To calculate the accuracy of a pressure transmitter, we need to consider both reference accuracy and on-site performance. The Total Probable Error (TPE) is obtained by adding together uncertainties such as the accuracy of the calibrated measurement interval, the effects of ambient temperature and the impact of static pressure.
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In the vast world of process engineering, pressure measurement is the cornerstone of efficient, safe and reliable operations.
As technologies evolve and industries advance, the need for accurate pressure measurement becomes ever more important.
For maintenance engineers, instrumentation and control engineers and process engineers, navigating the intricacies of pressure transmitters can sometimes be like looking for a needle in a haystack.
But never fear! For optimum performance, it's essential to understand the subtle nuances that influence a sensor's accuracy.
This article looks at the subject of pressure transmitters, to help maintenance engineers understand how to obtain accurate pressure measurements.
We'll start by exploring the importance of defining the accuracy required for specific process applications. Then we'll untangle the difference between on-site performance and reference accuracy, highlighting why this distinction is crucial.
Further on, we'll decode the multitude of operating conditions a pressure transmitter can encounter: from fluctuating ambient temperatures to variable static pressures, and their respective effects. Zero offset, range offset and their cumulative ramifications will also be discussed.
Finally, we'll provide you with a complete methodology for calculating the probable total error of a pressure transmitter.
By the end of this article, we hope you'll be equipped with the knowledge not only to select the right pressure transmitter , but also to guarantee its accuracy throughout its lifetime. Let's embark on this instructive journey together!
The first step is to define the performance required by the industrial application for the pressure measurement point.
On-site performance of pressure transmitters should generally be between 0.5 and 2.0% of the calibrated measurement range, depending on the application. The following performance targets are expected, on average, for all service classifications: plant safety and efficiency at 0.5%, environmental control at 1.0%, Scada system and distributed control system at 1.5%, and plant monitoring system and process optimization at 2.0%. Of course, these are only averages, and some customers will have higher or lower expectations depending on their specific needs. However, these figures give a general idea of the level of performance our customers are looking for.
On-site performance should not be confused with reference accuracy.
There are two distinct concepts when it comes to measurement systems:
This is the accuracy of a pressure transmitter under specific, controlled conditions, usually in the laboratory. It provides a standard or reference against which sensor performance can be compared. Reference accuracy includes the combined effects of non-linearity, hysteresis and non-repeatability under these defined conditions.
This refers to the performance of a sensor or measurement system under real-life conditions, or in the environment for which it is intended.
Several factors can influence on-site performance, including variations in ambient temperature, the effect of static pressure, stability over time, the influence of supply voltage, mounting position and other environmental factors.
On-site performance may differ from reference accuracy due to these external influences.
In practice, while a pressure transmitter may have excellent reference accuracy under controlled conditions, its performance on site may vary according to the complexities and unpredictabilities of the real environment. It is therefore essential to take both these factors into account when evaluating or deploying a pressure transmitter for a specific application.
The second step is to define the operating conditions to which the device will be exposed.
Depending on the application, pressure transmitters may be subject to significant variations in ambient temperature.
For example, if a pressure transmitter is used outdoors, the ambient temperature can vary from -20°C to 60°C. This is very different from laboratory use, where the ambient temperature is stable and air-conditioned.
The other parameter to take into account is the static pressure on the process.
In the case of differential pressure measurement, the higher the static pressure, the lower the accuracy. For absolute and relative pressure transmitters , the effect of static pressure is nil.
Knowing these factors that can influence accuracy enables us to calculate the Total Error Probable (TEP ), which defines the accuracy of the pressure transmitter under the application's installation conditions, when all individual sources of error are combined. This total performance error is the difference between the most positive and the most negative measurement deviation from the actual pressure. It is calculated by combining all possible errors within the application's operating conditions.
The probable total error value is used to define the worst-case performance of the pressure transmitter installed on site.
