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Bachelor Degree in Chemical Engineering Course: Process Instrumentation and Control

Bachelor Degree in Chemical Engineering Course: Process Instrumentation and Control ( Strumentazione e Controllo dei Processi Chimici ) Measuring devices of the main process variables Flow rate measurements Rev. 3.2 – March 28, 2019. FLOW RATE. MASS (m) (kg/s). VOLUMETRIC (V) (L/s).

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Bachelor Degree in Chemical Engineering Course: Process Instrumentation and Control

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  1. Bachelor Degree in Chemical Engineering Course: Process Instrumentation and Control (Strumentazione e ControllodeiProcessiChimici) Measuring devices of the main process variables Flow rate measurements Rev. 3.2 – March 28, 2019

  2. FLOW RATE MASS (m) (kg/s) VOLUMETRIC (V) (L/s) MOLAR (N) (kmol/s) FLOW RATEUNIT OF MEASUREMENT §2.2.1 pag. 9 Magnani, Ferretti and Rocco (2007) Process Instrumentation and Control - Prof M. Miccio

  3. FLOW RATE METERSCLASSIFICATIONS First classification(by contrast) Volumetric Mass Static Rotary Trasducer Non-Trasducer Intrusive Non-Intrusive Process Instrumentation and Control - Prof M. Miccio

  4. FLOW RATE METERSCLASSIFICATIONS Second Classification based on measuring principle Differential pressure Variable Area Velocity Direct Mass Measurement Rotary Process Instrumentation and Control - Prof M. Miccio

  5. SECOND CLASSIFICATION(based on principle of measurement) • Differential Pressure • Variable Area • Velocity • Direct Mass Measurement • Positive displacement • Turbine type • Open channel Process Instrumentation and Control - Prof M. Miccio

  6. CONTRACTION-BASED FLOW METERS • HYPOTHESES: • horizontal position • ρ = constant • v # f (r ) • Δploc= 0 • circular pipe 1 2 d1 d2 A1 A2 From Bernoulli’s principle (§ 2.2.4 page 15 - Magnani, Ferretti and Rocco, 2007): IDEAL CASE γ ideal flow coefficientof a contraction REAL CASE Velocity is not uniform in crosssectional area (ξ<1, real case) Local pressure drop (vortices formation) where β is the contraction ratio Process Instrumentation and Control - Prof M. Miccio

  7. CONTRACTION-BASED FLOW METERS • Hypotheses: • compressible fluid (Gas or Vapor); • small (P1 - P2); • K = calibration factor [m2] “PI ON TI” CORRECTION Process Instrumentation and Control - Prof M. Miccio

  8. CONTRACTION-BASED FLOW METERS(orifice plates, flow nozzles, Venturi meter) from Magnani, Ferretti and Rocco (2007) Process Instrumentation and Control - Prof M. Miccio

  9. d2 d1 ORIFICE PLATE or ORIFICE METER • for VOLUMETRIC FLOWRATE MEASUREMENT of GAS or LIQUIDS • sharp restriction of the cross sectional area of the fluid flow; • thin diaphragm thickness; • design and installation meeting to STANDARD REGULATIONS (e.g.: UNI) • orifice can be off-axis; • orifice plate can be shaped as a semicircle; • orifice plate can have a groove interacting with the fluid. Process Instrumentation and Control - Prof M. Miccio

  10. DIAPHRAGMSExamples vent (optional) Φ=2,5mm C.F.R. Internal tothe pipe purge (optional) Φ=2,5mm Process Instrumentation and Control - Prof M. Miccio

  11. ORIFICE PLATEINSTALLATION • Re > 500 • HORIZONTAL POSITION • Undisturbed and straight pipeline 20D upstream and 5D downstream d = orifice diameter D = pipe diameter β = d/D<1 Exploded view drawing Process Instrumentation and Control - Prof M. Miccio

  12. PRESSURE PROFILE OF A LIQUIDIN A CONTRACTION [(P/ρg)+(v2/2g)] Friction loss P Pressure drop due to the orifice Kinetic energy Pressure and potential energy orifice_meter.swf upstream downstream vena contracta Process Instrumentation and Control - Prof M. Miccio

  13. ORIFICE PLATEPOSITIONING OF PRESSURE SENSORS • at vena contracta • on the carrier ring • on the pipeline VENA CONTRACTA TAPS M =1* PIPE DIA N VARIES WITH b RATIO Process Instrumentation and Control - Prof M. Miccio

