Application of a new approach for modeling the oil field ...

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Application of a new approach for modeling the oil fieldformation damage due to mineral scaling

Alireza Rostami Amin Shokrollahi Khalil Shahbazi Mohammad HosseinGhazanfari

To cite this versionAlireza Rostami Amin Shokrollahi Khalil Shahbazi Mohammad Hossein Ghazanfari Application ofa new approach for modeling the oil field formation damage due to mineral scaling Oil amp Gas Scienceand Technology - Revue drsquoIFP Energies nouvelles Institut Franccedilais du Peacutetrole (IFP) 2019 74 pp62102516ogst2019032 hal-02171462

Application of a new approach for modeling the oil field formationdamage due to mineral scalingAlireza Rostami1 Amin Shokrollahi2 Khalil Shahbazi1 and Mohammad Hossein Ghazanfari2

1Department of Petroleum Engineering Petroleum University of Technology (PUT) PO Box 6198144471 Ahwaz Iran2Department of Chemical and Petroleum Engineering Sharif University of Technology (SUT) PO Box 113659465 Tehran Iran

Received 2 March 2019 Accepted 14 May 2019

Abstract Mineral scaling has been considered a great concern for developing the oil production from theunderground petroleum reservoirs One of the main causes of this phenomenon is known as the chemical incom-patibility of injected brine frequently sea water with the reservoir brine leading to the deposition of varioussupersaturated salts such as calcium carbonate calcium sulfate and barium sulfate In present communicationan evolutionary approach namely Gene Expression Programming (GEP) was employed for rigorous modelingof formation damage by mineral scaling of mixed sulfate salt deposition At first a large databank of damagedpermeability datapoints as a function of injected volume injection flowrate temperature differential pressureand ionic concentrations of the existing chemical species in the porous media was employed In this regard auser-friendly correlation was extended for the first time by the aforementioned technique in the literatureProfessional evaluation of the suggested GEP-based model was implemented by different statistical parametersand appealing visualization tools Having proposed the GEP-based correlation statistical parameters of theAverage Absolute Relative Deviation Percent (AARD) of 0640 and determination coefficient (R2) of0984 was calculated Accordingly it is demonstrated that the proposed model has a superior performanceand great potential for efficient prediction of damaged permeability due to the mixed sulfate salt scaling More-over the implemented outlier diagnosis technique verified the validity of the databank used for modeling aswell as the high robustness of the suggested model was confirmed In conclusion the developed correlationin this work can be of enormous practical value for skillful engineers and scientists in any academic studyand industrial applications dealing with mixed salt deposition

1 Introduction

In water injection scheme deposition of mineral scales hasbeen considered a great challenge for production develop-ment of subterranean petroleum reservoirs [1] Success ofa water injection project can be jeopardized by such scaleand even worse it can be terminated in the worst opera-tional conditions Therefore the efficiency of this processdepending upon the degree of pressure maintenance andthe oil production level can be reduced The amount offormation damage caused by the scaling is chiefly quantifiedby the well-known terms of permeability and porosityreduction [2 3]

The mechanism of permeability reduction leading to theformation damage in the porous media by precipitatedminerals is the deposition of the supersaturated mineralson the pore walls due to the attraction forces between thepore surface area and scale solid particles In such condition

a number of bridges made of the scale particles across thepore throats will be created as well as pore throats blockageby a single particle will strongly happen The degree of for-mation damage is affected by the features of minerals pre-cipitate The morphology and quantity of the growingcrystals on the pore walls are monitored by means of severalfactors including existence of impurities mixing rate tem-perature change and supersaturation owing to the variationin physical conditions (eg chemical incompatibility) [4ndash7]

Chemical incompatibility is classified as the main reasonof the severe oilfield scaling when incompatible waters aremixed While water is injected into the reservoir a reactionbetween the formation minerals and formation water withthe injected fluid will take place resulting in the establish-ment of scale formation through the porous media In otherwords based on the so-called phenomenon of the chemicalincompatibility the reservoir brine and injection water willundergo the strong chemical interactions together leading

Corresponding authors alirezarostamiput2014gmailcom alirezarostamiafpputacir shahbaziputacir

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (httpcreativecommonsorglicensesby40)which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Oil amp Gas Science and Technology - Rev IFP Energies nouvelles 74 62 (2019) Available online atA Rostami et al published by IFP Energies nouvelles 2019 ogstifpenergiesnouvellesfr

httpsdoiorg102516ogst2019032

REGULAR ARTICLEREGULAR ARTICLE

to the precipitation of the supersaturated mineralsPrecipitation of inorganic scale is dependent upon the ioniccomposition of fluid and the nature of scale due to theirinfluence on the molecular or atomic interaction amongstthe involved particles of commingling brines [8ndash11]

Precipitation instigates as long as the nucleation processhave turned on Nucleation is defined as the joining ofatoms attracted for establishing submicron nuclei Thepresence of impurities in fluid makes lower energy neededfor construction of such nuclei than the required energyfor a pure fluid Because the impure components performas proper sites for nucleation in which it is termed asheterogeneous nucleation The process of heterogeneousnucleation extensively takes place where suspendedinorganic particles exist in the formation water coming intocontact with the injection water [4 12ndash16]

Generally sea water is used as the injected fluid in bothsecondary and tertiary oil recovery processes which is richin sulfate and bicarbonate anionic chemical species Despitesea water as the injection fluid high contents of cationicspecies like calcium barium and strontium exist in theformation water which can form diverse types of sulfatescales (ie CaSO4 BaSO4 SrSO4) and carbonate scales(ie CaCO3) in the oilfield Hence sulfate and carbonatescales are recognized as the two key classes of scalingminerals in the oilfields [17 18] Notwithstanding carbonatescaling minerals in which they are extremely reliant onpressure alterations and pH changes sulfate scales com-monly happen on account of incompatible waters mixingand temperature ups and downs [19ndash21] In addition tothe sea water disposal water which is produced in associa-tion with oilfield production can also be recycled and re-injected into the reservoir even though the problem ofchemical incompatibility is still present in this case It isnoteworthy that injection of compatible water resourceswith the connate and formation water is something impos-sible to implement [22 23]

