Flowmeter with pitot tube with average pressure
- Publication number
- CA2239497A1 CA2239497A1 CA 2239497 CA2239497A CA2239497A1 CA 2239497 A1 CA2239497 A1 CA 2239497A1 CA 2239497 CA2239497 CA 2239497 CA 2239497 A CA2239497 A CA 2239497A CA 2239497 A1 CA2239497 A1 CA 2239497A1
- Grant status
- Patent type
- Prior art keywords
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- G01—MEASURING; TESTING
- G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
- G01F1/00—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through the meter in a continuous flow
- G01F1/05—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through the meter in a continuous flow by using mechanical effects
- G01F1/34—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through the meter in a continuous flow by using mechanical effects by measuring pressure or differential pressure
- G01F1/36—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through the meter in a continuous flow by using mechanical effects by measuring pressure or differential pressure the pressure or differential pressure being created by the use of flow constriction
- G01F1/40—Details or construction of the flow constriction devices
- G01F1/46—Pitot tubes
This information is used to calculate flow rate (Q) of the process fluid.
W O 97/25595 PCT~US96/20898 FLOWMETER WITH PILOT TUBE WITH AVERAGE PRESSURE
PRI~L~RY ~T.~M~rr BACKGROUND OF THE INVENTION
5The present invention relates to measurement of fluid flow. More specifically, the present invention relates to flow measurement of a process fluid using an averaging pitot tube type sensor.
Measurement of flow rate of process fluid is necessary to control industrial processes. In industrial processes, transmitters which measure flow rate (Q) are placed at remote locations in the field of a process control system. These transmitters transmit flow rate information to a control room. The flow rate information is used to control operation of the process.
As used herein, process fluid refers to both liquid and gaseous fluids.
One common means of measuring flow rate in the process control industry is to measure the pressure drop across a fixed restriction in the pipe, often referred to as a differential producer or primary element. The general equation for calculating flow rate through a differential producer can be written as:
Equation 1 Q - NCdE Yld2 ~i where Q = Mass flow rate (mass/unit time) N = Units conversion factor (units vary) Cd = Discharge coefficient (~;m~n~ionless) E = Velocity of approach factor (<l; men.~ionless) Yl = Gas expansion factor (dimensionless) W O 97/~5595 PCTAUS96t20898 d = Bore of differential producer (length) p = Fluid density (mass/unit ~olume) h = Differential pressure (force/unit area) Of the terms in this expression, only the units conversion factor, which is a constant, is simple to calculate. The other terms are expressed by equations that range from relatively simple to very complex. Some of the expressions contain many terms and require the raising of numbers to non-integer powers.
This is a computationally intensive operation.
There are a number of types of meters which can be used to measure flow. Head meters are the most common type of meter used to measure fluid flow rates.
They measure fluid flow indirectly by creating and measuring a differential pressure by means of an obstruction to the fluid flow. Using well-established conversion coefficients which depend on the type of head meter used and the diameter of the pipe, a measurement of the differential pressure may be translated into a mass or volume rate.
One technique for measuring a differential pressure for determining flow is through an averaging pitot tube type primary element. In general, an averaging pitot tube type primary element f,or indicating flow consists of two hollow tubes that sense the pressure at different places within the pipe. These tubes can be mounted separately in the pipe or installed together in one casing as a single device. This design includes a forward facing tube which measures total pressure (PTOT) . A second tube measures a down stream pressure. The differential pressure between the two tubes is proportional to the square of the flow as given in Equation 2.
W O 97/25595 PCT~US96n08g~
Q NKD2Y~ E~uation 2 where: N = Units conversion factor K = flow coefficient of the averaging pitot (~;m~ncionless) n = Pipe diameter (inches) Yl = Gas ~p~n~ion factor (~mpn~ionle p z Gas density (lbm/ft3) h = Differential pre~sure (inches H2) Accurate calculation o~ ~ow based upon pressure measurement requires accurate measurement o~
density (p) and the gas expansion factor (Yl) for use in Equation 1. These are calculated with exact equations, look up tables, polynomial approximations or other curve fitting techniques. Accurate determination of density (p) and the gas expansion ~actor (Yl~ requires an accurate value for the static pressure (PSTAT) for use in the above techniques. ~owever, the averaging pitot tube type primary element does not sense static pressure.
Neither the upstream or downstream facing tube provide~
an accurate indications of static pressure. In typical prior art transmitters, density (p) and the gas expansion factor (Yl) are calculated using a separate static pressure (PSTAT) measurement. For accuracy, this is spaced apart from the averaging pitot tube. This is inconvenient, requires an additional sensor, and requires and an additional entry into the process piping.
