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Fluid Phase Equilibria 364 (2014) 67– 74

Contents lists available at ScienceDirect

Fluid Phase Equilibria

j ourna l ho me page: www.elsev ier .com/ locate / f lu id

sphaltene precipitation of titration data modeling throughommittee machine with stochastically optimized fuzzy logic andptimized neural network

ojtaba Asoodeha,∗, Amin Gholamib, Parisa Bagheripoura

Islamic Azad University, Birjand Branch, Birjand, IranAbadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadan, Iran

r t i c l e i n f o

rticle history:eceived 5 April 2013eceived in revised form0 December 2013ccepted 17 December 2013vailable online 26 December 2013

eywords:sphaltene precipitationptimized neural networkptimized fuzzy logic

a b s t r a c t

Deposition of asphaltene during crude oil production is a challenging issue in oil industry which causesconsiderable loss of production efficiency as well as imposes negative impacts on production rates.Upon variation in pressure, temperature and crude oil composition, asphaltene begins to precipitateand deposits in reservoir rock and consequently causes formation damage owing to mechanisms ofwettability alteration and pore throat blockage. In the present study a sophisticated method, calledcommittee machine with optimized intelligent systems was utilized to predict the amount of asphal-tene precipitation from experimental titration data. The committee machine is composed of optimizedneural network and optimized fuzzy logic. Stochastic optimization of neural network and fuzzy logicby virtue of hybrid genetic algorithm-pattern search technique significantly enhances their efficiencies.The committee machine provides a further improvement in accuracy of final prediction through inte-

ybrid genetic algorithm-pattern searchechniqueitration data

grating optimized intelligent systems and consequent reaping of their benefits. The committee machinemodel was applied to experimental data reported in the open-source literature. It was observed thatthere was an acceptable agreement between experimental data and committee machine predicted val-ues. Finally, performance of committee machine model was compared with other intelligent systemsused for prediction of asphaltene precipitation. Results showed superiority of committee machine inasphaltene precipitation modeling to optimized neural network and optimized fuzzy logic.

© 2013 Elsevier B.V. All rights reserved.

. Introduction

Crude oil is mixture of different types of hydrocarbons and smallractions of non-hydrocarbon components [1]. SARA separations an example of group type analysis divides crude oil into fourain chemical categories known as saturates, aromatics, resins,

nd asphaltenes based on differences in solubility and polarity2]. Asphaltenes are the heaviest constitutes of oil mixtures thatnclude the most of heteroatoms (oxygen, sulfur, and nitrogen)nd organometallic constituents (nickel, vanadium, and iron) exist-ng in crude oil [3,4]. They comprise the part of crude oil whichemains insoluble by addition of low molecular weight alkanesike n-pentane or n-heptane but soluble in aromatic solvents such

s toluene and benzene. Asphaltenes are originally dissolved inrude oil at the initial reservoir fluid condition as colloid parti-les. Changes in pressure, temperature, and crude oil composition

∗ Corresponding author. Tel.: +98 9395161149.E-mail address: Asoodeh.mojtaba@gmail.com (M. Asoodeh).

378-3812/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.fluid.2013.12.016

destabilize the equilibrium of oil condition and consequently leadto destabilization and precipitation of asphaltene [5]. Precipitationand deposition of asphaltenes may cause complicated and seri-ous problems in both downstream and upstream operations. Indownstream operations, the precipitated asphaltene may depositin transportation pipelines, production facilities, and heat exchang-ers [6]. Furthermore, asphaltenes adsorption onto the upgradingcatalyst surface causes efficiency loss of catalysts [7]. In upstreamoperation, asphaltene instability may occur due to natural deple-tion or enhanced oil recovery (EOR) processes such as injection ofcarbon dioxide [8], nitrogen, methane [9], and water-alternating-gas (WAG) practice [10] that lead to impairment in permeabilityand porosity reduction in reservoirs and thus cause tremendousincrease in operational costs as well as adverse impact on pro-duction rates [11]. Hitherto, three model categories have beengenerally proposed to find out how much and when asphaltene

would be precipitated out of solution. The three employed modelsare molecular thermodynamic models [12], colloidal models [13],and scaling equation based models [14]. A rudimentary descriptionof the above models is given here:

6 ase Equilibria 364 (2014) 67– 74

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(i) Molecular thermodynamic models. This model is premisedupon the assumption that asphaltene is dissolved in crude oiland the crude oil is considered as a real solution. According tothis model, asphaltene precipitation is a thermodynamicallyreversible process [12].