Relatively good solubility of carbonate scaling mineralsmakes the easier inhibition of them by conventionaltechniques such as soaking with suitable acid dissolver thanthe sulfate scales Thus the deposition of such scalesdownstream of wellhead equipment can be resolved throughnonstop injection of an appropriate inhibitor into the trans-portation lines Nevertheless sulfate scales (eg bariumsulfate) have very poor solubility low tendency for reactingwith most acids great hardness and exposures of very littlesurface area at the time of deposition In consequencerestricted number of removal methods is existing in orderto preclude their deposition in sensitive regions For thisreason squeeze treatments of scale inhibitor are usuallyapplied so that sulfate mineral scaling will be inhibited indownstream or upstream of first completion and any mixinglocation [18 20 24 25]

Aiming for evaluating the impact of different parame-ters on scale deposition such as incompatibility of mixingfluids temperature pressure concentration of chemicalspecies present in commingling fluids innumerable investi-gations have been implemented [17 18 26 27] The impactof incompatible waters on the formation of carbonate and

calcium sulfate scales in the synthetic porous media wasextensively studied by Moghadasi et al [2] In continuumstudy more experimental and theoretical investigationswere conducted on the degree of permeability reductionas a measure of formation damage caused by calciumcarbonate and calcium sulfate scaling through mixingcarbonatesulfate rich and calcium rich solutions byMoghadasi et al [28]

Along with the experimental studies a number oftheoretical studies have been focused on the prediction ofmineral scale deposition in porous media [29ndash32] In viewof the hydrodynamic and kinetics of gypsum depositionJamialahmadi et al [33] have instituted a model withoutstanding performance for mathematical modeling ofdeposition and removal of gypsum scaling integrating theimpact of salt supersaturation injection flowrate andtemperature This model may work ineffectively in orderto predict the value of permeability reduction when mixedsalt precipitation happens in solution In more recent yearsSafari and Jamialahmadi [19] initiated a highly nonlinearsimulator on the basis of hydrodynamic kinetics and ther-modynamic laws for modeling deposition of both single salt(ie barium sulfate) and mixed salt (ie strontium sulfatein connection with barium sulfate) during fluid flowthrough porous media Then the authors optimized thekinetic coefficients by means of a hybrid approach namelyPattern Search (PS) algorithm in cooperation with ParticleSwarm Optimization (PSO) technique Finally they con-cluded that their model has an acceptable agreement withthe experimental data with deviations less than 10 [19]Even though the authors carried a great job out theirmodel is highly complex with lots of coefficients to be tunedSo there is a vital requisite for constructing a universalmodel in order to have a rapid and precise estimation of per-meability impairment for mixed sulfate salts scaling duringwater flooding process in the porous media

Genetic based calculations have been commonly used inpetroleum industry as a promising approach in estimatingseveral parameters [34ndash36] In recent years GeneExpression Programming (GEP) [37] as an evolutionaryalgorithm has been increasingly applied in different disci-plines of petroleum and chemical engineering The applica-tion of GEP [37] algorithm resulted in development ofaccurate models in wide varieties of petroleum industrywhich generally gives more precise estimates than the pre-existing models In accordance with GEP [37] mathematicalstrategy the optimum correlation format will be initiatedwithout any assumption about the form of equationSuccessful examples of GEP scheme applied in the litera-ture can be found in the work of several researchers in theopen literature [38 39]

In current study potential application of GEP algo-rithm as a powerful technique is presented so as to preparea possible solution to the all disadvantages earlier men-tioned in the field of mixed sulfate salt scaling in the porousmedia For this reason a large database was adopted fromthe open literature [40ndash43] Afterwards the database isdivided into two sets of training (about 341 datapoints)and testing (about 85 datapoints) According to the

A Rostami et al Oil amp Gas Science and Technology - Rev IFP Energies nouvelles 74 62 (2019)2

training dataset the GEP-based empirically derived equa-tion is developed Throughout various statistical parame-ters and visualization tools the performance of theproposed model is exhibited To the best of authors knowl-edge there is no report on modeling permeability impair-ment as a representative of formation damage caused bymixed sulfate salt scaling in the open literature To thisend the validity of the databank used for modeling isassessed by means of outlier analysis

2 Data gathering

Based on the previous modeling studies in the field of softcomputation it has been demonstrated that developmentof a comprehensive model is crucially in the need of a largedatabase A database with the feature of all-inclusivenessmakes the constructed model to be applied for a widerranges of operational conditions In other words the pro-posed model is not limited to a specific condition and canbe employed for mathematical description of the interestphenomenon at different conditions [35 44ndash62] In pre-sent research 431 datapoints of permeability reductionvalues as a function of temperature differential pressurevolume of injected water initial permeability flowrateand ionic concentrations of cationic species (ie strontiumcalcium and barium) and anionic species (ie sulfate) istaken from the open literature (see Supplementary Mate-rial) [40ndash43] This database is used for developing andtesting the capability of the proposed model For modeldevelopment and examining its capability nearly 80and 20 of the entire database are employed respectivelyThis data division is carried out by a random computa-tional process defined in GEP modeling Table 1 showsthe specification of the employed database for GEPmodeling

3 Gene expression programming

In an attempt to develop the genetic-based calculation themost recent version of genetic computational modelsnamely GEP in which the shortcomings of the precedinggenetic models like Genetic Algorithm (GA) and GeneticProgramming (GP) were modified in GEP computationstrategy [63] Unlike GP approach working with oneelement of Expression Trees (ETs) GEP scheme deals withtwo components including ETs and chromosomesSymbolic ETs are defined as the population individualsand the chromosomes are responsible for encoding andtranslating the candidate solution into a real candidatesolution as ETs [64] In this regard a typical chromosomeis categorized into functions and variableconstant termi-nals The constants are determined by the model programhowever the variables and functions are set as the inputs ofthe model For each gene the inputs and terminals arecorresponded to respectively genersquos head and genersquos tailwhich are related as follows [65]

t frac14 h n 1eth THORN thorn 1 eth1THORNwhere the symbols n h and t denote the largest functionarity the magnitude of genersquos head and the length ofgenersquos tail respectively Setting parameters of the usedGEP strategy for modeling damaged permeability in thisstudy are reported in Table 2 The similar translation pro-cedure is observed in biological genes encoded in DNAswhich are constantly transformed into proteins Owingto the structural features of the chromosomes and repro-duction processes accomplished to this technique unlim-ited modifications of programs are obtained leading toeffective solution to the problem [65] It is confirmed thatthe convergence speed of the GEP mathematical strategyis two to four orders of magnitude larger than that of the

