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Artificial neural network for permeability damage prediction due to sulfate scaling
Journal of Petroleum Science and Engineering 78 (2011) 575–581
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Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
Artificial neural network for permeability damage prediction due to sulfate scaling Reza Zabihi a, e, Mahin Schaffie b, e, Hossein Nezamabadi-pour c, e, Mohammad Ranjbar d, e,⁎ a
Department of Oil and Gas Engineering, Shahid Bahonar University of Kerman, Iran Department of Chemical Engineering, Shahid Bahonar University of Kerman, Iran c Department of Electrical Engineering, Shahid Bahonar University of Kerman, Iran d Department of Mining Engineering, Shahid Bahonar University of Kerman, Iran e Energy and Environmental Engineering Research Centre (EERC), Shahid Bahonar University of Kerman, Iran b
a r t i c l e
i n f o
Article history: Received 31 October 2010 Accepted 8 August 2011 Available online 19 August 2011 Keywords: Permeability damage Artificial neural network Barium sulfate scaling Waterflooding
a b s t r a c t Waterflooding is an important oil recovery method, which is used to maintain reservoir pressure and to increase oil productivity. One of the most common problems caused by waterflooding is inorganic scales formation especially barium sulfate scale, which occurs due to incompatibility of injected seawater and formation water, and causes formation permeability decline. Artificial neural networks (ANNs) are new tools, which application of them in petroleum industry has been extended. Since many factors have influence on permeability reduction due to barium sulfate scaling and relation of them with one another is complicated, in this research a model was presented for prediction of permeability damage due to formation of barium sulfate scale using MATLAB software, artificial neural network and waterflooding experimental data in Malaysian and Berea sandstone cores. To design the optimum ANN model, number of neurons, number of hidden layers and training function were studied. Finally, efficiency of the model was evaluated using new data. The proposed artificial neural network predicted permeability and its reduction during water injection with error about 2 percent. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Waterflooding is one of the enhanced oil recovery (EOR) methods, which is executed for reservoir pressure maintenance and increasing of oil recovery. Scale formation is an important problem of petroleum industry during water injection. The principal mechanisms of scale deposition are pressure drop or temperature variations and mixing of incompatible waters, which cause carbonate and sulfate scales precipitation, respectively. Sulfate scales mainly result from incompatibility between injected water and formation water. When two or more incompatible waters are mixed, they interact chemically and precipitate minerals. Usually seawater is used as injected water in waterflooding operation. Since seawater contains high concentration of sulfate anion and formation water contains high concentration of calcium, strontium and barium cations, mixing of them causes formation of sulfate scales such as calcium sulfate, strontium sulfate and barium sulfate (Crabtree et al., 1999; Frenier and Ziauddin, 2008; Khatami et al., 2010; Moghadasi et al., 2004). Barium sulfate is a kind of sulfate scales, which may precipitate in porous media of oil bearing formation, and causes permeability
⁎ Corresponding author at: Department of Mining Engineering, Shahid Bahonar University of Kerman, P.O. Box: 76175-133, Kerman, Iran. Tel.: + 98 341 2133818; fax: + 98 341 2113663. E-mail address: [email protected] (M. Ranjbar). 0920-4105/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2011.08.007
reduction and formation damage. Precipitation of barium sulfate scale was reported in some oilfields such as Forties and Brae (Collins, 2005; McElhiney et al., 2001). In addition the occurrence results in decrease of oil production and reduces of waterflooding operation efficiency. Although the main reason of barium sulfate scaling is incompatibility of injected and formation waters during hydrocarbon recovery operations, but some other factors such as concentration of sulfate and barium ions, pressure and temperature are effective on barium sulfate precipitation during mixing of formation and injected waters. Formation of barium sulfate increases with concentration of barium and sulfate ions in solution, and causes more permeability reduction. Moreover, pressure and temperature can be efficient and reduction of them may result in additional deposition of barium sulfate in porous media (Crabtree et al., 1999; Frenier and Ziauddin, 2008; Liu et al., 2009; Merdhah et al., 2010). One of the major tests is core flooding test, which is performed to investigate incompatibility of injected and formation waters before performing waterflooding operation. The test demonstrates scale formation effects on porous media and permeability decline by measuring pressure or flow rate reduction based on test method (Merdhah et al., 2010). In recent decades, various researches were done for study of permeability decline due to sulfate scales formation (McElhiney et al., 2001; Merdhah et al., 2010; Moghadasi et al., 2004). Moreover, some models have been presented for prediction of productivity decline and injectivity decline due to sulfate scaling (Bedrikovetsky et al., 2009a, 2009b).
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Preparation of core for coreflooding test is expensive. In addition, accomplishment of the test needs special experimental equipments. Therefore, presentation a model, which can be replaced of such tests and its results, conforms to test results, is more economic and needs less time. In recent years, applications of artificial neural networks especially multilayer neural networks in petroleum industry have been extended. Artificial neural networks (ANNs) are parallel distributed information processing models. The most important advantage of ANN rather than other methods is learning without requirement of given formula and generalization capability for solving new problems, so it can predict nonlinear complex systems (Elgibaly and Elkamel, 1998; Engelbrecht, 2007; Haykin, 1999). The main objective of this study is the designing of ANN model for prediction of permeability decline due to formation of barium sulfate scale in porous media with high accuracy during coreflooding. At first, the paper gives a summary about ANN and multilayer neural networks. Then, the methodology for determination of optimum ANN structure has been presented. Finally, the performance of ANN model in prediction of permeability after water injection has been evaluated using new data of Malaysian and Berea sandstone cores. 2. Multilayer neural networks with back propagation algorithm Artificial neural network is an information processing system which mimics the biological neural network of a human brain and is developed based on mathematical model of biological neural networks (Elgibaly and Elkamel, 1998; Groupe, 2007). In artificial neural networks, information processing is performed in many simple individual processors which are called neurons. When inputs (Ii =[I1, I2,…,In]) are implemented to the neuron, they are multiplied by associated weight of each connection (Wi =[W1, W2,…,Wn]). Then bias (b) of the neuron is added to summation of weighted inputs. Afterwards each neuron applies a linear or nonlinear transfer function (f) on its net input to produce its output (O) (Eq. (1)) (Elgibaly and Elkamel, 1998; Engelbrecht, 2007, Mohaghegh, 2000). O ¼ f ðWi :Ii þ bÞ
ð1Þ
Hyperbolic tangent, logistic sigmoid and linear functions are the most common activation (transfer) functions in artificial neural networks. Hyperbolic tangent and logistic sigmoid functions are used in hidden layer of ANN, whereas linear function is used in output layer of ANN for function estimation. Eqs. (2) and (3) are shown hyperbolic tangent and logistic sigmoid functions, respectively (Demuth et al., 2007; Groupe, 2007; Haykin, 1999). f ðxÞ ¼
1−expð−2xÞ 1 þ expð−2xÞ
ð2Þ
f ðxÞ ¼
1 ; 0:3 b a b 1 1 þ expð−axÞ
ð3Þ
As shown in Fig. 1, an artificial neuron has many inputs whereas only has one output. The output of each previous neuron is multiplied by the associated connection weight between two neurons and then enters the next neuron as an input (Engelbrecht, 2007; Mohaghegh, 2000; Nowroozi et al., 2009). There are different classifications of neural networks based on various properties. One of the usual classifications is based on training algorithms so that neural networks can be divided into two main groups of supervised and unsupervised. Unsupervised neural networks, which are also known as self-organizing maps, are called unsupervised because no feedback is produced during training. In the supervised training algorithm, both inputs and outputs are presented to the network and the network learns based on feedback (Engelbrecht, 2007; Haykin, 1999; Mohaghegh, 2000).