(ii) Colloidal models. This model presumes that asphaltene as solidparticle is dispersed in crude oil through peptizing by resin.Asphaltene precipitation is basically deemed as an irreversibleprocess in this category of models [13].

iii) Models, which are based on scaling equation. This group ofmodels succeeds to find quantitative formulation betweentitration data and amount of asphaltene precipitation byneglecting the complex nature of asphaltenes particles andtheir agglomeration [14].

Recent significant works on asphaltene precipitation proved theuperiority of intelligent systems compared with aforementionedategories. Open-minded petroleum scientists employed neuraletworks [2,15–18] fuzzy logic [19], and support vector machines20] to establish asphaltene precipitation models. Although previ-us studies showed the superiority of intelligent systems comparedith scaling equation and thermodynamic models, individual intel-

igent systems contain some flaws. Neural network is highly atisk of sticking in local minima and clustering-based fuzzy logic isestricted to membership functions with constant variances. How-ver, stochastic optimization of neural network and fuzzy logicodels wipes out aforementioned defects [21]. This study proposes

sophisticated method based on committee machine concept withptimized elements for estimation of asphaltene precipitation. Ele-ents of committee machine include optimized neural network

nd optimized fuzzy logic. Optimization of neural network anduzzy logic models by means of hybrid genetic algorithm-patternearch technique significantly enhances their efficiencies. Further-ore, use of committee machine concept produces an improvedodel which benefits advantages of both optimized neural net-ork and optimized fuzzy logic. In addition to optimization ofeural network and fuzzy logic, hybrid genetic algorithm-patternearch technique was used as combiner in committee machine tontegrate outputs of optimized intelligent systems. Results confirmhat the committee machine performs more efficiently than indi-idual intelligent models. This strategy is discussed in next section.

. Methods descriptions

In this study, three optimization strategies were followed toonstruct a sophisticated model estimating precipitated asphal-ene amount. First, neural network is optimized stochastically byirtue of hybrid genetic algorithm-pattern search technique. Sub-equently, a stochastic optimization is done to tune mean andpread of input membership functions in fuzzy logic model. Finally,

committee machine with optimized elements was assembled toenefit advantages of both optimized neural network and opti-ized fuzzy logic. In all optimization strategies, hybrid genetic

lgorithm-pattern search technique is utilized.

.1. Hybrid genetic algorithm-pattern search technique

Genetic algorithm (GA) is a global optimization method whichtarts with a random population of chromosome-like solutions andvolves to better solutions by applying genetic operations. Geneticlgorithm finds the global minimum of fitness function (function

hich its global minimum is desired). Therefore, a function meant

o be solved should be rearranged such that the global minimumf the rearranged function and the desired point of original func-ion are the same [22]. Evaluation of each chromosome (solution)

Fig. 1. General flowchart of hybrid genetic algorithm-pattern search technique(Asoodeh and Bagheripour [21]).

produces the corresponding fitness score which in turn is usedfor selection procedure and forming the succeeding populationafter applying genetic operations. This process continues until thedesired chromosome is achieved. For better performance of geneticalgorithm, a pattern search technique is integrated with GA. Thismeans, after each generation, all chromosomes are enhanced bymeans of pattern search technique. In the pattern search technique,the algorithm searches a set of points, called a mesh, around thecurrent chromosome. The mesh is formed by adding the currentchromosome to a scalar multiple of a set of vectors called a pat-tern [23]. After evaluating all points according to fitness function,the best solution in the mesh is substituted by current chromo-some. The flowchart of hybrid genetic algorithm-pattern searchtechnique is illustrated in Fig. 1 [21].

2.2. Stochastically optimized neural network

Neural networks (NNs) are computational models, inspired bybrain structure, mechanisms and functions which could be usedfor regression and classification purposes [24]. They can extractthe implicit dependency of input/output data space through thespecific architecture of their processing elements, called neurons.

