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Petroleum 1 (2015) 349e357

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Original article

Prediction of reservoir brine properties using radial basisfunction (RBF) neural network

Afshin Tatar a, **, Saeid Naseri b, Nick Sirach c, Moonyong Lee d, Alireza Bahadori c, *

a Young Researchers and Elite Club, North Tehran Branch, Islamic Azad University, Tehran, Iranb Department of Petroleum Engineering, Ahwaz Faculty of Petroleum Engineering Petroleum University of Technology, Ahwaz, Iranc Southern Cross University, School of Environment, Science and Engineering, PO Box 157, Lismore, NSW, Australiad School of Chemical Engineering, Yeungnam University, Gyeungsan, Republic of Korea

a r t i c l e i n f o

Article history:Received 17 August 2015Accepted 28 October 2015

Keywords:Reservoir brineIntelligent methodDensityEnthalpyVapor pressureRadial basis function neural network

* Corresponding author.** Corresponding author. Tel.: þ98 9398106818.

E-mail addresses: Afshin.Tatar@gmail.com (A. Tatedu.au (A. Bahadori).

Peer review under responsibility of Southwest Pe

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a b s t r a c t

Aquifers, which play a prominent role as an effective tool to recover hydrocarbon from reservoirs,assist the production of hydrocarbon in various ways. In so-called water flooding methods, thepressure of the reservoir is intensified by the injection of water into the formation, increasing thecapacity of the reservoir to allow for more hydrocarbon extraction. Some studies have indicatedthat oil recovery can be increased by modifying the salinity of the injected brine in water floodingmethods. Furthermore, various characteristics of brines are required for different calculations usedwithin the petroleum industry. Consequently, it is of great significance to acquire the exact infor-mation about PVT properties of brine extracted from reservoirs. The properties of brine that are ofgreat importance are density, enthalpy, and vapor pressure. In this study, radial basis functionneural networks assisted with genetic algorithm were utilized to predict the mentioned properties.The root mean squared error of 0.270810, 0.455726, and 1.264687 were obtained for reservoir brinedensity, enthalpy, and vapor pressure, respectively. The predicted values obtained by the proposedmodels were in great agreement with experimental values. In addition, a comparison between theproposed model in this study and a previously proposed model revealed the superiority of theproposed GA-RBF model.

Copyright © 2015, Southwest Petroleum University. Production and hosting by Elsevier B.V. onbehalf of KeAi Communications Co., Ltd. This is an open access article under the CC BY-NC-ND

license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Aquifers, which are rocks containing water, surround themajority of hydrocarbon reservoirs. The effect of the aquifer onreservoirs depends on the extent of the aquifer and the perme-ability of the rock. If these parameters are high enough, the

ar), alireza.bahadori@scu.

troleum University.

ier on behalf of KeAi

niversity. Production and hostcreativecommons.org/licenses/b

aquifer has a greater impact on the reservoir [1]. Aquifers, whichplay a prominent role as an effective tool to recover hydrocarbonfrom reservoirs, assist the hydrocarbon production in variousways such as: peripheral water drive, edge water drive, andbottomwater drive [2]. In so-called water flooding methods, thepressure of the reservoir is intensified by the injection of waterinto the formation, increasing the capacity of the reservoir toallow for more hydrocarbon extraction [1,3]. In the aforemen-tioned methods to recover hydrocarbon, brine would also beproduced in addition to hydrocarbon [4]. Brine production in-creases when the reservoir pressure drops [5]. In some caseseven if the most modern field management techniques areemployed, produced fluid from the reservoir may comprise of90% brine in volume [6]. Salty wet crude, recovered from thereservoir, lacks a good quality and causes some problemsimpeding hydrocarbon production. The brine production canhave some adverse effects on the efficiency of hydrocarbon

ing by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. This is an openy-nc-nd/4.0/).

A. Tatar et al. / Petroleum 1 (2015) 349e357350

production and can affect the extent of depletion. In some cases,wells should be closed in due to inadequate treatment facilities[4]. In addition to mentioned problems, some studies haveindicated that oil recovery can be increased by modifying thesalinity of the injected brine in water flooding methods [7].Furthermore, various characteristics of brines are required fordifferent calculations used within the petroleum industry [8,9].Consequently, it is of great significance to acquire the exact in-formation about PVT properties of brine extracted fromreservoirs.