Factors such as ambient temperature and static pressure have a certain influence on pressure transmitter accuracy and performance. Their influence affects both the zero point and the set measuring range of pressure transmitters, resulting in measurement deviations or inaccuracies.
We have first determined the accuracy required on site for the application, and determined the installation parameters that influence the accuracy of our measurement and their influence on zero offset and scale offset.
The next step is to calculate the probable total error, using the datasheet available on the pressure transmitter manufacturer's websitedatasheet technicaldatasheet ). This calculation is the sum of the square roots of the uncertainties associated with the reference accuracy and installation factors such as ambient temperature and the effect of static pressure.
The probable total error of the device includes the reference accuracy, the effect of ambient temperature, the effect of static pressure and is calculated using the following TPE formula:
Probable total error = ± √ ((E1)²+(E2)²+(E3)²)
E1 = Nominal accuracy of calibrated scale or reference accuracy
E2= Effect of ambient temperature
E3 = Effect of static pressure
E1. Nominal or reference accuracy
Nominal accuracy must be calculated on the calibrated or adjusted scale. Reference accuracy includes maximum uncertainty errors for hysteresis, non-linearity and non-repeatability.
E2. Effect of ambient temperature
pressure transmitters are calibrated in the laboratory at a stable ambient temperature. The ambient temperature at the place of application may be different. This temperature has an influence on the electronic components of the measuring instrument, and an inaccurate measurement may result. pressure transmitters manufacturers, such as Fuji Electric, generally express this effect in increments of 28°C.
E3. Effect of static pressure
Static pressure errors can be caused by several phenomena inside the pressure transmitter. These include the deformation of metal diaphragms under line pressure, and the balance of filling oil volumes. Suppliers generally define the influence of static pressure every 10 MPa of pressure variation. The effects of static pressure on a differential pressure transmitter can manifest themselves in zero and span shifts. This phenomenon is sometimes referred to as the "static pressure effect" or the "line pressure effect".
Effect on zero :
This is the offset of the sensor output signal when there is no differential pressure in the transmitter, but there is static pressure or line pressure applied.
Tip: the effect on zero can be eliminated by "zero adjustment" under static pressure conditions, which means that the transmitter can be recalibrated or adjusted under static pressure to bring its zero point back to the correct reference level.the transmitter is "informed" that the output current under static pressure, without differential pressure, should represent zero. This effectively compensates for the effects of static pressure on the zero reading.
Effect on scale :
This is the change in transmitter output range due to static pressure or line pressure.
For our example, we will consider the following service conditions for our application.
We use the Fuji Electric FKC differentialpressure transmitter datasheet below to calculate overall performance.
datasheetDownload the datasheet to discover the Fuji electric pressure transmitter technical datasheet !
So, first of all, let's consider the right model for the pressure measurement range required and for the application's operating conditions by following this pressure transmitters selection guide.
The scale setting should be set as close as possible to the upper limit of the sensor cell range to achieve the best accuracy.
For a pressure measurement of 0-100 mbar, we choose model FKC..33, which offers the closest range of 0/320 mbar.