The additional sen~or to sense static pressure (PSTAT) in the prior art is cumbersome, inconvenient, expensive and provides an additional source of errors.
SI~M~RY OF THE INrVENTION
The present invention provides a transmitter for measuring mass flow rate ~Q) using an averaging W O 97/2S595 PCTrUS~6/20898 pitot tube type primary element. The invention does not re~uire a separate static pressure measurement. One aspect of the invention includes a total pressure sensor senses total pressure (P~) of a proce~s fluid from one pitot tube. A second pressure sensor measures a differential pressure between the tubes of the primary element. Circuitry in the transmitter calculates static pressure ( PSTAT) based upon the total pressure. The calculated static pressure (PSTAT) is used to calculate fluid density (p) and the gas expansion factor (Yl).
Flow (Q) is calculated based upon the pressure measurements, the fluid density (p) and the gas expansion factor (Yl).
BRIEF ~E~CRIPTION OF THE DRAWINGS
15Figure lA shows a transmitter in accordance with the present invention coupled to a proces~ pipe.
Figure lB is a top cross sectional view showing an averaying pitot tube type primary element ~or use with the present invention.
20Figure lC shows the averaging pitot tube type primary element of Figure lC inserted in a process pipe.
Figure 2 is a graph showing a comparison of gas density at maximum flow calculated using total pressure and calculated using static pressure versus differential pressure.
Figure 3 is a graph showing the difference between total pressure and static pressure versus differential pressure ~or carbon dioxide gas in an 8 inch pipe.
30Figure 4 is a graph showing error in corrected static pressure calculated in accordance with the present invention versus differential pressure for carbon dioxide gas in an 8 inch pipe.
Figure 5 is a simplified block diagram showing a transmitter for determining flow rate (Q) in accordance with the present invention.
D~TAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Figure lA is a view of a process control system 10 including a transmitter 10 in accordance with the present invention coupled to proce~s piping 12.
Process piping 14 carries process fluid having a velocity (V) and a flow rate (Q). Pipe 12 conducts flow of a fluid, either a gas or a liquid, in the direction indicated by arrow 16.
The present invention does not require a separate measurement of static pressure (PSI'AT) and provides an accurate estimation of the PSTAT based upon 1~ the total pressure (P~), which is sensed by the forward facing tube in an averaging pitot tube type primary element, and the differential pressure (h) measured between the two tubes. The estimated of calculated static pressure is used in calculations for determ; n; ng fluid density (p) and the gas expansion factor (Yl).
The techni~ue for estimating static pressure requires less computational time and power than using typical prior art formulas.
Transmitter 10 includes transmitter electronics module 18 and sensor module 22. Transmitter electronics module 18 also preferably includes a boss 20 for accepting an input from a resistive temperature device (RTD), preferably a 100 ohm RTD which is typically inserted directly into the pipe or into a thermowell which is inserted into the pipe to measure the process fluid temperature. The wires from the RTD
are connected to one side of a terminal block in a temperature sensor housing 24. The other side of the W O 97/25595 PCT~US96/20898 terminal block is connected to wires which run through tube 26 and are coupled to boss 20.
Sensor module 22 includes a differential pressure sensor for measuring differential pressure (h) and a pressure sensor for measuring total pressure (PTOT)- The two sensors provide pressure signals which are digitized and provided to a microprocessor. Module 22 connects to primary element 14 through manifold 21 supported by mount 23. The compensated, linearized and digitized signals are provided to the electronics module 18. The electronics module 18 in transmitter 10 provides an output signal indicative of process conditions such as flow rate (Q) o~ the process ~luid flowing through pipe 12 to a remote location, by a 4-20 mA two-wire loop preferably formed using twisted pair conductors, through flexible conduit 28. Further, in accordance with the present invention, transmitter 10 also provides an output signal indicative of flow rate.
Transmitter 12 is coupled to primary element 14.
Primary element 14 may comprise, for example, a pitot tube such as that shown in U.S. Patent No. 4,154,100 to Harbaugh et al. issued May 15, 1979, entitled Method And Apparatus For Stabilizing The Flow Coefficient For Pitot-Type Flowmeters With A Downstream-Facing Port.
With other types of primary elements 14 such as orifice plates, nozzles or venturis, the pressure sensed by transmitter 10 is the static pressure (PSTAT) of the process fluid, for use in calculating the gas density (p) and the gas expansion factor (Y1). These values are used in calculating the flow rate. In the invention, transmitter 10 is used with an averaging pitot tube type primary element such as that shown in U.S. Patent No. 4,154,100, and the pressure measured on the upstream side of the pitot tube is an average value -.
