Viscosity of binary and multicomponent hydrocarbon fluids at highpressure and high temperature conditions: Measurements andpredictions

Khalil Kashefi, Antonin Chapoy n, Keith Bell 1, Bahman TohidiHydrates, Flow Assurance & Phase Equilibria Research Group, Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, UK

a r t i c l e i n f o

Article history:Received 1 November 2011Accepted 30 October 2013Available online 7 November 2013

Keywords:viscosity experimentcapillary tube viscometerHPHT conditionreservoir fluidviscosity prediction

a b s t r a c t

Viscosity estimation is essential for predicting flow regime and pressure drop through porous media andsurface facilities. The experimental data of reservoir fluid viscosity especially at high pressure and hightemperature condition are scarce and the need for knowledge of fluid property at this condition isincreasing.

In this communication, new experimental viscosity measurements at high pressure and high temper-ature are reported for three binary hydrocarbon systems: methane/heptane, methane/decane andmethane/toluene and three multi-component mixtures: a natural gas, a gas condensate and a syntheticvolatile oil. The measurements were conducted in a HPHT PVT cell equipped with capillary tube atpressures ranging from 34.5 to 138 MPa and temperature up to 473.15 K.

The experimental data obtained for these mixtures have been used to evaluate the performance ofdifferent viscosity models. The investigated viscosity models are the Lohrenz–Bray–Clark (LBC) correla-tion, the Pedersen correlation and a modified LBC correlation. Although the viscosity models wereapplied at challenging HPHT conditions, the predictions were in reasonable agreement with experi-mental results. In general, the Pedersen method showed slightly better viscosity predictions for thementioned hydrocarbon systems.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Knowledge of viscosity of reservoir fluids is in need to inves-tigate the flow behaviour of mixtures wherever transport ofmomentum occurs in fluid motion such as in pipelines, wellboreand porous media. Deep hydrocarbon reservoirs are increasinglybeing discovered world-wide. Due to their extreme conditions(i.e., high pressure/high temperature (HPHT)) the costs of explora-tion and drilling are considerably higher than conventional reser-voirs. In fact, drilling is one of the most expensive processes inthe development of high pressure, high temperature reservoirs.Optimising the number of wells, therefore, plays an important rolein minimising reservoir development expenditure.

Physical and rheological properties such as viscosity of reser-voir fluids at HPHT conditions are required to determine theoptimum number of wells and to design surface facilities. There-fore, experimental measurements of these properties are requiredto be made in laboratories. It is, however, impossible to measure

viscosity of hydrocarbon mixtures at all possible compositions in awide range of temperatures and pressures. Even if it were possible,the cost of obtaining all the necessary experimental data would beprohibitive. For these reasons, there are growing demands forreliable and accurate analytical predictive methods for viscositycalculation.

Petroleum and chemical industries employ several methods topredict the viscosity of fluids. The techniques described in theliterature can be categorised as empirical, semi-theoretical, andtheoretical models. Several reviews exist in the open sources thatreport viscosity prediction models for pure hydrocarbons andhydrocarbon mixtures with evaluation of the models (Monneryet al., 1995; Mehrotra et al., 1996; Boned et al., 2003; Yucel, 2005).Empirical and semi-theoretical approaches for viscosity calcula-tion like residual viscosity (Lohrenz et al., 1964), correspondingstates (Pedersen and Fredenslund, 1987) are more popular in theindustry.

There are limited experimental viscosity data for hydrocarbonmixtures at HPHT conditions. Different sources reported viscositydata for natural gases but almost none of them are at highpressure and high temperature conditions. Assael et al. (2001)reported natural gas viscosity data at 455 K and atmosphericpressure and also in the temperature range up to 353.15 K at

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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.2013.10.021

n Corresponding author. Tel.: þ44 131 451 3797.E-mail address: antonin.chapoy@pet.hw.ac.uk (A. Chapoy).1 In memory of our colleague who passed away before completion of this

manuscript.

Journal of Petroleum Science and Engineering 112 (2013) 153–160

pressures up to 15 MPa. Vogel et al. (2004) covered viscosity datafor up to 320.15 K at pressures up to 20 MPa for natural gases.There are some viscosity data on binary hydrocarbon systems suchas methane–decane in the literature; however, the data are not atHPHT conditions. Knapstad et al. (1990) performed viscosity testson methane–decane in the temperature range up to 423.15 K andpressure up to 40 MPa, Audonnet and Pádua (2004) coveredviscosity range for temperature up to 393.15 K and pressure upto 75 MPa, Canet et al. (2002) covered high pressure (up to135 MPa) and up to 373.15 K. The existing viscosity data forhydrocarbon mixtures in open sources are limited at both highpressure and high temperature. So there is a need to fill the gap inexperimental viscosity data for variety of hydrocarbon mixturesystems at HPHT conditions.

This study is focused on two main parts. First of all, theexperimental viscosity data for six different hydrocarbon fluidsat HPHT condition are presented. These measurements wereperformed in a HPHT rig equipped with a capillary tube atpressures ranging from about 35 to 135 MPa and temperature upto 473.15 K. The investigated systems were three binary hydro-carbon systems: methane/heptane, methane/decane and methane/toluene and three multi-component mixtures: a natural gas, a gascondensate and a synthetic volatile oil.

The experimental viscosity data obtained for these hydro-carbon mixtures have been used to investigate the reliability ofseveral viscosity predictive models. The Lohrenz–Bray–Clark (LBC)correlation, the Pedersen correlation and a modified LBC correla-tion are among the evaluated viscosity predictive techniques inthis work.

