- Email: [email protected]
Prediction of crude oil viscosity curve using artificial intelligence techniques
Journal of Petroleum Science and Engineering 86-87 (2012) 111–117
Contents lists available at SciVerse ScienceDirect
Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
Prediction of crude oil viscosity curve using artificial intelligence techniques M.A. Al-Marhoun, S. Nizamuddin ⁎, A.A. Abdul Raheem, S. Shujath Ali, A.A. Muhammadain Center for Petroleum & Minerals, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia
a r t i c l e
i n f o
Article history: Received 1 May 2011 Accepted 25 March 2012 Available online 1 April 2012 Keywords: viscosity bubble point Functional Networks Support Vector Machine
a b s t r a c t Viscosity of crude oil is an important physical property that controls and influences the flow of oil through rock pores and eventually dictating oil recovery. Prediction of crude oil viscosity is one of the major challenges faced by petroleum engineers in production planning to optimize reservoir production and maximize ultimate recovery. This paper presents prediction of the complete viscosity curve as a function of pressure using artificial intelligence (AI) techniques. The viscosity curve predicted using artificial intelligence techniques derived from gas compositions of Canadian oil fields closely replicated the experimental viscosity curve above and below bubble point pressure when compared with correlations of its class. Functional Networks with Forward Selection (FNFS) outperformed all the AI techniques followed by Support Vector Machine (SVM). © 2012 Elsevier B.V. All rights reserved.
1. Introduction Viscosity is defined as the internal resistance to flow exerted by a fluid. Crude oil viscosity is a very important physical property that controls and influences the flow of crude oil through porous media. It is an important parameter in the calculation of oil recovery either from natural depletion or from recovery techniques such as water-flooding or gas injection processes, and flow through pipes for designing the pipelines. Crude oil is a mixture of hundreds of hydrocarbons possessing various thermodynamic properties (Balabin et al., 2007, 2011; Balabin and Syunyaev, 2008); hence viscosity of crude oil mainly depends on three physical properties, namely, pressure, temperature and composition. Viscosity has inverse relation with temperature and direct relation with pressure. The viscosity is very sensitive to the amount of gas dissolved in oil. The changes in pressure and temperature can cause the release of low molecular weight gas components from liquid phase under equilibrium condition. The pressure at which the first bubble of gas appears is called bubble point pressure (BPP). The gas is released as the pressure is decreased and at ambient condition almost all of the gas is released from the oil. The oil without dissolved gas is termed as dead oil. Viscosity of a reservoir fluid not only depends on the liquid but also on the amount of gas in solution. Hence the viscosity of crude oil can be bifurcated into two parts: viscosity above bubble point and viscosity below bubble point (Ayoub et al., 2007). Crude oil above
⁎ Corresponding author at: Centre for Petroleum and Minerals, Research Institute, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. Tel.: + 966 501533545 (Mobile); + 966 3 8602265(Office). E-mail addresses: [email protected], [email protected] (S. Nizamuddin). 0920-4105/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2012.03.029
bubble point is termed as under-saturated oil where viscosity increases with the increase in pressure. This is due to the increase in oil density as the oil is compressed. In contrast, oil below bubble point is termed as saturated oil and its viscosity increases as the pressure is decreased. This is due to loss of lighter components resulting in an increase in oil density as the pressure decreases (Ayoub et al., 2007). Usually viscosity is measured in laboratory using bottom-hole sample at reservoir pressure and temperature conditions. Determining viscosity through the experimental procedures at all temperatures of interest sometimes becomes uneconomical due to large amount of time and money involved. Hence, various approaches are used to develop viscosity models that could predict viscosity without experimentation. The oil viscosity models available in the literature can be classified into three main categories based on: (1). Empirical correlations (2). Equation of state (EOS) (3). Artificial intelligence (Chemo-Metrics or Multivariate Data Analysis) methods 2. Literature review In the past 60 years many empirical correlations were developed for predicting viscosity. These correlations predict viscosity above bubble point, at bubble point, below bubble point and dead oil viscosity at standard conditions of atmospheric pressure and 60 °F. Al-Marhoun (2004) re-modified previously developed correlations so as to suit Middle East data. These correlations predicted undersaturated oil viscosity (Beal, 1946; Vasquez and Beggs, 1980; Ladebi, 1992), gas saturated oil viscosity (Al-Marhoun, 2004; Beggs and Robinson, 1975; Chew and Connally, 1959; Ladebi, 1992) and dead oil viscosity (Beggs and Robinson, 1975; Glasø, 1980; Ladebi, 1992).
112
M.A. Al-Marhoun et al. / Journal of Petroleum Science and Engineering 86-87 (2012) 111–117
Fig. 2. Pressure vs. viscosity plot for a sample well.
Fig. 1. A typical and fitted viscosity curve on the experimental data.
Elsharkawy et al. (2003) developed an empirical model to predict viscosity based on gas compositions using regression technique. Instead of predicting one value of viscosity, the whole curve for viscosity was predicted at different pressures using one empirical correlation. The accuracy of these correlations is limited to a particular region and the accuracy decreases when applied globally. Omole et al. (2009) developed back propagation neural network (BPNN) model to predict the viscosity of crude oil samples obtained from Niger delta region, Nigeria. The crude oil viscosity was predicted with a total of 32 data samples out of which 17 were used for training, 5 for validation and the remaining 10 for testing. The predictions were compared with the field data, and the predictions from empirical correlations, namely Chew–Connally, and Beggs–Robinson. The statistical analysis indicated that the viscosity predicted by BPNN model achieved the lowest average absolute relative error and the highest correlation coefficient as compared to existing empirical correlations.
