ON THE INACCURACY OF A MASSFLOW METER FOR SUPERCRITICAL ETHYLENE
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN A A N DE TECHNISCHE HOGESCHOOL DELFT, OP GEZAG VAN DE RECTOR MAGNIFICUS
P R O F . IR. L. HUISMAN, VOOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VAN DEKA-N E DEKA-N TE VERDEDIGEDEKA-N OP
WOENSDAG 16 NOVEMBER 1977 TE 14.00 UUR
DOOR
HIERONYMUS JOSEPH MARIA VAN ROOIJ elektrotechnisch ingenieur
GEBOREN TE HILVERSUM
DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR DE PROMOTOREN
Prof. Dr. Ir. C . J . M. D. Verhagen
en
CONTENTS
INTRODUCTION 1
1. DESCRIPTION AND EXPECTED INACCURACIES OF THE MASSFLOW 5 METER AND CALIBRATION UNITS
1.1. The massflow meter 5 1.2. The installation of the massflow meter 12
1.3. The calibration apparatus 15 1.3.1. The mechanical displacement prover 15
1.3.2. The density calibration apparatus 21 1.4. Expected inaccuracy of the massflow meter 26
2. PROGRAM OF THE EXPERIMENTS 27 2.1. Calibration of the piston prover 27
2.1.1. Calibration of the piston prover with 27 the master meter method
2.1.2. The determination of the volume of the 30 piston prover by the measurement of length
and diameter of the prover pipe
2.2. Calibration of the reference density meter 31
2.3. Calibration of the turbine meter 35 2.4. Calibration of the density meter 38 2.5. Installation of the massflow meter 39
3. OBSERVATIONS AND CALCULATIONS 40 3.1. Determination of the volume of the prover tank 40
3.2. Determination of the volume of the piston prover 40 3.2.1. Determination of the volume with the master 40
meter method
3.2.2. Inaccuracy of piston prover volume 44 3.2.3. Comparison of results of the determination 45
of the volume of the piston prover with the master meter method at various flow rates
3.2.4. Determination of the volume of the piston 47 prover by the measurement of length and
diameter of the prover pipe
3.3. Determination of the volume of the piston prover 50 under conditions of operation
3.4. Determination of the meter curve of the turbine 52 meter
3.4.1. Determination of leakage over the seals of 52 the piston
3.4.2. Determination of pressure and temperature 54 differences between prover pipe and Pr point
of turbine meter
3.4.3. Determination of the meter curve of the turbine 54 meter
3.4.4. Inaccuracy of reading of the turbine meter 58 under conditions of operation
3.5. Determination of the meter curve of the density meter 59 3.5.1. Determination cf the mass of the sphere 59 3.5.2. Determination of the volume of the sphere 59 3.5.3. Determination of the volume of the sphere at 62
conditions of operation
3.5.4. Determination of the meter curve of the 65 reference density meter
3.5.5. Inaccuracy of reading of the reference density 67 meter under conditions of operation
3.5.6. Determination of the meter curve of the density 68 meter
3.5.7. Inaccuracy of reading of the density meter 70 under conditions of operation
3.6. The reading of the massflow meter under conditions 71 of operation
4. CONCLUSIONS AND FINAL REMARKS 73
4.1. Conclusions 73 4.2. Final remarks 74 APPENDIX 1 : Definition of terminology 76
APPENDIX 2 : Comparison of ethylene density tables 81 APPENDIX 3 : Estimate of leakage of fluid over the seals 83
of the piston of the piston prover
APPENDIX 4 - 1 : Calculation of pressure and temperature 85 differences over the massflow meter
4 - 2 : Calculation of pressure and temperature 90 differences between the piston prover pipe
LIST OF SYMBOLS 94 REFERENCES 98 SUMMARY 100 SAMENVATTING 105 ACKNOWLEDGEMENTS 109 LEVENSBERICHT 110
INTRODUCTION
Ethylene has proved to be one of the most versatile and valuable raw materials for the petrochemical industry. In scale of operation and variety of products it is the most important of the lower olefins (world capacity 40 x 109 kg in 19751.
Ethylene is converted into a variety of products such as polyvinyl chloride (PVC), polyethylene, polystyrene and ethyl glycols
(anti-freeze). This has led to a symbiosis between refineries and chemical plants on the one side where the ethylene is produced in crackers which
for reasons of economy have very large capacities and a diversity of allied factories on the other hand where further processing takes place in much smaller units.
For reasons of economy and safety most of the ethylene is transported through pipelines from the producers of ethylene to the consumers. As a result of the large scale use of ethylene and in order to provide backing up facilities between producers these pipelines have grown to grids stretching over hundreds of kilometers and interlinking considerable numbers of producers and consumers. Various combinations of producers and consumers simultaneously make use of the transportation facilities of these grids.
For operational purposes and for settling accounts on deliveries Che quantities of ethylene delivered into or taken from a grid by each producer or consumer respectively have to be measured. To that end massflow meters are installed at each inlet and outlet of the grid. The output signals of these massflow meters are then integrated in order to measure the quantity of ethylene delivered.
The accuracy of these massflow meters is of direct importance for an efficient use of the capacity of the grid, for grid inventory calculations, for estimates of leakage of the pipeline and for procedures for settling accounts, which involve very large sums of money per massflow meter.
The massflow meters discussed in this study form part of an ethylene grid the major part of which is situated in The Netherlands.
Consequently the Dutch Service of Metrology has to approve of the type of massflow meter to be applied. Notwithstanding the fact that the meter reading is expressed in units of mass, this Service has not categorized the meter as a weighing equipment, but as a flow meter with facilities for density correction. For that kind of meters the limits set to the inaccuray are + 1% of reading in the range of 0,2-1 of the maximum flow and + 2% of reading in the range of the minimum flow to 0,2 of the maximum flow (Directive of European Economic Community L202/21, 1971).
In the industrial practice of custody transfer of large quantities of a product of high value these inaccuracy limits are felt to be unsatisfactory and a massflow meter should be pursued for this application which in order to arrive at a mutual acceptance and to avoid disputes between the parties concerned should read with an inaccuracy of about jf 0,5% of reading for the conditions of operation as stated below.
By this inaccuracy is meant that the difference between the massflow meter reading and the target value of the quantity which has passed through the meter in a certain time interval is within the bounds of about + 0,5% of that target value with a two-sided confidence interval of 95% and throughout the range of operation of the meter (appendix 1 ) . The value of this inaccuracy is initially obtained by the calibration of the massflow meter. The field performance of the massflow meter is checked by comparing the reading of two massflow meters of the kind which are installed in series at each inlet and outlet of the grid and by the calculation of the mass balance of the grid at regular intervals.
The system should operate on ethylene which is transported at pressures between 6-10 MPa, temperatures of 5-35 C and at massflows of 4000 - 50000 kg/h, i.e. volumetric flows of 10 - 120 m^/h. The transport pattern of ethylene in the grid is based on regular deliveries so that the flow through the massflow meters is steady. The ethylene in general has a purity of more than 99,9% of volume. For the given conditions of pressure and temperature ethylene is supercritical (P critical !5;5MPa, t critical ~9,5 C) and behaves as a gaseous fluid with densities of about 175 - 400 kg/m^.