2. Experimental tests

2.1. HPHT PVT cell

A capillary viscometer was installed into a HPHT rig configuredto examine phase properties of fluids at pressures and temperatures

of deep hydrocarbon reservoirs conditions. The experimental equip-ment can be utilised for investigating PVT phase behaviour andproperties of pure and multi-component reservoir fluid systemswith and without water. Dew point, bubble point, phase volumes,interfacial tension, density, and viscosity measurements are thecurrent capabilities of the mentioned apparatus. The PVT facility isable to perform measurement from ambient conditions to a max-imum pressure of 135 MPa at 523.15 K or 200 MPa at 473.15 K. Thecapillary tube currently in use has a measured length of 14.781 mand a calibrated internal diameter of 0.29653 mm. A schematic ofthe HPHT facility (configured for viscosity measurement) can beseen in Fig. 1. To calculate the internal diameter several purecompounds were selected, with viscosities covering the range ofviscosity that is expected to encounter during experimental studiesand where reliable literature data were available. Using the experi-mentally measured differential pressures and the literature data theabove internal diameter was calculated. The two ends of thecapillary tube are connected to two small-volume (15 cm3) cells,which are mounted inside a temperature controlled air bath thatcan be thermostatically regulated. The base of each cell is connectedto both sides of a push–pull motor driven pump which is respon-sible for flowing the test fluids around the equipment, (this is alsohow equilibrium is established). A sight-glass is installed at the topof one of the cells, along with a magnifying system and videocamera for visual observation and recording. Pressure is generatedand maintained by a 15 cm3 mercury hand pump that is usedalso in loading samples into the HPHT facility. All of the pipeworkand fittings are made from 316 grade stainless steel (all rated to206 MPa). High pressure Quartzdyne QS 30K-B (u(P)¼70.02 MPa)transducers are employed to monitor the pressure at various partsof the equipment and used to estimate the differential pressuregenerated across the capillary tube viscometer. The pressure trans-ducers are monitored and recorded via a PC through RS 232serial ports.

2.2. Procedures

The pressure vessel (the left-hand side cell in Fig. 1) which iscontaining the gravimetrically prepared sample was installed inthe thermostatically controlled air-bath. The rest of the highpressure equipment (the capillary tube, the right-hand side celland the piping) was evacuated then filled with clean mercury.Heating was then applied, the pressure increased and the fluidpumped back and forth through the capillary tube viscometer, sothat it could attain single-phase and thermal equilibrium. Thismixing process was repeated before starting viscosity measure-ments for each of the temperatures studied (323.15, 373.15, 423.15and 473.15 K).

Prior to making any viscosity measurements a very approx-imate bubble-point measurement was made at each temperature,to ensure all measurements would be above the system saturationpressure. This was done by transferring all of the sample fluid intothe cell equipped with the window and slowly reducing thepressure until bubbles could be seen rising inside the window.

Nomenclature

ζ viscosity reducing parameterρr reduced densityηo dilute gas viscosity (cP)η viscosity (cP)ηref viscosity of reference fluid (cP)

Fη corresponding state reducing factorP pressure (MPa)Pref equivalent pressureT temperature (K)Tr reduced temperatureTref equivalent temperatureVc critical molar volume (ft3/lb mol)

Fig. 1. Schematic diagram of the high pressure/high temperature facility.

K. Kashefi et al. / Journal of Petroleum Science and Engineering 112 (2013) 153–160154

2.3. Fluid preparation

Six hydrocarbon systems ranging from binary to multi-component were studied to extend the experimental viscositydata of hydrocarbon fluids investigated at HPHT conditions.

The compounds used in preparing synthetic fluids are as:methane (Grade N4.5, Air Products Ltd.), n-pentane (Aldrich,anhydrous, Z99%), n-heptane (99þ%, over Molecular Sieve,AcroSeals, Acros Organics, New Jersey, USA), n-decane (Z99%,Sigma-Aldrichs), Toluene (water o30 ppm, AcroSeals, AcrosOrganics, New Jersey, USA), n-hexadecane (Aldrich, anhydrous,Z99%) and n-C21 (Aldrich, 98%).

The selected hydrocarbon binary systems in this investigationare as n-heptane/methane, n-decane/methane and toluene/methane. The liquid hydrocarbons were prepared gravimetrically,combined with methane, to a nominal composition of 60 mol%hydrocarbon liquid/40 mol% methane (composition given inTable 1). Three more complex systems were also investigated: agas condensate (name hereafter GCB00-1), a natural gas and asynthetic volatile oil. The synthetic volatile oil was preparedgravimetrically (composition given in Table 2).

GCB00-1 was gravimetrically prepared by ‘livening’ a fullycharacterised dead condensate with a natural gas (compositiongiven in Table 3). The characterisation of the dead condensateincluded its fractionation into single carbon number cuts from C6s

through to C25s, on each of which molecular weight and densitymeasurements were made, as well as for the C26þ distillationresidue (Table 3).

The composition of the natural gas is listed in Table 4. All thesamples were loaded in a solvent cleaned and evacuated 15 cm3,(316 stainless steel) HPHT pressure vessel.

3. Viscosity models

Some of the popular viscosity predictive methods used bypetroleum industry have been reviewed in this section. ThePeng–Robinson (Peng and Robinson, 1976) equation of state witha Peneloux volume correction (Peneloux et al., 1982), here after

PR-EoS, was employed to model the phase equilibria and to predictfluid density.

3.1. The Lohrenz–Bray–Clark (LBC) method

Lohrenz et al. (1964) extended JST method (Jossi et al. 1962)for calculating the viscosity of mixtures of naturally occurringhydrocarbons known as LBC method. A generalised relationshipbetween viscosity and the fourth degree polynomial of thereduced density (ρr), of the form below (Eq. (1)), for non-polargaseous and liquid substances, was formulated

½ðη�ηoÞζþ10�4�1=4 ¼ 0:10230þ0:023364ρrþ0:058533ρ2r

�0:040758ρ3r þ0:0093324ρ4

r ð1Þ

where ζ is the viscosity reducing parameter which is the inverse ofcritical viscosity ηc ¼ ðMW1=2P2=3

c =Tc1=6Þ, ρr is the reduced density,

a0–4 are the correlation coefficients.For monatomic compounds, the dilute gas viscosity, ηo, can be

evaluated from the following empirical expression as a function of

Table 1Molar composition of gravimetrically prepared binary mixtures.

