Dead Oil Viscosity Mexican Crudo

Measurements and correlation of Mexican heavydead crude oil viscosities

Jos L. Mendoza de la Cruz a,n, Sergio Alvarez-Badillo b, Edgar Ramrez-Jaramillo a,Marco A. Aquino-Olivos a, Pedro Orea c

a Coordinacin de Investigacin y Desarrollo Tecnolgico de Aseguramiento de la Produccin de Hidrocarburos, Instituto Mexicano del Petrleo,Eje Central Lzaro Crdenas Norte 152, Col. San Bartolo Atepehuacan, 07730 Mexico, DF, Mexicob Direccin de Investigacin y Posgrado, Instituto Mexicano del Petrleo, Eje Central Lzaro Crdenas Norte 152, Col. San Bartolo Atepehuacan,07730 Mexico, DF, Mexicoc Programa de Ingeniera Molecular, Instituto Mexicano del Petrleo, Eje Central Lzaro Crdenas Norte 152, Col. San Bartolo Atepehuacan,07730 Mexico, DF, Mexico

a r t i c l e i n f o

Article history:Received 30 June 2011Accepted 3 September 2013Available online 27 September 2013

Keywords:heavy dead crude oildynamic viscositycorrelationviscometer

a b s t r a c t

This work presents reliable measurements for dynamic viscosity of representative heavy oil samplesfrom Mexican reservoirs. Most of the experimental data of dynamic viscosity were measured using aconstant force electromagnetic viscometer. The viscometer was calibrated using several viscositystandards based on a maximum standard deviation of 0.5% in all measurements for the three pistonsused. Dynamic viscosities of heavy dead crude oils were obtained at a temperature range from 397.1 to300.8 K, viscosities in the range of 10.97476.7 cP, oil API gravity from 11.5 to 19.4, and at a constantpressure of 0.1 MPa. The estimated uncertainty on viscosity was less than 71.0% over the temperaturerange of measurements. A new correlation approach was developed to estimate dynamic viscosities ofMexican heavy crude oils based on oil API gravity, and temperature.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

The knowledge of the dynamic viscosity of heavy and extra-heavy oils is very important in the petroleum industry; particu-larly, dynamic viscosity of dead crude oil can be used as inputinformation to simulators for designing of tubing or pipelines,pumping, optimizing production strategies, and transportationsystems as well as for heavy crude oil recovery processes(Barrufet and Setiadarma, 2003; Barrufet and Dexheimer, 2004;Naseri et al., 2005; Malallah et al., 2006; Ikiensikimama andOgboja, 2009). Nowadays, the enormous increase in oil demandand the progressive depletion of low-viscosity oil reservoirs haveled to the fast development of very large world resources of heavyand extra-heavy crude oils. However, production, distribution,transport, blending, and the conditioning process (dehydrationand desalted) of such crude oils are technological challenges dueto their very high viscosities (Barrufet and Setiadarma, 2003).

Generally, the very common practice for estimating dynamicviscosity of crude oils is by means of viscosity correlations.Nevertheless, it is well-known that most of these correlations

are inadequate to predict oil viscosities at a wide range ofoperating conditions such as temperature and pressure. Eventhough numerous viscosity correlations and prediction methodsare reported in the literature almost all of them are empirical(Beal, 1946; Beggs and Robinson, 1975; Vazquez and Beggs, 1980;Glas, 1980; Ng and Egbogah, 1990; Sutton and Farshad, 1990;Labedi, 1992; Kartoatmodjo and Schmidt, 1994; de Ghetto et al.,1995; Petrosky and Farshad, 1995; Elsharkawy and Alikhan, 1999;Dindoruk and Christman, 2004; Naseri et al., 2005; Hossain et al.,2005; Sattarin et al., 2007) or semi-empirical (Lohrenz et al., 1964;Little and Kennedy, 1968; Teja and Rice, 1982; Ahrabi et al., 1987;Johnson and Mehrotra, 1987; Mehrotra and Svrcek, 1988;Mehrotra, 1991; Miadonye, 1992; Orbey and Sandler, 1993;Barrufet and Setiadarma, 2003). The published correlations aremostly based on regional data thereby a universal correlationcapable of being applied to crude oils produced in a differentgeographic region is not available. This deviation is attributed tothe complexity of crude oil itself for different regions (Sattarinet al., 2007). Our study was focused on developing a heavy dead oilcorrelation for on-shore and off-shore Mexican crude oils withrespect to their nature.

On the other hand, there are difculties in obtaining reliableviscosity measurements (Bennison, 1998; Sattarin et al., 2007); theviscosity of crude oils is commonly measured by either the rollingball viscometer or the capillary tube viscometer. In the rolling ball

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/petrol

Journal of Petroleum Science and Engineering

0920-4105/$ - see front matter & 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.petrol.2013.09.003

n Corresponding author. Tel.: 52 559 175 6503.E-mail addresses: [email protected] (J.L. Mendoza de la Cruz),

[email protected] (S. Alvarez-Badillo), [email protected] (E. Ramrez-Jaramillo),[email protected] (M.A. Aquino-Olivos), [email protected] (P. Orea).

