Chemometrics and Intelligent Laboratory Systems 115 (2012) 18–24

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Chemometrics and Intelligent Laboratory Systems

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Assessment of the chemical composition of waters associated with oil productionusing PARAFAC

Fabiana Alves de Lima Ribeiro a,⁎, Francisca Ferreira do Rosário b, Maria Carmen Moreira Bezerra b,André Luis Mathias Bastos b, Vera Lúcia Alves de Melo b, Ronei Jesus Poppi a

a Laboratory of Chemometrics in Analytical Chemistry, Chemistry Institute, University Campinas (LAQQA/IQ/UNICAMP), Cidade Universitária Zeferino Vaz, POB 6154, 13083–970, Campinas, SP, Brazilb Centro de Pesquisas e Desenvolvimento Leopoldo Américo Miguez de Mello, Petróleo Brasileiro S.A. (CENPES/PETROBRÁS), Av. Horacio Macedo, 95, Cidade Universitária, Rio de Janeiro, RJ,CEP 21941–915, Brazil

⁎ Corresponding author at: Laboratório de QuimiomInstituto de Química, Universidade Estadual de CamCidade Universitária Zeferino Vaz, Caixa Postal 6154, CBrazil. Tel.: +55 19 3521 2134; fax: +55 19 3521 3023

E-mail addresses: falribeiro@gmail.com (F.A.L. Ribeir(R.J. Poppi).

0169-7439/$ – see front matter © 2012 Elsevier B.V. Alldoi:10.1016/j.chemolab.2012.04.001

a b s t r a c t

a r t i c l e i n f o

Article history:Received 3 October 2011Received in revised form 10 February 2012Accepted 3 April 2012Available online 11 April 2012

Keywords:PetroleumOil productionProduced waterPARAFACExploratory analysisPattern recognition

In this work, Parallel Factor Analysis (PARAFAC) was used to assess the composition of produced water in 8 oilwells, using their levels of salinity, calcium,magnesium, strontium, barium and sulphate (mg/L), collected duringthe years 2004 and 2005. This method allowed the identification of tracers for seawater and formation water, aswell as identification of standards related to seasonality. Themethod indicates that the variables salinity, calciumand strontium are associated with formation water, while magnesium and sulphate are associated with waterinjection. These variables may be used as tracers to distinguish seawater, used as injection water, and formationwater, and can be very useful to evaluate the produced water composition. Seasonality aspects are associatedwith the variation in the levels of sulphate and magnesium, which tend to increase over time while the levelsof barium usually decrease.Chemical patterns related to the original reservoirs of each oil well, called A, B and C, alsowere observed. Samplescollected in reservoir B presented the lowest salinity, calcium, strontium and barium levels and the highestmagnesium and sulphate levels, while samples from reservoir A showed intermediate levels for the samevariables. Reservoir C samples presented the highest values for salinity, calcium, strontium and barium, andthe lowest levels of sulphate.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

This study considers the case that oil production is associated with ahigher production ofwater than the production of oil itself. Thiswater isknown as produced water, and is the result of a mixture of the watersoriginally present at the petroleum reservoir, which can be classifiedas connatewater (or formationwater), saturationwater in the reservoirfluid, aquifer water and injected water [1,2]. Fig. 1 contains a flowchartillustrating the production of water, the types involved and theircharacteristics. The rate of produced water is dependent on thereservoir geology and exploitation strategy of the field, and can bedescribed in terms of chemical composition, and the resulting physicaland chemical properties [3–5].

Connatewater (or formationwater) is thewater naturally present inthe oil reservoir, which was retained in the pores and fissures of therock since its formation. Its chemical composition has been poorly

etria em Química Analítica,pinas (LAQQA/IQ/UNICAMP),ampinas, SP, CEP 13083–970,.o), ronei@iqm.unicamp.br

rights reserved.

studied and is considered to be similar to the aquifer. Quantification isvery difficult because it presents itself emulsified with oil phase and insmall quantities (up to 0.5% basic sediment and water produced in thefluid).

