Sierra 241-VTP, 240-VTP instruction manual Calculations for Gas Real Gas and Other Gas

Appendix C Fluid Calculations Series 24-HP Instruction Manual

Calculations for Gas (“Real Gas” and “Other Gas”)

Use this formula to determine the settings for “Real Gas; Gas” selections

and “Other Gas” selections entered in the Fluid Menu. The calculations for gas were taken from Richard W. Miller, Flow Measurement Engi- neering Handbook (Second Edition, 1989).

Density

The density for real gases is calculated from the equation:

GM w, Air p f

ρ =

Z f R0T f

Where G is the specific gravity, Mw is the molecular weight of air, pf is the flowing pressure, Z is flowing compressibility, Ro is the universal gas constant, and T is the flowing temperature.

The specific gravity, and Ro are known and are stored in a table used by the Vortex meter.

The hard coefficient to find is the compressibility, Z. Z is found using the Redlich-Kwong Equation (Miller page 2-18).

The Redlich-Kwong Equation uses the reduced temperature and pressure to calculate the compressibility factor. The equations are non linear and an iterative solution is used. The Vortex program uses Newton’s Method on the Redlich-Kwong equations to iteratively find the compressibility factor. The critical temperature and pressure used in the Redlich-Kwong equation are stored in the fluid data table with the other coefficients.

Viscosity

The viscosity for real gases is calculated using the exponential equation for two known viscosities. The equation is:

∝cP = aTKn

Where a and n are found from two known viscosities at two temperatures.

n= ln[(∝cP )2 /(∝cP )1 ]

ln(TK 2 / TK1 )

and

a= (∝cP )1

TKn1

C-2 IM-24-HP