Table 1 Statistical specifications of the database utilized for developing the correlation

Parameter Unit Minimum Average Maximum SDa

DP psi 10000 15012 20000 4085T C 5000 6671 8000 1248Q ccmin 855 1778 3133 537Ki md 1230 1299 1387 052Vinj PV 147 2372 8380 1555CCa2thorn ppm 780 959276 30 000 11 99984CBa2thorn ppm 10 61891 2200 91949CSr2thorn ppm 370 58381 1100 30136CSO2

4ppm 2750 285476 2960 105

Kd md 981 1205 1381 077a SD refers to the standard deviation which is calculated as follows

SD frac14 1N 1

XNifrac141

Si S 2 1

2

A Rostami et al Oil amp Gas Science and Technology - Rev IFP Energies nouvelles 74 62 (2019) 3

GP scheme [66] Figure 1 shows a typical two-genechromosome made of three terminals l m n and fourfunctions ldquo plusmn

p tanhrdquo with its decoded ET and corre-

sponding algebraic expression (correlation) with theKarva language illustration The authors used a well-known and optimized programming code for GEP model-ing to simulate the interested parameter in this study

Developing the correlation

Based on the existing literature concentrated on the mineralscale formation in porous media it is fully understood thatthe amount of permeability reduction as a measure offormation damage is under the influence of several indepen-dent variables These variables include ionic concentrationsof sulfate anion and divalent cations (ie calcium stron-tium barium) differential pressure temperature injectedvolume and flowrate [19 67ndash70] Therefore the proposedGEP-based model is extended as follows

Kd frac14 f P T Q V inj K i CCa2thorn CBa2thorn CSr2thorn CSO24

eth2THORNwhere the symbols Kd Ki DP T Q Vinj CCa2thorn CSr2thorn CBa2thorn and CSO2

4indicate the damaged permeability

initial permeability differential pressure temperatureflowrate injected volume concentration of calcium ionconcentration of strontium ion concentration of barium

ion and concentration of sulfate ion respectively Whenthe decision variables are defined the subsequent mathe-matical strategy will be applied to find the optimalequation format described as below

1 Population preparation Randomly selected individualchromosomal structures throughout checking variousalgebraic operators (eg

p plusmn) and set-

ting terminals as functions of output and input data[71]

2 Predicting fitness value For each individual theObjective Function (OF) is predicted by the subse-quent formulation

OF ieth THORN frac14 100N

XNi

K expdi Kpred

di

K exp

di eth3THORN

In equation (3) N denotes the number of datapointsand the superscripts ldquoexp and predrdquo are in turn rep-resentatives for experimental and predicted values ofpermeability reduction [71]

3 Individuals selection For replacement goals the OFvalue gives an indication to select the appropriateindividuals indicating suitable parents For this rea-son the so-called approach of tournament is utilizedto prepare the adequate variety of dataset during eachgeneration process [64 72]

4 Genetic operations Several operators including repli-cation mutation and inversion are applied for thegoals of genes modification and reproduction In repli-cation stage the chosen chromosomes used in step 3are accurately duplicated [71] Moreover through

Fig 1 A typical two-gene chromosome with its correspondingmathematical expression

Table 2 Setting parameters of the used GEP strategy formodeling damaged permeability in this study

GEP algorithm parameters Value

No of chromosomes 30No of genes 3Head size 7Linking function +Generations without change 2000Fitness function Root Mean Square ErrorInversion 000546Mutation 000138IS transposition 000546RIS transposition 000546One-point recombination 000277Two-point recombination 000277Gene transposition 000277Gene recombination 000277Permutation 000546Constants per gene 10Random chromosomes 00026Type of data Floating pointRandom cloning 000102Operators used +

p EXP INV

LN LOG X2 POW


the application of the mutation operator the effectiveadaptation of individualsrsquo population will be resultedby selecting randomly engaged nodes and replacingsaved information with the random primitive fromthe similar arity The mutation will be applied viaalteration in the magnitudes of genersquos head and genersquostail For this the mutation operation can be occurredeverywhere in chromosomal structure by introducingthe known quantity of mutation rate (pm) By dintof modifying the randomly chosen genersquos head newindividuals are developed in inversion process ofGEP modeling Having defined the well-known termof inversion rate (pi) the efficiency of inversion opera-tion can be evaluated simply [71]

5 Insertion and transposition sequence componentsThese transposable components can be shifted easilyfrom one location to another one in a chromosomalstructure [71] Ferreira [37] introduced three types ofsuch elements in his work as follows short fragmentswith first position function that move to the genersquo root(RIS components) short fragments with either firstposition terminal or first position function moving tothe genersquos head and whole genes that move to startof chromosomes

6 Recombination In this process three different types ofrecombination including one-point two-point andgene randomly select two chromosomes for exchangingcertain materials together resulting in the extension oftwo new chromosomes As a result a new generationwill be established Considering a user-defined stoppingcondition the aforementioned procedure will berepeated until the interested with satisfactory precisionwill be achieved For more information the interestedreaders are suggested to refer the extensive instancesexplained in the work of Ferreira [66]

4 Results and discussions

41 Benchmarks for evaluation of the proposedGEP model

In this section a GEP-based empirically derived equationwill be presented subsequently as a result of applyingGEP mathematical strategy for the first time in this fieldof study For better assessment of the proposed GEP-basedcorrelation various statistical quality measures are utilizedincluding the Average Absolute Relative Deviation Percent(AARD) Root Mean Square Error (RMSE) determina-tion coefficient (R2) and Average Relative DeviationPercent (ARD) One of the most important statistical cri-terion applied in a wide variety of mathematical andnumerical modeling in chemical and petroleum engineeringis calculation of the AARD value The AARD which isdefined as the degree of model precision directly indicatesthe total magnitude of the estimation error relative to thetarget experimental data The higher value of AARDshows the lower model accuracy The quantity of RMSEillustrates the amount of inaccuracy happened in the pro-cess of modeling In other words it shows the magnitude

of deviation between the real and simulated data The otherimportant and widely used statistical parameter is R2 whichshows the goodness of fit or it displays how well the modelestimates are matched with the actual data When thevalue of R2 approaches to unity the most satisfactoryagreement will be achieved The final benchmark is theARD value which shows the quality of deviation distribu-tion in the vicinity of zero deviation The lower ARDvalue near to zero confirms the more compacted concentra-tion of error distribution around the zero deviation In addi-tion to the parametric evaluation of the proposed modeldiverse graphical illustrations are utilized to confirm thesuperiority and large capability of the GEP-based empiri-cally derived correlation The most significant of all applieddiagrams are crossplot index plot and error distributionplot which will be represented subsequently in this study