Traditionally massflow meters for gaseous fluids comprise volumetric flow meters combined with facilities for the density correction of the volumetric flow measured.
The meter curve of these volumetric flow meters is either based
on a scientifically established relation between a number of quantities and the volumetric flow or is found from the calibration of the
meter under reference conditions of pressure and temperature of a gas against a standard.
An example of the former meter is the widely used orifice flow meter (American Gas Association, 1964). The latter method is employed for e.g. turbine meters or positive displacement meters which are calibrated on air at nominal conditions of temperature and humidity and nearly atmospheric pressure against a volumetric standard such as a bell prover (Bonner, 1974).
Density corrections for the measured volumetric flow are generally made indirectly by measuring the variables of state, i.e. the pressure and temperature for that volumetric flow. The gas equation for
non-ideal gases is used for calculating the density and making
corrections for the volumetric flow in order to arrive at the massflow. When considering massflow metering of gaseous ethylene as described above two more factors are noted which can adversely affect the meter in actual practice, i.e.:
- The high pressure at which the system has to operate,
- The supercritical state of ethylene at the conditions of the measurements.
with respect to the high pressure of operation experiments proved that the meter curve of turbine meters (Eujen, 1964) and positive displacement meters (Eujen, 1970) can only be predicted with in-accuracies larger than 1 to 1,5% at these high pressures on the basis of calibration of the meter at atmospheric conditions. On the other hand orifice type meters will certainly be inaccurate on ethylene by more than 1 to 2% (Preston et al, 1968) and recent studies (International Organization for Standardization, 1975) show that the interpretation of data, measured with this type of meter according to the various standards that are internationally applied, can give results which vary by up to 1,5%.
The supercritical state of ethylene is characterized by a strong non-linear relation between the density of the fluid and its tem-perature and pressure. The consequence of this is shown in fig. 1. This figure gives the lines of equal errors in density resulting from errors in pressure and temperature measurements of 50kPa and 1 C respectively. The density has been selected from a table as a function of pressure and temperature.
TEMPERATURE I'C}
E r r o r temperature measurement At = 1*C E r r o r p r e s s u r e measurement i P s S O k B a
Resulting error ^ in density drawn f o r equal p e r c e n t o g e s f r o m
^=>w
"I-)'
D a t a f r o m Physikalisch Techmsche B u n d e s a n s t o l t ( T h o m a s , 1976 )
PRESSURE I M P a l
lines of equal error in density fig.l
For the same reason a comparison between some tables used in com-mercial traffic which give density as a function of pressure and
temperature shows incongruities of more than one percent in this supercritical region (appendix 2 ) .
The considerations stated above lead to the conclusion that in order to realize a massflow meter for this application which measures with an inaccuracy of about + 0 , 5 % of reading,
i) the volumetric flow metering device should be calibrated under operational conditions of pressure and temperature, ii) density should be measured in a direct way, i.e. with a direct
density meter instead of indirectly by means of pressure and temperature measurements and tables,
iii) both volumetric meter and density meter should be calibrated with ethylene in order to avoid errors resulting from the use of existing tables which have insufficient accuracy. In this study a massflow metering system will be discussed which consists of a turbine meter as volumetric flow meter and a density meter which directly measures density.
Two calibration units are discussed.
One makes it possible to calibrate volumetric flowmeters such as the turbine meter with ethylene under its operational conditions of pressure and temperature.
The other calibration unit makes it possible to calibrate the density meter with ethylene under its operational conditions of pressure and temperature. The concepts of the calibration units and massflow meter, as discussed in chapter 1, are based on the assumption that an inaccuracy should result for the massflow meter reading which is about + 0,5% for the above-mentioned conditions of operation.
DESCRIPTION AND EXPECTED INACCURACIES OF THE MASSFLOW METER AND CALIBRATION UNITS
The massflow meter
The massflow meter comprises a turbine meter, a density meter and hardware for performing on-line massflow cal-culations with the flow and density data.
The turbine meter manufactured by Instromet (type SM-RI) is an axial turbine meter, i.e. the direction of the flow through the meter runs parallel with the rotor axis of the meter and the angular velocity of the rotor is propor-tional to the flow. Range 10 - 300 m^/h, according to the manufacturer.
The turbine meter has an internal diameter of 100 ram (4"). The rotor is made of aluminium and has 16 blades. The rotor axis is supported by two ball bearings which are
lubricated.
A proximity detector, the working of which is based on the operation of an oscillator that gets untuned in the proximity of the rotor metal, reacts on the rotor blades. Consequently this detector produces a pulse train signal the rate of which is proportional to the rotation speed of the rotor without taking noticeable energy from the rotor. With this construction about 16000 pulses/m^ are produced.
Upstream of the turbine meter the flow is conditioned with a straight length of pipe of about 1,3 m together with a flow straightening element in conformity with the code of the American Gas Association (1964).
The straightening element consists of a bundle of nineteen thinwalled tubes welded together. Each tube has a wall thickness of about 1,5 mm, an internal diameter of about 16 mm and a length of about 250 mm.
The density meter is manufactured by Schlumberger - Solartron (type NT3093E). The measuring of density by means of this instrument is based on the principle of influencing the resonance fequency of a vibrating cylinder (mass spring system) by means of the density of the surtounding fluid (Potter, 1969). Resonance is maintained electromagnetically in a loop circuit by using a drive coil amplifier and pick-up coils on the cylinder edge.
The resulting pulse rate signal from the amplifier has a frequency that is equal to the resonance frequency of
the cylinder. , The measuring range of the instrument is 0 - 400 kg/m
Massflow is calculated from the signals of the turbine and density meter.
3
The flow Q (m /h) is calculated on line from the pulse rate output signal f (pulses/s) of the turbine meter accor-ding the relation:
^0 ^ ^1^ ^ S ^
.C fThe coefficients C Q , C., ....C are determined from fitting the polynomial to the calibration points which are found from the calibration of the turbine meter with ethylene at a given condition of pressure and temperature and at various flow rates throughout its range of operation. So many terms of the polynomial will be used that it fits to the calibration points with an error of approximation the bounds of which are at maximum 0,1% of Q for the given range of operation.
In order to evaluate the performance of the turbine meter in the usual way of the literature on this subject, in this study the meter factor K = f/Q as a function of f (or Q) will be considered as computed from the polynomial given above.
This relationship computed for a turbine meter when calibrated on atmospheric air has the typical shape as shown in fig.2.
METERFACTOR K I P U L S E S / m 3 | 1 1 5 D D 9 • -TURBINEMETER 2 6 6 2 2 Q CALIBRATION POINTS ON ATMOSPHERIC AIR 2 0 0 , I, , FLOW Q I m ' / h l 300 1 I ' ' ! ' ' ' ' ! 750 1000 1Z5D 15DD OUTPUT FREQUENCY f IPULSES/sl
meter factor of turbine meter calibrated on atmospheric air fig. 2
Karlby et al. (1960) have given a derivation of the relation between K and Q based on a consideration of the balance between the driving and retarding torques on the rotor of the turbine meter as a function of the fluid flow through the meter.
It is derived that: M
K = C (1 ^ - YC ) PQ
where C , a constant, is determined by the design of the turbine meter and gives the ratio of f/Q in case the meter is not affected by any losses.
