This paper was prepared for presentation at the 14th SPE Middle East Oil & Gas Show and. Conference held in Bahrain International Exhibition Centre, Bahrain, ...
SPE 93765 Artificial Neural Networks Models for Predicting PVT Properties of Oil Field Brines E.A. Osman, SPE, and M.A. Al-Marhoun, SPE, King Fahd U. of Petroleum and Minerals
Copyright 2005, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the 14th SPE Middle East Oil & Gas Show and Conference held in Bahrain International Exhibition Centre, Bahrain, 12–15 March 2005. This paper was selected for presentation by an SPE Program Committee following review of information contained in a proposal submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to a proposal of not more than 300 words; illustrations may not be copied. The proposal must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
Abstract Knowledge of chemical and physical properties of formation water is very important in various reservoir engineering computations especially in water flooding and production. Ideally, those data should be obtained experimentally. On some occasions, these data are not either available or reliable; then, empirically derived correlations are used to predict brine PVT properties. These correlations offer a handy and an acceptable approximation of formation water properties. However, the success of such correlations in prediction depends mainly on the range of data at which they were originally developed. These correlations were developed using linear, non-linear, multiple regression or graphical techniques. Recently, researchers utilized artificial neural networks (ANN) to develop more accurate oil PVT correlations. The developed models outperformed the existing correlations. However, there is no similar research done so far to utilize the power of ANN in developing similar models for formation waters. In the present study, two new models were developed to predict different brine properties. The first model predicts brine density, formation volume factor (FVF), and isothermal compressibility as a function of pressure, temperature and salinity. The second model is developed to predict brine viscosity as a function of temperature and salinity only. An attempt was made to develop a comprehensive model to predict all properties in terms of pressure, temperature and salinity. The results were satisfactory for all other properties except for viscosity. This was attributed to the fact that viscosity depends only on temperature and salinity. The models were developed using 1040 published data sets. These data were divided into three groups: training, cross-validation and testing. Radial Basis Functions (RBF) and Multi-layer Preceptor (MLP) neural networks were utilized in this study. Trend tests were performed to ensure that the developed model would follow the physical laws. Results show that the
developed models outperform the published correlations in terms of absolute average percent relative error, correlation coefficient and standard deviation. Introduction PVT properties of oil field brines are very important in several reservoir engineering computations. These properties include formation volume factor (FVF), isothermal compressibility, density and viscosity. These properties are used in material balance calculations, water flooding, enhanced oil recovery and numerical reservoir simulations. The compressibility of water is a component of the reservoir fluid effective compressibility which is used in material balance calculations. Water formation volume factor is used in both material balance calculations and en evaluating wateroil ratios. Density and viscosity are widely used in mobility ration determination in water flooding and in reservoir simulation. Ideally, brine PVT data should be obtained from laboratory studies on bottom-hole collected samples. However, in some instances, these data are either not available or reliable; then, empirically derived correlations are used to predict brine PVT properties. There are many empirical correlations for predicting different brine PVT properties, they were developed using linear or non-linear multiple regression or graphical techniques. These correlations offer a handy and an acceptable approximation of formation water properties. However, the success of such correlations in prediction depends mainly on the range of data at which they were originally developed. Recently, researchers utilized artificial neural networks (ANN) to develop more accurate oil PVT correlations. The developed models outperformed the existing correlations. However, there is no similar research done so far to utilize the power of ANN in developing similar models for formation waters. The objective of this study is therefore, to develop new predictive models for brine density, formation volume factor (FVF), isothermal compressibility and viscosity based on Artificial Neural Networks (ANN). Two new models were developed to predict different brine properties. The first model predicts brine density, formation volume factor (FVF), and isothermal compressibility as a function of pressure, temperature and salinity. The second model is developed to predict brine viscosity as a function of temperature and salinity only. Also, developing a comprehensive model to predict all properties in terms of pressure, temperature and salinity was attempted. However, except for viscosity, results were satisfactory for all other properties. This is because viscosity depends only on temperature and salinity.
