE 164712 11

4. Walsh, M.P., Ansah, J., and Raghavan, R.: The New, Generalized Material Balance as an Equation of a Straight line: Part 1 Applications to Under-Saturated and Volumetric Reservoir, paper SPE 27684 presented at the 1994 SPE Permian Basin Oil and Gas Recovery Conference, March 16-18, Midland TX.

5. El-Banbi, Ahmed H., Forrest, J.K., Fan, L., and McCain, W.D., Jr.: Producing Rich-Gas-Condensate Reservoirs--Case History and Comparison Between Compositional and Modified Black-Oil Approaches, paper SPE 58988 presented at the SPE Fourth International Petroleum Conference and Exhibition, Villahermosa, Mexico. Feb. 1-3, 2000.

6. Coats, K.H.: Simulation of Gas Condensate Reservoir Performance, Paper SPE 10512, JPT, Oct. 1985, pp. 1870-1886. 7. McVay, D.A.: Generation of PVT Properties for Modified Black Oil Simulation of Volatile Oil and Gas Condensate

Reservoirs, Ph.D. Thesis, Texas A&M University, TX. 1994. 8. Walsh, M.P., and Towler, B.F.: Method computes PVT properties for Gas Condensate, OGJ, July 31, 1994, pp. 83-86. 9. Abdel Fattah, Khalid A.: Volatile Oil and Gas Condensate Fluid Behavior for Material Balance Calculations and Reservoir

Simulation, Ph.D. Thesis, Cairo University, 2005. 10. Ibrahim, M, El-Banbi, Ahmed H., El-Tayeb, S., and Sayyouh, H.: Changing Separator Conditions During Black-Oil and

Modified Black-Oil Simulation Runs, paper SPE 142462 presented at the SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain, 69 March 2011.

11. Coats, K.H., Smart, G.T.: Application of a Regression Based EOS PVT Program to Laboratory Data, SPERE (May 1986) 277-299.

12. McCain, W. Jr.: Analysis of Black Oil PVT Reports Revisited, Paper SPE 77386, Oct. 2002. 13. Vasquez, M. and Beggs, D.: Correlation for Fluid Physical Property Predictions, JPT, June 1989. 14. Al-Marhoun, M.A.: Evaluation of Empirically Derived PVT Properties for Middle East Crude Oils, Journal of Petroleum

Science and Engineering 42 (2004) pp.209-221. 15. McCain, W.D., Jr.: Heavy Components Control Reservoir Fluid Behavior, JPT (September 1994) 746-750. 16. Standing, M. B.: Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems, SPE, AIME, 1977. 17. EL-Banbi, Ahmed H., Abdel Fattah, Khalid A., and Sayyouh, M.H.: New Modified Black Oil Correlations for Gas

Condensate and Volatile Oil Fluids, Paper SPE 102240 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, TX. Sept. 24-27, 2006.

Table 1 - Reservoir Fluid Samples Properties

NO. SampleName SampleType C7+(%)Tres(F)

Psat(PSIG)

IGOR(Scf/Stb)

1 VO1 VolatileOil 19.0 249 4527 16782 VO2 VolatileOil 16.9 176 4460 N/A3 VO3 VolatileOil 14.9 246 4821 20004 VO4 VolatileOil 14.2 276 4375 25275 NC1 GasCondensate 12.7 312 5210 34136 NC2 GasCondensate 12.2 286 5410 42797 NC3 GasCondensate 11.7 238 4815 34058 GC1 GasCondensate 8.2 280 6750 55009 GC2 GasCondensate 8.2 215 4952 540310 GC3 GasCondensate 6.9 186 4000 598711 GC4 GasCondensate 6.5 312 5465 828012 GC5 GasCondensate 6.4 260 4525 720313 GC6 GasCondensate 5.9 267 4842 N/A14 GC7 GasCondensate 5.5 240 3360 N/A

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Fig. 1 Reservoir Fluid Samples Heptanes-Plus Range

Fig.2 Phase Plot from the tuned EOS for VO1 Fig.3 Comparison between EOS and Observed Relative volume values for VO1

Fig.4 Comparison between EOS and Observed Vapor Z-Factor values for VO1 Fig.5 Comparison between EOS and Observed Liquid Dropout values for VO1

C7+Range

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

VO1 VO2 VO3 VO4 NC1 NC2 NC3 GC1 GC2 GC3 GC4 GC5 GC6 GC7SampleName

VolatileOil

NearCritical

GasCondensate

0

1000

2000

3000

4000

5000

6000

100 0 100 200 300 400 500 600 700 800 900Temperature,F

Pressure,p

si

0

1

2

3

4

5

0 1000 2000 3000 4000 5000 6000 7000 8000

Pressure,psi

Relativ

eVolum

e

Rel.Vol.(EOS) Rel.Vol.(Obs.)