Table 1 Prediction of viscosity using various AI techniques, different combination of inputs parameters, and type of stratification. Inputs Rsb, μod
Methods
ELM, MLNR, SVM, FNBS, FBFN, BFFN ELM, MLNR, SVM, μod, Pb FNBS, FBFN, BFFN μod, ρoil, mole fractions ELM, MLNR, SVM, from C1–C7 + FNBS, FBFN, BFFN ELM, MLNR, SVM, μod, Rsb, Pb FNBS, FBFN, BFFN ELM, MLNR, SVM, μod, Rsb, Pb, ρoil FNBS, FBFN, BFFN ELM, MLNR, SVM, μod, Rsb, Set1 FNBS, FBFN, BFFN ELM, MLNR, SVM, μod, Rsb, Set2 FNBS, FBFN, BFFN ELM, MLNR, SVM, μod, Pb, TRes FNBS, FBFN, BFFN ELM, MLNR, SVM, μod, Pb, API gravity FNBS, FBFN, BFFN μod, Pb, TRes, API gravity ELM, MLNR, SVM, FNBS, FBFN, BFFN Set0, Set1, Set3 ELM, MLNR, SVM, FNBS, FBFN, BFFN Set0, Set2, Set3 ELM, MLNR, SVM, FNBS, FBFN, BFFN
Stratifications Total trials RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1, 2, 3
24
RBFN, FNFS,
1, 2, 3
24
Hajizadeh (2007a,b) used genetic algorithm techniques to predict reservoir fluid viscosity. Pressure, temperature, gas–oil ratio, and oil density were selected as input parameters. An impact analysis was performed on the input parameters indicating that the temperature has the greatest impact on the reservoir fluid viscosity followed by oil density, pressure and gas–oil ratio. The genetic algorithm indicated prediction of viscosity with a good accuracy for testing data. Oladiipo et al. (2009) used ANN-based models for predicting viscosity and wax deposition of petroleum reservoir fluids. The ANN architectures were trained using all the training algorithms available in the ANN MATLAB tool box. The input parameters defined were temperature, pressure and viscosity. The best algorithm that mimics the process of viscosity modeling was found to be “trainlm” (Levenberg Marquardt). The developed ANN models predicted viscosity behavior of crude oil better than those developed by regression techniques. Ayoub et al. (2007) developed an ANN model for predicting viscosity below bubble point and compared it with two viscosity correlations namely Khan et al. (1987) correlation and Ladebi (1992) correlation. ANN model was found to be successful in predicting viscosity below bubble point with a correlation coefficient reaching 99.3% outperforming previously mentioned correlations. Naseri et al. (2005) developed new correlations for predicting dead, saturated and under-saturated oil viscosities. These correlations are based on real data of different types of Iranian oils. Input parameters for these correlations are oil API gravity, saturation pressure, reservoir temperature and pressure, which are easily measured in oil fields. In comparison with correlations previously published in the literature, new correlations have a better accuracy and performance for predicting the viscosity of Iranian oils. Application of these correlations for other oil samples can result in errors. Elsharkwy and Gharbi (2001) presented a study to make comparison among several models developed using both classical regression techniques and ANN techniques for predicting saturated and under saturated viscosity. The comparison was achieved using 805 viscosity measurements of crude oil samples. These models use easily measured field parameters such as reservoir pressure, temperature, oil API gravity and gas gravity to predict crude oil viscosity curves. Labedi et al. (1992) developed correlations for light oil viscosity samples. A total of 100 oil samples were taken from the oil fields of Libya and were used to develop the correlations. Equations were developed using multiple-regression analysis to predict oil viscosity at atmospheric pressure (dead-oil viscosity), at saturation pressure, and above and below the saturation pressure. The developed correlations are functions of easily-obtainable data such as stock-tank oil gravity, reservoir pressure, and temperature. They have been found to adequately fit a
M.A. Al-Marhoun et al. / Journal of Petroleum Science and Engineering 86-87 (2012) 111–117
113
Fig. 3. Crossplot of the predicted versus measured μob with input parameters as Set0, Set2 and Set3 using AI techniques as ELM with Stratification 1.
gas/oil ratio at bubble point pressure, oil formation volume factor at bubble point pressure, undersaturated isothermal oil compressibility, dead-oil viscosity, saturated-oil viscosity and undersaturated-oil viscosity. The proposed correlations of this study predicted the PVT properties of GOM oils better than the correlations published in the literature, even when the coefficients of the published correlations are tuned. From the literature it is noted that the empirical correlations and equations of state (EOS) are region sensitive, i.e. they are developed using the PVT properties of crude oil samples collected from a particular region. As the geology changes, the crude oil composition changes, consequently the properties of crude oil also changes and hence the correlations need to be modified and the EOS need to be re-tuned to account for the regional characteristics prior to their application. To alleviate these limitations, artificial intelligence is becoming a powerful tool in the petroleum study. In this paper several AI methods were explored to predict the whole viscosity curve ranging from reservoir condition till atmospheric pressure with gas composition and other physical parameters of crude oil as input.
random selection of light crudes available in the literature and to be more practical and accurate than other available techniques. Hajizadeh (2007a,b) used fuzzy logic and neural network approach to predict crude oil viscosity at reservoir conditions as a function of easily determined physical properties. These two approaches can recognize possible patterns between input and output variables and successfully predict and model reservoir fluid viscosity. The neural network model predicted the crude oil viscosity with high accuracy. Elsharkwy (1998) used Radial Basis Function Neural Network (RBFN) model to predict oil formation volume factor, solution gas–oil ratio, oil viscosity, saturated oil density, under saturated oil compressibility, and evolved gas gravity. Input data to the RBFN model are reservoir pressure, temperature, stock tank oil gravity, and separator gas gravity. Accuracy of the model in predicting the solution gas–oil ratio, oil formation volume factor, oil viscosity, oil density, under saturated oil compressibility and evolved gas gravity has been compared with several published correlations. The comparison showed that the proposed model is much more accurate than these correlations in predicting the properties of the crudes. The behavior of the model in capturing the physical trend of the PVT data has also been checked against experimentally measured PVT properties of the test samples. Authors found that the proposed model is stable and reliable. Birol and Christman (2004) developed new empirical pressure– volume–temperature (PVT) correlations for Gulf of Mexico (GOM) oils as a function of commonly available field data using 100 PVT reports. The correlations have been developed for bubble point pressure, solution
The gas composition and physical parameters from 48 PVT reports were obtained from the Canadian oil fields. The PVT reports contain the results of standard flash liberation, differential liberation, separator tests, viscosity measurements, and gas analysis conducted on bottom hole fluid samples collected directly from Canadian oilfields. The oil
Fig. 4. Crossplot of predicted vs. experimental bubble point pressure predicted using SVM.
Fig. 5. Crossplot of predicted vs. experimental alpha values predicted using SVM.
3. Data processing
114
M.A. Al-Marhoun et al. / Journal of Petroleum Science and Engineering 86-87 (2012) 111–117
Fig. 6. Crossplot of predicted vs. experimental beta values predicted from SVM.
Fig. 7. Crossplot of predicted vs. experimental bubble point pressure predicted by FNFS.
viscosity was measured by a rolling ball viscometer at the reservoir. Statistical analysis was performed on these 48 well data points so as to remove the outliers using Cook's distance method and Chauvenet's criterion. 6 wells were removed as outliers as their oil properties were out of range when compared to those of the remaining 42 wells.
point pressure till reservoir pressure B–C. Point A corresponds to the dead oil or atmospheric condition and Patm and μod are corresponding pressure and viscosity values respectively. Point B corresponds to the bubble point condition and Pb and μob are corresponding pressure and viscosity values, respectively. As described earlier, before predicting the viscosity from the input data, an appropriate fit for the experimental data was determined using Eqs. (1) and (2).