Fig. 1. Schematic of an artificial neuron.
Back propagation is one of supervised training algorithms wherein initially all weights are adjusted randomly in this algorithm, then the neural output is compared with the target in the training dataset and error (difference between target and neuron output) is propagated backward to the network. During this back propagation, the weights are changed to decrease the error. This procedure is continued frequently until the produced outputs are acceptably close to target (Demuth et al., 2007; Mohaghegh, 2000; Saeedi et al., 2007). There are two stages in preparing neural networks: the training stage and the test stage. In training stage, connection weights are adjusted to supply the desired outputs whereas in test stage, accuracy of the trained neural network in predicting the outputs is assessed by examples which have not been seen by the neural network in training stage. Training is done by adjusting the weights until convergence between produced outputs and desired outputs (target) is acquired. Changing weights allows the network to improve its behavior in response to the inputs (Mohaghegh, 2000). Neural networks basis of the supervised training algorithm have the most applications in petroleum industry. Although there are various kinds of neural networks, but networks with feed forward back propagation learning algorithm are the most popular and heavily applied (Nowroozi et al., 2009; Saeedi et al., 2007; Zuluaga et al., 2002). Fig. 2 illustrates a schematic of a multilayer feed forward neural network. Multilayer feed forward neural networks are composed of one input layer, one or more hidden layers, and one output layer. The first hidden layer extracts main features and other hidden layers extract minor features, so the number of hidden layer is related to complexity of the problem. The number of neurons in the input layer corresponds to the number of input variables which are presented to the network as input. The number of neurons in each hidden layer is determined with trial and error. The number of neurons in output layer corresponds to the number of output variables which are desired (Mohaghegh, 2000; Saeedi et al., 2007; Zuluaga et al., 2002).
Fig. 2. Schematic of a multilayer feed forward neural network.
R. Zabihi et al. / Journal of Petroleum Science and Engineering 78 (2011) 575–581 Table 1 Physical and experimental properties of sandstone cores. Sandstone Physical properties of cores core Length Diameter Average Permeability (in.) (in.) porosity (md) (%) Malaysian 3 Berea 3
1 1
34.14 23.50
577
Table 3 Properties of train data set. Experimental properties
Parameter
Unit
Minimum
Maximum
Mean
Standard deviation
Temperature Differential (°C) pressure (psi)
Vinj T ΔP ki CBa2+ CSO2-4 kd
PV °c psi md ppm ppm md
1.89 50 75 12.3 250 2750 10.3
66.42 90 200 162.7 2200 2960 143.34
23.604 67.368 143.421 30.528 1378.947 2860.526 21.283
15.123 12.532 44.426 42.127 965.313 105.131 24.224
12.30–13.84 50–80 105.10–162.70 60–90
100–200 75–100
3. Experimental data
4.2. Selection of random train, test and performance datasets
The data used for this study are obtained from case studies. These studies were conducted to investigate the permeability reduction due to deposition of barium sulfate in Malaysian and Berea sandstone cores. Table 1 presents physical and experimental properties of cores and Table 2 shows composition of synthetic formation waters and seawaters. In these experiments, each core was saturated with synthetic formation waters, and then the flow rate across the core was continuously recorded in constant differential pressure during seawater injection. Finally, the permeability of core was computed with Darcy's linear flow equation. Moreover, effect of various parameters such as temperature, differential pressure and concentration of constituent ions (barium and sulfate) on permeability reduction were perused (Merdhah, 2007; Merdhah et al., 2010; Merdhah and Yassin, 2008; Merdhah and Yassin, 2009).
When a randomized sample is utilized for ANN training, ANN applies information which is more representative of the population. In addition, selection of random test and performance datasets causes better evaluation of ANN efficiency (Saeedi et al., 2007). In this research, 264 data from 18 Malaysian and 4 Berea sandstone cores are used for prediction of permeability decline due to formation of barium sulfate scale. Initially, 228 data from 19 cores is selected for training and testing of ANN. Among 228 data, 188 data for training and 40 data for testing of ANN were utilized randomly. Tables 3 and 4 present properties of train and test datasets, respectively. After determination of ANN with optimum structure, 36 data from 3 sandstone cores were used for investigation of designed ANN efficiency. Table 5 is shown properties of performance dataset. 4.3. Normalization of data
4. Methodology for developing of neural networks During this study, various processes including preprocessing of data, using various training and verification sets, investigation of training functions, determination of optimum hidden neural number and evaluation of hidden layer number were performed for designing ANN with excellent performance. The following paragraphs give short descriptions on the mentioned processes.
In the process of ANN, sometimes raw data may not be suitable to be utilized, thus raw data needs to undergo preprocessing. When values of input and output parameters are extremely low or high, therefore scaling of data should be performed (Saeedi et al., 2007). One approach for scaling of data is performed with following formula (Eq. (4)) which normalizes the data to values between −1 and 1 (Demuth et al., 2007): Xi′ ¼ 2
4.1. Selection of input parameters According to results of previous tests temperature (T), differential pressure (ΔP), volume of injected water (Vinj), initial permeability (ki), concentration of barium in formation water (CBa2+) and concentration of sulfate in injected seawater (CSO2-4 ) were identified as effective parameters in prediction of damaged permeability (kd) after seawater injection (Merdhah, 2007; Merdhah et al., 2010; Merdhah and Yassin, 2008; Merdhah and Yassin, 2009). Therefore, these parameters were considered as inputs of ANN model.
Table 2 Composition of synthetic formation waters and injected seawaters. Component
Sodium Potassium Magnesium Calcium Strontium Barium Chloride Sulfate Bicarbonate
Normal barium formation water (ppm)
High barium formation water (ppm)
Seawater 1 (ppm)
Seawater 2 (ppm)
42707 1972 102 780 370 250 66706 5 2140
42707 1972 102 780 370 2200 67713 5 2140
9749 340 1060 384 5.4 b 0.2 17218 2960 136
10804.5 375.05 1295.25 429.2 6.577 19307.45 2750 158.8
Xi −Xmin −1 Xmax −Xmin
ð4Þ
Where Xi is original value of parameter, X'i is normalized value of Xi, Xmin and Xmax are minimum and maximum values of Xi, respectively. Table 4 Properties of test data set. Parameter
Unit
Minimum
Maximum
Mean
Standard deviation
Vinj T ΔP ki CBa2+ CSO2-4 kd
PV °c psi md ppm ppm md
2.23 50 75 12.3 250 2750 10.59
57.43 90 200 162.7 2200 2960 90.18
23.069 67.368 143.421 30.528 1378.947 2860.526 20.448
12.777 12.667 44.904 42.580 975.693 106.262 20.985
Table 5 Properties of performance data set. Parameter
Unit
Minimum
Maximum
Mean
Standard deviation
Vinj T ΔP ki CBa2+ CSO2-4 kd
PV °c psi md ppm ppm md
1.89 50 75 12.96 250 2750 11.19
36.03 90 150 162.7 2200 2960 155.3
16.692 73.333 108.333 63.040 1550 2820 45.760
9.614 17.238 31.623 71.470 932.278 100.399 49.008
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Another approach for scaling of data, which is used for normalization of data in this study, is done using mean and standard deviation of training set (Eq. (5)). In this approach inputs and outputs are normalized so that they will have zero mean and unity standard deviation (Demuth et al., 2007). X′i ¼
Xi −μi σi
ð5Þ
where Xi is original value of parameter, X 'i is normalized value of Xi, μi and σi are mean and standard deviation values of Xi, respectively. 4.4. Determination of optimum hidden neural number Two of the parameters which have influence on ANN performance are the number of hidden neurons and the number of hidden layers. In order to determinethe optimum hidden neural number, ANN with one hidden layer and feed forward back propagation algorithm were considered and the number of neurons in first hidden layer was assigned from 1 to 15. Since ANN with one hidden layer may not extract total information from input parameters, ANN with two hidden layers and optimum neural number in the first hidden layer was considered and neural number for second hidden layer was evaluated from 1 to 8. 4.5. Investigation of training functions Another parameter which is very important for ANN training is training function. Therefore, after determination of optimum hidden neural number and evaluation of hidden layer number, ANN with various training functions was run and the best training function was determined. 4.6. Examination of activation function Another effective factor on ANN is activation function in hidden layer. In this part, hyperbolic tangent and logistic sigmoid were investigated as activation functions for hidden layer of ANN. In order to evaluatethe ANN model in all stages, total average absolute deviation (TAAD) was performed which is defined as: abs kmeasured −kpredicted 100 TAAD ð%Þ ¼ ∑ N kmeasured
ð6Þ
Where N is total number of data in each stage, kmeasured is measured permeability and kpredicted is predicted permeability by the ANN model after water injection.
