Flow measurement compensation technique for use with an averaging pitot tube type primary element

A transmitter in a process control system for measuring flow rate measures total pressure (P.sub.TOT) and differential pressure (h) of process fluid flowing through a process pipe. The static pressure (P.sub.STAT) is determined based upon the total pressure (P.sub.TOT). The calculated static pressure is used to determine the fluid density (.rho.) and the gas expansion factor (Y.sub.1) of the process fluid flowing in the pipe. This information is used to calculate flow rate (Q) of the process fluid.

BACKGROUND OF THE INVENTION 
The 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: 
##EQU1## 
where Q=Mass flow rate (mass/unit time) 
N=Units conversion factor (units vary) 
C.sub.d =Discharge coefficient (dimensionless) 
E=Velocity of approach factor (dimensionless) 
Y.sub.1 =Gas expansion factor (dimensionless) 
d=Bore of differential producer (length) 
.rho.=Fluid density (mass/unit volume) 
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 for 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. An example of an averaging 
pitot tube is shown in U.S. Pat. No. 4,154,100, entitled METHOD AND 
APATUS FOR STABILIZING THE FLOW COEFFICIENT FOR PITOT-TYPE FLOWMETERS 
WITH A DOWNSTREAM-FACING PORT. This design includes a forward facing tube 
which measures total pressure (P.sub.TOT) . 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. 
##EQU2## 
where: N=Units conversion factor 
K=flow coefficient of the averaging pitot (dimensionless) 
D=Pipe diameter (inches) 
Y.sub.1 =Gas expansion factor (dimensionless) 
.rho.=Gas density (lb.sub.m /ft.sup.3) 
h=Differential pressure (inches H.sub.2) 
Accurate calculation of flow based upon pressure measurement requires 
accurate measurement of density (.rho.) and the gas expansion factor 
(Y.sub.1) 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 (.rho.) and the gas 
expansion factor (Y.sub.1) requires an accurate value for the static 
pressure (P.sub.STAT) for use in the above techniques. However, the 
averaging pitot tube type primary element does not sense static pressure. 
Neither the upstream or downstream facing tube provides an accurate 
indications of static pressure. In typical prior art transmitters, density 
(.rho.) and the gas expansion factor (Y.sub.1) are calculated using a 
separate static pressure (P.sub.STAT) measurement. For accuracy, this is 
spaced apart from the averaging pitot tube. This is inconvenient, requires 
an additional sensor, and requires an additional entry into the process 
piping. 
The additional sensor to sense static pressure (P.sub.STAT) in the prior 
art is cumbersome, inconvenient, expensive and provides an additional 
source of errors. 
SUMMARY OF THE INVENTION 
The present invention provides a transmitter for measuring mass flow rate 
(Q) using an averaging pitot tube type primary element. The invention does 
not require a separate static pressure measurement. A total pressure 
sensor senses total pressure (P.sub.TOT) of a process 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 (P.sub.STAT) based upon the total pressure. The calculated 
static pressure (P.sub.STAT) is used to calculate fluid density (.rho.) 
and the gas expansion factor (Y.sub.1). Flow (Q) is calculated based upon 
the pressure measurements, the fluid density (.rho.) and the gas expansion 
factor (Y.sub.1).

