CA1301332C - Method and apparatus for measuring and providing corrected gas flow - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE

A method and apparatus is disclosed for measur-ing flowing gas and at least one variable for calculating gas flow corrected to a base value of that variable.
Illustratively, the measured variables are temperature and pressure, and devices are employed for measuring the temperature Tf and pressure Pf of the gas flowing through a conduit, and means in the illustrative form of a flow meter for measuring the volume Vf of the gas flowing through the conduit. Calculating means in the illustrative form of a programmed microprocessor is employed to calculate the corrected gas volume to base conditions in accordance with an expression including the supercompressibility factor. The supercompressibility factor is calculated according to an equation involving only whole number exponentiation and a selected set of coefficients. The calculation means selects a particular set of these coefficients in accordance with indications of pressure and/or temperature.

Description

METHOD AND APPARATUS FOR MEASURING AND PROVIDING
CO~RECTED GAS FLOW
~b~
ield of the Invention:
This invention relates ~o systems and methods for measuring gas flow, flow temperature and flow pressure and for determining with a high degree of accuracy the supercompressibility factor, from which a value of gas volume at base conditions of tempexature and pressure may be calculated.
Descrlption o~ the Prior Art:
Gas is compressible, the volume of which changes as a unction of temperature and pressure in accordance with the well known ideal gas laws. Natural gas is widely used as a fuel and, typically, is ~ransmitted via pipe-lines from a source to an end user. Conditions of temper-ature and pressure may vary widely throughout such a gas distribution system. To distribute and sell gas that is exposed to ~arying conditions of temperature and pressure, calculations must be made to convert the measured flow or line volume ~f of gas, in terms of cubic feet at varying flow or line conditions of flow or line temparature Tf and pressure Pf, to a standard cubic feet volume Vb at spec-ified, previously agreed upon base temperature Tb and base pressure Pb.
The basic gas law relationship can be expressed as:
PV - NRTZ (1) where:

P is absolute pressure V is volume N is mols of gas R is the universal gas constant T is the absolute ~emperature Z is the compressibility factor.
When dealing with a simple gas, such as N2 or 2~ the ideal gas laws serve very well, and Z may not be needed.
~Iowever, when ~here are mixtures of gases and complex hydrocarbons, it has been found that Boyle's and Charles' laws are in error~ Fuel gases tend to be easier to compress, up to around 2000 psig, than these laws would suggest. Above this pressure, the trend is reversed. The exact values are functions of the pressure, ~emperature and the gas composition. The ideal gas law is extended to the real conditions by the use of the compressibility factor Z.
From equation (1), the following relationship between base and flowing conditions may be derived:
. .
Pf Pa Tb Vb ~ Vf pv ~2) Pb Tf , where:
Vb is base volume Vf is flowing volume Pf is flowing pressure, gage P~ is atmospheric pressure Pb is base pxessure, absolute Tb is base temper2ture, absolute Tf is flowing temperature, absolute Fpv is supercompressibility factor , .
, .

~3~33~

The diffic~lt part of calculating base volume in accor-dance with equation (2) is to determine the supercompressibility factor Fpv which is a function of the flowing temperature and pressure, as well as the specific gravity and the compositi.on of the gas being measured.
One way of determining the supercompressibility factor Fpv is to utilize the equations and tables as those set forth in the "Manual for the Determination of Supercompressibility Factors for Natural Gas", PAR Re-search Projects WX;l9, published by the American Gas Associaticn (AGA). The supercompressibility factor Fpv is complex to calculate, as will be seen below, since it is a function of five variables: pressure, temperature, speciic gravity of the gas and the composition of the gas, in terms of mol ~ of the constituent gases such as nitrogen and carbon dioxide. The AGA NX-l9 method for determining the supercompressibility factor Fpv is as ~ollows:
r D + n Fpv= ~ --F--Dirl~-- (3) -3.25 - 1 681 M (4) , where Mc is mol % of CO2 and Mn is mol ~ of N.
F = __ 226.29 _ (5) T (99.15 + 211.9 G - Kt).
, where G is specific gravity = tadj + 460 ~6) ' ' , .

~0IL3~

" . .

, where tadj = [(t + 460)FT] - 460 and t is gas temperature, E' Kp = Mc ~ 0.392 Mn (7) F = 156.47 P (160.8 - 7.22 G + Kp) (8 i ~ 14 - 7 , 1000 (9) , where Padj = P Fp and P is gas pressure, psig m = .0330378 (T) 2 _ 0.0221323(~) 3 + 0.016353 (~) 5 (10) n = 0.265827(.) 2 + 0.0457697(~ ) 4 -0.133185 (~) 1 B = 3 - mn2 9 m ~2 (12) b = 9 n - 2 m n 3 - _ E
54 m ~3 2 m ~ ~13) D = [b + ~+ B3] 1/3 (14) The value of E is calculated based upon one of a number o equations, the particular equation being select-ed ~for a particular range of adjusted pressure and adjusted temperature. For example, E2 is calculated according to the following equation for an adjusted pressure range of 0 to 1300 psia and an adjusted temperature rate of -40F. to +8 5 F:

E2 ~ 1. - .00075k )2 3[2. - e 20(1.09 , )] _ 1.317 (1.09 ~ 4 ( ~ (1.69 _ ~ 2) (15~
U.S. Patent 4,173,891 of Johnson, assigned to the assignee of this invention, discloses a gas flow measuring and calculating sys~em for measuring values of ~;~V1332 line pressure, temperature and gas flow and for providing corrected indications of gas flow at base conditions of temperature and pressure. The Johnson system employs calculation means in the form of a microprocessor utiliz-ing the ideal gas laws and calculates the super-compressibility factor Fpv in accordance with equations (3) to (15) as set out above. These calculations comprise a number of computing steps, each step using an in_tially approximated value of the supercompressibility factor or the previously-calculated value. The Johnson system calculates these supercompressibility factors exactly, but at the expense of employing a lengthy and time consuming program to execute.
U.S. Patent 4,390,956 of Cornforth et al.
discloses a system employing the following simplified expression for the supercompressiblity factor Fpv:

Fpv ~ 1 = (Pf/QTf) (16) , where Q = P~
(F ~ 1) Tf (17) ~y considering only values of the supercomprèssibility factor Fpv for a limited range of flow temperature Tf, a linear fit of Q may be made as a function of T~. In particular, two rits or linear equations are required as a function of Tf permitting Q to be expressed as fcllows:

Q = S + CTf (18) ~3t~:133~

,where C and S may be expressed as linear equations as a function of the flow pressure Tf. Cornforth et al. states that the use of their simplified equations (16) to (18), as expxessed above, produces calculations of the corrected volume with an accuracy to within plus or minus 0.1~.
Thus, the prior art is left on the horns of a dilemma having either to program the lengthy equations of the AGA
NX-19 set or to use less complex equations that fit or approximate the values of supercompressibility with an appreciable sacrifice in accuracy. As the cost of natural gas has risen, the commercial necessity of accurately measuring and calculating gas flow to a set of base con-ditions, becomes more important.
The prior art, as exemplified by U.S. Patent 4,056,717 of Cornforth et al. and U.S. Patent 4,093,871 of Plumb et al., have further recognized the problem of employing a gas flow measuring and correcting circuit at remote locations, where power lines are not readily available, thus normally requiring the use of batteries as the energization source. If batteries are used, the energized circuitry needs to be designed to minimize power r~quirements or, otherwise, frequent battery replacement may be necessary, which would be, at least, inconvenient where the measuring and correcting circuitry is employed at remote locations. The Plumb et al. patent '871 dis-closes a measuring and correction circuit, which includes a first, relatively high power consuming portion and a second, relatively low power consuming portion. To minimize battery drainage, the battery is selectively connected for limited periods of time to the first por-tion. The Plumb et al. circuit employs a reed switch coupled to a gas flow meter to open and close, thus producing a train of pulses dependent upon the uncorrected gas fIow. Each of these pulses not only indicates a unit volume of uncorrected fluid flow, but also serves to apply ~V~3~2 ~`
the battery for a limlted period of time to the first portionj while the battery is continuously connected to the second portion.
The use of batteries to energize such measuring and correcting circuits not only ralses problems of battery drainage, but also problems of achieving accurate measurement of temperature and pressure as a result of the varying voltage levels produced by batteries due to fluctuations of ambient conditions, namely temperature, and to extended use. To some degree, complex and expen-sive voltage regulating circuits could be employed to ensure the supply of a substantially constant voltage level to such measuring and correcting circuits; however, such accurate voltage regulators are expensive and do not of themselves compensate for voltage fluctuations as would be applied to the temperature and pressure measuring elements. Such pressure and temperature elements may be resistive in nature and, thus, produce fluctuations in voltage thereacross; thus, such resistive devices output signals that not only vary as a function of pressure and temperature, but also as a function of the voltage supply level.
SUMMARY OF THE INVENTION
It is therefore an object of this invention to provide a new and improved system for measuring and corrscti~g measurements of flow volume as a function of pressure and temperature of the flow gas.
It is a more particular object of this invention to achieve a calculation of the gas supercompressibility factor to an accuracy within 0.06%, over applicable temperature and pressure ranges, of the results obtained by the AGA NX-l9 method.`
It is a still further object of this invention to provide a new and improved system for measuring a ~3(:~L33~2 corrected gas flow employing a processor for executing a simplified, shortened program.
It is a further object of this invention to provide a new and improved measuring and correcting system employing a processor executing a simplified, shortened program avoiding calculations using fractional ex-ponentiation.
It is stiLl another object of this invention to provide a new and improved system for measuring and correcting gas flow that avoids the problems of the prior art associated with fluc~uating voltage levels as would otherwise affect the accuracy with which pressure and temperature are measured.
It is a still further object of this invention to provide a new and improved method of deriving measure-ments of variables such as temperature and pressure that avoids or negates the effects of varying voltage levels.
It is a further object of this invention to provide a new and improved system employing variable measuring elements, whose output signals are dependent upon voltage levels, in a circuit that compensates for varying levels of voLtage to provide accurate indications of the measured variables.
In accordance with these and other objects, this invention is related to a method and apparatus for measur-ing flowing gas and at least one variable for calculating gas flow corrected to a base value of that variable.
Illustratively, the measured variahles are temperature and pressure, and devices are employed for measuring the temperature Tf and Pf of the gas flowing through a con-duit, and means in the illustrative form of a flow meter for measuring the volume Vf of the gas flowing through the conduit. Calculating means in the illustrative form of a microprocessor is employed to calculate th~ corrected gas volume to base conditions in accordance with an expression .
.

L3~
_9_ ~, including the supercompressibility factor. The super-compressibility factor is calculated according to an equation lnvolving only whole number exponentiation and a selected set of coefficients. The calculation means selects a particular set of these coefficients in ac-cordance with lndications of pressure and/or temperature.
A second aspect of this invention involves a method of taking measurements of variables with element(s) whose impedance varies as a function of the measured variable, and of a voltage derived from a fluc~uating supply source, e.g. a battery. A calibration process is ùsed, whereby the variable measuring element is exposed to a first calibration temperature, and ~irst and second signals are derived from ~he variable measuring element and a reference element. The variable measuring element is also exposed to a second, higher calibration variable, and corresponding third and fourth signals are derived fr~m the variable measuring element and the reference element. First and second calibra~ion ratios are taken as the ratios of the first and second, and third and fourth signals. Subsequently, the variable measuring element is exposed tc a present, unknown variable, and corresponding fifth and sixth signals are similarly derived to provide a present ratio of the fifth to sixth signals. The present ratio is interpolated with respect to the ~irst and second calibration ratios to provide a manifestation or signal indicative of the rneasured variable, which is substan-tially free of any fluctuation of the level of voltage applied thereto.
In a still further aspect of this invention, t~ere is disclosed a system for minimizing current drain in a battery energized system, comprising a first volatile memory energized by the battery at a first, relatively low power consumption rate, for storing a set of calculation variables, and a second, non-volatile memory energizable . --~3~33Z

by the battery at a second relatively high power consumption rate, for storing a back-up set of the calibrat.ion variables. A control mechanism in the form of a programmed microprocessor reviews the set of calculation variables stored in the first, volatile memory and, if any portion of the set is not correctly retained, the non-volatile memory is energized and the back up set of calibration variables is transferred to the first, volatile memory.
.In accordance with an embodiment of the invention, a process of measuring a variable employing a :voltage dependent element whose impedance varies as a function of the measured variable for providing a manifestation indiaative of the measured variable, wherein the process is comprised of the steps of applying a voltage to the variable measuring element and a reference element, whose impedance is relatively stable across at least a range of the variable between first and second calibration variables; exposing the variable measuring element to the first calibration variable, and deriving from the variable measuring element and the reference element corresponding fi.rst and seaond signals;
exposing the variable measuring element to the second calibrati.on variable, and deriving from the variable :measuring element and the reference element corresponding third and fourth signals; obtaining a first caIibration ratio of the first to the second signals and a second calibration ratio of the third to the fourth signals;
exposing the variable measuring element to an unknown variable and deriving from the variable measuring element and the reference element corresponding fifth and sixth signals, a fluctuating voltage being applied commonly to the variable measuring element and the reference element;