In recent years, various properties of brines such as density,vapor pressure, and enthalpy have gained attention andseveral studies have been conducted regarding these charac-teristics. Two methods have been utilized by different studiesto find accurate knowledge about different parameters relatingto brine: (1) experimental studies (2) studies to present esti-mative models. However, laboratory approaches are costly andtime consuming. Accordingly, if the experimental equipment isnot available, the latter method is employed [10]. There havebeen several reports presented regarding brine density, whichis considered as a crucial factor in many areas such as fluidinclusion studies, simulating fluid flow, and enhanced oil re-covery. In experimental scope, Ghafri et al. [11] measured thedensity of NaCl (aq) at temperatures between 283 and 472 Kand pressures up to 68.5 MPa and molality of 1.06, 3.16, and6 mol/kg. Kumar [12] reported the density of SrCl2 (aq) for atemperature range of (50e200) �C at 20.27 bar pressure up toa concentration of 2.7 mol/kg. Moreover, there are otherexperimental studies about density in literature [13e17].Concerning predictive models, Hass [18] used the empiricalMasson's rule to develop a model to predict the density ofvapor-saturated NaCl (aq). This model is capable of densityprediction in the range of (75e325) �C and up to a saturationof 7.3 molal. Phillips et al. [18] presented another model fordensity of brine, which is applicable for temperature range of(10e350) �C, molality range of (0.25e5) mol/kg, and pressuresup to 50 MPa. This model can predict the laboratory data witha maximum deviation of ±2%. Concerning enthalpy, Buseyet al. [19] used a calorimeter to find the enthalpies of NaCl (aq)for dilute solutions. They carried out this experiment forconcentrations of (0.1e5) mol/kg and at temperatures from(323e673) K. Comparing the results of the experiment withexisting data in the literature, they indicated that the calo-rimeter can measure enthalpy accurately, which can be appliedto find thermodynamic characteristics. Silvester and Pitzer [8]analyzed the thermodynamic parameters for NaCl (aq) anddeveloped equations to predict them for the temperaturerange of (298.15e573.15) K and molality range of (0e6) mol/kg. They also provided a table for values of thermodynamicparameters including enthalpy. Mayrath and Wood [20]measured the enthalpy of NaCl (aq) for molality in range of(0.1e6) mol/kg and temperature range of (348e476) K. Theyapplied the result to calculate the other parameters. This studyalso showed that flow calorimeter has the ability to measurethe thermodynamic characteristics at high temperatures in aquick and accurate way. Mayrath and Wood [21] also utilizedflow calorimeter to measure the enthalpy of the differentaqueous solutions. Concerning vapor pressure, Gibbard et al.[22] reported the vapor pressures of NaCl (aq) at a temperaturerange of (298e373) K and molality range of (1e6.1) mol/kg.Using the measured data, enthalpy, and freezing-point data,they computed parameters of the modified Debye-Huckel-power-series. They compared the results of this equation

with the experimental data and found good agreement be-tween them. Gibbard and Scatchard [23] conducted a similarinvestigation to Gibbard et al. [22] to measure the vaporpressure of LiCl (aq). Using the data, they presented a 25-parameter quantic equation and the results of the equationwere consist with the experimental data. Liu and Lindsay [24]utilized laboratory approaches to find the vapor pressure ofNaCl (aq) and water, and osmotic coefficients in the concen-tration range of 4 mol/kg to saturation and temperature rangeof (75e300) �C. Using the results of the experiments, theydeveloped a group of equations expressing the free energies ofNaCl (aq) over a wide range of temperatures and concentra-tions. Recently, Bahadori et al. [25] proposed an Arrhenius typefunction to prognosticate the characteristics of reservoir brineincluding density, vapor pressure, and enthalpy at a concen-tration range of (5e25)% salt content by mass and for tem-peratures above 30 �C. This model has eliminated some of thecomplexities of mathematics and allows petroleum engineersto calculate brine characteristics with fewer calculations thanthe previous models.

