An Adaptive Neuro-fuzzy Approach for Modeling of Water-In-oil Emulsion

8/10/2019 An Adaptive Neuro-fuzzy Approach for Modeling of Water-In-oil Emulsion

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K. Yetilmezsoy et al./ Colloids and Surfaces A: Physicochem. Eng. Aspects 389 (2011) 5062 51

ascertain what types form and howthese might be predicted fromthe available starting oil properties [2] .

Fingas and Fieldhouse [2] published a paper on oil spill emul-sion formation in which more than 300 oils or petroleum productswere studied. These oils were samples of commonly producedand transported oils. It was found that four clearly dened water-in-oil types were formed by oil when mixed with water. Thiswas shown by water resolution over time, by a number of rhe-ological measurements, and by the water-in-oil products visualappearance, both on the day of formation and one week later.Some emulsions were observed for a year or more, with theidentical results. The types are named stable water-in-oil emul-sions, meso-stable water-in-oil emulsions, entrained, and unstablewater-in-oil emulsions or those oils which do not form a water-in-oil type. The differences among the four types are large andare based on appearance, water content measurements and rhe-ological measurements. In a recent study, Ghosh and Rousseau [3]explored several factors related to crystal-stabilized water-in-oilemulsion formation and stability. It was reported that emulsierefcacy and the crystallization behaviour of incorporated lipidscould be signicantly impacted by surfactant interaction withother components in the continuous oil phase or at the interfaceof an emulsion. In another study, Drelich et al. [4] investigatedseveralproperties of emulsions, suchas water droplet sizedistribu-tion, oilwater interfacial tension, and rheological stressstrain, tobetter understand the role of particles in the formation and stabi-lizationof water-in-oilemulsions. Itwasconcluded thattheprocessof droplet formation during emulsication were impeded sincethe fragmentation of water into droplets required more energyin absence of surface-active emulsiers. Moreover, based on thehigh-resolutionFourier transformion cyclotronresonance (FT-ICR)mass spectrometry data, Czarnecki [5] reported that the com-position of the surface material collected from emulsied waterdroplets was different from asphaltenes, resins, and the parentoil. In another study, El Gamal et al. [6] evaluated the role of asphaltene, carbonate (calcite, magnesite, and dolomite), and claycontents (kaoliniteand montmorillonite) on the stability of water-in-oil emulsions and water cut determination was via both FT-IR spectra andphysicochemical properties (APIgravity, kinematic vis-cosity) of the tested samples. The study concluded that API gravityslightly decreased with the increase of asphaltene content from0.1 to 0.7 wt.%, indicating that asphaltene had a little effect on theemulsion density in comparison with that of water. In addition,the increase of the asphaltene content caused a slight decreasein kinematic viscosity due to formation of mechanical barriersvia hydrogen bonding around the water droplets. Furthermore,results of the study indicated that the acid number increased withincreasing asphaltene content due to the increase of donating pro-tons.

The literature reports that water-in-oil types are stabilized bybothasphaltenes and resins [2,7] , but excess resin content (asphal-

tene resin ratio, A/R > about 0.6) destabilizes the emulsion [2] . Ahigh asphaltene content (typically >10%) increases the viscosity of the oil such that a stable emulsion will not form. Viscous oils willonly uptake water as entrained water and will slowly lose much of this water over a period of about one week. Viscous oils (typically>1000 mPa s) will not form stableor meso-stable emulsions. Oils of low viscosity (typically 10,000 mPa s,i.e.HeritageHE05, Point ArguelloComingled,Orinoco,etc.)willalsonotform anyof these water-in-oil types andthus arealso classied

as unstable. Previous studies have found that the most important

factors to emulsion formation are asphaltene and resin contentsand the oil viscosity [2] .

Recently, several new models for the prediction of water-in-oilemulsions formationhavebeen reviewed [7] . Thesemodelsinitiallycalculated the formation of emulsions using a continuous uptakefunction and employing the physical and chemical properties of oil. Since these initial models were developed, the emulsicationproperties of more oils were measured and the properties of someof the oils in the existing set of oils have been re-measured. Thisenabled the models to be re-calculated on over 340 oils. The sta-bility was calculated using a 15-term model with only relativesuccess. The basis of these models is the result of the knowl-edgedemonstrated above-namely that emulsions are stabilized byasphaltenes, with theparticipation of resins. Findings of this groupand other groups show that the entire SARA (saturates, aromatic,resins, and asphaltenes) component affects the formation of emul-sions as the prime stabilizers, asphaltenes and secondarily resins,are only available for emulsion formation when the concentrationof the saturates and aromatics are at a certain level and when thedensity and viscosity are favorable [2] .

Considering the multivariate interactions and complex inter-relationships existing between variables in complex systems, suchas water-in-oil emulsions, the conventional regression techniquesare not capable of capturing the non-linear structure of a spe-cic process as good as the articial intelligence-based models.Therefore, in thelast decade,becauseof their robustness, highcapa-bility of predictive capabilities and exible behaviours to handlethe multi-objective criteria in a straightforward manner, articialintelligence-basedmodeling techniqueshave becomemore sophis-ticated in modeling of several complex environmental problems,such as modeling of high-rate anaerobic wastewater treatmentsystems [8] , prediction of tropospheric ozone concentration lev-els [9] , controlling of anaerobic digestion process [10] , predictionof wastewater treatment plant performance [11] , modeling of thedissolved oxygen uctuations [12] , controlling of leachate ow-rate in a municipal solid waste landll site [13] , prediction of efuent volatile solid and methane yield in an anaerobic digester[14] , forecasting of solid waste composition [15] , modeling leach-ing behaviour of solidied wastes [16] , prediction of biogas andmethane production rates in a pilot-scale anaerobic digestion sys-tem [17] , modeling of completely mixed activated sludge reactorvolume [18] , prediction of iron concentration in sand ltrationefuent [19] , modelingof up-ow anaerobicsludge blanket reactor[20] , and prediction of pressurevolumetemperature propertiesof crude oil systems [21] .