M in the first loss term indicates a constant retarding torque which is due to the friction of the bearings with respect to the fluid driving torque pQ .
This torque has a dominant effect on the meter factor at low flow rates reducing its value as shown by the steep slope of the curve of fig. 2 (Q <30 m^/h).
Y C . in the second loss term indicates the retarding torque which is due to the fluid friction of the rotor blades where Y is a factor of proportionality.
It is derived (Karlby, 1960) that C,, the drag coefficient, is a function of the Reynolds number Re of the fluid,
where Re ~ Q/v and V is the kinematic viscosity of the fluid. Cf gives the curvature of K as shown in fig. 2 for
30 <Q <250 m3/h and the flat path of K at high flow rates (Q >250 m3/h).
Once for a turbine meter K is determined from the calibration of the meter on ethylene as described above the factors have to be evaluated which cause the meter factor to deviate
from K when the turbine meter is used on ethylene throughout its range of operation at conditions of pressure and temperature differing from the calibration conditions.
From the relationship between K and Q as given above it can be expected that two factors can affect the meter factor when used throughout its range of operation. These factors are:
- The change in densityp of the fluid:
The density of the fluid can vary over the range of operation of the turbine meter from about 175 to 400 kg/m3.
The density of the fluid influences the first loss term in the expression given for K.
In order to estimate the effect of a change in density of the fluid on K, the magnitude of M , i.e. the retarding torque of the bearings, is estimated.
As a first order approximation this can be done from the consideration that on atmospheric air for a flow of air Q . which is just insufficient to start the rotation of the rotor of the turbine metei; K is zero. For this situation the second loss term is negligible with respect to the first loss term, so that:
M
K (0 . ) = 0 = C (1 2 _ ^ )
min m Q Q Z .
air ^min
Experimentally it is found that for this type of turbine meter Q . on atmospheric air is about 5 m-'/h so that:
m m "n ^ '^air ^™i" ~ ^^ kgm^/h^ 3 where p . ~ 1 kg/m air 3 A change in density of ethylene from 175 - 400 kg/m will cause a maximum relative change in K at the lowest flow of interest of 10 m^/h.
3 3
At p = 400 kg/m and Q = 10 m /h the meter factor is: 400 m 400x100
3 3
At p = 175 kg/m and Q = 10 m /h the meter factor is:
~ r M -
-21—^
'^175'" ^ 175x100'
The relative change in the meter factor owing to these conditions is then:
§^,O0^_hlll^ 100
* ^'^175'' '^400^ J 25 25 175x100 400x100 jQQ ;0,08 %If the turbine meter should be calibrated at densities of about 280 kg/m i.e. at densities halfway between maximum and minimum occurring densities, this error could be halved to 0,04%.
- The change in kinematic viscosity v of the fluid: The kinematic viscosity of the fluid can vary over the range of operation of the turbine meter from about 10,0 X 10~° m^/s at a pressure of 6 MPa and a temperature of 25°C to 12,7 X 10"8 m^/s at a pressure of 10 MPa and a temperature of 5 C.
The kinematic viscosity of the fluid influences the second loss term in the expression given for K which was a function of the Reynolds number. Whereas the kinematic viscosity of atmospheric air
is about 15 x 10~ m /s, the influence of a change of the kinematic viscosity of ethylene on the meter factor has to be compared to changes in the meter factor as established on atmospheric air at equal Reynolds numbers, i.e. at flows of ethylene which are more than a factor 100 lower than flows of air.
From fig. 2 it can be seen that the meter factor on air is constant for flows higher than about 250 m-^/h so that it can be expected that this situation is realized on ethylene for flows lower than the minimum flow of interest of 10 m^/h. Consequently it is expected that changes in the kinematic viscosity of the ethylene will have no effect on the meter factor.
Resuming the above the bounds of the expected errors in the reading of the turbine meter with the exception of the calibration errors are:
an error of approximation of at maximum 0,1%
for the meter curve established from the calibrations of the turbine meter at one condition of pressure and temperature,
- a systematic error of at maximum 0,04% for the use of the meter curve established above throughout the range of operation of the massflow meter. This error is maximum at the lowest flow of interest of 10 m3/h and decreases to the square with increasing flow.
The density p (kg/m ) is calculated on line from the time period of the pulse rate output signal T (ms) of the density meter according to the relation:
p = C" + C" T + C" T^ 0 1 2
The coefficients C", CV and C" are determined from fitting the polynomial to the calibration points of the density meter as found from the calibration of the density meter with ethylene at various densities throughout its range of operation, i.e. each density being taken at a certain condition of temperature and pressure. According to Potter (1969) this polynomial of three terms will fit to the calibration points with an error of approximation the bound of which is at maximum 0,1% of p. Once the relation between p and T has thus been established, the factors have to be evaluated which adversely effect the accuracy of this relationship when the density meter is used on ethylene throughout its range of operation at conditions of pressure and temperature differing from the calibration conditions.
These factors are:
- The temperature coefficient of the density meter: According to the manufacturer's specifications the density meter has a temperature coefficient of 0,005% of the full scale density of 400 kg/m per C. From fig. 3 it can be seen that the maximum change in temperature which can occur for a given density is about 20 C, viz. the isochore ofp ss275 kg/m3. For the given temperature coefficient this gives a relative change inp of 0,4 kg/m3 or a systematic error of about 0,15% of reading.
The change in velocity of sound of the fluid for a given density:
T E M P E R A T U R E
D A T * t O O M IKTERf4ATI0NAL UNION OP PURE ANO APPLIED CHEMISTRY i ANGUS 1972 1
isotaches and isochores of ethylene fig. 3
From fig. 3 it can be seen that the maximum change of velocity of sound for a given,density is about 75 m/s, viz. the isochore of 275 kg/m .
Now Potter et al (1974) have given a derivation of the relation between p and T based on a consideration of the energy contributed by the vibrating walls of the cylinder of the density meter to the standing wave motion in the surrounding fluid which shows the influence of the velocity of sound of the fluid.
The first order approximation of this derivation is:
where S, is the distance of 0,016 m along which the fluid moves in the vibrational mode of the meter. c is the velocity of sound of the fluid. The relative change in p which is due to a change in the velocity of sound of the fluid 6c in percentages follows
'^°"= ^ , 0 0 = 1 ° ° ! ^ 6 c
P p 9c
^ 3 T -' 3 c •^0,3%
where T Ks 1 ms is the timeperiod of the pulse rate output signal of the density meter for the given conditions.
This relative change of p of 0,3% causes a systematic error of reading of about 0,3%.
From fig. 3 it can be seen that for the given situation temperature and velocity of sound change in the same way. Consequently the systematic errors resulting from the change of temperature and velocity of sound can be halved to 0,08% and 0,15% of reading respectively by selecting the calibration points of the density meter for each selected isochore halfway between the highest and the lowest isotaches cutting that isochore.
Resuming the above the bounds of the expected errors in the reading of the density meter with the exception of the calibration errors are:
- an error of approximation of at maximum 0,1% for the meter curve established from the calibrations of the density meter.
a systematic error of at maximum 0,23% for the use of the meter curve established above throughout the range of operation of the massflow meter.
1.2 The installation of the massflow meter.
The massflow meter is installed as shown in fig. 4.
