Flowmeter fluid composition correction

Abstract: In a method for correcting the flow measurement of a gaseous fluid of interest for changes in the composition of that fluid in a flowmeter 10 of the microanemometer class, an uncorrected flow value signal 21 for the fluid of interest in relation to a microanemometer sensor output is corrected by applying a correction factor to the flow value signal based on certain unique physical parameters of the fluid of interest which nominally include thermal conductivity, k, specific heat, c p , and density, q.

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to fluid flow measurement and, more particularly, addresses overcoming inaccuracies in flow measurement. The invention eliminates errors in mass and volumetric flow rates measured for gaseous fluids with respect to compositional changes in the fluid of interest. 2. Related Art Hot film microanemometer packages for general use are known for both uni- and bi-directional flow applications. An example of such a device is illustrated and described in U.S. Patent 4,501,144 to Higashi et al. The microanemometers or "microbridges" themselves are quite inexpensive to produce. As will be described in greater detail below, such microanemometers are capable of quite accurate flow sensing when directly exposed to a stream of fluid flowing past, especially if such flow is laminar. In this manner such a sensor can be used to directly measure the dynamic flow characteristics of the fluid. Whiles such a sensing system can be used to approximately measure mass flow, a great deal of error has been experienced with respect to changes in composition of the measured fluid in prior devices using the system. Thus, a need has existed for a mass or volumetric flowmeter which is less sensitive to changes in the composition of the measured fluid. In DE-A-1 232 358, a volume measurement is corrected by various physical parameters e.g. specific gravity. There is no measurement of specific heat or thermal conductivity. US-A-1 769 358 refers to correction of flow rate for specific heat (in its claim 6), but there is no reference to thermal conductivity. EP-A-0 291 953 refers to specific heat ratio in the calculation of intake air amount. SUMMARY OF THE INVENTION In accordance with the present invention, it has been discovered that certain relationships exist between 1) the nulled flow, i.e. the flow signal corrected by subtracting the value corresponding to the signal obtained at zero flow, and 2) fluid properties including specific heat, cp, thermal conductivity, k, and density, q. In addition, certain similar relationships exist between (1) the nulled sensor output, i.e., the voltaic sensor signal or other related electrical measurement nulled by subtracting the value obtained at zero flow, and (2) c p , k, and q. The present invention provides apparatus for compensating the mass or volume flow measurement of a gaseous fluid of interest for changes in the composition of that fluid in a flowmeter (10) having a first dynamic microbridge exposed to the flow and producing a flow-related output signal, the apparatus comprising means to obtain an uncorrected nulled microbridge sensor output (S o ) for the fluid of interest; means to obtain an uncorrected nulled mass flow value (M o ) or volumetric flow value (V o ) for the fluid of interest in relation to the microbridge sensor output; means to obtain the specific heat (c p ) thermal conductivity (k) and density (q) of the gaseous fluid; and means to apply a correction factor normalized with reference to a particular gas to the flowrate signal to obtain the corrected mass flow value (M o *) or corrected volumetric flow value (V o *) and sensor output S o * according to a relationship selected from: M o */M o = (k/k o ) X 1 (c p /c po ) X 2 or M o */M o = (k/k o ) X 1 (c p /c po ) X 2 (q/q o ) X 3 or V o */V o = (k/k o ) Z 1 (c p /c po ) Z 2 or V o */V o = (k/k o ) Z 1 (c p /c po ) Z 2 (q/q o ) Z 3 and S o */S o = 1 or S o */S o = (k/k o ) Y 1 (c p /c po ) Y 2 or S o */S o = (k/k o ) Y 1 (c p /c po ) Y 2 (q/q o ) Y 3 Where: M* = corrected mass flow S* = corrected output (sensor) V* = corrected volumetric flow k/k o = normalized thermal conductivity c p /C po = normalized specific heat q/q o = normalized density o = refers to the base or reference gas X₁, X₂, X₃, or Y₁, Y₂, Y₃, or Z₁, Z₂, and Z₃ are exponents. Thus, based on representative modeling, what appears to be gas-independent correction factors have been found. These factors are equivalent to parallel shifts of deviating log signal vs. log flow curves, until overlap with a chosen reference curve is achieved. These