Although several other articial intelligence-based modelingstudies in therecent literature havebeen proposed in solving prob-lems of various real-life engineering problems, to the best of theauthors knowledge, there are no systematic papers specicallydevoted to a study of the implementation of an adaptive neuro-fuzzy model for prediction of water-in-oil emulsions stability, the

most important characteristic of a water-in-oil mixture. Therefore,without requiringa complex model structureand tedious parame-ter estimation procedures, clarication of the place of the presentsubject in the scheme of ANFIS methodology can be considered asa particular eld of investigation to assess the water-in-oil emul-sionsstabilityby combining theadvantages of botharticial neuralnetworks and the fuzzy-logic methodology.

In this study, the development of an articial intelligence mod-eling scheme using the ANFIS methodology was described. Theproposed neuro-fuzzy model deals with resin, saturate, asphal-tene, aromatics, viscosity and density data as the input variableswhichare readily availablefor most of the oils. Thesedataareread-ily available for most oils. On the basis of the above-mentionedfacts, the specic objectives of this study were: (1) to develop

an ANFIS-based neuro-fuzzy model for forecasting of water-in-oil


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52 K. Yetilmezsoy et al. / Colloids and Surfaces A: Physicochem.Eng. Aspects 389 (2011) 5062

emulsionstability based on the empirical data andthe correspond-ing physical knowledge of water-in-oil emulsion formation undervarious visual stability conditions; (2) to compare the proposedarticial intelligence-based model with the conventional multipleregression-basedapproachby means ofvarious descriptive statisti-cal performance indicators suchas R2 , MSE,MAE,RMSE,IA, FV, FA2,etc.; and (3) to verify the prediction performance of the proposedneuro-fuzzy model by several testing data randomly selected fromthe experimental domain.

2. Materials and methods

2.1. Summary of methodology

Detailed methodologywas given in the literature [2] . Emulsionswere created in an end-over-end rotary mixer (associated design)usingarticial seawater(3.3%NaCl). Theapparatus wasmaintainedat 15 C. For those oils that did not form any sign of water uptake,no further studies were carried out. All formation studies werecarried out at least twice to ensure accuracy. Experiments werealso repeated if the analytical results were not within 10%. Sam-pling was found to be important to the repeatability of results as

excess water or oil may be present along with the emulsied prod-uct. The starting oils were analyzed for SARA (saturates, aromatics,resins, andasphaltenes)content, viscosityanddensity.Theemulsi-ed or water-containing samples were analyzed for water contentand a series of rheological studies. Oil property data including theessential input parameters, such as density, viscosityand the SARAcontents used for this study can be found in the literature [2,7] .

Table 1 summarizes the properties of the different types of water-in-oil mixtures that have been classied [2] . This Tableshows that these mixtures are largely distinguishable as soon asthey are created. The types can be easily separated on the basis of duration, column4. This shows thelenth of time that the water-in-oil mixture stays intact. The only two types that are more difcultto separateare stable andmeso-stable emulsions. Themajordiffer-

ence, thatis thebreakdownof themeso-stableemulsionswill occurwithin one week after formation. However, rheological measure-ments after formation show that there are orders-of-magnitudedifferences between the two on the rst day. The greatest differ-encebetweenthestarting oilsfor stableandmeso-stableemulsionsaretheratio of viscosityincrease(averages:stable400,rst dayand850 after one week; meso-stable 7, rst day and 5 after one week)and starting oil resin content (stable 9%; meso-stable 16%) [2] .

The greatest differences between the starting oils for entrainedwater-in-oil compared to stable and meso-stable emulsions arethe viscosity of the starting oil (entrained starting oil averages60,000mPa s compared to 300mPa s for stable emulsions and1300mPa s for meso-stable emulsions). The ratio of viscosityincrease for the water-in-mixture also shows large differences(entrained= 2, rst day and 1 after one week; stable 400, rst dayand 850 after one week; meso-stable 7, rst day and 5 after oneweek). Unstable water-in-oil emulsions are those oils that do notform any type of water-in-oil mixture and are characterized bythe fact that the oil does not hold signicant amounts of water.These oils have viscosities that are very low or very high. The lightproducts include fuels such as diesel fuel. The heavy products aretypically very heavy, viscous oils.

2.2. Adaptive neuro-fuzzy inference system (ANFIS)

Thearticial neural network-based methodshave been success-fully used in various disciplines for modeling, however, the lackof interpretation is one of the major drawbacks of its utilization.

Wieland et al. [22] reported that one of the major shortcomings T

a b l e 1

P r o p e r t i e s a n d c h a r a c t e r i s t i c s o f t h e d i f f e r e n t w a t e r - i n - o

i l t y p e s [ 2 ] .