Journal of Petroleum Science and Engineering 110 (2013) 184192

viscometer, the time required by the steel ball to travel throughthe uid is correlated to its density and viscosity. In addition, thismethod is limited and subject to errors, because density at thesame temperatures and pressures is needed as a multiplier tocalculate the dynamic viscosity value; it is common that thisdensity is measured in a pVT cell connected to the viscometer andit is very difcult to achieve the same pressures and temperaturesused in the density measurements (Barrufet et al., 1993; Estrada-Baltazar et al., 1998; Iglesias-Silva et al., 1999). The apparatusdescribed here is based on a simple and reliable electromagneticconcept. Two coils move a mobile element back and forthmagnetically at a constant force; the main advantages of thisviscometer are the small amount of sample needed and the shorttime required for a measurement; we measured the dynamicviscosity of heavy dead crude oils at temperatures ranging from397.1 to 300.8 K, and viscosities in the range of 10.9147476.729 cPat a pressure of 0.1 MPa. The oil samples were collected fromrepresentative monophasic-bottom-hole uids of Mexican reser-voirs, after they were ashed at atmospheric conditions. Moreover,we used experimental measurements of viscosity from eldslocated in the area in order to test the viability of using thiscorrelation. Statistical comparisons indicated that the new correla-tion developed in the present work reduces the error involved inpredicting the dynamic viscosity of Mexican heavy crude oilswhen existing correlations in literature are employed. The pro-posed correlation, based on a database of 104 viscosity data, showssignicant improvement (from 11% to 90%) over previous correla-tions published in the literature; therefore, the aim of this rstpaper is to develop a dynamic viscosity correlation for Mexicanheavy dead crude oils, which can reliably be used by reservoirengineers for evaluating crude oil and/or mixture viscosity as wellas by chemical engineers for designing of oileld and reneryprocesses.

2. Reservoir uids, viscosity standards and methods

A reliable set of 98 dynamic viscosity data from Mexican offand on-shore heavy dead crude oil samples was measured in ourlaboratory over the last ten years; six viscosity data sets werecollected from another laboratory. All the viscosity standards usedin this investigation were supplied by Cannon Instrument Com-pany; they were used without further purication or analysis. TheASTM-D5002 procedure was used to measure density and relativedensity of dead crude oil samples.

In order to measure the performance of the proposed correla-tion here, we adopted two forms of analysis: (i) quantitativeanalysis by means of statistical error analysis and (ii) qualitativeanalysis using cross plots. The existing oil viscosity correlationswere assessed for their performances using statistical parameters(see Appendix) and performance plots. From the general evalua-tion, we utilized the percent mean absolute relative error as thescreening criterion (Hossain et al., 2005; Ikiensikimama andOgboja, 2009).

2.1. Crude oil characterization

The majority of dead crude oils used here have a high contentof asphaltenes. Asphaltene fraction was extracted from crude oilsby addition of an excess of n-heptane (ASTM D 3279-97). Themaltenes fraction was separated in saturates, aromatics, and resinsusing a procedure by an HPLC technique as has been describedelsewhere (Buenrostro-Gonzalez et al., 2001). Table 1 shows thedifferent fractions for ve dead crude oils. Unfortunately, we donot have information of the SARA analysis for crude oils 1 and 7.

3. Experimental section

3.1. Description of the viscometer

The viscometer (model SPL 440) used in this work wasdesigned and manufactured by Cambridge Applied Systems (CAS,USA) to make viscosity measurements of liquids for a viscosityrange of 0.210,000 cP (mPa s) at pressures up to 137.9 MPa(20,000 psi) and for temperatures up to 463.2 K (190 1C). Theinternal volume of the viscometer is less than 2 mL (Jakewaysand Goodwin, 2005). The six pistons (0.22, 0.510, 120, 10200,1002000, and 50010,000 cP) were calibrated by the manufac-turer with an uncertainty of 71% of full scale. In this study, basedon the viscosity of the uids analyzed, we used only three pistonsin the viscosity range from 10 to 10,000 cP.

3.2. Operation

The operation principle of this apparatus is based on a simpleand reliable electromagnetic concept which uses solely one mova-ble constituent through a uid in a small measurement chamber(MC). A schematic diagram of the viscometer is shown in Fig. 1. Aferromagnetic piston (P) is immersed into the MC which is oodedcontinuously with the uid sample to be analyzed. The viscometercontains two magnetic coils (C) inside a stainless steel body(B) which are placed surrounding the MC; the P inside the MC ismagnetically forced back and forth at a constant force. When theMC is lled up with the uid sample, the inner B coil is activatedand the magnetic force exerted on the P pulls it down toward thebase of the MC; thus, it forces the uid sample to ow around thepiston toward the sensor opening where it interchanges with thenormal ow of the uid sample. Simultaneously, the upper A coilis used to magnetically monitor the piston motion downstream. On

Table 1SARA analysis of the most of heavy dead crude oils used in this work.

Group Crude oil

2 3 4 5 6

Saturates 26.23 15.50 12.89 16.49 17.32Aromatics 31.03 28.61 40.05 10.33 44.51Resins 29.92 33.75 31.86 60.18 30.78Asphaltenes 13.82 22.14 15.13 12.96 7.34

Fig. 1. Schematic diagram of the constant force electromagnetic viscometer.

J.L. Mendoza de la Cruz et al. / Journal of Petroleum Science and Engineering 110 (2013) 184192 185

the upward piston stroke, fresh uid sample is pulled around the Pto the bottom of the MC. The ow detector continuously diverts theuid sample from the uid stream into the outer region of the MC.The motion of the P into and out of the MC drags a fresh uidsample into the rear region of the MC continuously refreshing theMC; this motion of the P is detected magnetically by means of thetwo magnetic coils.