SOLATING VALVE
massflow meter set-up fig. 4
The meter run with the flow straightening elements is installed immediately upstream of the turbine meter. Together with the turbine meter it forms one piece of equipment which further on will be denoted as turbine meter. Immediately downstream of the turbine meter a spoolpiece with an internal diameter of about 150 mm and containing the density meter is installed. The density meter has been mounted in a conduit that is perpendicular to the centre line of the spoolpiece. This construction is made for maintenance reasons i.e. it makes it possible to remove the meter from the spoolpiece under conditions of operation.
By mounting the density meter in a conduit it is achieved that as a result of heat conduction through the conduit wall the fluid temperature in the meter equals the fluid temperature in the spoolpiece. A small purge flow surrounding the vibrating cylinder of the density meter is taken from a pressure tapping on the upstream section of the spoolpiece.
The spoolpiece and density meter are insulated. The purpose of this arrangement is to ensure that the fluid surrounding the vibrating cylinder of the density meter has the same properties with regard to pressure, temperature and compo-sition as the fluid has at the pressure reference point(Pr) of the turbine meter, i.e. at the location of the rotor blades.
It can be shown that the density of the fluid taken from the pressure tapping as shown in fig. 4 differs at maximum less than -0,03% of the density of the fluid at the pressure reference point (appendix 4-1) so that a systematic error results from this installation which is less than -0,03% of reading.
This error is at maximum -0,03% for the highest flow of interest of 120 m /h and its decrease is quadratic with decreasing flow.
Now it was derived in 1.1. that a systematic error results in the reading of the turbine meter of 0,04% which error is maximum at the lowest flow of interest of 10 m3/h and decreases to the square with increasing flow.
Consequently combining this error and the error mentioned above for the installation of the massflow meter still means that a final systematic error results in the reading of the turbine meter the bound of which is at maximum 0,04%.
1.3 The calibration apparatus
The turbine meter is calibrated by means of a mechanical displacement prover. The density meter is calibrated against a reference density meter of similar design, the meter curve of which is established by a weighing-method.
1.3.1. The mechanical displacement prover
The mechanical displacement prover (piston prover) is shovm in fig. 5. 20 METER
;? 9 9 9 ^ 'M
^^-CxK l-H B-CX3-piston prover fig. 5The prover consists of a honed pipe with a sealed piston, detector switches, control valves, a two-position fourway diverter valve and a check valve. The piston is employed to displace the fluid between reference points 2 and 5. As a consequence a calibrated volume (of about 1 m3) of fluid is displaced through the meter which is connected in series with the prover.
The basic design of a piston prover for application on liquids is given in standard 2531 of the American Petroleum Institute (1963). As it will be discussed, the design of this prover is adapted as to the following points to make it suitable for application on supercritical ethylene:
the meter to be calibrated is placed between the piston prover pipe and the fourway valve to avoid leakage of fluid between meter and piston prover,
- through control valves B and C the whole prover circuit can be flushed with ethylene preceding the launching of the piston for such a period of time that for the turbine meter and the rest of the prover circuit stationary conditions of operation are reached,
the arrangement of the control valves B and C and a launching section allow the piston to enter the cali-brated volume of the prover pipe at uniform speed, the total structure of piston prover and meter is posi-tioned in one plane to prevent the fluid from gaining radial momentum,
- the prover pipe is honed in order to reduce the leakage of fluid over the piston to a_sufficiently low level up to the lowest flow of 10 m /h,
the total structure of piston prover and meter is insulated so as to make that calibration of a meter happens at conditions which can be considered to be adiabatic.
It is the task of the Dutch Service of Metrology to calibrate the volume of the piston prover.
This Service requires that the volume of the piston prover is calibrated with an inaccuracy of some hundredths of a percent and that it is so large that for the volume of fluid displaced during a prover run the turbine meter produces at least 10000 pulses.
3
The turbine meter produces about 16000 pulses/m so that this means that the calibrated volume of the piston prover should be bigger than 0,6 m .
A nominal volume of 1 m3 is chosen which is in accordance with the standard prover tank of the Service of Metrology which will be used for the calibration procedures. The volume of the piston prover is calibrated according two different methods, i.e:
i) Calibration on water using a master meter according to the procedures described in standard 2531 of the American Petroleum Institute (1963). This method is executed by the Dutch Service of Metrology. To obtain the required inaccuracy of some hundredths of a percent of the calibrated volume by means of this method a positive displacement meter delivering 40000 pulses/m3 is used as a master meter.
This master meter is calibrated against a standard prover tank of about 1 m by repeated measurements. So many repetitions are made that a random error results for the mean of the readings of the meter the bound of which is about 0,01%.
The volume of the piston prover is then calibrated against the master meter for a number of repeated measurements. So many repetitions are made that a random error results for the mean of the readings of the volume of the piston prover the bound of which is about 0,01%.
During these calibrations readings of the gauge pressures and temperatures of the prover pipe at Pi and Tl (fig. 5) and the master meter are made in order to correct the master meter reading for changes in the volume of the water owing to pressure and temperature differences between prover pipe and master meter. The readings of the pressures and temperatures are made with random errors the bounds of which are 5 kPa and 0,1 C respectively, so that it is expected that a systematic error results in the reading of the master meter owing to the correction made for changes in the volume of water between prover pipe and master meter which does not contribute in a significant way to the total error.
) Calibration by measurements of the length and diameter of the prover pipe which method will be evaluated as an alternative for the time-consuming master meter method. This method is executed by the manufacturer when the honing of the prover pipe is completed. The distance between the centre points of switches 2 and 5 is determined by adding the measurements of the distances between the centre points of switches 2 and 3, 3 and 4 and 4 and 5 respectively.
The centre points are driven in the prover pipe so that they coincide with the centre line of switches 2, 3, 4 and 5 when mounted.
The measurement of each of the distances between the respective switches is made with a random error the bound of which is 0,004%, so that the distance between switches 2 and 5 is determined with a random error the bound of which is 0,007%.
The mean inner diameter of the prover pipe is calculated as the mean of the measurements of the inner diameters of the prover pipe which are made in a horizontal and vertical way throughout the pipe.
The measurements of the inner diameter are made with a random error the bound of which is 0,02%,
The volume of the piston prover established in this way is also determined by the switchingr-moment of switches 2 and 5.
The systematic error of these switches for this application in detecting the piston according to the manufacturer is at maximum 0,4 mm per switch. On a length of about 14 m between switches 2 and 5 this results in a systematic error of the volume of piston prover, the bound of which is at maximum 0,006%.
Under conditions of operation of the piston prover the gauge pressure and temperature of the ethylene in the prover pipe are measured at P and T respectively. The volume of the prover pipe is then corrected for expansion owing to this pressure and temperature under the conditions of operation.
Readings of the gauge pressure and temperature at P. and T are made with random errors the bounds of which are smaller than 0,5% and 0,5 C respectively and it is expected that they give a systematic error in the value of the volume of the prover pipe under conditions of operation which does not contribute in a significant way to the
total error.
The honed pipe of the piston prover is made of carbon steel (ASTM A53 grade B) with an internal diameter of about 300 mm (12").
For the given range of available standard pipe diameters of about 250 mm (10"), 300 mm (12") and 400 mm (16") the 300 mm pipe is preferred for the reason that for a given volume of 1 m^ the length between switches 2 and 5 is about 14 m.