W a t e r - i n - o i l t y p e

C o l o r

A p p e a r a n c e

D u r a t i o n

T y p i c a l

w a t e r

c o n t e n t ( % )

V i s c o s i t y

i n c r e a s e

f r o m

s t a r t i n g o i l

( o n e d a y )

V i s c o s i t y

i n c r e a s e

f r o m

s t a r t i n g o i l

( o n e w e e k )

T y p i c a l s t a r t i n g o i l p r o p e r t i e s

D e n s i t y

( g / m L )

V i s c o s i t y

( m P a s )

R e s i n

c o n t e n t

( % )

A p h a l t e n e

c o n t e n t

( % )

A / R

r a t i o

S t a b l e e m u l s i o n s

R e d - b r o w n

s o l i d

> 3 0 d a y s

7 5

4 0 0

8 5 0

0 . 9

3 0 0

9

5

0 . 6

M e s o - s t a b l e e m u l s i o n

R e d - b r o w n

v i s c o u s l i q u i d

< 7 d a y s

6 0

7

5

0 . 9

1 3 0 0

1 6

8

0 . 5

E n t r a i n e d w a t e r

B l a c k

s h i n y , v i s c o u s

< 2 d a y s

4 5

2

1

0 . 9 7

6 0 , 0

0 0

1 8

1 2

0 . 7 5

O i l s t h a t d o n o t f o r m a n y w a t e r - i n - o i l m i x t u r e o r U n s t a b l e

O i l s w i t h i n s u f c i e n t a s p h a l t e n e s a n d

v i s c o s i t y

L i k e s t a r t i n g o i l

l i k e s t a r t i n g o i l

< 6

1

1

0 . 8 6

7 0

5

1

0 . 2

O i l s w i t h h i g h a s p h a l t e n e s a n d

v i s c o s i t y

L i k e s t a r t i n g o i l

l i k e s t a r t i n g o i l

< 7

1

1

0 . 9 6

4 9 0 , 0 0 0

2 4

1 4

0 . 5 8


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of articial neural networks (ANNs) is that they do not revealcausal relationships between major system components and thusare unable to improve the explicit knowledge of the user. Anotherproblem is due to the fact that reasoning is only done from theinputs to theoutputs.In cases wherethe opposite is requested (i.e.,deriving inputs leading to a given output), neural networks canhardlybe used. Thereare also some basic aspects of fuzzy inferencesystem that are in need of better understanding [23] . In order toovercome the problematic conditions of ANNs and fuzzy systems,a new system combining the ANNs and the fuzzy system, calledtheadaptivenetwork-based fuzzy inference system, was proposedby Jang [23] . Jang and Sun [24] expressed that adaptive neuro-fuzzy inference systems and the adaptive network-based fuzzyinference systems have the same aim. Therefore, they used adap-tive neuro-fuzzy inference systems (ANFIS) to stand for adaptivenetwork-based fuzzy inference systems.

Operation of the ANFIS looks like feed forward back propagated(FFBP) articial neural network. Consequent parameters are calcu-lated forward while premise parameters are calculated backward[25] . The ANFIS is composed of two parts, antecedent and conclu-sion, whichare connected to each other by fuzzy rules based on thenetwork form. There are two learning methods in neural sectionof the system: hybrid learning method and back propagation (BP)learning method. In fuzzy section, only zero or rst-order Sugenoinference system or Tsukamoto inference system can be used, andoutput variables are obtained by applying fuzzy rules to fuzzy setsof input variables [19,23,2527] :

Rule1 : If x is A1 and y is B1 , then f 1 = p1 x + q1 y + r 1 (1)

Rule2 : If x is A2 and y is B2 , then f 2 = p2 x + q2 y + r 2 (2)

where p1 , p2 , q1 and q2 , are linear parameters, and A1 , A2 , B1 andB2 nonlinear parameters. A two input rst-order Sugeno FIS modelconsisting of twoinputs andrules is depicted in Fig.1a, andthe cor-responding equivalent ANFIS architecture is illustrated in Fig. 1b.The corresponding equivalent ANFIS architecture consists of velayers, namely, a fuzzy layer, a product layer, a normalized layer, adefuzzy layer and a total output layer.

As shown in Fig. 1b, each node in the ANFIS architectureis char-acterized by a node function with xed or adjustable parameters.Model parameters values are determined through the learning ortraining phase of a neural network, while model performance isevaluated by thesufciently tted training and testing data. More-over, model performance evaluates error values such as root meansquare error (RMSE),which are in turnminimized by backpropaga-tionand thehybridlearningalgorithms allowedby ANFIS.As shownthroughtheANFIS architecture, nodes found in thesamelayer havesimilar functions. The following sections discuss the relationshipbetween the output and input of each layer in the ANFIS.

As seen in Fig. 1b, Layer 1 is the fuzzy layer , in which x and yare the input of nodes A1 , A2 , B1 and B2 , respectively. A1 , A2 , B1

and B2 are thelinguistic labels used in the fuzzy theoryfor dividingthe membership functions. Parameters in this layer are referredto as premise parameters. Every node i in Layer 1 is an adaptivenode with a specic function. Nodes in Layer 1 implement fuzzymembership functions, mapping input variables to correspondingfuzzy membership values. The membership relationship betweenthe output and input functions of this layer can be expressed as[28] :

Q 1,i = Ai ( x), for i = 1, 2 or (3)

Q 1,i = B j ( y), for j = 1, 2 (4)

where x (or y) is the input to node i, and Ai (or B j) is the linguisticlabel (such as small, large, etc.) associated with this node function.