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The models were developed based on 1040 published data sets collected from literature. These data were divided into three groups: training (520 data sets), cross-validation (260 data sets) and testing (260 data sets). Dividing data to: training, cross validation and testing using the ratio of 2:1:1 is recommended by most researchers in the field of artificial neural networks. Radial Basis Functions (RBF) and Multilayer Preceptor (MLP) neural networks were utilized in this study. Trend tests were performed to ensure that the developed model would follow the physical laws. Results show that the developed models outperform the published correlations in terms of absolute average percent relative error, correlation coefficient and standard deviation. ANNs are biologically inspired non-algorithmic, nondigital, massively parallel distributive and adaptive information processing systems. They resemble the brain in acquiring knowledge through learning process, and storing knowledge in inter-neuron connection strengths. Brine PVT Empirical Correlations The importance of developing and using empirical correlations for PVT properties was realized more than six decades ago. Many studies were carried out to develop new PVT correlations for oil and formation water properties. Most of these properties require the knowledge of solid content of the water or salinity. This could be measured in the lab or determined from well logs. Mc-Cain1 reviewed the formation water correlations for bubble point pressure, formation volume factor, density, solution gas oil ratio, isothermal compressibility and viscosity. In this paper, McCain recommended the use of specific correlations, published in his book2, to predict different brine properties. Also, many other investigators developed correlations for oil field brines. In 1946 Beal3 developed correlations to predict the viscosity behavior of air, water, natural gas and crude oil at different pressures and temperatures. Ossify 4 developed correlations to predict the isothermal compressibility of formation water. Rowe and Chou5 developed correlations for brine density. In a comprehensive study, Numbere6 developed correlations to predict most of the brine properties. A good review of other formation water empirical correlations is available in Ref. 7. Oil PVT Neural Network Models Recently, artificial neural network models were used extensively in most of petroleum engineering applications. Applications of ANN in petroleum engineering were discussed by many authors8-12. However, only few publications are available in literature for ANN applications in predicting PVT properties. Garb and Elsharkawy13-14 published neural network models for estimating Pb and Bob for Middle East crude oils. Elsharkawy15 presented a new technique to model the behavior of crude oil and natural gas systems using a radial basis function neural network model (RBFNM). The model can predict Bob, solution gas-oil ratio, Rs, oil viscosity, saturated oil density, undersaturated oil compressibility, and evolved gas gravity. Al-Shammasi16 presented neural network models and compared their performance to numerical correlations. A novel approach for predicting the complete PVT behavior of reservoir oils and gas condensates using
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Artificial Neural Network (ANN) was introduced by Varotsis et al.17. The method uses key measurements that can be performed rapidly either in the lab or at the well site as input to an ANN. In their comparative study, McCain et al.18 considered three independent means for developing Pb correlations, namely, non-linear regression of a model, neural network models, and non-parametric regression. Osman et al.19 developed a new ANN model to predict the Bob at the bubble-point pressure, based 803 published data sets from the Middle East, Malaysia, Colombia, and Gulf of Mexico fields. Finally, Al-Marhoun and Osman20 developed another ANN model to predict the Bob at the bubble-point pressure, for Saudi crude oils. There is no similar research done so far to utilize the power of ANN in developing similar models for formation waters. Data Acquisition and Analysis Published data4 were used in the present study to develop the ANN models. A total of 1040 data sets, each one contain reservoir temperature, reservoir pressure, water salinity, water density, formation volume factor, isothermal compressibility and viscosity. Of the 1040 data points, 780 were used to train the model, of which 520 were used to train the ANN models and 260 to cross-validate the relationships established during the training process. The remaining 260 data sets were kept to test the model to evaluate its accuracy and trend stability. A statistical description of the training and testing data are given in Table 1 and Table 2, respectively. Neural Networks An artificial neural network is a computer model that attempts to mimic simple biological learning processes and simulate specific functions of human nervous system. It is an adaptive, parallel information processing system, which is able to develop associations, transformations or mappings between objects or data. It is also the most popular intelligent technique for pattern recognition to date. The basic elements of a neural network are the neurons and their connection strengths (weights). Given a topology of the network structure expressing how the neurons (the processing elements) are connected, a learning algorithm takes an initial model with some “prior” connection weights (usually random numbers) and produces a final model by numerical iterations. Hence “learning” implies the derivation of the “posterior” connection weights when a performance criterion is matched (e.g. the mean square error is below a certain tolerance value). Learning can be performed by “supervised” or “unsupervised” algorithm. The former requires a set of known input-output data patterns (or training patterns), while the latter requires only the input patterns. This is commonly known as the feed forward model, in which no lateral or backward connections are used21. Several advantages can be attributed to ANNs rendering them suitable to applications such as considered here. First, an ANN learns the behavior of a database population by selftuning its parameters in such a way that the trained ANN matches the employed data accurately. Secondly, if the data used are sufficiently descriptive22, the ANN provides a rapid and confident prediction as soon as a new case, which has not been “seen” by the model during the training phase, is applied.
