Chris Boljkovac ## Orifice Meter Flow Correction and Compensation

### Overview

Flow measurements using orifice meters are commonly configured to indicate mass flowrate. This calculation assumes that the fluid being measured is at the same conditions as the fluid used in the meter’s design. Flow correction and compensation factors can be applied to increase meter accuracy. If a meter is re-designed using revised fluid properties, a correction factor can be applied to historic mass flow measurements. If measurements of flowing conditions are available, a mass flow compensation factor can be applied.

This post describes the following,

1. Calculation of mass flowrate of a vapour at design conditions
2. Correction of vapour mass flowrates at revised design conditions
3. Compensation of vapour mass flowrates to measured/flowing conditions
4. Calculation of vapour standard volumetric flowrate from mass flowrate

### Background

Measurement of vapour mass flow through an orifice meter can be described by the following,

$${F_M}={N}{C_d}{E_v}{Y}{d^2}\sqrt{\rho_{T,P}}\sqrt{\Delta{P}} (1)$$

where,

$F_M$ is mass flowrate of gas
$N$ is units conversion factor
$C_d$ is discharge coefficient
$E_v$ is velocity approach factor
$Y$ is gas expansion factor
$d$ is orifice bore size
$\rho_{T,P}$ is gas density, flowing conditions
$\Delta{P}$ is pressure drop across orifice

Orifice meters can be designed using Flowel® software (Emerson) using the Exact Flow Calculation mode at typical operating (i.e. design) conditions. Coefficients in (1) are considered to change little over the operating conditions of the meter and are considered constant. Equation (1) then becomes,

$$F_D = F_{max}\sqrt{\Delta{P}} (2)$$

where,

$F_D$ is mass flowrate at design conditions
$F_{max}$ is maximum mass flowrate (flow at full-scale pressure drop)

Equation (2) also assumes that fluid density is also at the design conditions. Compensation of $F_D$ for deviations from design conditions to measured/flowing conditions is described below.

### Flow Correction for Meter Re-Design

Meter accuracy is increased when the meter design conditions are close to the actual operating conditions. When an orifice meter is re-designed using updated operating conditions it’s possible to apply the new design to historic flowrates. Since orifice meter design calculates $F_{max}$, it’s possible to calculate a meter range correction factor ($RCF$) as,

$$RCF=\frac{F_{max,2}}{F_{max,1}} (3)$$

where,

$RCF$ is meter range correction factor
$F_{max,1}$ is maximum mass flowrate (flow at full-scale pressure drop), previous design
$F_{max,2}$ is maximum mass flowrate (flow at full-scale pressure drop), new design

From equation (1), the mass flowrate using the new meter design simply becomes,

$${F_{D,2}}={(RCF)}{F_{D,1}} (4)$$

where,

$F_{D,1}$ is mass flowrate at design conditions, previous design
$F_{D,2}$ is mass flowrate at design conditions, new design

### Flow Compensation

Meters don’t operate at the conditions used in meter design. If suitable measurements are available a mass flowrate compensation factor ($MCF$) can be calculated to compensate for changes in measured/flowing density (i.e. fluids not at $\rho_{T,P}$, in equation (1) above) and improve meter accuracy. For orifice meters in vapour service configured to indicate mass flowrate, the compensation factor is,

$$MCF=\sqrt{\left[\frac{M_M}{M_D}\right]\left[\frac{P_M}{P_D}\right]\left[\frac{Z_D}{Z_M}\right]\left[\frac{T_D}{T_M}\right]} (5)$$

where,

$M_M$ is molecular weight, measured/flowing conditions
$M_D$ is molecular weight, design conditions
$P_M$ is operating pressure (absolute), measured/flowing conditions
$P_D$ is operating pressure (absolute), design conditions
$T_M$ is operating temperature (absolute), measured/flowing conditions
$T_D$ is operating temperature (absolute), design conditions
$Z_M$ is ideal gas compressibility factor, measured/flowing conditions
$Z_D$ is ideal gas compressibility factor, design conditions

The compensated vapour mass flowrate is therefore,

$$F_M=(MCF)F_D (6)$$

and, when a meter correction factor also needs to be applied,

$$F_M=\left(RCF\right)(MCF)F_D (7)$$

### Calculation of Standard Volumetric Flow

The standard volumetric flowrate can be calculated from corrected and compensated mass flowrate as,

$$V_M=F_M{v/M}_M (8)$$

where,

$V_M$ is volumetric flowrate of gas, standard conditions
$F_M$ is mass flowrate of gas
$v$ is molar volume of gas, standard conditions
$M_M$ is molecular weight of gas