~3~332 - lOa -: deriving a present ratio of the fifth to sixth signals;
interpolating the present ratio with respect to the first S and second calibration ratios to provide the manifestation of the measured variable substantially free of any fluctuation of the level of the voltage.
In accordance with another embodiment, a measuring and calculating system for providing with high accuracy a manifestation of gas volume Vb corrected to give base conditions of pressure Pb and temperature Tb of a gas flowing through a conduit, wherein the system is comprised of first apparatus for measuring the temperature Tf of the gas flowing through the conduit and for providing a first signal indicative thereof; second apparatus for measuring the pressure Tf of the gas ` flowing through the conduit and providing a second signal indicative thereof; third apparatus for measuring the volume Vf of the yas flowing through the conduit providing a third signal indicative thereof; calculating apparatus for calculating gas volume Vb corrected to the given base conditions in accordance with the following equation:
b = (V~) Pf Tb (Fpv) Pb Tf where Fpv is the supercompressibility factor; and supercompressibility calculating apparatus comprising apparatus for calculating the supercompressibility factor in accordance with an equation involving only whole number exponentiation and a selected set of coefficients from a plurality of coefficient sets, and apparatus for selecting the set in accordance with the first and second signals.
In accordance with another embodiment, apparatus for measuring a variable is comprised of a variable measuring element having an impedance which L3~332 - lOb -varies as a function of the vari.able; a reference element whose impedance is relatively stable with respect to that of the variable measuring element across a range of the variable between first and second calibration variables;
apparatus for applying a voltage to each of the variable measuring element and the reference element; calibration apparatus for deriving from the variable measuring element and the reference element first and second signals respectively when the variable measuring element is exposed to the first calibration variable, and third and fourt~ signals respectively when the variable measuring device is exposed to the second, calibration variable, and for obtaining a first calibration ratio of the first to the second signals and a second calibration ratio of the third to the fourth signals; and control apparatus including measuring apparatus for deriving fi~th and sixth signals respectively from the variable measuring element and the reference element when the variable measuring element is exposed to a present variable to be measured and for obtaining a present ratio of the fifth to the sixth signals, and interpolation apparatus for interpolating the present ratio with respect to the first and second calibration ratios to provide a manifestation of the variable free of variations in the level of the voltage.
In accordance with another embodiment, a battery energized system for measuring a variable and for performing calculations involving the measured variable and a set of calculation variables, wherein the system is comprised of apparatus for measuring the variable and for providing a signal indicative thereof; first volatile apparatus energizable by the battery at a first, relatively low power consumption rate, for storing the ~3C~3;~

-- lOc --set of calculation variables; second non-volatile apparatus energizable by the battery at a second, S relatively high power consumption rate, for storing a back-up set of the calculation variables; and control apparatus comprising apparatus coupled to the measuring apparatus and the first memory apparatus for effecting the calculations involving the variable signal and the set of calculation variables, apparatus for reviewing the set of calculation variables as stored in the first memory apparatus to provide a first manifestation indicative that the set of calculation variables is intact and to provide a second manifestation indicative 15 that at least one of the set of calculation variables has been lost, and apparatus responsive to the second manifestation for energizing and transferring from the second memory apparatus the back-up set of calculation variables to the first memory apparatus.
BRIEF DESCRIPqlION OF THE DRAWINGS
A detailed description of the preferred embodiment of this invention is hereafter made with specific reference to the drawings, in which:
Figure 1 i5 a ~unctional block diagram of the apparatus or system for measuring and correcting gas flow as a function of measured temperature and pressure in accordance with the teachings of this invention;
Figures 2A-2F are detailed schematic diagrams of the circuit elements of the system as shown in Figure 1;.
Figure 3 is a high level flow diagram of the program as executed by the microprocessor incorporated in the system as shown in Figures 1/ 2A and 2B;
Figure 4 is a chart showing the 11 regions determined in accordance with measurements of temperature -` ~3~)1332 ~ lOd -and pressure, for selecting one of a corresponding 11 sets of coefficients to be used n the calculation of the S supercompressibility factor Fpv by the micxoprocessor incorporated in the system as shown in Figures 1, 2A and 2B; and Figure 5 is a chart of the 11 sets of coefficients, one set of which is selected in accordance with the chart of Figure 4.

~3~L332 DE~AILED DESCRIPTION OF THE PRE~ERRED EMBODIMENT
Referring now to the drawin~s and in particular to Figure 1, a corrected gas flow measuring system is indicated by the general numeral 10. In a preferred embodiment of ~his invention, this system 10 is implement-ed by a programmed microprocessor 11 for receiving and processing a series of pulses generated by a gas flow meter 13 coupled to a gas conduit or line, each meter pulse indicative of a unit volume of the gas flow through the line. The receipt of each meter pulse by the pro-grammed microprocessor 11 provides an uncorrected in-dication of the gas unit volume of gas flow through the line for the presen~ measurements of the flow pressure Pf within the line, as taken by a pressure measuring device 28, and of the flow temperature Tf of the gas within the line, as measured by a temperature measuring device 30.
As will be explained, the application of each meter pulse to the microprocessor 11 initiates the calculation in accordance with a simplified algorithm or equation to correct the measured gas flow to base conditions of pressure Pb and temperature Tb. The resultant calcu-lations are outputted by a general terminal interface 14 to a portable recorder 27. The gas flow meter 13 is coupled to a general input/output 16, whereby the series of meter pulses is applied via the input/output 16 and a turn-on logic circuit 12 to the microprocessor 11.
Resultant calculations of corrected volume for this line volume increment, are outputted through the general input/output 16 to a totalizer 54, which accumulates corrected volume.
The corrected gas flow measuring system 10 is battory powered so that it may be used in remote loca-tions, where normal AC power is not available. To reduce battery drainage, each pulse of the gas flow meter 13 is applied to a turn-on logic circuit 12 to initiate the 13C1133~

operation of the microprocessor 11, the sampling or the outputs of the pressure and ternperature measuring ~evices 28 and 30 and the calculation of corrected yas volume at base conditions. The samples of flow temperature Tf and flow pressure Pf are taken by an analog input circuit 21 and are converted from analog to digital values by an analog-to-digital (A/D) conver~er 19.
Further, the calculation of the supercompressibility factor Fp~ requires the st~rage and availability of a set of calculation variables including specific gravity G, Mc and Mn, indicative of the mol ~'s of carbon dioxide and nitrogen, i.e., the illustrative constituents of the natural gas measured by this system 10, and a plurality of sets of coefficients to be entered into the simplified equation or algorithm used for the calculation of the supercompressibility factor ~pv In accordance with the teachings of this invention, there are a plurality of sets of coefficients, each set correspond-ing to particular range o~ measured pressure and tempera-ture. These coe~ficients and caLculation variables are stored within a low power memory 34, as shown in Figure 2B
and included generally within the block of the micropro-cessor 11 as shown in Figure 1. A backup set of the calculation variables is also stored in a high power, non-volatile memory 18, in case they are lost from the low power memory 34. Lightning or accidentaL discharge of static electricity in the vicinity of the corrected gas flow measuring system 10, can possibly effect data loss from the low power memory 34. In the course of performing a calculation, the microprocessor 11 performs an error check of these constants and coefficients within the low power memory 34 and, if there is an error, a power switch 24 is closed to energize the high power, non-volatile memory 18 and to effect a dump of these constants and coefficients into the low power memory 34. After the ~L3C)~L33:~