W097/2559~ PCT~S96/20898 of the total, sometimes called stagnation, pressure (PTOT) A second tube faces at an angle to the direction of flow such that a differential pressure (h) is developed between the tubes. The total pressure ~PTOT) is higher than the static pressure ( PSTAT), such that using (PTOT) to calculate the gas density and gas expansion factor will result in errors in the flow rate.
Figures lB and lC show a more detailed view of averaging pitot tube type p~imary element 14 which penetrates into pipe 12. Element 14 includes an elongated body 30A carrying a ~orward facing pitot tube 30B and a second, downstream facing pitot tube 30C.
Tubes 30B and 30C include a plurality of openings 32 and 34, respectively, distributed along the length of the tubes. The multiple openings ensure that an average pressure is measured across the entire flow 16. Tubes 30B and 30C connect to sensor body 22 of transmitter 10 through piping 21A and 21B and manifold 21.
To illustrate the error in flow calculations when using PTOT as an estimate Of PSTAT~ it is instructive to evaluate some examples. The following procedure is used.
1. Assume a pipe size, fluid, pressure and temperature range. The pressure assumed in this step is the static pressure, PSTAT-2. Based on the operating ranges, calculate PMIN~ PMID' P~X~ and TMIN~ TMID~ TMAX to evaluate the performance over the entire range of pressure and temperature.
3. At the nine combinations of P and T from step 2, calculate the flow rates through 3s a reference orifice flow meter at differential pressure ranging from 2.5 to 250 inches H2O.
W O 97~5595 PCT~US96/20898 4. Calculate the exact total pressure PTOT
from PSTAT using the Equation:
P~T PSTA~ 2 ~ 4 ( 2 )( APS~AT)( gc) Equation 3 where: PTOT = Total Pressure (psia) PSTAT = Static Pressure (psia) Q = Mass flow rate (lbm/sec) A = Area of pipe (in2) R~ = Specific gas constant (~/Mol Wt) T = Absolute temperature (~R) gc = gravitational proportionality constant ~ = ratio of specific heats (isentropic exponent) Equation 3 relates PTOT and PSTAT In addition, the temperature used in the expression is the total temperature. For the purposes of thi~ analysis the temperature measured by an RTD will be.assumed to represent the total temperature. For details see "Generalized Flow Across and Abrupt Enlargement"
(Benedict, Wyler, Dudek and Gleed, Transactions of ASME, Journal of Power Engineering, July 1976, 327-334). The total pressure (PTO~) calculated using this relationship represents the upstream pressure which would be otherwise measured by the transmitter 10 using tube 30B.
The procedure continues: .
5. Compare the density calculations using the values o:E static pressure PSTAT and calculated values of total pressure, PTO~' 6. Calculate the differential pressure (h) drop across an averaging sensor using Equation 2.
The effect on flow measurement error of using the total pressure (P~) rather than the static pressure -W O 97/2559S PCTrUS96/20898 (PSTAT) i8 illustrated by evaluating the differences that result when the two pressures are used to calculate the density of gases. This is shown in Figure 2. The density calculated using the total pressure (PTC~T) is S higher than the density calculated using the static pressure ~PSTAT)' As shown in Figure 3~ di~ference increases as the flow rate increases and as the static pressure decreases. Figure 2 shows a comparison of the maximum error in gas density as a function of static pressure ~or the three gases used in this analysis. The data was calculated ~or flow in an 8 inch pipe.
An inspection of the equations 1 and 2 does not readily reveal the relationship between the total pressure (PTOT)I the static pressure (PSTAT) and the di~ferential pressure (h). However, if the difference between the total pressure and the static pressure is plotted against differential pressure it is nearly linear ~see Figure 3). It is also ~airly insensitive to the static press~re and temperature.
The total pressure (PTOT) can be corrected to approximate the static pressure (PSTAq~) by exploiting this nearly linear relationship. Since the total pressure and static pressure converge to the same value at zero flow rate, the relationship between the total pressure and the static pressure can be expressed as:
PTOT PSTAT ~lh Equation 4 or PSTAT PTOT Clh Equation 5 where C1 is the average slope over the operating range o~ pressure and temperature. Figure 4 shows that the estimation technique of Equation 5 is very accurate in W O 97n5595 PCT~US96/20898 estimating static pressure (PSTAT)~ even at large differential pressures (h). In one embodiment, accuracy of the PSTAI' calculation could }:)e increased by using a polynomial of higher degree in h.
Figure 5 is a simplified block diagram showing transmitter 10 for implementing the present invention.