Fig. 3. Investigation of optimum neuron number in first hidden layer.
In the third step, efficiency of various training functions was evaluated (Fig. 5). The ANN model with Levenberg–Marquardt algorithm and Bayesian regularization (BR) as training function had the best performance and the lowest TAAD for train and test data sets. In addition, hyperbolic tangent had better efficiency rather than logistic sigmoid as activation function of ANN in hidden layers. According to the presented investigations, the ANN with two hidden layers was chosen as optimal. The first and second hidden layers include 9 and 3 neurons in their own structures, correspondingly. Also, the ANN training algorithm was Levenberg–Marquardt algorithm with Bayesian regularization (BR) and activation function of hidden layers was hyperbolic tangent. Table 6 presents weights and biases of neurons in the designed ANN. The main ANN model results in training stage is shown in Fig. 6. As can been seen in this figure, there is a very good agreement between experimental data and trained one so that TAAD was 0.69% in this stage. Then, the network was used to simulate data in test stage. Fig. 7(a) and (b) shows results of the main ANN model in test stage for Malaysian and Berea sandstone cores, respectively. The regression constant (R) which also appears in Figs. 6 and 7 shows the agreement of trained or predicted permeability with its measured value. In the ideal situation, when these values are exactly similar, R is equal to 1 (broken line). Moreover, Table 7 presents comparison between measured permeability and predicted permeability by the model for some of the test data and confirms that the main ANN predicted permeability with high accuracy to measured values. TAAD of the main ANN in prediction of permeability after waterflooding was 1.06% in test stage. Fig. 8 shows comparison between predicted of ANN and measured values of permeability for Malaysian and Berea sandstone cores in performance stage. In this stage, TAAD of the model was 2.03%
5. Results and discussion To design ANN model with maximum performance, ANN with one hidden layer was considered in the first step and optimum number of neurons was determined as mentioned already (Fig. 3). As shown in Fig. 3, TAAD for test dataset decreases with increase of neuron number from 1 to 9. So, ANN learning rate has increased with increase of neuron number from 1 to 9 and ANN generalization has improved. On the other hand, TAAD for test dataset increases with the increase of neuron number from 9 to 15. Therefore, increase of neuron number from 9 to 15 cannot improve the ANN generalization. Thus, optimum number of neurons in first hidden layer was equal to 9. In the second step, ANN with two hidden layers was considered so that there were 9 neurons in first hidden layer. Then, the number of neurons in second hidden layer was evaluated (Fig. 4), in which 3 neurons had minimum TAAD. So, the optimum number of neurons in the second hidden layer was 3.
Fig. 4. Investigation of optimum neuron number in second hidden layer.
R. Zabihi et al. / Journal of Petroleum Science and Engineering 78 (2011) 575–581
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Fig. 5. Evaluation of various training functions in training of the ANN model.
which states the ability of the designed ANN model in prediction of permeability after water injection. 6. Conclusions Using actual core flooding data, a neural network model was developed to predict permeability after waterflooding and its reduction due to barium sulfate scaling. A feed forward back propagation algorithm was utilized to design the neural networks. Permeability decline data due to deposition of barium sulfate in 18 sandstone cores of Malaysia and 4 Berea sandstone cores were used to train, test and evaluation the neural networks. Although various parameters have influence on permeability reduction caused by barium sulfate scaling, in this research the more important parameters such as temperature, differential pressure, volume of injected water, initial permeability, barium concentration of formation water and sulfate concentration of injected seawater were considered as input parameter for designing of the model. Based on the studies, which were done in this research, the ANN model with 9 neurons in first hidden layer and 3 neurons in second
Fig. 6. Correlation between predicted permeability and its measured value in training stage for (a) Malaysian and (b) Berea sandstone cores.
hidden layer was defined as the best ANN model, whereas training algorithm of the ANN model was Levenberg–Marquardt algorithm with Bayesian regularization and activation function was hyperbolic tangent. The main ANN model predicted permeability with a total average absolute deviation (TAAD) of 1.06% in test stage. In addition, efficiency of the designed ANN was investigated with new data of Malaysian and Berea sandstone cores. The ANN model predicted permeability with TAAD of
Table 6 Weights and biases of neurons in the designed ANN model. Weight vector First hidden layer neuron
Input layer neuron
1 2 3 4 5 6 1 2 3
Second hidden layer neuron
1
2
3
4
5
6
7
8
9
0.1835 − 0.0765 − 0.2112 0.2195 0.4837 0.3081 − 0.5563 0.2353 − 0.9215
0.0322 − 0.0442 − 0.0290 − 0.5034 0.1070 0.1919 0.5522 − 0.4172 0.8046
1.3280 − 0.5069 − 0.8176 0.2404 1.8818 − 1.6098 − 0.3034 1.3744 − 0.2574
0.4449 0.2057 0.0947 − 1.1643 − 0.0242 − 0.2471 − 8.0216 − 3.3870 4.8278
− 0.0233 − 0.0064 − 0.0361 0.0297 0.0117 − 0.0247 − 0.6412 0.2440 − 0.6277
0.1207 0.0274 0.0435 − 0.0336 0.0537 0.2165 0.5876 − 0.3684 0.6132
0.2339 − 0.0942 − 0.2491 − 0.2826 − 0.4419 − 0.7841 − 0.5919 0.4875 − 0.6952
0.1080 − 0.0452 − 0.1237 − 1.5966 − 0.0923 0.0555 0.5864 0.1639 1.7671
1.9209 − 0.7188 − 0.4141 2.4216 0.8133 − 0.4669 − 2.3231 − 1.4577 0.9890
Bias vector First hidden layer neuron
b
1
2
1.2807
− 1.1514
3
4
5
6
7
8
9
− 2.9232
3.0381
2.5470
− 1.8302
1.3526
− 0.6046
− 4.6936
Second hidden layer neuron
b
1
2
3
− 0.7061
0.1821
− 0.7467
580
R. Zabihi et al. / Journal of Petroleum Science and Engineering 78 (2011) 575–581
Fig. 7. Correlation between predicted permeability and its measured value in test stage for (a) Malaysian and (b) Berea sandstone cores.
