Difference between revisions of "Dranchuk correlation"

Revision as of 12:24, 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.

A_1..A_{11}

coefficients

\rho_r

= reduced density, dimensionless

P

= Pressure, psia

P_{pc}

= pseudo critical pressure, psia

P_{pr}

= pseudoreduced pressure, dimensionless

SG_g

= gas specific density, dimensionless

T

= temperature, °R

T_{pc}

= pseudo critical temperature, °R

T_{pr}

= pseudoreduced temperature, dimensionless

z

= gas compressibility factor, dimensionless

↑ 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 56: / Line 56: @@
 === Nomenclature ===
 :<math> A_1..A_{11} </math> coefficients
+:<math> \rho_r </math> = reduced density, dimensionless
 :<math> P </math> = Pressure, psia
-:<math> P_{pc} </math> = Pseudo critical pressure, psia
+:<math> P_{pc} </math> = pseudo critical pressure, psia
 :<math> P_{pr} </math> = pseudoreduced pressure, dimensionless
 :<math> SG_g </math> = gas specific density, dimensionless
-:<math> T </math> = Temperature, °R
+:<math> T </math> = temperature, °R
-:<math> T_{pc} </math> = Pseudo critical temperature, °R
+:<math> T_{pc} </math> = pseudo critical temperature, °R
-:<math> T_{pr} </math> = Pseudo critical temperature, °R
+:<math> T_{pr} </math> = pseudoreduced temperature, dimensionless
 :<math> z </math> = gas compressibility factor, dimensionless
 === References ===