The hydrocarbon oil remained in contact with the connate water forbillions of years, leading to saturation of the gas with water vapor(known as saturation water). According to the pressure and tempera-ture variations in the course of process of oil production, that watercan evaporate or condense. This water is produced in significantvolumes over gas fields with characteristics of freshwater, since it isfrom evaporated water.

The water belonging to the underground aquifers generally havehigh levels of salts, increasing with depth, and the chemical composi-tion of this type of water varies with the geochemistry of the reservoirrock.

Injectionwater is thewater used during oil recovery operations, andmay be derived from different sources such as underground aquifers,the water produced by the reservoir itself and seawater. In offshoreplatforms, the latter alternative has been the most widely used due toits availability and economic viability [1,3,5,6].

The knowledge of formation and injection water composition datacan lead to important understanding about the behavior of the oilwell during routine operations, and forecast the occurrence of possible

1. Saturation Water2. Connate Water

Process Cronology Produced WaterComposition

•start of production•water injection

Saturation Water+

Aquifer Water

Aquifer Water

Aquifer Water+

Injection Water

Injection Water

•Formation Water Breakthrough

•Water/oil Contact•Injection Water Breakthrough

•Process Development

•depletion of the reservoir efficiency ofinjected water

1. fresh water, low volume2. emulsified, trace composition

Gradual increase of salinity and BSW*

*BSW: basic sediment and water

High salinity and BSW*

Intermediate salinity, variable chemical composition with time, increasing BSW*

Low salinity, high BSW*

Fig. 1. Flowchart illustrating the production of water.

19F.A.L. Ribeiro et al. / Chemometrics and Intelligent Laboratory Systems 115 (2012) 18–24

problems that may cause process stoppages, such as scale formation,with significant impact on productivity and production costs. However,the sampling of formation water has several operational limitations,which result in contamination by drillingfluidfiltrate. So, it is a very dif-ficult analytical task the determination of the percentage of formationwater and the drilling filtered in the mixture of fluids and there is noguarantee that the fluid samples are representative of formationwater [2–4,7,8].

The seawater used as injection water is rich in sulphate and carbon-ate, while the formation water that exists naturally within the reservoirpores or associated aquifer usually contains significant amounts ofprecipitating cations such as barium, strontium and calcium. Due totechnological limitations in the formationwater sampling is impossibleto accurately determine the fraction of each kind of water in producedwater. This information would be important for understanding thebehavior of the productionwell during the extraction of oil, and preven-tion of possible process failures resulting from incompatibility betweenthe two types of water.

Despite this, the analysis of production water can provide valuableinformation about the formation water fraction and there is already an-alytical methods established for its chemical composition [2,3,9–12].The simplest way of monitoring the chemical variation of the producedwater is the visual inspection of time series of individual analytes. Irreg-ularities in the variability of some species may indicate the occurrenceof characteristic events. For example the abrupt fall in barium levels inexcess of sulfate anion is indicative of scale formation since the BaSO4

is a typical mineral present in saline deposits [2,3,12]. However, thisapproach is limited because the irregularities in the analytes variabilitymay have many different causes and requires themonitoring of severalspecies simultaneously.

The use of univariate statistical analysis for assessment of chemicalcomposition of produced water is not sufficient to identify the percent-age of formation water and filtrate, since it is not common to havetracers for both fluids, causing loss of relevant information that couldlead to an understanding of the physicochemical behavior of thewater mixture [3,13]. The use of bivariate graphs (Ex.: Ba2+ vs. SO4

2−)usually improves significantly the identification of these events, butthe multivariate approach provides more complete results, because itallows to monitor the entire system simultaneously [3,8,12,13]. Multi-variate analysis has been used as an alternative approach to evaluatethe chemical composition of producedwaters, especially Principal Com-ponent Analysis (PCA) and Partial Least Squares (PLS)methods, and canbe used to identify chemical tracers for formation and injection water.These multivariate techniques allow the evaluation of many variablessimultaneously, minimizing, in this way, the risk of losing relevant in-formation [3,4,7]. These techniques are capable of detecting samplingclusters and outlier presence, as well as identifying the variables thathave some influence on the behavior of the samples.

