pbms assign. 2

8/6/2019 PBMS Assign. 2

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UNIVERSITY OF TRINIDAD & TOBAGOUNIVERSITY OF TRINIDAD & TOBAGO

B.A.Sc. PETROLEUM ENGINEERINGB.A.Sc. PETROLEUM ENGINEERING

COURSE CODE: PBMS 220BCOURSE CODE: PBMS 220B

COURSE NAME:COURSE NAME:

PHASE BEHAVIOUR OF MULTICOMPONENT SYSTEMSPHASE BEHAVIOUR OF MULTICOMPONENT SYSTEMS

ASSIGNMENT #2:ASSIGNMENT #2:

CALCULATING VISCOSITY USING Lee et al correlationCALCULATING VISCOSITY USING Lee et al correlation

DATE SUMBITTED:DATE SUMBITTED: 19/02/0919/02/09


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The Law of Corresponding States

The P rinciple of Corresponding States as stated by Van Der Waals:

Substances behave alike at the same reduced states. Substances at same reduced

states are at corresponding states. Therefore all fluids, when compared at the same

reduced temperature and reduced pressure, have approximately the same

compressibility factor, and all deviate from the ideal gas behaviour to about the same

degree.

This law is more accurate if the gases have similar molecular characteristics. Since

most of the gases the petroleum engineer deals with are composed primarily of

molecules of the same class of organic compounds known as paraffin hydrocarbons,

the theory holds true.The Law of Corresponding States was extended to cover mixtures of gases which are

closely related. However, obtaining the critical point for multicomponent mixtures

was somewhat difficult; which eventually lead to the development of pseudocritical

temperature and pseudocritical pressure.

These quantities are defined as: cjj

ipcTyT = and cj

j

jpcPyP = .

Where iy is the mole fraction of the i-th component, cjT and cjP are the

pseudocritical temperature and pseudocritical pressure of the individual components

of the gas mixture. These two equations are often referred to as Kays mixture rules.

The pseudocritical properties were devised simply for use in correlating physical

properties, since pseudocritical properties are not equal to the actual critical properties

of a gas mixture. Physical properties of gas mixtures are correlated with

pseudoreduced temperature and pseudoreduced pressure.

,,pc

pr

pc

prP

PP

T

TT ==

Application of the Law of Corresponding States:


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It is used extensively for thermodynamic correlations, which is its most popular

application. Most thermodynamic correlations have been made viable and general

because of the application of the principle of corresponding states. An example is the

popular Z-chart of Standing and Katz, shown in Figure 1 below. This chart allows us

to determine the gas compressibility factor for a real gas, which is used in the EOS:

pV = znRT. Where z represents [vol. of real gas/vol. of ideal gas] p. This equation

can then be manipulated to calculate Vg, g, Bg, Eg, Cg and other thermodynamic fluid

properties.

Figure 1:Standing-Katz Compressibility Factor Chart(Reference: Standing and Katz, Trans. AIME, 1942)


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Figure 2: Pseudocritical Pressure and Temperature vs. S.G.


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Problem:

Calculate viscosity using Lee et al correlation for:

Specific Gravity(s.g.) Temperature (F) Pressure (psia)

0.55, 0.72, 0.88

150 1500

170 1815

195 2000

And discuss any trends observed.

Solution:

* Optimized LGE variables were used in the calculation of X, K, and Y.

S.G.Mw (lb/lb-

mole) P pc(psia) T pc(R) T abs (F) T abs (R) P abs (psia) P pr Tpr z factor (g/cc) X K Y g(cp)

0.55 15.93 672 334 150 610 1500 2.23 1.83 0.915 0.064 5.528 126.192 1.315 0.0146

170 630 1815 2.70 1.89 0.92 0.075 5.420 129.699 1.311 0.0155

195 655 2000 2.98 1.96 0.93 0.078 5.295 134.013 1.306 0.0162

0.72 20.85 660 382 150 610 1500 2.27 1.60 0.85 0.090 5.534 118.19 1.315 0.0149

170 630 1815 2.75 1.65 0.855 0.105 5.426 121.64 1.311 0.0161

195 655 2000 3.03 1.71 0.865 0.110 5.301 125.88 1.306 0.0169

0.80 23.17 650 400 150 610 1500 2.31 1.53 0.81 0.105 5.537 114.83 1.316 0.0153

170 630 1815 2.79 1.58 0.82 0.122 5.401 118.24 1.310 0.0166

195 655 2000 3.08 1.64 0.84 0.126 5.276 122.45 1.305 0.0174

Mw of Air = 28.96

R (lb-mole R) = 10.732


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Variable Original LGE Optimized LGE

k1 9.379 16.717500

k2 0.01607 0.041919

k3 1.5 1.402560k4 209.2 212.209000

k5 19.26 18.134900

x1 3.448 2.125740

x2 986.4 2063.710000

x3 0.01009 0.001193

y1 2.447 1.098090

y2 0.2224 -0.039285

Table 1: Values for constants in the LGE equation

Procedure for the Determination of Gas Viscosity using Lee, Gonzalez, and Eakin,

Correlation (Lee, et al):

Using the specific gravity, values of the pseudocritical temperatures (Tpc) and

pressures (Ppc) were read off from a graph of pseudocritical temperature and

pressure vs. specific gravity (Fig.2)

Using these values the reduced temperatures and pressures were then

calculated using the following equations: Ppr= Pabs/ Ppc and Tpr= Tabs/ Tpc

Using Fig.1 the gas compressibility factor (z-factor) was found for each value

of Pprand Tpr.