Binary no. Component Composition 7

(mole%)

1 n-Heptane 58.0 0.05Methane 42.0 0.09

2 n-Decane 61.0 0.07Methane 39.0 0.11

3 Toluene 59.8 0.04Methane 40.2 0.06

Table 2Molar composition of gravimetrically prepared synthetic volatile oil.

Component Composition

(mole%) 7

Methane 86.5 0.102n-Pentane 1.7 0.012n-Decane 1.8 0.006n-Hexadecane 1.8 0.004nC21 8.2 0.007

Table 3Semi-Gravimetric Compositions of Gas Condensate (GCB00-1) (SG: standardgravity).

Component Measured MW SG (15.5 1C) Semi-gravimetrica

(Wt%) (mole%)

C1 16.04 40.55 69.62C2 30.07 14.35 13.14C3 44.10 14.72 9.19iC4

58.12 1.42 0.67nC4 58.12 5.13 2.43iC5 72.15 1.15 0.44nC5 72.15 1.48 0.57C6s 88.5 0.678 1.80 0.56C7s 92 0.733 1.99 0.60C8s 103 0.757 2.36 0.63C9s 116 0.778 1.76 0.42C10s 131 0.790 1.32 0.28C11s 147 0.789 1.26 0.24C12s 161 0.809 0.95 0.16C13s 173 0.822 1.02 0.16C14s 186 0.839 1.04 0.15C15s 203 0.837 0.85 0.12C16s 215 0.843 0.73 0.09C17s 229 0.841 0.80 0.10C18s 246 0.843 0.60 0.07C19s 258 0.854 0.51 0.05C20þ 384 0.88b 4.21 0.31

a The gas condensate was gravimetrically prepared by ‘livening’ a fullycharacterised dead condensate with a natural gas.

b C20þ Calculated values: derived from HTGC weight distributions and mea-sured values of C20s to C26þ cuts.

Table 4Composition of natural gas using GC.

Component Molecular weight Composition

(Mole%)

C1 16.043 88.83C2 30.069 5.18C3 44.096 1.64iC4

58.123 0.16nC4 58.123 0.27iC5 72.15 0.04nC5 72.15 0.04CO2 44.01 2.24N2 28.01 1.6

K. Kashefi et al. / Journal of Petroleum Science and Engineering 112 (2013) 153–160 155

reduced temperature, Tr:

ηoζi ¼ 0:00034T0:94r for Tro1:5 ð2Þ

ηoζi ¼ 0:0001778½4:58Tr�1:67�5=8 for Tr41:5 ð3ÞA procedure for calculating the viscosities of hydrocarbon

mixtures has been developed by Lohrenz et al. (1964) throughapplication of appropriate mixing rules. The mixture reducingparameter, ζ, can be calculated by molar averaging the mixturecritical properties and molecular weight, as shown below

ζ ¼ ∑ni ¼ 1ðxiTciÞ1=6

∑ni ¼ 1ðxiPciÞ2=3∑n

i ¼ 1ðxiMWiÞ1=2ð4Þ

Low pressure fluid viscosity is calculated by the formulation ofHerning and Zipprer (1936) of the form

ηo mix ¼∑n

i ¼ 1ðxiηoiffiffiffiffiffiffiffiffiffiffiffiMWi

pÞ

∑ni ¼ 1ðxi

ffiffiffiffiffiffiffiffiffiffiffiMWi

pÞ

ð5Þ

where ηo is defined above, xi is the mole fraction of component “i”in the mixture, MWi is the molecular weight of component “i” inthe mixture and the critical density can be calculated as below

ρc ¼1Vc

¼ 1∑n

i¼ 1iaC7þ

ðxiVciÞþxC7þ ðVcÞC7þð6Þ

where ðVCÞC7þ is the critical molar volume of the C7þ fraction

calculated from the following expression:

VcC7þ ¼ 21:573þ0:015122 MWC7þ �27:656 SGC7þ

þ0:070615 MWC7þ SGC7þ ð7Þ

where MWC7þ is the molecular weight of the C7þ fraction and

SGC7þ is the specific gravity of the C7þ fraction. The unit of ðVCÞC7þ

is ft3/lb mol.

3.2. The modified LBC (HW2) (Al-Syabi et al., 2001)

Al-Syabi et al. (2001) modified the LBC method by applying thereduced temperature (Tr) and the molecular weight (MW) to theformulation to develop a new correlation. Al-Syabi et al. (2001)present two different formulations for methane (Eq. (8)) andheavier hydrocarbons (Eq. (9)).

ðΔηrþ10�4Þ1=4 ¼ 0:10202þ0:055258ρr�0:01143ρ2r

þ0:0047894ρ3r þ7:94� 10�5T �3:2508

r ρ4r ð8Þ

ðΔηrþ10�4Þ1=4 ¼ 0:094754þ0:062016ρr

�0:0010273T �2:0183r MW0:44620ρ2

r

þ0:00040403T �2:47063r MW0:19188ρ3

r

þ0:000086159T �1:1577r MW0:58683ρ4

r ð9Þ

The procedure employed in calculating mixture viscosity usingEqs. (8) and (9) are similar to that employed by the LBC method.