Multivariate techniques are applied to the analysis of two-dimensionaldata arrays of the type samples×variables (in this case, variables=chemical species). However, in the case of the data set evaluated inthis study, other important information such as those related to season-ality is given. In this case every data element is indexed by three indices:one identifying the sample date, one the chemical variable, and one theoil well and the use of a multi-waymethod, a natural extension of mul-tivariate analysis, is more appropriated [14–17]. The use of a 3-waymethod in this case provide better possibilities for exploring data andmodel interpretability than classical 2-way multivariate method.

PARAFAC (Parallel Factor Analysis) is a natural extension for themultivariate technique PCA for multi-way data and can be used as a

Table 1Sampling period for each oil well.

P-01 P-06 P-07 P-10 P-13 P-15 P-17 PR-02

Jan/04 x x – – x – x –

Feb/04 x x – – x – x –

Mar/04 x x – – x – x –

Apr/04 x x – – x – x –

May/04 x x – – x – x xJun/04 x x – x x – x xJul/04 x x – – x – x xAug/04 x x x x x – x xSep/04 x x – x x – x xOct/04 x x – – x – x xNov/04 – x x x – x x –

Dec/04 x x x – x x x xJan/05 – x x – – x – –

Feb/05 x x x x x – x xMar/05 x x x x x – x xApr/05 x x x x x – x xMay/05 x x x x x x x xJun/05 – – – – – – – –

Jul/05 x x x x x x x xAug/05 x x x – – x x xSep/05 – x x – – – x –

Oct/05 x x x x - x x xNov/05 – x x – x – x –

Dec/05 x x x x x x x x

(–) Missing data.(x) Sampling.

20 F.A.L. Ribeiro et al. / Chemometrics and Intelligent Laboratory Systems 115 (2012) 18–24

pattern recognition method [18–22]. It also allows identification oftrends and natural clusters in the data, besides being useful in detectingoutlier samples. This method also allows identification of the influenceof variables on sample behavior and it might be useful in tracer identi-fication for injection water and formation water that can be used forbetter evaluation of the production water [14–17].

The results described in this work include assessment of the chemi-cal composition of produced water by PARAFAC, with the main goal ofidentifying tracers for formation water and injection water, as well aspatterns related to seasonality. Samples of produced water were col-lected during the years 2004 and 2005 in various production oil wellssituated at different oilfield reservoirs and were analyzed by usingPARAFAC as an exploratory tool. After this preliminary analysis, a refer-ence sample consisting of seawater (used as injection water) collectedin the same location of the oil wells was used for comparative purposes.Subsequently analysis by multivariate PCA was also performed in thedata set and results were compared with those obtained by PARAFAC.

This study is a real-world application related to a prominent researcharea. There is no registry in the literature of the use of PARAFAC for pat-tern recognition studies for characterization of water associated withpetroleum extraction and, therefore, these results contribute to thedissemination of the wide potential of the technique for petrochemicalapplications.

1.1. Parallel Factor Analysis (PARAFAC)

PARAFAC is an analysis method similar to PCA, but applied to three-or N-way data arrays of the type X (I, J, K, …). Most applications inchemistry involve three-way arrays, so their description will be gener-alized to this type of arrangement. Overall, the PARAFACmodel decom-poses the X array (I, J, K) in three loadingmatricesA, B and C containing,respectively, the elements aif, bif, cKF. Each matrix is related to eachdimension of X: the sample mode (mode I), the variables mode J andthe variables K.