Transmitter 10 includeA microprocessor 40 coupled to analog to digital converter 42. Analog to digital converter 42 connects to pressure sensors 44 and 46 for sensing a pressure (PTOT) from tube 30B and a differential pressure (h) from tube 30C, respectlvely.
Sensors 44 and 46 coupled to primary element 14 shown in Figure lA. Analog to digital converter 42 also receives a temperature input from temperature sensor 24.
Microprocessor 40 operates in accordance with instructions stored in memory 50 at a clock rate determined by clock 52. Memory 50 also stores information for microprocessor 40. Input/output circuitry 54 connects to process control loop 28A
through terminal connections 56. Loop 28A carries current I from a remote source of power, which is used by input/output circuitry 54 to generate power for transmitter 10. In one embodiment, transmitter 10 is wholly (or exclusively) powered by loop current I.
Information is transmitted over loop 28A by input/output circuitry 54 by controlling the value of current I of control loop 28A. Additionally, input/output circuitry 54 may digitally modulate information onto loop 28A.
Transmitter 12 is also capable of receiving instructions over loop 28A. Microprocessor 40 uses the e~uations discussed above and accurately calculates flow rate (Q) using the total pressure (P~OT) to determine ~luid density (p~.
W O 97/25595 PCT~US96/20898 The present invention provides an estimated value of static pressure (PSTAT) based upon the pressure (PTOT) and the differential pre~3sure (h~ from an averaging pitot tube type primary element. This eliminates the extra sensor in the prior art used to measure static pressure and the extra intrusion into the flow tube.
Although the present invention has been described with reference to preferred embodiments, workers skilled in the art will recognize that changes may be made in form and detail without departing from the spirit and scope of the invention. For example, additional analog-to-digital convertors or microprocessors may also be used to optimize the system.
~urther, any type of averaging pitot tube primary element may be used. It should also be understood, that the step of calculating static pressure (PSTAT) may be implemented directly in other equations such as those used to calculate density (p), the gas expansion factor (Y1) or the flow rate (Q).
a total pressure sensor for sensing total pressure (PTOT) of the process fluid using the generally forward facing tube;
a differential pressure sensor for sensing a differential pressure (h) in the process fluid between the generally forward facing tube and the second tube;
circuitry which calculates flow rate (Q) based upon the total pressure (PTOT), the differential pressure (h), fluid density (p), and the gas expansion factor (Y1) wherein fluid density (p) and the gas expansion factor (Y1) are calculated as a function of the total pressure (PTOT); and I/O circuitry for coupling to a process control loop and transmitting the calculated flow rate (Q) on the process control loop.
PTOT - PSTAT C1h where: C1 is a constant.
sensing a total pressure (PTOT) generated by an averaging pitot tube type primary element;
sensing a differential pressure (h) generated by the averaging pitot tube type element; and calculating flow rate (Q) based upon static pressure (PSTAT), total pressure (PTOT) and differential pressure (h), wherein static pressure (PSTAT) is determined based upon total pressure (PTOT) and differential pressure (h).
calculating fluid density (p) based upon the calculated static pressure (PSTAT), the fluid density (p) for use in calculating flow rate (Q).
calculating gas expansion factor (Y1) based upon the calculated static pressure (PSTAT), the gas expansion factor (Y1) for use in calculating flow rate (Q).
PTOT - PSTAT = C1h where: C1 is a constant.
transmitting the flow rate (Q) over a process control loop.
measuring temperature of the process fluid; and including the temperature of the process fluid in the step of calculating flow rate (Q).
Priority Applications (2)
|Application Number||Priority Date||Filing Date||Title|
|US08582905 US5817950A (en)||1996-01-04||1996-01-04||Flow measurement compensation technique for use with an averaging pitot tube type primary element|
|Publication Number||Publication Date|
|CA2239497A1 true true CA2239497A1 (en)||1997-07-17|
Family Applications (1)
|Application Number||Title||Priority Date||Filing Date|
|CA 2239497 Abandoned CA2239497A1 (en)||1996-01-04||1996-12-31||Flowmeter with pitot tube with average pressure|
Country Status (7)
|US (1)||US5817950A (en)|
|JP (1)||JP4020433B2 (en)|
|CN (1)||CN1105292C (en)|
|CA (1)||CA2239497A1 (en)|
|DE (2)||DE69629211D1 (en)|
|EP (1)||EP0871848B1 (en)|
|WO (1)||WO1997025595A1 (en)|
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|US5365795A (en) *||1993-05-20||1994-11-22||Brower Jr William B||Improved method for determining flow rates in venturis, orifices and flow nozzles involving total pressure and static pressure measurements|
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