More details on neural network can be found in several papers[25,26]. Neural network with back-propagation learning algorithmis highly at risk of sticking in local minima. In other words, it is veryprobable that a trained neural network does not mine all implicit

M. Asoodeh et al. / Fluid Phase Equilibria 364 (2014) 67– 74 69

Fig. 2. Schematic diagram of committee machine model. Weights and biases of neural network and membership functions’ parameters of fuzzy logic are optimized bym optimo of comp

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eans of hybrid genetic algorithm-pattern search (GA-PS) technique to constitute

ptimized neural network, fuzzy logic, and optimized fuzzy logic are used as inputs

roduce final output of committee machine.

nformation available in input/output data space due to stickingn local minima. Therefore, the need for a surrogate algorithmor training of neural network is sensed. For this purpose, hybridenetic algorithm-pattern search technique (shown in Fig. 1) istilized to stochastically optimize neural network and to extractptimal values of connection weights and biases. For more detailsefer to Asoodeh and Bagheripour [21].

.3. Stochastically optimized fuzzy logic

Fuzzy inference system or reasoning based on fuzzy logic referso formulating a set of input data into an output data using theuzzy set theory. A fuzzy inference system consists of five majorteps: fuzzification of input variables, application of fuzzy operatorsAND, OR, and NOT) in the rule’s antecedent, implication from thentecedent to the consequent, aggregation of consequent across theules, and defuzzification [27]. This procedure is explained in detailsn a number of papers [28,29]. Different approaches are used fornding the fuzzy sets’ centers (or fuzzification step), including sub-ractive clustering, c-mean clustering, back-propagation algorithmnd etc. however, subtractive clustering is more effective approachmong others in estimating number of fuzzy sets and centers [30].t also reduces computation compared with similar clustering tech-iques [31]. Beside these benefits, there is a major drawback withubtractive clustering. It has no control on variances of Gaussianembership functions. By using hybrid genetic algorithm-pattern

earch technique (Fig. 1) for finding centers and variances of fuzzyets (Gaussian membership functions), the mentioned flaw is elim-nated.

.4. Committee machine

A committee machine has a parallel framework that produces final output by combining the results of individual intelli-ent systems [32]. The committee machine devotes a weightactor to each model (optimized neural network and optimized

ized neural network and optimized fuzzy logic models. Outputs of neural network,mittee machine. These outputs in an optimal linear combination, mined by GA-PS,

fuzzy logic) indicating its involvement in overall prediction ofprecipitated asphaltene amount. Weight factor allocation is donethrough hybrid genetic algorithm-pattern search tool in committeemachine. In other words, hybrid GA-PS technique, as a stochasticoptimization tool, extracts optimal weight corresponding to eachmodel and constitutes an optimal linear combination of intelligentmodels, called committee machine [33,34]. In this study, a com-mittee machine is constructed which is fed by neural network,optimized neural network, fuzzy logic, and optimized fuzzy logic(Fig. 2).

3. Input/output data space

Dataset of this study originates from open-source experimentaldata available in literature [35]. A crude oil sample was deliveredfrom Caoqiao in China (at the Shengli Oil Field). Table 1 demon-strates the compositions and properties of the mentioned sample.The amount of asphaltene precipitation was measured at fourtemperatures in a range between 293 K and 338 K with a tem-perature interval of 15 K. At each temperature, seven n-alkanes(pentane, hexane, heptane, octane, nonane, decane, and dode-cane) were employed as precipitants at various dilution ratios. Allexperiments were implemented at atmospheric pressure (i.e. thepressure was held constant throughout the experimental proce-dure). Asphaltene precipitation is segregated from crude oil andn-alkanes mixture by having the mixture filtered through use ofWhatman No. 42 [35]. In all model constructions, a valid and logi-cal relationship between inputs and outputs is sought. In this study,such a relationship between input/output data space exists. How-ever, for clarification the logical dependency between inputs andoutput is briefly explained. By considering the scaling equation [14],three variables, namely solvent type (solvent molar mass), dilu-

tion ratio (the ratio of the solvent to the oil), and the temperaturein which asphaltene precipitation occurs, have strong effects onformation of asphaltene precipitations. Two opposite ideas aboutthe temperature effect subsist. Some studies have reported more

70 M. Asoodeh et al. / Fluid Phase Equilibria 364 (2014) 67– 74

Table 1Compositions (mol%) and properties of the degassed Caoqiao crude oil and separatorgas [35].