When the piston reaches the bottom of the MC, the upper Acoil is activated and the lower coil B is used then to monitor thedisplacement of the P's upward stream. During this reverse cycle,sample uid is pulled in behind the P. When P reaches thedeector fence, the inner B coil is again activated and theprocess is repeated. As the piston is driven back and forth, boththe retaining fence and the piston motion continuously refresh theuid sample inside the MC. Since measurement of the motion ofthe P is made in two directions, variations in travel time due tovibration, orientation, and ow are assumed to be negligible.Throughout the cycle, the temperature of the uid sample ismeasured using a temperature sensor (RTD) mounted at the baseof the MC. The time required for the piston to move a xeddistance is then accurately related to the dynamic viscosity of theuid. Thus, the higher the viscosity of the uid inside the MC, theslower the piston motion .

3.3. Calibration and validation of the viscometer

In order to determine accurate values of the viscosity it is veryimportant to carry out a careful calibration of the apparatus, aswell as the temperature sensor and the pressure transducer usedin experiments. Viscosity standards supplied by Cannon Instru-ments Company were used by the manufacturer to calibrate all thepistons covering the viscosity range of 0.210,000 cP; kinematicviscosity measurements at temperatures of 2040 1C were madeusing Cannon and Cannon-Ubbelohde Master viscometers accord-ing to ASTM D2162. Measurements at lower and higher tempera-tures were determined by Cannon-Ubbelohde Laboratory Standardviscometers; the expanded uncertainty of the measurements at95% condence over the temperature range of 40 1C to 150 1Cwas as follow: (i) up to 1000 mm2/s (70.44%), (ii) between 1000and 10,000 mm2/s (70.55%), and (iii) greater than 10,000 mm2/s(70.74%). The assigned accuracy of the primary viscosity standard[water at 20 1C (ITS-90) with a viscosity of 1.0016 cP or kinematicviscosity of 1.0034 mm2/s as listed in ISO 3666] was 70.17%.

In our laboratory, the viscometer pistons were recalibrated inthe measuring range of 1010,000 cP (three pistons: 10200 cP,1002000 cP, and 50010,000 cP) with several calibration uidswith a maximum standard deviation of 0.5% (for calibration uids).To validate the calibration process, viscosity measurements withsome viscosity standards were carried out at various temperaturesin order to verify the accuracy of each piston used; the differencesbetween our results and those reported by the supplier were lessthan 75% over the temperature range of interest; the repeat-ability was about 71%.

3.4. Temperature measurement and regulation of the viscometer

The viscometer was thermostated by circulating white mineralfrom a stirred uid bath (Polystat, Cole Parmer, model 12105-10)through an insulating jacket that surrounded the stainless steel body,with a stability of 70.01 1C. Heating tapes were used for heating allthe external tubing lines from the viscometer. The temperature of theviscometer was measured with a platinum resistance thermometerwith a nominal resistance of 100 (RTD) which is mounted andwelded at the base of MC and is connected to a digital indicator. TheRTD and the digital panel meter were calibrated with a platinum

resistance thermometer (T100-450) with an overall uncertainty of70.1 1C in the working temperature range.

3.5. Pressure measurement and generation of the viscometer

A high pressure positive displacement pump (maximum workingpressure of 103.4 MPa, total volume of 500 mL) was used to transferthe uid as well as to reach the desired pressure in the whole system.Pressures were measured by means of a transducer (Heise, model901A, pressure range from 0 to 68.9 MPa) connected to the measure-ment circuit. The pressure transducer was calibrated against a deadweight balance (Pressurements, model M 2 200/4, accuracy of 0.015%in full scale). The estimated uncertainty of the pressure measurementswas 70.02% in the working pressure range.

3.6. Procedure

Fig. 2 shows the schematic diagram of the experimental setupused in this investigation to measure liquid viscosities. Firstly, analiquot (approximately 1015 mL) of crude oil to be studied isplaced in a high pressure cylinder (CYL, volume capacity 250 mLand maximum pressure 68.9 MPa); the pressure is provided bymeans of a positive displacement pump (P, pressure maximum68.9 MPa, volume displacement capacity 500 mL). Once the sam-ple is loaded inside the cylinder, the next step is to connect itthrough valves V4 and V5; then, a vacuum pump (VP) is connectedthrough V7 to evacuate the entire system until a suitable vacuumis attained (usually after 2030 min). In viscosity measurements ofthe reservoir uid, the viscometer is lled with each uid at leastto the temperature of 371.0 K and cooled to the lowest tempera-ture (303.0 K) while continuously oscillating the piston before

Fig. 2. Schematic diagram for measuring of the dynamic viscosity at differentpressure and temperature conditions. CTC: circulating bath; RCT: resistancetemperature detector; VP: vacuum pump; DPI: digital pressure indicator; HF:hydraulic uid; M: manometer; DP: positive displacement pump; V: viscometer;and RV: relief valve.

J.L. Mendoza de la Cruz et al. / Journal of Petroleum Science and Engineering 110 (2013) 184192186

starting measurements. After thermal equilibrium is achieved, thesystem pressure is increased up to 0.1 MPa, and viscosity measure-ments are obtained (Heredia-Castro, 2007).