, memory dump, the power switch 24 is opened, thus reducing battery drainage. In a similar fashion, a power switch 26 is closed to energize the A/D converter 19 for a relative-ly brief period sufficient to permit the A/D conversion o.
the sampled line temperature and line pressure measure-ments. The A/D converter l9 is a relatively high power consuming device and its brief energization extends the battery life.
As illustrated in Figure 1, the pressure measur-ing and temperature measuring devices 28 and 30 ara coupled to a pressure and temperature input circuit 21, which in turn is coupled to the A/D converter 19~ Fur-ther, the system 10 employs a real time clock 38 shown in Figure 2B, whereby an array or histogram of daily or hourly measurements of pressure, temperature and gas volume may be stored in the low power memory 34 and, upon interrogation, may be read through the terminal interface 14 to the portable terminal 27.
Reerring now to Figures 2A - 2F, there is shown a detailed schematic o~ the elemen~s comprising the corrected gas flow and measuring system 10. For the sake of clarity, many interconnections between the elements of the system 10 are not shown, but rather indicated by identi~ying the terminal(s) associated with one or more elements by the same designation, understanding that the interconnection couples those elements together. For example, ~he microprocessor 11, as shown in Figure 2A, is interconnected by a data bus 32 from its outputs D0 to D7, to the turn-on logic 12~ and to the low power memory 34, among other elements. In particular, the data bus 32 is coupled to a decoder 64 o' the turn-on logic 12b and ls coupled to the low power memory 34. The low power memory 34 comprises a pair of read-only-memories (ROM) 34a and 34b for storing the program, as will be explained with respect to Figure 3, and a plurality of sets of ' :

~30~33Z
coefficients used in the calculation of the supercom-pressibility factor Fpv, and a random-access-memory (R~M) 34c for providing short term storage of the measured variables and calculation variables. The non-volatile memory 18 stores a back-up set of the parameters used for volume calculation as stored in the RAM 34c. Further, the microprocessor 11 includes 16 address terminals A0 to A15, which are coupled by an address bus 36 to each of the ROM's 34a and 34b, and the RAM 34c of the low power memory 34 and to an address decoder 40, among other elements. In particular, selected lines of the address bus 36 are variously connected to selected of a plurality of decoders 66a, 66b and 66c that comprise the address decoder 40.
The outputs of the decoders 66a, 66b and 66c generate a number of control signals that are applied throughout the system 10 to control data processing, output signals and transfer data between the elements of system 10. In a similar fashion, selected lines of the address bus 36 are coupled to inputs of a real tlme clock 44, whiah is coupled to receive the output of an oscillator 28, as shown in Figure 2A.
As shown in Figure 2C, the microprocessor 11 is connected via the data bus 32 and a latch 17 to the power switch 2~, which selectively energizes the high power, non-volatile memory 18. The memory 18 is also coupled by the address bus 36 and the data bus 32 to the micropro-cessor 11. The turn-on logic 12 is illustrated in Figures 2B and 2C as being comprised oE a number of elements generally grouped within the blocks 12a and 12b.
The gas flow meter 13, as generally shown in Figure 1 and in de~ail in Figure 2~, comprlses a volume switch 46, which is closed in response to the passage of a unit of volume of the gas to be measured. The volume switch 46 is coupled by the gas meter input 16, which comprises a 5chmitt Trigger 76, to supply a pulse-like ~ 3V~332 signal VTON to the turn-on logic 12b and in particular, to the clock input C of the flip-flop 68a, as shown in Figure 2C. In turn, the Q output of the flip-flop 68a goes high, and a corresponding output ON is generated by a NOR gate 70 and applied to a one-shot multi-vibrator 72 of the turn on logic 12a. The multi-vibrator 72 actuates an AND gate 74 after a suitable delay to generate and apply a signal to the interrupt terminal RES of the microprocessor 11, to initiate the next set of calculations of the supercom-pressibility factor Fpv and the corrected gas flow. In effect, each closing of the volume switch 46 initiates execution of ~he program as will be explained with respect to Figure 3.
A main oscillator 15 includes a crystal 22 for generating a 3.6 MHz signal, which i5 divided down and applied to the microprocessor 11 to time various events thereinl and an ADCLOCK to the A/D converter 19 to time its operations. The ON signal is applied to the main osclllator 15 to initiate its operation.
A write-enable switch 19 is shown in Figure 2C
and, upon closing, permits writing of data into the non-volatile, high power memory 18. The write-enable switch 19 is ~hrown by the operator and is a protection mechanism to prevent undesired writing ir.to the memory 18.
The closing o the swltch 19 sends a signal through the latch 64 of the turn-on logic 12b to the microprocessor 11 indicating that the switch 19 is closed. In turn, the microprocessor 11 causes a 02W signal to be generated, which is applied through switch 19 to the write-enable terminal WE of the non-volatile, high power memory 18, thus permitting data to be written therein.
Referring now to Figure 2E, there is shown a power supply 37 coupled to a battery pack for providing a voltage, e.g., +5 volts, to the various elements of the system lO. A negative power supply 39 is provided, as :' ~ .

-16- ~3~3~2 shown in Figure 2D, to provide a negative voltage to the analog input circuit 21 and the A/D converter 19, thus serviny to actuate and energize these circuits. The battery pack is also connected to a voltage regulating switch 26, which when actuated by an ~ON signal applied a regulated, switched voltage 5S to the temperature an~
pressure measuring devices 30 and 28, the analog input circuit 21, a pair of operational amplifiers 80a and 80b, and the AID converter 19. As will be explained later, it is not necessary that the switch 26 be of a relatively high precision and, thus, a costly piece of equipment, but may be of conventional design as may be secured at relatively low cost.
When the microprocessor 11 has completed executins the program, as shown in Figure 3, it commands via the data bus 32 the address decoder 66, to cause decoder 66b to generate a signal VTOF~, which resets the flip-flop 68a of the turn-on logic 12b, thus causing the QN signal to go high. As a result, the main oscillator 15 is turned off and the CLOCK and ADCLOCK signals as applied respectively to the microprocessor 11 and the A/D converter 19, are turned off~ Furthex, the -5 OSC signal is likewise deenergized and removed from the negative power supply 39, whereby the -S volts is removed from the analog input circuit 21~ Thus, after the program has been run to take measurements of flow temperature Tf and flow pressure Pf, to calculate the supercompressibility factor Fpv and to calculate the base gas volume Vb, power and clock signals are removed from the analog input circuit 21, the A/D
converter 19 and the microprocessor 11, whereby these relatively high power consuming elements are disposed in a "sleep" mode, until the next unit volume of gas flows through the gas flow meter 13 and its volume switch 46 closes. The closing of the volume switch 46, as explained above, initiates the application of power and clock 3~332 signals to ~he analog lnput circuit 21, the A/D converte~
19 and the microprocessor 11 causing them once agair. to operate ln their "run" mode. In this fashion, the power drained from the battery is reduced and its life extended.
A battery check circuit 41 monitors the output ; VBAT out of the battery and, if below a preset limit e.g., 6.4 volts, a turn-off signal PORL is generated. The PORL
signal is applied to the set terminal of the flip-flop 68b of the turn-on logic 12b, which is set to render high the ON signal, thus removing the clock signal and disposing the microprocessor 11 in its "sleep" mode.
As shown in Figure 2D, the analog input circuit 21 takes the form of a multiplexer having four inputs; the first input to terminals X3 and Y3 is derived from the temperature measuring device 30, which assumes the form of a temperature sensitive resistor. The second input to terminals X2 and Y2 of the circuit 21 is taken from the pressure measuring device 28, which takes the form of a strain gauge-type devlce. The third input to terminals Xl and Yl is connected to ground, whereby an offset voltage as would be indicative o that residual or error voltage as added onto the input signals applied to the other three inputs of ~he analog input circuit 21. A ~ourth input to terminals X0 and Y0 is coupled to a reference voltage divider 58 comprising series connected resistors R53 and R54, which couple the voltage SS to ground; the resistors R53 and R54 are temperature stable resistors, whose resistance vary but slightly over at least the extended ambient temperature range of interest, e.g., -40 to +160F. The resistances of the resistors R53 and R54 do vary slightly with temperature, but are deemed temperature stable relative to the devices 28 and 30, whose impedances vary greatly with temperature. The analog input circuit 21 is controlled by a pair of signals M0 and Ml to con=rol :
:
:

, . .
..