PARAFAC is defined by the structural model by Eq. (1). The trilinearmodel is adjusted tominimize the quadratic sum of residues, eijk, as de-scribed in Eq. (1), where f is the number of factors in the model. ThePARAFAC model can also be represented by the matrix Eq. (2), wherethe matrices A, B and C have, respectively, the dimensions I×F, J×FandK×F, and the symbol |⊗ | represent the Khatri-Rao product [14–17].

xijk ¼XF

f¼1

aif bjf ckf þ eijk ð1Þ

X ¼ AðC ⊗j jBÞT þ E ð2Þ

2. Material and methods

2.1. Data set

The data set consists of water samples from 8 oil wells, collectedmonthly during January 2004 to December 2005. The samples werecharacterized according to their level of salinity, calcium, magnesium,barium, strontium and sulphate (mg/L) in order to detect possiblevariations on production water composition over time during routineprocess operations. Salinity level was estimated bymeasuring the chlo-ride level using titration. Ion chromatography (IC) was used to analyzesulphate. The other variable levels were measured by inductivelycoupled plasma-optical emission spectroscopy (ICP-OES). There wasno data collection during the month of June 2005 and this sample wasexcluded from analysis. Other missing data can be seen on Table 1 andthey were treated by Not-a-Number (NaN) [23,24].

A reference sample consisting of seawater collected in the same loca-tion of the oil wells was used to compare the composition of formation

water fromwells with the seawater used as injectionwater. This samplewas tested for the same chemical variables by using the samemethodol-ogies that were used for the production water samples.

2.2. Data array and data analysis

The data set was organized in an X cube (I, J, K) with I=23monthsof data collection, J=6 chemical variables (salinity, calcium, magne-sium, strontium, barium and sulphate) and K=8 oil wells and analyzedby using the PARAFACmethod initialized by singular value decomposi-tion (SVD) and data scaled on mode 2 (variables mode) [7–13]. Coreconsistency test (CORCONDIA)was used in order tofind the appropriat-ed number of factor for the model [25].

With the goal of comparing the formation water composition ofeach oil well with the seawater, a reference sample was inserted inthe X cube and the PARAFAC was remodeled. To enable this referencesample to be inserted in the cube, a slice was set up by repeating thecontents of the chemical variables involved along the K axis.

For comparative purposes, the data set were analyzed using the PCAtechnique, traditionally applied to such studies. For this purpose, thedata were organized in the matrix X (I, J), where I=samples of eachoil well×23 months plus a seawater sample (totalizing 185 samples)and J=6 variables. Missing data were excluded (see Table 1).

PARAFAC and PCA were performed by using the Nway Toolbox3.00 [14] and PLS Toolbox [26], respectively, both for MatLab 7.8 [27].

3. Results and discussion

3.1. Effects of seasonality

The factors number was optimized by using the core consistencytest (CORCONDIA test), that evaluates the adequacy of the PARAFACmodel, by verifying the X quadratic sum of residues, the trilinear consis-tency and the number of iteration needed [15]. The CORCONDIA testwas performed in triplicate to verify reproducibility, varying factorsfrom 1 to 6 and indicated two factors as the most suitable for modeling,describing 97.92% of the total variation and a CORCONDIA average valueof 100%.

21F.A.L. Ribeiro et al. / Chemometrics and Intelligent Laboratory Systems 115 (2012) 18–24

Fig. 2 shows the loadings plots for Modes 1 (sampling dates), 2(chemical variables) and 3 (oil wells). Mode 1 shows the clear sepa-ration of samples on factor 2 according to the sampling year. This be-havior is associated with the variation in levels of sulphate andmagnesium that presented positive values of loadings on this factorin Mode 2, and the level of barium which presents negative values.This means that the concentrations of sulphate and magnesium in-crease over time and the levels of barium usually decrease.

Factor 1 describes the sample distribution according to their levels ofsalinity, calcium, strontium and magnesium, which tend to increaseover this factor. The formation water contains levels of salinity, calciumand strontium relatively higher than seawater while the latter containshigher levels of magnesium and sulphate [1–5]. For oil wells where in-jection of seawater occurs, the salinity, calcium and strontium levelstend to decrease with time and these variables can be used as tracersfor formation water portion in produced water. Similarly, the magne-sium and sulphate levels tend to be higher in seawater and usually in-crease with time in the oil wells, caused by the seawater injection.Therefore, these variables can be used as tracers of the proportion ofseawater in the sample [1–4,28]. This behavior can be clearly seen inmode 3, where the oil wells P-06 and P-15, which have presentedhigher loading values of magnesium and sulphate and lower values ofsalinity, calcium and strontium, have received injections of seawater.