4. Results and discussion

In this work, dynamic viscosity data of seven heavy dead crudeoils from Mexican reservoir have been used. A reliable set of 104Mexican off and on-shore dead crude oil viscosities was collectedover the last 10 years in the Laboratorio de Productividad de Pozos(LPP) from the Instituto Mexicano del Petrleo; 98 dynamic viscos-ity data sets were measured at LPP while the rest of them werecollected from another laboratory. Most of the oil samples weremeasured at a temperature range of 397.1300.8 K; for oil APIgravity, data were considered in the range from 11.5 to 19.4.

4.1. Statistical parameters

The basic statistical parameters used for correlation perfor-mance evaluation were average percentage relative error (APRE),average absolute percentage relative error (AAPRE), standarddeviation, and correlation coefcient (r2). See Appendix for moredetails.

4.2. Development of the viscosity correlation

The correlation for heavy dead crude oil viscosity was devel-oped by plotting ln(1/T1/3) vs. ln ln[(od1)API3] on Cartesiancoordinates. The plots revealed a series of straight lines of constantslope (Fig. 3). It was found that each of these lines corresponded toa different crude oil API gravity; then, these lines were tted withan empirical equation to obtain

od ea

API31 1

where

a 39;053:9772T 1:3683

and T [] in K.Table 2 shows the obtained parameters for each set of dynamic

viscosity corresponding to different heavy crude oils used. It isevident that all viscosity data for each crude oil follow a linealbehavior, as shown in Fig. 1 and Table 2.

4.3. Evaluation and analysis of dead crude oil correlationspublished in literature

Several published correlations for dead oil viscosity data werecompared with the data set measured and collected at the LPP. Alist of these correlations can be found elsewhere (Orbey andSandler, 1993; Petrosky and Farshad, 1995). The majority of theoil viscosity correlations were assessed and analyzed by compar-ing the predicted and measured viscosities in our lab, their trends;their values of AAPRE, APRE, standard deviation, and correlationcoefcient, which are the main criteria for evaluating the correla-tions presented here.

As the rst step, calculated dynamic viscosities were comparedwith measured viscosities at different temperatures for eachcorrelation by plotting them as a function of temperature. Fig. 4shows a sample graph of a heavy crude oil (Oil 3) from Mexicanreservoirs in ln(od) vs. temperature coordinates. It can beobserved that all the correlations underestimate the viscosity.Table 3 gives the results of proposed correlation and also of othersfor estimating dead oil viscosity; this table shows that thesuggested correlation to predict the dynamic viscosity for Oil3 has the lowest average absolute percentage relative error (AAPRE%) and standard deviation in comparison with currently availablecorrelations. Sattarin et al. (2007) correlation has the biggestAAPRE % and standard deviation. This correlation is not shownin the plot. Fig. 4 shows the predicted vs. experimental dynamicviscosities in the temperature range from 319 to 379 K and forviscosities in the range of 27317 cP.

For higher viscosities, we analyzed Oil 4 for those correlationsthat predict the viscosities with a good approximation as well asfor those correlations for predicting such transport property withhigh errors, including in both analyses of our proposed correlation.From Fig. 5 we can observe that Bennison's correlation predic-ted the viscosity behavior with good accuracy in the temperature

2.3

2.4

2.5

2.6

2.7

2.8

2.9

-2.02 -2.00 -1.98 -1.96 -1.94 -1.92 -1.90 -1.88

ln ln

[(od

+1)A

PI3 ]

ln (1/T1/3)

Oil 1

Oil 2

Oil 3

Oil 4

Oil 5

Oil 6

Oil 7

Fig. 3. Behavior of viscosity as a function of temperature.

Table 2List of obtained values using ln vs. ln ln model.

Crude oil Experimental data Lineal behavior

m b r2

1 14 4.9447 12.2268 0.9992 20 4.1240 10.6471 0.9923 13 3.6080 9.6009 0.9954 17 4.2946 10.9158 0.9965 15 4.9137 12.1411 0.9996 19 3.8717 10.0899 0.9887 6 3.3419 9.0849 0.998

1

10

100

1000

310 320 330 340 350 360 370 380 390

od

(cP)

Temperature (K)

Experimental BealBeggs-Robinson GlasNg-Egbogah Kartoatmodjo-SchmidtPetrosky-Farshad BennisonElsharkawy-Alikhan Proposed correlation

Fig. 4. Predicted dead crude oil viscosity vs. temperature compared with experi-mental data for Oil 3 (oil API gravity of 19.4).


range from 313 to 343 K (relative error less than 10%), whichcorresponds to viscosities of 1700200 cP while at higher tem-peratures the relative error was signicant. Beal's correlationoverestimates the viscosities up to 353 K (maximum relative errorof 50%) and at higher temperatures the viscosity is underestimatedwith a maximum error of 39%. The proposed correlation in thisstudy overestimated the viscosity in all ranges of temperaturewith a maximum deviation of 21%. Fig. 6 shows the rest of thecorrelations analyzed here. We can observe that most of thecorrelations, except for the Ng and Egbogah model, underestimatethe viscosity values. Table 4 summaries the comparisons among

the predictions of different dead crude oil viscosity correlationsand the measured Oil 4 viscosities. KartoatmodjoSchmidt andLabedi correlations have bigger values of AAPRE %, DMax %, andstandard deviation for this type of heavy dead oil.