4. AI techniques used A total of eight AI techniques were explored in this study. These include Extreme Learning Machine (ELM), Support Vector Machine (SVM), Radial Basis Functional Network (RBFN), Multi Linear Regression (MLNR), Functional Network Forward Selection (FFN), ForwardBackward Functional Network (FB-FN), Backward–Forward Functional Network (BF-FN), and Functional Network Backward Elimination Selection (FNBS). Each of these AI techniques was used and the method which predicted viscosity with minimum average absolute percentage error was selected. 5. Problem statement and approach A typical plot of viscosity vs. pressure curve is shown in Fig. 1. This viscosity curve can be divided into two parts, one from atmospheric pressure till bubble point pressure, A–B and another from bubble
Fig. 8. Crossplot of predicted vs. experimental alpha values predicted using FNFS.
P−P atm β μ b ¼ μ od þ ðμ ob −μ od Þ P b −P atm μ a ¼ μ ob þ α ðP−P b Þ
ðP > Pb Þ
ðPbPb Þ
ð1Þ ð2Þ
where α (alpha) and β (beta) are the coefficients of the two viscosity curves. The performance of the fitting Eqs. (1) and (2) was checked by using bubble point pressure (Pb) and atmospheric pressure (Patm) as anchors. Further, the coefficients α and β for all the samples were determined by Eqs. (1) and (2) respectively for each of the oil sample. With anchors at bubble point (Pb) and atmospheric pressure (Patm), the curves were fitted again using Eqs. (1) and (2), respectively. A typical fit on the experimental data is shown in Fig. 2.
Fig. 9. Crossplot of predicted vs. experimental beta values predicted using FNFS.
M.A. Al-Marhoun et al. / Journal of Petroleum Science and Engineering 86-87 (2012) 111–117 Table 2 Correlation coefficient estimation, R.
SVM FNFS
115
Table 3 RMSE estimation.
μob
α
β
0.84 0.88
0.79 0.54
0.28 0.56
6. Strategy for defining input parameters and selecting AI technique The strategy adopted for defining input parameters to predict viscosity required a large number of iterations. These included not only defining appropriate input parameter set but also parallely selecting the AI technique which gives the best prediction of viscosity curve among the above mentioned AI techniques. Three stratifications were also used for sorting the data into training and testing data set. These includes, Stratification 1 selects data randomly; Stratification 2 uses first 70 data points for training and remaining 30 data points for testing; and Stratification 3 includes selecting first 30 points for testing and remaining 70 points for training. For optimum performance various combinations of input parameters were explored with all the AI techniques available as shown in Table 1. Crossplots were made for predicted vs. experimental viscosity values for each set of input parameters for the training and testing dataset and with each AI technique, respectively. The input parameter set, the stratification and the AI technique which gave maximum correlation coefficient (R) values were selected. Hence after 128 trials, the input parameters Set0, Set2, Set3 with stratification 1 were chosen to be the best option with AI techniques FNFS and SVM respectively.
7. Prediction of viscosity curves Prediction of viscosity curves is carried out using the following approach. (1). The experimental data is divided into two sets: the training set and the testing set. A part of the training data is used for validation of the model during training. (2). First, the AI model is trained with the input datasets Set0, Set2 and Set3 to predict viscosity at bubble point pressure (μob). A typical cross plots for experimental vs. predicted bubble point values for training and testing can be seen in Fig. 3.
Fig. 10. Pressure vs. viscosity plot for Well no. 2 predicted using SVM.
SVM FNFS
μob
α
β
0.34 0.31
4.15 × 10− 5 5.6 × 10− 5
0.07 0.06
(3). Next, the AI model is trained with the input datasets Set0, Set2 and Set3 to predict the parameters α and β of Eqs. (1) and (2) respectively. (4). From the predicted μob, α and β values and with dead oil viscosity known from the experimental value, the whole viscosity curve above and below the bubble point is generated using Eqs. (1) and (2) respectively. For comparison of our results from AI prediction, we also predicted the viscosity curve from Birol and Christman (2004) Correlations. Saturated-Oil-Viscosity Correlation (μobp) was used to predict the part of the curve from bubble point viscosity till dead oil viscosity as shown in Eq. (3). B
μ obp ¼ A⋅ðμ oD Þ
ð3Þ a4
where A ¼
and B ¼
a1 a3 Rs þ expða2 Rs Þ expða5 Rs Þ
a6 a8 Rs a9 þ expða7 Rs Þ expða10 Rs Þ
ð3aÞ
ð3bÞ
The part of the curve from bubble point viscosity till reservoir condition is calculated using the under-saturated-oil-viscosity correlation (μo) as given by Eq. (4). A μ o ¼ μ obp þ a6 ⋅ p−pbp ⋅10 Where A ¼ a1 þ a2 ⋅ log μ obp þ a3 ⋅ logRs þ a4 ⋅μ obp : logRs þ a5 ⋅ p−pbp :
ð4Þ
ð4aÞ
Crossplots for the predicted vs. experimental values of the μob, α and β after training with SVM and FNFS techniques is shown in Figs. 4, 5, 6, 7, 8 and 9 respectively. Tables 2 and 3 show the correlation coefficient (R) and RMSE values respectively, for the three parameters μob, α, and β which were predicted using SVM and FNFS.
Fig. 11. Pressure vs. viscosity plot for Well no. 2 predicted using FNFS.
116
M.A. Al-Marhoun et al. / Journal of Petroleum Science and Engineering 86-87 (2012) 111–117 Table 4 Comparison of absolute percentage (APE) error using FNFS, SVM and Birol's correlation for unseen or tested wells.
Fig. 12. Comparison of average absolute percentage testing error for viscosity curve using Set0, Set2 and Set3 as input and predicted by FNFS.
Well number
APE using FNFS
APE using SVM
APE using Birol's correlation
1 2 3 4 5 6 7 8 9 10 11 12 13 14 AAPE
4.47 4.17 11.51 7.83 8.22 7.64 3.80 14.11 38.38 6.38 22.31 19.90 34.67 5.80 13.51
12.04 6.92 12.77 2.36 7.30 1.54 3.66 5.75 28.59 17.98 26.59 21.40 39.49 29.22 15.42
18.29 14.57 8.95 20.54 27.12 12.16 17.02 17.75 27.51 14.30 8.84 25.20 20.45 16.67 17.81
absolute percentage error (AAPE) in predicting viscosity curve using FNFS, SVM and Birol's correlation was found to be 13.51, 15.42 and 17.81 respectively. The average absolute percentage error plots of the predicted viscosity curve i.e. the remaining 30% of the unseen data using FNFS, SVM and Birol's correlation can be seen in Figs. 12, 13 and 14 respectively. Table 4 compares the absolute percentage error values of predicted viscosity curve for the 30% unseen testing data. 8. Conclusion In the present work a comparative study has been performed to predict viscosity curve using different AI techniques such as ELM, MLNR, SVM, RBFN, FNFS, FNBS, FBFN, and BFFN. Following conclusions can be made from this study:
Fig. 13. Comparison of average absolute percentage testing error for viscosity curve using Set0, Set2, Set3 as input and predicted by SVM.