shifts, i.e., correction factors, are then expressed in terms of power function of normalized gas properties. The correction factors are individual with respect to gas compensation and all sensor output vs. flow (mass or volumetric) curves obtained for different individual gas species are equal except for the individual constant factors. In an illustrative embodiment the present invention makes use of a second microbridge sensor not directly exposed to the flowing fluid, but in more remote communication with that fluid that can be used to measure certain parameters related to the fluid which require a more static environment. Such a sensor is used for the direct measurement of thermal conductivity, k, and specific heat,c p , in accordance with a known technique which allows the accurate determination of both properties in a sample of interest using a single sensing system. In addition these properties allow the determination of the density, or q. The present invention also provides a method for compensating the mass or volume flow measurement of a gaseous fluid of interest for changes in the composition of that fluid in a flowmeter (10) having a first dynamic microbridge exposed to the flow and producing a flow-related output signal, the method comprising obtaining an uncorrected nulled microbridge sensor output (S o ) for the fluid of interest; obtaining an uncorrected nulled mass flow value (M o ) or volumetric flow value (V o ) for the fluid of interest in relation to the microbridge sensor output; obtaining the specific heat (c p ) thermal conductivity (k) and density (q) of said gaseous fluid; and applying a correction factor normalized with reference to a particular gas to the flowrate signal to obtain the corrected mass flow value (M o *) or corrected volumetric flow value (V o *) and sensor output S o * according to a relationship selected from: M o */M o = (k/k o ) X 1 (c p /c po ) X 2 or M o */M o = (k/k o ) X 1 (c p /c po ) X 2 (q/q o ) X 3 or V o */V o = (k/k o ) Z 1 (c p /c po ) Z 2 or V o */V o = (k/k o ) Z 1 (c p /c po ) Z 2 (q/q o ) Z 3 and S o */S o = 1 or S o */S o = (k/k o ) Y 1 (c p /c po ) Y 2 or S o */S o = (k/k o ) Y 1 (c p /c po ) Y 2 (q/q o ) Y 3 Where: M* = corrected mass flow S* = corrected output (sensor) V* = corrected volumetric flow k/k o = normalized thermal conductivity c p /C po = normalized specific heat o = refers to the base or reference gas X₁, X₂, X₃, or Y₁, Y₂, Y₃, or Z₁, Z₂, and Z₃ are exponents. BRIEF DESCRIPTION OF THE DRAWINGS In the drawings: Figure 1 includes a schematic diagram showing a sectional view of a flowmeter and a schematic of associated I/O devices for the flowmeter of the invention; Figure 2 is a graphic representation depicting output vs. mass flow measurement in linear coordinates, with its associated uncorrected error; Figure 3 shows the same data as Figure 2 plotted as sensor resistance vs. nulled mass flow in a log-log plot in order to make the differences in data points at low flow more visible; Figure 4 shows curves of nulled mass flow vs. nulled output for several gases illustrating the basic similarity of calibration mass flow curves for diverse species; Figure 4a shows curves of nulled volume vs. nulled output for several gases also illustrating the basic similarity of the volumetric flow curves for diverse species. Figure 5 shows the correlation of experimental mass flow outputs for CO₂ and air based on CH₄ applying correction factors to M o and S o based on k and c p to Figure 4; Figure 6 shows the correlation of experimental volumetric flow measurements for various gases applying correction factors to S o and V o based on k and c p to the species of Figure 4a; Figure 7 depicts a corrected version of Figures 2 and 3 for experimental nulled microbridge sensor output vs. mass flow measurements for various gases based on supplying a correction factor based on k, c p , and q, to M o only; and Figure 8 depicts another solution for Figures 2 and 3 for experimental nulled microbridge sensor output vs. mass flow measurements for various gases based on applying a correction based on k and c p only and only to M o . DETAILED DESCRIPTION Figure 1 depicts one embodiment of a flowmeter utilizing the concept of the present invention. The system is depicted as an integral part of a length of pipe, as a pipe, as a gas pipe, or other conduit or meter body member 10 which can easily be adapted to fit into almost any existing piping scheme as between a pair of spaced unions, couplings or the like. The basic system includes a pair of filter members 11 and 12 flanking a capillary system which includes means for reducing the conduit diameter