In other words, Q 1,i is the membership grade of a fuzzy set A= ( A1 ,

A2 , B1 , or B2 ) and it species the degree to which the given input x (or y) satises a quantier A. Q 1,i denotes the output functions,and Ai ( x) or B j( x) usually denotes the Gaussian curve or thegeneralized bell-shaped membership functions with a maximumequal to 1 and a minimum equal to 0, such as [23,29] :

Ai ( x) =1

1 + [( x c i/a i)2 ]bi

(5)

or

Ai ( x) = exp x c i

a i

2 (6)

where {a i, bi and c i} is the parameter set. As the values of theseparameters change, the bell-shaped functions vary accordingly,thus exhibiting various forms of membership functions on linguis-tic label, Ai. In fact, any continuous and piecewise differentiablefunctions, such as commonly used trapezoidal and triangular-shaped membership functions, can also be used as node functionsin this layer [23] :

Layer 2 is the product layer that consists of two xedcircle nodeslabelled , which multiply theincomingsignals and provides theoutputs of the product. The output w1 and w2 are theweight func-tions of the next layer. The output of this layer is the product of theinput signal, which is dened as follows [19,23,28] :

Q 2,i = w i = Ai ( x) Bi ( y), for i = 1, 2 (7)

where Q 2,i denotes the output of Layer 2. Each node output repre-sents the ring strength of a rule [23,29] .

The third layer is the normalized layer , whosenodes are labelledN. The ith node calculates the ratio of the ith rules ring strengthto the sum of all rules ring strengths. Its function is to normalisethe weight function in the following process [19,23,28,29] :

Q 3,i = w i =wi

w1 + w2, for i = 1, 2 (8)

where Q 3,i denotes the output of Layer 3. The outputs of this layerare called normalized ring strengths.The fourth layer is the defuzzy layer , whose nodes are adaptive.

Every node i in this layer is an adaptive node with a specic func-tion. The output equation is wi( pi x + qi y + r i), where pi, qi and r idenote the linear parameters or so-called consequent parameters of the node. The defuzzy relationship between the input and outputof this layer can be dened as follows [19,23,28,29] :

Q 4,i = w i f i = wi( pi x + qi y + r i), for i = 1, 2 (9)

whereQ 4,i denotes the outputof Layer 4, w i is thenormalized ringstrength from Layer 3, and { pi , qi , r i} is the parameter set of thisnode.

Thefthlayeris the totaloutputlayer ,whosenodeislabelled .

The output of this layer is the total of the input signals, which rep-resents the vehicle shift decision result. The results can be writtenas [19,23,28,29] :

Q 5,i = overalloutput =i

w i f i = iwi f i

iwi(10)

where Q 5,i denotes the output of Layer 5.ANFISallowstousetwo learningalgorithms,such as backpropa-

gationand hybridmethod,whichseeks to minimizesome measureof error,such as RMSE, the root mean of sumof squared differencesbetween observed and predicted data. Hybrid learning rule whichcombines the gradient method and least squares estimate to iden-tify optimal parameters [23] . For the hybrid-learning algorithm, it

can be observed that when the values of the premise parameters


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A1

A 2

B1

B 2

X

X

Y

Y

w 1

w 2

x y

f = p x + q y + r 1 1 1 1

f = p x + q y + r 2 2 2 2

w f + w f1 1 2 2f =

w + w 1 2

= w f + w f1 1 2 2

A1

A 2

B1

B 2

x

y

N

Nw 2

w 1 w 1

w 2

x y

x y

w f1 1

w f2 2

f

Layer 1 (Fuzzy layer)

Layer 2 (Product layer)

Layer 3 (Normalized layer)

Layer 4 (Defuzzy layer)

Layer 5 (Total output layer)

Forward passBackward pass

a

b

Fig. 1. A two input rst-order SugenoFIS model with two rules and (b) equivalent ANFIS architecture.

are xed, the overall output can be expressed as a linear combina-tion of the consequent parameters ( Fig. 1a). The output f in Fig. 1bcan be expressed as follows [29] :

f =w1

w1 + w2 f 1 +

w2w1 + w2

f 2 (11)

f = w1 ( p1 x + q1 y + r 1 ) + w2 ( p2 x + q2 y + r 2 ) (12)

f = w1 xp1 + w1 yq1 + w1 r 1 + w2 xp2 + w2 yq2 + w2 r 2 (13)

which is the linear in the consequent parameters, { p1 , q1 , r 1 , p2 , q2 ,r 2 }.

Although ANN and fuzzy-logic models are the basic areas of articial intelligenceconcept,the ANFIS combines these twometh-ods and uses the advantages of both methods. Since the ANFIS is

an adaptive network which permits the usage of ANN topologytogether with fuzzy logic, it includes the characteristics of bothmethods and also eliminates some disadvantages of their lonelyused case. Therefore, this technique is capable of handling com-plex and nonlinear problems. Even if the targets are not given, theANFIS may reach the optimum result rapidly. In addition, there isno vagueness in ANFIS as opposed to ANNs [25,30] . Moreover, thelearning duration of ANFIS is very short compared to ANN-basedmodels. It implies that ANFIS may reach to the target faster thanANN. Therefore, when a more sophisticated system with a high-dimensional data is implemented, the use of ANFIS instead of ANNwould be more fasterandappropriate to overcome thecomplexityof the problem [25] .

In the ANFIS structure, the implication of the errors is different

from that of the ANN case. In order to nd the optimal result, the

epoch size is not limited. In training of high-dimensional data, theANFIS can give results with the minimum total error compared toANN and fuzzy-logic methods. Moreover, the fuzzy-logic methodseems to be the worst in contrast to others at a rst look, sincethe rule size is limited and the number of membership functionsof fuzzy sets were chosen according to the intuitions of the expert.However, if differenttypesof membershipfunctions andtheir com-binations had been tested and more membership variables andmore rules had been used to enhance the prediction performanceof the proposed diagnosis system, better results would have beenavailable [17,25] .