3.3. The Pedersen method (Pedersen et al., 1984; Pedersen andFredenslund, 1987)

The origin of this method is Tham and Gubbins (1970)technique which was developed for predicting the viscosity ofpure liquid hydrocarbons. Pedersen et al. (1984) generalised theabove method for gas and liquid mixtures by employing Mo andGubbins (1974) mixing rules for calculating the mixture criticalproperties. Based on the above method, the viscosity of anysubstance can be determined from the below expression

ηðP; TÞ ¼ ηcηc;ref

!ηref ðPref ; Tref ÞFη ð10Þ

where η(P,T) is the viscosity of fluid of interest, ηref(Pref, Tref) is theviscosity of reference fluid, Pref and Tref are the equivalent pressureand temperature, respectively, proposed by the authors. ηc is thecritical viscosity,

ηc ¼ CMW1=2P2=3

c

T1=6 ð11Þ

Pc and Tc are the critical pressure (atm) and temperature (K),respectively, C is the constant, Fη is the corresponding statereducing factor, taken as the ratio of the rotational coupling factorof fluid of interest and the reference fluid.

4. Results and discussion

The experimental viscosity data and the evaluation of thepreviously mentioned models are presented in this section.Viscosity data of binaries 1–3 and the more complex fluids alongwith the prediction results are tabulated in Tables 5–10 andplotted in Figs. 2–7. The errors in viscosity measurements whichare reported in these tables are calculated for each data pointusing the propagation of errors (uncertainties) law.

The experimental viscosity data generated in this work wereused to evaluate the above mentioned viscosity models. Thedeviations of each method from experimental viscosity dataare illustrated against the experimental data in Figs. 2–7 for allof the experiments. The mentioned graphs are discussed later inthis section.

Table 5Measured and predicted viscosities of Binary no. 1 (methane/n-heptane).

T P η u(η) Pedersen LBC HW2

(K)a (MPa)b (cP) η Dev η Dev η Dev(cP) (%) (cP) (%) (cP) (%)

323.15 34.56 0.219 70.003 0.189 14 0.212 3 0.193 12323.15 51.81 0.254 70.003 0.219 14 0.258 �2 0.222 13323.15 68.97 0.286 70.004 0.247 14 0.301 �5 0.246 14323.15 86.16 0.323 70.004 0.275 15 0.342 �6 0.268 17323.15 103.43 0.356 70.005 0.303 15 0.380 �7 0.287 19323.15 120.69 0.393 70.005 0.331 16 0.416 �6 0.304 23323.15 131.03 0.414 70.005 0.348 16 0.436 �5 0.314 24373.15 34.56 0.154 70.002 0.141 9 0.109 6 0.115 0373.15 51.73 0.181 70.002 0.164 9 0.142 0 0.142 0373.15 68.97 0.209 70.003 0.186 11 0.175 �8 0.164 �1373.15 86.23 0.235 70.003 0.207 12 0.207 �13 0.184 0373.15 103.49 0.262 70.003 0.228 13 0.239 �17 0.202 1373.15 120.76 0.287 70.004 0.248 14 0.270 �19 0.218 4373.15 138 0.315 70.004 0.268 15 0.301 �22 0.232 6423.15 34.56 0.115 70.002 0.111 4 0.149 3 0.147 4423.15 51.74 0.142 70.002 0.131 8 0.189 �4 0.175 3423.15 69.02 0.162 70.002 0.149 8 0.227 �9 0.198 5423.15 86.22 0.184 70.002 0.166 10 0.264 �12 0.219 7423.15 103.51 0.204 70.003 0.183 10 0.300 �14 0.237 9423.15 120.7 0.227 70.003 0.199 13 0.334 �16 0.254 12423.15 137.94 0.246 70.003 0.214 13 0.366 �16 0.269 15473.15 34.56 0.092 70.001 0.091 1 0.084 9 0.092 0473.15 51.74 0.112 70.002 0.109 3 0.111 1 0.117 �5473.15 68.99 0.132 70.002 0.125 6 0.138 �5 0.139 �5473.15 86.21 0.151 70.002 0.139 8 0.166 �10 0.158 �5473.15 103.46 0.169 70.002 0.153 9 0.194 �15 0.175 �4473.15 120.73 0.188 70.002 0.166 12 0.222 �18 0.190 �1473.15 137.94 0.205 70.003 0.179 13 0.249 �22 0.204 0

a Uncertainty on temperature u(T)¼70.1 K.b uncertainty on pressure u(P)¼70.04 MPa.

K. Kashefi et al. / Journal of Petroleum Science and Engineering 112 (2013) 153–160156

4.1. Methane–heptane (Binary no. 1)

The results of the viscosity experiments performed on themethane/n-heptane binary (58.0 mol% n-heptane) system arereported in Table 5. At 323.15 K a very approximate value of19.7 MPa for the bubble point was observed but the bubblesformed were very small in size and proved very difficult toobserve. The bubble points at 373, 423 and 473 K were 12.9,12.65 and 11.08 MPa, respectively and the critical temperature andpressure of this system are 510.9 K and 8.04 MPa (calculated usingthe PR-EoS). The experiments started from about 34 MPa for alltemperatures which would be in the single phase. The sample wasmixed again before starting the first viscosity measurement onthis fluid at 34 MPa and 323.15 K (0.21970.003 cP). The equili-brium pressure was raised in steps of about 17 MPa to a maximumof about 130 MPa at 323.15 K (0.41470.005 cP). The other experi-mentally measured isotherms for the mentioned binary areat 373.15, 423.15 and 473.15 K up to 135 MPa. The experi-mental data are reported in Table 5. These results show that theviscosity increases with increasing pressure and/or a decreasingtemperature.

Deviations between predicted and experimental viscosities arealso listed in Table 5 and illustrated in Fig. 2. The Pedersden, LBCand HW2 methods predict the viscosity of this binary systemreasonably well with average absolute deviations of 10.7%, 9.8%and 7.5%, respectively (Table 11). In general, the discussed modelscan calculate viscosity of this mixture more accurately at lowerviscosity conditions (high temperature and low pressure).

