# Development of new empirical correlation for prediction of oil formation volume factor of crude oil for a major part of oil fields of Upper Assam basin.

Introduction

Reservoir fluid properties form the basis of many petroleum engineering calculations. The evaluation of oil and gas reserves, fluid flow through porous media, multiphase flow in pipe, surface and sub-surface equipment design, and production system optimization all depend heavily on reservoir fluid properties. These properties play a significant role in reservoir technology for calculating recovery efficiency of a reservoir and for predicting future performance as well (Dake, 1978). Hence it is very much essential to have a good knowledge of these fluid's physical properties such as Oil Formation Volume Factor ([B.sub.o]), Bubble Point Pressure ([P.sub.b]), Solution Gas Oil ratio ([R.sub.s]), Oil gravity ([[gamma].sub.o]), Compressibility (c), Viscosity ([mu]), etc.

The reservoir fluid properties are usually determined by laboratory experiments. But sometimes due to unavailability of experimentally measured PVT properties these fluid properties are determined from empirically derived correlations. PVT correlations are developed based on analysis of the available measured field data. It was found that almost all reservoir fluid properties could be correlated as functions of pressure, temperature, oil gravity and gas gravity (Ahmed, et al., 2005).

Since the 1940's, reservoir engineers realized the importance of developing empirical correlations for PVT properties and such studies resulted in the development of some new correlations. From a review of literature survey of various authors (Standing, 1962, Glaso, 1980, Al-Marhoun, 1988, Labedi, 1990, Al-Shammasi, 2001, etc.), it is observed that the best suited correlation for oil formation volume factor, Bo, is that of A.A. Al-Shammasi's (2001). Shammasi used global data in establishing the correlations based on artificial neural network (ANN) and for the present study Shammasi's correlation is taken as the reference.

The objective of the present study is to develop a suitable correlation for predicting oil formation volume factor (Bo) as a function of solution gas oil ratio, stock tank oil relative density, reservoir temperature based on laboratory analyzed PVT data collected from different wells for parts of oil fields of Upper Assam Basin (Figure-1). As discussed earlier for the present study Shammasi's correlation is taken as reference.

Methodology: (For Development of oil formation volume factor, ([B.sub.o]) Correlation):

Data acquisition & analysis:

For the present study, a total of 135 (one hundred thirty five) numbers of laboratory analyzed PVT data sets comprising of solution gas oil ratio, stock tank oil relative density and reservoir temperature data have been collected from the wells of the study area which are given in Table-1. The maximum and minimum values of PVT properties for evaluation of oil FVF correlation are given in Table -2.

To see the goodness of fit of Shammasi's model, the value of [R.sup.2], i.e., the coefficient of multiple determination, also called goodness of measure of fit and measure of predictive power of model, has been determined.

[R.sup.2] is defined as follows: [R.sup.2] = Regression sum of squares/Total sum of Squares = 1 - Residual/Error sum of Squares /Total sum of Squares

Here the value of [R.sup.2] is found to be 90.1% and this indicates (measure of goodness of fit) that 90.1% of variation in the value of [B.sub.o] is due to Rs/[[gamma].sub.o] and (T - 60)/[[gamma].sub.o] which in turn indicates that the Shammasi's model is highly satisfactory to our observation.

Referring to A.A. Shammasi's correlation for oil formation volume factor, the new correlation is evaluated by doing regression analysis. The best model that fits all the 135 experimental data points was found to be:

[B.sub.o] = 0.776 + a (Rs/[[gamma].sub.o]) + b [(T- 60)/[[gamma].sub.o]] (i)

Where a and b are unknown coefficients and the value of which are found to be:

By putting the value of coefficients 'a' and 'b' in equation-(i), the new correlation for oil formation volume factor for the present study is given as:

Bo = 0.776 + 0.0002911(Rs/[[gamma].sub.o]) + 0.002625 [(T-60)/[[gamma].sub.o]] (ii)

Comparison of the correlation

Based on the above calculations, and utilizing the PVT data set (given in table no. 1) the Oil Formation Volume Factor (Bo) for the newly developed correlation and after Shammasi's correlation are determined and a comparative study has been made to see the efficacy of the newly developed & the Shammasi's correlation with the experimental PVT data. (Given in Table-3).

From the study, it is seen that, deviation in percent of present estimated value is less for the newly developed correlation than the Shammasi's correlation indicating better accuracy of the newly developed correlation. (Das et. al., 2006, 2007).. It is seen that there is a deviation in percent of present estimated and Shammasi's value of Oil FVF from the experimental value which are given in Table-4. The results are sorted by absolute average relative error, which provides a means to rank the methods.