In this study, the ANFIS (Adaptive Neuro-Fuzzy Inference Sys-tem) Editor GUI (graphical user interface) in the Fuzzy LogicToolbox within the framework of MATLAB V7.0 (The MathWorks,

Inc., USA, R14)software [31] , runningonaCPUN280(Intel

AtomTM

Processor 1.66GHz, 0.99GB of RAM) PC, was used for modelingand simulation purposes. In the computational method, grid par-tition and subtractive clustering fuzzy inference systems weretried to generate the optimum fuzzy rule base sets. Grid partitionmethod includes eight (i.e. trimf , trapmf , gbellmf , gaussmf , gauss2mf , pimf , dsigmf , psigmf ) membership functiontypes.Theoptimumrulenumbers are generally obtained by human experts. This methodmay produce excessivenumber of rules whichis then pruned man-ually or automatically. The subtractive clustering method assumeseach data point is a potential cluster centre and calculates a mea-sure of the likelihood that each data point would dene the clustercentre, based on the density of surrounding data points. The algo-rithm selects the data point with the highest potential to be the

rst cluster centre, removes all data points in the vicinity of the


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Table 2Data statistics of model variables considered in theANFIS modeling.

ANFIS subsets Data statistics Input variables Output variable

Transformed variables Saturates (%) Aromatics (%) Resins (%) Asphaltenes (%) Stability

Exp(Density) ln(Viscosity)

Training set (224 data) Minimum 2.150 0.000 11.200 2.000 0.000 0.000 19.500Maximum 2.767 17.454 98.000 67.700 50.800 37.500 29.100Average 2.471 5.723 56.480 26.196 11.493 5.855 7.732

Range 0.617 17.454 86.800 65.700 50.800 37.500 48.600Testing set(34 data) Minimum 2.244 0.693 24.000 3.000 1.000 0.000 18.400

Maximum 2.737 14.634 96.000 55.000 38.300 23.100 21.000Average 2.468 5.434 56.668 27.535 9.903 5.926 8.465Range 0.493 13.940 72.000 52.000 37.300 23.100 39.400

Overall set(258 data) Minimum 2.150 0.000 11.200 2.000 0.000 0.000 19.500Maximum 2.767 17.454 98.000 67.700 50.800 37.500 29.100Average 2.471 5.685 56.505 26.372 11.284 5.864 7.829Range 0.617 17.454 86.800 65.700 50.800 37.500 48.600

that 14 remaining parameters all contributed to the accuracy of the nal result and that none of them could be cut without affect-ing the outcome of the model. Detailed denitions of the modelcomponents and the corresponding procedures for calculating theregression model can be found in thework of Fingas [35] . The classof theresulting emulsion andits simplied version of this equationare then calculated as follows:

Stability = 60 .78 (0 .294) St (0 .778) Rt + (98 .51)( A/R)t

+ (0 .0286)( V )t 3 + (0.000902)( Rt )3 (0.000143)( At )3

+ (26 .49)( A/R)3t (4.635) ln( V t ) (2 .48) ln( Rt )

(47 .44) ln ( A/R)t (3.096 10 7 )[Exp(V t )]2

(5 .957)[ Exp( A/R)t ]2 (0.596)[log( Dt )]2 (39 .102)[log( A/R)t ]

2

(14)

Stability = 60 .78 (0 .294) A- (0.778) B- + (98 .51) C -+ (0 .0286) D- + (0.000902) E - (0 .000143) F - + (26 .49) G- (4 .635) H - (2 .48) I - (47 .44) J -

(3 .096 10 7 )K - (5 .957) L- (0 .596) M - (39 .102) N - (15)

where S t is the transformed saturate content abbreviated as A-here, Rt is the transformed resin content abbreviated as B- , ( A/R)is the transformed asphaltene/resin ratio abbreviated as C - , (V t )

3 isthe cube of the transformed natural logarithm (ln) of viscosity asabbreviated D- , (Rt )

3 is the cube of the transformed resin contentas abbreviated E - , ( At )

3 is the cube of the transformed asphaltene

content as abbreviated F - , ( A/R)3t is the cube of the transformed

A/R ratio as abbreviated G- , ln ( V t ) is the natural logarithm (ln) of the transformed natural logarithm of viscosity as abbreviated H - ,ln ( Rt ) is thenaturallogarithm (ln) of thetransformed resin content

as abbreviated I -, ln ( A/R)t is the natural logarithm (ln) of trans-formed A/R ratio as abbreviated J -, [Exp(V t )]2 is the exponential of

thetransformednaturallogarithmofviscosity- squared as abbrevi-ated K - , [Exp( A/R)t ]

2 is the exponential of the transformed A/R ratio squared as abbreviated L- , [log( Dt )]

2 is the logarithm (base 10) of exponential of thedensity squared as abbreviated M - , [log( A/R)t ]

2

is the logarithm (base 10)of thetransformed A/R ratio squared asabbreviated N - .