. . ~

-18- 13~332 which of the four lnputs is applied to the input circuit's output X and Y.
The output of the analog input circuit 21 is in turn connected via the pair of operational amplifiers 80a and 80b to the inputs INHI and INLO of the A/D converter 19. In a fashion similar to that of the analog input circuit 21, a reference voltage divider 62 comprised of series connected reference resistors R58 and R59, is connected to the inputs RIN+ and RIN- of the A/D converter 19, whereby a comparison of a reference voltage developed across a reference resistor R59 of the voltage divider 62 may be made with the output of the analog input circuit 21 to provide a digital signal indicative of the analog input circuit's output. The A/D converter 19 is coupled by the data bus 32 to the microprocessor 11 and is commanded by an ADRUN signal from the microprocessor 11 to effect an A/D conversion; thereafter, the A/D converter 19 applies an ADSTAT signal to the microprocessor 11, indica~ing the completion of the commanded A/D conversion. In particular, the microprocessor 11 executes the program, as shown in Figure 3, to send a command signal via the data bus 32 to the latch 17 to first generate the enabling signal XON, which in turn actuates the switch 26, thereby energizing the pressure and temperature measuring devices 28 and 30, the analog input circuit 21 and the A/D
converter 19. In particular, the enabling signal XON is applied via an inverter to the power switch 26, as shown in Figure 2D. The power switch 26 not only functions as a switch but as a voltage regulator to apply a regulated reerence voltage 5S, upon being actuated by the enabling signal XON, to the devices 28 and 30, the aralog input circuit 21 and the A/D converter 19. Next, the microprocessor 11 trar.smits a command signal via the data bus 32 to the latch 17, to generate the ADRUN signal as applied to the A/D converter 19, thus actuating the A/D
. ---19- ~3~L33;~
.

converter 19 to convert the input analog signal to a corresponding digital signal. Upon completion o~ the A/D
conversion, the ~/D converter 19 generates the ADS~AT
signal, which is applied via the latch 64 and the data bus 32 to inform the microprocessor 11 of the completion of the A/D conversion. Tha inverted XON signal is also applied to the I input of the analog input circuit 21, enabling this circuit~
The details of the terminal interface 14 are shown in Figure 2E The microprocessor 11 is connected to a UART 48 via the data bus 32, which in turn supplies a series of autputs to the portable recorder 27, a~s -hown in Figure 1. The portable terminal 27 includes a keyboard and a suitable display, whereby the operator may enter various constants to be used in the calculations performed by the program. The terminal 27 is illustratively an RS-232 compatible terminal.
The general input/output 16 includes a latch 50 coupled to the data bus 32 to receive inpu~ signals, to a fault indicator 52 and to the mechanical counter or totalizer 54, whereby a total or accumulated indication of corrected flow may be provided. The microprocessor 11 transmits a command via the data bus 32 to the latch 50, which outputs the command signals M0 and Ml, whereby the analog input circuit 21 is commanded to select one of its four input3 to be applied to the A/D converter 19. The fault indicator 52 provides a visual indication to the operator that the pressure and temperature measuring devices 28 and 30 are operating out of range, that the constants stored in the non-volatile, high power memory 18 have been lost, that the battery is low, and other malfunctions of the system 10.
Figure 3 is a high level flow diagram of the pxogram s~ored in ~he ROM's 34a and 34b of the low power memory 34, as shown in Figure 2 B, and executed by the ` -20- ~3~33%

microprocessor 11 for accumulating the pulses of the gas flow meter 13, for taking samples of flow temperature Tf and fLow pressure Pf and for calculating an indication or manifestation indicative of gas flow corrected to base temperature Tb and pressure Pb. Initially, step 100 responds to the measurement by the gas flow meter 13 of a unit volume of gas flow and, in particular, to the closing of the volume switch 46 as shown in Figure 2E to generate a VTON signal as applied to the turn-on logic 12a, which in turn applies after an appropriate delay provided by the one-shot ~ulti-vibrator 72 an RES signal to the micropro-cessor 11, whereby the following steps 102 to 132 are executed as will be explained with respect to Figure 3.
The closing of the volume switch 46 initiates the exe-cution of the program by the microprocessor 11. In that period between the completion of the execution of the program and its next execution, the corrected gas flow measuring system 10 is disposed in its "sleep" mode, wherein relatively little current is drawn from the battery. On the alo~ing o~ the vol~me switch 46, the system 10 is operated in its "run" mode, wherein samples of flow temperature T and pressure P~ are taken, these analo~ samples are converted into digital ~orm, and calculatlons of the supercompressibility factor Fpv and the base gas volume Vb axe made. In the "run" mode, the system draws increased power from the battery for that limited period of time corresponding to the execution of the program. Upon completing the execution of the pro-gram, the system returns to its "sleep" mode.
Next, step 102 provides a warm-up period before step 104 tests the low power memory 34 and, in particular, the RAM 34c, which stores the constants and coefficients to be used subsequen~ly in calculations of the super-compressiblity factor Fpv and base gas flow Vb. Each gas or mixture of gases to be measured has a particular set Qf ~" -21- ~3~332 constants, which are stored within the RAM 34c. Once a particular mixture of gas is determined to be measured and the corresponding set of calculation variables is stored within the RAM 34c, the values of the stored calculation variables are summed in an initialization or calibration procedure and that sum is stored in a known location within the ~AM 34c and the non-volatile, high power memory 18. In order to ensure the integrity of the calculation variables as stored within the RAM 34c, step 104 executes a CHECR SUM subroutine, whereby the coefficients and constants as stored within the RAM 34c are again summed and the sum compared with the previous sum as stored in the known location. The CHECK SUM subroutine searches for the first in a sequence of locations where the constants and coe~ficients are stored, and repeatedly addresses each o the sequence of these locations adding that value to the previously summed value until the las~ known address is accessed.
At that point, the current sum is compared with the previously obtained sum and if there is a match, indicating the integrity of the RAM 34c, the program continues wi~h step 112, wherein the flow temperature Tf and flow pressure Pf may be sampled. Otherwise, as shown in Figure 3, the program moves to step 106 as shown in Figure 3, which effects an energization of the relatively high power, non~voltage memory 18 and, thereafter, a downloading of a backup set of the calculation variables from the memory 18 to the RAM 34c. Initially, the power switch 24 is closed, whereby an energizing voltage is applied to the non-volatile memory 187 thereafter, the CHECK SUM subroutine is again run on the contents of the non-volatile memory 18, i.e., each location, where the calculation variables are stored, is sequentially summed until the last storage locatlon within the memory 18 is accessed; the final sum is then compared with the , .