Table 6Measured and predicted viscosities of Binary no. 2 (methane/n-Decane).

T P η u(η) Pedersen LBC HW2

(K)a (MPa)b (cP) η Dev η Dev η Dev(cP) (%) (cP) (%) (cP) (%)

323.15 12.73 0.343 70.004 0.274 20 0.309 10 0.284 17323.15 17.24 0.361 70.005 0.291 19 0.333 8 0.301 17323.15 34.45 0.43 70.005 0.356 17 0.419 3 0.360 16323.15 51.72 0.502 70.006 0.422 1 0.498 1 0.410 18323.15 68.94 0.574 70.007 0.488 15 0.570 1 0.453 21323.15 86.14 0.648 70.008 0.557 14 0.637 2 0.492 24323.15 103.42 0.728 70.009 0.629 14 0.699 4 0.526 28323.15 120.68 0.812 70.01 0.704 13 0.757 7 0.557 31323.15 137.87 0.902 70.011 0.783 13 0.810 10 0.585 35373.15 14.64 0.225 70.003 0.197 13 0.141 9 0.148 5373.15 17.29 0.233 70.003 0.204 12 0.213 �6 0.205 �1373.15 34.49 0.284 70.004 0.252 11 0.277 �15 0.247 �3373.15 51.71 0.332 70.004 0.297 11 0.339 �22 0.284 �2373.15 68.98 0.381 70.005 0.341 10 0.399 �26 0.317 0373.15 86.21 0.43 70.005 0.386 10 0.457 �29 0.346 2373.15 103.48 0.479 70.006 0.432 10 0.512 �31 0.372 5373.15 120.67 0.532 70.007 0.478 10 0.564 �32 0.395 7373.15 137.92 0.586 70.007 0.526 10 0.209 7 0.203 10423.15 15.38 0.155 70.002 0.148 5 0.221 5 0.213 9423.15 34.49 0.202 70.003 0.191 5 0.298 �5 0.267 6423.15 51.74 0.241 70.003 0.226 6 0.370 �12 0.312 6423.15 68.98 0.278 70.004 0.260 7 0.439 �15 0.352 8423.15 86.23 0.316 70.004 0.293 7 0.504 �17 0.387 10423.15 103.47 0.353 70.004 0.326 8 0.565 �18 0.418 13423.15 120.69 0.391 70.005 0.359 8 0.622 �17 0.446 16423.15 137.91 0.427 70.005 0.392 8 0.676 �15 0.472 19473.15 15.59 0.111 70.002 0.115 �3 0.098 11 0.108 3473.15 34.5 0.154 70.002 0.152 1 0.156 �2 0.161 �473.15 51.75 0.187 70.002 0.181 3 0.211 �13 0.201 �7473.15 68.98 0.217 70.003 0.209 4 0.265 �22 0.235 �8473.15 86.25 0.247 70.003 0.235 5 0.319 �29 0.266 �8473.15 103.48 0.277 70.004 0.261 6 0.372 �34 0.293 �6473.15 120.72 0.308 70.004 0.286 7 0.423 �37 0.318 �3473.15 137.93 0.338 70.004 0.312 8 0.472 �40 0.340 �1

a Uncertainty on temperature u(T)¼70.1 K.b uncertainty on pressure u(P)¼70.04 MPa.

Table 7Measured and predicted viscosities of Binary no. 3 (methane/toluene).

T P η u(η) Pedersen LBC HW2

(K)a (MPa)b (cP) η Dev η Dev η Dev(cP) (%) (cP) (%) (cP) (%)

323.15 34.54 0.238 70.003 0.226 5 0.218 9 0.204 14323.15 51.79 0.27 70.003 0.255 6 0.251 7 0.227 16323.15 69.04 0.303 70.004 0.284 6 0.283 7 0.248 18323.15 86.32 0.334 70.004 0.311 7 0.312 7 0.266 20323.15 103.46 0.367 70.005 0.339 8 0.340 7 0.282 23323.15 120.63 0.401 70.005 0.366 9 0.366 9 0.297 26323.15 137.89 0.435 70.006 0.394 10 0.390 10 0.310 29373.15 34.62 0.166 70.002 0.166 0 0.116 6 0.123 0373.15 51.88 0.191 70.002 0.190 1 0.143 1 0.146 �1373.15 69.06 0.216 70.003 0.211 2 0.168 �2 0.165 0373.15 86.29 0.239 70.003 0.232 3 0.193 �5 0.183 1373.15 103.53 0.265 70.003 0.252 5 0.217 � 0.198 3373.15 120.72 0.288 70.004 0.272 6 0.241 �8 0.212 5373.15 137.99 0.311 70.004 0.292 6 0.263 �9 0.225 7423.15 34.56 0.123 70.002 0.129 �5 0.157 5 0.157 5423.15 51.83 0.145 70.002 0.149 �3 0.188 2 0.180 6423.15 69.00 0.165 70.002 0.167 �1 0.217 0 0.200 8423.15 86.25 0.185 70.002 0.184 0 0.244 �2 0.217 9423.15 103.48 0.203 70.003 0.201 1 0.270 �2 0.233 12423.15 120.71 0.223 70.003 0.216 3 0.295 �3 0.247 14423.15 138.03 0.241 70.003 0.232 4 0.319 �3 0.260 16473.15 34.67 0.096 70.001 0.104 �8 0.090 7 0.098 �2473.15 51.79 0.116 70.002 0.122 �5 0.112 3 0.120 �4473.15 69.02 0.134 70.002 0.138 �3 0.134 0 0.139 �4473.15 86.26 0.151 70.002 0.153 �1 0.156 �3 0.156 �3473.15 103.48 0.169 70.002 0.167 1 0.178 �5 0.171 �1473.15 120.71 0.182 70.002 0.180 1 0.199 �9 0.185 �1473.15 138.07 0.197 70.003 0.193 2 0.219 �11 0.197 0

a Uncertainty on temperature u(T)¼70.1 K.b uncertainty on pressure u(P)¼70.04 MPa.