2.5. Measuring of the goodness of the estimate

The visual and numerical methods are used to measure thegoodness of the estimate as an important part of model devel-opment [38] . Kolehmainen [39] reported that although visual

methods make it possible to get an intuitivehold of the model per-formance, whereas numerical methods can provide a more robustground forcomparing andenhancing themodels fromthe scienticpoint of view. In theliterature,variousdescriptivestatistical indica-tors such as coefcient of determination ( R2 ), mean-absoluteerror(MAE), root mean-square error (RMSE), systematic and unsystem-atic RMSE (RMSES and RMSEU, respectively), mean-square error(MSE), index of agreement (IA), the factor of two (FA2), fractionalvariance(FV),proportionof systematic error (PSE), andintercept ( a)and slope ( b) of the adjustedline ( y = bx + a) between observed andpredicted values can be used as helpful tools to describe modelsprediction performance and the error [3944] .

Table 3Thevaluesused to correct oil property input parameters andthe arithmetic to perform themulti-functional transformations [35] .

Oil property input parameter Mathematical form Correction value Description of the arithmetic a

Density Exponential (Exp) 2.5 If exp(density) < 2.5 then Dt =2.5 exp(density)If exp(density)> 2.5 then Dt =exp(density) 2.5

Viscosity Natural logarithm (In) 5.8 If ln (viscosity) < 5.8 then V t = 5.8 ln (viscosity)If ln(viscosity)> 5.8 then V t = ln(viscosity) 5.8

Saturates Standard (%) 45 If saturates < 45 then S t = 45 (saturates)If saturates> 45 then S t =(saturates) 45

Resins Standard (%) 10 If resins< 10 then Rt = 10 (resins)If resins> 10 then Rt = (resins) 10

Asphaltenes Standard (%) 4 If asphaltenes< 4 then At = 4 (asphaltenes)If asphaltenes> 4 then At =(asphaltenes) 4

Asphaltene/Resin ratio ( A/R) Standard 0.6 If ( A/R)< 0.6 then( A/R)t = 0.6 ( A/R)If ( A/R)> 0.6 then( A/R)t = ( A/R) 0.6

a Multi-functional transformations are indicated with t indice.


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Values of range of influence (ROI)

0,520,500,480,460,44 0,620,600,580,560,54

T e s

t i n g

R M S E

2,0

2,2

2,4

2,6

2,8

3,0

3,2

3,4

3,6ROI = 0.45 - 0.60SF = 1.25

AR = 0.50RR = 0.15Minimum testing RMSE = 2.1666(ROI = 0.54)

a

Values of squash factor (SF)

1,361,341,321,301,281,261,241,221,201,18

T e s

t i n g

R M S E

2,0

2,2

2,4

2,6

2,8

3,0

3,2

SF = 1.20 - 1.35

ROI = 0.54 AR = 0.50RR = 0.15Minimum testing RMSE = 2.1666(SF = 1.25)

b

Values of accept ratio (AR)

0,560,540,520,500,480,460,44

T e s

t i n g

R M S E

1,0

1,5

2,0

2,5

3,0

3,5 AR = 0.45 - 0.55ROI = 0.54SF = 1.25RR = 0.15Minimum testing RMSE = 2.1666(AR = 0.50, others have no effect)

c

Values of reject ratio (RR)

0,220,200,180,160,140,120,100,08

T e s

t i n g

R M S E

2,0

2,2

2,4

2,6

2,8

3,0

3,2RR = 0.10 - 0.20ROI = 0.54SF = 1.25

AR = 0.50Minimum testing RMSE = 2.1666(RR = 0.15)

d

Fig. 2. Effect of clustering parameters on prediction performance of theANFIS model.

Table 4Parameters of Gaussian membership functions(MF1MF4) forthe optimum ANFIS structure(ROI= 0.54, SF= 1.25, AR= 0.50, RR= 0.15, epoch number= 21).

Gaussian membership functions: f ( x, ,c )=exp( ( x c )2 /2 2 )

Input1,exp(density) Input2,ln(viscosity) Input3,saturates Input4,aromatics Input 5,resins Input 6,asphaltenes

c c c c c c

MF1 0.1421 2.377 3.365 2.782 16.57 73 12.54 21 9.699 5 7.158 0.9992MF2 0.1469 2.438 3.292 6.618 16.57 44 12.55 37 9.699 12 7.157 7MF3 0.1047 2.641 3.331 10.03 16.57 28 12.55 32 9.698 23 7.161 17MF4 0.0882 2.416 3.339 4.494 16.57 50 12.54 38 9.7 10.8 7.158 0.9992

indicates the variance and c represents Gaussian MFs centre.

and its value in subset is called membership function [45] . In fuzzymodels, the shape of membership functionsof fuzzy sets canbe tri-angular, trapezoidal, bell-shaped, Gaussian, sigmoidal, or anotherappropriate form, depending on the nature of the system being

studied [36,46,47] . Reddy and Raju [48] reported that Gaussianmembership function performed better than trapezoidal function,as it demonstrated a smoother transition in its intervals, and theachieved results were closer to the actual effort. Using trapezoidal

Table 5Fuzzy rule base of theoptimum rst-order Sugenotype ANFIS structure(ROI= 0.54, SF= 1.25, AR= 0.50, RR= 0.15, epoch number= 21).