Viscosity trend as a function of temperature is another impor-tant criterion in order to select the best correlation for develop-ment or modication (Dindoruk and Christman, 2004). Thederivatives of the viscosities with respect to temperature wereapplied for Oil 4 as it can be seen in Fig. 7. From this behavior, we

Table 3Statistical parameters for dead oil viscosity correlations compared with Oil 3.

Correlation Statistical parameters

AAPRE (%) APRE (%) DMax (%) s (%)

Beal 59 59 74 62BeggsRobinson 75 75 80 78Glas 56 59 80 61Egbogah 59 59 84 64NgEgbogah 62 62 135 79KartoatmodjoSchmidt 43 43 75 50Labedi 55 4 125 67PetroskyFarshad 58 58 86 64Bennison 63 63 75 66ElsharkawyAlikhan 52 52 76 57Naseri et al. 71 71 88 75Sattarin et al. 78 78 85 81This work 13 4 21 14

10

100

1000

10000

300 320 340 360 380 400

od

(cP)

Temperature (K)

Experimental

Beal

Bennison

Proposed correlation

Fig. 5. Best correlations for predicting dead crude oil viscosity vs. temperaturecompared with experimental data for Oil 4 (oil API gravity of 12.0).

1

10

100

1000

10000

300 320 340 360 380 400

od

(cP)

Temperature (K)

Experimental Beggs-Robinson

Glas Ng-Egbogah

Kartoatmodjo-Schmidt Petrosky-Farshad

Elsharkawy-Alikhan Proposed correlation


Table 4Statistical parameters for dead oil viscosity correlations compared with Oil 4.



Beal 38 38 52 41BeggsRobinson 86 86 89 89Glas 43 15 80 51Egbogah 65 65 90 7080NgEgbogah 38 24 63 44KartoatmodjoSchmidt 159 155 437 215Labedi 134 77 490 19,724PetroskyFarshad 55 32 90 64Bennison 51 51 52 52ElsharkawyAlikhan 52 52 74 58Naseri et al. 61 60 94 70Sattarin et al. 57 57 92 65This work 26 25 59 32

-250

-200

-150

-100

-50

0300 320 340 360 380 400

dod

/dT

Temperature (K)

Experimental

Beal

Bennison


Fig. 7. Viscosity derivatives vs. temperature compared with the best correlationsfor Oil 4.

10

100

1000

10000

300 320 340 360 380

od

(cP)

Temperature (K)

Experimental

Beal

Ng-Egbogah

Bennison


Fig. 8. Best correlations for predicting dead crude oil viscosity vs. temperaturecompared with experimental data for Oil 1 (oil API gravity of 11.5).


can observe that Bennison's correlation is the closest in compar-ison with Beal's and our proposed correlations at high tempera-tures. However, at temperatures lower than 320 K our model is theclosest.

Finally, we analyzed our proposed correlation with thosecorrelations available in literature for Oil 1, which were measuredin a temperature range from 308 to 375 K corresponding toviscosities of 7477 and 78 cP, respectively. Fig. 8 shows the bestcorrelations for dynamic viscosity data for Oil 1. It can be observed

that most of these correlations underestimate the viscosity value,except for the Ng and Egbogah correlations at temperatures higherthan 196 K. Table 5 summarizes the comparison between predic-tions and experimental data for Oil 1. In Fig. 8 and Table 5, it can beobserved that our proposed correlation was better than others topredict the experimental viscosity data, up to a temperature of323 K corresponding to the viscosities of 2000 cP. At lowertemperatures of 323 K, Beal's correlation predicts the viscosityvalue with a good approximation. The viscosity behavior predictedby Bennison correlation is similar to that estimated by Bealcorrelation. Fig. 9 shows the comparisons among predictions andexperimental data using other correlations for Oil 1. In Fig. 9 andTable 5, we can see that BeggRobinson, Egboga, KartoatmodjoSchmidt, and Labedi correlations are inappropriate for predictingviscosities of heavy crude oils. Tables 6 and 7 show summaries ofthe statistical parameters obtained for dead crude oil correlationsavailable in the literature, including our proposed correlation.

Following the viscosity trend as a function of temperature,Fig. 10 shows the derivatives of the viscosity data with respect totemperature for Oil 1. It can be seen that Beals's correlations is theclosest in comparison with NgEgbogah, Bennison, and ourproposed correlation. The derivative dod/dT, calculated from allthese correlations, undergoes a deviation as temperature of crudeoil is decreased.

The performance of the various dead oil viscosity correlationswas evaluated and analyzed for all heavy oil data used. For allcorrelations, both quantitative and qualitative statistical calcula-tions were done. Figs. 11 and 12 show the cross plots for viscositiesof the seven samples of heavy oil (Oil 17) compared with the bestcorrelations and those correlations inappropriate to predict thedynamic viscosity of heavy oil; we included our proposed correla-tion in both of these gures. Table 8 shows some statisticalparameters for the most common published dead oil correlationsincluding the one proposed for the Mexican heavy dead crude oils.The statistical parameters used for these comparisons are in theAppendix.

In Figs. 11 and 12, and Table 8, we can observe that Beal andBennison correlations are the closest in order to predict deadcrude oil viscosities for this type of heavy oil from Mexicanreservoirs. The rest of the viscosity correlations are inadequate tobe applied. The results obtained of AAPRE, and APRE, for ourproposed correlation, are lower than those obtained with cur-rently available correlations. From statistical parameters analyzed,the proposed correlation shows signicant improvement (from11% to 90%) over all correlations evaluated and analyzed. It isimportant to point out that the proposed correlation is only

Table 5Statistical data for dead oil viscosity correlations compared with Oil 1.