at 13 and 14 in conjunction with accessing a split bundle containing parts 15 and 16 of capillary tubes. The reducing sections 13 and 14 create a plenum effect to reduce pressure losses in conjunction with entry and exit of the fluid to the capillary bundle. This, in turn, reduces overall system pressure drop and velocity head effect. A microbridge or microanemometer sensor package for sensing flow through the system is depicted generally. It contains individual microbridge sensors for dynamic and static fluid sensing respectively. Electrical connections pins, connect the microanemometer to a source of power for the heater or heaters shown by block 20 and external signal receiving means 21 and accompanying signal and data processing means 22 to interpret the output. The desired output may take any suitable form or display and is represented by block 23. The remote or static microbridge or microanemometer 18a communicates with the flowing fluid of interest via an opening in the meter member 24 in the sensor package 17 such that a representative composition is observed in what is basically a static environment with respect to flow. Because compositional changes in the flowing fluid of interest occur relatively slowly in comparison to flow velocities, the response of the remote microbridge sensor remains timely. Generally, with respect to the thin film microbridge or anemometer sensors such as those depicted by reference numerals 18 and 18a, recently very small and very accurate microbridge semiconductor chip sensors have been described in which etched semiconductor microbridges are used as condition or flow sensors. Such sensors might include, for example, a pair of thin film sensors flanking a thin film heater. Semiconductor chip sensors of the class described are treated in a more detailed manner in one or more of patents such as 4,478,076, 4,478,077, 4,501,144, 4,555,939, 4,651,564 and 4,683,159 all of common assignee with the present invention. To the extent necessary additional details with respect to the microbridge sensors may be incorporated by reference from these cited documents. For the purposes of the present application, it should suffice to say that if the dynamic flow sensor 18, for example, comprises a pair of thin film sensors symmetrically flanking a thin film heater, for example, the sensor can be used to sense flow in either direction. That is, of course, provided that the chip assembly positions the sensor in the proper orientation so that the flow meets the microbridge at a right angle in the assembled meter. This further allows the flowmeter system of the present invention to be reversible with respect to the conduit system of the fluid of interest as it is then quite laterally symmetrical. The sensor 18, then, is directly exposed to the stream of fluid flowing past it in the conduit. This sensor is used to directly measure the dynamic flow characteristics of the fluid. The second microanemometer sensor 18a which may be mounted back-to-back with the sensor 18, as illustrated in Figure 1, enables other parameters of the fluid to be measured simultaneously with the dynamic flow. As stated above, while the sensor 18a is not directly exposed to the flowing fluid, it is in direct communication with that fluid and can be used to measure certain parameters related to the fluid which are facilitated by a more static environment. Such a sensor can be used for the direct measurement of thermal conductivity, k, and specific heat, c p , in accordance with a technique which allows the accurate determination of both properties and a sample of interest using a single sensing system. That technique contemplates generating an energy or temperature pulse in one or more heater elements disposed in and closely coupled to the fluid medium of interest. Characteristic values of k and c p of the fluid of interest then cause corresponding changes in the time variable temperature response of the heater to the pulse. Under relatively static sample flow conditions this, in turn, induces corresponding changes in the time variable response of or more temperature responsive sensors coupled to the heater principally via the fluid medium of interest. The thermal pulse of this source need be only of sufficient duration that the heater achieve a substantially steady-state temperature for a short time. This pulse produces both steady-state and transient conditions in the sensor. Thermal conductivity, k, and specific heat, c p , can be sensed within the same sensed thermal pulse by using a steady-state temperature plateau to determine k, which is then used with the rate of change temperature in