It is evident from preceding explanations that researchershave attempted to provide precise knowledge about the PVTproperties of brine in order to apply them in computation withother important parameters. However, most of the studies useexperimental or thermodynamic models that require a lot oftime and calculations. In recent years, soft computing ap-proaches such as Support Vector Machines (SVMs), Fuzzy Logic(FL), Genetic Algorithms (Gas), and Artificial Neural Networks(ANNs) have been adopted by different researchers in variousparts of the petroleum industry to eliminate such difficultiesbecause of their great capacity for analysis and modeling ofcomplex subjects [26e31]. Regarding the use of these models inthe prediction of brine PVT properties, Arabloo et al. [2] pro-posed a model employing the least squares support vectormachine technique to estimate liquid saturation vapor pressure,density and enthalpy of formation water. They showed that theresults of this model are in good agreement with experimentaldata.

Although the presented models using different methods tostudy the brine characteristics are valuable, further studies areneeded to provide a more straightforward and accurate estima-tion of brine properties. To achieve this goal, artificial neuralnetwork has been applied in this communication. This studyaims to develop three different intelligent models to predict thereservoir brine properties including density, enthalpy, and vaporpressure at vapor saturation pressure. After the development ofthe models, their accuracy will be investigated. Moreover, theresults will be compared with Bahadori et al. [25] and Arablooet al. [2].

2. Details of intelligent model

Artificial neural networks (ANNs), considered as a branch ofartificial intelligence, have the capacity to learn, store and recallinformation if a suitable database is provided [32]. ANNs,incorporating a set of interconnected nodes, are computationalmodels. Complex relationships can be modeled employing ANNs[33]. Ability for processing a huge data bank and capability togeneralize the relationships between various variables are themain merits of neural networks. In addition to the aforemen-tioned advantages of ANNs, there are some prominent problemswith such approaches such as: noticeable computation stress,and probability to over-fitting [34,35].

A. Tatar et al. / Petroleum 1 (2015) 349e357 351

A powerful strategy in ANN is the radial basis function(RBF) network. A crucial privilege of RBFN is that it possessesonly three layers, making modeling efficient [36]. RBFNs canrespond appropriately to a data set that is not applied in thetraining process [37]. Because of RBFNs own nonlinearapproximation properties, they model complicated relation-ships, and in these processes, perceptron neural networks canconduct the modeling by only employing multiple interme-diary layers [38,39]. When RBFNs are utilized to develop amodel it is necessary to determine the number of processingunits, the hidden unit activation function, a rule to model aspecific task, and an algorithm for the training process tospecify the variables of the network. In the training process,which is to find the RBFN weights, the network variables areoptimized using a set of data in order to fit the outputs of thenetwork to the determined inputs. A cost function, typicallythe mean square error, is used to assess the fit [40,41]. Afterthe training process, the developed RBFN model can be uti-lized with test data that is not adopted in the training process.Online learning allows the network to estimate the new dataset with good precision [39].

The common approximation theory creates a solid basis forRBFN [42]. There are three beneficial properties shared betweenRBFN architecture and classical regularization networks [43,44]:

1. It can approximate any continuous functions that haveseveral statistical variables on a compact domain with anadjustable precision, if the number of units is enough.

2. The result is optimum in minimizing a function which com-putes its oscillation.

3. Because the unknown coefficients are linear, the approxi-mation enjoys the best approximation characteristics.

The RBFN structure is depicted in Fig. 1. It comprises threelayers including the input layer, hidden layer, and output layer.Each node (neuron) acts as a nonlinear activation function andemploys a RBF (f(r)) in hidden layer. An input vector whichundergoes a nonlinear transform in the hidden layer consti-tutes the input layer, that is, the hidden layer is composed ofRBF. The net input for the RBF activation function is the vectordistance between its weight and the input vector multipliedby the relevant bias. The output layer, a linear combiner, mapsthe nonlinearity into a new space. Using an additional neuronin the hidden layer, it is feasible to model the biases of theoutput layer neurons. This additional neuron possesses aconstant activation function f0(r) ¼ 1. Linear optimizationmethod can be applied by RBF to gain a universal optimum

Fig. 1. Schematic representation of RBFN [42].

way to solve the adaptable weights in the minimum MSEsense.