Table 8Measured and predicted viscosities of the gas condensate (GCB00-1).

T P η u(η) Pedersen LBC HW2

(K)a (MPa)b (cP) η Dev η Dev η Dev(cP) (%) (cP) (%) (cP) (%)

323.15 41.45 0.057 70.001 0.063 �11 0.051 11 0.052 8323.15 51.88 0.065 70.001 0.070 �8 0.057 12 0.059 9323.15 69.09 0.076 70.001 0.080 �6 0.066 13 0.068 10323.15 86.23 0.087 70.001 0.089 �2 0.075 14 0.076 12323.15 103.68 0.099 70.001 0.097 2 0.083 16 0.083 16323.15 121.07 0.108 70.002 0.105 3 0.091 15 0.089 17323.15 138.06 0.119 70.002 0.112 6 0.099 17 0.095 20373.15 41.72 0.048 70.001 0.052 �8 0.038 1 0.037 2373.15 51.88 0.052 70.001 0.058 �11 0.043 3 0.043 3373.15 69.02 0.062 70.001 0.067 �8 0.050 8 0.051 6373.15 86.23 0.071 70.001 0.075 �5 0.056 9 0.058 6373.15 103.46 0.08 70.001 0.082 �2 0.062 11 0.065 8373.15 120.71 0.089 70.001 0.088 1 0.069 12 0.071 9373.15 137.97 0.097 70.001 0.095 2 0.075 12 0.076 10423.15 41.61 0.038 70.001 0.044 �17 0.043 11 0.043 10423.15 51.9 0.044 70.001 0.050 �14 0.048 7 0.049 6423.15 69.00 0.054 70.001 0.058 �8 0.056 9 0.058 6423.15 86.21 0.062 70.001 0.065 �5 0.064 10 0.066 7423.15 103.5 0.07 70.001 0.072 �2 0.071 11 0.073 9423.15 120.68 0.078 70.001 0.078 1 0.078 12 0.079 11423.15 137.95 0.085 70.001 0.083 2 0.085 13 0.084 13473.15 41.52 0.034 70.001 0.040 �17 0.034 �1 0.033 2473.15 51.86 0.039 70.001 0.045 �15 0.039 0 0.038 2473.15 69.07 0.047 70.001 0.053 �12 0.045 3 0.046 3473.15 86.29 0.056 70.001 0.059 �5 0.051 8 0.052 6473.15 103.51 0.064 70.001 0.065 �1 0.057 11 0.059 8473.15 120.7 0.069 70.001 0.070 �1 0.062 10 0.064 7473.15 137.94 0.076 70.001 0.075 1 0.067 11 0.070 9

a Uncertainty on temperature u(T)¼70.1 K.b uncertainty on pressure u(P)¼70.04 MPa.

K. Kashefi et al. / Journal of Petroleum Science and Engineering 112 (2013) 153–160 157

4.2. Methane–decane (Binary no. 2)

Viscosity measurements were carried out on the methane/n-decane binary (61.0 mol% n-decane) and are reported in Table 6. A

Table 9Measured and predicted viscosities of the natural gas (NG).

T P η u(η) Pedersen LBC HW2

(K)a (MPa)b (cP) η Dev η Dev η Dev(cP) (%) (cP) (%) (cP) (%)

323.15 34.61 0.028 70.001 0.028 1 0.029 �4 0.028 2323.15 51.88 0.036 70.001 0.034 4 0.037 �3 0.036 0323.15 69.08 0.043 70.001 0.040 8 0.044 �3 0.043 �1323.15 86.25 0.049 70.001 0.044 10 0.051 �3 0.050 �2323.15 103.52 0.055 70.001 0.048 12 0.057 �4 0.056 �2323.15 120.7 0.06 70.001 0.052 13 0.063 �6 0.062 �3323.15 137.79 0.064 70.001 0.055 13 0.070 �9 0.067 �5373.15 34.6 0.026 70.001 0.025 3 0.024 4 0.023 7373.15 51.9 0.032 70.001 0.031 3 0.030 �4 0.029 1373.15 69.00 0.038 70.001 0.036 6 0.035 �1 0.034 3373.15 86.23 0.042 70.001 0.040 5 0.040 �3 0.039 1373.15 103.56 0.048 70.001 0.043 10 0.045 �1 0.044 1373.15 120.78 0.053 70.001 0.047 12 0.049 �2 0.048 �1373.15 137.79 0.057 70.001 0.050 13 0.053 �2 0.053 �1423.15 34.6 0.025 70.001 0.024 3 0.026 1 0.025 6423.15 51.79 0.029 70.001 0.029 0 0.033 �3 0.031 3423.15 69.06 0.035 70.001 0.033 5 0.039 �2 0.037 2423.15 86.27 0.039 70.001 0.037 5 0.044 �5 0.043 �3423.15 103.51 0.044 70.001 0.040 9 0.049 �3 0.049 �2423.15 120.72 0.048 70.001 0.043 10 0.054 �3 0.054 �2423.15 137.78 0.052 70.001 0.046 12 0.060 �5 0.059 �3473.15 34.63 0.024 70.001 0.024 0 0.023 2 0.023 4473.15 51.83 0.028 70.001 0.028 �1 0.029 �2 0.027 2473.15 69.05 0.033 70.001 0.032 4 0.033 �1 0.032 4473.15 86.27 0.037 70.001 0.035 5 0.038 �2 0.036 3473.15 103.5 0.041 70.001 0.038 7 0.042 �1 0.040 2473.15 120.75 0.045 70.001 0.041 9 0.045 �1 0.044 1473.15 137.75 0.049 70.001 0.043 12 0.049 0 0.048 2

a Uncertainty on temperature u(T)¼70.1 K.b Uncertainty on pressure u(P)¼70.04 MPa.