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

0 1000 2000 3000 4000 5000

Pressure,psi

Vapo

rZFa

ctor

VaporZfactor(EOS) VaporZfactor(Obs.)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1000 2000 3000 4000 5000

Pressure,psi

Liqu

idDr

opou

t,fraction

Liq.Sat.(EOS) Liq.Sat.(Obs.)

SPE 164712 13

Fig.6 Comparison between EOS and Observed Moles Recovered values for VO1

Table 2- Saturation Pressure Correlation Parameters (Volatile Oils)

Table 3- Saturation Pressure Correlation Parameters (Gas Condensates)

Table 4- Solution Gas-Oil Ratio (Known Psat) Correlation Parameters

Table 5- Solution Gas-Oil Ratio (Unknown Psat) Correlation Parameters

Table 6- Oil Formation Volume Factor (Known Psat) Correlation Parameters

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 500 1000 1500 2000 2500 3000 3500 4000

Pressure,psi

Moles

Recovered,

fraction

EOS Obs

Fluid SeparatorStages A0 A1 A2 A3 A4VO 2Stages 0.064 1.00 0.005 5.77 1.73VO 3Stages 0.033 1.06 0.004 6.22 1.83

Fluid SeparatorStages A0 A1 A2 A3 A4GC 2Stages 729 0.06 0.007 0.97 0.38GC 3Stages 762 0.06 0.017 0.96 0.38

Fluid SeparatorStages A0 A1 A2 A3 A4 A5GC 2Stages 1.51E04 1.06 43.99 6.24 10.10GC 3Stages 1.78E04 1.13 36.44 774.33 332.73 9.15VO 2Stages 4.88E04 0.63 407.53 8.32 3.48VO 3Stages 4.26E04 0.55 356.32 1200.33 524.59 4.00

Fluid SeparatorStages A0 A1 A2 A3 A4 A5GC 2Stages 1.5E08 6.47E04 0.12 4.94 0.0007GC 3Stages 1.1E08 6.94E04 0.12 1597.13 698 0.001VO 2Stages 1.0E07 1.42E04 0.08 7.80 0.001VO 3Stages 9.2E08 1.27E04 0.07 988.22 433 0.001

Fluid SeparatorStages A0 A1 A2 A3 A4 A5GC 2Stages 5.55E05 0.721 3193 1.6E05 0.0022GC 3Stages 7.25E05 0.690 3396 3.0E05 6.6E05 0.0020VO 2Stages 1.81E04 0.294 4382 1.6E05 0.0007VO 3Stages 1.82E04 0.268 4444 1.1E05 4.7E05 0.0006

14 SPE 164712

Table 7- Oil Formation Volume Factor (Unknown Psat) Correlation Parameters

Table 8- Initial Condensate-Gas Ratio (Rvi) Correlation Parameters

Table 9- Condensate-Gas Ratio (Known Psat) Correlation Parameters

Table 10- Condensate-Gas Ratio (Unknown Psat) Correlation Parameters

Table 11- Gas Formation Volume Factor (Unknown Psat) Correlation 1 Parameters

Table 12- Gas Formation Volume Factor (Unknown Psat) Correlation 2 Parameters

Fluid SeparatorStages A0 A1 A2 A3 A4 A5GC 2Stages 2.1E08 3.7E04 1.00 9.4E06 6.5E05GC 3Stages 1.9E08 3.6E04 1.05 4.0E05 7.0E05 3.8E05VO 2Stages 3.8E08 7.4E05 0.97 1.4E05 6.3E04VO 3Stages 3.8E08 6.8E05 0.98 1.2E05 4.3E05 5.8E04