The output of the network for an input pattern x is shown inthe following form:

yiðxÞ ¼XJ2k¼1

wkifðkx� ckkÞ (1)

For i¼ 1,...,J3, where yi(x) represents the i th output of the RBF,wki denotes the connection weight from the k th hidden unit tothe i th output unit, ck is prototype of center of the k th hiddenunit, and k : k indicates the Euclidean norm. The RBF f(.) isusually considered as the Gaussian function [42].

For a set of N pattern pairs of {(xp,yp)}, Equation (1) can bewritten in matrix form:

Y ¼ WTF (2)

where W ¼ [w1,...,wJ3] shows a J2� J3 is weight matrix in whichwi ¼ (u1i,...,uJ2i)T, F ¼ [f1,...,fN] denotes a J2�N matrix,fp ¼ (fp,1,...,fp,J2)T is the output of the hidden layer for the pwthsample, fp;k ¼ fð��xp � ck

��Þ, Y ¼ [y1 y2 yN] indicates a J3�Nmatrix, and yp¼ (yp,1,...,yp,J3)T.

The fluctuation of the value of the radial function is associatedto the distance from a central point. Among several types ofradial basis functions, the most common one is the Gaussianfunction, Equation (1) [37]. In addition to the Gaussian function,some other radial basis can be found in the literature [44e46]. Inthis study, Gaussian function is preferred due to its greatflexibility.

fðrÞ ¼ e�r2

2s2 (3)

where, r> 0 indicates a distance between a data point x and acenter c, s denotes the width parameter which the smoothnessof the interpolating function is governed by this parameter, thatis greater than zero.

More information about RBFNs is provided in a previousstudy, namely, Tatar et al. [47].

3. Result and discussion

3.1. Data acquisition

To develop a valid and reliable model it is necessary toincorporate authentic raw data, which covers a wide range ofvariables. A review of recent studies indicates that at the vaporsaturation pressure, the thermodynamic properties of brineincluding density, enthalpy, and vapor pressure are functions oftemperature and brine salt concentration. The same data setused by Bahadori et al. [25] and Arabloo et al. [2] is incorporatedin this study. The details of the experimental data are listed inTable 1.

Table 1Statistical parameters of the raw experimental data.

Parameter Minimum Maximum Average Standarddeviation

Temperature 38 316 176.7273 88.66405Brine salt content, fraction 0.05 0.25 0.15 0.071362Reported density, kg/m 750 1199 1001.473 107.9569Reported enthalpy, kJ/kg 151.849 1375.058 674.0685 348.9729Reported vapor pressure, kPa 111 12,461 3530.273 3392.843

Table 2The optimal adjusting parameters determined by GA.

Model Spread MNN

Density 1.97 22Enthalpy 0.83 34Vapor pressure 0.57 73

A. Tatar et al. / Petroleum 1 (2015) 349e357352

3.2. Model development

Matlab® 2014a implementation of RBF code was utilized tomodel the thermodynamic properties of the reservoir brine.This code has some adjusting parameters among which themost important ones are two parameters of Spread andMaximum Number of Neuron. The optimal values of theaforementioned parameters lead to the acquiring of the bestperformance of the networks. Although it is possible todetermine the tuning parameters with trial and error, anoptimization algorithm was utilized for this task. Owing to itsgreat flexibility, Genetic Algorithm (GA) was utilized in thisstudy. To develop the GA-RBF models, firstly the data set wasdivided by the ratio of 4:1 for train and test data sets for thetrio density, enthalpy, and vapor pressure. The division wassuch that there is no local accumulation of train or test data.Then, 100 pairs of random values for Spread and MNN were

Fig. 2. The convergent to the optimal model for reservoir brine (a) density, (b) enthalpy

generated. The convergence to the optimal values is depictedin Fig. 2. The optimum values were acquired after 40 genera-tion, which are listed in Table 2.