2.03% in performance stage. Using this model, permeability and its reduction due to formation of barium sulfate scale can be determined without doing any core flooding test.
Table 7 Comparison between predicted permeability by ANN and measured values for some of test data. Data no.
Vinj (PV)
T ΔP (°C) (psi)
ki (md)
CBa2+ (ppm)
CSO2-4 (ppm)
kmeasured (md)
kpredicted (md)
AAD (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
22.64 44.19 16.82 30.72 44.41 25.16 20.36 57.43 16.51 8.78 14.09 22.97 33.9 26.48 15.84 7.96 42.66 18.77 20.71
50 50 70 70 70 80 80 80 50 50 50 70 70 70 80 60 60 90 90
12.76 13.52 12.4 13.34 12.3 12.85 12.7 12.36 13.84 13.6 13.7 12.53 13.55 12.41 12.83 105.1 105.1 162.7 162.7
2200 2200 2200 2200 2200 2200 2200 2200 250 250 250 250 250 250 250 2200 2200 2200 2200
2960 2960 2960 2960 2960 2960 2960 2960 2750 2750 2750 2750 2750 2750 2750 2960 2960 2960 2960
10.84 11.44 11.25 11.78 10.64 11.47 11.79 10.59 13.03 13.31 13.38 12.02 12.77 11.99 12.65 90.18 40.25 79.52 78.83
11.03 11.39 11.16 11.80 10.71 11.35 11.84 10.62 13.00 13.35 13.33 11.91 12.78 11.95 12.59 90.43 40.22 81.62 80.54
1.73 0.46 0.76 0.13 0.68 1.02 0.42 0.31 0.23 0.32 0.36 0.88 0.04 0.36 0.47 0.27 0.07 2.64 2.17
AADð%Þ ¼
100 200 100 150 200 100 150 200 100 150 200 100 150 200 150 75 75 100 100
abs kmeasured −kpredicted 100 kmeasured
Fig. 8. Predicted of permeability by ANN model and its comparison with measured data for (a) Malaysian sandstone core, (b) Malaysian and (c) Berea sandstone cores in performance stage.
Symbols b CBa2 + CSO2-4 f Ii kd ki kmeasured kpredicted N O P R T Vinj Wi Xi Xmax
bias concentration of barium in formation water concentration of sulfate in injected seawater activation function input vector of neuron damaged permeability initial permeability measured permeability after waterflooding predicted permeability by ANN number of data output of neuron pressure regression constant temperature volume of injected water connection weight original parameter maximum value of original parameter
R. Zabihi et al. / Journal of Petroleum Science and Engineering 78 (2011) 575–581
Xmin X 'i
minimum value of original parameter normalized value of original parameter
Greek letters Δ difference mean value of original parameter μi σi standard deviation of original parameter
Abbreviations ANN Artificial Neural Network AAD Average Absolute Deviation (%) ¼ 100 × abs kmeasured −kpredicted = kmeasured TAAD PV abs
Total Average Absolute Deviation (%) ¼ Pore Volume absolute
100 abs kmeasured −kpredicted ∑ kmeasured N
Units inch (in.) × 2.54 = centimeters (cm) pounds/square inch (psi) × 6.894757E + 03 = pascal (Pa) darcy (d) × 1.0133E-12 = square meter (m 2) Acknowledgments The authors would like to thank National Iranian Oil Company (N.I. O.C.) for supporting this study. The authors are also grateful to Mr. Jafari, Mr. Khatami and Mr. Shadravanan for guidance and assistance. References Bedrikovetsky, P.G., Mackay, E.J., Silva, R.M.P., Patricio, F.M.R., Rosário, F.F., 2009a. Produced water re-injection with seawater treated by sulphate reduction plant: Injectivity decline, analytical model. J. Petrol. Sci. Eng. 68, 19–28. Bedrikovetsky, P., Silva, R.M.P., Daher, J.S., Gomes, J.A.T., Amorim, V.C., 2009b. Welldata-based prediction of productivity decline due to sulphate scaling. J. Petrol. Sci. Eng. 68, 60–70.
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Collins, I.R., 2005. Predicting the location of barium sulfate scale formation in production systems. Paper SPE 68309, 1–6. Crabtree, M., Eslinger, D., Fletcher, P., Johnson, A., King, G., 1999. Fighting scale—removal and preventions. Schlumberger Oilfield Review, pp. 30–35. Demuth, H., Beale, M., Hagan, M., 2007. Neural Network Toolbox 5 User's Guide. The MathWorks Inc., USA. Elgibaly, A.A., Elkamel, A.M., 1998. A new correlation for predicting hydrate formation conditions for various gas mixtures and inhibitors. Fluid Phase Equilib. 152, 23–42. Engelbrecht, A.P., 2007. Computational Intelligence. Wiley Ltd, England. Frenier, W.W., Ziauddin, M., 2008. Formation, removal and inhibition of inorganic scale in the oilfield environment, first ed. SPE Publishing, USA. Groupe, D., 2007. Principle of Artificial Neural Networks, second ed. World Scientific Publishing Co., Singapore. Haykin, S., 1999. Neural Networks a Comprehensive Foundation, Second ed. Prentice Hall International Inc, USA. Khatami, H.R., Ranjbar, M., Schaffie, M., Emady, M.A., 2010. Development of a fuzzy saturation index for sulfate scale prediction. J. Petrol. Sci. Eng. 71, 13–18. Liu, X., Li, J., Zhu, Q., Feng, J., Li, Y., Sun, J., 2009. The analysis and prediction of scale accumulation for water-injection pipelines in the Daqing Oilfield. J. Petrol. Sci. Eng. 66, 161–164. McElhiney, J.E., Sydansk, R.D., Lintelmann, K.A., Benzel, W.M., Davidson, K.B., 2001. Determination of in-situ precipitation of barium sulphate during coreflooding. Paper SPE 68309, 1–11. Merdhah, A.B., 2007. The study of scale formation in oil reservoir during water injection at high-barium and high-salinity formation water. M.Sc. Thesis, Universiti Teknologi Malaysia. Merdhah, A.B., Yassin, A.M., 2008. Study of scale formation due to incompatible water. J. Teknol. 49, 9–26. Merdhah, A.B., Yassin, A.M., 2009. Scale formation due to water injection in Berea sandstone cores. J. Appl. Sci. 18, 3298–3307. Merdhah, A.B., Yassin, A.M., Muherei, M.A., 2010. Laboratory and prediction of barium sulfate scaling at high-barium formation water. J. Petrol. Sci. Eng. 70, 79–88. Moghadasi, J., Müller-Steinhagen, H., Jamialahmadi, M., Sharif, A., 2004. Model study on the kinetics of oil field formation damage due to salt precipitation from injection. J. Petrol. Sci. Eng. 43, 201–217. Mohaghegh, S.D., 2000. Virtual intelligence and its application in petroleum engineering; 1. Artificial neural networks. J. Petrol. Technol. 1–24 September.. Nowroozi, S., Ranjbar, M., Hashemipour, H., Schaffie, M., 2009. Development of a neural fuzzy system for advanced prediction of dew point pressure in gas condensate reservoirs. Fuel Process. Technol. 90, 452–457. Saeedi, A., Camarda, K.V., Liang, J.T., 2007. Using neural networks for candidate selection and well performance prediction in water-shutoff treatments using polymer gels—a field case study. SPE Production & Operation, pp. 417–424. November. Zuluaga, E., Alvarez, H.D., Velasquez, J.D., 2002. Prediction of permeability reduction by external particles invasion using artificial neural networks and fuzzy models. J. Can. Petrol. Technol. 41 (6), 19–24.