the transient condition to determine c p . In addition, it has been found that once the values of the specific heat and thermal conductivity have been determined, these measurements can be used to determine the density or specific gravity, ρ, or q, of the fluid of interest as a function of c p , k, according to an empirical polynomial relationship. The availability of all the measurements characterizing the fluid which can be derived from the combination of the exposed and static microanemometer sensors to the flowmeter allows for or enables one to make the determination of the corrections in accordance with the present invention. Of course, the parameters as k, c p and q, of the gas can be determined by other means if such are desirable in other applications. Figure 2 shows the nulled sensor output plotted vs. nulled mass flow for six different gasses. Of course, the same mass flow of any fluid of interest should produce the same output voltage, i.e., all curves should coincide. The raw or uncorrected data shows considerable deviation among the various gases. Figure 3 represents the data of Figure 2 plotted as log-log functions. There the signal output is shown in terms of nulled sensor resistance rather than voltage output to expand the vertical axis. Figure 3, demonstrates the disparities of Figure 2 somewhat more dramatically, especially at the lower flow rates, i.e., <100 mg/min. In some cases discrepancies or errors of as much 100% or more occur at low flow rates for a given sensor output. The data of Figures 2 and 3 were obtained by operating the flow sensor heater at constant temperature or temperature rise above the ambient temperature. Figures 4 and 4a are noteworthy because it illustrates certain similarities which have been found to exist among the gases involved in the mass flow measurements. The curves, while not congruent, are strikingly similar in shape indicating some type of parallel shift especially when plotted on a log-log plot as in Figure 4. This view is not as evident in the linear-linear plot of Figure 4a. Complete congruency, of course, indicates consistent, error-free measurement. The similarity in shape of the nulled measurements indicates that a constant correction factor might be possible for each gas if the basis of or reasons for the variation in readings among the species were known. According to the invention, shift correction factors in the form of simple, constant factors for each gas have been found to equilibrate mass or volumetric flow measurements with sensor output. This has been accomplished by using factors derived from the individual gas properties like k, c p , and q. Additional factors may be used depending on the required accuracy of the corrected signal. It has been found that such correction factors can be based on evaluating the least squares solution to the following expressions: M*/M o = Ak x 1 c p x 2 S*/S o = Bk y 1 c p y 2 This approach was applied to correct the discrepancies of Figure 4 as shown in Table 1, et seq, as normalized with reference to CH₄. Where: V = volumetric V o nulled volumetric measurement Given the problem to find: A, B, X₁, ..., Y₁. ... so that M*/M o = Ak X 1 c p X 2 S o */S o = Bk Y 1 c p Y 2 For any gas: SOLUTION: A = 1/(k o X 1 c po X 2 ) FOR CH4 B = 1/(k o Y 1 c po Y 2 ) FOR CH4 X₁ = .6816 X₂ = 1.748 Y₁ = .7611 Y₂ = .01087 Where the subscript (o) refers to the base or reference gas. In this case the reference gas is methane. This solution for mass flow in which the sensor is supplied in a constant current mode is reproduced graphically in Figure 5. Also using CH₄ as the reference gas and operating the sensor in the constant current mode volumetric correlation for air, except for the natural gas data in Figure 4a. The same set of data as in Figures 4a and 5 are shown in Figure 6. This also shows good correlation. Given the number of parameters and the number of gases in this set of data, a critical scientist might question the general validity of the premise were it not for a great deal of other corroborating data. Consistency appears to verify the solution. Figure 7 depicts a corrected version of Figure 3 also using CH₄ as the reference gas. In this case the microbridge heater was operated in a constant temperature mode rather than at constant current input. In this correction it should be noted that S o was not corrected and an additional factor with respect to density, q/q o was also used. Figure 8 depicts another solution or corrected version of Figures 2 or 3 in which the sensor is also operated in a constant temperature mode and the sensor output is uncorrected. This solution differs from that of Figure 