This length is sufficient to expect only a very small influence of the error of the switches 2 and 5 on the calibrated volume, i.e. a systematic error the bound of which is at maximum 0,006%.
For the given diameter of the prover pipe the highest velocity of the piston (at a flow of 120Tii3/h) is about 0,6 m/s.
A launching length of pipe of about 4 m between switches 1 and 2 enables the piston to accelerate to the velocity of the fluid flow through the prover pipe so that it enters the calibrated volume of the prover pipe with the velocity of the fluid.
The prover pipe is honed. The resulting roughness of the internal surface of the pipe is less than 0,5 ym (20 R u ) . The aluminum piston is provided with spring loaded
teflon seal rings, three of which are installed.
Two rings in series provide sealing when the piston is moved to the meter (proof run), one ring provides sealing when the piston is returned to its start position (return run). For this sealing configuration it is estimated that the leakage over the piston with ethylene is less than 0,002% of the displaced volume (appendix 3) at the lowest
flow of interest of 10 m /h. This leakage causes a systematic error in the reading of the volume of the piston prover
the bound of which is 0,002% so that this error does not contribute in a significant way to the total error. A carbon steel ring which is mounted around the piston enables the detection of the piston position. The detector switches are proximity switches which detect ferrous materials such as the steel ring around the piston. Each switch
is mounted on the surface of the honed pipe and detects via a window of austenitic stainless steel mounted in
the pipewall. This stainless steel window has been welded into the pipe wall and is honed as an integral part of the honed pipe.
The whole prover pipe and piping between prover pipe and meter is insulated so that the displacement of the fluid from prover pipe through the meter can be considered to happen adiabatically. Under these conditions at high flow-rates (120 m3/h) the pressure and temperature differences between the fluid in the prover pipe and the Pr point of the turbine meter can cause a change in volume of the displaced fluid of about 0,1% (appendix 4-2).
However, this is a systematic effect which is to be corrected for.
Resuming the above the bounds of the expected errors in the volume of the piston prover are:
i) with the master meter method at maximum 0,02% resulting from:
a random error of at maximum 0,02% from errors of 0,01% of the master meter and 0,01% of the determination of the volume of the piston prover against the master meter,
ii) with the length/diameter measurement method at maximum 0,03% resulting from:
a random error of at maximum 0,02% from errors of 0,02% in the diameter measurement and 0,007% in the length measurement,
- a systematic error of 0,01% from the rounded off error of 0,006% of switches 2 and 5. This error in the now determined volume of the piston prover is considered as a systematic error in the following when calibrating turbine meters against the piston prover.
The calibration of a turbine meter with ethylene against the piston prover takes place as follows:
Presume that the piston is near switch 1, the fourway valve A is positioned as shown in fig. 5, valve B is open and valve C is closed. As a consequence the fluid flow through the piston prover then goes from near switch 1 to switch 5.
Step 1
When the desired conditions of operation of pressure, temperature and flow in the prover circuit have become
stable (i.e. variations less than 10 kPa and 0,1 C respectively), C is opened and B is then closed. The fluid flow through
the piston prover and the meter will remain undisturbed. Step 2
Now C is slightly closed. The resulting differential pressure
over C will launch the piston. The rate of closure of C is slow enough to deliver a minimum force to overcome static friction and accelerate the piston and to minimize upsets in the fluid flow but so fast that C is just closed, when the piston passes the inlet branch at C. Consequently the piston will then move at uniform speed. The piston passes the detector switches 2 and 5 which in sequence start and stop the counter of the pulse rate signal of the turbine meter and a clock signal which is used to measure the time period between the activation of switches 2 and 5 respectively.
When the piston arrives at the end of the prover pipe the check valve D opens because of the differential pressure created by the piston. The meter reading is accepted when the temperature at T. and the gauge pressure at P during the prover run have not changed more than 10 kPa and 0,1 C respectively.
Step 3
The fourway valve turns 90 degrees, changing the direction of the flow from 5 to 1, valve B is partly opened.
Step 4
As soon as detector switch 1 signals the arrival of the piston at its start position, valve B is fully opened and the fourway valve is returned to its original position. A new calibration sequence can now be initiated.
In this way the turbine meter is calibrated by determining the meter factor K = f/Q = n'/V (pulses/m ) as a function of Q, where n' is the number of pulses of the pulse rate output signal of the turbine meter as gated by switches 2 and 5 respectively.
V is the volume of the piston prover under conditions
¥
r .operation and corrected for the pressure and temperature differences between prover pipe and meter.
The meter factor is determined with an error which results from errors in n' and V .
-The turbine meter delivers about 16000 pulses/m , so that the gating of the output signal of the turbine meter causes a random error in n' the bound of which is 2 pulses on a total of 16000 pulses, i.e. 0,013%.
V , as derived , is determined with the master meter method with a systematic error the bound of which is 0,02%. Resuming the above the bounds of the expected errors of a calibration point of the turbine meter are:
- a random error of 0,01% resulting from the error of 0,013% in n',
- a systematic error of 0,02% resulting from the error in V
pr
1.3.2. The density calibration apparatus
The density meter is calibrated against a reference density me t e r.
The curve of the reference density meter for ethylene under various conditions of pressure and temperature is determined by a weighing-method. For that purpose a sphere has been constructed of chromium-molybdene steel which has been nickel plated. The density meter cell can be screwed into this sphere as shown in fig. 7. This set-up will be denoted further as sphere.
sphere fig. 7
the sphere for calibration of the reference density meter (pressure transmitter P, shown with socket).
The mass and the volume of the sphere are determined. The sphere is then filled with ethylene. The mass of the ethylene in the sphere is determined, its volume is known and consequently the density of the ethylene can be calculated. By measuring the time period of the pulse rate signal
of the density meter the relationship between this signal and the density of ethylene can be established. This procedure can be repeated for ethylene at various densities.
The constructional dimensions of the sphere are based on the consideration that the ratio of tare mass of the sphere to the mass of the ethylene stored in the sphere should be kept low for sufficient accuracy of weighing. The bigger the sphere the more favourable this ratio will be.
A sphere has been constructed with a diameter of about 200 mm. The mass of a sphere having this size is about 20 kg.
The lowest density of ethylene of interest is about 175 kg/m and this means a mass of about 1 kg when stored in the sphere.
A balance is used for weighing which measures with a random error the bound of which is smaller than 20 mg on 30 kg. This means that the mass of the empty sphere of 20 kg is measured with a random error which is of no significance with respect to the total error.
The volume of the sphere for conditions of operation is determined with distilled water.
The water is enclosed in the sphere under conditions of pressure and temperature which correspond to the conditions of operation. The mass of this water is about 5 kg so that this mass is determined with a random error which is of no significance with respect to the total error. The density of the water is selected from a table for the presure and temperature of the water in the sphere (Kell, 1975).
The bounds of the random errors in the pressure and temperature measurements are 0,25% and 0,1 C respectively and it can
be seen from the table that the density of the water for these conditions is selected with a random error the bound of which is 0,02%.
Consequently the volume of the sphere is determined with a random error the bound of which is 0,02%.