42 Assessment of the proposed GEP model

Based on the GEP processing a user-friendly equation isdeveloped which can be used for fast estimation of damagedpermeability by this novel approach for the first time in thebulk of research have been paying attention to the forma-tion damage caused by mineral scaling The proposedempirically-derived GEP equation is given as below

log Kdeth THORN frac14 A1 thorn A2 thorn A3 eth4THORN

A1 frac14T V inj

Q K ieth THORNQ T 2 log CBa2thorn thorn C Sr2thorn thorn CCa2thorn thorn C SO2

4

277550702075275

n o

eth5THORN

A2 frac14407928649580713Q2

P 243561403505515eth THORN2 00656999407983034 T 146554080471316f g

eth6THORN

A3 frac14 00266417196782303 ln 302487101618176 QV inj

2

eth7THORNwhere the units of Kd Ki DP T Q Vinj CCa2thorn CSr2thorn CBa2thorn and CSO2

4in the above equations are md md psi

C ccmin PV ppm ppm ppm and ppm respectivelyThe statistical details of the proposed GEP-derived corre-lation for the individual sets of training test and totaldatabase are shown in Table 3 Based on this table thevalues of R2 ARD AARD and RMSE for the totaldatabase are 09843 00355 06409 and 00967respectively It means that the AARD lt 1 and R2 gt098 which show the satisfactory performance of the pro-posed correlation Moreover this table confirms the suc-cessful testing of the proposed model because of thebetter performance of the test set than the training set

The results of GEP predictionscalculations against theexperimental damaged permeability are indicated in


Figure 2 As can be seen in this crossplot a compressedcloud of datapoints can be observed around the unit slopeline or 45 line which shows the better agreement of theGEPmodel estimates in comparison with the correspondingmeasured data of damaged permeability Because the mostideal performance of a model will be achieved when the pre-dictions and actual data are the same leading to settling ofthe datapoints on unit slope line For GEPmodel the valuesof AARD RMSE and ARD are acceptably nearby thezero error value and the R2 value is close to unity The

other characteristic diagram for justified judgment ofthe GEPmodel is represented in Figure 3 exhibiting the dis-tribution of GEP predictions error against the actual dataof damaged permeability In Figure 3 the relative deviationpercent mainly changes in an acceptable range of 2 to 2Furthermore the total value of ARD which is equal to00355 demonstrates that the central focus of relativeerror distribution is sufficiently near to zero value Figure 4shows the schematic diagram for the error distributionof the proposed GEP-based equation versus the data

Table 3 The statistical parameters of the developed GEP model for prediction of damaged permeability

Parameter Value

Training setR2a 09841Average relative deviation b 00629Average absolute relative deviation c 06565Root mean square errord 00990Number of data samples 345Test setR2 09858Average relative deviation 00746Average absolute relative deviation 05782Root mean square error 00872Number of data samples 86TotalR2 09843Average relative deviation 00355Average absolute relative deviation 06409Root mean square error 00967Number of data samples 431a Determination coefficient

R2 frac14 1PNifrac141

Kdeth THORNexpi ethKdTHORNpredi

2PNi

Kdeth THORNexpi Kdeth THORN 2

b Average relative deviation percent (ARD)

ARD frac14 100N

XN

ifrac141

Kdeth THORNexpi Kdeth THORNpredi

Kdeth THORNexpi

c Average absolute relative deviation percent (AARD)

AARD frac14 100N

XN

ifrac141


Kdeth THORNexpi

d Root mean square error (RMSE)

RMSE frac14PN

ifrac141 Kdeth THORNexpi Kdeth THORNpredi

2N

0B

1CA

12


frequency Having focused on this figure a normal distribu-tion can be easily observed for both training and test sub-sets indicating the symmetry in the outcomes fromcurrent paper

43 Outlier diagnosis

It has been known that the reliability of a utilized databasedirectly affects the accuracy and validity of the constructedmodel Nonetheless proper data measurement is often notpracticable and diverse types of undesirable experimental

errors originated from human and equipment mistakesmay diffuse into the measurements Such unwanted devia-tions in experimental work are accounted as a menace tothe success of modeling Hence detection of these suspectedmeasurements from data is vital for anymodeling study [67]

In an attempt to distinguish the invalid data theso-called technique of Leverage Value Statistics (LVS)was conducted in current study The statistical techniqueof LVS is commonly applied for describing the outlier datadetecting the existing arrangement between the indepen-dent and dependent parameters As it was previouslyexplained the suggested GEPmodel has a robust capabilityfor predicting impaired permeability as a result of mineralscaling In LVS processing mathematical strategies containthe computation of Hat matrix and residual values forwhole database For calculating the residuals the deviationbetween the target and the corresponding GEP predictedvalue have to be calculated for each datapoint BesidesHat matrix includes the GEP model estimates and the tar-get experimental data as below [73ndash76]

H frac14 X XtXeth THORN1Xt eth8THORNIn equation (8) X is defined as the two-dimensional Hatmatrix in which the possible area of the problem lay onthe diagonal of this matrix and the symbol t denotesthe transpose operator The total numbers of the modelparameters and used data determine the number of thecolumns (n) and rows (m) of the Hat matrix respectively

The well-known diagram of William is broadly appliedto recognize the suspected data according to the calculatedresiduals and the values of Hat matrix estimated by theequation (8) The relationship between the standardizedresiduals (R) and H indices are shown in Williamrsquos plotA cautionary leverage limit (H) is calculated as 3(n + 1)m The criterion for measurement acceptability is

Fig 2 Comparison between experimental damaged permeabil-ity and GEP predictionscalculations

Fig 3 Illustration of relative error distribution versus thedamaged permeability

Fig 4 Distribution of relative deviation in the experimentaldataset including train set and test set


the presence of data in the cut-off limit of residuals that isequal to plusmn3 (indicated by two horizontal lines in Williamrsquosplot) In Figure 5 the result of outlier analysis is repre-sented in which the most of data exist in the range of3 R 3 and 0 H H verifying the high truthfulnessand robustness of the GEP-based model in this study Withrespect to the H and R ranges three classes of outliers canbe suggested including Regression Bad High Leverage andGood High Leverage outliers [73ndash76]