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Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
Artificial neural network for permeability damage prediction due to sulfate scaling Reza Zabihi a, e, Mahin Schaffie b, e, Hossein Nezamabadi-pour c, e, Mohammad Ranjbar d, e,⁎ a
Department of Oil and Gas Engineering, Shahid Bahonar University of Kerman, Iran Department of Chemical Engineering, Shahid Bahonar University of Kerman, Iran c Department of Electrical Engineering, Shahid Bahonar University of Kerman, Iran d Department of Mining Engineering, Shahid Bahonar University of Kerman, Iran e Energy and Environmental Engineering Research Centre (EERC), Shahid Bahonar University of Kerman, Iran b
a r t i c l e
i n f o
Article history: Received 31 October 2010 Accepted 8 August 2011 Available online 19 August 2011 Keywords: Permeability damage Artificial neural network Barium sulfate scaling Waterflooding
a b s t r a c t Waterflooding is an important oil recovery method, which is used to maintain reservoir pressure and to increase oil productivity. One of the most common problems caused by waterflooding is inorganic scales formation especially barium sulfate scale, which occurs due to incompatibility of injected seawater and formation water, and causes formation permeability decline. Artificial neural networks (ANNs) are new tools, which application of them in petroleum industry has been extended. Since many factors have influence on permeability reduction due to barium sulfate scaling and relation of them with one another is complicated, in this research a model was presented for prediction of permeability damage due to formation of barium sulfate scale using MATLAB software, artificial neural network and waterflooding experimental data in Malaysian and Berea sandstone cores. To design the optimum ANN model, number of neurons, number of hidden layers and training function were studied. Finally, efficiency of the model was evaluated using new data. The proposed artificial neural network predicted permeability and its reduction during water injection with error about 2 percent. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Waterflooding is one of the enhanced oil recovery (EOR) methods, which is executed for reservoir pressure maintenance and increasing of oil recovery. Scale formation is an important problem of petroleum industry during water injection. The principal mechanisms of scale deposition are pressure drop or temperature variations and mixing of incompatible waters, which cause carbonate and sulfate scales precipitation, respectively. Sulfate scales mainly result from incompatibility between injected water and formation water. When two or more incompatible waters are mixed, they interact chemically and precipitate minerals. Usually seawater is used as injected water in waterflooding operation. Since seawater contains high concentration of sulfate anion and formation water contains high concentration of calcium, strontium and barium cations, mixing of them causes formation of sulfate scales such as calcium sulfate, strontium sulfate and barium sulfate (Crabtree et al., 1999; Frenier and Ziauddin, 2008; Khatami et al., 2010; Moghadasi et al., 2004). Barium sulfate is a kind of sulfate scales, which may precipitate in porous media of oil bearing formation, and causes permeability
⁎ Corresponding author at: Department of Mining Engineering, Shahid Bahonar University of Kerman, P.O. Box: 76175-133, Kerman, Iran. Tel.: + 98 341 2133818; fax: + 98 341 2113663. E-mail address: [email protected] (M. Ranjbar). 0920-4105/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2011.08.007
reduction and formation damage. Precipitation of barium sulfate scale was reported in some oilfields such as Forties and Brae (Collins, 2005; McElhiney et al., 2001). In addition the occurrence results in decrease of oil production and reduces of waterflooding operation efficiency. Although the main reason of barium sulfate scaling is incompatibility of injected and formation waters during hydrocarbon recovery operations, but some other factors such as concentration of sulfate and barium ions, pressure and temperature are effective on barium sulfate precipitation during mixing of formation and injected waters. Formation of barium sulfate increases with concentration of barium and sulfate ions in solution, and causes more permeability reduction. Moreover, pressure and temperature can be efficient and reduction of them may result in additional deposition of barium sulfate in porous media (Crabtree et al., 1999; Frenier and Ziauddin, 2008; Liu et al., 2009; Merdhah et al., 2010). One of the major tests is core flooding test, which is performed to investigate incompatibility of injected and formation waters before performing waterflooding operation. The test demonstrates scale formation effects on porous media and permeability decline by measuring pressure or flow rate reduction based on test method (Merdhah et al., 2010). In recent decades, various researches were done for study of permeability decline due to sulfate scales formation (McElhiney et al., 2001; Merdhah et al., 2010; Moghadasi et al., 2004). Moreover, some models have been presented for prediction of productivity decline and injectivity decline due to sulfate scaling (Bedrikovetsky et al., 2009a, 2009b).
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Preparation of core for coreflooding test is expensive. In addition, accomplishment of the test needs special experimental equipments. Therefore, presentation a model, which can be replaced of such tests and its results, conforms to test results, is more economic and needs less time. In recent years, applications of artificial neural networks especially multilayer neural networks in petroleum industry have been extended. Artificial neural networks (ANNs) are parallel distributed information processing models. The most important advantage of ANN rather than other methods is learning without requirement of given formula and generalization capability for solving new problems, so it can predict nonlinear complex systems (Elgibaly and Elkamel, 1998; Engelbrecht, 2007; Haykin, 1999). The main objective of this study is the designing of ANN model for prediction of permeability decline due to formation of barium sulfate scale in porous media with high accuracy during coreflooding. At first, the paper gives a summary about ANN and multilayer neural networks. Then, the methodology for determination of optimum ANN structure has been presented. Finally, the performance of ANN model in prediction of permeability after water injection has been evaluated using new data of Malaysian and Berea sandstone cores. 2. Multilayer neural networks with back propagation algorithm Artificial neural network is an information processing system which mimics the biological neural network of a human brain and is developed based on mathematical model of biological neural networks (Elgibaly and Elkamel, 1998; Groupe, 2007). In artificial neural networks, information processing is performed in many simple individual processors which are called neurons. When inputs (Ii =[I1, I2,…,In]) are implemented to the neuron, they are multiplied by associated weight of each connection (Wi =[W1, W2,…,Wn]). Then bias (b) of the neuron is added to summation of weighted inputs. Afterwards each neuron applies a linear or nonlinear transfer function (f) on its net input to produce its output (O) (Eq. (1)) (Elgibaly and Elkamel, 1998; Engelbrecht, 2007, Mohaghegh, 2000). O ¼ f ðWi :Ii þ bÞ
ð1Þ
Hyperbolic tangent, logistic sigmoid and linear functions are the most common activation (transfer) functions in artificial neural networks. Hyperbolic tangent and logistic sigmoid functions are used in hidden layer of ANN, whereas linear function is used in output layer of ANN for function estimation. Eqs. (2) and (3) are shown hyperbolic tangent and logistic sigmoid functions, respectively (Demuth et al., 2007; Groupe, 2007; Haykin, 1999). f ðxÞ ¼
1−expð−2xÞ 1 þ expð−2xÞ
ð2Þ
f ðxÞ ¼
1 ; 0:3 b a b 1 1 þ expð−axÞ
ð3Þ
As shown in Fig. 1, an artificial neuron has many inputs whereas only has one output. The output of each previous neuron is multiplied by the associated connection weight between two neurons and then enters the next neuron as an input (Engelbrecht, 2007; Mohaghegh, 2000; Nowroozi et al., 2009). There are different classifications of neural networks based on various properties. One of the usual classifications is based on training algorithms so that neural networks can be divided into two main groups of supervised and unsupervised. Unsupervised neural networks, which are also known as self-organizing maps, are called unsupervised because no feedback is produced during training. In the supervised training algorithm, both inputs and outputs are presented to the network and the network learns based on feedback (Engelbrecht, 2007; Haykin, 1999; Mohaghegh, 2000).