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Possibly, the most important aspect of ANNs is their ability to discover patterns in data that are so obscure as to be imperceptible to normal observation and standard statistical methods. This is particularly the case for data exhibiting significantly unpredictable nonlinearities23. Traditional correlations are based on simple models, which often have to be stretched by adding terms and constants in order for them to become flexible enough to fit experimental data, whereas neural networks are marvelously self-adaptable. Using a sufficiently large database for training, ANNs allow property values to be accurately predicted over a very wide range of input data11. An ANN model can accept substantially more information as input to the model, thereby, improving significantly the accuracy of the predictions and reducing the ambiguity of the requested relationship. Moreover, ANNs are fast-responding systems. Once the model has been “educated” predictions about unknown fluids are obtained with direct and rapid calculations without the need for tuning or iterative computations. Furthermore, an outstanding attribute of the ANNs is their capability of becoming increasingly “expert” by retraining using larger databases. Continuous enrichment of the ANN “knowledge” eventually leads to a predictive model exhibiting higher accuracy of predicting PVT properties11. Radial Basis Functions Networks (RBF) RBF networks have a number of advantages over MLPs. First, they can model any non-linear function using a single hidden layer, which removes some design-decisions about numbers of layers. Second, the simple linear transformation in the output layer can be optimized fully using traditional linear modeling techniques, which are fast and do not suffer from problems such as local minimum which plague MLP training techniques. RBF networks can therefore be trained extremely quickly (i.e. orders of magnitude faster than MLPs). Experience indicates that the RBF's more eccentric response surface requires a lot more units to adequately model most functions. Of course, it is always possible to draw shapes which are most easily represented one way or the other, but the balance does not favor RBFs. Consequently, an RBF solution will tend to be slower to execute and more space consuming than the corresponding MLP (but it was much faster to train, which is sometimes more of a constraint). RBFs are also more sensitive to the "curse of dimensionality," and have greater difficulties if the number of input units is large: this problem is discussed further in a later section.24 Development of Neural Network Models In this study, both back propagation (BPN) and Radial Basis Functions (RBF) networks were used. RBF used to develop the general ANN model to predict brine density, compressibility and formation volume factor. BPN was used to develop the viscosity model. A backpropagation network is multi-layered and information flows from the input to the output through at least one hidden/middle layer. Each layer contains neurons that are connected to all neurons in the neighboring layers. The connections have numerical values (weights) associated with them, which will be adjusted during the training phase. Training is completed when the network is able to predict the given output. For the first model, the first
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layer consists of three neurons representing the input values of reservoir temperature, pressure and salinity. The second (hidden) layer consists of thirty-eight neurons. The third layer contains three neurons representing the output values of compressibility, formation volume factor and density. Simplified schematic of the used neural networks is illustrated in Fig. 1. The second model, viscosity model, consists of two neurons in the first layer represents the input parameters of temperature and salinity. The hidden layer consists also of two neurons; and the output layer contains single neuron only representing the predicted viscosity. Simplified schematic of the used neural networks is illustrated in Fig. 2. An attempt was made to develop comprehensive model to predict compressibility, formation volume factor density and viscosity in terms of pressure, temperature and salinity. However, results were satisfactory for all properties except for