  14. ORIFICE PLATEPOSITIONING OF PRESSURE SENSORS • at vena contracta • on the carrier ring • on the pipeline LINE TAPS on the pipeline CORNER TAPS on the carrier ring β Process Instrumentation and Control - Prof M. Miccio

  15. FLOW NOZZLE Installation Flow Nozzle • It measures the pressure drop before and after a contraction of the cross section of the pipe. • It measure ΔP by means a differential manometer. • It is easy to be replaced in piping with flow nozzles having a more wide range because it can assume different values of β Process Instrumentation and Control - Prof M. Miccio

  16. VENTURI METER Venturi meter consists of a converging and a diverging sections. The decrease in the section of the pipeline, due to the inverse proportionality that links the velocity to the section of the pipeline, determines, at constant flow, an increase in velocity (continuity equation). Process Instrumentation and Control - Prof M. Miccio

  17. VENTURI METER • The Venturi meter shape allows the homogeneity and the axial symmetry of the vena contracta. In improves the local flow regime of the fluid and the pressure meaurements from which depends the precision of the flow rate measure. • The variation of the inner contour of the Venturi meter, the small imperfection and roughness of the internal surface on the Venturi meter and the installation eccentricity are negligible and they don't have much influence on the measurements. • Venturi meter shows a better repeatability of the measurement with time because of the few scratches produced by the small solid particles transported by fluid do not influence the instrument indications. • With the same contract ratio with the other contraction-based devices Venturi meter has greater accuracy and lower pressuredrop than the other contraction flow rate sensors but it is more expensive. NOTE: It is fundamental to take into account cavitation in the design and the construction of a Venturi meter. The pressure in vena contracta must not be lower the vapor pressure of the liquid. Cavitation can produce considerable damage to the sensor and to the pipeline. Process Instrumentation and Control - Prof M. Miccio

  18. SECOND CLASSIFICATION(based on principle of measurement) • Differential Pressure • Variable Area • Velocity • Direct Mass Measurement • Positive displacement • Turbine type • Open channel Process Instrumentation and Control - Prof M. Miccio

  19. ROTAMETERVariable Area Volumetric Flowmeter • It consists of a transparent tapered pipe, slightly conical, placed vertically with an upward fluid. • A graduated scale is reported externally. • A body (“float”) having a greater density than fluid is located internally. • The float is made on different shapes, as spherical and conical, depending on the application and the fluid. • The flow rate measurement is performed by the observation of the position of the float on the graduated scale. The position is taken on the lowest section flow, corresponding to the section of the diameter for a sphere and of the base for a cone. • A higher volumetric flow rate through a given area increases flow speed and drag force, so the float will be pushed upwards. • The cross section available to the fluid increases when the float is raised, i.e. to increase the flow rate. • A hard-set in placed on the top of the column to avoid severe impact with the upper zone of the rotameter. • A spring is placed at the bottom of the rotameter in order to prevent damage of the instrument for abrupt interruption of the flow. • Pipes made of steel are used for rotameter performing at high pressure. In this case the external indicator is coupled with an electromagnetic float. Process Instrumentation and Control - Prof M. Miccio

  20. ROTAMETER When the float is stable on a specified position, an equilibrium of forces occurs. Readings are directly performed on the graduated scale of the flowrate on the transparent column Process Instrumentation and Control - Prof M. Miccio

  21. ROTAMETER Process Instrumentation and Control - Prof M. Miccio

  22. ROTAMETERvariable area Volumetric FlowMETER video Rotameter.avi Process Instrumentation and Control - Prof M. Miccio

  23. ROTAMETERHypotheses (2) (1) • For a generic float we can indicate: • the bottom position of the float (1), when the sectional area for the fluid flow becomes to reduce • the position of minimum sectional area for the fluid flow (2), • with the subscript “0” the quantity referred to the float. • Spherical float • Steady state • Constant ρ • Section area S2<<S1 • z2 - z1  V0/A0; (where: V0 is the volume of the float, A0 is the projected area of the float) • Local and Distributed Pressure drops are negligible • z v ≠ f(r) • Surface for pressure forces = Projected area → A1 = A2= A0 Process Instrumentation and Control - Prof M. Miccio