Fig. 1. Schematic of an artificial neuron.
Back propagation is one of supervised training algorithms wherein initially all weights are adjusted randomly in this algorithm, then the neural output is compared with the target in the training dataset and error (difference between target and neuron output) is propagated backward to the network. During this back propagation, the weights are changed to decrease the error. This procedure is continued frequently until the produced outputs are acceptably close to target (Demuth et al., 2007; Mohaghegh, 2000; Saeedi et al., 2007). There are two stages in preparing neural networks: the training stage and the test stage. In training stage, connection weights are adjusted to supply the desired outputs whereas in test stage, accuracy of the trained neural network in predicting the outputs is assessed by examples which have not been seen by the neural network in training stage. Training is done by adjusting the weights until convergence between produced outputs and desired outputs (target) is acquired. Changing weights allows the network to improve its behavior in response to the inputs (Mohaghegh, 2000). Neural networks basis of the supervised training algorithm have the most applications in petroleum industry. Although there are various kinds of neural networks, but networks with feed forward back propagation learning algorithm are the most popular and heavily applied (Nowroozi et al., 2009; Saeedi et al., 2007; Zuluaga et al., 2002). Fig. 2 illustrates a schematic of a multilayer feed forward neural network. Multilayer feed forward neural networks are composed of one input layer, one or more hidden layers, and one output layer. The first hidden layer extracts main features and other hidden layers extract minor features, so the number of hidden layer is related to complexity of the problem. The number of neurons in the input layer corresponds to the number of input variables which are presented to the network as input. The number of neurons in each hidden layer is determined with trial and error. The number of neurons in output layer corresponds to the number of output variables which are desired (Mohaghegh, 2000; Saeedi et al., 2007; Zuluaga et al., 2002).
Fig. 2. Schematic of a multilayer feed forward neural network.
R. Zabihi et al. / Journal of Petroleum Science and Engineering 78 (2011) 575–581 Table 1 Physical and experimental properties of sandstone cores. Sandstone Physical properties of cores core Length Diameter Average Permeability (in.) (in.) porosity (md) (%) Malaysian 3 Berea 3
1 1
34.14 23.50
577
Table 3 Properties of train data set. Experimental properties
Parameter
Unit
Minimum
Maximum
Mean
Standard deviation
Temperature Differential (°C) pressure (psi)
Vinj T ΔP ki CBa2+ CSO2-4 kd
PV °c psi md ppm ppm md
1.89 50 75 12.3 250 2750 10.3
66.42 90 200 162.7 2200 2960 143.34
23.604 67.368 143.421 30.528 1378.947 2860.526 21.283
15.123 12.532 44.426 42.127 965.313 105.131 24.224
12.30–13.84 50–80 105.10–162.70 60–90
100–200 75–100
3. Experimental data
4.2. Selection of random train, test and performance datasets
The data used for this study are obtained from case studies. These studies were conducted to investigate the permeability reduction due to deposition of barium sulfate in Malaysian and Berea sandstone cores. Table 1 presents physical and experimental properties of cores and Table 2 shows composition of synthetic formation waters and seawaters. In these experiments, each core was saturated with synthetic formation waters, and then the flow rate across the core was continuously recorded in constant differential pressure during seawater injection. Finally, the permeability of core was computed with Darcy's linear flow equation. Moreover, effect of various parameters such as temperature, differential pressure and concentration of constituent ions (barium and sulfate) on permeability reduction were perused (Merdhah, 2007; Merdhah et al., 2010; Merdhah and Yassin, 2008; Merdhah and Yassin, 2009).
When a randomized sample is utilized for ANN training, ANN applies information which is more representative of the population. In addition, selection of random test and performance datasets causes better evaluation of ANN efficiency (Saeedi et al., 2007). In this research, 264 data from 18 Malaysian and 4 Berea sandstone cores are used for prediction of permeability decline due to formation of barium sulfate scale. Initially, 228 data from 19 cores is selected for training and testing of ANN. Among 228 data, 188 data for training and 40 data for testing of ANN were utilized randomly. Tables 3 and 4 present properties of train and test datasets, respectively. After determination of ANN with optimum structure, 36 data from 3 sandstone cores were used for investigation of designed ANN efficiency. Table 5 is shown properties of performance dataset. 4.3. Normalization of data
4. Methodology for developing of neural networks During this study, various processes including preprocessing of data, using various training and verification sets, investigation of training functions, determination of optimum hidden neural number and evaluation of hidden layer number were performed for designing ANN with excellent performance. The following paragraphs give short descriptions on the mentioned processes.
In the process of ANN, sometimes raw data may not be suitable to be utilized, thus raw data needs to undergo preprocessing. When values of input and output parameters are extremely low or high, therefore scaling of data should be performed (Saeedi et al., 2007). One approach for scaling of data is performed with following formula (Eq. (4)) which normalizes the data to values between −1 and 1 (Demuth et al., 2007): Xi′ ¼ 2
4.1. Selection of input parameters According to results of previous tests temperature (T), differential pressure (ΔP), volume of injected water (Vinj), initial permeability (ki), concentration of barium in formation water (CBa2+) and concentration of sulfate in injected seawater (CSO2-4 ) were identified as effective parameters in prediction of damaged permeability (kd) after seawater injection (Merdhah, 2007; Merdhah et al., 2010; Merdhah and Yassin, 2008; Merdhah and Yassin, 2009). Therefore, these parameters were considered as inputs of ANN model.
Table 2 Composition of synthetic formation waters and injected seawaters. Component
Sodium Potassium Magnesium Calcium Strontium Barium Chloride Sulfate Bicarbonate
Normal barium formation water (ppm)
High barium formation water (ppm)
Seawater 1 (ppm)
Seawater 2 (ppm)
42707 1972 102 780 370 250 66706 5 2140
42707 1972 102 780 370 2200 67713 5 2140
9749 340 1060 384 5.4 b 0.2 17218 2960 136
10804.5 375.05 1295.25 429.2 6.577 19307.45 2750 158.8
Xi −Xmin −1 Xmax −Xmin
ð4Þ
Where Xi is original value of parameter, X'i is normalized value of Xi, Xmin and Xmax are minimum and maximum values of Xi, respectively. Table 4 Properties of test data set. Parameter
Unit
Minimum
Maximum
Mean
Standard deviation
Vinj T ΔP ki CBa2+ CSO2-4 kd
PV °c psi md ppm ppm md
2.23 50 75 12.3 250 2750 10.59
57.43 90 200 162.7 2200 2960 90.18
23.069 67.368 143.421 30.528 1378.947 2860.526 20.448
12.777 12.667 44.904 42.580 975.693 106.262 20.985
Table 5 Properties of performance data set. Parameter
Unit
Minimum
Maximum
Mean
Standard deviation
Vinj T ΔP ki CBa2+ CSO2-4 kd
PV °c psi md ppm ppm md
1.89 50 75 12.96 250 2750 11.19
36.03 90 150 162.7 2200 2960 155.3
16.692 73.333 108.333 63.040 1550 2820 45.760
9.614 17.238 31.623 71.470 932.278 100.399 49.008
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Another approach for scaling of data, which is used for normalization of data in this study, is done using mean and standard deviation of training set (Eq. (5)). In this approach inputs and outputs are normalized so that they will have zero mean and unity standard deviation (Demuth et al., 2007). X′i ¼
Xi −μi σi
ð5Þ
where Xi is original value of parameter, X 'i is normalized value of Xi, μi and σi are mean and standard deviation values of Xi, respectively. 4.4. Determination of optimum hidden neural number Two of the parameters which have influence on ANN performance are the number of hidden neurons and the number of hidden layers. In order to determinethe optimum hidden neural number, ANN with one hidden layer and feed forward back propagation algorithm were considered and the number of neurons in first hidden layer was assigned from 1 to 15. Since ANN with one hidden layer may not extract total information from input parameters, ANN with two hidden layers and optimum neural number in the first hidden layer was considered and neural number for second hidden layer was evaluated from 1 to 8. 4.5. Investigation of training functions Another parameter which is very important for ANN training is training function. Therefore, after determination of optimum hidden neural number and evaluation of hidden layer number, ANN with various training functions was run and the best training function was determined. 4.6. Examination of activation function Another effective factor on ANN is activation function in hidden layer. In this part, hyperbolic tangent and logistic sigmoid were investigated as activation functions for hidden layer of ANN. In order to evaluatethe ANN model in all stages, total average absolute deviation (TAAD) was performed which is defined as: abs kmeasured −kpredicted 100 TAAD ð%Þ ¼ ∑ N kmeasured
ð6Þ
Where N is total number of data in each stage, kmeasured is measured permeability and kpredicted is predicted permeability by the ANN model after water injection.