7 only in the elimination of the density factor, q/q o . It does show some discrepancy with respect to He which is understood of in terms of its very different k and c p properties. During operation, the above method would normally be implemented as outlined using one or more of the steps explained below, in order to convert a sensed signal, S o , to a correct mass flow M o * or volumetric flow V o *; it being further recognized that the required degree of accuracy and other considerations will occur to those applying these corrections and influence the choice of correction made on degree: 1) Sense signal, S, and convert it to its corrected version, S*, according to any of the following alternatives based on the particular gas or combination involved; S o */S o = 1 (with constant temperature heater operation) or S o */S o = (k/k o ) Y 1 (c p /c po ) Y 2 or S o */S o = (k/k o ) Y 1 (c p /c po ) Y 2 (q/q o ) Y 3 or S o */S o = (k/k o ) Y 1 (c p /c po ) X 2 (q/q o ) Y 3 2. Determine the uncorrected flow, M o , by using the standard calibration curve: M o = (S o *) or V o = (S o *) or M o or V o = a o + a₁f₁(S o *) + a₂f₂(S o *) Where M o (or V o , as the case may be) are intermediate undefined quantities that resembles mass or volumetric flow but which need further corrective processing in accordance with step 3 to represent actual flow, or by iterating: S* = b₀+ b₁g₁(M o ) + b₂g₂(M o ) + ... for example, a result may be S* = 0 + 4.8179 exp (-15.038/V .57 ) - 5.1324 exp (-44.204/V .6 ) where a₀, a₁ ...a n , b₀, b₁...b n are constants; f₀, f₁ ...f n and g₀, g₁...g n are functions. 3) Find the corrected flow M o * or V o * according to the alternate M o */M o = (k/k o ) X 1 (c p c po ) X 2 or M o */M o = (k/k o ) X 1 (c p c po ) X 2 (q/q o ) X 3 or M o */M o = (k/k o ) X 1 (C p C po ) X 2 (q/q o ) X 3 or V o */V o = (k/k o ) Z 1 (C p C po ) Z 2 where Z₁, Z₂ are exponents As for example in Figure 4a Z₁ = 0.771, Z₂ = 0.8547 Y₁ = 0.7611, Y₂ = 0.01087 with k o and c po referring to the reference for CH₄, which then converted to Figure 6. Utilisation of data from the composition correction technique enables the derivation of a measurement of the energy value for the gas flow. For example, having determined the composition of the gas flow during a measurement, and being aware of the calorific and other characteristics of the constituents of the mixture as determined, it is readily feasible to derive the energy value of the gas flow at that instant, and hence with appropriate summation or integration over time, measurement of the total energy content supplied can readily be achieved. Clearly, such a feature can be readily implemented into the microbridge by appropriate design and operation of the data processing means 22, and affords a substantial technical and highly marketable advance over existing microbridge fluid flowmeters and over fluid flowmeters utilising other technologies. Thus, the present invention embodies methods of determining the energy value of gas flows, particularly utilising composition correction techniques as described hereinbefore, and also embodies means to implement such methods. It thus has been shown that the present invention enables great strides to be made with respect to achieving an inexpensive, very accurate, system for measuring and monitoring mass flow, volumetric flow or energy content. This was accomplished by the recognition and solution of a problem long plaguing flow measurement. The application of know physical parameters of gases to compensate for compositional changes will enable widespread use of microanemometer flow sensors in situations heretofore closed to them.

Claims: Apparatus for compensating the mass or volume flow measurement of a gaseous fluid of interest for changes in the composition of that fluid in a flowmeter (10) having a first dynamic microbridge exposed to the flow and producing a flow-related output signal, comprising means to obtain an uncorrected nulled microbridge sensor output (S o ) for the fluid of interest; means to obtain an uncorrected nulled mass flow value (M o ) or volumetric flow value (V o ) for the fluid of interest in relation to the microbridge sensor output; means to obtain the specific heat (c p ) thermal conductivity (k) and density (q) of the gaseous fluid; and means to apply a correction factor normalized with reference to a particular gas to the flowrate signal to obtain the corrected mass flow value (M o *) or corrected volumetric flow value (V o *) and sensor output S o * according to a relationship selected from: M o */M o = (k/k o ) X 1 (c p /c po ) X 2 or M o */M o = (k/k o ) X 1 (c p /c po ) X 2 (q/q