A typical viscosity curve predicted using SVM, Birol's correlation and FNFS, Birol's correlation is shown in Figs. 10 and 11 respectively. From the plots it can be seen that the predictions from FNFS model outperformed SVM model followed by Birol's correlation. The average
• For the prediction of complete viscosity curve, an effective two-step process was developed in this work. First the bubble point viscosity is predicted and then using the predicted μob and experimental μod as anchors, the complete curve is predicted. This approach has led to a significant reduction in errors in prediction. • Instead of using oil components directly as inputs, they were grouped appropriately and their molecular weights were also introduced in order to develop an effective input–output relationship using the AI model. Such groupings include sum of mole fraction of nonhydrocarbon (MolFracNH), sum of mole fraction of lighter components (MolFracC1–C3), sum of mole fraction of medium hydrocarbons (MolFracC4–C6) and mole fraction (MolFracC7–C10) and their apparent molecular weights and dead oil viscosity in addition to C7 + molecular weight and API and reservoir temperature. • Prediction of viscosity curve using FNFS was closer to experimental data followed by SVM than the empirical correlations in literature. • Among the above mentioned techniques FNFS predicted the viscosity with minimum error and with input parameter combinations Set0, Set2 and Set3. Acknowledgments The authors thankfully acknowledge King Fahd University of Petroleum & Minerals for supporting this research. Appendix A
Fig. 14. Comparison of average absolute percentage testing error for viscosity curve predicted using Birol's Correlation.
P Pb Patm
Pressure, psi Bubble point pressure, psi Atmospheric pressure, psi
M.A. Al-Marhoun et al. / Journal of Petroleum Science and Engineering 86-87 (2012) 111–117
μa μb μob μod ρoil Rs Rsb Sgb Bob T TRes Set 0 Set 1
Set 2
Set 3
Viscosity above bubble point, cp Viscosity below bubble point, cp Viscosity at bubble point, cp Dead oil viscosity, cp Density of oil, g/m 3 Solution gas oil ratio, SCF/STB (m 3/m 3) Solution gas–oil ratio at bubble point, SCF/STB (m 3/m 3) Specific gravity at bubble point Oil formation volume factor (FVF) at bubble point Temperature, °F Reservoir temperature, °F Non-hydrocarbons which include CO2, H2S and N2 Mole Fractions of C1, C2, C3, iC4, nC4, iC5, nC5, C6, C7+, and apparent mole fractions from C1–C7, apparent molecular weights of C1, C2, C3, iC4, nC4, iC5, nC5, C6, C7+. Sum of mole fractions of gasses: C1–C3, liquids: C4–C6 and heavier components: C7 + and their apparent molecular weights. API gravity, reservoir temperature (TRes), bubble point pressure (Pb), dead oil viscosity (μod).
A.1. AI techniques used
SVM RBFN MLNR FNFS FB-FN BF-FN FNBS ELM
Support Vector Machine Radial Basis Functional Network MLN Regression Functional Network Forward Selection Forward–Backward Functional Network Backward–Forward Functional Network Functional Network Backward Elimination Selection Extreme Learning Machine
References Al-Marhoun, M.A., 2004. Evaluation of empirically derived PVT properties for Middle East crude oils. J. Petrol. Sci. Eng. 42, 209–221.
117
Ayoub, M.A., Raja, D.M., Al-Marhoun, M.A., 2007. Evaluation of below bubble point correlations and construction of a new neural network model. SPE 108439, SPE Asia-Pacific Oil and Gas Conference. Balabin, R.M., Syunyaev, R.Z., 2008. Petroleum resins adsorption onto quartz sand: near infrared (NIR) spectroscopy study. J. Colloid Interface Sci. 318, 167. Balabin, R.M., Safieva, R.Z., Lomakina, E.I., 2007. Comparison of linear and nonlinear calibration models based on near infrared (NIR) spectroscopy data for gasoline properties prediction. Chemom. Intell. Lab. Syst. 88, 183. Balabin, R.M., Syunyaev, R.Z., Schmid, T., Stadler, J., Lomakina, E.I., Zenobi, R., 2011. Asphaltene adsorption onto an iron surface: combined near infrared (NIR), Raman, and AFM study of the kinetics, thermodynamics, and layer structure. Energy Fuel 25, 189. Beal, C., 1946. The viscosity of air, water natural gas crude oil and its associated gases at oil field temperatures and pressures. Trans. AIME. 165, 94. Beggs, H.D., Robinson, J.R., 1975. Estimating the Viscosity of Crude Oil Systems. J. Petr. Tech. 27, 1140–1141. Birol, Dindoruk, Christman, P.G., 2004. PVT Properties and viscosity correlations for Gulf of Mexico oils. SPE Reserv. Eval. Eng. 427–437. Chew, J., Connally, C.A., 1959. A Viscosity Correlation for Gas Saturated Crude Oils. Trans. AIME. 216, 23. Elsharkawy, A.M., Hassan, S.A., Hashim, Y.S.Kh., Fahim, M.A., 2003. New compositional models for calculating viscosity of crude oils. Petroleum Society's Canadian International Petroleum Conference. Elsharkwy, A.M., 1998. Modeling the properties of crude oil and gas systems using RBF network. SPE Asia Pacific Oil and Gas Conference, Australia. Elsharkwy, A.M., Gharbi, R.B.C., 2001. Comparing classical and neural regression techniques in modeling crude oil viscosity. Adv. Eng. Softw. 32, 215–224. Glasø, O., 1980. Generalized Pressure-Volume-Temperature Correlations. J. Petr. Tech. 32, 784–795. Hajizadeh, Y., 2007a. Intelligent prediction of reservoir fluid viscosity. SPE Production and Operations Symposium, Oklahoma, U.S.A. Hajizadeh, Y., 2007b. Prediction of crude oil viscosity with genetic algorithm. Latin American & Caribbean Petroleum Engineering Conference, Argentina. Khan, S.A., Al-Marhoun, M.A., Duffuaa, S.O., Abu-Khamsin, S.A., 1987. Viscosity Correlations for Saudi Arabian Crude Oils, 5th SPE Middle East Oil Show, Bahrain. Ladebi, R., 1992. Improved correlations for predicting the viscosity of light crudes. J. Petrol. Sci. Eng. 8, 221–234. Naseri, A., Nikazar, M., Dehghani, S.A.M., 2005. A correlation approach for prediction of crude oil viscosities. J. Petrol. Sci. Eng. 47, 163–174. Oladiipo, A., Bankole, A., Taiwo, E., 2009. Artificial Neural Network Modeling of viscosity and wax deposition potential of Nigerian crude oil and gas condensate. 33rd Annual SPE International Technical Conference and Exhibition Abuja, Nigeria. Omole, O., Falode, O.A., Deng, A.D., 2009. Prediction of Nigerian crude oil viscosity using artificial neural network. Pet. Coal 51, 181–188. Vasquez, M., Beggs, H.D., 1980. Correlation for Fluid Physical Property Predictions. J. Petr. Tech. 32, 968–970.