Fig. 3. Investigation of optimum neuron number in first hidden layer.
In the third step, efficiency of various training functions was evaluated (Fig. 5). The ANN model with Levenberg–Marquardt algorithm and Bayesian regularization (BR) as training function had the best performance and the lowest TAAD for train and test data sets. In addition, hyperbolic tangent had better efficiency rather than logistic sigmoid as activation function of ANN in hidden layers. According to the presented investigations, the ANN with two hidden layers was chosen as optimal. The first and second hidden layers include 9 and 3 neurons in their own structures, correspondingly. Also, the ANN training algorithm was Levenberg–Marquardt algorithm with Bayesian regularization (BR) and activation function of hidden layers was hyperbolic tangent. Table 6 presents weights and biases of neurons in the designed ANN. The main ANN model results in training stage is shown in Fig. 6. As can been seen in this figure, there is a very good agreement between experimental data and trained one so that TAAD was 0.69% in this stage. Then, the network was used to simulate data in test stage. Fig. 7(a) and (b) shows results of the main ANN model in test stage for Malaysian and Berea sandstone cores, respectively. The regression constant (R) which also appears in Figs. 6 and 7 shows the agreement of trained or predicted permeability with its measured value. In the ideal situation, when these values are exactly similar, R is equal to 1 (broken line). Moreover, Table 7 presents comparison between measured permeability and predicted permeability by the model for some of the test data and confirms that the main ANN predicted permeability with high accuracy to measured values. TAAD of the main ANN in prediction of permeability after waterflooding was 1.06% in test stage. Fig. 8 shows comparison between predicted of ANN and measured values of permeability for Malaysian and Berea sandstone cores in performance stage. In this stage, TAAD of the model was 2.03%
5. Results and discussion To design ANN model with maximum performance, ANN with one hidden layer was considered in the first step and optimum number of neurons was determined as mentioned already (Fig. 3). As shown in Fig. 3, TAAD for test dataset decreases with increase of neuron number from 1 to 9. So, ANN learning rate has increased with increase of neuron number from 1 to 9 and ANN generalization has improved. On the other hand, TAAD for test dataset increases with the increase of neuron number from 9 to 15. Therefore, increase of neuron number from 9 to 15 cannot improve the ANN generalization. Thus, optimum number of neurons in first hidden layer was equal to 9. In the second step, ANN with two hidden layers was considered so that there were 9 neurons in first hidden layer. Then, the number of neurons in second hidden layer was evaluated (Fig. 4), in which 3 neurons had minimum TAAD. So, the optimum number of neurons in the second hidden layer was 3.
Fig. 4. Investigation of optimum neuron number in second hidden layer.
R. Zabihi et al. / Journal of Petroleum Science and Engineering 78 (2011) 575–581
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Fig. 5. Evaluation of various training functions in training of the ANN model.
which states the ability of the designed ANN model in prediction of permeability after water injection. 6. Conclusions Using actual core flooding data, a neural network model was developed to predict permeability after waterflooding and its reduction due to barium sulfate scaling. A feed forward back propagation algorithm was utilized to design the neural networks. Permeability decline data due to deposition of barium sulfate in 18 sandstone cores of Malaysia and 4 Berea sandstone cores were used to train, test and evaluation the neural networks. Although various parameters have influence on permeability reduction caused by barium sulfate scaling, in this research the more important parameters such as temperature, differential pressure, volume of injected water, initial permeability, barium concentration of formation water and sulfate concentration of injected seawater were considered as input parameter for designing of the model. Based on the studies, which were done in this research, the ANN model with 9 neurons in first hidden layer and 3 neurons in second
Fig. 6. Correlation between predicted permeability and its measured value in training stage for (a) Malaysian and (b) Berea sandstone cores.
hidden layer was defined as the best ANN model, whereas training algorithm of the ANN model was Levenberg–Marquardt algorithm with Bayesian regularization and activation function was hyperbolic tangent. The main ANN model predicted permeability with a total average absolute deviation (TAAD) of 1.06% in test stage. In addition, efficiency of the designed ANN was investigated with new data of Malaysian and Berea sandstone cores. The ANN model predicted permeability with TAAD of
Table 6 Weights and biases of neurons in the designed ANN model. Weight vector First hidden layer neuron
Input layer neuron
1 2 3 4 5 6 1 2 3
Second hidden layer neuron
1
2
3
4
5
6
7
8
9
0.1835 − 0.0765 − 0.2112 0.2195 0.4837 0.3081 − 0.5563 0.2353 − 0.9215
0.0322 − 0.0442 − 0.0290 − 0.5034 0.1070 0.1919 0.5522 − 0.4172 0.8046
1.3280 − 0.5069 − 0.8176 0.2404 1.8818 − 1.6098 − 0.3034 1.3744 − 0.2574
0.4449 0.2057 0.0947 − 1.1643 − 0.0242 − 0.2471 − 8.0216 − 3.3870 4.8278
− 0.0233 − 0.0064 − 0.0361 0.0297 0.0117 − 0.0247 − 0.6412 0.2440 − 0.6277
0.1207 0.0274 0.0435 − 0.0336 0.0537 0.2165 0.5876 − 0.3684 0.6132
0.2339 − 0.0942 − 0.2491 − 0.2826 − 0.4419 − 0.7841 − 0.5919 0.4875 − 0.6952
0.1080 − 0.0452 − 0.1237 − 1.5966 − 0.0923 0.0555 0.5864 0.1639 1.7671
1.9209 − 0.7188 − 0.4141 2.4216 0.8133 − 0.4669 − 2.3231 − 1.4577 0.9890
Bias vector First hidden layer neuron
b
1
2
1.2807
− 1.1514
3
4
5
6
7
8
9
− 2.9232
3.0381
2.5470
− 1.8302
1.3526
− 0.6046
− 4.6936
Second hidden layer neuron
b
1
2
3
− 0.7061
0.1821
− 0.7467
580
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Fig. 7. Correlation between predicted permeability and its measured value in test stage for (a) Malaysian and (b) Berea sandstone cores.
2.03% in performance stage. Using this model, permeability and its reduction due to formation of barium sulfate scale can be determined without doing any core flooding test.