Rule number Description of fuzzy rule

1 If e xp(density) i s e xp(density)MF1 and I n(viscosity) i s l n (viscosity)MF1 a nd s aturates i s s aturatesMF1 and aromatics i s a romaticsMF1 andresins is resinsMF1 and asphaltenes is asphaltenesMF1 then stability= 12.12 *exp(density)+ 0.349 ln (viscosity) 0.5194 saturates 0.5119 aromatics+ 0.2484 resins + 1.15 asphaltenes + 59.53

2 If exp(density) is exp(density)MF2 and ln(viscosity) is ln(viscosity)MF2 and saturates is saturatesMF2 and aromatics is aromaticsMF2 andresins is resinsMF2 and asphaltenes is asphaltenesMF2 thenstability= 273 exp(density) 0.3048 ln (viscosity) + 2.699 saturates+ 2.818 aromatics+ 3.657 resins+ 4.855 asphaltenes 1022

3 If exp(density) is exp(density)MF3 and ln(viscosity) is ln(viscosity)MF3 and saturates is saturatesMF3 and aromatics is aromaticsMF3 andresins is resinsMF3 and asphaltenes is asphaltenesMF3 then stabil-ity= 30.42 exp(density)+ 0.2781 ln (viscosity) 0.9714 saturates 0.8273 aromatics 0.7427 resins 0.4864 asphaltenes + 148

4 If exp(density) is exp(density)MF4 and ln(viscosity) is ln(viscosity)MF4 and saturates is saturatesMF4 and aromatics is aromaticsMF1 andresins is resinsMF4 and asphaltenes is asphaltenesMF4 then stabil-ity= 196.8 exp(density)+ 12.86 ln(viscosity) 10.66 saturates 9.464 aromatics 9.934 resins + 5.094 asphaltenes + 1448


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Number of training epochs1101009080706050403020100

T e s t

i n g

R M S E

2,08

2,10

2,12

2,14

2,16

2,18

2,20

ROI = 0.54SF = 1.25

AR = 0.50RR = 0.15Number of training epochs = 1 - 100(Minimum testing RMSE = 2.0907)(Optimum number of epoch = 21)

Fig. 3. Dependence between testing RMSE and number of epochs used in trainingprocess.

membership function, a few attributes were assigned the maxi-mum degreeof compatibilitywhen they should have beenassignedlower degrees. To overcome the above limitation and linearity, itwas proposed to use continuous Gaussian membership function[48] . Theeffectiveness of using Gaussianmembership function washighlighted in several other studies [4952] . Based on the above-mentioned facts, in this study, the Gaussian membership functionwas considered for modeling as it is more popular and simple. Inthe present case, input variables were fuzzied with four Gaus-sian membership functions, which were labelled as MF1MF4. Theparameters of these membership functions are given in Table 4 .The rule base of rst-order Sugeno inference system reecting thephysical property of theproposed model along with the respectivemembership functions is given in Table 5 , with the optimum con-sequent parameters obtained after the ANFIS training. The outputvariable is the linear function of the input variables.

inputs inputmf

and

rules outputmf

Aggregatedoutput

output

EXP(Density)

LN(Viscosity)

Saturates

Aromatics

Resins

Asphaltenes

rule 1

rule 2

rule 3

rule 4

MF1

MF2

MF3

MF4

Stability

Fig. 4. Optimum ANFIS model structure for estimation of water-in-oil emulsionsstability (ROI =0.54, SF= 1.25, AR= 0.50, RR= 0.15, epoch number= 21, number of Gaussian

MFs =4).

In this study, theproposed ANFIS model was tested with 34 dif-ferent experimental data used as the testing set randomly selectedfrom theoverall water-in-oil emulsions data set. To verify the pre-diction performance of the proposed the ANFIS model, predictedstability values were also evaluated for different visual stabil-ity conditions, such as oils that form water-in-oil mixtures (i.e.entrained, meso-stable and stable conditions) and oils that do notform water-in-oil mixtures (i.e. unstable conditions including oilswith insufcient asphaltenes and insufcient viscosity, and highlyviscous oils). Fordifferentvisual stabilityconditions andtheoveralltestingdata, ANFIS-based predictedresults withthe correspondingdescriptive statistics are summarized in Table 6 .

As seen in Table 6 , the proposed ANFIS model demonstrated averysatisfactory prediction performance for different visual stabil-ity groups with very high determination coefcients ranging fromabout 0.88 to 0.97. This canbe ascribed to thecapability of articialintelligence-based models capturing the dynamic behaviour andcomplex interactions between multi-input and output variablesin a highly non-linear system, such as formation of water-in-oilmixtures. Based on the obtained results, it is also concluded thatMATLAB environment seems to be quite promising and givesinsight intothe generalizationcapabilityof theANFIS-basedmodel.Testing results showed that themajor inaccuracy lies only with oiltypes that do not form water-in-oil mixtures ( Table 6 ). This is dueto the fact that there are several distinct types of oils or fuels in thisclass (i.e. oils with insufcient asphaltenes and insufcient viscos-ity, and highly viscous oils), and each very different, and becauseof the possible presence of emulsion breakers or asphaltene sus-penders in these oils indicating unstables conditions.

3.2. Comparison of the tested models

In order to assess the performance of the proposed models(ANFIS-based model and the conventional regression model), pre-diction results were assessed by several descriptive statistical


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Table 6ANFIS predicted results fordifferent visual stability conditions (responses for 34 differentexperimental data used as thetesting set).

Visual stability condition Measured stability ANFIS predicted stability R2 Best linear equation

Min Average Max Min Average Max x: measured data y: predicted data

Oils that form water-in-oil mixtures 9.70 +1.10 +21.0 9.40 +2.10 +22.20 0.937 y = 0.9575 x + 1.0737Oils that do notform water-in-oil mixtures 18.40 15.10 5.90 19.70 15.70 6.30 0.878 y = 0.9149 x 1.8602Overall testing data 18.40 8.50 +21.0 19.70 8.40 +22.20 0.967 y = 1.3024 x + 0.3610

Table 7Descriptive performance indices for the overall testing data.

