Figure 4-1 Example of Mass Flow Compensation using Multiplier/Divider Algorithm

Example - Mass Flow Compensation

A gas flow rate of 650 SCFM develops a differential pressure of 90" H 2O across an orifice plate at reference conditions of 30 psig and 140F. Compensate this gas flow for temperature and pressure variations.

Flow = K DPf x Pf x Tref

Tf Pref

Apply Multiplier/Divider Algorithm:

Where:

f = flowing conditions

ref = reference conditions (in absolute units)

PV = K

(Input A x Ratio A+ BiasA ) x (Input C x Ratio C + Bias C )

 

 

(Input B x Ratio B + Bias B )

 

 

X (Calc HI – Calc LO )

 

 

 

 

 

 

 

 

 

 

 

 

 

Assign inputs using Engineering units:

 

 

 

 

Let:

 

 

 

 

 

 

 

 

Input A = DPf = IN1 (in H 2O)

 

 

 

 

Input B = Tf = IN2 + Bias2 = IN2 F + 460 ( R)

 

 

Input C = Pf= IN3 + Bias3 = IN3psig + 14.7(psia)

 

Tref

 

= 140 F + 460 = 600 R

 

 

 

 

Pref

 

= 30 psig + 14.7 = 44.7 psia

 

 

 

 

Calc Hi

= 650.0

Flow in SFCM at Reference Conditions

Calc Lo = 0.0

 

 

 

 

 

 

K = to be determined next

 

 

 

 

Note: If temperature and pressure signals are already ranged in absolute units,

no Bias is required for inputs B and C.

 

 

 

 

PV = Q

SCFM

=

DPf x (IN3 + 14.7)

x

K2

x

(650.0 - 0.0)

 

 

(IN2 + 460)

 

 

 

 

 

 

 

 

Note: When IN2 and IN3 are at the reference conditions of 600 R (140 F) and 44.7psia (30 psig) respectively and DPf = 90" H2O, the equation must calculate 650 SCFM. To accomplish this, divide the DP value by "90" to normalize the equation.

Q

SCFM

=

 

DP f

x

(IN3 + 14.7)

x

 

 

Tref

x

650

 

 

 

 

 

90

 

(IN2 + 460)

 

 

Pref

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Rearranging terms:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Q SCFM =

DPf

x (IN3 + 14.7)

x

1

 

x

 

Tref

 

x 650

Example continued

 

 

 

 

 

 

 

 

 

 

(IN2 + 460)

 

 

 

 

90

 

 

 

Pref

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

on next page

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable

 

Constant = K

 

22049

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

102

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