Table 10Measured and predicted viscosities of the synthetic volatile oil.

T P η u(η) Pedersen LBC HW2

(K)a (MPa)b (cP) η Dev η Dev η Dev(cP) (%) (cP) (%) (cP) (%)

323.15 76.23 0.273 70.003 0.218 20 0.280 �3 0.192 30323.15 86.38 0.293 70.004 0.231 21 0.316 �8 0.206 30323.15 103.51 0.329 70.004 0.253 23 0.379 �15 0.226 31323.15 120.77 0.367 70.005 0.274 25 0.443 �21 0.245 33323.15 137.92 0.404 70.005 0.296 27 0.506 �25 0.262 35373.15 69.24 0.18 70.002 0.125 0 0.119 5 0.111 11373.15 86.34 0.206 70.003 0.132 1 0.131 2 0.120 11373.15 103.51 0.233 70.003 0.148 6 0.166 �6 0.140 11373.15 120.74 0.259 70.003 0.163 9 0.204 �14 0.159 11373.15 137.95 0.286 70.004 0.177 12 0.244 �22 0.176 12423.15 62.25 0.125 70.002 0.190 14 0.286 �29 0.192 13423.15 69.15 0.134 70.002 0.162 10 0.177 2 0.146 19423.15 86.31 0.157 70.002 0.180 13 0.223 �8 0.168 19423.15 103.57 0.179 70.002 0.197 15 0.272 �17 0.188 19423.15 120.71 0.2 70.003 0.214 17 0.323 �25 0.206 20423.15 137.92 0.222 70.003 0.231 19 0.375 �31 0.223 22473.15 55.44 0.09 70.001 0.100 �11 0.086 4 0.085 5473.15 69.07 0.106 70.001 0.112 �6 0.104 1 0.101 5473.15 86.24 0.125 70.002 0.126 �1 0.130 �4 0.119 5473.15 103.5 0.144 70.002 0.139 3 0.159 �11 0.137 5473.15 120.71 0.163 70.002 0.151 7 0.191 �17 0.153 6473.15 137.94 0.182 70.002 0.163 11 0.225 �24 0.168 7

a Uncertainty on temperature 7u(T)¼70.1 K.b Uncertainty on pressure u(P)¼70.04 MPa.

0

0.1

0.2

0.3

0.4

0.5

0.6

25 50 75 100 125 150

Vis

cosi

ty,

/ cP

P/ MPa

Fig. 2. Predicted and experimental viscosity of Binary 1 (42.0 mole% methane and58.0 mole% heptane). Black lines: predictions using the Pedersen model. Dottedlines: predictions using the LBC model. Broken lines: predictions using the HW2model. This work: (●), T¼323.15 K (△), T¼373.15 K (◆), T¼423.15 K. (◇),T¼473.15 K.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 25 50 75 100 125 150

Vis

cosi

ty,

/ cP

P / MPa

Fig. 3. Predicted and experimental viscosity of Binary 2 (39.0 mole% methane and61.0 mole% decane). Black lines: predictions using the Pedersen model. Dottedlines: predictions using the LBC model. Broken lines: predictions using theHW2 model. This work: (●), T¼323.15 K (△), T¼373.15 K (◆), T¼423.15 K. (◇),T¼473.15 K.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

25 50 75 100 125 150

Vis

cosi

ty,

/ cP

P / MPa

Fig. 4. Predicted and experimental viscosity of Binary 3 (40.2 mole% methane and59.8 mole% toluene). Black lines: predictions using the Pedersen model. Dottedlines: predictions using the LBC model. Broken lines: predictions using theHW2 model. This work: (●), T¼323.15 K (△), T¼373.15 K (◆), T¼423.15 K. (◇),T¼473.15 K.

K. Kashefi et al. / Journal of Petroleum Science and Engineering 112 (2013) 153–160158

very approximate bubble point was observed at 12.07 MPa at323.15 K. The sample was mixed again before starting measure-ments at about 12.73 MPa (0.34370.004 cP). The equilibriumpressure was raised in eight pressure steps to a maximum of137.87 MPa (0.90270.011 cP). Approximate bubble point pressures

of 13.44, 14.13 and 13.44 MPa were observed for 373.15, 423.15 and473.15 K, respectively, before performing the viscosity measurementsat each of these temperatures (simply to ensure the measurementswere carried out in the liquid phase region). Also the calculated(using the PR-EoS) critical temperature and pressure for this binaryare as 597.7 K and 6.29 MPa.

The Pedersen, LBC and HW2 predict the viscosity of methane/decane binary with the average absolute deviation of 9.7%, 15.1%and 10.9%, respectively (Table 11). The models can predict thetrend of viscosity in the range of pressure and temperature. Table 6and Fig. 3 present the deviation percentage and the trend for eachmodel versus pressure for this binary.

4.3. Methane–toluene (Binary no. 3)

When the methane/toluene binary (59.8 mol% toluene) samplewas loaded into the HPHT rig and equilibrated by mixing at323.15 K, an approximate bubble point pressure of 27.58 MPawas measured. The approximate measured bubble points for thementioned binary at 373.15, 423.15 and 473.15 K are about 24.82,20.96 and 19.20 MPa, respectively. Also the calculated (with thePR-EoS) critical temperature and pressure for this binary are as555.4 K and 11.5 MPa. The pressure range for this test was 34.47 to137.90 MPa with steps of 17.24 MPa between viscosity measure-ments. As can be seen from the results in Table 7 the measuredviscosity for this fluid ranges from 0.09670.001 cP at 473.15 K and34.67 MPa to 0.43570.006 cP at 323.15 K and 137.89 MPa.