Error analysis

Statistical Error Analysis

To check the accuracy of the newly developed model, both statistical and the graphical means are used for comparative evaluation. Two statistical error parameter, average percent relative error (Er) and average absolute percent relative error (Ea) are calculated as:

a. average percent relative error ([E.sub.r]) which is a measure of the relative deviation in percent, from the experimental data is calculated as:

[E.sub.r] = (1/nd) [SIGMA]Ei...

b. Average absolute percent relative error ([E.sub.a]) which is a measures of the relative absolute deviation in percent, from the experimental values is calculated as:

[E.sub.a] = (1/nd) [SIGMA]I[SIGMA]iI...

Where nd = number of data points and [E.sub.i] = the relative deviation in percent of an estimated value from experimental value and is calculated as:

[E.sub.i]=[[([X.sub.exp]-[X.sub.est])/[X.sub.exp]].sub.i] X 100; i= 1, 2, 3 ... [n.sub.d]

[X.sub.est], [X.sub.exp] are the estimated and experimental value respectively.

Lower the value of Er and Ea, better will be the result.

For the present study, the value of Er and Ea for both the Shammasi's and the newly developed model are calculated as:

It is observed that though Er (-4.0779%) value for Shammasi's study is lower than the newly developed correlation and the Ea (6.884%) value which is considered as a significant statistical parameter to check the accuracy of the results is lower for newly developed correlation than the Shammasi's correlation, which is indicative of better accuracy. The higher accuracy of the predicted results indicates that the neural network was successfully trained.

Graphical analysis

In graphical analysis, crossplots (which indicate the degree of agreement between the. experimental and predicted values) for the newly developed correlation and Shammasi's correlation are drawn (Fig--2 & Fig--3). The crossplot of Fig. 3, shows that the majority of data points of both experimental and Shammasi's correlation are widely scattered and highly deviated from the 45[degrees] line. But the crossplot in Fig--2, shows that the data points of both experimental and present estimated values are more closer to the 45[degrees] line indicating the excellent agreement between the experimental and the present calculated values which in turn indicates that the newly developed correlation is more suitable than the reference correlation.

To see the accuracy of the data and also to have a lucid visualization, a comparative plot of Oil Formation Volume Factor for both the experimental (laboratory analyzed) and newly developed model vs number of data points has been made. The plots (Fig-4) show that most of the points for both the newly developed and experimental values coincides which indicate the better accuracy of the newly developed correlation.

Conclusion

1. Based on the above study a new empirical correlation to predict the oil formation volume factor has been developed (taking as reference of Shammasi's correlation with modified calculated coefficients), using artificial neural networks based on 135 PVT data sets collected from different oil fields of Upper Assam Basin.

2. From a detailed study on the comparative evaluation and different graph/plots (Fig-2, Fig-3 & Fig-4), it is seen that there is a perfect closeness between the experimental (laboratory analyzed) and newly developed model. This new developed model provides predictions of the formation volume factor with an absolute average percent error of 6.884%.

3. Though the present Oil Formation Volume factor correlation has been developed specially only for a major part of Oil fields in Upper Assam Basin, this correlation can be used for all the types of oil & gas mixtures with properties falling within the ranges of data (as given in Table- 2) and this can be considered as an excellent and reliable predictive tool for estimating oil formation volume factor for the oil fields of Upper Assam Basin.

Acknowledgment

The authors are grateful to the TIFAC, under the Department of Science and Technology, Government of India and Oil and Natural Gas Corporation Limited (ONGCL) authority for funding the research project and providing necessary data. We are also thankful to Institute of Reservoir Studies (IRS), ONGCL, Ahmedabad, and Regional Research Laboratory (RRL), Jorhat for giving us opportunity to study the literature. The authors are also thankful to Oil India Ltd., Duliajan for their help and co-operation while preparing this paper. The authors are also thankful to Prof S. Kakoti, Statistics Department, Dibrugarh University for his kind help and cooperation while preparing this paper.