I 22 ~3~3~

prede~ermined sum and if there is an agreement, indicating the integrity of the set of calculation variables stored within the non-volatile, high power memory 18, the backup set of calculation variables is downloaded into the RAM
34c. If the sum of the calculation variables within the non-volatile, high power memory 18 does not agree with the predetermined sum, the program moves to its standard turn-off procedure, whereby the system 10 is disposed in its "sleep" mode. If the CHECK SUM subroutine fails to indicate that the contents of the memory 18 are intact, the microprocessor 11 commands via the data bus 32 and the latch 50 for the fault indicator 52 to provide a visual manlfestation o~ such failure.
After the backup set of calculation variables has been downloaded in step 108 from the non-volatile, high power memory 18 to the RAM 34c, a further CHECK SUM
subroutine is executed on the newly entered contents of the RAM 34c. If the obtained sum agrees with the pre-determined sum, step 110 opens the power switch 24, whereby the non-volatile, high power rnemory 18 is de-energized, and the program continues with step 112.~
However, if either the sacond CHECK SUM subroutine check of the non-volatile, high power memory 18 or the CHECK SUM
subroutine check of the RAM 34c after the backup set o~
constants and coef~icients have been downloaded to the RAM
34c fails, then the system 10 goes into its "sleep" mode, wherein non volatile memory 18, the A/D converter 19, the analog input circuit 21 and the pressure and temperature measuring devices 28 and 30 are deenergized, and further the fault indicator 52 is energized to provide an alarm manifestation indicative of system shutdown.
Next, step 112 determines whether ~he sample outputs of the pressure and temperature measuring devices 28 and 30 are to be used and, if so, the program moves to step 114. If the devices 28 and/or 30 are not to be used, 13~33~

the program moves to step 122, wherein the supercom-presslbility factor Fpv is calculated using previously entered values of flow pressure Pf and/or temperature T~.
One or both of the devices 28 and 30 may have failed and the programming of step 112 permits the system to still be used. Further, the system 10 may be employed where the pressure and/or temperature may he known to be relative constant values and therefore need not be measured. If the pressure and temperature measuring devices 28 and 30 are used, step 114 actuates the power switch 26, applying the switched voltage 5S to the A/D converter 19 and the analog input circuit 21. The microprocessor 11 applies its M0 and Ml signals to command the analog input circuit 21 to sequentially sample i~s X3-Y3 input to obtain an in-dication of the flow temperature T~, its X2-Y2 input to obtain a value of line pressure P~, its Xl-Yl input to obtain the offset voltage appearing at ground and, ~inally, its X0-Y0 terminal to sample the reference voltage appearing across resistor R54 of the reference voltage di~ider 58. After each sampling, the analog values as derived from the analog input circuit 21 are applied to the ~/D converter 19 to derive corresponding, digital samples or coun~s indicative of flow temperature Tf , flow pressure P~, the ofset voltage and a tempera-ture independent reference voltage.
~ he integrity of these samples is double checked in a number of ways. First the level of the switched voltage 5S is checked to determine whether i~ is overrange and of the correct polarity. In addi~ion, the operation of the A/D converter 19 is checked by measuring the time of conversion and if the A/D conYersion has taken too long, there is indication of the faulty operation of the A/D converter 19. If either the voltage level of the switched voltage 5S is not within predefined limits or the A/D conversion takes too long, predetermined values of -24- ~3~1332 pressure and temperature, e.g., 0 pounds per square inch and 60F., are used in the subsequent calculations of the supercompressibility factor Fpv.
Thereaf~er, step 118 opens the power switch 26, whereby ~he voltage provided by the switch 26 is removed from the A/D converter 19. By energizing the A/D convert-er 19 and the analog input circuit 21 for limited periods of time, the battery drainage is minimized and battery life extended. The measurements of pressure, temperature and reference voltage as obtained in step 118 are processed in step 120 to compare or interpolate these measurements of temperature and pressure with initially derived, calibrated values of temperature and pressure taken at predetermined, calibration conditions. The interpolation procedure provides accurate measurements of pressure and temperature that substantially eLiminates any errors caused by variations in the level of the output voltage of the switch 26. Such variation or fluctuation occurs often as temperature varies. In particular, the outputs of step 120 are digital signals or counts indica-tive o~ flow pressure P either in lbs./in.~ or kilo pascals (a metric measurement o pressure) or of flow temperature T either in degrees centigrade or Fahrenheit.
;~eore the system 10 is run to execute the program shown in Figure 3, an initial calibration ;procedure is carried out to obtain ratios of a temperature count to reference voltage count at two predetermined calibration temperatures. Typically, if the system is to be used in a temperature range of 32 to 70F, the calibration temperatures are selected to be 32 and 70F, and coxresponding count ratios are obtained, as will now be discussed. First, the temperature transducer 30 is disposed at the relatively low calibration temperature, e.g., 32F, which is precisely measured by any of well known, precision temperature measuring devices. The ~ ~25 ~3~33Z

operator enters the measured temperature through the portable terminal 27 and the terminal interface 14 to the microprocessor 11, which then commands the A/D converter 19 to obtain analog slgnals from the temperature measuring device 30 and the voltage reference divider 58, and to provide corresponding digital signals or counts; the ratio of these two counts is stored in the high power, known volatile memory 18 and the RAM 34c, along with the operator input value of the corresponding, measured low calibration temperature. A similar ratio of the output of the temperature m~asuring device and th~ voltage reference divider 58 and an operator input value of the corresponding temperature is obtained at the higher calibration temperature, e.g., 70F. At the end of the temperature calibration procedure, there are two pairs of ratios stored in the high power, non-volatile memory 18 and the RAM 34c. A similar calibration procedure is carried out for the pressure measuring device 28, whereby the ratios of the low and high pressure counts to the reference voltage counts are stored in the memory 18 and the RAM 34c, along with operator input values of cali-bration pressure as precisely measured by the operator.
Illustratlvely, the low and high calibration pressures are 0 and 100 lbs./in.~. The calibration temperature and pressure ratios are thus obtained during the calibration procedure and are stored in the high power, non-volatile memory 18 and the R~M 34c for later use in step 120.
~ eturning now to a consideration of the program shown in Figure 3, step 118 deactivates the switch 26, thus removing the switched voltage 5S from the analog input circuit 21 and the A/D convertex 19. Then, step 120 takes the current counts indicative of the measured flow temperature Tf and pressure Pf, and the reference voltage level from the A/D conver~er 19 and, firs~, forms ratios of pressure to reference voltage and temperature to ~ -26- ~3V~332 reference voltage, before interpolating these count ratios with respect to the calibration ratios or pressure and temparature obtained in the manner described above. The details of the step or subroutine 120 to obtain a precise value of pressure will now be explained. First, a sample output Pf of the pressure measuring device 28 is obtained and is converted by the A/D converter 19 to a corresponding digital value or count. A check is made to determine whether the A/D converter 19 has operated improperly, i.e., has the A/D conversion taken too long, and, if not, the digital output of the A/D converter 19 is converted into an appropriate numerical form that can be operated on by the program executed by the microprocessor 11. Then the polarity and magnitude of the pressure count are checked. If correct, a count corresponding to the offset voltage is subtracted from each of the pressure count, the temperature count and the reference count.
Then a ratio of the count corresponding to the pressure measuxement less voltage offset, to the voltage reference level is obtained. Then, the difference between the presently measured pre~sure and the low calibration pressure is obtained, before the difference between the high and Low calibration pressures, i.e., the pressure range, is obtained. Next, the fraction of present pre~sure ~o the pressuro ranye is obtained as the ratio of the dif~erence between the current pressure and the low calibration pressure, to the pressure range~ Next, that fraction is multiplied times the pressure range and, then, added to the low calibration pressure to provide an interpolated, highly accurate measurement of the value of pressure that is independen~ of the level of the switched voltage 5S of the switch 26 and is substantially independent of the differences from one system 10 to the next. Subroutine 120 also operates on the sampled output of the temperature measuring device 30 to obtain similar 133%