This error is treated as a systematic error in the following when considering the calibration of the density meters. The mass of the ethylene in the sphere which at minimum is about 1 kg is determined by weighing with a random error which is of no significance with respect to the total error.
Consequently the density of the ethylene is determined with a systematic error, resulting from the error in the volume of the sphere the bound of which is 0,02%.
The ethylene in the sphere has a certified purity of 99,9% of volume.
The error resulting from the influence of the impurities on the density of the ethylene in the sphere follows from calculation of the difference of the mass fractions of ethvlene with a purity of 100% of volume and of ethylene with a maximum impurity of 0,1% of volume. The mass
fractions for the normally occuring components are calculated from multiplying their % of volume and mole weights as follows: 0,045% of volume of C-H,(30) = 1,35 2. 6 0,040% of volume of CH, (16) = 0,64 0,005% of volume of 0^ (32) = 0,16 0,010% of volume of -^^ (28) = 0,28 99,900% of volume of C2H2(28) = 2191,10 100% of impure ethylene = 2799,63 100% of pure ethylene (28) = 2800,00
Consequently the influence of the impurities on the density of the ethylene is:
6p ^ 2800,00 - 2799,63 ^ „ p 2800,00 • ^"" "'"^^°
This means that a systematic error results in the density of the ethylene owing to impurities the bound of which is 0,01%.
The sphere is then immersed into a thermostat bath and, the system is given enough time to get stabilized. Calibration of the reference density meter is done by reading the time period of the pulse rate output
signal of the meter at a given density together with the pressure and temperature of the ethylene in the sphere. The time period reading T is made by counting pulses of a 10 MHz oscillator which is gated by two consecutive pulses of the reference density meter. The meter curve of the reference density meter is established according the relation:
p = c' + C ; T + CiT^+ C^t + C c U 1 z t c
The coefficients C', C,', C', C and C are determined from fitting the polynomial to the calibration points of the reference density meter, where t and c are the temperature and velocity of sound of the ethylene respectvely at which a reading is made.
In view of these correction terms it follows from Potter (1969) that this polynomial will fit to the calibration points with an error of approximation smaller than 0,1% of p.
Resuming the above the bounds of the expected errors of a reading of the reference density meter are:
a systematic error of at maximum 0,03% resulting from errors in the density and impurities of the ethylene.
an error of approximation of 0,1% for the meter curve of the reference density meter established from the calibrations of the reference density meter.
Calibration of a density meter against the reference density meter is done as follows. Both meters are screwed in containers and their measuring sections are completely immersed into a thermostat bath as shown in fig. 8. The meters are interconnected with tubing thus permitting a free path to the fluid between the meters.
After supplying ethylene of the desired density to the system, the supply valve A is closed and the temperature of the system is given enough time to get stabilized. The time period readings of the output signals of the reference density meter and the density meter under calibration are then made. These calibrations of the density meter are made at about the same densities and conditions of pressure and temperature at which the reference density meter has been calibrated.
Resuming the above it is expected that the bounds of the errors of a calibration point of the density meter are:
an error of approximation of 0,1% resulting from the error of 0,1% in the reading of the reference density meter.
a systematic error of 0,04% resulting from a systematic error of 0,03% in the reading of the reference density meter and of 0,01% owing to the impurity of the ethylene.
Q
VACUUM PUMP®
L1
THERMOSTAT BATHset-up to calibrate density meter against reference density meter
1.4. Expected inaccuracy of the massflow meter
Fig. 9 shows schematically the various elements which determine the inaccuracy of the massflow meter.
The expected random, systematic and approximation errors as derived in section 1.1. to 1.4. are shown in the encirclement of each element.
The error progression for each following element is shown at the connection lines between the encirclements.
STANDARD ^ STANDARD OF
OF LENGTH MASS STANDARD OF MASS
b 10 331 a 10 30)
MASSFLOW METER READING b . a . 0 6
estimated inaccuracy of reading of massflow meter on ethylene Conditions of operation; Q (10-120 m / h ) ; P(6-10MPa);t(5-35°C), Errors shown in % of determined quantities.
Bounds of random, systematic and approximation errors indicated with symbols r, b and a respectively.
Errors marked with • are in the error progression absorbed in other sources of error.
In encirclements errors in the quantities determined are shown. At interconnections error progression is shown.
2 . PROGRAM OF EXPERIMENTS
2.1. Calibration of the piston prover
Before being taken into service the piston prover must be calibrated in order to determine the volume between the detector switches 2 and 5.
This nominal volume, i.e. the volume at standard conditions of pressure and temperature is determined by means of two different methods described in 1.3.1.
The first method is based on the master meter method on water. This calibration method is derived from the standard of mass.
The second method consists of measuring the distance between switches 2 and 5 and the inner diameter of the prover pipe. This calibration method is derived from the standard of length.
Results of both methods of calibration will be given in chapter 3.
2.1.1. Calibration of the piston prover with the master meter method
The following equipment, property of the Dutch Service of Metrology, is used.
Positive displacement (PD) meter M; Avery and Hardoll -60 m per hour
ax '^
output-40000 pulses/m' 3 Prover tank V ; nominal volume - 1000 dm
at 20°C
Temperatures and gauge pressures of the water are measured with the following equipment (fig. 10).
- Two bourdon type pressure transmitters located at P and P^.
These transmitters have a range of 0 - 500 kPa,g and measure with a random error with a bound of 5 kPa. Three resistance (Pt) thermometers located at T , T„ and T-.
These thermometers have a range of 0 - 30 C and measure with a random error with a bound of 0,1 C.
PROVER TANK
calibration set-up piston prover fig. 10
The procedure for calibration as executed by the Dutch Service of Metrology is as follows:
i) The prover tank V is calibrated against their standard at Dordrecht.
The prover tank is wetted, drained and calibrated according to the certified test methods set for this equipment when it is used as volume prover.
ii) At the location of the piston prover the whole circuit, as shown in fig. 10 including the prover tank is filled with water from the supply tank. The system is then inspected in order to ascertain whether there are no leakages and whether that all air has been vented and the water has been drained from the prover tank according to the above-mentioned test methods. The piston.prover is first calibrated at a flow of about 60 m /h according to the following sequence. 1. The meter M is calibrated against the prover
tank V with the piston in position 1. For this purpose valve B is opened and the water is pumped
from the supply tank through meter M and back into the supply tank. The bypass of the meter is checked for leakages by means of the double block and bleed system.
2. When temperatures in the system have become stable to about 0,1 C, Xj and X are closed and checked for leakage by means of the bleed system. The initial indication of the counter of meter M is then taken and X, is opened so that the water is pumped into the prover tank Vx-During the filling of the prover tank V the temperature and pressure readings at T„ and P are taken at regular intervals.
3. When the water in the prover tank V reaches the graduated scale, X_ is closed and the reading of the counter of meter M is taken. X and X are then opened and the water is pumped back again into the supply tank.
4. When the liquid in the prover tank has become stable, its level and temperature are read. 5. Steps 1 up to 4 inclusive are repeated in the
way described in 1.3.1.
6. After the completion of the calibration of meter M the piston prover is calibrated against meter M at the same flow. To that end the water is pumped through the circuit and back into the
supply tank until the flow, pressure and temperature in the circuit have become stable.
Valve C is then opened and B is closed.
