A general model for the viscosity of waxy oils

8/10/2019 A general model for the viscosity of waxy oils

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S .M . Al -Zahrani , T .F . Al -Fariss / Chemical Engineering and Processing 37 (1998) 433437 434

Table 1Wax content and API gravity of different Saudi crude oils

API gravityWax content (wt.%)Field

36.52.5BerriZulfa 2.1 33.5

1.9Safaniya 26.81.8 40.6Marjan

Table 3Predicted parameters for the waxy oil

A (s 1) B (Pa) C (K) D (wt.%) 1 n

8.9041 104 2.6288 10 7 6720.71 6.75 10 2 1.353

agreement with the model reported previously by Bailey

[13] for the hyperbolic case. More details regarding thismodel can be found elsewhere [12].

Based on this model, the viscosity may have thefollowing form:

= B 1 [( + A 1A 1 )n 1](1 / n ) (2)

where A, B , and n are shear stress-shear rate modelparameters. Their mathematical expressions can befound elsewhere [12].

The effect of temperature on viscosity has been inves-tigated by keeping both, the wax concentration and the

shear rate, constant. It was found experimentally thatas the temperature decreases, shear stress increasesmeaning that the viscosity increased with decreasing thetemperatures. It was also observed experimentally thatthe viscosity dropped more quickly with decreasingshear rate at low shear rate and temperatures than athigher shear rates and higher temperatures. These nd-ings indicate that the viscosity depends on the tempera-ture exponentially and may have the following form:

eC / T (3)

where C is a constant and T is the temperature (K).Combining the effect of temperature (Eq. (3)) and theeffect of the shear rate (Eq. (1)) gives the followingform:

= B 1 [( + AA )n 1](1 / n )eC / T (4)

In this work the effect of the wax concentration onthe viscosity of the waxy oil has been investigated bykeeping both the shear rate and the temperature, con-stant. It was found that the viscosity varies exponen-tially with the wax concentration as follows:

eD

W

(5)

2. Experiment

The waxy oils were prepared by adding parafn waxto a denite amount of Saudi base oil. The mixture isthen heated for 2 h until a homogenous mixture wasachieved. Four different samples were prepared withfour different wax concentrations (namely, 2, 4, 6 and8% by weight). These concentrations being selectedbecause they have the same level of wax concentrationas that of the Saudi oil.

A HAKKE (Rotovisco model RV-12) rotational-typeviscometer was used to measure the viscosity. Theviscosity was measured at six different temperatures(i.e. 9, 12, 15, 18, 21, and 24C). These temperatureswere selected because the pipelines which carry theSaudi crude oil working in this range of temperatureduring the winter time. Each experiment was performedve times; thus each gure point represents a mean of ve experiments. Prior to each run the temperature wasraised to 40C; then the mixture was allowed to cool tothe desired temperature, so that the homogeneity of themixture was assured.

3. Modelling analysis

Al-Zahrani [12] reported the following generalizedmodel which relates the shear stress to the shear ratefor shear thinning uids.

= B [( + AA )n 1](1 / n ) (1)

This model describes the Newtonian behaviour with orwithout yield stress when n= 1. It also describes the

behaviour of the hyperbolic uid when n = 2. This is in

Table 2Properties of Saudi crude oil

Values PropertiesProperties Values

447Molecular weight Pour point (C) ( 23.3)NilHydrogen sulde28API gravity (API)

455Average boiling point (C) Sulfur (wt.%) 2.79Aniline point (C) 213 Carbon residues (wt.%) 6.75Latent heat of combustion (kJ /kg) Vanadium (ppm)453.9 67.9

4Salt content as NaCl per 1000 bbl crude Nickel (ppm) 16.7Iron (ppm) 1.0Nitrogen (wt.%) 0.168Ash (ppm) 110


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Fig. 1. Viscosity versus shear rate for 4 wt.% wax on base oil (Thesolid line represents the calculated viscosity by the model while thesymbols represent the experimental data).

Fig. 3. Viscosity versus shear rate at different wax concentration atT = 9C. (Viscosity versus shear rate for 2 wt.% wax on base oil (Thesolid line represents the calculated viscosity by the model while thesymbols represent the experimental data).

where D is a constant and W is the wax concentration(wt.%).