o ) X 3 or V o */V o = (k/k o ) Z 1 (c p /c po ) Z 2 or V o */V o = (k/k o ) Z 1 (c p /c po ) Z 2 (q/q o ) Z 3 and S o */S o = 1 or S o */S o = (k/k o ) Y 1 (c p /c po ) Y 2 or S o */S o = (k/k o ) Y 1 (c p /c po ) Y 2 (q/q o ) Y 3 Where: M* = corrected mass flow S* = corrected output (sensor) V* = corrected volumetric flow k/k o = normalized thermal conductivity c p /C po = normalized specific heat q/q o = normalized density o = refers to the base or reference gas X₁, X₂, X₃, or Y₁, Y₂, Y₃, or Z₁, Z₂, and Z₃ are exponents. Apparatus according to Claim 1 characterised in that the relationship is M o */M o = (k/k o ) X 1 (c p /c po ) X 2 and S o */S o = 1. Apparatus according to Claim 1 characterised in that the relationship is V o */V o = (k/k o ) Z 1 (c p /c po ) Z 2 and S o */S o = 1. Apparatus according to Claim 1, characterised in that the relationship is M o */M o = (k/k o ) X 1 (c p /c po ) X 2 (q/q o ) X 3 and S o */S o = 1. Apparatus according to Claim 1, characterised in the relationship is v o */v o = (k/k o ) Z 1 (c p /c po ) Z 2 (q/q o ) Z 3 and S o */S o = 1. Apparatus according to any preceding Claim, characterised by a second microbridge means in relatively static communication with the fluid of interest to determine k and c p . Apparatus according to any preceding Claim characterised by means to normalise the correction factors with respect to CH₄. Apparatus according to any preceding Claim characterised by means to obtain correction factors for a plurality of gases. Apparatus according to Claim 8 characterised by means to obtain correction factors for CH₄, CO₂, O₂, air, C₃H₈, Ar and He. Apparatus according to any preceding Claim, characterised by means to utilise the composition correction data to determine the energy value of the fluid flow. A method for compensating the mass or volume flow measurement of a gaseous fluid of interest for changes in the composition of that fluid in a flowmeter (10) having a first dynamic microbridge exposed to the flow and producing a flow-related output signal, comprising obtaining an uncorrected nulled microbridge sensor output (S o ) for the fluid of interest; obtaining an uncorrected nulled mass flow value (M o ) or volumetric flow value (V o ) for the fluid of interest in relation to the microbridge sensor output; obtaining the specific heat (c p ) thermal conductivity (k) and density (q) of the gaseous fluid; and applying a correction factor normalized with reference to a particular gas to the flowrate signal to obtain the corrected mass flow value (M o *) or corrected volumetric flow value (V o *) and sensor output S o * according to a relationship selected from: M o */M o = (k/k o ) X 1 (c p /c po ) X 2 or M o */M o = (k/k o ) X 1 (c p /c po ) X 2 (q/q o ) X 3 or V o */V o = (k/k o ) Z 1 (c p /c po ) Z 2 or V o */V o = (k/k o ) Z 1 (c p /c po ) Z 2 (q/q o ) Z 3 and S o */S o = 1 or S o */S o = (k/k o ) Y 1 (c p /c po ) Y 2 or S o */S o = (k/k o ) Y 1 (c p /c po ) Y 2 (q/q o ) Y 3 Where: M* = corrected mass flow S* = corrected output (sensor) V* = corrected volumetric flow k/k o = normalized thermal conductivity c p /C po = normalized specific heat o = refers to the base or reference gas X₁, X₂, X₃, or Y₁, Y₂, Y₃, or Z₁, Z₂, and Z₃ are exponents. A method according to Claim 11 characterised in that the relationship is M o */M o = (k/k o ) X 1 (c p /c po ) X 2 and S o */S o = 1. A method according to Claim 11, characterised in that the relationship is V o */V o = (k/k o ) Z 1 (c p /c po ) Z 2 and S o */S o = 1 A method according to Claim 11 characterised in that the relationship is M o */M o = (k/k o ) X 1 (c p /c po ) X 2 (q/q o ) X 3 and S o */S o = 1. A method according to Claim 11, characterised in that the relationship is v o */v o = (k/k o ) Z 1 (c p /c po ) Z 2 (q/q o ) Z 3 and S o */S o = 1. A method according to any of Claims 11 to 15 characterised in that K and c p are determined by a second microbridge means in relatively static communication with the fluid of interest. A method according to any of Claims 11 to 16 characterised by normalising the correction factors with respect to CH₄. A method according to any of Claims 11 to 17 characterised by obtaining correction factors for a plurality of gases. A method according to Claim 18 characterised by obtaining correction factors for CH₄, CO₂, O₂, air, C₃H₈, Ar and He. A method according to any of Claims 11 to 19 characterised by utilising the composition correction data to determine the energy value of the fluid flow.

Inventors: BONNE ULRICH, BONNE, ULRICH
Applicants: HONEYWELL INC, HONEYWELL INC.
Application year: 1989
Main classification: G01F15
IPC codes: G01F1, G01F15