The orifice is normally used for flow measurement of liquid, gas, and steam. The orifice produces differential pressure (DP) across the plate and it is sensed by DP type transmitter. This Differential pressure then square rooted to convert into the equivalent flow.

Square rooting can be done either at DP type flow transmitter side or at the control system side. Flow output is valid when we operate the plant at the specified operating conditions as per flow element sizing calculation.

In the industry, practically, these parameters like design temperature and design pressure cannot be maintained throughout the operation. Once the pressure/temp varies, density will be affected due to which Volume will change and the DP transmitter cannot detect the density changes.

The volumes of gas/steam measured are highly affected by pressure and temperature. This is when we require pressure, temperature compensation where in actual operating conditions will be used.

This type of compensation is applicable when we have DP type flow elements like Orifice, venturi, pitot tube, etc, and Gas or Steam as a service application. Pressure and temperature (PT) compensation convert a volumetric gas flow at specific conditions into an equivalent volumetric flow at base conditions.

Commonly, density measurement is not used, another approach is to measure Molecular weight (online/offline) and then compensate with design molecular weight.

PT (P&T) compensation is a complete makeover of the traditional orifice. This produces a resultant value for flow that is more accurate because it is compensated for the error effects of the other variables at the operating conditions.

The PT calculations are based on absolute temperature and pressure.

## Pressure Temperature Compensation

The complete arrangement will look as per the following P&ID figure.

In general, the pressure transmitter installed at the upstream side of the flow element, and the temperature transmitter installed downstream so that it does not distort the velocity profile in the flow element.

Nowadays, a Multi-variable transmitter is commonly used to avoid such an above arrangement which has compete DP, Pressure, and/ Temperature measurement as part of the transmitter itself. There are options available in Multi-variable transmitters like separate RTD / Thermocouple for temperature measurement.

Vortex transmitter is also available with integrated Pressure and/ temperature compensation which can be suitable to use in the Steam / Gas application.

Various examples are simulated in Conval sizing software to get better clarity. Pressure and temperature changes are simulated and compensated outputs are compared. This is to know how PT compensation really matters !!

## Example Calculations

Let’s take an example of H_{2 }Gas where in Orifice is calibrated/designed for DP of 100 mBar, Input Pressure 35 Bara, Input Temp 300 K, Flow is 30,000 m^{3}/hr, where orifice Beta ratio found from Conval Software output is 0.52034.

Now, we take reverse calculation, keeping the orifice bore fixed, and change the input pressure from 35 Bara to 30 Bara. The flow output calculated is 27,790 m^{3}/hr. Assume that density measurement is not available.

Resultant compensated flow due to change in pressure can be derived by the following equation

Flow Compensated = = 30,000 *SQRT(30/35) = ~ 27,774 m 3 /hr

Hence, for this example 5 Bara reduction in pressure w.r.t. to design condition, resulted in 7.3% less flow (when you have pressure compensation in place.)

Lets now look at what happens when temperature changes from 300 K to 325 K keeping other parameters the same as design. The flow output calculated is 28843 m^{3}/hr.

Resultant compensated flow due to change in temperature can be derived by the following equation

Flow Compensated = 30,000 * SQRT(300/325) =~ 28,823 m3/hr

Hence, for this example, a 25 K increase in temperature resulted in a 3.8% less flow.

In this example, If we take temperature and pressure change together w.r.t design condition, then flow output is 26,719 m^{3}/hr

Resultant compensated flow due to change in pressure and temperature can be derived by the following equation

Flow Compensated = 30,000 * SQRT((30*300/(35*325)) = ~ 26,684 m3/hr

Since Conval software calculates the exact properties of H_{2} gas based on the operating conditions so there is a difference in flow output calculated by Conval and equation. However, the equation mentioned is valid to implement.

Similarly, if we have a molecular weight (MW) changes w.r.t design then Flow compensated can be calculated as per the below equation.

Altogether, the flow compensated can be calculated with actual temperature, actual pressure, and actual molecular weight, etc.

Molecular weight can be known from Lab analysis or online analyzer.

**Pressure values shall be in Bar(a), Temp shall be in K**.

Flow-based on DP = flow calculated from square rooted actual DP reading

All the design inputs/ reference conditions can be known from the flow element sizing sheet. Actual parameters will be part of the analog input signal to the control system.

The equation shown above is derived from Euler’s equation of continuity and Bernoulli’s principle. Derivation of this formula is out of the scope of this article.

It is very much important to pass-on correct flow compensation equation based on process requirement (Pressure compensation/ Temperature compensation / P&T compensation / P, T & MW Compensation) along with your design parameter and ranges to control system vendor to have this flow compensation calculation implemented inside the PLC/ DCS.

Some control system supplier has flow compensation blocks into their library. However, verification of compensated flow output is necessary.

### Exercise for you

Design Pressure 40 Bar(a), Design Temp 375K, Calibrated Flow range 0-5000 Kg/hr, DP type flow transmitter is calibrated at 0-2500 mmH_{2}O.

When your field pressure transmitter reading is 35 Bar(a), Temp transmitter reading is 340K, and DP FT reads 1250 mmH_{2}O then what will be P&T compensated flow output?

The correct answer is 3473.06 Kg/hr.

Please let us know in the comment box if you find difficulty in solving it.

Author: Jatin Katrodiya

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