viscosity. This is because viscosity depends only on temperature and salinity. As mentioned earlier, the data were divided into two groups: training group (780 data sets) and testing group (260 data sets). The training group is split into two groups: the first (520 data sets) was used to train the network; the second (260 data sets) was used to test the error during the training, this was called cross validation. It gives the ability to monitor the generalization performance of the network and prevent the network to over fit the training data. Over-training a network must be avoided and it is important to frequently monitor the error as training progresses. It has been shown that over training a network causes the network to memorize results rather than generalize. Then, the resulted model can perfectly predict the data similar to training data, but it will perform badly if new cases submitted to the network. The cross-validation method used in this study utilized as a checking mechanism in the training algorithm to prevent over-training. Tables 3 to 6 should be examined carefully. Table 3 indicates the sensitivity analysis of the general ANN model. It compares the training and verification error for each of the input parameters and ranked them according to their importance and contribution to the predicted parameter. The model depends mainly on temperature then the pressure and salinity comes second and in the same level. Similar results were obtained for both training and verification indicating the robustness of the model. Table 4 indicates the regression analysis of the general ANN model. Regression analysis for all output variables: FVF, compressibility and density; is given in all of the three data groups: training, validation and testing. In order to judge the model, error standard deviation should be less than that of data, which is achieved for all the output parameters. Also, error, standard deviation and correlation coefficient should are found, more or less, the same which verify the model robustness. Similarly, Tables 5 and 6 demonstrate the same tests for the viscosity model. Statistical Error Analysis Statistical error analysis is performed to compare the performance and accuracy of the new model to other empirical correlations. Average absolute percent relative error, minimum and maximum absolute percent error, and standard deviation were used as comparison criteria.
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Results and Discussion After training the neural networks, the models become ready for testing and evaluation. To perform this, the last data group (260 data sets), which was not seen by the neural network during training, was used. To compare the performance and accuracy of the new models to other empirical correlations, two correlations for each property were used. Namely, Meehan and McCain5 correlations for formation volume factor, Ossify 4 and Whitson7 correlations for brine compressibility, for Ossify 4 and Rowe6 correlations for brine density, and Meehan and McCain5 correlations brine viscosity. The statistical results of the comparison for ANN models are given in Table 7. The Artificial Neural Network Models outperform all the empirical correlations. The proposed model showed high accuracy in predicting the FVF values, error standard deviation of 0.00168 compared to 0.62 for Meehan and 0.62 for McCain. The absolute percent relative error is an important indicator of the accuracy of the models. For ANN model, it was 0.0981%, while other correlations indicate higher error values of 0.56% for McCain and 1.04 for Meehan Correlation. For compressibility values, ANN model results in error standard deviation of 1.0428 compared to 6.77 for Whitson and 11.82 for Ossify. The average absolute percent relative error for ANN model was only 1.0643%, compared to 4.67% for Whitson and 8.51 for Ossify Correlation. For brine density, and viscosity, similar trend was observed as illustrated in Table 7. Figures 3-14 illustrate scatter diagrams of the predicted versus experimental properties’ values. These cross plots indicates the degree of agreement between the experimental and the predicted values. If the agreement is perfect, then all points should lie on the 45º degrees line on the plot. Figures 3-5 showed these plots for the predicted FVF using McCain, Meehan correlations and ANN