Volumetric flow rate of process fluids is a critical parameter in process control and optimization within the chemical and petrochemical industries. Reflecting this, the chemical and petrochemical industries are the single largest users of industrial flowmeters, spending $1 billion annually. There is now a new class of flowmeters that may show advantages over conventional flow measurement technologies for applications important to the chemical and petrochemical industries.
Industrial flowmeters often fall into two technology-based categories: old technology and new technology flowmeters. The old technology category refers to flow measurement technologies in use for more than seventy years, and includes turbine meters, orifice plates, and variable area flowmeters.
The new technology category includes technologies that have emerged over the past thirty to fifty years. The major types of new technology flowmeters include Coriolis, electromagnetic, ultrasonic, and vortex flowmeters. Typically, new technology flowmeters offer advantages over old technology flowmeters in performance, functionality, and reliability. Each type has evolved to serve various aspects of the diverse range of applications within the industrial flowmeter landscape. Despite the diverse array of measurement technologies currently available, the chemical and petrochemical processing industries continue to have unmet needs for accurate, reliable, and economical monitoring of many single and multiphase flow applications, including large-diameter pipes and liquid-conveyed solid particle slurries.
Sonar flow measurement technology was first introduced into the oil and gas industry in 1998 for use in down hole multiphase flow metering applications, and it is currently being adapted for use in other industries including the chemical and petrochemical industries. The measurement principle involves characterizing the speed at which coherent vortical structures flow past an array of pressure or strain-based sensors, mounted axially along the pipe.
Because the coherent structures within the process fluid are inherent features of the turbulent boundary layer, no internal geometry is required to generate these structures. This measurement principle is distinct from other existing flow measurement technologies, and has attributes that differentiate it from existing flow measurement technologies. From an array signal processing perspective, sonar-based flow measurement is analogous to beam-forming applications developed over several decades for underwater sonar-based navigation. Sonar-based measurements can be implemented using pressure transducers directly ported into the process fluid or using strain-based sensors clamped-on to the outside of the process piping. With its ability to clamp on to existing process lines eliminating any process-wetted hardware, the clamp-on configuration is particularly well suited for many corrosive and abrasive process flows commonly encountered in the chemical and petrochemical industries.
The relevant structures within a turbulent process flow can show the time-averaged axial velocity is a function of radial position, from zero at the wall to a maximum at the centerline of the pipe. You can characterize the flow near the wall by steep velocity gradients and transitions to relatively uniform core flow near the center of the pipe. The turbulent eddies are superimposed over a time-averaged velocity profile. These coherent structures contain fluctuations with magnitudes typically less than 10% of the mean flow velocity and carry along with the mean flow. Experimental investigations established that eddies generated within turbulent boundary layers remain coherent for several pipe diameters and convect at roughly 80% of maximum flow velocity.
The Reynolds number (Re), based on pipe diameter (D), characterizes many of the engineering properties of the flow. The Reynolds number is a nondimensional ratio representing the relative importance of inertial forces to viscous forces within a flow:
Where ρ is the fluid density, µ is the dynamic viscosity, U is the volumetrically averaged flow velocity, and v (= µ/ρ) is the kinematic viscosity.
The critical Reynolds number for pipe flows, above which flows are considered turbulent, is ~2,300. Most flows in the chemical and petrochemical industries have a Reynolds number ranging from 100,000 to several million, well within the turbulent regime. In addition to demarcating a boundary between laminar and turbulent flow regimes, the Reynolds number is a similarity parameter for pipe flows, i.e., flows in geometrically similar pipes with the same Reynolds number are dynamically similar.
Coherent structures within turbulent pipe flows
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The sonar-based flowmeter uses the convection velocity of coherent structures (eddies) inherent within turbulent pipe flows to determine the volumetric flow rate. The sonar-based algorithms determine the speed of the turbulent eddies by characterizing both the temporal and spatially frequency characteristics of the flow field. For a series of coherent eddies convecting past a fixed array of sensors, the temporal and spatial frequency content of pressure fluctuations are related through a dispersion relationship, expressed as follows:
Here k is the wave number, defined as k = 2π/λ in units of 1/length, ω is the temporal frequency in rad per second, and Uconvect is the convection velocity or phase speed of the disturbance. The dispersion relationship basically states that temporal variations observed at a fixed location are proportional to the convection speed and inversely proportional to the spatial wavelength of the disturbance.
In sonar array processing, the spatial/temporal frequency content of time-stationary sound fields is often displayed using "k-ω plots." K-ω plots are three-dimensional power spectra in which the power of a sound field decomposes into bins corresponding to specific spatial wave numbers and temporal frequencies. On a k-ω plot, the power associated with a pressure field convecting with the flow distributes in regions that satisfy the dispersion relationship developed above. For turbulent boundary flows, this region is "the convective ridge," and the slope of this ridge on a k-ω plot indicates the speed of the turbulent eddies. Thus, identifying the slope of the convective ridge provides a means to determine the convection speed of the turbulent eddies, and with calibration, the precise volumetric flow rate within a pipe.