C is closed again slowly, thereby launching the piston.
7. The piston operates switches 2 and 5. The signals of 2 and 5 are used to start and stop the counter of the meter M in sequence. During the piston run pressure and temperature readings are made at regular intervals. At the end of the run the meter counter is read.
8. The piston is then returned to its starting position. To that end the meter bypass is opened and X,
and X- are closed.
Fourway valve A turns 90 changing the direction of the flow through the piston prover and valve B is partly opened. As soon as the piston reaches its startig position, B is fully opened.
9. Steps 6 to 8 are repeated as described in 1.3.1. 10. After the completion of the calibration of the
piston prover the meter M is again calibrated against prover tank V so as to check whether no significant changes have taken place in the reading of meter M. •
This procedure again follows step 1 through 5 inclusive.
iii) In order to check whether systematic errors arise from the movement of the piston or leakage over the piston for this method of volume determination the calibration runs described above are repeated at
different flows of about 40, 12 and 4 ni3/h respectively.
2.1.2. Determination of the volume of the piston prover by the measurement of length and diameter of the prover pipe. As an alternative for the calibration of the piston prover with the master meter method on water, its volume is determined
from measurements of the length and diameter of the prover pipe. These measurements are made after the honing of
the pipe as an inspection of its tolerances by the manufacturer. The diameter of the pipe is measured with a displacement
transducer which is fixed to a "three pointed" carriage (fig. 11).
One point of this carriage is spring loaded so that the device is self-centering when brought into the pipe. This diameter meter measures with a random error with a bound of 0,05 mm.
DISPLACEMENT TRANSDUCER
THR£E"P0INTED"CARRIAGE
self centering inner diameter meter fig. 11
With this meter deviations from the diameter of the pipe at the entrance flange are measured throughout the prover pipe horizontally and vertically over the length of the prover pipe at each half meter.
The diameter of the pipe is measured with a micrometer at the entrance flange.
The distance of the prover pipe between the centre points of switches 2 and 5 is measured with a vernier calliper
which has a nominal length of 5 m and a division in millimeters. With this device the distances are measured between the
centre points of switches 2 and 3, 3 and 4 and 4 and 5 respectively.
The calliper measures with a random error with a bound of 0,2 mm.
Both the micrometer and vernier calliper are calibrated against standards which are kept at the same environmental temperature as the honed pipe of the piston prover.
Calibration of the reference density meter
The meter curve of the reference density meter for ethylene is determined by a weighing-method with the set-up described in 1.3.2.
All weighings are made by the Dutch Service of Metrology on their standard balance at Dordrecht.
Weighings are made by interchanging the object to be weighed with standards of mass according the weighing-method of Borda. In this way the balance used measures with a random error with bounds of 20 mg on a scale of 30 kg.
The following steps are made to calibrate the reference density meter.
1. Weighing of the sphere.
The sphere filled with atmospheric air is weighed. 2. The sphere is then filled with distilled water by means
of the set-up shown in fig. 12.
water filling set-up of the sphere fig. 12
Valves A,C,D and E are open, B is closed. The vacuum pomp reduces the pressure in the sphere until it is smaller than 10 Pa whilst the ice bath prevents oil vapours from entering into the sphere.
A small quantity of water is allowed to enter the sphere by slightly opening and closing the needle valve B. This evacuation and entrance of water is repeated several times.
E is then closed, B is opened and the sphere fills up with water from the supply tank. Subsequently, the piston of the pressure pump is withdrawn to its starting position, D is closed and the water in the sphere is pressurized by means of the pump to about 10 MPa. 3. Now C is closed and the sphere weighed. Immediately
after the weighing the room temperature, humidity and barometric pressure are measured so that the density of air can be determined in order to correct the weighings for buoyancy.
4. The volume of the water in the sphere is calculated from the ratio of its mass and density. The mass of the water is determined according to the procedures of steps 1 to 4.
The density of the water is selected from a table as a function of its pressure and temperature. In order to determine the corresponding pressure and temperature of the water in the sphere and the pressure expansion coefficient of the sphere, the sphere is totally immersed in a thermostat bath which is kept at a constant temperature of about 20°C.
A calibrated glass, partially filled with distilled water, is connected to the sphere as shown in fig. 13.
thermostat bath fig. 13
For this set-up the absolute pressure is read at P and the temperature at T,.
The pressure, temperature and volume of the calibrated glass are real with random errors with bounds of 0,25%, 0,1°C and 0,1 cm^ respectively.
Enough time is spent on waiting the temperature in the sphere to become stable. This is checked by waiting so long that no longer significant changes are observed in the time period reading of the pulse rate signal of the density meter. A temperature and pressure reading at P^ and T^ are then made and the volume of the water in the calibrated glass is determined.
Now valve C is opened an instant to reduce the pressure in the sphere. Then C is closed again and as soon as the system has become stable, pressure, temperature and volume readings are made.
The sphere is then filled with ethylene. To this end a supply cylinder is used with ethylene of a certified purity of 99,9% of volume which has a pressure of about 6 MPa at 15°C.
The supply cylinder together with an intermediate cylinder is connected to the sphere as shown in fig. 14.
SUPPLY CYLINDER ETHYLENE
7<
THERMOSTAT BATH THERMOSTAT BATH
ethylene filling set-up for sphere fig. 14
This intermediate cylinder serves as a heat pump to condense ethylene with a density of about 400 kg/m3 into the sphere.
This density of ethylene is about the maximum density at which the reference density meter should be calibrated
for the given range of operation.
The pumping procedure is as follows: F is closed, E and C are opened and the vacuum pump decreases the pressure in the system to less than 10 Pa. Then E is closed, C is open. Baths I and II are now lowered in temperature to about 5 C and F is opened.
p i s t o n prover f i g . 15
Ethylene will fill the sphere, F and C are closed and the temperature of bath II is increased to about 40 C. As soon as this temperature has been reached, C is opened and more ethylene will flow from the cylinder into the sphere. C is closed again and bath II cooled down to about 5 C.
F is opened once more, ethylene from the supply flows into the cylinder and F is closed again. The heat pumping cycle is repeated by increasing the temperature of bath II and delivering more ethylene from the cylinder into the sphere. This procedure will go on until the pressure of the ethylene in the sphere is about 10 MPa. At this pressure and a temperature of 5 C ethylene has a density of about 400 kg/m3.
6. The sphere is now disconnected from the system, dried and weighed on the balance according to the method described in step 3 in order to determine the density of the enclosed ethylene.
7. When the weighing is finished, the sphere is completely immersed in a thermostat bath, the temperature of which can be adjusted from 5 to 35 C.
Measurements are made for various temperatures throughout this range. For each adjustment enough time is spent on waiting for the temperature in the sphere to become stable. This is checked by waiting until no longer significant changes are observed in the time period reading of the pulse rate signal of the density meter. Readings of the time period of the pulse rate signal of the density meter, the pressure of the sphere and the temperature of the bath are then made.
8. Steps 6 and 7 are repeated for various densities throughout the range from 400 down to 175 kg/m3.
These densities are obtained successively by venting an apportioned amount of ethylene from the sphere. Calibration of the turbine meter
The turbine meter is calibrated against the piston prover according to the set-up shown in fig. 15.