model, respectively. Compared to other cross plots, Fig. 5 shows the tightest cloud of points around the 45º degrees line indicating an excellent agreement between the experimental and the calculated data values. Figures 6-8 showed these plots for the predicted compressibility using Ossify, Whitson correlations and ANN model, respectively. Again, Fig. 8 shows the tightest cloud of points around the 45º degrees line indicating an excellent agreement between the experimental and the calculated data values. Figures 9-11 showed these plots for the predicted density using Rowe, Ossify correlations and ANN model, respectively. Both Ossify correlation and ANN model showed agreement between measured and the predicted density values. Finally, Figures 12-14 showed similar plots for the predicted viscosity using McCain, Meehan correlations and ANN model, respectively. Fig. 14 shows the excellent agreement and hence demonstrates the out performance of the ANN model. Thus, the ANN model outperforms other empirical correlations. The higher accuracy of the predicted results indicates that the neural network was successfully trained. Group Error and Trend Analysis The above discussion shows that the developed models outperform other empirical correlations in predicting formation water properties. A group error analysis was conducted to study the behavior of the developed models at
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different ranges of input parameters. Figures 15-17, illustrate the group error analysis for temperature, pressure and salinity, respectively, for FVF values predicted by ANN model. While figures 18-20, illustrate the same for isothermal compressibility values predicted by ANN model. Finally, figures 18-20, illustrate the group error analysis for temperature, and salinity for viscosity values predicted by ANN model. The developed ANN models achieved the lowest absolute average percent error consistently for all ranges of different properties. These findings prove the superiority of the developed ANN models over other correlation. Now, the models should be tested to ensure that they are physically correct. In order to perform these tests, trend tests must be conducted. The general ANN model was tested using hypothetical intermediate data points, and the dependence of FVF, FVF, compressibility, and density on temperature, pressure and salinity. Figures 23-25, illustrate the trend analysis for temperature, pressure and salinity, respectively, for compressibility values predicted by ANN model. Similar tests were done to test the effect of temperature, pressure and salinity on the predicted values of FVF and for the brine density. Finally, figures 26-27, illustrate the same for ANN viscosity Model. Results demonstrate the fact that the developed models obey the physical rules and follow the same trends of other correlations. Conclusions 1. Two new models were developed to predict the bubblepoint pressure, and the oil formation volume factor at the bubble-point pressure for Saudi crude oils. The models were based on artificial neural networks, and developed using 1040 published data sets. 2. Of the 1040 data sets, 520 were used to train the Artificial Neural Network models, 260 to cross-validate the relationships established during the training process and adjust the calculated weights, and the remaining 260 to test the model to evaluate its accuracy. 3. The results show that the developed general ANN model provides better predictions and higher accuracy than the published empirical correlations. The present model provides accurate predictions of the formation volume factor, isothermal compressibility and brine density. In addition, the developed viscosity model outperforms published empirical correlations. 4. Group Error Analysis was conducted and showed that the developed models consistently provide predictions with lowest error compared to other empirical correlations 5. Trend analysis was performed to check the behavior of the predicted values of brine density, formation volume factor (FVF), isothermal compressibility and viscosity for any change in reservoir temperature, pressure and salinity. The models’ behaviors were found to be physically correct. Nomenclature Er = Ea = Emax = = Emin RMS =
average percent relative error average absolute percent relative error Maximum absolute percent relative error Minimum absolute percent relative error root mean square error