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
FIG. 1A is a view of a process control system including a transmitter 10 in 
accordance with the present invention coupled to process piping 12. 
Process piping 12 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 (P.sub.STAT) and provides an accurate estimation of the 
P.sub.STAT based upon the total pressure (P.sub.TOT), 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 static pressure is used in calculations for determining fluid 
density (.rho.) and the gas expansion factor (Y.sub.1). The technique 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 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 (P.sub.TOT). 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) of the process 
fluid 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 10 
is coupled to primary element 14. Primary element 14 may comprise, for 
example, a pitot tube such as that shown in U.S. Pat. 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 
(P.sub.STAT) of the process fluid, for use in calculating the gas density 
(.rho.) and the gas expansion factor (Y.sub.1) 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. 
Pat. No. 4,154,100, and the pressure measured on the upstream side of the 
pitot tube is an average value of the total, sometimes called stagnation, 
pressure (P.sub.TOT) 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 (P.sub.TOT) is higher than the static pressure 
(P.sub.STAT), such that using (P.sub.TOT) to calculate the gas density and 
gas expansion factor will result in errors in the flow rate. 
FIGS. 1B and 1C show a more detailed view of averaging pitot tube type 
primary element 14 which penetrates into pipe 12. Element 14 includes an 
elongated body 30A carrying a forward 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 P.sub.TOT as an 
estimate of P.sub.STAT, 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, P.sub.STAT. 
2. Based on the operating ranges, calculate P.sub.MIN, P.sub.MID, 
P.sub.MAX, and T.sub.MIN, T.sub.MID, T.sub.MAX 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 a reference orifice flow meter at differential pressure 
ranging from 2.5 to 250 inches H.sub.2 O. 
4. Calculate the exact total pressure P.sub.TOT from P.sub.STAT using the 
Equation: 
##EQU3## 
where: P.sub.TOT =Total Pressure (psia) 
P.sub.STAT =Static Pressure (psia) 
Q=Mass flow rate (lb.sub.m /sec) 
A=Area of pipe (in.sup.2) 
R.sub.g =Specific gas constant (R.sub.u,/Mol Wt) 
T=Absolute temperature (.degree.R) 
g.sub.c =gravitational proportionality constant 
.gamma.=ratio of specific heats (isentropic exponent) 
Equation 3 relates P.sub.TOT and P.sub.STAT. In addition, the temperature 
used in the expression is the total temperature. For the purposes of this 
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 
(P.sub.TOT) 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 of static pressure 
P.sub.STAT and calculated values of total pressure, P.sub.TOT. 
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.sub.TOT) rather than the static pressure (P.sub.STAT) is illustrated by 
evaluating the differences that result when the two pressures are used to 
calculate the density of gases. This is shown in FIG. 2. The density 
calculated using the total pressure (P.sub.TOT) is higher than the density 
calculated using the static pressure (P.sub.STAT) . As shown in FIG. 3, 
the difference increases as the flow rate increases and as the static 
pressure decreases. FIG. 2 shows a comparison of the maximum error in gas 
density as a function of static pressure for the three gases used in this 
analysis. The data was calculated for flow in an 8 inch pipe. 
An inspection of the equations 1 and 2 does not readily reveal the 
relationship between the total pressure (P.sub.TOT), the static pressure 
(P.sub.STAT) and the differential pressure (h). However, if the difference 
between the total pressure and the static pressure is plotted against 
differential pressure it is nearly linear (see FIG. 3). It is also fairly 
insensitive to the static pressure and temperature. 
The total pressure (P.sub.TOT) can be corrected to approximate the static 
pressure (P.sub.STAT) 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: 
EQU P.sub.TOT -P.sub.STAT -C.sub.1 h Equation 4 
or 
EQU P.sub.STAT =P.sub.TOT -C.sub.1 h Equation 5 
where C.sub.1 is the average slope over the operating range of pressure and 
temperature. FIG. 4 shows that the estimation technique of Equation 5 is 
very accurate in estimating static pressure (P.sub.STAT), even at large 
differential pressures (h) . In one embodiment, accuracy of the P.sub.STAT 
calculation could be increased by using a polynomial of higher degree in 
h. 
FIG. 5 is a simplified block diagram showing transmitter 10 for 
implementing the present invention. Transmitter 10 includes 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 
(P.sub.TOT) from tube 30B and a differential pressure (h) from tube 30C, 
respectively. Sensors 44 and 46 coupled to primary element 14 shown in 
FIG. 1A. 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 10 is also 
capable of receiving instructions over loop 28A. Microprocessor 40 uses 
the equations discussed above and accurately calculates flow rate (Q) 
using the total pressure (P.sub.TOT) to determine fluid density (.rho.). 
The present invention provides an estimated value of static pressure 
(P.sub.STAT) based upon the pressure (P.sub.TOT) and the differential 
pressure (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. 
Further, any type of averaging pitot tube primary element may be used. It 
should also be understood, that the step of calculating static pressure 
(P.sub.STAT) may be implemented directly in other equations such as those 
used to calculate density (.rho.), the gas expansion factor (Y.sub.1) or 
the flow rate (Q).