Minati Das * and M.A. Chowdhury

Department of Petroleum Technology, Dibrugarh University, Dibrugarh 786004, India

* Corresponding Author E-mail: minatidas@yahoo.com

Reservoir fluid properties form the basis of many petroleum engineering calculations. The evaluation of oil and gas reserves, fluid flow through porous media, multiphase flow in pipe, surface and sub-surface equipment design, and production system optimization all depend heavily on reservoir fluid properties. These properties play a significant role in reservoir technology for calculating recovery efficiency of a reservoir and for predicting future performance as well (Dake, 1978). Hence it is very much essential to have a good knowledge of these fluid's physical properties such as Oil Formation Volume Factor ([B.sub.o]), Bubble Point Pressure ([P.sub.b]), Solution Gas Oil ratio ([R.sub.s]), Oil gravity ([[gamma].sub.o]), Compressibility (c), Viscosity ([mu]), etc.

The reservoir fluid properties are usually determined by laboratory experiments. But sometimes due to unavailability of experimentally measured PVT properties these fluid properties are determined from empirically derived correlations. PVT correlations are developed based on analysis of the available measured field data. It was found that almost all reservoir fluid properties could be correlated as functions of pressure, temperature, oil gravity and gas gravity (Ahmed, et al., 2005).

Since the 1940's, reservoir engineers realized the importance of developing empirical correlations for PVT properties and such studies resulted in the development of some new correlations. From a review of literature survey of various authors (Standing, 1962, Glaso, 1980, Al-Marhoun, 1988, Labedi, 1990, Al-Shammasi, 2001, etc.), it is observed that the best suited correlation for oil formation volume factor, Bo, is that of A.A. Al-Shammasi's (2001). Shammasi used global data in establishing the correlations based on artificial neural network (ANN) and for the present study Shammasi's correlation is taken as the reference.

The objective of the present study is to develop a suitable correlation for predicting oil formation volume factor (Bo) as a function of solution gas oil ratio, stock tank oil relative density, reservoir temperature based on laboratory analyzed PVT data collected from different wells for parts of oil fields of Upper Assam Basin (Figure-1). As discussed earlier for the present study Shammasi's correlation is taken as reference.

Methodology: (For Development of oil formation volume factor, ([B.sub.o]) Correlation):

Data acquisition & analysis:

For the present study, a total of 135 (one hundred thirty five) numbers of laboratory analyzed PVT data sets comprising of solution gas oil ratio, stock tank oil relative density and reservoir temperature data have been collected from the wells of the study area which are given in Table-1. The maximum and minimum values of PVT properties for evaluation of oil FVF correlation are given in Table -2.

To see the goodness of fit of Shammasi's model, the value of [R.sup.2], i.e., the coefficient of multiple determination, also called goodness of measure of fit and measure of predictive power of model, has been determined.

[R.sup.2] is defined as follows: [R.sup.2] = Regression sum of squares/Total sum of Squares = 1 - Residual/Error sum of Squares /Total sum of Squares

Here the value of [R.sup.2] is found to be 90.1% and this indicates (measure of goodness of fit) that 90.1% of variation in the value of [B.sub.o] is due to Rs/[[gamma].sub.o] and (T - 60)/[[gamma].sub.o] which in turn indicates that the Shammasi's model is highly satisfactory to our observation.

Referring to A.A. Shammasi's correlation for oil formation volume factor, the new correlation is evaluated by doing regression analysis. The best model that fits all the 135 experimental data points was found to be:

[B.sub.o] = 0.776 + a (Rs/[[gamma].sub.o]) + b [(T- 60)/[[gamma].sub.o]] (i)

Where a and b are unknown coefficients and the value of which are found to be:

Coefficient Shammasi's Present Value Value a 0.0004120 0.0002911 b 0.0006500 0.0026250

By putting the value of coefficients 'a' and 'b' in equation-(i), the new correlation for oil formation volume factor for the present study is given as:

Bo = 0.776 + 0.0002911(Rs/[[gamma].sub.o]) + 0.002625 [(T-60)/[[gamma].sub.o]] (ii)

Comparison of the correlation

Based on the above calculations, and utilizing the PVT data set (given in table no. 1) the Oil Formation Volume Factor (Bo) for the newly developed correlation and after Shammasi's correlation are determined and a comparative study has been made to see the efficacy of the newly developed & the Shammasi's correlation with the experimental PVT data. (Given in Table-3).

From the study, it is seen that, deviation in percent of present estimated value is less for the newly developed correlation than the Shammasi's correlation indicating better accuracy of the newly developed correlation. (Das et. al., 2006, 2007).. It is seen that there is a deviation in percent of present estimated and Shammasi's value of Oil FVF from the experimental value which are given in Table-4. The results are sorted by absolute average relative error, which provides a means to rank the methods.