When the conditions3R 3 andHH are fulfilledthe outlier is called ldquoGoodHigh Leveragerdquo In this outlier themeasurements do not adequately affect the determinationcoefficient and accommodate nearly on the regression linewhich passes through the measured data even thoughthey have large values of leverage The measurements withR values larger than 3 or less than 3 are under the classof ldquoBad High Leveragerdquo outlier which is a serious intimida-tion for strong modeling The intercept and the slope ofthe regression line are extremely affected by this outlierThe final type of outlier is named as ldquoRegressionrdquo not dis-turbing the valid range and it has no impact on the regressionline in spite of having large values of residual [73ndash76]

In this study for recognizing the more likely invaliddata the Hat values were calculated via equation (8) thenthe Williamrsquos plot was drawn in Figure 5 Accordingly it isclear that just 1 datapoint of 427 datapoints is recognizedas the off-range (outlier) data As a consequence the sug-gested GEP-derived model in this study is reliable and effi-ciently precise owing to the fact that the datapoints arewidely held in the interior region of 3 lt R lt 3 and0 lt H lt 00493

5 Conclusion

In current study GEP as an evolutionary mathematicalstrategy was applied in order to estimate the damagedpermeability as a result of mixed salt scaling For thispurpose an extensive database was taken from the open

literature to develop a user-friendly and empirically-derivedequation by this novel approach The processed databasewas grouped into two subsets of training and test Thetraining group includes 80 of the entire database usedfor model development as well as testing group includes20 of the whole database applied for examining the modelMoreover various schematic diagrams including crossplotindex plot and relative distribution plot were employedfor better model evaluation Calculation of different statis-tical quality measures for the proposed model results in theAARD of 0640 the R2 of 0984 RMSE of 0097 and theARD of 0036 Therefore the GEP-based model devel-oped in this study has proven to have an excellent precisionand superior performance in estimating the impairedpermeability in comparison with the experimentally mea-sured datapoints Finally the proposed tool in this studyis of tremendous practical value for quick and cheap predic-tion of impaired permeability in water flooding schemesduring co-precipitation of mixed sulfate salts

Supplementary Material

Supplementary Material is available at httpsogstifpenergiesnouvellesfr102516ogst2019032olm

References

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2 Moghadasi J Jamialahmadi M Muumlller-Steinhagen HSharif A Ghalambor A Izadpanah MR Motaie E(2003) Scale formation in Iranian oil reservoir and produc-tion equipment during water injection in InternationalSymposium on Oilfield Scale Society of Petroleum Engi-neers Aberdeen United Kingdom

3 Lindlof JC Stoffer KG (1983) A case study of seawaterinjection incompatibility 35 1256ndash1262

4 Aliaga DA Wu G Sharma MM Lake LW (1992) Bariumand calcium sulfate precipitation and migration inside sand-packs SPE-19765-PA SPE Formation Evaluation 7 0179ndash86

5 Boon JA Hamilton T Holloway L Wiwchar B (1983)Reaction between rock matrix and injected fluids in cold lakeoil sand ndash spotential for formation damage J Can PetTechnol 22 04 55ndash66

6 Cusack F Brown DR Costerton JW Clementz DM(1987) Field and laboratory studies of microbialfines plug-ging of water injection wells Mechanism diagnosis andremoval J Pet Sci Eng 1 39ndash50

7 El-Hattab MI (1985) Scale deposition in surface andsubsurface production equipment in the Gulf of Suez JPet Technol 37 09 1640ndash1652

8 Bayona HJ (1993) A review of well injectivity performancein Saudi Arabiarsquos Ghawar field seawater injection programin Middle East Oil Show Society of Petroleum EngineersBahrain

9 Stalker R Collins IR Graham GM (2003) The impact ofchemical incompatibilities in commingled fluids on theefficiency of a produced water reinjection system A North

Fig 5 Detection of probable outliers and applicability domainof the GEP model


Sea example in International Symposium on OilfieldChemistry Society of Petroleum Engineers Houston Texas

10 Bedrikovetsky P Marchesin D Shecaira F Serra ALMarchesin A Rezende E Hime G (2001) Well impairmentduring seaproduced water flooding Treatment of labora-tory data in SPE Latin American and Caribbean PetroleumEngineering Conference Society of Petroleum EngineersBuenos Aires Argentina

11 Ahmed SJ (2004) Laboratory study on precipitation of cal-cium sulphate in berea sandstone cores Doctoral dissertationKing Fahd University of Petroleum ampMinerals Saudi Arabia

12 Gunn DJ Murthy MS (1972) Kinetics and mechanisms ofprecipitations Chem Eng Sci 27 1293ndash1313

13 Liu S-T Nancollas GH (1975) The crystal growth anddissolution of barium sulfate in the presence of additives JColl Interf Sci 52 582ndash592

14 Walton AG Fuumlredi H Elving PJ Kolthoff IM (1967)The formation and properties of precipitates Vol 23Interscience Publishers New York pp 36ndash38

15 Nancollas GH Eralp AE Gill JS (1978) Calcium sulfatescale formation A kinetic approach Soc Pet Eng J 18133ndash138

16 Nancollas GH Purdie N (1963) Crystallization of bariumsulphate in aqueous solution Trans Faraday Soc 59 735ndash740

17 Mitchell RW Grist DM Boyle MJ (1980) Chemicaltreatments associated with North Sea projects J PetTechnol 32 904ndash912

18 Yuan M (1989) Prediction of sulphate scaling tendency andinvestigation of barium and strontium sulphate solid solutionscale formation Doctoral dissertation Heriot-Watt Univer-sity Edinburgh

19 Safari H Jamialahmadi M (2014) Thermodynamics kinet-ics and hydrodynamics of mixed salt precipitation in porousmedia Model development and parameter estimationTransp Porous Media 101 477ndash505

20 Safari H Jamialahmadi M (2014) Estimating the kineticparameters regarding barium sulfate deposition in porousmedia A genetic algorithm approach Asia-Pacific J ChemEng 9 256ndash264

21 Vitthal S Sharma MM (1992) A Stokesian dynamics modelfor particle deposition and bridging in granular media JColl Interf Sci 153 314ndash336

22 Andersen KI Halvorsen E Saeliglensminde T Oslashstbye NO(2000) Water management in a closed loop ndash Problems andsolutions at brage field in SPE European PetroleumConference Society of Petroleum Engineers Paris France