| Models | Static pressure limit MPa {bar} | Measurement ranges kPa {mbar} MIN | Measurement ranges kPa {mbar} MAX | Possible settings kPa {m bar} |
|---|---|---|---|---|
| FKC 11 | -0.1 to + 3.2 {-1 to + 32} | 0.1 {1} | 1 {10} | ±1 {±10} |
| FKC 22 | -0.1 to + 10 {-1 to + 100} | 0.1 {1} | 6 {60} | ±6 {±60} |
| FKC 33 | -0.1 to + 16 {-1 to + 160} | 0.32 {3.2} | 32 {320} | ±32 {±320} |
| FKC 35 | -0.1 to + 16 {-1 to + 160} | 1.3 {13} | 130 {1300} | ±130 {±1300} |
| FKC 36 | -0.1 to + 16 {-1 to + 160} | 5 {50} | 500 {5000} | ±500 {±5000} |
| FKC 38 | -0.1 to + 16 {-1 to + 160} | 30 {300} | 3000 {30000} | ±3000 {±30000} |
| FKC 43 | -0.1 to + 42 {-1 to + 420} | 0.32 {3.2} | 32 {320} | ±32 {±320} |
| FKC 45 | -0.1 to + 42 {-1 to + 420} | 1.3 {13} | 130 {1300} | ±130 {±1300} |
| FKC 46 | -0.1 to + 42 {-1 to + 420} | 5 {50} | 500 {5000} | ±500 {±5000} |
| FKC 48 | -0.1 to + 30 {-1 to + 300} | 30 {300} | 3000 {30000} | ±3000 {±30000} |
| FKC 49 | -0.1 to + 30 {-1 to + 300} | 500 {5000} | 20000 {200000} | {+20000,-10000} {+200000,-100000} |
Accuracy of calibrated measurement range or reference accuracy
| Accuracy: (including linearity, hysteresis & repeatability) |
| For models from 32 kPa to 3000 kPa |
| EMR > 1/10 of maximum scale: ±0.065% of EMR or ±0.04% of EMR as an option |
| EMR < à 1/10 de l’échelle maximale : ± (0.015 + 0.005 × Ech.max/EMR ) % de l’EMR |
The best reference accuracy, including maximum uncertainty errors for hysteresis, non-linearity and non-repeatability, is ± 0.04% of scale for the Fuji Electric FKC pressure transmitter.
E1 = 0.04 % *100
E1= 0.04 mbar
Effect of ambient temperature
| Influence of temperature |
|---|
| The values below are given for temperature variations of 28°C between -40°C and +85°C. |
| Max. measurement range | Effect on zero (% of TRA) | Total effect (% of TRA) |
|---|---|---|
| "1"/100 mmCE {10 mbar} "2"/600 mmCE {60 mbar} | ± (0.125+0.1 Ech.max/EMR)% (0.125+0.1 Ech.max/EMR) | ± (0.15+0.1 Ech.max/EMR)% (0.15+0.1 Ech.max/EMR) |
| "3"/32kPa {320mbar} "5"/130kPa {1300mbar} "6"/500kPa {5000mbar} "8"/3000 kPa {30000mbar} "9"/20000 kPa {200000mbar} | ±(0.075+0.0125 Ech.max/EMR)% % (0.075+0.0125 Ech.max/EMR) | ±(0.095+0.0125 Ech.max/EMR)% % (0.095+0.0125 Ech.max/EMR) |
In our example, the ambient temperature difference is 28°C.
Here we consider the total effect of the temperature effect.
E2 = ± (0.095 + 0.0125*320)%
E2= ± 0.135 mbar
Influence of static pressure
| Static pressure | Effect on zero (% of maximum scale) |
|---|---|
| "1" / 100 mmCE {10 mbar} "2" / 600 mmCE {60 mbar} | ± 0.1% / 0.1 MPa {1 bar} ± 0.063% / 1 MPa {10 bar} |
| "3" "4" | ±0.035% / 6.9 MPa {69bar} ±0.035% / 6.9 MPa {69bar} |
We consider here the zero offset of the static pressure effect.
E3 = ± 0.035*320%
E3 = ± 0.112 mbar
We can now calculate the probable total error.
Probable total error (FTE)
Probable total error = ± √ ((E1)²+ (E2)²+ (E3)²)
E1= Nominal accuracy of calibrated scale
E2= Effect of ambient temperature per 28°C
E3 = Effect of static pressure per 6.9 MPa
TPE = SQRT ((0.04)^2+(0.135)^2+(0.112)^2)
TPE= 0.179 mbar
TPE= 0.179% of measuring range
The process application required an accuracy of ± 0.2% of span. The sensor will measure a differential pressure of 100 mbar under normal operating conditions. The required performance of the field-installed sensor will be ±0.5 mbar. We can conclude that the Fuji Electric FKC differential pressure transmitter is suitable for this application. To complete our analysis of pressure performance, we can add a further factor influencing on-site pressure accuracy.