ratios of temperature Tf to reference voltage, and then, subsequently interpolates that present temperature ratio between two cali~ration ratios obtained at the low and high cali~ratlon temperatures, to provide a precise value of temperature that is substantially independent of the output level of the switched voltage 5S from switch 26.
Next, step 122 calculates the supercom-pressibility factor Fpv. The AGA NX~l9 procedure for calculating the supercompressibility factor Fpv i5 a lengthly series of equations (see equations 3 to 15, set out above) that use fractional exponen~iation and covers pressure and temperature ranges of 0 to 5Q00 psig and -40 to +240F, respectively. These equations are used to generate a table by sectioning the P-T range into eight smaller regions. Observation of equation (15) above indicates that fractional exponentiation, i.e., the calculation of 2.3, requires a lengthy program requiring extended time for a microprocessor to execute. In accor~
dance with the teachings of this invention, a least squares curve-fitting routine was developed to fit the supercompressibility factor Fpv generated by the AGA NX-l9 procedure to provide the following 9-coefficient, equation:

F = A + ~x ~ Cy2 + Dy + Ey3 + Fxy + Gxy2 + Hxy3 + I~2 (16) , where:

KT = Mc + 1.681 Mn (17) F = _ 226.29 T 99O15 + 211.9 SG - KT (18) ` -28- ~3~

adj ((~f + 460) FT) - 460 (19) Kp = Mc ~ .392 Mn (20) F = _ 156.47 (21) P 160.8 - 7.22 SG + K2 Padj ~ Pf . Fp (22) .
y Pad; 123) x =
Tad~ 70 (24) , where A to I are the equation coefficients as discussed above, Kp is a diluent pressure cons~ant, Fp is a pressure adjusting factor, Padj is ~he adjusted pressure in psig, K~ is the diluent temperature constant, Ft is the pressure adjusting factor, Tadj is the adjusted temperature in degrees Fahrenheit, and SG i.s the specific gravity of the 10wing~gas. The measured values of flowing pressure Pf and flowing temperature Tf are inserted into equations (19) and t22), and the subroutine 122 effects a series of calculations starting irst with equation (17) and con-tinulng in sequence to equatio~ 4), until the values of x and y are derived and inserted into equation (1~). The values of mol ~ o carbon dioxide Mc and mole % of nitrogen Mn, and specific gravity SG are stored in the non-volatile memory 18 and the RAM 34c and are entered into the equations (17j, ~18), (20) and ~21) as noted above.
One equation could not fit the entire pressure and temperature range ~or the calculations of the super-compressibility factor Fp~. As a result, the pressure and temperature range was divided into 11 regions, as shown in Figure 4, each of the 11 regions defining a set of A to I
..

13~L3;3;2 " ~

coefficients as shown in Figure 5. Referring to Figure 4, region 1 includes values of adjusted temperature Tadj of 116 to 240F., and adjusted pressure in the range of 0 to 1500 psig. If the values of Tadj and Padj as calculated by equations (19) and (2Z), respectively, fall within those ranges, the coefficients A to I of region 1 are accessed as stored in the ROM's 34a and 34b and that set is entered into equation (16), and the supercompres-sibili~y factor Fpv is calculated. In particular, the subroutine 122 compares the calculated values of Tadj and Padj with a sequence of sets of Iimits, whereby through a process of elimination, the corresponding one region is determined. For example, if the value of adjusted temper-ature Tadj is greater than 116, the first region is determined and that set of coefficients is taken from the table reproduced above and inserted into the above equation (16). However, if the adjusted pressure Tadj is less than 116F. and the adjusted pressure Padj is less than 75 psig, region 11 is determined. In a similar fashion, each of the remaining regions is determined by ~his logical process of elimination.
The sets of coefficients A to I for expression (16) and th~ constant terms o~ the expressions (17 to 24) are stored in the ROMs 34a and 34b. The particular values of base temperature Tb, base pressure Pb, the calibration temperatures and pressures, and the mol %'s of the gas constituents for a particular situation, are entered by the portable terminal 27 to be stored in the RAM 34c. The corresponding calibration ratios are calculated by the microprocessor 11 and then stored in the RAM 34c~ As explained above, a back-up set of these calculation variables is also stored in the non-volatile memory 18.
In order to check the accuracy of the values of the supercompressibility factor Fpv as obtained from the least squares fi~ted expression 16, reproduced above, with -30- ~3~332 those values obtained from the AGA NX-l9 procedure, a computer program was written to effect calculations of values by both procedures, at every O.S psig and 0.~F.
over a range of adjusted temperature of -30 to 240F. and adjusted pressure of 0 to lS00 psig. The maximum error between these two procedures of 0.06%.
Next, step 124 inserts the value of the super-compressibility factor Fpv calculated in step 122, into the following equation to calculate base volume Vb from line volume Vf corrected for conditions of base pressure Pb and temperature Tb:

~b Vf Pf Tb FPV 2 (25) Pb f The number of pulses from the gas flow meter 13 is ac-cumulated to provide an indication of measured uncorrected gas volume V~ In order to distribute and sell natural gas, it is necessary to agree upon the base conditions including base pressure Pb and base temperature Tb.
Further, the line and base gas flow rates are calculated using the calculations o~ measured and base volume alony with time rom the real time clock 44.
~ ext, step 128 stores measured values o~ pres-sure, temperature and volume as a function of time into a volume survey memory as stored in RAM 34c. The micropro-cessor 11 responds to the indication of real time as provided by the real time clock 44, ~o periodically store measurements of pressure, temperature and volume for each regular period of time, e.g., daily or hourly. There-after, the microprocessor 11 transmits a command via the data bus 32 to increment the mechanical counter or totalizer 54 and an external totalizer as coupled to the general input/output 16, as shown in Figure 2F. There-after, step 132 turns off the system 10, deenergizing ~he , .