Beal 38 38 52 41BeggsRobinson 86 86 89 89Glas 43 15 80 51Egbogah 65 65 90 7080NgEgbogah 38 24 63 44KartoatmodjoSchmidt 159 155 437 215Labedi 134 77 490 19,724PetroskyFarshad 55 32 90 64Bennison 51 51 52 52ElsharkawyAlikhan 52 52 74 58Naseri et al. 61 60 94 70Sattarin et al. 57 57 92 65This work 26 25 59 32

10

100

1000

10000

300 320 340 360 380

od

(cP)

Temperature (K)

ExperimentalBeggs-RobinsonGlasKartoatmodjo-SchmidtPetrosky-FarshadElsharkawy-AlikhanProposed correlation


Table 6AAPRE and APRE for dead oil viscosity correlations for the rest of the heavy crude oils.

Correlation Oil 2 Oil 4 Oil 5 Oil 6 Oil 7

AAPRE (%) APRE (%) AAPRE (%) APRE (%) AAPRE (%) APRE (%) AAPRE (%) APRE (%) AAPRE (%) APRE (%)

Beal 69 69 28 5 21 21 41 41 64 64BeggsRobinson 83 83 72 72 79 79 61 61 68 68Glas 57 57 69 57 45 11 38 35 60 60Egbogah 64 64 40 26 59 59 46 41 58 58NgEgbogah 46 7 61 60 35 1 126 126 79 79KartoatmodjoSchmidt 45 26 343 343 148 145 43 8 53 51Labedi 104 35 318 294 134 70 118 63 86 7PetroskyFarshad 57 57 76 36 58 32 47 39 60 60Bennison 68 68 14 11 34 34 44 44 67 67ElsharkawyAlikhan 59 59 26 4 43 41 36 29 52 51Naserti et al. 71 71 48 18 60 58 57 57 73 73Sattarin et al. 87 87 56 31 41 41 69 69 81 81This work 39 39 42 42 19 1 51 51 33 12


applicable to Mexican heavy crude oils, a type of oil in the APIgravity range of 11.5 to 19.4, and its applicability to other regionsshould be checked.

5. Conclusions

Dynamic viscosities of heavy dead crude oil from Mexicanreservoirs were measured using a constant force electromagneticviscometer. Dynamic viscosity reliable measurements of heavydead oil samples were obtained at a temperature range from 397.1

to 300.8 K, and viscosities in the range of 10.97476.7 cP, oil APIgravity from 11.5 to 19.4, and at a constant pressure of 0.1 MPawith an estimated uncertainty on viscosity less than 71.0% overthe temperature range of measurements.

The new correlation developed, based on a database of 104viscosity data for heavy dead oils, shows signicant improvement(from 11% to 90%) over previous correlations published in theliterature. An average percentage relative error of 33% wasachieved. Several empirical models for estimating the viscosityof dead oils were evaluated using dynamic viscosity data of crudeoils from Mexican reservoirs. It was found that most of thepublished models for predicting the dynamic viscosity of heavy

Table 7Standard deviation and DMax for dead oil viscosity correlations for the rest of the heavy crude oils.

Correlation Oil 2 Oil 4 Oil 5 Oil 6 Oil 7

sa (%) DMax (%) sa (%) DMax sa (%) DMax (%) sa (%) DMax (%) sa (%) DMax (%)

Beal 71 88 32 50 22 28 46 74 71 80BeggsRobinson 86 89 74 76 82 84 63 72 76 78Glas 64 92 88 162 54 98 49 81 70 84Egbogah 71 94 47 73 67 85 55 85 72 87NgEgbogah 55 97 82 159 44 100 150 255 115 219KartoatmodjoSchmidt 53 87 397 633 208 441 50 76 65 83Labedi 135 290 467 1056 199 512 155 342 117 218PetroskyFarshad 67 96 98 207 66 96 58 90 74 91Bennison 71 88 18 33 36 38 49 71 73 72ElsharkawyAlikhan 65 87 31 53 49 63 44 68 63 76Naserti et al. 76 97 56 83 69 92 64 91 82 91Sattarin et al. 89 96 65 96 52 86 71 85 88 87This work 41 58 45 58 23 37 58 92 41 58

-700

-600

-500

-400

-300

-200

-100

0300 320 340 360 380

dod

/dT

Temperature (K)

ExperimentalBealNg-EgbogahBennisonProposed correlation

Fig. 10. Viscosity derivatives vs. temperature compared with the best correlationsfor Oil 1.

0

2000

4000

6000

8000

0 2000 4000 6000 8000

Pred

icte

d (c

P)

Measured (cP)

BealNg-EgbogahBennisonProposed correlation

Fig. 11. Comparison of the proposed heavy dead oil viscosity correlation with thebest correlations.

0

2000

4000

6000

8000

0 2000 4000 6000 8000

Pred

icte

d (c

P)

Measured (cP)

Beggs-Robinson Glas

Kartoatmodjo-Schmidt Petrosky-Farshad

Elsharkawy-Alikhan Proposed correlation

Fig. 12. Comparison of the proposed heavy dead oil viscosity correlation with theother correlations available in the literature.

Table 8Statistical data for dead oil viscosity correlations compared with the proposedcorrelation.

