Difference between revisions of "Dranchuk correlation"

Revision as of 11:53, 25 April 2017

z = 1-z+ \left(A_1 +\frac{A_2}{T_{pr}} +\frac{A_3}{T^3_{pr}} +\frac{A_4}{T^4_{pr}} +\frac{A_5}{T^5_{pr}} \right)\ \rho_r+ \left(A_6 +\frac{A_7}{T_{pr}} +\frac{A_8}{T^2_{pr}} \right)\ \rho^2_r -A_9\ \left(\frac{A_7}{T_{pr}}+\frac{A_8}{T^2_{pr}}\right) +A_{10}\ \left(1+A_{11}\ \rho^2_r\right)\ \frac{\rho^2_r}{T^3_{pr}} \ e^{-A_{11}\ \rho^2_r}

^[2]

where

T_{pc} = 99.3+180\ SG_g-6.94\ SG^2_g

P_{pc} = 4.6+0.1\ SG_g-0.258\ SG^2_g

T_{pr} = \frac{T}{T_{pc}}

P_{pr} = \frac{P}{P_{pc}}

\rho_r = \frac{0.27\ P_{pr}}{({z\ T_{pr}})}

To avoid the Liquid loading the gas velocity should be above the Liquid loading velocity.

The higher the gas rate the higher the gas velocity.

The lower the wellhead flowing pressure the higher the gas rate.

The bigger the tubing ID the higher the gas rate.

In case when the gas rate is limited by the Reservoir deliverability smaller tubing ID will increase the gas velocity.

z

= gas compressibility factor, dimensionless

P

= Pressure, psia

T

= Temperature, °R

P_{pc}

= Pseudo critical pressure, psia

T_{pc}

= Pseudo critical temperature, °R

SG_g

= gas specific density

↑ Standing, M. B.; Katz, D. L. (December 1942). "Density of Natural Gases". Transactions of the AIME. Society of Petroleum Engineers. 146 (SPE-942140-G).
↑ Dranchuk, P. M.; Abou-Kassem, H. (July 1975). "Calculation of Z Factors For Natural Gases Using Equations of State". The Journal of Canadian Petroleum. 14 (PETSOC-75-03-03).

@@ Line 32: / Line 32: @@
 +A_{10}\ \left(1+A_{11}\ \rho^2_r\right)\ \frac{\rho^2_r}{T^3_{pr}}
 \ e^{-A_{11}\ \rho^2_r}
-</math><ref name=Turner/>
+</math><ref name= Dranchuk/>
 where
 :<math>  T_{pc} =  99.3+180\ SG_g-6.94\ SG^2_g</math>