Contents lists available at SciVerse ScienceDirect
Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
Prediction of crude oil viscosity curve using artificial intelligence techniques M.A. Al-Marhoun, S. Nizamuddin ⁎, A.A. Abdul Raheem, S. Shujath Ali, A.A. Muhammadain Center for Petroleum & Minerals, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia
a r t i c l e
i n f o
Article history: Received 1 May 2011 Accepted 25 March 2012 Available online 1 April 2012 Keywords: viscosity bubble point Functional Networks Support Vector Machine
a b s t r a c t Viscosity of crude oil is an important physical property that controls and influences the flow of oil through rock pores and eventually dictating oil recovery. Prediction of crude oil viscosity is one of the major challenges faced by petroleum engineers in production planning to optimize reservoir production and maximize ultimate recovery. This paper presents prediction of the complete viscosity curve as a function of pressure using artificial intelligence (AI) techniques. The viscosity curve predicted using artificial intelligence techniques derived from gas compositions of Canadian oil fields closely replicated the experimental viscosity curve above and below bubble point pressure when compared with correlations of its class. Functional Networks with Forward Selection (FNFS) outperformed all the AI techniques followed by Support Vector Machine (SVM). © 2012 Elsevier B.V. All rights reserved.
1. Introduction Viscosity is defined as the internal resistance to flow exerted by a fluid. Crude oil viscosity is a very important physical property that controls and influences the flow of crude oil through porous media. It is an important parameter in the calculation of oil recovery either from natural depletion or from recovery techniques such as water-flooding or gas injection processes, and flow through pipes for designing the pipelines. Crude oil is a mixture of hundreds of hydrocarbons possessing various thermodynamic properties (Balabin et al., 2007, 2011; Balabin and Syunyaev, 2008); hence viscosity of crude oil mainly depends on three physical properties, namely, pressure, temperature and composition. Viscosity has inverse relation with temperature and direct relation with pressure. The viscosity is very sensitive to the amount of gas dissolved in oil. The changes in pressure and temperature can cause the release of low molecular weight gas components from liquid phase under equilibrium condition. The pressure at which the first bubble of gas appears is called bubble point pressure (BPP). The gas is released as the pressure is decreased and at ambient condition almost all of the gas is released from the oil. The oil without dissolved gas is termed as dead oil. Viscosity of a reservoir fluid not only depends on the liquid but also on the amount of gas in solution. Hence the viscosity of crude oil can be bifurcated into two parts: viscosity above bubble point and viscosity below bubble point (Ayoub et al., 2007). Crude oil above
⁎ Corresponding author at: Centre for Petroleum and Minerals, Research Institute, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. Tel.: + 966 501533545 (Mobile); + 966 3 8602265(Office). E-mail addresses: [email protected], [email protected] (S. Nizamuddin). 0920-4105/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2012.03.029
bubble point is termed as under-saturated oil where viscosity increases with the increase in pressure. This is due to the increase in oil density as the oil is compressed. In contrast, oil below bubble point is termed as saturated oil and its viscosity increases as the pressure is decreased. This is due to loss of lighter components resulting in an increase in oil density as the pressure decreases (Ayoub et al., 2007). Usually viscosity is measured in laboratory using bottom-hole sample at reservoir pressure and temperature conditions. Determining viscosity through the experimental procedures at all temperatures of interest sometimes becomes uneconomical due to large amount of time and money involved. Hence, various approaches are used to develop viscosity models that could predict viscosity without experimentation. The oil viscosity models available in the literature can be classified into three main categories based on: (1). Empirical correlations (2). Equation of state (EOS) (3). Artificial intelligence (Chemo-Metrics or Multivariate Data Analysis) methods 2. Literature review In the past 60 years many empirical correlations were developed for predicting viscosity. These correlations predict viscosity above bubble point, at bubble point, below bubble point and dead oil viscosity at standard conditions of atmospheric pressure and 60 °F. Al-Marhoun (2004) re-modified previously developed correlations so as to suit Middle East data. These correlations predicted undersaturated oil viscosity (Beal, 1946; Vasquez and Beggs, 1980; Ladebi, 1992), gas saturated oil viscosity (Al-Marhoun, 2004; Beggs and Robinson, 1975; Chew and Connally, 1959; Ladebi, 1992) and dead oil viscosity (Beggs and Robinson, 1975; Glasø, 1980; Ladebi, 1992).
112
M.A. Al-Marhoun et al. / Journal of Petroleum Science and Engineering 86-87 (2012) 111–117
Fig. 2. Pressure vs. viscosity plot for a sample well.
Fig. 1. A typical and fitted viscosity curve on the experimental data.
Elsharkawy et al. (2003) developed an empirical model to predict viscosity based on gas compositions using regression technique. Instead of predicting one value of viscosity, the whole curve for viscosity was predicted at different pressures using one empirical correlation. The accuracy of these correlations is limited to a particular region and the accuracy decreases when applied globally. Omole et al. (2009) developed back propagation neural network (BPNN) model to predict the viscosity of crude oil samples obtained from Niger delta region, Nigeria. The crude oil viscosity was predicted with a total of 32 data samples out of which 17 were used for training, 5 for validation and the remaining 10 for testing. The predictions were compared with the field data, and the predictions from empirical correlations, namely Chew–Connally, and Beggs–Robinson. The statistical analysis indicated that the viscosity predicted by BPNN model achieved the lowest average absolute relative error and the highest correlation coefficient as compared to existing empirical correlations.