Component Degassed oil Separator gas

CO2 0 2.96N2 0 1.18C1 0 89.37C2 0 3.34C3 0 2.10i-C4 0 0.32n-C4 0 0.26i-C5 0.16 0.22n-C5 0.58 0.15n-C6 1.2 0.12C7+ 98.06C11+ 87.16C7+ molecular weight (g/mol) 503.6C7+ density (at 293 K) 0.9526Reservoir temperature 343Bubble point pressure at 343 K (MPa) 9.8Gas oil ratio (GOR, m3/m3) 30.2Saturates (wt.%) 38.0Aromatics (wt.%) 47.6n-C5 Asphaltene (wt.%) 7.26

aweiIe(iuaap

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Fig. 3. Number of fuzzy rules and mean square error (MSE) of test data versus clus-tering radius for subtractive clustering based fuzzy logic model. Specification of onefor clustering radius produces the best fuzzy model.

Resins (wt.%) 18.6

sphaltene precipitates out of solution as temperature increases,hile others contend that temperature might result in opposite

ffect [36]. In dataset of this study [35], a reverse relationships observed between asphaltene precipitation and temperature.ncrease in carbon number of the paraffinic precipitant will gen-rate less asphaltene precipitation, while increase in dilution ratioratio of solvent volume to weight of crude oil) gives rise to anncrease in asphaltene yield [37]. As a result, dilution ration, molec-lar weight of solvent, and temperature were used as an input datand corresponding amount of precipitated asphaltene was useds output. Table 2 demonstrates the statistics of data used in thisaper.

. Results and discussion

This section is devoted to model construction and evaluation.irstly two different models, called fuzzy logic and neural networkre constructed to estimate precipitated asphaltene amount in Sec-ions 4.1 and 4.3, respectively. Subsequently, a novel stochasticptimization approach is employed to enhance efficiency of fuzzyogic and neural network models using hybrid genetic algorithm-attern search technique in Sections 4.2 and 4.4, correspondingly.

n next stage (Section 4.5), a sophisticated committee machinetrategy is used to improve accuracy of final prediction throughombination of different models constructed in Sections 4.1–4.4.ventually, a comparison among results of different models isrought in Section 4.6 to provide evidences showing how optimiza-ion strategies enhance accuracy of final prediction. Furthermore, aomparison between results of proposed strategy and well-known

caling equation by Hu and Guo [35] is provided in this section tohow superiority of proposed strategy.

able 2tatistical description of datasets used for developing predictive models [35].

Parameter Min Max Average

Dilution ratio (mL/g) 2.3 24.3 12.07955Temperature (K) 293 338 312.4318Molecular weight of solvent (g/mol) 72.15 170.33 116.1417Amount of asphaltene precipitation (wt.%) 0.12 7.06 2.964602

4.1. Fuzzy logic model

At the first stage of this study a fuzzy inference system wasconstructed to estimate asphaltene amount using the Takagi andSugeno model [38]. Optimal number of fuzzy rules was obtainedthrough trial and error. It means different values for clustering radiiwere assigned and performance of constructed model correspond-ing to each clustering radius was evaluated. The model with thehighest performance was chosen as optimal model. Optimal valueof clustering radius defines optimal number of fuzzy rules in con-sequent. Results showed that specification of one for clusteringradius produces the best model estimating precipitated asphal-tene amount (Fig. 3). To assess the reliability of the constructedfuzzy model, test data were used and corresponding precipitatedasphaltene amount was predicted. This assessment is illustrated inFig. 4(a) using the concept of correlation coefficient.

4.2. Stochastically optimized fuzzy model

In next step, the fuzzy model was constructed by means ofhybrid genetic algorithm-pattern search (GA-PS) technique. In thisstage, GA-PS technique is used instead of subtractive clusteringto find optimal parameters of fuzzy formulation between inputsand asphaltene amount. After introducing the mean square errorfunction of fuzzy formulation into GA-PS, appropriate member-ship functions’ parameters are achieved. Run of hybrid GA-PS tool(Fig. 5(a)) leads to finding optimal membership functions whichin turn causes reducing mean square error. After run of GA-PStool, extracted input membership functions are as illustrated inFig. 6. This figure shows that GA-PS tool offers only two mem-bership functions for solvent molar mass in spite of other inputs.Although four freedom possibilities for membership functions ofsolvent molar mass have been defined, GA-PS tool determined twomembership functions. It implies, in addition to optimizing centersand variances of Gaussian membership functions, it is possible tooptimize number of membership functions by GA-PS tools. Fig. 4(b)shows the correlation coefficient between measured and predictedprecipitated asphaltene amount by optimizing fuzzy logic model.