For this system, the Pedersen corresponding state approachpredicts the viscosity with an average absolute deviation of 4% andit is slightly superior to other models (Table 11). Fig. 4 and Table 7show the deviation of the investigated methods versus pressurefor this binary.

4.4. Gas condensate (GCB00-1)

The gas condensate (GCB00-1) sample was mixed beforestarting the measurements to ensure the sample was at equili-brium. Measurements of viscosity were then preformed in pres-sure steps from about 41.37 to 137.90 MPa and temperaturesof 323.15, 373.15, 423.15 and 473.15 K. The approximates criticaltemperature and pressure of this system were calculated using thePR-EoS as 386 K and 18.4 MPa, so at above mentioned measure-ment temperatures the system would be in the single phaseregion. The data in Table 8 show the viscosity increases withincreasing pressure and/or decreasing temperature.

Fig. 5 shows the deviation of the viscosity models againstpressure for this system and it is also tabulated in Table 8.Generally, for this recombined reservoir fluid, the predictions ofalmost all models are in good agreement with the experimentaldata (Table 11).

0

0.02

0.04

0.06

0.08

0.1

0.12

25 50 75 100 125 150

Vis

cosi

ty,

/ cP

P / MPa

Fig. 5. Predicted and experimental viscosity of the gas condensate (compositiongiven in Table 3). Black lines: predictions using the Pedersen model. Dotted lines:predictions using the LBC model. Broken lines: predictions using the HW2 model.This work: (●), T¼323.15 K (△), T¼373.15 K (◆), T¼423.15 K. (◇), T¼473.15 K.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

25 50 75 100 125 150

Vis

cosi

ty,

/ cP

P / MPa

Fig. 6. Predicted and experimental viscosity of the natural gas (composition givenin Table 4). Black lines: predictions using the Pedersen model. Dotted lines:Predictions using the LBC model. Broken lines: Predictions using the HW2 model.This work: (●), T¼323.15 K (△), T¼373.15 K (◆), T¼423.15 K. (◇), T¼473.15 K.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

25 50 75 100 125 150

Vis

cosi

ty,

/ cP

P / MPa

Fig. 7. Predicted and experimental viscosity of the synthetic volatile oil (composi-tion given in Table 2). Black lines: predictions using the Pedersen model. Dottedlines: predictions using the LBC model. Broken lines: predictions using the HW2model. This work: (●), T¼323.15 K (△), T¼373.15 K (◆), T¼423.15 K. (◇),T¼473.15 K.

Table 11Absolute average deviation (AAD, %) between experimental values and predictionsfor the systems investigated in this work.

System Pedersen LBC HW2

Binary 1 10.7 9.8 7.5Binary 2 9.7 15.1 10.9Binary 3 4.0 5.3 8.9Natural gas 6.9 2.8 2.4Synthetic oil 12 13.8 15.8Gas condensate 6.3 9.8 8.5

Overall 8.3 9.4 9.0

K. Kashefi et al. / Journal of Petroleum Science and Engineering 112 (2013) 153–160 159

4.5. Natural gas

The viscosity tests performed on the natural gas (NG) arereported in Table 9. Measurements of viscosity were conductedin pressure range from about 34.47 to 137.90 MPa and tempera-tures of 323.15, 373.15, 423.15 and 473.15 K. The calculated criticaltemperature and pressure of the system are 211 K and 6.25 MPaand the calculated cricondentherm and cricondenbar are 235 Kand 6.74 MPa, respectively. The reported viscosity data of naturalgas (Table 9) show that the viscosity increases with increasingpressure and/or decreasing temperature, i.e., a typical gas hydro-carbon viscosity behaviour at high pressure.

Fig. 6 and Table 9 evaluate the deviation of the predicted viscosityfrom experimental values for natural gas (NG) at each experimentaldata point. The Pedersen corresponding state approach can predictthe experimental data of NG viscosity reasonably well (Table 11) andas expected both LBC and the HW2 approach are in excellentagreement with the measurements for this rich-methane system.

4.6. Synthetic volatile oil

Before making any viscosity tests on the synthetic volatile oil,approximate bubble point observations were made. The estimatedbubble points for this fluid at 323.15, 373.15, 423.15 and 473.15 Kare about 69.29, 61.36, 55.85 and 49.99 MPa, respectively. To makesure about the decreasing trend of bubble points with tempera-ture, the bubble points were also calculated with the PR-EoS at thementioned temperatures and resulted in 58.7, 55.6, 52.7, and48.1 MPa. The experimental viscosity data are reported for therange of mentioned temperatures and up to 137.90 MPa inTable 10.

Fig. 7 illustrates the deviation and trend of predicted viscositydata against experimental viscosity data measured for syntheticvolatile oil. The models have difficulties predicting the viscosity ofthis fluids, particularly high deviation (420%) are observed at thelowest temperature (Table 11).

5. Conclusions

A previously developed HPHT PVT cell was used to generatenew viscosity data of hydrocarbon systems. A series of viscositymeasurements have been performed on three binary hydrocarbonsystems: methane/heptane, methane/decane and methane/toluene and three multi-component mixtures: a natural gas, agas condensate and a synthetic volatile oil. Viscosity data has beengenerated in a temperature range from 323.15 to 473.15 K and upto 137.90 MPa. The results can provide valuable information toevaluate and develop viscosity predictive techniques appropriatefor extreme conditions.

The reported experimental data were used to assess someviscosity models and compare their performance. The investigated

viscosity models were in relatively good agreement withthe experimental results as these challenging conditions. ThePedersen corresponding state method, with an AAD of about 8%was found to be slightly superior compared to the other models.Overall this model without any tuning resulted in relativelyaccurate viscosity predictions.

Acknowledgment

The research work on which the present paper is based wasequally sponsored by Total, Marathon Oil Corporation and Schlum-berger, which is gratefully acknowledged.

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