23 Paulo J Mackay EJ Menzies N Poynton N (2001)Implications of brine mixing in the reservoir for scalemanagement in the Alba field in International Symposiumon Oilfield Scale Society of Petroleum Engineers AberdeenUnited Kingdom

24 Mackay E (2003) Predicting in situ sulphate scale depositionand the impact on produced ion concentrations Chem EngRes Des 81 326ndash332

25 McElhiney JE Sydansk RD Lintelmann KA BenzelWM Davidson KB (2001) Determination of in-situprecipitation of barium sulphate during coreflooding inInternational Symposium on Oilfield Scale Society ofPetroleum Engineers Aberdeen United Kingdom

26 Weintritt DJ Cowan JC (1967) Unique characteristics ofbarium sulfate scale deposition J Pet Technol 19 1381ndash1394

27 Read PA Ringen JK (1982) The use of laboratory tests toevaluate scaling problems during water injection in SPE

Oilfield and Geothermal Chemistry Symposium Society ofPetroleum Engineers Dallas Texas

28 Moghadasi J Jamialahmadi M Muumlller-Steinhagen HSharif A (2004) Formation damage due to scale formation inporous media resulting from water injection in SPE Interna-tional Symposium and Exhibition on Formation DamageControl Society of Petroleum Engineers Lafayette Louisiana

29 Chang F Civan F (1991) Modeling of formation damagedue to physical and chemical interactions between fluids andreservoir rocks in SPE Annual Technical Conference andExhibition Society of Petroleum Engineers Dallas Texas

30 Yeboah YD Somuah SK Saeed MR (1993) A new andreliable model for predicting oilfield scale formation in SPEInternational Symposium on Oilfield Chemistry Society ofPetroleum Engineers New Orleans Louisiana

31 Bertero L Chierici GL Gottardi G Mesini EMormino G (1988) Chemical equilibrium models Their usein simulating the injection of incompatible waters SPE-14126-PA SPE Reservoir Engineering 3 01 288ndash294

32 Thomas LG Albertsen M Perdeger A Knoke HHKHorstmann BW Schenk D (1995) Chemical characteriza-tion of fluids and their modelling with respect to their damagepotential in injection on production processes using an expertsystem in SPE International Symposium on Oilfield Chem-istry Society of Petroleum Engineers San Antonio Texas

33 Jamialahmadi M Muller-Steinhagen H (2008) Mechanismsof scale deposition and scale removal in porous media Int JOil Gas Coal Technol 1 81ndash108

34 Creton B Leacutevecircque I Oukhemanou F (2019) Equivalentalkane carbon number of crude oils A predictive model basedon machine learning Oil Gas Sci Technol ndash Rev IFPEnergies nouvelles 74 30

35 Rostami A Shokrollahi A Ghazanfari MH (2018) Newmethod for predicting n-tetradecanebitumen mixture den-sity Correlation development Oil Gas Sci Technol ndash RevIFP Energies nouvelles 73 35

36 Sales LdPA Pitombeira-Neto AR de Athayde Prata B(2018) A genetic algorithm integrated with Monte Carlosimulation for the field layout design problem Oil Gas SciTechnol ndash Rev IFP Energies nouvelles 73 24

37 Ferreira C (2006) Designing neural networks using geneexpression programming In Applied soft computing technolo-gies The challenge of complexity Springer Berlin Heidelbergpp 517ndash535

38 Gharagheizi F Ilani-Kashkouli P Farahani N MohammadiAH (2012) Gene expression programming strategy forestimation of flash point temperature of non-electrolyteorganic compounds Fluid Phase Equilib 329 71ndash77

39 Gharagheizi F Eslamimanesh A Sattari M MohammadiAH Richon D (2013) Development of corresponding statesmodel for estimation of the surface tension of chemicalcompounds AIChE J 59 613ndash621

40 Merdhah A (2007) The study of scale formation in oilreservoir during water injection at high-barium and high-salinity formation water in Chemical and NaturalResources Engineering Universiti Teknologi Malaysia

41 Merdhah AB Yassin M Azam A (2008) Study of scale for-mation due to incompatible water Jurnal Teknologi 49 9ndash26

42 Merdhah A Yassin A (2009) Scale formation due to waterinjection in Berea sandstone cores J Appl Sci 9 3298ndash3307

43 Merdhah AB Yassin AAM Muherei MA (2010)Laboratory and prediction of barium sulfate scaling athigh-barium formation water J Pet Sci Eng 70 79ndash88


44 Rostami A Kamari A Joonaki E Ghanaatian S (2018)Accurate estimation of minimum miscibility pressure duringnitrogen injection into hydrocarbon reservoirs in 80th EAGEConference and Exhibition 2018 Copenhagen Denmark

45 Rostami A Shokrollahi A (2017) Accurate prediction ofwater dewpoint temperature in natural gas dehydratorsusing gene expression programming approach J Mol Liq243 196ndash204

46 Moghadasi R Rostami A Hemmati-Sarapardeh AMotie M (2019) Application of Nanosilica for inhibition offines migration during low salinity water injection Experi-mental study mechanistic understanding and model devel-opment Fuel 242 846ndash862

47 Rostami A Arabloo M Lee M Bahadori A (2018)Applying SVM framework for modeling of CO2 solubility inoil during CO2 flooding Fuel 214 73ndash87

48 Kamari A Pournik M Rostami A Amirlatifi AMohammadi AH (2017) Characterizing the CO2-brineinterfacial tension (IFT) using robust modeling approachesA comparative study J Mol Liq 246 32ndash38

49 Rostami A Masoudi M Ghaderi-Ardakani A Arabloo MAmani M (2016) Effective thermal conductivity modeling ofsandstones SVM framework analysis Int J Thermophys37 1ndash15

50 Rostami A Kalantari-Meybodi M Karimi M Tatar AMohammadi AH (2018) Efficient estimation of hydrolyzedpolyacrylamide (HPAM) solution viscosity for enhanced oilrecovery process by polymer flooding Oil Gas Sci Technol ndashRev IFP Energies nouvelles 73 22

51 Rostami A Arabloo M Ebadi H (2017) Genetic program-ming (GP) approach for prediction of supercritical CO2

thermal conductivity Chem Eng Res Des 122 164ndash17552 Rostami A Hemmati-Sarapardeh A Karkevandi-