Table 1 Prediction of viscosity using various AI techniques, different combination of inputs parameters, and type of stratification. Inputs Rsb, μod
Methods
ELM, MLNR, SVM, FNBS, FBFN, BFFN ELM, MLNR, SVM, μod, Pb FNBS, FBFN, BFFN μod, ρoil, mole fractions ELM, MLNR, SVM, from C1–C7 + FNBS, FBFN, BFFN ELM, MLNR, SVM, μod, Rsb, Pb FNBS, FBFN, BFFN ELM, MLNR, SVM, μod, Rsb, Pb, ρoil FNBS, FBFN, BFFN ELM, MLNR, SVM, μod, Rsb, Set1 FNBS, FBFN, BFFN ELM, MLNR, SVM, μod, Rsb, Set2 FNBS, FBFN, BFFN ELM, MLNR, SVM, μod, Pb, TRes FNBS, FBFN, BFFN ELM, MLNR, SVM, μod, Pb, API gravity FNBS, FBFN, BFFN μod, Pb, TRes, API gravity ELM, MLNR, SVM, FNBS, FBFN, BFFN Set0, Set1, Set3 ELM, MLNR, SVM, FNBS, FBFN, BFFN Set0, Set2, Set3 ELM, MLNR, SVM, FNBS, FBFN, BFFN
Stratifications Total trials RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1
8
RBFN, FNFS,
1, 2, 3
24
RBFN, FNFS,
1, 2, 3
24
Hajizadeh (2007a,b) used genetic algorithm techniques to predict reservoir fluid viscosity. Pressure, temperature, gas–oil ratio, and oil density were selected as input parameters. An impact analysis was performed on the input parameters indicating that the temperature has the greatest impact on the reservoir fluid viscosity followed by oil density, pressure and gas–oil ratio. The genetic algorithm indicated prediction of viscosity with a good accuracy for testing data. Oladiipo et al. (2009) used ANN-based models for predicting viscosity and wax deposition of petroleum reservoir fluids. The ANN architectures were trained using all the training algorithms available in the ANN MATLAB tool box. The input parameters defined were temperature, pressure and viscosity. The best algorithm that mimics the process of viscosity modeling was found to be “trainlm” (Levenberg Marquardt). The developed ANN models predicted viscosity behavior of crude oil better than those developed by regression techniques. Ayoub et al. (2007) developed an ANN model for predicting viscosity below bubble point and compared it with two viscosity correlations namely Khan et al. (1987) correlation and Ladebi (1992) correlation. ANN model was found to be successful in predicting viscosity below bubble point with a correlation coefficient reaching 99.3% outperforming previously mentioned correlations. Naseri et al. (2005) developed new correlations for predicting dead, saturated and under-saturated oil viscosities. These correlations are based on real data of different types of Iranian oils. Input parameters for these correlations are oil API gravity, saturation pressure, reservoir temperature and pressure, which are easily measured in oil fields. In comparison with correlations previously published in the literature, new correlations have a better accuracy and performance for predicting the viscosity of Iranian oils. Application of these correlations for other oil samples can result in errors. Elsharkwy and Gharbi (2001) presented a study to make comparison among several models developed using both classical regression techniques and ANN techniques for predicting saturated and under saturated viscosity. The comparison was achieved using 805 viscosity measurements of crude oil samples. These models use easily measured field parameters such as reservoir pressure, temperature, oil API gravity and gas gravity to predict crude oil viscosity curves. Labedi et al. (1992) developed correlations for light oil viscosity samples. A total of 100 oil samples were taken from the oil fields of Libya and were used to develop the correlations. Equations were developed using multiple-regression analysis to predict oil viscosity at atmospheric pressure (dead-oil viscosity), at saturation pressure, and above and below the saturation pressure. The developed correlations are functions of easily-obtainable data such as stock-tank oil gravity, reservoir pressure, and temperature. They have been found to adequately fit a
M.A. Al-Marhoun et al. / Journal of Petroleum Science and Engineering 86-87 (2012) 111–117
113
Fig. 3. Crossplot of the predicted versus measured μob with input parameters as Set0, Set2 and Set3 using AI techniques as ELM with Stratification 1.
gas/oil ratio at bubble point pressure, oil formation volume factor at bubble point pressure, undersaturated isothermal oil compressibility, dead-oil viscosity, saturated-oil viscosity and undersaturated-oil viscosity. The proposed correlations of this study predicted the PVT properties of GOM oils better than the correlations published in the literature, even when the coefficients of the published correlations are tuned. From the literature it is noted that the empirical correlations and equations of state (EOS) are region sensitive, i.e. they are developed using the PVT properties of crude oil samples collected from a particular region. As the geology changes, the crude oil composition changes, consequently the properties of crude oil also changes and hence the correlations need to be modified and the EOS need to be re-tuned to account for the regional characteristics prior to their application. To alleviate these limitations, artificial intelligence is becoming a powerful tool in the petroleum study. In this paper several AI methods were explored to predict the whole viscosity curve ranging from reservoir condition till atmospheric pressure with gas composition and other physical parameters of crude oil as input.
random selection of light crudes available in the literature and to be more practical and accurate than other available techniques. Hajizadeh (2007a,b) used fuzzy logic and neural network approach to predict crude oil viscosity at reservoir conditions as a function of easily determined physical properties. These two approaches can recognize possible patterns between input and output variables and successfully predict and model reservoir fluid viscosity. The neural network model predicted the crude oil viscosity with high accuracy. Elsharkwy (1998) used Radial Basis Function Neural Network (RBFN) model to predict oil formation volume factor, solution gas–oil ratio, oil viscosity, saturated oil density, under saturated oil compressibility, and evolved gas gravity. Input data to the RBFN model are reservoir pressure, temperature, stock tank oil gravity, and separator gas gravity. Accuracy of the model in predicting the solution gas–oil ratio, oil formation volume factor, oil viscosity, oil density, under saturated oil compressibility and evolved gas gravity has been compared with several published correlations. The comparison showed that the proposed model is much more accurate than these correlations in predicting the properties of the crudes. The behavior of the model in capturing the physical trend of the PVT data has also been checked against experimentally measured PVT properties of the test samples. Authors found that the proposed model is stable and reliable. Birol and Christman (2004) developed new empirical pressure– volume–temperature (PVT) correlations for Gulf of Mexico (GOM) oils as a function of commonly available field data using 100 PVT reports. The correlations have been developed for bubble point pressure, solution
The gas composition and physical parameters from 48 PVT reports were obtained from the Canadian oil fields. The PVT reports contain the results of standard flash liberation, differential liberation, separator tests, viscosity measurements, and gas analysis conducted on bottom hole fluid samples collected directly from Canadian oilfields. The oil
Fig. 4. Crossplot of predicted vs. experimental bubble point pressure predicted using SVM.
Fig. 5. Crossplot of predicted vs. experimental alpha values predicted using SVM.
3. Data processing
114
M.A. Al-Marhoun et al. / Journal of Petroleum Science and Engineering 86-87 (2012) 111–117
Fig. 6. Crossplot of predicted vs. experimental beta values predicted from SVM.
Fig. 7. Crossplot of predicted vs. experimental bubble point pressure predicted by FNFS.
viscosity was measured by a rolling ball viscometer at the reservoir. Statistical analysis was performed on these 48 well data points so as to remove the outliers using Cook's distance method and Chauvenet's criterion. 6 wells were removed as outliers as their oil properties were out of range when compared to those of the remaining 42 wells.
point pressure till reservoir pressure B–C. Point A corresponds to the dead oil or atmospheric condition and Patm and μod are corresponding pressure and viscosity values respectively. Point B corresponds to the bubble point condition and Pb and μob are corresponding pressure and viscosity values, respectively. As described earlier, before predicting the viscosity from the input data, an appropriate fit for the experimental data was determined using Eqs. (1) and (2).
