Enhancing DP-based flow measurement with dynamic compensation
20 June 2016
Henk van der Bent describes how a multivariable pressure transmitter with built-in dynamic compensation can correct many of the errors and inaccuracies that occur in differential pressure based flow measurements. He also explains how modern flowmeters can ensure ease of integration with FDT technology based tools.
Differential pressure (DP) transmitters form the core of many field instrumentation systems, and are widely used to measure the flow rate, pressure and density of liquids, gases and steam, as well as the level of liquid in a tank.
DP transmitters have evolved in response to the demands for increasing accuracy and reliability, as well as enhanced computing and communication facilities to ease their integration into plant-wide monitoring, control and in particular, plant asset management systems.
Advances from Yokogawa have included the DPharp digital resonance sensor which eliminated the error-prone A/D convertor required by analogue sensors, and provided stability and precision, accuracy, response and repeatability. The combination of a digital sensor with integrated processing circuitry provides sensor diagnostics and high integrity, and allows full digital integration in a fieldbus based control system.
DPharp is a micro-electro-mechanical-system (MEMS) based silicon-resonant sensor that helps ensure precision and long-term stability. The technology is inherently fail-safe. Moreover, its design allows differential pressure and static pressure to be transmitted from a single sensor, allowing basic pressure measurements to be used as the basis of flow and level metering.
The result is a multivariable transmitter that is able to act as an ‘all-in-one’ instrument, integrating the functions of a DP transmitter, a pressure gauge, a thermometer and a flow computer. It employs a flow-rate calculation method to achieve a mass-flow calculation cycle of 100ms. By adopting a Reynolds number compensation algorithm, all flow calculation parameters are optimised and a mass flow accuracy rate as good as 1% of actual flow rate is achieved.
The multivariable transmitter is compatible with a range of primary devices, including orifice plates, nozzles, averaging pitot and venturi tubes, and can be used with a wide range of fluids, including general fluids, steam and natural gas. Application information, such as the primary devices and fluid data required for mass flow calculation, is input using a mass flow parameter configuration tool that runs on a PC and is downloaded to the transmitter. In operation, the flowmeter computes standard volumetric or mass flow from measured DP and flowing density using actual measured pressure and temperature, unlike standard DP transmitters which assume pressure and temperature – and therefore flowing density – to be constant.
In DP flow measurements, the variation in flowing density is only one of a number of potential sources of error. One source of error is the primary element. The accuracy of orifice plates, for example, can degrade over time as the plate loses its sharpness. A typical accuracy figure might be 1% of rate. Another source of error is the DP transmitter. This accuracy is expressed as a percentage of upper range value (URV), and is magnified by the square-law relationship between flow and differential pressure.
Traditional DP flowmeters
Traditionally, DP-based flowmeters have featured a 3:1 ‘turndown’. This figure that expresses the range over which the accuracy is perceived to be acceptable – 30-100% of flow for a 3:1 turndown. If the accuracy of the DP transmitter is assumed to be ±0.2% URV, at 100% flow the accuracy is ±0.2% plus the error of the plate. At 70% flow (49% DP due to the square-law relationship), the accuracy would be ±0.4%; at 50% flow (25% DP) it would be ±0.8%; and at 25% flow (6.25% DP) it would be ±3.2%. The plate adds ±1% over the full range and, when ±2.5% total accuracy is perceived to be acceptable, that accuracy is reached at around 30% flow - hence the 3:1 turn down. Turndown is often increased to 9:1 by using two DP transmitters over the same plate with different ranges, a switching mechanism and a flow computing function.
Although today’s DP transmitters are more accurate than ±0.2%, accuracy is still expressed as a percentage of URV, and the square-law relationship between flow and DP is still applicable. It could be argued that a turndown of better than 5:1 is not normally achieved. The error due to pressure (±0.5 bar) and temperature fluctuations (±10°C) in gas or steam flows can easily be of the order of magnitude of ±2%.
The flow factor k in the basic formula above is a constant compensating for the differences between theory and real life. It is calculated as part of the orifice calculation, and is valid only for one particular set of operating conditions – making it another potential source of error. It is dependent on the discharge coefficient, the gas expansion factor and velocity of approach factor.