Error analysis

Statistical Error Analysis

To check the accuracy of the newly developed model, both statistical and the graphical means are used for comparative evaluation. Two statistical error parameter, average percent relative error (Er) and average absolute percent relative error (Ea) are calculated as:

a. average percent relative error ([E.sub.r]) which is a measure of the relative deviation in percent, from the experimental data is calculated as:

[E.sub.r] = (1/nd) [SIGMA]Ei...

b. Average absolute percent relative error ([E.sub.a]) which is a measures of the relative absolute deviation in percent, from the experimental values is calculated as:

[E.sub.a] = (1/nd) [SIGMA]I[SIGMA]iI...

Where nd = number of data points and [E.sub.i] = the relative deviation in percent of an estimated value from experimental value and is calculated as:

[E.sub.i]=[[([X.sub.exp]-[X.sub.est])/[X.sub.exp]].sub.i] X 100; i= 1, 2, 3 ... [n.sub.d]

[X.sub.est], [X.sub.exp] are the estimated and experimental value respectively.

Lower the value of Er and Ea, better will be the result.

For the present study, the value of Er and Ea for both the Shammasi's and the newly developed model are calculated as:

Correlation Er Value Ea Value Newly developed -0.86034% 6.88400% Shammasi's Study -4.07790% 9.35780%

It is observed that though Er (-4.0779%) value for Shammasi's study is lower than the newly developed correlation and the Ea (6.884%) value which is considered as a significant statistical parameter to check the accuracy of the results is lower for newly developed correlation than the Shammasi's correlation, which is indicative of better accuracy. The higher accuracy of the predicted results indicates that the neural network was successfully trained.

Graphical analysis

In graphical analysis, crossplots (which indicate the degree of agreement between the. experimental and predicted values) for the newly developed correlation and Shammasi's correlation are drawn (Fig--2 & Fig--3). The crossplot of Fig. 3, shows that the majority of data points of both experimental and Shammasi's correlation are widely scattered and highly deviated from the 45[degrees] line. But the crossplot in Fig--2, shows that the data points of both experimental and present estimated values are more closer to the 45[degrees] line indicating the excellent agreement between the experimental and the present calculated values which in turn indicates that the newly developed correlation is more suitable than the reference correlation.

To see the accuracy of the data and also to have a lucid visualization, a comparative plot of Oil Formation Volume Factor for both the experimental (laboratory analyzed) and newly developed model vs number of data points has been made. The plots (Fig-4) show that most of the points for both the newly developed and experimental values coincides which indicate the better accuracy of the newly developed correlation.

Conclusion

1. Based on the above study a new empirical correlation to predict the oil formation volume factor has been developed (taking as reference of Shammasi's correlation with modified calculated coefficients), using artificial neural networks based on 135 PVT data sets collected from different oil fields of Upper Assam Basin.

2. From a detailed study on the comparative evaluation and different graph/plots (Fig-2, Fig-3 & Fig-4), it is seen that there is a perfect closeness between the experimental (laboratory analyzed) and newly developed model. This new developed model provides predictions of the formation volume factor with an absolute average percent error of 6.884%.

3. Though the present Oil Formation Volume factor correlation has been developed specially only for a major part of Oil fields in Upper Assam Basin, this correlation can be used for all the types of oil & gas mixtures with properties falling within the ranges of data (as given in Table- 2) and this can be considered as an excellent and reliable predictive tool for estimating oil formation volume factor for the oil fields of Upper Assam Basin.

Acknowledgment

The authors are grateful to the TIFAC, under the Department of Science and Technology, Government of India and Oil and Natural Gas Corporation Limited (ONGCL) authority for funding the research project and providing necessary data. We are also thankful to Institute of Reservoir Studies (IRS), ONGCL, Ahmedabad, and Regional Research Laboratory (RRL), Jorhat for giving us opportunity to study the literature. The authors are also thankful to Oil India Ltd., Duliajan for their help and co-operation while preparing this paper. The authors are also thankful to Prof S. Kakoti, Statistics Department, Dibrugarh University for his kind help and cooperation while preparing this paper.

Minati Das * and M.A. Chowdhury

Department of Petroleum Technology, Dibrugarh University, Dibrugarh 786004, India

* Corresponding Author E-mail: minatidas@yahoo.com

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Author: | Das, Minati; Chowdhury, M.A. |
---|---|

Publication: | International Journal of Petroleum Science and Technology |

Date: | Jan 1, 2011 |

Words: | 1609 |

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