Overpressure effect
Overpressure refers to a situation in which the pressure exceeds the maximum calibrated range of the measuring device. Such conditions may arise in the event of an accident or other abnormal situation. The accuracy of pressure transmitters is also affected by overpressure. pressure transmitters manufacturers, such as Fuji Electric, generally express this effect in terms of maximum operating pressure.
| Static pressure | Effect on zero (% of maximum scale) |
|---|---|
| "1" / 100 mmCE {10 mbar} "2" / 600 mmCE {60 mbar} | ± 0.96 % / 3.2 MPa {32 bar} ± 0.31 % / 10 MPa {100 bar} |
| "3" "3" "4" "4" | ± 0.10 % / 16 MPa {160 bar} FKC 35, 36, 38 ± 0.15 % / 16 MPa {160 bar} FKC 33 ± 0.26 % / 42 MPa {420 bar} FKC 43, 45, 46 ± 0.06 % / 10 MPa {100 bar} FKC 48, 49 |
E4 = ± 0.15*320%
E4= ± 0.6 mbar
We can now calculate the total accuracy, including the overpressure effect of the range.
Total accuracy = ± √ ((E1)²+(E2)²+(E3)²+(E4)2)
TA = SQRT ((0.04)^2+(0.135)^2+(0.112)^2+(0.6)^2)
TA = 0.62639 mbar
TA = 0.62639 % of measuring range
Thanks to the calculation of the Total Probable Error (TPE) and an adapted method, we can now calculate the periodicity of pressure transmitter calibration.
Pressure measurement remains a fundamental aspect in guaranteeing the efficiency and safety of process engineering operations, in accordance withIEC 61298-2 test methods and procedures. Its accuracy is essential, given the diversity and complexity of applications in different sectors.
The comprehensive exploration of pressure transmitters in this article has highlighted the importance of understanding both reference accuracy and on-site performance, as well as the factors that influence these parameters, including the effects of ambient temperature, static pressure impacts, zero shifts and span shifts.
Thanks to a systematic explanation, we have revealed how to calculate the Total Probable Error (TPE), taking into account various uncertainties such as the accuracy of the calibrated range, ambient temperature influences and the effects of static pressure. The example given, using the Fuji Electric FKC differential pressure transmitter datasheet , further simplifies the practical application of this knowledge.
In essence, when selecting a pressure transmitter, it is imperative to ensure that it not only complies with the required performance parameters, but also withstands variable site conditions, thus guaranteeing its accuracy throughout its operational life. By integrating the information provided, maintenance and process engineers can undoubtedly make more informed decisions, improving the reliability and efficiency of their systems.
When choosing a pressure transmitter, it's important to opt for a device with minimal environmental impact.
The advanced floating cell technology of Fuji Electric pressure transmitters offers high immunity to temperature variations, static pressure and overpressure commonly found in the process industry, and considerably reduces overall measurement error.
Fuji Electric's high-performance class pressure transmitters are designed to revolutionize pressure measurement. They are thermally characterized during the manufacturing process to improve reference accuracy and minimize the influence of ambient temperature and static pressure.
This unique thermal characterization process, known as 4D gyration, has enabled us to characterize the pressure transmitter cell over a temperature range from -40 to +85°C.
Data are collected during the manufacturing process by recording zero offset and range at different temperatures using an automated manufacturing process. A non-linear curve-fitting algorithm is used to characterize the unique behavior of the pressure transmitter.
Compensation data is permanently loaded into each pressure transmitter cell during this process to actively compensate for the effects of the thermal environment. The result is a reference accuracy (including hysteresis, non-linearity and non-repeatability) of less than +0.04% of full scale over this wide temperature-compensated range.
Eliminate potential errors when measuring differential pressure: save time and energy by relying on a single device designed specifically for accurate differential pressure measurements.
Contact Fuji Electric France today to find out more about our high-performance class pressure transmitters and harness the full potential of precise pressure measurement.
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