Difference between revisions of "Beggs and Robinson Oil Viscosity correlation"

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__TOC__
 
__TOC__
  
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=== Brief ===
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== Beggs and Robinson Oil Viscosity correlation ==
  
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[[Beggs - Robinson correlation|Beggs - Robinson]] is an empirical correlation for the '''oil viscosity''' published in '''1975''' <ref name= BR1975/>.
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[[Beggs and Robinson Oil Viscosity correlation|Beggs and Robinson]] is an empirical correlation for the '''oil viscosity''' published in '''1975''' <ref name= BR1975/>.
  
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=== Math & Physics ===
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[[File:Beggs and Robinson.png|thumb|right|400px|link=https://www.pengtools.com/pvtCalculator?paramsToken=b79727e91f05b72cbb6d99afcb588636|Beggs and Robinson oil viscosity correlation in the PVT Software]]
 +
 
 +
== Math & Physics ==
  
 
Dead oil viscosity:
 
Dead oil viscosity:
  
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:<math>\mu_{od} = 10^X-1</math><ref name= {Beggs - Robinson}/>
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:<math>\mu_{od} = 10^x-1</math>
  
 
where:
 
where:
  
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A0 = -1.163<br/>
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:<math>x = T^{-1.163} \times e^{(13.108-6.591/SG_{o})}</math>
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A1 = 13.108<br/>
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−
A2 = 6.591<br/>
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Saturated oil viscosity (P < P<sub>b</sub>):
 +
 
 +
:<math>\mu_{os} = A \mu_{od}^B</math>
  
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:<math>X = T^{A_0} \times e^{A_1-A_2/SG_{o}}</math>
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where:
  
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Saturated oil viscosity:
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:<math> A = 10.715\ (R_s + 100)^{-0.515} </math>
  
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:<math>\mu_{os} =  \alpha1 \mu^{\alpha2}_{od}</math>
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:<math> B = 5.44\ (R_s + 150)^{-0.338} </math>
 +
 
 +
Undersaturated oil viscosity (P > P<sub>b</sub>):
 +
 
 +
:<math>\mu_{o} =  \mu_{os} (P/P_b)^m </math><ref name=VB1980/>
  
 
where:
 
where:
  
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B0 = 10.715<br/>
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:<math>m = 2.6\ P^{1.187}\ e^{(-11.513-8.98 \times 10^{-5}\ P)}</math>
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B1 = 5.615<br/>
+
 
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B2 = 0.515<br/>
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== Example. Calculation of the oil viscosity ==
 +
Example source <ref name=1987PEH/>
 +
===Input data===
 +
:<math>T</math> = 137 F°
 +
:<math>SG_o</math> = 0.922 or 22 API
 +
:<math>R_s</math> = 90 scf/stb
 +
 
 +
Calculate the saturated oil viscosity?
 +
 
 +
===Solution===
 +
x = 1.2658
 +
:<math>\mu_{od}</math> = 17.44 cP
 +
A = 0.719
 +
B = 0.853
 +
:<math>\mu_o</math> = 8.24 cP
 +
 
 +
The solution is available in the online PVT calculator software model at [https://www.pengtools.com/pvtCalculator?paramsToken=b79727e91f05b72cbb6d99afcb588636 www.pengtools.com]
  
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:<math> \alpha1 = B_0 * (B_1 * R + 100)^B2) </math>
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== Application range ==
 +
Description of the Data Used<ref name= BR1975/>:
  
−
C0 = 5.44<br/>
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:<math>  20 \le R_s \le 2,070 </math>
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C1 = 5.615<br/>
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:<math>  0.75 \le SG_o \le 0.96 </math>
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C2 = 0.338<br/>
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:<math>  0 \le P \le 5250 </math>
 +
:<math>  70 \le T \le 295 </math>
  
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:<math> \alpha2 = C_0 * pow(C_1 * R + 150, -C_3) </math>
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Number of oil systems = 600<BR/>
 +
Number of dead oil observations = 460<BR/>
 +
Number of live oil observations = 2,073<BR/>
  
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=== Discussion  ===
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== Nomenclature ==
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=== Workflow  ===
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:<math> A </math> = coefficient
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=== Application range ===
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:<math> B </math> = coefficient
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=== Nomenclature ===
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:<math> m </math> = coefficient
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:<math> A_0..A_{2} </math> = coefficients
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:<math> P </math> = pressure, psia
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:<math> B_0..B_{2} </math> = coefficients
+
:<math> R_s </math> =  solution gas-oil ratio, scf/stb
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:<math> C_0..C_{2} </math> = coefficients
+
:<math> SG_o </math> = oil specific gravity, dimensionless
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:<math> P </math> = pressure, MPA
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:<math> T </math> = temperature, °F
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:<math> P_{bp} </math> = bubble point pressure, MPA
+
:<math> x </math> = coefficient
−
:<math> R_s </math> =  oil gas ration, m3/m3
 