The gas density was then calculated using the following equation:

abs

wabs

gzRT

MP

37.62=

Where, Mw = molecular weight of the gas in lb/lb-mole

= S.G. of gas Mw of air

R = Universal gas constant = 10.732 (psia cu ft)/(lb-mole deg R)

62.37 = Conversion constant: 1g/cc = 62.37lbm/ft3

g is in g/cc

The factors X, K and Y were then calculated using the following equations:

XyyY

TMkk

TMkkK

MxT

xX

w

k

w

w

21

54

21

32

1

3)(

=

++

+=

++=


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Effect of Pressure on Gas Viscosity

0.0145

0.0150

0.0155

0.0160

0.0165

0.0170

0.0175

1450 1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000 2050

Pressure (psia)

GasViscosity(cp)

S.G = 0.55 S.G = 0.72 S.G = 0.80

Effect of Temperature on Gas Viscosity

0.0145

0.0150

0.0155

0.0160

0.0165

0.0170

0.0175

605 610 615 620 625 630 635 640 645 650 655 660

Temperature (deg.R)

GasViscosity(cp)

S.G = 0.55 S.G = 0.72 S.G = 0.80

Finally the gas viscosity was calculated using the equation:

)exp(104 Y

gXK

=

Graphs of pressure versus gas viscosity and temperature versus gas viscosity

were plotted for each value of specific gravity.


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Discussion of Observed Trends:

Effect of Temperature on Gas Viscosity

As the temperature of the gas increases so does the gas viscosity, however this

increase is non-linear. Unlike liquids, the viscosity of gases increases as temperature

increases and is approximately proportional to the square of the temperature i.e.

2T . This is due to the increase in the frequency of intermolecular collisions at

higher temperatures. Since most of the time the molecules in a gas are moving

freely through the void, anything that increases the number of times one

molecule makes contact with another, will decrease the ability of the molecules as

a whole; to engage in coordinated movement. The more these molecules collide

with one another, the more disorganized their motion becomes. At low pressures, gas

viscosity increases as temperature increases, however, at high pressures gas

viscosity decreases as temperature increases.Hence the effect of temperature on

gas viscosity is dependent on system pressure.

Effect of Pressure on Gas Viscosity

Gas viscosity decreases as reservoir pressure decreases, and vice versa. The

molecules are further apart at lower pressures and move past each other more

easily. From the viscosity vs. pressure graph it can be seen that as pressure is

increased the viscosity increases, this increase is almost linear in nature. Generally at

low pressures; gas viscosity decreases as the pressure decreases since the

molecules become widely separated. However at high pressures the gas behaves

as a liquid as the molecules become closer together and therefore viscosity

increases.

Effect of Composition on Gas Viscosity

It can be seen that generally as the specific gravity or molecular weight increases so

does the viscosity. The higher the molecular weight the higher the viscosity. This is

true for both oil and gas, since as the molecular weight increases, so does the

length of the alkane chain.The increase in chain length increases the amount of

cross-linkages, and hence the amount of entanglement taking place between the

alkane molecules which make up the hydrocarbon resulting in more interactionsand hence increased viscosity. i.e. increased resistance to flow.


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.

Effect of Pressure on Liquid Viscosity

A decrease in pressure causes a decrease in viscosity, provided that the only

effect of pressure is to compress the liquid. For reservoir fluids there is an

additional parameter which affects viscosity. A decrease in the amount of gas in

solution in the liquid causes an increase in viscosity, and the amount of gas in

solution is also a direct function of pressure. The viscosity of a liquid is related

directly to the type and size of the molecules which make up the liquid. i.e.

composition.


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References:

Canadian International Petroleum Conference paper 2004-2004-214

Comparison of Correlations for viscosity of Sour Natural Gas. O. Jeje, L.

Mattar SPE 75721- Simplified Correlations of Hydrocarbon Gas Viscosity and Gas

Density- F.E. Londono, R.A. Archer, and T. A. Blasingame, Texas A&M U.

The Properties of Petroleum Fluids 2nd Ed. William D. McCain, Jr. PennWell

Books, PennWell Publishing Company. Tulsa, Oklahoma.

pbms assign. 2

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