Talkhooncheh A Husein MM Shamshirband S RabczukT (2019) Modeling heat capacity of ionic liquids using groupmethod of data handling A hybrid and structure-basedapproach Int J Heat Mass Trans 129 7ndash17

53 Karkevandi-Talkhooncheh A Rostami A Hemmati-Sarapardeh A Ahmadi M Husein MM Dabir B (2018)Modeling minimum miscibility pressure during pure andimpure CO2 flooding using hybrid of radial basis functionneural network and evolutionary techniques Fuel 220270ndash282

54 Rostami A Arabloo M Kamari A Mohammadi AH(2017) Modeling of CO2 solubility in crude oil during carbondioxide enhanced oil recovery using gene expression pro-gramming Fuel 210 768ndash782

55 Rostami A Kamari A Panacharoensawad E Hashemi A(2018) New empirical correlations for determination of Min-imum Miscibility Pressure (MMP) during N2-contaminatedlean gas flooding J Taiwan Ins Chem Eng 91 369ndash382

56 Rostami A Arabloo M Esmaeilzadeh S Mohammadi AH(2018) On modeling of bitumenn-tetradecane mixtureviscosity Application in solvent-assisted recovery methodAsia-Pacific J Chem Eng 13 e2152

57 Rostami A Hemmati-Sarapardeh A Shamshirband S(2018) Rigorous prognostication of natural gas viscositySmart modeling and comparative study Fuel 222 766ndash778

58 Rostami A Baghban A Mohammadi AH Hemmati-Sarapardeh A Habibzadeh S (2019) Rigorous prognostica-tion of permeability of heterogeneous carbonate oil reser-voirs Smart modeling and correlation development Fuel236 110ndash123

59 Rostami A Shokrollahi A Esmaeili-Jaghdan Z GhazanfariMH (2019) Rigorous silica solubility estimation in super-heated steam Smart modeling and comparative study Env-iron Prog Sustain Energy doi 101002ep13089 in press

60 Rostami A Ebadi H (2017) Toward gene expressionprogramming for accurate prognostication of the critical oilflow rate through the choke Correlation development Asia-Pacific J Chem Eng 12 884ndash893

61 Rostami A Ebadi H Arabloo M Meybodi MK BahadoriA (2017) Toward genetic programming (GP) approach forestimation of hydrocarbonwater interfacial tension J MolLiq 230 175ndash189

62 Rostami A Ebadi H Mohammadi AH Baghban A(2018) Viscosity estimation of Athabasca bitumen in solventinjection process using genetic programming strategyEnergy Sources Part A Recovery Utilization Env Eff 40922ndash928

63 Ferreira C (2001) Gene expression programming A newadaptive algorithm for solving problems Compl Syst 1387ndash129

64 Koza JR (1992) Genetic programming On the program-ming of computers by means of natural selection MIT PressCambridge Massachusetts USA

65 Teodorescu L Sherwood D (2008) High energy physicsevent selection with gene expression programming ComputPhys Commun 178 409ndash419

66 Ferreira C (2006) Gene expression programming Mathe-matical modeling by an artificial intelligence 2nd ednSpringer Berlin Heidelberg

67 Shokrollahi A Safari H Esmaeili-Jaghdan Z GhazanfariMH Mohammadi AH (2015) Rigorous modeling ofpermeability impairment due to inorganic scale depositionin porous media J Pet Sci Eng 130 26ndash36

68 Moghadasi J Muumlller-Steinhagen H Jamialahmadi MSharif A (2004) Model study on the kinetics of oil fieldformation damage due to salt precipitation from injection JPet Sci Eng 43 201ndash217

69 Yassin MR Arabloo M Shokrollahi A Mohammadi AH(2014) Prediction of surfactant retention in porous media Arobust modeling approach J Dispers Sci Technol 351407ndash1418

70 BinMerdhah AB Yassin AAM Muherei MA (2010)Laboratory and prediction of barium sulfate scaling at high-barium formation water J Pet Sci Eng 70 79ndash88

71 Kamari A Arabloo M Shokrollahi A Gharagheizi FMohammadi AH (2015) Rapid method to estimate theminimum miscibility pressure (MMP) in live reservoir oilsystems during CO2 flooding Fuel 153 310ndash319

72 Ferreira C (2002) Gene expression programming in problemsolving In Soft computing and industry Springer Londonpp 635ndash653

73 Goodall CR (1993) Computation using the QR decompo-sition in Handbook of Statistics Elsevier AmsterdamNorth Holland 467ndash508

74 Eslamimanesh A Gharagheizi F Mohammadi AHRichon D (2013) Assessment test of sulfur content of gasesFuel Process Technol 110 133ndash140

75 Gramatica P (2007) Principles of QSAR models validationInternal and external QSAR Comb Sci 26 694ndash701

76 Fayazi A Arabloo M Shokrollahi A Zargari MHGhazanfari MH (2014) State-of-the-art least square supportvector machine application for accurate determination ofnatural gas viscosity Ind Eng Chem Res 53 945ndash958


Introduction

Data gathering

Gene expression programming


Results and discussions

Benchmarks for evaluation of the proposed GEP model

Assessment of the proposed GEP model

Outlier diagnosis

Conclusion


References

Application of a new approach for modeling the oil field formationdamage due to mineral scalingAlireza Rostami1 Amin Shokrollahi2 Khalil Shahbazi1 and Mohammad Hossein Ghazanfari2

1Department of Petroleum Engineering Petroleum University of Technology (PUT) PO Box 6198144471 Ahwaz Iran2Department of Chemical and Petroleum Engineering Sharif University of Technology (SUT) PO Box 113659465 Tehran Iran

Received 2 March 2019 Accepted 14 May 2019

Abstract Mineral scaling has been considered a great concern for developing the oil production from theunderground petroleum reservoirs One of the main causes of this phenomenon is known as the chemical incom-patibility of injected brine frequently sea water with the reservoir brine leading to the deposition of varioussupersaturated salts such as calcium carbonate calcium sulfate and barium sulfate In present communicationan evolutionary approach namely Gene Expression Programming (GEP) was employed for rigorous modelingof formation damage by mineral scaling of mixed sulfate salt deposition At first a large databank of damagedpermeability datapoints as a function of injected volume injection flowrate temperature differential pressureand ionic concentrations of the existing chemical species in the porous media was employed In this regard auser-friendly correlation was extended for the first time by the aforementioned technique in the literatureProfessional evaluation of the suggested GEP-based model was implemented by different statistical parametersand appealing visualization tools Having proposed the GEP-based correlation statistical parameters of theAverage Absolute Relative Deviation Percent (AARD) of 0640 and determination coefficient (R2) of0984 was calculated Accordingly it is demonstrated that the proposed model has a superior performanceand great potential for efficient prediction of damaged permeability due to the mixed sulfate salt scaling More-over the implemented outlier diagnosis technique verified the validity of the databank used for modeling aswell as the high robustness of the suggested model was confirmed In conclusion the developed correlationin this work can be of enormous practical value for skillful engineers and scientists in any academic studyand industrial applications dealing with mixed salt deposition