Fluid SeparatorStages A0 A1 A2 A3 A4 A5VO 2Stages 1.6E23 6.7E02 52.94 93.72 40.36 4.7E03VO 3Stages 9.9E27 4.8E02 63.82 112.41 48.25 5.3E03

Fluid SeparatorStages A0 A1 A2 A3 A4 A5GC 2Stages 8.6E08 1.9E04 0.606 1.2E05 5.0E02GC 3Stages 8.7E08 2.0E04 0.634 1.2E04 2.2E04 4.9E02VO 2Stages 3.1E07 9.3E04 1.493 3.8E04 7.4E02VO 3Stages 3.0E07 9.4E04 1.554 1.7E03 2.3E03 7.2E02

Fluid SeparatorStages A0 A1 A2 A3 A4 A5GC 2Stages 4.6E09 2.5E04 2.6E01 8.5E06 2.4E+02GC 3Stages 2.0E09 2.3E04 2.9E01 1.4E03 2.4E03 2.3E+02VO 2Stages 4.7E07 1.4E03 2.3E+00 3.7E04 4.6E+02VO 3Stages 4.6E07 1.4E03 2.4E+00 1.7E03 2.3E03 4.5E+02

Fluid SeparatorStages A0 A1 A2 A3 A4GC 2Stages 3626 1.07 3.1E05 0.0021GC 3Stages 3695 1.08 1.4E04 1.8E04 0.0022VO 2Stages 3015 1.07 8.9E05 0.0027VO 3Stages 2988 1.07 1.7E04 1.5E04 0.0029

Fluid SeparatorStages A0 A1 A2 A3 A4GC 2Stages 349 .78 8.9E06 0.0020GC 3Stages 343 .77 3.3E05 7.5E05 0.0020VO 2Stages 449 .81 2.7E05 0.0020VO 3Stages 435 .81 9.4E07 5.2E05 0.0020

SPE 164712 15

Table 13- Under-Saturated Oil Formation Volume Factor Correlation Parameters

Fig. 7- Rs Cross Plot for VO known Psat (Three Stage Separator) Fig. 8- Bo Cross Plot for VO known Psat (Three Stage Separator)

Fig. 9- RV Cross Plot for VO known Psat (Three Stage Separator) Fig. 10- Bg Cross Plot for VO (Entire P. Range) (Three Stage Separator)

Fluid SeparatorStages A0 A1 A2 A3 A4 A5GC 2Stages 1.4E04 6.1E06 1.4E04 0.997 8.1E08GC 3Stages 1.3E04 6.1E06 1.4E04 0.997 8.0E07 1.2E06VO 2Stages 7.1E05 8.6E05 1.0E04 0.952 1.3E06VO 3Stages 7.0E05 8.8E05 1.0E04 0.951 5.4E06 1.4E05

R2=0.9661

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Rs(Obs),Mscf/Stb

Rs(C

alc),M

scf/Stb R

2=0.915

1

1.5

2

2.5

3

3.5

4

1 1.5 2 2.5 3 3.5 4

Bo(Obs),rbbl/Stb

Bo(C

alc),rb

bl/Stb

R2=0.9726

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Rv(Obs),Stb/Mscf

Rv(C

alc),St

b/Mscf

R2=0.9724

0.5

0.75

1

1.25

1.5

1.75

2

0.5 0.75 1 1.25 1.5 1.75 2

Bg(Obs),rbbl/Mscf

Bg(C

alc),rb

bl/M

scf

16 SPE 164712

Fig. 11- (F vs. Eo) for VO 1 (Two Stage Separator)

Table 14- Comparison Between GMBE and Simulation IOIP/GIIP

y=17447371.084xR2=0.993

000E+0

20E+6

40E+6

60E+6

80E+6

100E+6

120E+6

140E+6

160E+6

180E+6

200E+6

0.00 2.00 4.00 6.00 8.00 10.00 12.00

Eo,bbl/STB

F,bb

l

SampleName

SampleType EOS_STOIIP(STB)

MBal_STOIIP(STB)

ERROR(%)

VO1 VolatileOil 15110447 17828640 18VO2 VolatileOil 14361290 15373341 7VO3 VolatileOil 11714572 12684897 8VO4 VolatileOil 12663336 15610385 23