Correlation Statistical parameter

APRE (%) AAPRE (%) r2 (%)

Beal 39 45 0.87BeggsRobinson 73 73 0.45Glas 22 52 0.60NgEgbogah 43 64 0.80KartoatmodjoSchmidt 83 123 0.84PetroskyFarshad 32 59 0.19Bennison 47 47 0.81ElsharkawyAlikhan 40 45 0.60This work 6 33 0.84


dead oils are unreliable in a wide temperature range. Fromstatistical analysis, it was demonstrated that the correlationproposed is one of the best in comparison with those publishedin the literature, which could be used to predict better outcomes infuture works.

Acknowledgments

This work was conducted at the Instituto Mexicano del Petrleoand nancially supported by the Laboratorio de Productividad dePozos (rea de Termodinmica de Altas Presiones).

Appendix

To compare the performances of the empirical correlations,statistical error analysis was performed. The following statisticalparameters were used for comparison:

A1. Average percentage relative error (APRE)

This parameter is a measure of the relative deviation of thepredicted values from the experimental values in percentage, andis expressed as

APRE 1nn

i 1100preexp=exp A1

where exp and pre are the experimental and predicted viscosities,respectively. The smaller the APRE is the more evenly distributedthe positive and negative differences between predicted andmeasured values are.

A2. Average absolute percentage relative error (AAPRE)

This statistical parameter measures the average value of theabsolute relative deviation of the measured valued from experi-mental data; this parameter is dened as

AAPRE 1nn

i 1100jpreexp=exp

A2

The smaller APPRE implies a better correlation. For similarvalues of AAPRE, the lowest standard deviation value denes thebest correlation. If the exp is close to zero the value of APRE andAAPRE can be signicantly high.

A3. Standard deviation

The standard deviation of the average absolute percentagerelative error (AAPRE) is dened in Eq. (A2), and it is a measureof the percent relative absolute spread or dispersion of the datadistribution:

%SDA sa

n

i 1100

preexpexp

" #2=n1

vuut A3

A lower value of standard deviation means a smaller degree ofdispersion. The accuracy of the correlation is determined by thevalue of the standard deviation, where a smaller value indicateshigher accuracy. The value of the standard deviation is usuallyexpressed as a percentage.

A4. The correlation coefcient

It represents the degree of success in reducing the standarddeviation by regression analysis, dened by

r1

n

i 1exppre2i =

n

i 1exp2i

sA4

where

1nn

i 1expi A5

The value of the correlation coefcient varies from 0 to 1. Acoefcient of zero indicates no relationship between the experi-mental and the predicted values while a 1 coefcient indicates aperfect positive relationship.

The performance plot (cross plot) is a graph of the predicted vs.measured properties with a reference 451 line to readily ascertainthe correlations tness and accuracy. A perfect correlation wouldplot as a straight line with a slope of 451 (see Figs. 11 and 12). Inaddition to the statistical parameters, this is necessary for select-ing the best of the very good correlations.

A5. The deviation maximum

DMax Max 100 preexpexp

!A6

References

Ahrabi, F., Ashcroft, S.J., Shearn, R.B., 1987. High pressure volumetric phasecomposition and viscosity data for a North Sea crude oil and NGL mixtures.Chem. Eng. Res. Des. 67, 329334.

Barrufet, M.A., Dexheimer, D., 2004. Use of an automatic data quality controlalgorithm for crude oil viscosity data. Fluid Phase Equilib. 219, 113121.

Barrufet, M.A., Tantawy, M., Iglesias-Silva, G.A., Salem, K., 1993. Liquid viscosities ofcarbon dioxidehydrocarbons from 310 K to 403 K. J. Chem. Eng. Data 41, 436.

Barrufet, M.A., Setiadarma, A., 2003. Reliable heavy oilsolvent viscosity mixingrules for viscosities up to 450 K and high pressure using a mercury capillaryviscometer. J. Pet. Sci. Eng. 40, 1726.

Beal, C., 1946. The viscosity of air, water, natural gas, crude oil and its associatedgases at oil eld temperatures and pressures. Trans. AIME 165, 94115.

Beggs, H.D., Robinson, J.R., 1975. Estimating the viscosity of crude oil systems. J. Pet.Technol. 9, 11401141.

Bennison, T.G., 1998. Prediction of heavy oil viscosity. In: Presented at the IBC HeavyOil Field Development Conference, 24 December. AEA Technology, London.

Buenrostro-Gonzalez, Espinosa-Pea, M., Andersen, S.I., Lira-Galeana, C., 2001. Pet.Sci. Technol. 19 (3 & 4), 299316.

de Ghetto, G., Paone, F., Villa, M., 1995. Pressurevolumetemperature correlationsfor heavy and extra heavy oils. In: Proceedings of the Society of PetroleumEngineers 30316, International Heavy Oil Symposium.

Dindoruk, B., Christman, P.G., 2004. PVT properties and viscosity correlations forGulf of Mexico oilsSPE Reserv. Eng.427437

Elsharkawy, A.M., Alikhan, A.A., 1999. Models for predicting the viscosity of MiddleEast crude oils. Fuel 78, 891903.

Estrada-Baltazar, A., Iglesias-Silva, G.A., Barrufet, M.A., 1998. Experimental liquidviscosities of pentane and pentanedecane from 298.15 K to 373.15 K and upto 25 MPa. J. Chem. Eng. Data 43, 601604.

Glas, O., 1980. Generalized pressurevolumetemperature correlation for crude oilsystem. J. Pet. Technol. 2, 785795.