Barium concentration is usually low in seawater and high in forma-tionwater, and tends to decrease in time in oil wells where injection oc-curs. However, this species precipitate in the presence of sulphateanion, which reduces the amount of available barium in the water.Thus, barium is not a suitable tracer for water injection. However, mix-ture of formation water containing high concentrations of barium withinjection water containing high sulphate concentrations favor the for-mation of salt precipitates of barium sulphate, which usually are depos-ited in the pipes. Thus, abrupt decreases in the levels of barium inproduced water, with concomitant presence of high sulphate concen-trations may be associated with scaling formation for example [1–4,28].

Fig. 2. Loading plots of

Mode 3 also describes the oil well distribution according to theirlevels of chemical variables. For factor 1, the levels of salinity, calciumand strontium in the oil wells increases in the following order:

P� 06≪P� 07bP� 01;P−15bP� 17bP� 13bPR� 02bP� 10

The levels of these chemical variables are significantly lower forthe oil well P-06. Factor 2 describes increases in the levels of magne-sium and sulphate in the oil wells, which follows the order:

P� 17bP� 10; P� 13bPR� 02bP� 01bP� 07bP� 06bP� 15

The increasing order of the level of barium in the samples of theseoil wells follows the reverse order.

3.2. Reservoir characterization

Fig. 3 shows the loadings plot of Mode 3, presenting in detail thelocations of the oil wells for factors 1 and 2 and their respective oilfieldreservoirs.

The oil well P-06 (located on reservoir B) presented the lowest load-ing values for factor 1, which means that this well has the lowest levelsfor the variables salinity, calcium and strontium. This well alsopresented high loading values for factor 2, indicating high levels forthe variables sulphate and magnesium, and low values for the variablebarium. The oil well P-15 (located on reservoir C) also presented highlevels of sulphate and magnesium, and low values for the variablebarium. Well P-06 and well P-15 were the only oil wells that receivedseawater injection and was expected to present high level of variablessulphate and magnesium, and low levels of variable barium.

Due to the small number of samples originating from reservoirs Band C, it was not possible to evaluate the chemical characteristics ofthese reservoirs that could allow identifying their differences. Sincethe data set consists of historical samples of several oil wells collectedduring routine operations for oil extraction it is not possible to repeat

PARAFAC model.

Fig. 3. Loading plot of Mode 3 showing the oilfield reservoirs.Fig. 4. Loading plots of PARAFAC model (Mode 1) with reference sample.

22 F.A.L. Ribeiro et al. / Chemometrics and Intelligent Laboratory Systems 115 (2012) 18–24

the experiments to increase the number of samples in order to make abetter chemical characterization of each reservoir.

The oil wells P-01 and P-07, located in reservoir A, presented inter-mediate values of loadings and occupied the central region of the plot.This indicates that these wells showed intermediate levels for thevariables described above.

The wells P-10, P-13, P-17 and PR-02, from reservoir C, showed thehighest loadings values for factor 1, and the lowest values for factor 2.This means that these wells showed the highest levels of the variablessalinity, calcium, strontium and barium, and lowest values for thevariables sulphate and magnesium.

3.3. Formation water vs. seawater

A slice containing the average composition of seawater from thelocal area was projected on the previous PARAFAC model and the re-sults can be seen on Fig. 4. This reference sample presented the lowestloading values for factor 1, and highest loading values for factor 2. Thehigh loadings in factor 1 are associated with variables salinity, calciumand strontium, followed by barium, and the high loadings in factor 2are associated with variables magnesium and sulphate. It means thatthe reference sample contains lower levels of salinity, calcium, stron-tium and barium, and higher levels of magnesium and sulphate, whencompared with the oil well samples. These results confirm those previ-ously obtained, which show that the variables salinity, calcium andstrontium, and also barium, can be used such as tracers of formationwater (from oil wells), and the variables magnesium and can be usedsuch as tracers of injection water (from seawater).