SampleName

SampleType EOS_GIIPMSCF

MBal_GIIPMSCF

ERROR%

NC1 NearCritical 38712208 36317597 6NC2 NearCritical 37197692 32884012 12NC3 NearCritical 39709708 35588587 10GC1 GasCondensate 50497036 44672755 12GC2 GasCondensate 45546884 43311130 5GC3 GasCondensate 48092008 43808088 9GC4 GasCondensate 42919356 41842871 3GC5 GasCondensate 44155820 41464689 6GC6 GasCondensate 46457824 43642928 6GC7 GasCondensate 50783260 46557199 8

SPE 164712 17

Fig. 12- Reservoir Pressure for MBO and Comp. Simulation for VO1 Fig. 13- Producing Gas Oil Ratio for MBO and Comp. Simulation for VO1

Table 15- New MBO PVT Correlations Average Absolute Error

0

1000

2000

3000

4000

5000

6000

7000

0 500000 1000000 1500000 2000000 2500000 3000000 3500000

CumOilProduction,STB

ReservoirP

ressure,

psi

Pr_Models Pr_W&T

0

5

10

15

20

25

30

35

40

45

50

0 500000 1000000 1500000 2000000 2500000 3000000 3500000

CumOilProduction,STB

Prod

ucingG

OR,

MScf/Stb

PGOR_Models PGOR_W&T

RSquare Avg.Error RSquare Avg.Error RSquare Avg.Error RSquare Avg.ErrorSaturationPressureCorrelation 3% 12% 3% 12%SolutionGasOilRatioCorrelation(KnownPsat) 96% 12% 88% 21% 97% 11% 89% 19%SolutionGasOilRatioCorrelation(UnKnownPsat) 97% 11% 78% 28% 97% 11% 79% 26%OilFormationVolumeFactorCorrelation (KnownPsat) 92% 6% 82% 10% 92% 6% 81% 10%OilFormationVolumeFactorCorrelation (UnKnownPsat) 96% 4% 70% 11% 96% 4% 70% 11%CondensateGasRatioCorrelation(KnownPsat) 96% 15% 85% 22% 97% 15% 85% 22%CondensateGasRatioCorrelation(UnKnownPsat) 96% 16% 80% 25% 97% 15% 80% 25%GasFormationVolumeFactorCorrelation (Model1) 100% 9% 100% 13% 100% 9% 100% 13%GasFormationVolumeFactorCorrelation (Model2) 98% 11% 98% 16% 98% 12% 99% 16%UnderSaturatedSolutionGasOilRatioCorrelation(KnownPsat) 8% 14% 10% 15%UnderSaturatedSolutionGasOilRatioCorrelation(UnKnownPsat) 9% 25% 10% 27%UnderSaturatedOilFormationVolumeFactorCorrelation 1% 1% 1% 1%UnderSaturatedCondensateGasRatioCorrelation(KnownPsat) 9% 16% 11% 16%UnderSaturatedCondensateGasRatioCorrelation(UnKnownPsat) 12% 24% 14% 26%UnderSaturatedGasFormationVolumeFactorCorrelation 35% 36%

2StageSeparator 3StagesSeparatorVO GCVO GC

18 SPE 164712

Table 16 Error Comparison Between This Work, Abdel Fattahs and Standing Correlations for All Volatile Oil Samples Combined

Method Rs Rv Bo Bg

New Correlation 8 26.8 1.8 0.5

Abdel Fattah Correlation 33.2 42 5.3 7.6

Standing Correlation 62.5 N/A 18.9 64

Fig. 14 - Rs Correlations Comparison for Gas Condensate Test Sample Fig. 15 Bo Correlations Comparison for Gas Condensate Test Sample

Fig. 16 Rv Correlations Comparison for Gas Condensate Test Sample Fig. 17 Bg Correlations Comparison for Gas Condensate Test Sample

SPE 164712 19

Fig. 18 - Rs Correlations Comparison for Volatile Oil Test Sample Fig. 19 - Bo Correlations Comparison for Volatile Oil Test Sample

Fig. 20 Rv Correlations Comparison for Volatile Oil Test Sample Fig. 21 Bg Correlations Comparison for Volatile Oil Test Sample