3.3. Accuracy of the proposed model and validation

3.3.1. Models validationBoth statistical and graphical methods are used in this study

to validate the proposed GA-RBF models.

, and (c) vapor pressure. The vertical values indicate the cost function (MSE value).

(a) (b)

R = 0.99999

700

800

900

1000

1100

1200

1300

700 800 900 1000 1100 1200 1300

Pred

icte

d D

ensi

ty (k

g/m

3 )

Experimental Density (kg/m3)

Train Data

Test Data

Best Fit Line

R = 1

0

200

400

600

800

1000

1200

1400

0 200 400 600 800 1000 1200 1400 1600

Pred

icte

d E

ntha

lpy

(kJ/

kg)

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Train Data

Test Data

Best Fit Line

(c)

R = 1

0

2000

4000

6000

8000

10000

12000

14000

0 2000 4000 6000 8000 10000 12000 14000

Pred

icte

d Va

por

Pres

sure

(kPa

)

Experimental Vapor Pressure (kPa)

Train Data

Test Data

Best Fit Line

Fig. 3. The cross-plot of the performance of the proposed GA-RBF models for (a) density, (b) enthalpy, and (c) vapor pressure.

A. Tatar et al. / Petroleum 1 (2015) 349e357 353

For the graphical method different plots are utilized. Thefirst plot to discuss is the cross-plot. Fig. 3 shows the crossplot for train and test data sets for trio of the proposedmodels. In this plot, the vertical axis is the predicted values bythe GA-RBF method and the horizontal axis shows theexperimental values. Better prediction of the proposed modelsresult in accumulation of data points in close vicinity of the45� line.

The error relative deviation for the proposed models isdepicted in Fig. 4. As it is obvious the relative error deviation forthe proposed models for the reservoir brine density, enthalpy,and vapor pressure is not more than 0.0015, 0.006, and 0.004,respectively.

The error distribution is depicted in Fig. 5. As it is obvious, fortrio models, the error distribution has a symmetric trend aroundthe center of 0.

Four different statistical parameters of correlation factor(R2), Average Absolute Relative Deviation (AARD), StandardDeviation (STD), and Root Mean Squared Error (RMSE) areutilized (Equations (2)e(5)) to investigate the accuracy of theproposed models. The formulation of these parameters is asfollows.

R2 ¼ 1�PN

i¼1�lPredðiÞ � lExpðiÞ

�2PN

i¼1

�lPredðiÞ�lExp

�2 (4)

%AARD ¼ 100N

XNi¼1

�lPredðiÞ � lExpðiÞ

�lExpðiÞ

(5)

RMSE ¼

0BBB@PN

i¼1�lPredðiÞ � lExpðiÞ

�2N

1CCCA

0:5

(6)

STD ¼XNi¼1

�lPredðiÞ � lExpðiÞ

�2N

!0:5

(7)

These parameters represent the accuracy and validity of theproposed models. The values of the mentioned parameters arepresented in Table 3. The RMSE values of 0.270810, 0.455726, and

(a)

(b)

-0.002

-0.0015

-0.001

-0.0005

0

0.0005

0.001

0.0015

0.002

700 800 900 1000 1100 1200 1300

% R

elat

ive

Dev

iatio

n

Experimental Density (kg/m3)

Train DataTest Data

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0 200 400 600 800 1000 1200 1400 1600

% R

elat

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Train DataTest Data

(c)

-0.004

-0.003

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0.003

0.004

0 2000 4000 6000 8000 10000 12000 14000

% R

elat

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iatio

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Experimental Vapor Pressure (kPa)

Train DataTest Data

Fig. 4. The relative error deviation of the proposed GA-RBF models for (a) density, (b) enthalpy, and (c) vapor pressure.

A. Tatar et al. / Petroleum 1 (2015) 349e357354

Fig. 5. The error distribution plot of the proposed GA-RBF models for (a) density, (b) enthalpy, and (c) vapor pressure.

A. Tatar et al. / Petroleum 1 (2015) 349e357 355

1.264687 for density, enthalpy, and vapor pressure indicate thegood performance of the proposed GA-RBF methods.