  24. (2) (1) ROTAMETERFlow equation Force balance (scalar) equation on the float (a) P1A1 - P2A2 - ρ0V0g = 0 where: P1 : fluid pressure in position (1); P2: fluid pressure in position (2) (with P2<P1 for the Bernoulli’s principle) P1A1 = upstream force exerted by the fluid pressure on the float P2A2 = downstream force exerted by the fluid pressure ρ0V0g= weight of the float Since the hypothesis: A1=A2=A0 (b)P1A0 - P2A0 - ρ0V0g = 0 Bernoulli’s equation For section (1) and (2) and considering a constant density, we have: (c) Continuity equation (d) where S1>>S2 e v2>>v1 Process Instrumentation and Control - Prof M. Miccio

  25. ROTAMETERFlow equation Equation (c) becomes: (e) From the force balance eq. (b) we obtain: (f) From the previous assumption : (g) where V0 is the volume of the float NOTE: The assumption (g) is dimensionally correct, but is not properly exact for a sphere. Process Instrumentation and Control - Prof M. Miccio

  26. ROTAMETERFlow equation Replacing eqs. (f) and (g) in (e) we obtain: By simplification it becomes: Considering the continuity equation: Factorizing in v2: Process Instrumentation and Control - Prof M. Miccio

  27. ROTAMETERFlow equation and solving for v2 we obtain: The flow coefficient for a contraction γ is: And multiplying by S2 the right and the left hand sides we have the final equation: NOTE: S2 is a linear function of the position of the float due to the conical shape of the pipe The mass flow rate can be calculated from the volumetric flow rate as: Process Instrumentation and Control - Prof M. Miccio

  28. ROTAMETERRelationshipbetweenFlowrate and Height of the float The geometric dependence of the surface area of the throttling section S2on the height of float lifting His defined according to the scheme in figure is: whereis the angle of the cone-forming line with relation to the pipe axis. For pipes with small conicity (from the order of 1:100) and not long float travel, the expression gets insignificant values and it can be ignored. Process Instrumentation and Control - Prof M. Miccio

  29. ROTAMETERRelationshipbetweenFlowrate and Height of the float • So we can obtain the relationship between the Volumetric Flowrate and on the • height of float lifting His defined according to the scheme in figure is: • Multiplying the two sides of this equality by the density of the fluid ρ, we will get the generalized characteristic of the rotameter for measuring the mass • flow ṁ: Process Instrumentation and Control - Prof M. Miccio

  30. ROTAMETERCalibration The volumetric flow rate of a rotameter is expressed as normal-liters per hour for the calibration conditions. If the instrument is used in a different condition than the calibration conditions the measurement needs a correction as: where: ρn is the calibration density; is the corrected measure; is the actually read flow rate. Process Instrumentation and Control - Prof M. Miccio

  31. ROTAMETERCalibration Volumetric flow rate: For an ideal gas: If P = constant the correction becomes: On the other hand, if T = constant we have: Process Instrumentation and Control - Prof M. Miccio

  32. ROTAMETER Accuracy: 1% of the measurement at 100% of the flow rate  (3 10)% of the measurement at 10% of the max flow rate Measuring range: up to 30 kg/s (H2O), up to 1 kg/s (air) •  Advantages • Linear relation flow rate – float position • Constant pressure drop across the float • Easy to read • Easy to install and to use in laboratories and pilot plants • Disadvantages • A proper calibration is needed for each fluid at specific temperature and pressure • Correction formulas when it is used in condition different from calibration • It is not an electrical transducer • Only vertical installation • Requires "reinforced" model or non-transparent tube for high working pressures Process Instrumentation and Control - Prof M. Miccio

  33. SECOND CLASSIFICATION(based on principle of measurement) • Differential Pressure • Variable Area • Velocity • Direct Mass Measurement • Positive displacement • Turbine type • Open channel Process Instrumentation and Control - Prof M. Miccio

  34. FLOWMETERS based on measurement of velocity Process Instrumentation and Control - Prof M. Miccio

  35. SECOND CLASSIFICATION(based on principle of measurement) • Differential Pressure • Variable Area • Velocity • Direct Mass Measurement • Positive displacement • Turbine type • Open channel Process Instrumentation and Control - Prof M. Miccio

  36. CORIOLIS METERS Working principle They use the Coriolis effect. The measuring element is subjected to a vibration “simulating” the rotation of it; the Coriolis effect produces a force depending on the mass flow rate. The measurement is independent from both the flow regime and a possible variation of fluid properties. TOPVIEW SIDEVIEW from Magnani, Ferretti and Rocco (2007) Process Instrumentation and Control - Prof M. Miccio

