Difference between revisions of "Dranchuk correlation"

Revision as of 10:43, 25 April 2017

z = 1+ \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}

^[1]

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

= flow area, ft^2

P

= flowing wellhead pressure, psia

q_g

= gas rate, MMscf/d

\rho_g

= gas density, lbm/ft3

\rho_L

= liquid density, lbm/ft3

\sigma

= surface tension, dyne/cm (ref values: 60 - water, 20 - condensate) ^[1]

T

= flowing temperature, °R

v_g

= gas velocity, ft/sec

z

= gas compressibility factor at flowing P & T, dimensionless

↑ ^1.0 ^1.1 Turner, R. G.; Hubbard, A. E.; Dukler (Nov 1969). "Analysis and Prediction of Minimum Flow Rate for the Continuous Removal of Liquids from Gas Wells". Journal of Petroleum Technology (SPE-2198-PA): 1475–1482.

@@ Line 9: / Line 9: @@
 === Math & Physics ===
 equation on gas compressibility factor z
-    A1 = 0.3265
+A1 = 0.3265<br/>
-    A2 = –1.0700
+A2 = –1.0700<br/>
-    A3 = –0.5339
+A3 = –0.5339<br/>
-    A4 = 0.01569
+A4 = 0.01569<br/>
-    A5 = –0.05165
+A5 = –0.05165<br/>
-    A6 = 0.5475
+A6 = 0.5475<br/>
-    A7 = –0.7361
+A7 = –0.7361<br/>
-    A8 = 0.1844
+A8 = 0.1844<br/>
-    A9 = 0.1056
+A9 = 0.1056<br/>
-    A10 = 0.6134
+A10 = 0.6134<br/>
-    A11 = 0.7210
+A11 = 0.7210<br/>
 :<math> z =  1+
 \left(A_1