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r = correlation coefficient Acknowledgement The authors wish to thank the Department of Petroleum Engineering, King Fahd University of Petroleum and Minerals for the facilities utilized to perform the present work and for their support.
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References 1. 2. 3. 4. 5. 6.
7. 8.
9.
10.
11. 12. 13.
McCain, W. D.: “Reservoir fluid property correlationsState of the Art,” SPERE, (May 1991) 266. McCain, W.D. Jr.: The Properties of Petroleum Fluids, second edition, PennWell Books, Tulsa (1989). Beal, C.,: “The Viscosity of Air, water, Natural Gas, Crude Oil and its Associated Gases at Oilfield Temperatures and Pressures,” Trans. AIME Vol. 165, 1946 Numbere, D. T.: “Correlations for the Physical Properties of Petroleum Reservoir Brines,” MS Thesis, Stanford University, 1977. Ossify, T.L., “The Effect of Salt, Gas, Temperature, and Pressure on the Compressibility of Water,” SPE Reservoir Engineering, February 1988, pp. 175-181 Rowe, A.M. and Chou, J.C.S., “Pressure-VolumeTemperature-Concentration Relation of Aqueous NaCl Solutions,” Journal of Chemical and Engineering Data, Vol. 15, No. 1, 1970, pp. 61-65. Whitson, C.H. and Brule, M.R. Phase Behavior, SPE Monograph Series, SPE, Richardson, Texas, 2000. Kumoluyi, A.O. and Daltaban, T.S.: “High-Order Neural Networks in Petroleum Engineering,” paper SPE 27905 presented at the 1994 SPE Western Regional Meeting, Longbeach, California, USA, March 23-25. Ali, J. K.: “Neural Networks: A New Tool for the Petroleum Industry,” paper SPE 27561 presented at the 1994 European Petroleum Computer Conference, Aberdeen, U.K., March 15-17. Mohaghegh, S. and Ameri, S.,:" A Artificial Neural Network As A Valuable Tool For Petroleum Engineers," SPE 29220, unsolicited paper for Society of Petroleum Engineers, 1994. Mohaghegh, S.:" Neural Networks: What it Can do for Petroleum Engineers," JPT, (Jan. 1995) 42. Mohaghegh, S.:" Virtual Intelligence Applications in Petroleum Engineering: Part 1 - Artificial Neural Networks,” JPT (September 2000). Garb, R.B. and Elsharkawy, A.M.: “Neural-Network Model for Estimating the PVT Properties of Middle East Crude
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Oils,” paper SPE 37695 presented at the 1997 SPE Middle East Oil Show and Conference, Bahrain, March 15–18. Garb, R.B. and Elsharkawy, A.M.: “Universal NeuralNetwork Model for Estimating the PVT Properties of Crude Oils,” paper SPE 38099 presented at the 1997 SPE Asia Pacific Oil & Gas Conference, Kuala Lumpur, Malaysia, April 14-16. Elsharkawy, A.M.: “Modeling the Properties of Crude Oil and Gas Systems Using RBF Network,” paper SPE 49961 presented at the 1998 SPE Asia Pacific Oil & Gas Conference, Perth, Australia, October 12-14. Al-Shammasi, A.A.,: “Bubble Point Pressure and Oil Formation Volume Factor Correlations,” paper SPE 53185 presented at the 1997 SPE Middle East Oil Show and Conference, Bahrain, March 15–18. Varotsis N., Gaganis V., Nighswander J., and Guieze P.,: “A Novel Non-Iterative Method for the Prediction of the PVT Behavior of Reservoir Fluids,” paper SPE 56745 presented at the 1999 SPE Annual Technical Conference and Exhibition, Houston, Texas, October 3–6. McCain W. D. Jr., R. Soto B., Valko, P.P., and Blasingame, T. A. “Correlation Of Bubble point Pressures For Reservoir Oils - A Comparative Study,” paper SPE 51086 presented at the 1998 SPE Eastern Regional Conference and Exhibition held in Pittsburgh, PA, 9–11 November. Osman, E. A., Ahmed, O.A., and Al-Marhoun, M.A.,: “Prediction of Oil PVT Properties Using Neural Networks,” Paper SPE 68233, presented at the 2001 SPE Middle East Oil Show and Conference, Manama, March 17-20. Al-Marhoun, M.A., and Osman, E. A.,: “Using Artificial Neural Networks to Develop New PVT Correlations for Saudi Crude Oils,” Paper SPE 78592, presented at the 10th Abu Dhabi International Petroleum Exhibition and Conference (ADIPEC), Abu Dhabi, UAE, October 8-11, 2002. Bishop, C.: Neural Networks for Pattern Recognition, Oxford University Press, NY (1995). Fauset, L.: Fundamentals of Neural Networks, Prentice Hall, NJ, USA, 1996. Hornik, K., “Multilayer Feedforward Networks are Universal Approximators”, Neural Networks, (1989), Vol. 2, 359. Statistica Neural Networks, Statsoft, Tulsa, Oklahoma, USA, 2000.