Comparing Fig. 4(a) and (b) it is obvious that optimization of fuzzylogic significantly enhances the precision of final prediction.

M. Asoodeh et al. / Fluid Phase Equilibria 364 (2014) 67– 74 71

Fig. 4. Cross-plots showing the correlation coefficient between measured and predicted asphaltene amount by (a) fuzzy logic, (b) optimized fuzzy logic, (c) neural network,(d) optimized neural network, and (e) committee machine (final model). This figure shows optimized models (b and d) performed better than non-optimized models (a andc (a–d).

4

poctaapals

). Eventually, committee machine (e) performed better than all individual models

.3. Neural network model

In the next step, a three-layered neural network with back-ropagation learning algorithm was constructed. Optimal numberf hidden neurons was assigned through trial and error pro-ess. The neural network is then trained by Levenberg–Marquardtraining function (Fig. 7). The training process ceases in 8th iter-tion (epochs) of back-propagation algorithm. Back-propagationlgorithm has identified this point as global minimum. Different

arameters play significant roles in occurrence of over-fitting in

neural network such as number of data point, number of hiddenayers, number of hidden nodes, type of training function, and etc. inituations where number of data points are not as much as desired

it is possible to prevent over-fitting by regulating other mentionedparameters. Appropriate regulations in this model ensure greatreduction of probability of over-fitting. To evaluate the perfor-mance of neural network, test data were input to constructed modeland precipitated asphaltene amount was predicted. Fig. 4(c) showsthe correlation coefficient between measured and predicted valuesby neural network.

4.4. Stochastically optimized neural network model

In this stage, the constructed neural network is stochasticallyoptimized by virtue of hybrid genetic algorithm-pattern search(GA-PS) technique. The embedded mathematical formulation in

72 M. Asoodeh et al. / Fluid Phase Equilibria 364 (2014) 67– 74

Fig. 5. Plot showing the best and mean fitness values for asphaltene amount esti-mation fitness function after 300 generations for (a) optimized neural network, (b)optimized fuzzy logic, and (c) committee machine.

Fig. 6. Gaussian membership functions extracted by hybrid genetic algorithm-pattern search technique for input data.

Fig. 7. Graph showing mean square of error for training, test, and validation dataversus neural network epochs. Back-propagation algorithm defines 8th epochs asglobal minimum.

neural network is converted to an appropriate fitness function ofGA-PS using the mean square function concept. The fitness func-tion is then introduced to GA-PS technique and optimal weightsand biases of neural network are achieved after run of GA-PS(Fig. 5(b)). In other words, GA-PS technique extracts the optimalvalues of weights and biases such that mean square error of predic-tion reaches its minimum value. Fig. 4(d) illustrates the quality ofoptimized neural network in asphaltene prediction using the con-cept of correlation coefficient. Comparison between Fig. 4(c) and (d)proves the superiority of stochastically optimized neural networkcompared with back-propagation neural network.

4.5. Committee machine model

Up to now, four optimized and non-optimized fuzzy logicand neural network models were constructed through Sections4.1–4.4. These models are now employed as feeds of commit-tee machine to develop an improved model which contains allbeneficial advantages of mentioned models. Committee machineprovides an optimal linear combination of aforementioned mod-els, mined by hybrid genetic algorithm-pattern search technique.GA-PS tool allots an optimal weight factor to each individual modeland minimizes mean square error of prediction through the geneticevolutionary process (Fig. 5(c)). The assigned weight factor indi-cates degree of involvement of each model in committee machineconstruction. To extract optimal weights of contribution of eachmodel in overall prediction of precipitated asphaltene followingfitness function is introduced to genetic algorithm.

MSECM = 1k

k∑

i=1

[w1 × NNi + w2 × FLi + w3 × ONNi

+ w4 × OFLi − Ti]2

This function shows the MSE of committee machine where w1, w2,w3 and w4 are the weight coefficients corresponding to the resultsof neural network, fuzzy logic, optimized neural network, and opti-mized fuzzy logic methods, respectively. Ti is the target value andk is the number of training data. All regulations done before run ofgenetic algorithm are illustrated in Table 3.

Performance of constructed committee machine is shown inFig. 4(e) using the concept of correlation coefficient. Fig. 4 providesa comparison opportunity among different models constructed in

this study. This figure verifies committee machine provides furtherimprovement in final prediction of asphaltene precipitation. A com-parison between measured and predicted precipitated asphalteneamount by committee machine versus sample is shown in Fig. 8.