~3~33Z

main oscillator 15, thus removing the CLOCK and ADCLOCK
signals from and disposing the microprocessor 11 into a low power state, to wait for the next pulse received from the gas flow meter 13, i.e., the system 10 is returned to its "sleep" mode. In this fashion, the system 10 is only disposed briefly in its "run" mode, wherein samples of pressure and temperature are taken and calculations of the supercompressibility factor Fpv and corrected gas flow are calculated, to minimize battery drainage and increace battery life.
In considering this invention, it should be remembered that the presen~ disclosure is illustrative 8~1y and the scope of the invention should be determined solely by the appended claims.

Claims (14)

1. A process of measuring a variable employing a voltage dependent element whose impedance varies as a function of the measured variable for providing a manifes-tation indicative of the measured variable, said process comprising the steps of:
a) applying a voltage to said variable measur-ing element and a reference element, whose impedance is relatively stable across at least a range of the variable between first and second calibration variables;
b) exposing said variable measuring element to said first calibration variable, and deriving from said variable measuring element and said reference element corresponding first and second signals;
c) exposing said variable measuring element to said second calibration variable, and deriving from said variable measuring element and said reference element corresponding third and fourth signals;
d) obtaining a first calibration ratio of said first to said second signals and a second calibration ratio of said third to said fourth signals;
e) exposing said variable measuring element to an unknown variable and deriving from said variable measuring element and said reference element corresponding fifth and sixth signals, a fluctuating voltage being applied commonly to said variable measuring element and said reference element;
f) deriving a present ratio of said fifth to sixth signals;
g) interpolating said present ratio with respect to said first and second calibration ratios to provide said manifestation of the measured variable substantially free of any fluctuation of the level of said voltage.

2. The process of measuring said variable as claimed in claim 2, wherein said step of interpolating includes obtaining a first difference between said present ratio and one of said first and second calibration ratios, obtaining a fraction as the quotient of said first differ-ence to a second difference between said first and second calibration ratios, and obtaining said manifestation of said measured variable as the product of said fraction and a third difference between said first and second cali-bration variables.

3. The process of measuring said variable as claimed in claim 2, wherein said one calibration ratio is obtained for a corresponding one of said first and second calibration variables, and said step of interpolating further includes the step of summing said product to said one variable to obtain said manifestation of said measured variable.

4. The process for measuring said variable as claimed in claim 1, wherein said variable is temperature and said impedance of said element varies as a function of temperature.

5. The process for measuring said variable as claimed in claim 1, wherein said variable is pressure and said impedance of said element varies as a function of pressure.

6. Apparatus for measuring a variable compris-ing:
a) a variable measuring element having an impedance which varies as a function of said variable;
b) a reference element whose impedance is relatively stable with respect to that of said variable measuring element across a range of said variable between first and second calibration variables;

c) means for applying a voltage to each of said variable measuring element and said reference ele-ment;
d) calibration means for deriving from said variable measuring element and said reference element first and second signals respectively when said variable measuring element is exposed to said first calibration variable, and third and fourth signals respectively when said variable measuring device is exposed to said second, calibration variable, and for obtaining a first cali-bration ratio of said first to said second signals and a second calibration ratio of said third to the fourth signals; and e) control means including measuring means for deriving fifth and sixth signals respectively from said variable measuring element and said reference element when said variable measuring element is exposed to a present variable to be measured and for obtaining a present ratio of said fifth to said sixth signals, and interpolation means for interpolating said present ratio with respect to said first and second calibration ratios to provide a manifestation of said variable free of variations in the level of said voltage.

7. A measuring and calculating system for providing with high accuracy a manifestation of gas volume Vb corrected to given base conditions of pressure Pb and temperature Tb of a gas flowing through a conduit, said system comprising:
a) first means for measuring he temperature Tf of the gas flowing through the conduit and for provid-ing a first signal indicative thereof;
b) second means for measuring the pressure Pf of the gas flowing through the conduit and providing a second signal indicative thereof;

c) third means for measuring the volume Vf of the gas flowing through the conduit and providing a third signal indicative thereof;
d) calculating means for calculating gas volume Vb corrected to said given base conditions in accordance with the following equation:
Vb = (Vf) (FpV) 2 where Fpv is the supercompressibility factor; and e) supercompressibility calculating means comprising means for calculating said supercompressibility factor in accordance with an equation involving only whole number exponentiation and a selected set of coefficients from a plurality of coefficient sets, and means for selecting said set in accordance with said first and second signals.

8. The measuring and calculating system as claimed in claim 7, wherein said equation takes the form of:
Fpv - A + Bx + Cy2 + Dy + Ey3 + Fxy + Gxy2 + Hxy3 + Ix2 , where A to I is said selected set of coefficients.

9. The measuring and calculating system as claimed in claim 8, wherein said supercompressibility calculating means further comprises means for calculating x and y as follows:

X = Y = Padj, where Padj is the adjusted pressure and Tadj is adjusted temperature, and said set of coefficients is selected in accordance with values of said adjusted temperature and adjusted pressure.

10. The measuring and calculating system as claimed in claim 9, wherein said supercompressibility factor calculating means further comprises means for calculating adjusted pressure as follows:

adj = Pf ? Fp , where Fp is the pressure adjusting factor, means for calculating the temperature adjusting factor as follows:

Tadj = ((Tf + 460) FT) - 460 , where FT is the temperature adjusting factor, means for calculating the pressure adjusting factor as follows:

FT = , where SG is the specific gravity of the gas flowing through said conduit and KT is the diluent temperature constant, means for calculating the diluent temperature constant as follows:

KT = Mc + 1.681 Mn , where Mc is the mol % of carbon dioxide in the flowing gas and Mn is the mol % of nitrogen in the flowing gas, means for calculating the pressure adjusting factor as follows:

Fp = , where Kp is the diluent pressure constant, means for calculating the diluent pressure constant as follows:

Kp = Mc - .392 Mn .

11. A battery energized system for measuring a variable and for performing calculations involving the measured variable and a set of calculation variables, said system comprising:
a) means for measuring the variable and for providing a signal indicative thereof;
b) first volatile means energizable by the battery at a first, relatively low power consumption rate, for storing said set of calculation variables;
c) second non-volatile means energizable by the battery at a second, relatively high power consumption rate, for storing a back-up set of said calculation variables; and d) control means comprising means coupled to said measuring means and said first memory means for effecting said calculations involving said variable signal and said set of calculation variables, means for reviewing said set of calculation variables as stored in said first memory means to provide a first manifestation indicative that said set of calculation variables is intact and to provide a second manifestation indicative that at least one of said set of calculation variables has been lost, and means responsive to said second manifestation for energizing and transferring from said second memory means said back-up set of calculation variables to said first memory means.

12. The battery energized system as claimed in claim 11, wherein the said measuring means provides said variable signal in analog form and there is further included means for converting said analog variable signal into a corresponding digital, variable signal, and said energizing means energizing said converting means for a relatively brief period of time to permit the conversion of said analog, variable signal to said digital, variable signal.

13. The battery energized system as claimed in claim 10, wherein said energizing means is responsive to said first manifestation for effecting said calculations involving said variable signal and said intact set of calculation variables.

14. The battery energized system as claimed in claim 10, wherein said energizing means first energizes said measuring means to provide said variable signal, before energizing said converting means to effect said conversion.