4. AI techniques used A total of eight AI techniques were explored in this study. These include Extreme Learning Machine (ELM), Support Vector Machine (SVM), Radial Basis Functional Network (RBFN), Multi Linear Regression (MLNR), Functional Network Forward Selection (FFN), ForwardBackward Functional Network (FB-FN), Backward–Forward Functional Network (BF-FN), and Functional Network Backward Elimination Selection (FNBS). Each of these AI techniques was used and the method which predicted viscosity with minimum average absolute percentage error was selected. 5. Problem statement and approach A typical plot of viscosity vs. pressure curve is shown in Fig. 1. This viscosity curve can be divided into two parts, one from atmospheric pressure till bubble point pressure, A–B and another from bubble
Fig. 8. Crossplot of predicted vs. experimental alpha values predicted using FNFS.
P−P atm β μ b ¼ μ od þ ðμ ob −μ od Þ P b −P atm μ a ¼ μ ob þ α ðP−P b Þ
ðP > Pb Þ
ðPbPb Þ
ð1Þ ð2Þ
where α (alpha) and β (beta) are the coefficients of the two viscosity curves. The performance of the fitting Eqs. (1) and (2) was checked by using bubble point pressure (Pb) and atmospheric pressure (Patm) as anchors. Further, the coefficients α and β for all the samples were determined by Eqs. (1) and (2) respectively for each of the oil sample. With anchors at bubble point (Pb) and atmospheric pressure (Patm), the curves were fitted again using Eqs. (1) and (2), respectively. A typical fit on the experimental data is shown in Fig. 2.
Fig. 9. Crossplot of predicted vs. experimental beta values predicted using FNFS.
M.A. Al-Marhoun et al. / Journal of Petroleum Science and Engineering 86-87 (2012) 111–117 Table 2 Correlation coefficient estimation, R.
SVM FNFS
115
Table 3 RMSE estimation.
μob
α
β
0.84 0.88
0.79 0.54
0.28 0.56
6. Strategy for defining input parameters and selecting AI technique The strategy adopted for defining input parameters to predict viscosity required a large number of iterations. These included not only defining appropriate input parameter set but also parallely selecting the AI technique which gives the best prediction of viscosity curve among the above mentioned AI techniques. Three stratifications were also used for sorting the data into training and testing data set. These includes, Stratification 1 selects data randomly; Stratification 2 uses first 70 data points for training and remaining 30 data points for testing; and Stratification 3 includes selecting first 30 points for testing and remaining 70 points for training. For optimum performance various combinations of input parameters were explored with all the AI techniques available as shown in Table 1. Crossplots were made for predicted vs. experimental viscosity values for each set of input parameters for the training and testing dataset and with each AI technique, respectively. The input parameter set, the stratification and the AI technique which gave maximum correlation coefficient (R) values were selected. Hence after 128 trials, the input parameters Set0, Set2, Set3 with stratification 1 were chosen to be the best option with AI techniques FNFS and SVM respectively.
7. Prediction of viscosity curves Prediction of viscosity curves is carried out using the following approach. (1). The experimental data is divided into two sets: the training set and the testing set. A part of the training data is used for validation of the model during training. (2). First, the AI model is trained with the input datasets Set0, Set2 and Set3 to predict viscosity at bubble point pressure (μob). A typical cross plots for experimental vs. predicted bubble point values for training and testing can be seen in Fig. 3.
Fig. 10. Pressure vs. viscosity plot for Well no. 2 predicted using SVM.
SVM FNFS
μob
α
β
0.34 0.31
4.15 × 10− 5 5.6 × 10− 5
0.07 0.06
(3). Next, the AI model is trained with the input datasets Set0, Set2 and Set3 to predict the parameters α and β of Eqs. (1) and (2) respectively. (4). From the predicted μob, α and β values and with dead oil viscosity known from the experimental value, the whole viscosity curve above and below the bubble point is generated using Eqs. (1) and (2) respectively. For comparison of our results from AI prediction, we also predicted the viscosity curve from Birol and Christman (2004) Correlations. Saturated-Oil-Viscosity Correlation (μobp) was used to predict the part of the curve from bubble point viscosity till dead oil viscosity as shown in Eq. (3). B
μ obp ¼ A⋅ðμ oD Þ
ð3Þ a4
where A ¼
and B ¼
a1 a3 Rs þ expða2 Rs Þ expða5 Rs Þ
a6 a8 Rs a9 þ expða7 Rs Þ expða10 Rs Þ
ð3aÞ
ð3bÞ
The part of the curve from bubble point viscosity till reservoir condition is calculated using the under-saturated-oil-viscosity correlation (μo) as given by Eq. (4). A μ o ¼ μ obp þ a6 ⋅ p−pbp ⋅10 Where A ¼ a1 þ a2 ⋅ log μ obp þ a3 ⋅ logRs þ a4 ⋅μ obp : logRs þ a5 ⋅ p−pbp :
ð4Þ
ð4aÞ
Crossplots for the predicted vs. experimental values of the μob, α and β after training with SVM and FNFS techniques is shown in Figs. 4, 5, 6, 7, 8 and 9 respectively. Tables 2 and 3 show the correlation coefficient (R) and RMSE values respectively, for the three parameters μob, α, and β which were predicted using SVM and FNFS.
Fig. 11. Pressure vs. viscosity plot for Well no. 2 predicted using FNFS.
116
M.A. Al-Marhoun et al. / Journal of Petroleum Science and Engineering 86-87 (2012) 111–117 Table 4 Comparison of absolute percentage (APE) error using FNFS, SVM and Birol's correlation for unseen or tested wells.
Fig. 12. Comparison of average absolute percentage testing error for viscosity curve using Set0, Set2 and Set3 as input and predicted by FNFS.
Well number
APE using FNFS
APE using SVM
APE using Birol's correlation
1 2 3 4 5 6 7 8 9 10 11 12 13 14 AAPE
4.47 4.17 11.51 7.83 8.22 7.64 3.80 14.11 38.38 6.38 22.31 19.90 34.67 5.80 13.51
12.04 6.92 12.77 2.36 7.30 1.54 3.66 5.75 28.59 17.98 26.59 21.40 39.49 29.22 15.42
18.29 14.57 8.95 20.54 27.12 12.16 17.02 17.75 27.51 14.30 8.84 25.20 20.45 16.67 17.81
absolute percentage error (AAPE) in predicting viscosity curve using FNFS, SVM and Birol's correlation was found to be 13.51, 15.42 and 17.81 respectively. The average absolute percentage error plots of the predicted viscosity curve i.e. the remaining 30% of the unseen data using FNFS, SVM and Birol's correlation can be seen in Figs. 12, 13 and 14 respectively. Table 4 compares the absolute percentage error values of predicted viscosity curve for the 30% unseen testing data. 8. Conclusion In the present work a comparative study has been performed to predict viscosity curve using different AI techniques such as ELM, MLNR, SVM, RBFN, FNFS, FNBS, FBFN, and BFFN. Following conclusions can be made from this study:
Fig. 13. Comparison of average absolute percentage testing error for viscosity curve using Set0, Set2, Set3 as input and predicted by SVM.