3.3.2. Comparison with other modelsAt this point the model be will compared with the models

developed by Bahadori et al. [25] and Arabloo et al. [2]. As it was

Table 3Statistical parameters of the proposed models.

R 2̂ AARD STD RMSE N

Density (kg/m3) Train Data 0.999997 0.015685 0.000203 0.198078 44Test Data 0.999981 0.032111 0.000492 0.457985 11All Data 0.999994 0.018971 0.000281 0.27081 55

Enthalpy (kJ/kg) Train Data 0.999999 0.041015 0.000544 0.342832 44Test Data 0.999995 0.157145 0.002061 0.753854 11All Data 0.999998 0.064241 0.001047 0.455726 55

Vapor pressure (kPa) Train Data 1.000000 0.045491 0.000743 1.037936 88Test Data 1.000000 0.088732 0.001377 1.920398 22All Data 1.000000 0.054139 0.000897 1.264687 110

mentioned in the literature review, Bahadori et al. [25] devel-oped an Arrhenius type function to predict the reservoir brineproperties. Arabloo et al. [2] proposed two intelligent modelsbased in Least Square Support Vector Machine (LSSVM) to pre-dict the reservoir brine properties. Comparison of the statisticalvalues is listed in Table 4e6. The RMSE is plotted in Fig. 6 in orderto have a better understanding of the comparison.

Table 4Comparison of the developed models with the predictors proposed by Bahadoriet al. [25] and Arabloo et al. [2] to predict reservoir brine density.

Parameter Dataset Bahadori [25] Arabloo [2] GA-RBF

R2 Train 1.0000 0.999997Test e 0.9999 0.999981All 0.9999 0.9999 0.999994

RMSE Train e 0.341 0.198078Test e 0.481 0.457985All 0.949 0.454 0.27081

Table 6Comparison of the developed models with the predictors proposed by Bahadoriet al. [25] and Arabloo et al. [2] to predict reservoir brine vapor pressure.

Parameter Dataset Bahadori [25] Arabloo [2] GA-RBF

R2 Train e 1.0000 1.000000Test e 1.0000 1.000000All 0.9985 1.0000 1.000000

RMSE Train e 1.371 1.037936Test e 1.642 1.920398All 139.972 1.796 1.264687

Fig. 6. Comparison Between the RMSE of the developed models in this study with the pdensity, (b) enthalpy, and (c) vapor pressure.

Table 5Comparison of the developed models with the predictors proposed by Bahadoriet al. [25] and Arabloo et al. [2] to predict reservoir brine enthalpy.

Parameter Dataset Bahadori [25] Arabloo [2] GA-RBF

R2 Train e 0.9999 0.999999Test e 0.9999 0.999995All 0.9999 0.9999 0.999998

RMSE Train e 0.418 0.342832Test e 0.709 0.753854All 2.199 0.561 0.455726

A. Tatar et al. / Petroleum 1 (2015) 349e357356

The comparison between the previously developed modelsand the models developed in this study indicate the superiorityof the GA-RBF models.

4. Conclusions

Comprehensive and estimative models using radial basisfunction (RBF) neural network as a soft computing methodwere developed to predict some PVT characteristics of reser-voir formation water such as: density, enthalpy, and liquidsaturation pressure. A huge database incorporating a widespectrum of experimental data points was collected from openliterature in order to present and investigate the models. Co-efficient of determination (R2) between the outcome of theproposed models and laboratory data for density, enthalpy,and liquid saturation pressure of formation brine are 0.999994,0.999998, and 1.000000, respectively. To interpret the perfor-mance of the proposed models, the results of the models arecompared with the laboratory data points as well as with othermodels presented in the literature, namely, Bahadori et al. [25]and Arabloo et al. [2]. The models of this study were superiorto compared models, as evidenced by the results of the sta-tistical quality measures. The developed GA-RBF model iscapable of accurate prognostication of PVT characteristics ofthe formation brine without having the complexity of thethermodynamic models and without conducting some costlyand lengthy experiments.

roposed model by Bahadori et al. [25] and Arabloo et al. [2] for reservoir brine (a)

A. Tatar et al. / Petroleum 1 (2015) 349e357 357

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