TABLE 1: STATISTICAL DESCRIPTION OF THE INPUT DATA USED FOR TRAINING AND CROSS VALIDATION (780 DATA SETS)
Property Temperature, F Pressure, psi Salinity, WT% Brine FVF, bbl/STB Brine Viscosity, cp Brine Density, gm/cc Brine Compressibility
Min
Max
60 384 14.7 10000 0.0 25 0.973 1.151 0.137 1.927 0.869 1.213 1.34E-06 5.51E-06
Average
St. Dev
Skewness
Kurtosis
220.662 4395.926 12.471 1.043 0.532 1.050 2.71E-06
104.1809 4016.2462 7.555 0.04 0.3974 0.0684 7.055E-07
0.0123 0.3376 -0.0117 0.4419 1.5355 -0.1286 0.9133
-1.2420 -1.4633 -1.2366 0.6765 1.7169 -0.4698 1.2619
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TABLE 2: STATISTICAL DESCRIPTION OF THE INPUT DATA USED FOR TESTING (260 DATA SETS)
Property
Min
Temperature, F Pressure, psi Salinity, WT% Brine FVF, bbl/STB Brine Viscosity, cp Brine Density, gm/cc Brine Compressibility
Max
60 384 14.7 10000 0.0 25 0.972 1.149 0.137 1.927 0.877 1.203 1.32E-06 5.36E-06
Average
St. Dev
Skewness
Kurtosis
226.015 4395.926 12.588 1.044 0.509 1.05 2.68E-06
101.325 4016.2462 7.3608 0.04 0.3823 0.0697 7.244E-07
-0.0333 0.3376 0.0404 0.3389 1.6878 0.0183 0.5848
-1.167 -1.4633 -1.0991 0.8096 2.3734 -0.801 0.3501
TABLE 3: SENSITIVITY ANALYSIS FOR ANN GENERAL MODEL
Training
Verification
Rank Error Ratio Rank Error Ratio
TF 1 9.08E-07 28.963 1 1.14E-06 23.918
P 3 5.66E-07 18.058 3 7.18E-07 16.884
S 2 7.22E-07 23.044 2 7.71E-07 16.892
TABLE 4: REGRESSION ANALYSIS FOR ANN GENERAL MODEL Data Mean Data Std. Dev. Error Mean Error Std. Dev. Abs. Mean Error Std. Dev. Ratio Correlation Data Mean Data Std. Dev. Error Mean Error Std. Dev. Abs. Mean Error Std. Dev. Ratio Correlation Data Mean Data Std. Dev. Error Mean Error Std. Dev. Abs. Mean Error Std. Dev. Ratio Correlation
TRAINING FVF
VERIF. FVF
TESTING FVF
1.0447 0.0392 -0.0032 0.0019 0.0032 0.0474 0.9989 TRAINING Cw 2.73E-06 6.69E-07 6.30E-09 1.70E-08 1.39E-08 0.0254 0.9997 TRAINING ρw 1.0491 0.0673 0.0095 0.0057 0.0096 0.0851 0.9964
1.0422 0.0398 -0.0031 0.0018 0.0031 0.0442 0.9991 VERIF. Cw 2.66E-06 6.97E-07 6.95E-09 2.22E-08 1.71E-08 0.0318 0.9995 VERIF. ρw 1.0510 0.0675 0.0088 0.0053 0.0090 0.0779 0.9970
1.0416 0.0420 -0.0031 0.0017 0.0031 0.0400 0.9992 TESTING Cw 2.68E-06 7.97E-07 4.32E-09 2.25E-08 1.79E-08 0.0283 0.9996 TESTING ρw 1.0512 0.0726 0.0093 0.0052 0.0093 0.0712 0.9975
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TABLE 5: SENSITIVITY ANALYSIS FOR ANN VISCOSITY MODEL TF S 1 2 Rank 0.4464 0.1163 Training Error 41.9099 10.916 Ratio 1 2 Rank 0.3659 0.1007 Verification Error 40.4643 11.1361 Ratio
TABLE 6: REGRESSION ANALYSIS FOR ANN VISCOSITY MODEL Data Mean Data Std. Dev. Error Mean Error Std. Dev. Abs. Mean Error Std. Dev. Ratio Correlation
TRAINING
VERIFICATION
TESTING
0.54898 0.42035 -0.00008 0.01066 0.00736 0.02536 0.99968
0.51069 0.34311 0.00022 0.00906 0.00636 0.02640 0.99966
0.49629 0.38431 0.00079 0.00981 0.00692 0.02553 0.99967
TABLE 7: STATISTICAL ANALYSIS OF THE RESULTS FOR DIFFERENT BRINE PROPERTIES EMPIRICAL CORRELATIONS AND DEVELOPED ANN MODELS Property Correlation Er EA Emin Emax STDEV 1.04 1.04 0.09 2.94 0.62 Meehan 0.35 0.56 0.0 2.14 0.69 Brine FVF McCain ANN (Present Study) -0.0031 0.0981 0.0018 0.4327 0.00168 -4.52 8.51 0.0 40.09 11.82 Ossify -2.67 4.67 0.01 21.66 6.77 Compressibility Whitson ANN (Present Study) -1.15 1.0643 0.0105 5.921 1.0428 0.15 0.15 0.03 0.24 0.05 Ossify 3.94 3.94 0.0 9.21 2.07 Brine Density Rowe ANN (Present Study) 0.00929 0.1305 0.0005 0.6372 0.00518 -1.70 3.69 0.02 20.66 4.7 Meehan -5.78 6.92 0.01 17.46 5.58 Brine Viscosity McCain ANN (Present Study) 0.1586 1.908 0.025 13.003 2.284
S T P S
Fig. 1- Schematic of General ANN Model
FVF Cw ρw
µ T
Fig. 2- Schematic of Viscosity ANN Model
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1.15
1.15
FVF-McCain
FVF-Meehan 1.10
Predicted F
Predicted F
1.10
1.05
1.00
1.05
1.00
0.95 0.95
0.97
0.99
1.01
1.03
1.05
1.07
1.09
1.11
1.13
0.95 0.95
1.15
0.97
0.99
Measured FVF
1.01
1.03
1.05
1.07
1.09
1.11
1.13
1.15
Measured FVF
Fig. 3- Cross Plot of McCain’s Correlation for FVF.
