# Improving flowmeter calibration

## Instrumentation engineers should understand the common methods used in measuring viscosity and their effects on final flowmeter calibration data.

June 3, 2016

Calibrating a flowmeter is an essential part of any well-controlled process. However, accurate meter calibration not only requires a precision calibrator but also an accurate method to measure viscosity. Other than indicating a viscosity value on the calibration data sheet, calibration labs do not always expose their viscosity measurement methods.

Background

Calibration is a comparison between the reading of a device and traceable standards. The process establishing this relationship is a set of interrelated measurements and operations, which provide the comparison. Flow measurement does not rely on a single parameter, nor does a flow-based calibration.

Measurement of the volume or mass flow of a fluid depends on establishing verifiable measurements representing all the variables. The flow measurement may be the quantity collected over time or the actual rate of flow.

The volume measured by the calibration standard may be different from the volume passed through the meter under test if temperature measurements are incorrect. Temperature affects fluid viscosity, density, and the bore diameter of the flowmeter under test. This combination of fluid variables, coupled with how accurately they are measured and their effects on the calibration standard, will influence the uncertainty of the final calibration results (see Figure 1).

Understanding viscosity

Viscosity is a measure of a fluid’s internal or intermolecular resistance to shear stress, which influences the velocity profile in the pipe. When viewing a fluid flowing between two plates, the shear stress is the relationship between the forces exerted on the top plate to the area of the plate. Therefore, τ (shear stress) = F/A. Shear rate takes into account the height between the two plates combined with the velocity of the top plate, or γ (shear rate) = v/h. Dynamic viscosity is the shear stress (τ)/shear rate (γ). These equations apply to ideal or Newtonian fluids.

What are Newtonian fluids? These fluids have shearing stress that is related linearly to the rate of shearing strain. They are referred to as "true liquids" because their viscosity is not impacted by shear, such as those found in agitation or pumping. Most common fluids, such as water and hydrocarbons, are considered Newtonian fluids.

Some flowmeters are more sensitive to viscosity than others. But to some degree, they are all affected because viscosity changes the flow profile. Knowing the viscosity of a liquid is undeniably one of the most essential parts of a liquid flowmeter calibration.

Viscosity measurements can be accomplished by using several methods, which vary in equipment cost and measurement time. The most widely used instruments for measuring viscosities are glass capillary (ASTM D445), rotational (ASTM D2983), and Stabinger (ASTM D7042 equivalent to D445) viscometers. The Stabinger high-precision viscometer requires clean filter fluid to achieve superior accuracy (see Figure 2).

Flow calibration facilities cannot, and do not, use customer-specific liquid for each calibration. Not only would this be extremely time-consuming and less than environmentally friendly, it would also be cost-prohibitive and possibly hazardous. Therefore, calibration facilities use a solvent/oil blend with a measured kinematic viscosity that matches the customer’s fluid. This is based on the Reynolds number relationship (Reynolds number, or Re, is a dimensionless quantity used to help predict similar flow patterns in different fluid flow situations).

Re = (ρ x V x D)/µ

Where Re is the Reynolds number, ρ is density, D is the piper diameter, and µ is dynamic viscosity.

The fluid viscosity value in a positive displacement (PD) flowmeter calibrator is generated using a temperature/viscosity table, which is developed by inputting the actual kinematic viscosity value at two diverse temperature points. Temperature sensors, built into the calibrator piping, supply the actual fluid operating temperature used to extract the viscosity value from the temperature/viscosity table. A real-time fluid temperature and viscosity value is then recorded for each data point collected over the entire calibration flow range of the meter. It is worth noting that in a closed-loop calibration system, the fluid increases in temperature as it is continuously circulated through the piping.

Therefore, the precision of the calibration relies on the accuracy of:

• The initial fluid viscosity measurement as determined by a viscometer
• The accuracy of the fluid temperature measurements during the calibration.

Impact on calibration data

There are many types of liquid flowmeters in the industry including PD, rotameter, turbine, differential pressure, orifice, and Coriolis. To some degree, viscosity and density will have either a minor or major effect on the type of flowmeter being calibrated. In each case, knowing the operating viscosity and density of the fluid being measured is essential for establishing a credible calibration.

Viscosity becomes even more critical when using a turbine flowmeter in the nonlinear, but repeatable, region. The viscosity and density must be replicated during the calibration to produce accurate calibration data. Density is mentioned because it is required for Coriolis meters to calculate volumetric flow rate, much the same as for a turbine meter, which requires fluid density to calculate the mass flow rate. It is important to note that density and viscosity will change when temperature and pressure vary. As such, the calibrator data acquisition system must compensate for these variables and calculate, in real time, the flow rate in the desired unit of measure.

A good example when trying to see the effects of viscosity on calibration data is to look at the calibration of a nonlinear, but repeatable (±0.25%), low-flow turbine meter with a range of 0.125 to 1.25 gallons per minute (gpm). Turbine meters measure flow using a rotor that spins freely at a rotational speed proportional to the velocity and viscosity of the fluid. Figure 1 shows a nonlinear, low-flow turbine meter, which would be a worst-case scenario. The more linear the meter, the less sensitive it is to a viscosity shift (see Figure 3).

The flowmeter in Figure 3 was to be calibrated with a fluid viscosity of 1.2 centistokes (cSt). When an error of only 1 cSt was inserted into the calibration data, the plot shifted to the left, which resulted in a 1.9% K-factor shift. A lab without the proper equipment or procedures could easily mismeasure the viscosity by 10%. Other types of meters, such as rotameters, are sensitive to density and thus kinematic viscosity, where the density term is part of the equation for calculating the volumetric flow rate.