This set-up comprises a pressure control and flow control of the ethylene which flows through the piston prover. The flow control signal Fc is derived from a turbine meter and acts on a control valve which together with the turbine meter has been installed upstream of the piston prover.
The pressure control signal is derived from a bourdon tube pressure transmitter P^ and acts on the control valve downstream of the piston prover.
By means of these controls a flow and pressure are selected during a prover run for which the turbine meter has to be calibrated.
Flow can be selected from about 10 - 120 m /h, pressures can be selected from about 7 - 9 MPa. Temperature of the ethylene is ground temperature which varies from about 5 - 25°C.
Before a prover run is made the desired flow and pressure are set and valve B is kept open until enough time has elapsed to have the conditions of operation of the piston prover circuit and turbine meter of temperature, flow and pressure stabilized.
These conditions are observed with a thermometer located at T j , the pulse rate output signal of the turbine meter under calibration and a pressure transmitter located at Pi P has a range of 0 - 10 MPa,g and Ti has a range of 0 - 30 C. The sequence of a prover run is then started by opening valve C, closing valve B, etc. as described in 1.3.1. During the prover run the pulse counter of the turbine meter and a clock are started by switch 2 and stopped by switch 5. When the piston passes by each of the switches during the run the temperature and gauge pressure are measured at T, and P . The results of the prover run are accepted when the temperature at T and the pressure at P during the prover run have not changed more than 0,1 C and 0,1% respectively.
Two possible sources of systematic errors are determined by a special metering-procedure i.e. the leakage over the sealrings of the piston and the pressure and temperature differences between piston prover pipe and pressure reference (Pr) point of the turbine meter under calibration.
The rate of leakage over the sealrings is determined by means of the set-up shown in fig. 16.
The wet gasmeter M^ , which is installed at the end of the piston prover pipe near switch 5, has a capacity of 0 - 5 0 dm3/h and is adjusted for 20 dm3/h so that for this range its inaccuracy can be neglected. The gas which passes from the prover pipe through the gasmeter is vented to the atmosphere.
P measures the pressure difference between the prover pipe and the atmosphere.
P can be read with a random error with a bound of 70 Pa in the range of 0 - 15 kPa,g.
(^)
,2J
9
s
CLOSED -ex] 1—i-NITROGEN SUPPLY- ^
1 1
SPOOLP«CE J. ^ CLOKO METilt1
©
14^
set-up for the measurement of leakage over the piston fig. 16
The system between the "closed" valves is filled with nitrogen at nearly atmospheric pressure.
By creating a differential pressure over the piston it is moved to a position under switch 2, i.e. in such a way that switch 2 remains activated and so much time is spent on waiting for the pressure of the nitrogen in the piston prover pipe to become too low to drive the gasmeter. The pressure of nitrogen on the upstream side of the piston is then increased to some kPa, a pressure small enough not to drive the piston, and the flow of nitrogen downstream the piston is measured over a period of time with the gasmeter. The experiment is repeated for various pressures of nitrogen on the upstream side of the piston all of which are too small to drive the piston. This series of measurements is repeated for the piston positioned under switches 3, 4 and 5 respectively.
The pressure and temperature differences between prover pipe and turbine meter are measured between P, and the Pr point of the turbine meter (fig. 15) at various flows with ethylene for the given range of operation of the turbine meter.
The pressure difference is measured with a differential pressure transmitter which has a range of 0 - 30 kPa and can be read with a random error with a bound of 150 Pa. The temperature difference is measured with two sets of copper-constantane thermocouples.
To that end one couple is inserted into the piston prover pipe at P and one into the fluid stream at the Pr point of the turbine meter whilst the constantane wires are interconnected.
The electromotoric force between the two copper wires is then measured with a microvoltmeter. With this set-up temperature differences can be read with a random error with a bound of 0,02°C in the range of 0 - 0,2 C.
2.4. Calibration of the density meter
As described in 1.3.2., the density meter is calibrated against the reference density meter.
To this end both meters are screwed in containers so that the measuring parts of both meters are immersed in a thermostat bath according to the set-up shown in fig. 8. The meters are interconnected with tubing to permit a
free path to the fluid between the meters.
Ethylene of a certified purity of more than 99,9% of volume and of the desired maximum density is supplied to this system from the heat pump system as described in 2.2.
After ethylene of the desired density has been supplied to the system,the temperature of the system is given enough time to get stabilized.This is checked by waiting until no longer significant changes are observed in the time period reading of the pulse rate signal of the reference density meter.
Then time period readings of the pulse rate signals of the reference density meter and the density meter under calibration are made in the way as described in 2.2. These measurements are repeated for various densities
throughout the range of the meter. The densities are obtained by successively venting each time an apportioned amount of ethylene from the system.
Installation of the massflow meter
In order to determine whether errors arise in the massflow measurements from the installation of the turbine meter and the density meter according to the set-up shown in
fig. 4, pressure and temperature differences are measured between the turbine meter and the density meter.
These measurements are made under the conditions of operation of the system with ethylene at various flowrates.
The pressure difference is measured between the Pr point of the turbine meter and the tapping-point of the density meter. The pressure difference is measured with a differential
pressure transmitter which has a range of 0 - 15 kPa and can be read with a random error with a bound of 70 Pa. The temperature difference is measured between the Pr point of the turbine meter and the location of the density meter. The density meter is left away. The temperature difference is measured with two sets of copper-constantane thermocouples each of which is inserted at one of the above-mentioned places.
The constantane wires are interconnected and the electromotoric force between the copper wires is measured with a
micro-voltT^eter.
With this set-up temperature differences can be read with a random error with bounds of 0,02°C in the range of 0 - 0,2°C.
3. OBSERVATIONS A N D CALCULATIONS
The diagram of fig. 9 shows stepwise the main quantities that have to be determined to finally establish the inaccuracy of reading of the massflow meter.
In the following the observations and calculations required for the determination of each of these quantites and their errors are discussed along the lines of fig. 9 and in accordance with appendix I.
Based on the consideration that for these measurements as a rule no more than two to three sources of errors determine the error of each of these quantities, errors the bounds of which are smaller than 0,003% of the respective quantity are considered not to contribute in a significant way to the total error to be derived for the reading of the massflow meter and consequently will be neglected in the error calculations.
The bound of the total error in percentages of the respective quantity, calculated from the various sources of errors, will then be rounded off to the closest hundredth of a percent.
3.1 Determination of the volume of the prover tank 3 The prover tank V with a nominal volume of 1000 dm at atmospheric pressure and 20 C is calibrated by the Dutch Service of Metrology in accordance with their standard test procedures.
These procedures imply the calibration of prover tank V against a 100 dm3 tank, the volume of which is derived from the standard of mass by weighing.
As a result of six calibrations it is found that the volume of the prover tank is:
V^(0;20) = V^(l-6) = 999,94 dm'^ at 0 Pa,g and 20°C and s- = 0,002% (n = 6)
T
so that r- = 0,005% T
In the following this error in the value of V now determined will be considered as a systematic error.
3.2. Determination of the volume of the piston prover
3.2.1. Determination of the volume with the master meter method (fig. 10)
The volume V of the piston prover is determined by the Dutch ServicS of Metrology by first calibrating the positive displacement (PD) meter M against prover tank V„, then calibrating