Heredia-Castro, M. del R., 2007. Determinacin de la viscosidad dinmica de uidosde yacimientos mexicanos desde la regin de subenfriado hasta la presin desaturacin, usando un viscosmetro electromagntico a fuerza constante. Tesisde Licenciatura, Universidad Autnoma Metropolitana, Unidad Azcapotzalco.

Hossain, M.S., Sarica, C., Zhang, H.Q., Rhyne, L., Greenhill, K.L., 2005. Assessmentand development of heavy-oil viscosity correlations. In: SPE/PS-CIM-CHOA97907 PS2005-407 Presented at the 2005 SPE International Thermal Opera-tions and Heavy Oil Symposium, Nov. 13. Calgary, Alberta, Canada.

Iglesias-Silva, G.A., Estrada-Baltazar, A., Hall, K.R., Barrufet, M.A., 1999. Experimen-tal liquid viscosity of pentaneoctanedecane mixtures from 298.15 to373.15 K up to 25 MPa. J. Chem. Eng. Data 44, 13041309.

Ikiensikimama, S.S., Ogboja, O., 2009. Evaluation of empirically derived oil viscositycorrelations for the Niger Delta crude. J. Pet. Sci. Eng. 69, 214218.

Jakeways, C.V., Goodwin, A.R.H., 2005. The viscosity and density of 1-pro-pene,1,1,2,3,3,3-hexauorooxidized, polymd and polydimethylsiloxane at


temperatures from (313 to 373) K and a pressure of 0.1 MPa. J. Chem.Thermodyn. 37, 10931097.

Johnson, S.E., Mehrotra, A.K., 1987. Viscosity of Athabasca bitumen using the extendedprinciple of corresponding states. Ind. Eng. Chem. Res. 26, 22902298.

Kartoatmodjo, F., Schmidt, Z., 1994. Large data bank improves crude physicalproperty correlation. Oil Gas J. 4, 5155.

Labedi, R., 1992. Improved correlations for predicting the viscosity of light crudes.J. Pet. Sci. Eng. 8, 221234.

Little, J.E., Kennedy, H.T., 1968. Calculating the viscosity of hydrocarbon systemswith pressure, temperature, and composition. Soc. Pet. Eng. J. 6, 157162.

Lohrenz, J., Bray, B.C., Clark, C.R., 1964. Calculating viscosities of reservoir uid fromtheir composition. J. Pet. Technol. 10, 11701176.

Malallah, A., Garbhi, R., Algharaib, M., 2006. Accurate estimation of the word crudeoil PVT properties using graphical alternating conditional expectation. EnergyFuels 20, 688698.

Mehrotra, A.K., 1991. Generalized one parameter viscosity equation for light andmedium hydrocarbon. Ind. Eng. Chem. Res. 30, 13671372.

Mehrotra, A.K., Svrcek, Y., 1988. One parameter correlation for bitumen viscosity.Chem. Eng. Res. Des. 66, 323327.

Miadonye, A., 1992. One parameter correlation in the estimation of crude oilviscosity. In: SPE 26206, December. Department of Chemical Engineering,Lakehead University, Thunder Bay, Canada.

Naseri, A., Nikazar, M., Mousavi-Dehghani, S.A., 2005. A correlation approach forprediction of crude oil viscosities. J. Pet. Sci. Eng. 47, 163174.

Ng, T.J., Egbogah, E.O., 1990. An improved temperature-viscosity correlation forcrude oil systems. J. Pet. Sci. Eng. 5, 197200.

Orbey, H., Sandler, S.I., 1993. The prediction of the viscosity of liquid hydrocarbons andtheir mixtures as a function of temperature and pressure. Can. J. Chem. Eng. 71, 437.

Petrosky, J., Farshad, F., 1995. Viscosity correlation for the Gulf of Mexico oils. In:SPE 29468 Presented at the 1996 SPE Production Operations Symposium Held,April 24. Oklahoma City, OK, U.S.A.

Sattarin, M., Modarresi, H., Bayat, M., Teymori, M., 2007. New viscosity correlationsfor dead crude oils. Pet. Coal 49 (2), 3339.

Sutton, R.P., Farshad, F., 1990. Evaluation of empirically derived PVT properties for Gulf ofMexico crude oils. In: SPE 13172 SPE Reservoir Engineering, Feb. pp. 7986.

Teja, A.S., Rice, P., 1982. Generalized corresponding state method for the viscosity ofliquid mixturesx. Can. J. Chem. Fundam. 20, 7779.

Vazquez, M., Beggs, H.D., 1980. Correlations for uid physical prediction. J. Pet.Technol., 968970.


Measurements and correlation of Mexican heavy dead crude oil viscositiesIntroductionReservoir fluids, viscosity standards and methodsCrude oil characterization

Experimental sectionDescription of the viscometerOperationCalibration and validation of the viscometerTemperature measurement and regulation of the viscometerPressure measurement and generation of the viscometerProcedure

Results and discussionStatistical parametersDevelopment of the viscosity correlationEvaluation and analysis of dead crude oil correlations published in literature

ConclusionsAcknowledgmentsAppendixA1. Average percentage relative error (APRE)A2. Average absolute percentage relative error (AAPRE)A3. Standard deviationA4. The correlation coefficientA5. The deviation maximum

References

Documents

Dead Oil Viscosity Mexican Crudo