M. Asoodeh et al. / Fluid Phase Eq

Table 3Regulations done before run of genetic algorithm.

Parameter/setting Type/value Parameter/setting Type/value

Population type Double vector Mutation function GaussianPopulation size 50 Chromosomes Crossover function ScatteredInitial range [0 1] Hybrid function Pattern searchScaling function Rank Generations 1000Selection function Roulette Stall generations 500Elite preservation 2 Fitness tolerance 1.0E−6Crossover fraction 0.6 Time limit Infinity

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ig. 8. A comparison between measured asphaltene amount and predicted valuesy committee machine. Results indicate the predicted values are in good agreementith reality.

his figure states that predicted values by committee machine aren good agreement with reality and confirms the robustness ofommittee machine approach.

.6. Comparison of models

According to recent studies, instead of thermodynamic mod-ls, scaling equations are more common approaches for makinguantitative formulation between titration data and asphaltenerecipitation. Since committee machine, proposed in this study is ofhe same nature as scaling equations owing to using the same inputarameters; it is more appropriate to make a comparison betweenommittee machine and one of the best scaling equations for show-ng superiority of committee machine. Hu and Guo [35] modeled aata set which is employed in this study by the use of scaling equa-ion method. They found scaling equation as a potent predictive

odel which can estimate the amount of asphaltene precipitationith satisfactory accuracy. Table 4 makes a comparison between

ommittee machine, neural network, fuzzy logic, optimized neuraletwork, optimized fuzzy logic, and Hu and Guo scaling equationsing concepts of correlation coefficient and mean square error.

able 4omparison among different models developed in this study and one of the bestcaling equation models proposed by Hu and Guo [35] using concepts of correlationoefficient and mean square error. This table shows committee machine was capablef significantly improving accuracy of final prediction and outperformed Hu and Guocaling equation.

Model Correlation coefficient Mean square error

Hu and Guo [35] 0.964 0.69396Committee machine 0.990 0.02718Fuzzy logic 0.971 0.08195Optimized fuzzy logic 0.974 0.042112Neural network 0.954 0.04446Optimized neural network 0.979 0.031857

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uilibria 364 (2014) 67– 74 73

This table obviously shows superiority of committee machine toHu and Guo scaling equation.

5. Conclusions

Precipitation and deposition of asphaltene is one of the impor-tant issues in oil industry which causes remarkable problemsduring crude oil production. In this study, three optimizationapproaches were followed to develop an improved model for esti-mating asphaltene precipitation. Hybrid genetic algorithm-patternsearch (GA-PS) technique was used as the sole stochastic optimiza-tion method. Results indicated GA-PS is capable of handling bothhighly heterogeneous problems (such as optimizing neural net-work (NN) and optimizing fuzzy logic (FL)) and not-complicatedproblem (such as committee machine construction). Use of GA-PS tool for optimizing NN and FL enhances their efficiencies andforces them to converge into optimal quantitative formulation. Inaddition, committee machine concept enforces further accuracy tooptimized FL and optimized NN through optimal linear combina-tion of them. Employment of the mentioned strategy for asphalteneprecipitation modeling proved that predicted values are in goodagreement with experimental data. Generally, following points areconcluded from the results of this study:

a) Use of hybrid GA-PS technique instead of back-propagationalgorithm for training of neural network ensures achieving ofoptimal quantitative formulation for asphaltene precipitationprediction.

b) Contrary to subtractive clustering, which exclusively manipu-lates mean (center) of Gaussian membership functions, hybridGA-PS is capable of optimizing both mean and variances ofGaussian membership functions. As a result, optimal fuzzy for-mulation would be achieved if GA-PS tool is used instead ofsubtractive clustering.

c) In addition to optimizing means (centers) and variances ofGaussian membership function, it is possible to optimize num-ber of membership functions through the use of GA-PS tool.

d) In conditions where there are multiple options to solve a prob-lem, by little additional computation, a committee machine(CM) could be constructed to achieve more precise results.

e) Although hybrid GA-PS tool converges to global minimumregardless of from which initial condition it starts its run, con-vergence speed of hybrid GA-PS is low. Thus, substituting afaster algorithm for future works is suggested.

(f) Implementation of the propounded strategy provides an accu-rate, quick and cost-effective way of estimating amount ofasphaltene precipitated out of solution.

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