A typical viscosity curve predicted using SVM, Birol's correlation and FNFS, Birol's correlation is shown in Figs. 10 and 11 respectively. From the plots it can be seen that the predictions from FNFS model outperformed SVM model followed by Birol's correlation. The average
• For the prediction of complete viscosity curve, an effective two-step process was developed in this work. First the bubble point viscosity is predicted and then using the predicted μob and experimental μod as anchors, the complete curve is predicted. This approach has led to a significant reduction in errors in prediction. • Instead of using oil components directly as inputs, they were grouped appropriately and their molecular weights were also introduced in order to develop an effective input–output relationship using the AI model. Such groupings include sum of mole fraction of nonhydrocarbon (MolFracNH), sum of mole fraction of lighter components (MolFracC1–C3), sum of mole fraction of medium hydrocarbons (MolFracC4–C6) and mole fraction (MolFracC7–C10) and their apparent molecular weights and dead oil viscosity in addition to C7 + molecular weight and API and reservoir temperature. • Prediction of viscosity curve using FNFS was closer to experimental data followed by SVM than the empirical correlations in literature. • Among the above mentioned techniques FNFS predicted the viscosity with minimum error and with input parameter combinations Set0, Set2 and Set3. Acknowledgments The authors thankfully acknowledge King Fahd University of Petroleum & Minerals for supporting this research. Appendix A
Fig. 14. Comparison of average absolute percentage testing error for viscosity curve predicted using Birol's Correlation.
P Pb Patm
Pressure, psi Bubble point pressure, psi Atmospheric pressure, psi
M.A. Al-Marhoun et al. / Journal of Petroleum Science and Engineering 86-87 (2012) 111–117
μa μb μob μod ρoil Rs Rsb Sgb Bob T TRes Set 0 Set 1
Set 2
Set 3
Viscosity above bubble point, cp Viscosity below bubble point, cp Viscosity at bubble point, cp Dead oil viscosity, cp Density of oil, g/m 3 Solution gas oil ratio, SCF/STB (m 3/m 3) Solution gas–oil ratio at bubble point, SCF/STB (m 3/m 3) Specific gravity at bubble point Oil formation volume factor (FVF) at bubble point Temperature, °F Reservoir temperature, °F Non-hydrocarbons which include CO2, H2S and N2 Mole Fractions of C1, C2, C3, iC4, nC4, iC5, nC5, C6, C7+, and apparent mole fractions from C1–C7, apparent molecular weights of C1, C2, C3, iC4, nC4, iC5, nC5, C6, C7+. Sum of mole fractions of gasses: C1–C3, liquids: C4–C6 and heavier components: C7 + and their apparent molecular weights. API gravity, reservoir temperature (TRes), bubble point pressure (Pb), dead oil viscosity (μod).
A.1. AI techniques used
SVM RBFN MLNR FNFS FB-FN BF-FN FNBS ELM
Support Vector Machine Radial Basis Functional Network MLN Regression Functional Network Forward Selection Forward–Backward Functional Network Backward–Forward Functional Network Functional Network Backward Elimination Selection Extreme Learning Machine
References Al-Marhoun, M.A., 2004. Evaluation of empirically derived PVT properties for Middle East crude oils. J. Petrol. Sci. Eng. 42, 209–221.
117
Ayoub, M.A., Raja, D.M., Al-Marhoun, M.A., 2007. Evaluation of below bubble point correlations and construction of a new neural network model. SPE 108439, SPE Asia-Pacific Oil and Gas Conference. Balabin, R.M., Syunyaev, R.Z., 2008. Petroleum resins adsorption onto quartz sand: near infrared (NIR) spectroscopy study. J. Colloid Interface Sci. 318, 167. Balabin, R.M., Safieva, R.Z., Lomakina, E.I., 2007. Comparison of linear and nonlinear calibration models based on near infrared (NIR) spectroscopy data for gasoline properties prediction. Chemom. Intell. Lab. Syst. 88, 183. Balabin, R.M., Syunyaev, R.Z., Schmid, T., Stadler, J., Lomakina, E.I., Zenobi, R., 2011. Asphaltene adsorption onto an iron surface: combined near infrared (NIR), Raman, and AFM study of the kinetics, thermodynamics, and layer structure. Energy Fuel 25, 189. Beal, C., 1946. The viscosity of air, water natural gas crude oil and its associated gases at oil field temperatures and pressures. Trans. AIME. 165, 94. Beggs, H.D., Robinson, J.R., 1975. Estimating the Viscosity of Crude Oil Systems. J. Petr. Tech. 27, 1140–1141. Birol, Dindoruk, Christman, P.G., 2004. PVT Properties and viscosity correlations for Gulf of Mexico oils. SPE Reserv. Eval. Eng. 427–437. Chew, J., Connally, C.A., 1959. A Viscosity Correlation for Gas Saturated Crude Oils. Trans. AIME. 216, 23. Elsharkawy, A.M., Hassan, S.A., Hashim, Y.S.Kh., Fahim, M.A., 2003. New compositional models for calculating viscosity of crude oils. Petroleum Society's Canadian International Petroleum Conference. Elsharkwy, A.M., 1998. Modeling the properties of crude oil and gas systems using RBF network. SPE Asia Pacific Oil and Gas Conference, Australia. Elsharkwy, A.M., Gharbi, R.B.C., 2001. Comparing classical and neural regression techniques in modeling crude oil viscosity. Adv. Eng. Softw. 32, 215–224. Glasø, O., 1980. Generalized Pressure-Volume-Temperature Correlations. J. Petr. Tech. 32, 784–795. Hajizadeh, Y., 2007a. Intelligent prediction of reservoir fluid viscosity. SPE Production and Operations Symposium, Oklahoma, U.S.A. Hajizadeh, Y., 2007b. Prediction of crude oil viscosity with genetic algorithm. Latin American & Caribbean Petroleum Engineering Conference, Argentina. Khan, S.A., Al-Marhoun, M.A., Duffuaa, S.O., Abu-Khamsin, S.A., 1987. Viscosity Correlations for Saudi Arabian Crude Oils, 5th SPE Middle East Oil Show, Bahrain. Ladebi, R., 1992. Improved correlations for predicting the viscosity of light crudes. J. Petrol. Sci. Eng. 8, 221–234. Naseri, A., Nikazar, M., Dehghani, S.A.M., 2005. A correlation approach for prediction of crude oil viscosities. J. Petrol. Sci. Eng. 47, 163–174. Oladiipo, A., Bankole, A., Taiwo, E., 2009. Artificial Neural Network Modeling of viscosity and wax deposition potential of Nigerian crude oil and gas condensate. 33rd Annual SPE International Technical Conference and Exhibition Abuja, Nigeria. Omole, O., Falode, O.A., Deng, A.D., 2009. Prediction of Nigerian crude oil viscosity using artificial neural network. Pet. Coal 51, 181–188. Vasquez, M., Beggs, H.D., 1980. Correlation for Fluid Physical Property Predictions. J. Petr. Tech. 32, 968–970.