How can viscosity vary? A new 55-gallon drum of MIL-PRE-7024F Type II Stoddard solvent has a viscosity of between 1.12 and 1.22 cSt, as received (a variance of greater than 8%). Over time, the lighter elements in the solvent evaporate, which increases the viscosity. Viscosity could also be affected by the cleanliness of the calibrator piping and filters. If a more viscous fluid were previously used in the calibrator, and the flushing cycle were insufficient, the 1.12 cSt fluid could now be different. Therefore, it is best to measure the fluid viscosity out of the calibrator and not the drum. There are multiple reasons for viscosity errors, the worst being to not measure it at all.

When asking a calibration lab about the uncertainty of its primary standard calibrator, it is wise to also inquire about the uncertainty of the viscosity and density measurements. The two go hand-in-hand to produce the best calibration data that truly represents the meter technology capability.

Different labs will have a different bias, relative to the U.S. National Institute of Standards and Technology (NIST). The labs may, or may not, correct for bias, depending on whether they participated in a NIST round-robin exercise or sent their check standard meters to NIST for periodic calibration. As a reminder, precision is the ability to repeat the flow value, and bias is how far away it is from the true NIST value. As such, precision and bias correlation is needed to provide the correct flow calibration.

Choosing a calibration facility

Calibration labs accredited by NIST’s National Voluntary Laboratory Accreditation Program (NVLAP) have their calibrators’ uncertainties documented in their Scope of Accreditation. The uncertainty or precision of their calibrators can be found on the NIST website. This information provides the uncertainty of each calibrator used to calibrate customers’ flowmeters.

NVLAP provides an unbiased, third-party evaluation and recognition of performance. This accreditation signifies that a laboratory has demonstrated that it operates in accordance with NVLAP management and technical requirements pertaining to quality systems, personnel, accommodation and environment, test and calibration methods, equipment, measurement tractability, sampling, handling of test and calibration items, and test and calibration reports.

An NVLAP facility is in full conformance with the standards of the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC), including ISO/IEC 17025-2005: General requirements for the competence of testing and calibration laboratories; and in compliance with ANSI/NCSL Z540.3-2006: Requirements for the Calibration of Measuring and Test Equipment. This type of facility will have processes and procedures in place to ensure consistent and repeatable calibrations that include viscosity and density measurements.

The performance of an accredited calibration service lab depends solely on its ability to measure and provide accurate flowmeter data to its customers. When it comes to accurately measuring the flow of liquid through a meter, the viscosity must be known and controlled in the calibrator. Often, the calibration lab’s method for measuring viscosity-and the accuracy of the equipment measuring that viscosity-is not considered by the customer. However, the inability of a calibration lab to accurately measure the viscosity of a test fluid, whether due to the equipment or methodology, can cause added uncertainty that might render the calibration results inadequate. Therefore, it is essential that the viscosity measurement method be known, and considered, when choosing a calibration service.

Using the right equipment

Some of the most dramatic improvements in flow calibrator technology have involved the evolution of PD calibrators. PD systems are dynamic primary standard calibrators, which take into account the varying conditions under which flowmeters operate. These calibrators are able to accurately measure fluid temperature and correct for density, viscosity, and other variables that can shift a meter’s output. As such, they can typically achieve uncertainties in liquid of +/-0.05% of flow rate (see Figure 4).

The heart of the primary standard PD system is a precision-honed, nickel-chromium-plated, and polished cylinder with a piston and seals. The piston is coupled to a ground and polished shaft exiting the cylinder through a seal. The shaft is attached to a high-resolution linear encoder (one millionth of an inch), which tracks the piston displacement. Isostatic, steady-state, continuous flow, and leak-free conditions, as close to ideal as possible, are required to obtain uncertainties of ± 0.05% of reading or better.

Knowing the precise diameter of the cylinder and the rate of travel determines the volume of flow. It also means that the temperature of the cylinder must be known to compensate for thermal expansion or contraction affecting the volume. These variables are measured and used in algorithms to provide very accurate, real-time volumetric flow data.

Users should heed a word of caution when selecting a calibration service for turbine meters, which only use water as a calibration media. Water is abrasive and will cause additional flowmeter bearing drag that is not present in hydrocarbon applications. No calculation exists that can develop a new K-factor, or calibration curve, with a viscosity lubricity variable. Empirical data are used to develop a conversion factor, which only applies to a single flowmeter design and does not correlate with other meter manufacturers’ designs. Any change in rotor design or bearing material will render the correlation factor obsolete. A water and glycol mixture is becoming a consideration to minimize toxic waste, as well as issues with vapor odor and fire hazards. Glycol provides lubricity and can be mixed in the water to develop various kinematic viscosities for calibration.

Next steps

Having primary standard flow calibration equipment with respectable uncertainty is a requirement for any calibration service laboratory. The supporting measurements of viscosity and density cannot be compromised. The calibration results depend on every measurement made in the process, and particular attention should be given to viscosity. Most viscosity measurement methods are operator- and process-dependent and, therefore, vulnerable to potential error. Careful attention must be paid to the selection of a primary standard calibration laboratory and the processes used to consistently produce repeatable results. NVLAP-accredited calibration laboratories offer a safeguard by having processes and audits to verify competency.

With viscosity being such an important part of any flowmeter calibration service lab, it would be wise to seek not only calibrator uncertainty certification but also to pay attention to the necessity of accurate viscosity calibration techniques. Viscosity error results in undetectable flow calibration shifts and loss of accurate meter history.

Ron Madison is Manager, Calibrator Sales & Marketing, Cox Flow Measurement, a division of Badger Meter. He has extensive experience with precision test and measurement instruments with a specific emphasis in flowmeters.