The result of an orifice calculation is the diameter of the hole in relation to the pipe diameter – the ß-ratio. When a fluid is flowing through a pipe with an orifice plate, the flowing area reduction is abrupt, causing the smallest flowing area (Vena contracta) to be downstream of the plate. The discharge coefficient compensates for the difference between theory and real life. However, the discharge coefficient is flow profile (Reynolds) dependant and varies with the flow velocity, pipe internal diameter, flowing density and flowing viscosity. In turn, the latter three parameters are affected by flowing temperature.
When a gas or steam flow passes the orifice plate it is compressed upstream of the plate due to the obstruction caused by the plate. Downstream of the plate it expands again. The gas expansion factor corrects for density differences between the pressure taps, and it depends on the ß-ratio, the isentropic coefficient (correcting for theoretical versus real-life expansion), differential pressure and static pressure. Again, temperature has an effect as well. Finally, the velocity of approach factor is dependent on the ß-ratio (d/D), which in turn is dependent on temperature. The pipe and orifice plate material expands or contracts as temperature changes, and the velocity of approach factor corrects for changes in ß-ratio due to temperature fluctuation.
The error in flow factor k increases with decreasing flow rate, contributing to overall flowmeter accuracy. A primary element of a DP based flowmeter is sized for one particular set of operating conditions. When in real life the conditions change – lower pressure, higher temperature, lower flow rate – the user would like to re-calculate the flow-rate/DP relationship for every new set of conditions. The multivariable transmitter is able to correct for pressure and temperature variations and can compensate continuously for the effects of changing operating conditions on the flow factor. Using a flow configuration wizard, it can be set up to act as a flow computing device.
There are two options – basic mode and auto compensation mode. In basic mode, the transmitter only compensates for pressure and temperature fluctuations with a constant flow factor, similar to a standard DP transmitter with a separate flow computer, resulting in a turndown of say 5:1. However, in the auto compensation mode, it dynamically compensates for fluctuating conditions and their effects on the flow factor, reducing the error basically to the uncertainty intrinsic to the primary element. Consequently, the accuracy specification of ±1% of flow rate (assuming the primary element to be ideal) over a 10:1 turndown in flow terms (equivalent to 100:1 turndown in DP terms) is only valid in the auto compensation mode. So, with its 10:1 turndown, the multivariable transmitter eliminates the need for a separate flow computer, and can replace one or two DP transmitters and a pressure transmitter over the same plate, while achieving good performance over a wide flow range.
The flow computer is configured using a portable software application, FlowNavigator, which is based on FDT technology that is able to interrogate a DIPRR (AIChE) physical properties database for 126 fluids and gases as well as pipe and plate material property databases. Its compressibility equations meet international standards including the AGA 8 and ISO12213 natural gas equations (either simplified or using the full molecular weight composition method), IAPWS-IF97 formulation for water and steam, or custom compensation based on user-defined density and viscosity data.
An important benefit of the transmitter is provided by its communication capabilities, which allows it to interface with other elements of an integrated plant-wide operation. As a result, it is possible to carry out remote configuration and diagnosis using industry standard tools such as FDT technology. FDT is a proven industrial open interface specification. A key component of FDT (Field Device Tool) is the device Device Type Manager (DTM), a portable software application.
Through DTMs FDT technology facilitates the management and configuration of sensors, actuators, flowmeters, transmitters and other field devices connected to process automation and plant asset management systems as well as PC-based device configuration and management tools, regardless of the communications protocol used.
The DTM for the multivariable transmitter features an add-on flow configuration wizard which can be integrated in any FDT frame application. The add-on module features the flow configuration wizard configuring the transmitter for a specific flow application and, enabled by FDT capabilities, can also access the fluid and material property databases and features the ‘obtain flow coefficient’ function where the transmitter calculates the flow rate, flowing density and discharge coefficient, on the basis of manually entered values for differential pressure, pressure and temperature to verify the correctness of the flow configuration. This reduces the commissioning effort for this type of device. FDT technology frees users from the need to learn configuration methods from different manufacturers and eliminates the constraint of having to install devices from the same manufacturer more efficient plant operations to be realised.
Henk van der Bent is marketing manager Field Networks at Yokogawa Europe B.V.
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