Since the generalized model reported by Al-Zahranai[12] is able to model the non-Newtonian uids asproved previously at a single temperature and waxconcentration, then by combining the effects of theshear rate, temperature and wax concentration, one

ends up with the following expression for the viscosity

of the waxy oil:

= B [( + AA )n 1](1 / n )e(C / T + D W ) (6)

where A, B , C , D and n are the model parameters.These parameters can be determined by least squarenonlinear regression analysis on 240 sets of data. The

Fig. 4. Viscosity versus shear rate at different wax concentration atT = 15C. Viscosity versus shear rate for 2 wt.% wax on base oil.(The solid line represents the calculated viscosity by the model whilethe symbols represent the experimental data).

Fig. 2. Viscosity versus shear rate for 8 wt.% wax on base oil (Thesolid line represents the calculated viscosity by the model while thesymbols represent the experimental data).


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5. Conclusions

The proposed viscosity model predicts very well theviscosity of the waxy oils tested. It has the advantagesof describing the dependence of the shear rate, tempera-ture, the wax concentration and the exibility of ac-commodating the Newtonian and non-Newtonianuids with or without yield stress. The proposed viscos-ity model provides an excellent rheological t with anaverage error of 2.5% in the range of shear rate investi-gated and therefore can be assumed to describe thesteady state behaviour of the waxy oils. It is quite clearfrom the reported gures and analysis in this work thatthe proposed viscosity model may describe the rheolog-ical behaviour of many waxy oils or polymer melts andsolutions. Therefore, this viscosity model can be usedsafely in the design of piping system to handle the crudeoils in petrochemical industries in general and speci-cally in Saudi Arabia oil industries.

References

[1] R.B. Bird, W.E. Steward, E.W. Lightfoot, Transport Phenom-ena, 1st edn, Wiley, New York, 1960, pp. 370.

[2] A. Skelland, Non-Newtonian Flow and Heat Transfer, 1st edn,

Wiley, New York, 1967, pp. 25200.[3] D.V. Boger, A.L. Halmos, Non-Newtonian ow. I. Characteri-

zation of uid behaviour, Am. Inst. Chem. Eng. J. (Module C)2.2 (1981) 814.

[4] E.G. Barry, Pumping of non-Newtonian waxy crude oils, J. Inst.Pet., (Mobile and Development Corporation, NJ) 57 (1971) 554.

[5] D.F. Cooper, J.W. Smith, E.J. Ryan, G. Alexander, Transienttemperature effects in predicting start up characteristics of gelling-type crude oils, Heat Transfer, National Research Coun-

cil for Canada, Canada, 1978.[6] H.P. Aranha, Study of ow improvers for transportation of Bombay high crude oils through submarine pipelines, J. Pet.Tech. 33 (1981) 25932598.

[7] C. Irani, J. Zajac, Handling of high pour point west Africancrude oils, J. Pet. Tech. 34 (2) (1982) 289298.

[8] G. Rojas, Rheological behaviour of extra-heavy crude oils fromthe Orinco oil, Belt Venezuela, Published in the Oil Sands of Canada-Venezuela, (1977) 284 302.

[9] T.F. Al-Fariss, Viscosity-temperature shear rate correlation of crude oil and polymers, J. Eng. Sci. 14 (2) (1988) 231245.

[10] M.F. Ali, M. Saleem, Composition and properties of straightrun naphtha cuts from Saudi Arabia crude oil, Arabian J. Sci.Eng. 11 (3) (1986) 251258.

[11] M.F. Ali, M.H. Hasan, A.M. Bukhari, M. Saleem, Arabiancrude fraction analyzed, Hydrocarbon Processing, (Feb 1985)8386.

[12] S.M. Al-Zahrani, A generalized rheological model for shearthinning uids, J. Pet. Sci. Eng. 17 (3 /4) (1997) 211215.

[13] W.J. Bailey, Hyperbolic rheological model for drilling uids,(1996) Paper SPE 36025.

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A general model for the viscosity of waxy oils

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