  37. CORIOLIS METERS Process Instrumentation and Control - Prof M. Miccio

  38. CORIOLIS MASS FLOWMETERVibrating tube configuration Process Instrumentation and Control - Prof M. Miccio

  39. CORIOLIS MASS FLOWMETER Direct measurement of mass flow rate [kg/s] Recommended to measure flow rate for liquids and fairly dense gases. Measuring range (liquids) from 0.001 kg/s to 20 kg/s Accuracy 0.25% of the measurement Repeatability 0.15% of the measurement Rangeability 100:1 Installation No restrictions (vertical installation is better)  Advantages Small pressure drop  Disadvantages Expensive Process Instrumentation and Control - Prof M. Miccio

  40. ELECTRONIC THERMAL MASS FLOWMETER • Thermal Mass Flow Meters (and Controllers) make use of the heat conductivity of fluids (gases or liquids) to determine mass flow. • Three implementations: • for gases, by-pass principle • for gases, inlineprinciple • for liquids, inlineprinciple ] following the anemometricprinciple flowz.flv Process Instrumentation and Control - Prof M. Miccio

  41. ELECTRONIC THERMAL MASS FLOWMETER for gases, by-pass principle The sensor is mounted as a by-pass to the main channel, where a patented flow resistance splitter takes care of proportional flow division, also under varying process conditions. A part of the gas stream flows through the sensor, and is warmed up by heaters RHT1 and RHT2. Consequently the measured temperatures T1 and T2 drift apart. The temperature difference is directly proportional to mass flow. Electrically, temperatures T1 and T2 are in fact temperature dependent resistors RHT1 and RHT2. This laminar flow element consists of a stack of stainless steel disc with high-precision etched flow channels, having similar characteristics as the flow sensor. http://www.bronkhorst.com Process Instrumentation and Control - Prof M. Miccio

  42. ELECTRONIC THERMAL MASS FLOWMETER Process Instrumentation and Control - Prof M. Miccio

  43. ELECTRONIC THERMAL MASS FLOWMETER Process Instrumentation and Control - Prof M. Miccio

  44. ELECTRONIC THERMAL MASS FLOWMETER Process Instrumentation and Control - Prof M. Miccio

  45. ELECTRONIC THERMAL MASS FLOWMETER for gases, inlineprinciple http://www.bronkhorst.com Mass Flow Meters with inline sensor (no by-pass) consist of a straight flow channel, into which two stainless steel probes protrude; a heater probe and a temperature sensor probe. A constant temperature difference (ΔT) is created between the two probes and the energy required to maintain this ΔT is proportional to the mass flow rate (CTA: Constant Temperature Anemometry) . Mass flow can be measured with low pressure drop. Compared to traditional thermal MFMs and MFCs with by-pass, they are less sensitive to humidity and contamination. Process Instrumentation and Control - Prof M. Miccio

  46. ELECTRONIC THERMAL MASS FLOWMETER • Advantages • Direct measurement of mass flow rate [kg/s] • Accuracy up to: • εa=  0.75% • εf =  0.25% • Rangeability from 10:1 to 100:1 • Other characteristics • Recommended for “very clean” gas • Adjustable to measurement of flow rate for liquids with special and expensive devices Process Instrumentation and Control - Prof M. Miccio

  47. SECOND CLASSIFICATION(based on principle of measurement) • Differential Pressure • Variable Area • Velocity • Direct Mass Measurement • Positive displacement • Turbine type • Open channel Process Instrumentation and Control - Prof M. Miccio

  48. POSITIVE-DISPLACEMENT METER DEFINITION A fluid (liquid or gas) quantity meter that separates and captures definite volumes of the flowing stream one after another and passes them downstream, while counting the number of operations. Process Instrumentation and Control - Prof M. Miccio

  49. ROTARY METERS Classification Positive Displacement Momentum transfer The axis is normalto the flow direction The axis is coincidentto the flow direction Process Instrumentation and Control - Prof M. Miccio

  50. rotary vane flowmeter from ISA Certified Control Systems Technician (CCST) program http://www.isa.org Rotation velocity of rotor N. of “units of volume” carried for unit of time fluid volumetric flow rate Process Instrumentation and Control - Prof M. Miccio

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