−
:<math> SG_g </math> = gas specific gravity, dimensionless
 
−
:<math> T </math> = temperature, °R
 
−
:<math> Y_{oil_API} </math> = oil API gravity, dimensionless
 
  
−
=== References ===
+
:<math> \mu </math> = viscosity, cP
 +
 
 +
====Subscripts====
 +
:b - bubble point <BR/>
 +
:od - dead oil <BR/>
 +
:os - saturated oil <BR/>
 +
:o  - undersaturated oil <BR/>
 +
 
 +
== References ==
 
<references>
 
<references>
−
<ref name=BB1975>{{cite journal
+
<ref name=BR1975>{{cite journal
 
  |last1=Beggs|first1=H. D.
 
  |last1=Beggs|first1=H. D.
 
  |last2= Robinson |first2=J. R.
 
  |last2= Robinson |first2=J. R.
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}}</ref>
 
}}</ref>
  
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<ref name={Beggs - Robinson}>
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<ref name=VB1980>
 
{{cite journal
 
{{cite journal
−
  |last1= Vazquez |first1=M.
+
  |last1= Vasquez |first1=M.
 
  |last2= Beggs |first2=H.D.
 
  |last2= Beggs |first2=H.D.
 
  |title=Correlations for Fluid Physical Property Prediction.
 
  |title=Correlations for Fluid Physical Property Prediction.
Line 75: Line 107:
 
  |url=https://www.onepetro.org/journal-paper/SPE-6719-PA
 
  |url=https://www.onepetro.org/journal-paper/SPE-6719-PA
 
  |url-access=registration  
 
  |url-access=registration  
 +
}}</ref>
 +
<ref name=1987PEH>
 +
{{cite book
 +
|last1= Beggs |first1=H. Dale
 +
|title=Oil System Correlations (1987 PEH Chapter 22)
 +
|date=1987
 +
|publisher=Society of Petroleum Engineers
 +
|url=https://www.onepetro.org/book/peh/spe-1987-22-peh
 +
|url-access=registration
 
}}</ref>
 
}}</ref>
 
</references>
 
</references>
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[[Category:pengtools]]
 
[[Category:pengtools]]
 
[[Category:PVT]]
 
[[Category:PVT]]
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{{#seo:
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|title=Beggs and Robinson oil viscosity correlation
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|titlemode= replace
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|keywords=oil viscosity, Beggs and Robinson correlation, dead oil viscosity
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|description=Beggs and Robinson correlation is an empirical correlation for the oil viscosity published in 1975.
 +
}}

Latest revision as of 12:15, 28 September 2020

Beggs and Robinson Oil Viscosity correlation

Beggs and Robinson is an empirical correlation for the oil viscosity published in 1975 [1].

Beggs and Robinson oil viscosity correlation in the PVT Software

Math & Physics

Dead oil viscosity:

\mu_{od} = 10^x-1

where:

x = T^{-1.163} \times e^{(13.108-6.591/SG_{o})}

Saturated oil viscosity (P < Pb):

\mu_{os} = A \mu_{od}^B

where:

A = 10.715\ (R_s + 100)^{-0.515}
B = 5.44\ (R_s + 150)^{-0.338}

Undersaturated oil viscosity (P > Pb):

\mu_{o} = \mu_{os} (P/P_b)^m [2]

where:

m = 2.6\ P^{1.187}\ e^{(-11.513-8.98 \times 10^{-5}\ P)}

Example. Calculation of the oil viscosity

Example source [3]

Input data

T = 137 F°
SG_o = 0.922 or 22 API
R_s = 90 scf/stb

Calculate the saturated oil viscosity?

Solution

x = 1.2658

\mu_{od} = 17.44 cP

A = 0.719 B = 0.853

\mu_o = 8.24 cP

The solution is available in the online PVT calculator software model at www.pengtools.com

Application range

Description of the Data Used[1]:

20 \le R_s \le 2,070
0.75 \le SG_o \le 0.96
0 \le P \le 5250
70 \le T \le 295

Number of oil systems = 600
Number of dead oil observations = 460
Number of live oil observations = 2,073

Nomenclature

A = coefficient
B = coefficient
m = coefficient
P = pressure, psia
R_s = solution gas-oil ratio, scf/stb
SG_o = oil specific gravity, dimensionless
T = temperature, °F
x = coefficient
\mu = viscosity, cP

Subscripts

b - bubble point
od - dead oil
os - saturated oil
o - undersaturated oil

References

  1. ↑ 1.0 1.1 Beggs, H. D.; Robinson, J. R. (September 1975). "Estimating the Viscosity of Crude Oil Systems"Free registration required. Journal of Petroleum Technology. 27(09) (SPE-5434-PA). 
  2. ↑ Vasquez, M.; Beggs, H.D. (1980). "Correlations for Fluid Physical Property Prediction."Free registration required. Society of Petroleum Engineers (SPE-6719-PA). 
  3. ↑ Beggs, H. Dale (1987). Oil System Correlations (1987 PEH Chapter 22)Free registration required. Society of Petroleum Engineers. 
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