Fig. 4-Cross Plot of Meehan’s Correlation for FVF.
1.15
6.E-06
Compressibility-Osif
FVF-ANN 5.E-06
Predicted Compress
Predicted F
1.10
1.05
4.E-06
3.E-06
1.00 2.E-06
0.95 0.95
1.00
1.05
1.10
1.E-06 1.E-06
1.15
2.E-06
Measured FVF
3.E-06
4.E-06
5.E-06
6.E-06
Measured Compressibility
Fig. 5- Cross Plot of ANN Model for FVF.
Fig. 6- Cross Plot of Osif’s Correlation for Compressibility.
6.E-06
6.E-06
Compressibility-ANN CompressibilityWhitson
5.E-06 Predicted Compressib
Predicted Compress
5.E-06
4.E-06
3.E-06
3.E-06
2.E-06
2.E-06
1.E-06 1.E-06
4.E-06
2.E-06
3.E-06
4.E-06
5.E-06
6.E-06
Measured Compressibility
Fig. 7- Cross Plot of Whitson’s Correlation for Compressibility.
1.E-06 1.E-06
2.E-06
3.E-06
4.E-06
5.E-06
6.E-06
Measured Compressibility
Fig. 8- Cross Plot of ANN Model for Compressibility.
SPE 93765
9
1.3
1.3
Density-Rowe
Density-Osif 1.2
Predicte
Predicte
1.2
1.1
1.1
1.0
1.0
0.9
0.9
0.8 0.8
0.9
0.9
1.0
1.0
1.1
1.1
1.2
1.2
1.3
0.8 0.8
1.3
0.9
0.9
1.0
1.0
1.1
1.1
1.2
1.2
1.3
1.3
Measured Density
Measured Density
Fig. 9- Cross Plot of Rowe’s Correlation for Density.
Fig. 10- Cross Plot of Osif’s Correlation for Density.
1.3
2.50
Viscosity-McCain
2.25
Density-ANN
2.00
1.2
Predicted Visco
Predicte
1.75
1.1
1.0
1.50 1.25 1.00 0.75 0.50
0.9
0.25
0.8 0.8
0.9
1.0
1.1
1.2
0.00 0.00
1.3
0.25
0.50
0.75
Fig. 11- Cross Plot of ANN Model for Density.
1.75
2.00
2.25
2.50
2.00
1.75
1.75
1.50 1.25 1.00
1.50 1.25 1.00
0.75
0.75
0.50
0.50
0.25
0.25
0.25
0.50
0.75
1.00
Viscosity-ANN Model
2.25
Predicted Visco
Predicted Visco
1.50
2.50
Viscosity-Meehan
2.00
0.00 0.00
1.25
Fig. 12- Cross Plot of McCain’s Correlation for Viscosity.
2.50 2.25
1.00
Measured Viscosity
Measured Density
1.25
1.50
1.75
2.00
2.25
2.50
Measured Viscosity
Fig. 13- Cross Plot of Meehan’s Correlation for Viscosity.
0.00 0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
Measured Viscosity
Fig. 14- Cross Plot of ANN Model for Viscosity.
2.50
10
SPE 93765
1.8
Meehan McCain ANN
1.6 1.4
AAPE
1.2 1.0 0.8 0.6 0.4 0.2 0.0 60
