At SOLV®, we often receive inquiries about discrepancies between software results and flow computers. We have identified common reasons why calculations might exceed the verification tolerance. Here, we outline these reasons to provide clarity and assist users in achieving accurate results.
When verifying flow computer calculations, the customary tolerance used is ±0.001% of the Reference Value. Vertical bars (||) indicate the unsigned (absolute) percentage value of the verification tolerance, which is derived as follows:
Achieving a tolerance of ±0.001% relies on high-quality inputs for the verification calculation. Here, we emphasize the importance of input precision to achieve this verification tolerance. While there is no one-size-fits-all rule, attention to the sensitivity of outputs to inputs and potential input discrepancies can help us get close to the reference value.
In our experience, discrepancies between FLOWSOLV® results and those of the flow computer typically arise in the following areas:
- Data Entry: Simple mistakes in number entry, either in the flow computer or FLOWSOLV® verification software.
- Mixed Engineering Units: Confusion in using absolute or gauge pressures, upstream, downstream, or measured temperatures, to name a few.
- Insufficient Significant Digits/Figures: Numbers are often rounded for ease of display or to avoid reporting insignificant figures. For example, a pressure measurement of 52.34525 bar displayed to seven significant figures might be used in calculations with more significant figures than displayed. We recommend a minimum of 6 significant figures to ensure the ±0.001% tolerance is always achieved.
While data entry errors or mixed engineering units can be solved with a bit of detective work, we will focus on the effects of significant figures (SF) from here onwards.
Golden Rules:
- It’s very difficult to verify a flow computer using live inputs. Always use keypad-entered values in the flow computer (off-line or in maintenance mode first).
- Even if a number is only displayed to two decimal places, a flow computer should use significantly more decimal places. Increase the display resolution of the flow computer if possible and enter a keypad value of at least 6 SF.
- Ensure that the input numbers for verification are not cascaded from another calculation. Understanding the overall calculation sequence can greatly help trace discrepancies in a flow computer.
- Most flow computer manufacturers provide a Snapshot or Live Values Report. This is convenient for collecting all data needed to verify a calculation. However, the data must come from the same calculation cycle (typically 500 milliseconds) and be of sufficient resolution (significant digits/figures) to permit meaningful number comparison.
So why is using full precision values on the calculation input side important? If you find a greater than ±0.001% difference between the FLOWSOLV® reference value and the flow computer test value, and you are certain of all your input numbers, it may be because the inputs used to calculate the test value are rounded in the flow computer.
Case Study Using API MPMS Chapter 11.1:2004 Calculation
We have prepared three simple case studies to illustrate the impact of significant figures and display rounding on API MPMS 11.1:2004. The example uses observed temperature, observed pressure, and base density to calculate density at observed conditions.
The reference value for observed density is calculated using inputs with 8 significant figures (SF). This reference value is shown in yellow in the tables below, and test values are compared to this value. Test values that deviate more than 0.001% from the reference value are shown in red.
Case 1: Significant Figures of Input Temperature, Pressure, and Density All Varied
In this case, the calculation inputs are varied from 1 to 7 SF. If the input values were rounded, they would be rounded down to give the same value but with fewer SF.
In this example, the tolerance of 0.001% was achieved with inputs of 6 SF.
Case 2: Significant Figures of Density Varied, Temperature and Pressure Constant
In this case, the input base density is varied from 1 to 7 significant figures (SF), while the pressure and temperature input SF remain constant. To achieve a 0.001% tolerance between the reference value and the test value, only 5 SF are needed for the density input. This is fewer than when all values are varied because we are only dealing with the sensitivity of a single (density) input.
The results of varying only temperature from 1 to 7 SF are not shown here, but similar to Case 2, 5 SF are needed for inputs to achieve the 0.001% tolerance. In liquid calculations, both temperature and density significantly affect the resultant base density.
Case 3: Significant Figures of Pressure Varied, Temperature and Density Constant
In this case, the input pressure is varied from 1 to 7 SF, while the temperature and density inputs are constant. To be within tolerance, only 2 SF are needed for pressure inputs. Since the calculated density is not highly sensitive to pressure in liquid calculations, fewer SF are required. However, in gas calculations, the resultant density would be far more sensitive to pressure, necessitating a higher number of SF to achieve the tolerance. Therefore, a one-size-fits-all rule cannot be applied when recommending the number of input SF to achieve tolerance.
Conclusions
We have demonstrated that the number of significant figures in inputs has a significant impact on achieving the ±0.001% flow computer verification tolerance. The precise number of significant figures required depends on the calculation and the sensitivity of the output to the input. For example, gas calculations are not particularly sensitive to temperature but are far more sensitive to composition and pressure, while liquid calculations are more sensitive to temperature.
A general rule of 6 significant figures for inputs is good measurement practice to eliminate the effects of number rounding as a source of error in flow computer verifications. If you are writing a flow computer specification, including this guideline can help with Factory Acceptance Testing and during its operational life phase.
To avoid issues with your flow computer vendor, ensure you have checked for data entry errors, mismatched engineering units, and significant figures discrepancies before sending a “we have a problem” email.