1 Introduction

In water injection scheme deposition of mineral scales hasbeen considered a great challenge for production develop-ment of subterranean petroleum reservoirs [1] Success ofa water injection project can be jeopardized by such scaleand even worse it can be terminated in the worst opera-tional conditions Therefore the efficiency of this processdepending upon the degree of pressure maintenance andthe oil production level can be reduced The amount offormation damage caused by the scaling is chiefly quantifiedby the well-known terms of permeability and porosityreduction [2 3]

The mechanism of permeability reduction leading to theformation damage in the porous media by precipitatedminerals is the deposition of the supersaturated mineralson the pore walls due to the attraction forces between thepore surface area and scale solid particles In such condition

a number of bridges made of the scale particles across thepore throats will be created as well as pore throats blockageby a single particle will strongly happen The degree of for-mation damage is affected by the features of minerals pre-cipitate The morphology and quantity of the growingcrystals on the pore walls are monitored by means of severalfactors including existence of impurities mixing rate tem-perature change and supersaturation owing to the variationin physical conditions (eg chemical incompatibility) [4ndash7]

Chemical incompatibility is classified as the main reasonof the severe oilfield scaling when incompatible waters aremixed While water is injected into the reservoir a reactionbetween the formation minerals and formation water withthe injected fluid will take place resulting in the establish-ment of scale formation through the porous media In otherwords based on the so-called phenomenon of the chemicalincompatibility the reservoir brine and injection water willundergo the strong chemical interactions together leading

Corresponding authors alirezarostamiput2014gmailcom alirezarostamiafpputacir shahbaziputacir

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (httpcreativecommonsorglicensesby40)which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Oil amp Gas Science and Technology - Rev IFP Energies nouvelles 74 62 (2019) Available online atA Rostami et al published by IFP Energies nouvelles 2019 ogstifpenergiesnouvellesfr

httpsdoiorg102516ogst2019032

REGULAR ARTICLEREGULAR ARTICLE












2 Data gathering








4ppm 2750 285476 2960 105


SD frac14 1N 1

XNifrac141

Si S 2 1

2













p plusmn) and set-




XNi

K expdi Kpred

di

K exp

di eth3THORN








p EXP INV

LN LOG X2 POW












A1 frac14T V inj


4

277550702075275

n o

eth5THORN

A2 frac14407928649580713Q2

P 243561403505515eth THORN2 00656999407983034 T 146554080471316f g

eth6THORN

A3 frac14 00266417196782303 ln 302487101618176 QV inj

2









Parameter Value




2PNi



ARD frac14 100N

XN

ifrac141


Kdeth THORNexpi


AARD frac14 100N

XN

ifrac141


Kdeth THORNexpi


RMSE frac14PN


2N

0B

1CA

12
















5 Conclusion





References




















































































Introduction

Data gathering






Outlier diagnosis

Conclusion


References












2 Data gathering








4ppm 2750 285476 2960 105


SD frac14 1N 1

XNifrac141

Si S 2 1

2













p plusmn) and set-




XNi

K expdi Kpred

di

K exp

di eth3THORN








p EXP INV

LN LOG X2 POW












A1 frac14T V inj


4

277550702075275

n o

eth5THORN

A2 frac14407928649580713Q2

P 243561403505515eth THORN2 00656999407983034 T 146554080471316f g

eth6THORN

A3 frac14 00266417196782303 ln 302487101618176 QV inj

2









Parameter Value




2PNi



ARD frac14 100N

XN

ifrac141


Kdeth THORNexpi


AARD frac14 100N

XN

ifrac141


Kdeth THORNexpi


RMSE frac14PN


2N

0B

1CA

12
















5 Conclusion





References




















































































Introduction

Data gathering






Outlier diagnosis

Conclusion


References












p plusmn) and set-




XNi

K expdi Kpred

di

K exp

di eth3THORN








p EXP INV

LN LOG X2 POW












A1 frac14T V inj


4

277550702075275

n o

eth5THORN

A2 frac14407928649580713Q2

P 243561403505515eth THORN2 00656999407983034 T 146554080471316f g

eth6THORN

A3 frac14 00266417196782303 ln 302487101618176 QV inj

2









Parameter Value




2PNi



ARD frac14 100N

XN

ifrac141


Kdeth THORNexpi


AARD frac14 100N

XN

ifrac141


Kdeth THORNexpi


RMSE frac14PN


2N

0B

1CA

12
















5 Conclusion





References




















































































Introduction

Data gathering






Outlier diagnosis

Conclusion


References











A1 frac14T V inj


4

277550702075275

n o

eth5THORN

A2 frac14407928649580713Q2

P 243561403505515eth THORN2 00656999407983034 T 146554080471316f g

eth6THORN

A3 frac14 00266417196782303 ln 302487101618176 QV inj

2









Parameter Value




2PNi



ARD frac14 100N

XN

ifrac141


Kdeth THORNexpi


AARD frac14 100N

XN

ifrac141


Kdeth THORNexpi


RMSE frac14PN


2N

0B

1CA

12
















5 Conclusion





References




















































































Introduction

Data gathering






Outlier diagnosis

Conclusion


References




Parameter Value




2PNi



ARD frac14 100N

XN

ifrac141


Kdeth THORNexpi


AARD frac14 100N

XN

ifrac141


Kdeth THORNexpi


RMSE frac14PN


2N

0B

1CA

12
















5 Conclusion





References




















































































Introduction

Data gathering






Outlier diagnosis

Conclusion


References















5 Conclusion





References




















































































Introduction

Data gathering






Outlier diagnosis

Conclusion


References









































































Introduction

Data gathering






Outlier diagnosis

Conclusion


References

Application of a new approach for modeling the oil field ...

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