Performance indice Oils that form water-in-oil mixtures Oils that do not form water-in-oilmixtures (unstable conditions)

Overall testing data ( n =34)

ANFIS model MRM a ANFIS model MRM a ANFIS model MRM a

R2 0.937 0.595 0.878 0.447 0.967 0.731R 0.968 0.771 0.937 0.669 0.983 0.855MAE 2.374 5.089 1.152 2.988 1.657 3.854RMSE 2.775 7.056 1.437 4.238 2.091 5.573RMSES 1.117 4.143 0.654 1.729 0.359 2.891RMSEU 2.541 5.193 1.279 2.615 2.064 4.765PSE 0.193 0.636 0.261 0.437 0.0303 0.368MSE 7.702 49.781 2.066 17.959 4.387 31.062IA 0.981 0.855 0.962 0.769 0.991 0.916

FV 0.0111 0.135 0.0238 0.324 0.0489 0.156FA2 1.153 8.889 0.960 1.237 1.039 4.388

a Multiple regression model.

Number of testing outputs4035302520151050

A b s o l u t e r e s i

d u a l e r r o r

-5

0

5

10

15

20

25

ANFIS residualsMultiple regression model residuals

Number of testing outputs4035302520151050

W a t e r - i n - o

i l e m u l s i o n s t a b

i l i t y

-30

-20

-10

0

10

20

30

Measured data point ANFIS modelMultiple regression model

Oils (insufficient asphaltenes andinsufficient viscosity + highly viscous)that do not form water-in-oil mixture

Oils (insufficient asphaltenes andinsufficient viscosity + highly viscous)that do not form water-in-oil mixture

Oils (entrained, meso-stableand stable emulsions) thatform water-in-oil mixture

Oils (entrained,meso-stable andstable emulsions)that form water-in-oilmixture

a

b

Fig. 5. Head-to-head comparison of performance of ANFIS testing outputs and theconventional regression model for different visual stability conditions (responsesfor34 differentexperimental data used as the testing set).

indicators for different visual stability conditions and the overalltesting data. Results are summarized in Table 7 .

As seen in Table 7 , descriptive performance indices such asMAE, MSE, RMSE, IA,FA2 clearly revealedthat the proposed ANFIS-based model produced very small deviations and exhibited asuperior predictive performance on estimation of the water-in-oil emulsions stability compared to the multiple regression-basedmodel. Foroverall testingset, thevalueof determination coefcient(R2 =0.967) indicated that only 3.3% of the total variations werenot explained by the ANFIS model in prediction of the water-in-oil emulsions stability. However, for the multiple regression-basedmodel, about 26.9% of total variations did not t the experi-mental data in estimation of the water-in-oil emulsions stability(R2 = 0.731).Moreover, thelinearregression ( y = ax + b) between theANFIS testing outputs and the corresponding targets showed thattheforecasted datawereobviously agreed withthe measureddata.Theobtained Rvalueswerealso very high ( R= 0.9370.983), imply-inga satisfactory correlation between themeasuredvalues and theANFIS testing outputs. Since the FV and PSE values were found tobe very low for each visual stability condition, it can be concludedthat theANFIS model implies a satisfactory prediction of water-in-oil emulsion formation. To conclude, thehead-to-head comparisongraphs clearly showed that the conventional regression approachdid not yield satisfactory predictions of the stability values as goodas the proposed neuro-fuzzy model ( Fig. 5).

4. Conclusions

The most important characteristic of a water-in-oil mixture ortype is its stability. Properties change very signicantly for eachtype of water-in-oil mixture and stability is the key to under-standing the difference between these types even on the rst day.However, modeling of water-in-oil emulsion formation is very dif-cult becauseof complexity of thedeningvariousdistinct types of oils in different visual stability conditions and their physical inter-actions in a highly non-linear water-in-oil mixture system. Sincethe multiple regression-based models are very complex and time-consuming, in this study, an articial intelligence-based modeling

scheme was conducted as an important objective to develop an


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[47] O.Acaroglu,L.Ozdemir,B.Asbury,A fuzzylogicmodelto predict specic energyrequirement for TBM performance prediction, Tunnel UnderSpace Technol. 23(2008) 600608.

[48] Ch.S. Reddy,K.V.S.V.N. Raju, An improved fuzzy approach forCOCOMOseffortestimationusing gaussian membershipfunction, J. Software 4 (2009)452459.

[49] V. Kreinovich, C. Quintana,R. Lea, O. Fuentes,A. Lokshin, S.Kumar, I. Boricheva,

L. Reznik, What non-linearity to choose? Mathematical foundations of fuzzy

control,in: Proceedings of the1992 InternationalConferenceon FuzzySystemsand Intelligent Control, Louisville, KY, 1992, p. 64.

[50] G. Ulutagay, V. Kreinovich, Density-based Fuzzy Clustering as a First Step toLearning the Rules: Challenges and Possible Solutions, University of Texas atEl Paso, Computer Science Department, Abstracts of 2011 Reports, TechnicalReport UTEP-CS-11-41, August, 2011, p. 20.

[51] S.H. Karimi-Googhari, T.S. Lee, Applicability of adaptive-neuro fuzzy inferencesystems in daily reservoir inow forecasting, Inter. J. Sof. Comput. 6 (2011)7584.

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An Adaptive Neuro-fuzzy Approach for Modeling of Water-In-oil Emulsion