3.4. PCA analysis

A PCA model was performed in order to compare with PARAFACmodeling and the model (3 factors describing 96.85% of total variance)was capable to identify sample clusters related to each oil well over fac-tors 1 and 2, and to distinguish the reference sample (seawater) whichpresented low and high score values on factors 1 and 2 respectively(Fig. 5(a), Table 2).

From the scores plot analysis can be affirmed that the seawater con-tains the lowest levels of salinity, calcium, strontium and barium, andthe highest levels ofmagnesium and sulphate (factors 1 and 2). The dis-tribution of reference sample and oil wells along the factor 1 can be

explained in terms of increasing levels of the variables salinity, calcium,strontium and barium (positive scores) and decreasing level of sulphate(negative scores) on factor 1 approximately in the order: referencesample bbbP-06bP-07, P-15bP-01bP-13, P-17, PR-02bP-10. Factor 2describes the increasing levels of magnesium and sulphate in the oilwells, especially the oil well P-15, which showed the highest levels forthese variables.

Factor 3 is related to the barium level (positive loadings) and con-tributes to distinguish oil wells P-10 and P-17 from P-13 and PR-02whose presented distinct levels of this chemical variable (Fig. 5(b)).This factor also contributes to identify samples from P-17 which pre-sented unusual contends of barium as those collected on August/2004, November/2004 and December/2005.

4. Conclusions

Application of PARAFAC to characterize water produced duringroutine operations in oil extractions enable the identification oftracers for formation water and injection water taking account thechemical composition of different oil wells and their respectiveseasonal aspects. These results were due to the ability of the methodin analyzing higher order data sets, which would not be possibleby use of univariate or classical multivariate techniques (for two-dimensional data), such as HCA, PCA etc.

PARAFAC can be used as a formal methodology to: (i) outlier identi-fication, (ii) tracer identification, (iii) exploratory analysis to identifysample clusters and their relations with variables (chemical, seasonalor others) and (iv) comparing sample clusters to reference samples.

PARAFAC allowed identifyingmagnesium and sulphate as tracers forseawater used as injection water (Factor 2), and the variables salinity,calcium and strontium as tracers for formation water (Factor 1). Theanalysis also shows a clear difference between samples collected in2004 and 2005. This was caused mainly by the levels of magnesiumand sulphate that tend to increase over time, and the levels of bariumthat tend to decrease over time.

The methodology showed the characteristic chemical compositionof oil reservoir A. Due to the small number of samples originatingfrom reservoirs B and C, it was not possible to evaluate the chemicalcharacteristics of these reservoirs that could allow the identification oftheir differences. Inclusion of additional samples is not possible due totechnological limitations during sampling.

Fig. 5. PCA scores with reference samples: (a) factors 1 vs. 2 and (b) factors 1 vs. 3.

23F.A.L. Ribeiro et al. / Chemometrics and Intelligent Laboratory Systems 115 (2012) 18–24

The performance of the PARAFAC method was compared with thetraditional bilinear PCA analysis, and both were very efficient in outlieridentification and chemical characterization of oil wells taking into

Table 2Loadings of PCA model.

Factor 1 Factor 2 Factor 3

Salinity 0.4565 0.2172 −0.3005Ca2+ 0.4840 0.1119 −0.1961Mg2+ 0.0522 0.8331 0.1216Ba2+ 0.3742 −0.1080 0.9035Sr2+ 0.4990 0.0766 −0.0734SO4

2− −0.4069 0.4783 0.1863

Variables in bold case have presented significant loading values at the correspondingfactors.

account all the variables simultaneously, as expected. However,PARAFAC showed to be more appropriate to model three-way data setproviding best visualization of samples seasonal patterns.

Acknowledgments

This work was done as part of a research project involving LAQQA/IQ/UNICAMP and CENPES/PETROBRÀS. The authors would you like tothank to PETROBRÀS S.A. for financial support.

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