Table 7 Comparison between predicted permeability by ANN and measured values for some of test data. Data no.
Vinj (PV)
T ΔP (°C) (psi)
ki (md)
CBa2+ (ppm)
CSO2-4 (ppm)
kmeasured (md)
kpredicted (md)
AAD (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
22.64 44.19 16.82 30.72 44.41 25.16 20.36 57.43 16.51 8.78 14.09 22.97 33.9 26.48 15.84 7.96 42.66 18.77 20.71
50 50 70 70 70 80 80 80 50 50 50 70 70 70 80 60 60 90 90
12.76 13.52 12.4 13.34 12.3 12.85 12.7 12.36 13.84 13.6 13.7 12.53 13.55 12.41 12.83 105.1 105.1 162.7 162.7
2200 2200 2200 2200 2200 2200 2200 2200 250 250 250 250 250 250 250 2200 2200 2200 2200
2960 2960 2960 2960 2960 2960 2960 2960 2750 2750 2750 2750 2750 2750 2750 2960 2960 2960 2960
10.84 11.44 11.25 11.78 10.64 11.47 11.79 10.59 13.03 13.31 13.38 12.02 12.77 11.99 12.65 90.18 40.25 79.52 78.83
11.03 11.39 11.16 11.80 10.71 11.35 11.84 10.62 13.00 13.35 13.33 11.91 12.78 11.95 12.59 90.43 40.22 81.62 80.54
1.73 0.46 0.76 0.13 0.68 1.02 0.42 0.31 0.23 0.32 0.36 0.88 0.04 0.36 0.47 0.27 0.07 2.64 2.17
AADð%Þ ¼
100 200 100 150 200 100 150 200 100 150 200 100 150 200 150 75 75 100 100
abs kmeasured −kpredicted 100 kmeasured
Fig. 8. Predicted of permeability by ANN model and its comparison with measured data for (a) Malaysian sandstone core, (b) Malaysian and (c) Berea sandstone cores in performance stage.
Symbols b CBa2 + CSO2-4 f Ii kd ki kmeasured kpredicted N O P R T Vinj Wi Xi Xmax
bias concentration of barium in formation water concentration of sulfate in injected seawater activation function input vector of neuron damaged permeability initial permeability measured permeability after waterflooding predicted permeability by ANN number of data output of neuron pressure regression constant temperature volume of injected water connection weight original parameter maximum value of original parameter
R. Zabihi et al. / Journal of Petroleum Science and Engineering 78 (2011) 575–581
Xmin X 'i
minimum value of original parameter normalized value of original parameter
Greek letters Δ difference mean value of original parameter μi σi standard deviation of original parameter
Abbreviations ANN Artificial Neural Network AAD Average Absolute Deviation (%) ¼ 100 × abs kmeasured −kpredicted = kmeasured TAAD PV abs
Total Average Absolute Deviation (%) ¼ Pore Volume absolute
100 abs kmeasured −kpredicted ∑ kmeasured N
Units inch (in.) × 2.54 = centimeters (cm) pounds/square inch (psi) × 6.894757E + 03 = pascal (Pa) darcy (d) × 1.0133E-12 = square meter (m 2) Acknowledgments The authors would like to thank National Iranian Oil Company (N.I. O.C.) for supporting this study. The authors are also grateful to Mr. Jafari, Mr. Khatami and Mr. Shadravanan for guidance and assistance. References Bedrikovetsky, P.G., Mackay, E.J., Silva, R.M.P., Patricio, F.M.R., Rosário, F.F., 2009a. Produced water re-injection with seawater treated by sulphate reduction plant: Injectivity decline, analytical model. J. Petrol. Sci. Eng. 68, 19–28. Bedrikovetsky, P., Silva, R.M.P., Daher, J.S., Gomes, J.A.T., Amorim, V.C., 2009b. Welldata-based prediction of productivity decline due to sulphate scaling. J. Petrol. Sci. Eng. 68, 60–70.
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Collins, I.R., 2005. Predicting the location of barium sulfate scale formation in production systems. Paper SPE 68309, 1–6. Crabtree, M., Eslinger, D., Fletcher, P., Johnson, A., King, G., 1999. Fighting scale—removal and preventions. Schlumberger Oilfield Review, pp. 30–35. Demuth, H., Beale, M., Hagan, M., 2007. Neural Network Toolbox 5 User's Guide. The MathWorks Inc., USA. Elgibaly, A.A., Elkamel, A.M., 1998. A new correlation for predicting hydrate formation conditions for various gas mixtures and inhibitors. Fluid Phase Equilib. 152, 23–42. Engelbrecht, A.P., 2007. Computational Intelligence. Wiley Ltd, England. Frenier, W.W., Ziauddin, M., 2008. Formation, removal and inhibition of inorganic scale in the oilfield environment, first ed. SPE Publishing, USA. Groupe, D., 2007. Principle of Artificial Neural Networks, second ed. World Scientific Publishing Co., Singapore. Haykin, S., 1999. Neural Networks a Comprehensive Foundation, Second ed. Prentice Hall International Inc, USA. Khatami, H.R., Ranjbar, M., Schaffie, M., Emady, M.A., 2010. Development of a fuzzy saturation index for sulfate scale prediction. J. Petrol. Sci. Eng. 71, 13–18. Liu, X., Li, J., Zhu, Q., Feng, J., Li, Y., Sun, J., 2009. The analysis and prediction of scale accumulation for water-injection pipelines in the Daqing Oilfield. J. Petrol. Sci. Eng. 66, 161–164. McElhiney, J.E., Sydansk, R.D., Lintelmann, K.A., Benzel, W.M., Davidson, K.B., 2001. Determination of in-situ precipitation of barium sulphate during coreflooding. Paper SPE 68309, 1–11. Merdhah, A.B., 2007. The study of scale formation in oil reservoir during water injection at high-barium and high-salinity formation water. M.Sc. Thesis, Universiti Teknologi Malaysia. Merdhah, A.B., Yassin, A.M., 2008. Study of scale formation due to incompatible water. J. Teknol. 49, 9–26. Merdhah, A.B., Yassin, A.M., 2009. Scale formation due to water injection in Berea sandstone cores. J. Appl. Sci. 18, 3298–3307. Merdhah, A.B., Yassin, A.M., Muherei, M.A., 2010. Laboratory and prediction of barium sulfate scaling at high-barium formation water. J. Petrol. Sci. Eng. 70, 79–88. Moghadasi, J., Müller-Steinhagen, H., Jamialahmadi, M., Sharif, A., 2004. Model study on the kinetics of oil field formation damage due to salt precipitation from injection. J. Petrol. Sci. Eng. 43, 201–217. Mohaghegh, S.D., 2000. Virtual intelligence and its application in petroleum engineering; 1. Artificial neural networks. J. Petrol. Technol. 1–24 September.. Nowroozi, S., Ranjbar, M., Hashemipour, H., Schaffie, M., 2009. Development of a neural fuzzy system for advanced prediction of dew point pressure in gas condensate reservoirs. Fuel Process. Technol. 90, 452–457. Saeedi, A., Camarda, K.V., Liang, J.T., 2007. Using neural networks for candidate selection and well performance prediction in water-shutoff treatments using polymer gels—a field case study. SPE Production & Operation, pp. 417–424. November. Zuluaga, E., Alvarez, H.D., Velasquez, J.D., 2002. Prediction of permeability reduction by external particles invasion using artificial neural networks and fuzzy models. J. Can. Petrol. Technol. 41 (6), 19–24.