The fundamental principle behind sonar-based flow measurements shows that axial arrays of pressure transducers can be used in conjunction with sonar processing techniques to determine the speed at which naturally occurring turbulent eddies convect within a pipe. However, to provide an accurate flow measurement, the relationship between the speed of these turbulent eddies and the volumetrically averaged flow rate within the pipe must be quantified through calibration. To this end, three geometrically similar sonar-based flowmeters with diameters of 3 inches, 6 inches, and 16 inches were tested for flows ranging from 20 to 20,000 gallons per minute (gpm). First, testers determined the convection velocity using the sonar-based techniques, normalized by the volumetrically averaged flow rate supplied by the calibration facility as a function of the Reynolds number. The measured convection velocity, i.e., the slope of the convective ridge, ranged between 99% and 102% of the volumetrically averaged flow rate over the entire range test. A low-order Reynolds number calibration was developed from this data for this class of meters.
The testers plotted the volumetric flow rate measured by the calibrated sonar-based flowmeters versus reference flow. Calibration data was recorded for the three flowmeters with volumetrically averaged flow velocities ranging from 3-30 feet per second. Using the Reynolds number calibration for the three geometrically scaled meters, the sonar-based meter measured the volumetric flow rate to within 0.5% accuracy over a combined operating range from 20 gpm to 20,000 gpm. It is important to note that the sonar flow metering methodology has no fundamental size or flow rate limitations, being applicable to turbulent flows in pipes of all diameters and Reynolds numbers. Further-more, similarity laws suggest, and data from the tests supports, the relationship between convection velocity and flow rate from geometrically similar meters of any size can be calibrated with a single Reynolds number-based calibration.
Strain-based clamp-on configuration
An 8-inch diameter sonar-based flowmeter using siz clamp-on strain-based sensors. |
Sonar-based flow measurements have been performed with (1) arrays of ported pressure transducers or (2) with strain-based sensors clamped on the existing process lines.
The ability to clamp on and measure single and multiphase industrial flows is an important feature of sonar-based flow metering technology. In one example an 8-inch sonar-based flowmeter using six strain-based sensors clamped onto a schedule 40 stainless steel pipe. In this investigation, the clamp-on flowmeter measured the flow rate of water to within 1% accuracy over of range of 500 gpm to 5,000 gpm in an 8-inch pipe.
Clamp-on 8-inch sonar-based flow management
Volumetric flow rate measured using the sonar-based flowmeter versus reference flow rate. |
The calibration data demonstrates that sonar-based flowmeters can provide an accurate, first principles-based, flow measurement over a range of pipes using either ported pressure or clamp-on-based strain sensors in clean, single-phase (water) applications. However, unlike many conventional flow metering technologies, sonar-based flow measurement is equally well suited for both single and multiphase flows.
To evaluate the applicability of sonar-based flow measurement technology to multiphase flows important to the chemical processing industry, a field trial was conducted on a 3-inch flow line carrying a near-boiling, water-conveyed slurry of 1/8-inch to 1-inch polymer crumbs ranging from 0 to 8% mass fraction. Liquid-conveyed, solid-particle slurries are widely used in chemical manufacturing. Due to the erosive nature of the flow, varying chemical composition, potential for clogging, and other reasons, an accurate and reliable flow measurement of these slurries has proved difficult for conventional flowmeter technologies.
For the field trial, a ported-pressure spool piece met the specifications of the plant operator. The spool piece housed five flush-mounted pressure transducers and was fabricated using standard 3-inch, 150-pound flanges. Prior to installation, the spool piece was hydrostatically tested to 250 pounds per square inch. As a benchmark, the sonar-based flowmeter was compared with the output of a 3-inch electromagnetic (mag) flowmeter installed in-line on the same process piping. The end result: The mag meter and sonar-based flowmeter show good correlation, demonstrating the applicability of sonar-based flow measurement technology to this important class of multiphase slurries.
Sonar-based flow measurement is a new class of flow metering technology well suited for chemical and petrochemical applications. Sonar flowmeters use sonar array processing technology to determine the speed at which naturally occurring turbulent eddies flow through a process flow.
Sonar flowmeters can work with either port-pressure configurations or with strain-based clamp-on sensors.
Data shows the ability of sonar-based flow metering technology to track the speed of turbulent eddies within process lines. Calibration data confirmed the speed of the turbulent eddies closely tracks the volumetrically averaged flow velocity in the pipe. Exploiting similarity laws, a Reynolds-number-based calibration was developed for a set of three geometrically similar, sonar-based flowmeters to demonstrate 0.5% accuracy over of range of flow rates spanning 20 gpm to 20,000 gpm.
Results from a field trial of a sonar-based flowmeter on a water-conveyed, polymer slurry show the sonar-based flowmeter performed comparably with an existing electromagnetic flowmeter monitoring the same process line. MP
Daniel L. Gysling, Ph.D., and Douglas H. Loose work at Wallingford, Conn.-based CiDRA Corp. Gysling is the chief technology officer for Industrial Sensing Solutions and holds several patents in the area of fluid dynamic devices.
