William H.Clingman and Lyn Kennedy Consultants, Precision Machine Products, Inc.
Kenneth R.Hall and James Holste Chemical Engineering Faculty
Texas A&M University
ABSTRACT
A classic method of measuring energy delivered is to use an orifice meter run and a circular chart recorder to obtain an integrated value for the flow. This flow measurement is combined with an average calorific value to obtain energy delivered. This method can be biased when changes in the calorific value correlate
with changes in the flow. This classic method is next compared with two newer methods of measuring energy delivered. The first method uses a flow computer which has as inputs the pressure, temperature, and
pressure differential from an orifice meter. This method also uses continuous measurements of relative density and calorific value. The output from the flow computer is the instantaneous energy flow. The second
method uses a new energy flowmeter that is under development. It directly measures energy flow without measuring either calorific value or volumetric flow.
INTRODUCTION
The general trend in the natural gas industry is to move toward therm billing of large customers. These large customers are primarily power plants and industrial customers. Because the cost of fuel is rising and because therm billing is applied to the larger users, a premium can be paid for more precise measurement of the energy delivered. This paper covers our field experience with different methods of making this measurement.
The experiments were carried out at a Lone Star Gas meter run outside of Bryan, Texas. The gas at this site is odorized before distribution and the flow measurement is used to control the automatic addition of odorant. Downstream about one mile from the site is a City of Bryan municipal power plant, which is a major user of the gas. Remaining gas is distributed to the City of Bryan. About five miles upstream from the site is a Champlin gas plant, which is the source of the gas. Gas flows at the site are of the order of 500,000
SCFH to 1,000,000 SCFH in an 8 inch line. The calorific value varies between 1000 and 1180 BTU/SCF depending on the amount of ethane left in the residue gas by the Champlin gas plant.
Three methods for measuring energy delivered from the site are compared. The first method is the classic method using an orifice flowmeter with circular charts and an average calorific value over the time period being billed. The integrated volumetric flow over the time period corrected to standard conditions is obtained from the circular chart. This integrated flow is multiplied by the average calorific value to obtain energy delivered.
The second method uses a flow computer to calculate and record both the instantaneous and integrated energy being delivered from the site. Continuous inputs to the flow computer are the pressure differential across the orifice plate, the absolute temperature and pressure at the orifice, the relative density of the gas from a gravitometer, and the calorific value from a calorimeter.
The third method uses a new device being developed under a contract with the Gas Research Institute. This device is an energy flowmeter that measures the energy delivered directly without measuring either integrated flow or calorific value. The device consists of two main components, a flow separator and a Flow Titrator . The flow separator splits off a sample stream from the main flow. The flow separator operates so that the ratio of the main flow to the sample flow is independent of the flow rate and the gas composition.
This ratio is called the split. The second component is a Flow-Titrator, which mixes a stoichiometric flow of air with the fuel sample stream. This stoichiometric air flow multiplied by the split is proportional to the energy being delivered in the main line.
In the following section of this paper, each of the three methods is described in more detail by giving the specific parameters of the test equipment at Bryan. This section is then followed with a discussion of some of the measurement errors associated with the classical method. These errors in principle can be eliminated by using either a flow computer or the new energy flowmeter. The final section presents the experimental results comparing these three methods of energy measurement at the Bryan test site.
TEST EQUIPMENT
In the classical method of energy measurement at the Bryan test site, the flow measurement was made by Lone Star Gas with an orifice meter run. This run consisted of a 5 inch orifice in an 8 inch line. A standard meter run was used with a flow straightener 10 feet upstream from the orifice. The differential pressure measurement was taken from flange taps and recorded on a seven day circular chart. Also recorded on the chart was the temperature and pressure of the gas in the line. All measurements of the calorific value and relative density were made at the Champlin gas plant about five miles upstream from the orifice meter. No other fuel was added to the line, however, between the two measuring points so the gas composition was the same at both points. A Therm-Titrator was used for the calorific value measurement and a Ranerex gravitometer for relative density. The two instruments were read hourly and these readings were averaged to obtain an average calorific value and average relative density for the measurement period.
The circular chart was calculated by the Lone Star measurement department. This was done by tracing the pressure and differential pressure curves with an integrater and using an average value of the gas temperature. The average relative density was used in determining the meter factor for the orifice plate. The integrated volumetric flow was multiplied by the average calorific value to obtain the delivered energy.
When energy delivered was measured by the flow computer the same orifice meter run was used. A Rosemont differential pressure transducer, however, was used across the flange taps to obtain an electrical signal for input to the flow computer. A pressure transducer was also inserted in the line at the orifice meter run to provide a continuous electric input to the flow computer. The flow computer was manufactured by
Elliot Automation in Houston. Additional inputs to the computer were the calorific value and relative density of the gas. These were measured continuously by a GB-2000 instrument from Precision Measurement Incorporated (PMI). This instrument is a combination of the Therm-Titrator and a new PMI instrument for measuring relative density. Although the flow computer was provided with a temperature input, the temperature sensor had not yet been installed when the data presented in this paper were collected.
The temperature of the gas as recorded on a circular chart at the site varied from 83° to 87°F. An average temperature of 85°F was programmed into the flow computer. From all of these continuous inputs, the calculated instantaneous energy flow in the line was displayed on a strip chart recorder. The flow computer used the relative density and NX-19 procedure to correct for supercompressibility.
The equipment for the third method of measurement, the energy flowmeter, consists of two main components: a Flow Separator and a Flow-Titrator. The flow separator is illustrated in Figure 1. The flow divides into two streams, a main flow and a sample flow. In each flow stream there is a constrictor which produces a small pressure drop, In the main stream this constrictor consists of 720 parallel rectangular channels, each with a length of one inch and dimension of 1/16″×7/16″. The hydraulic diameter of each channel is 7/64″. The channels are arranged in concentric rings about the center of the flow constrictor. This constrictor is in the 8″ line at Bryan and is located just downstream of an elbow and shut-off valve. A sample line extends from the center of this flow constrictor to the outside of the spool piece which contains it. Outside of the spool piece there is a capillary in the sample line which acts as a second flow constrictor.
Placed downstream from both constrictors are pressure ports which lead to a Rosemont differential pressure gauge. The sample flow to the Flow-Titrator is regulated by a control value. The minicomputer of the Flow- Titrator controls the sample flow so that the pressures are the same downstream from the flow constrictors.
The design insures that the upstream pressures are the same.
Under these conditions, the pressure drop across the flow constrictors is on the order of ½ psi with a flow in the 8 inch line on the order of 600,000 SCFH. The ratio of the main flow to the sample flow is called the split. The split during most of the experiments at Bryan has been about 300,000. The split can be changed by altering the capillary dimensions. It is a characteristic of the flow separator design that the split is invariant with changes in the flow and gas composition.
The variation of the split with flow in laboratory tests is shown in Table 1. The separator tested was of similar design to that at Bryan except that many fewer channels were used and the split was much less. The channels had the same dimensions as at Bryan. The laboratory tests were made using air. The main gas flow (air) was
Table 1. SPLIT VERSUS FLOW
Slotted Plug Expanding To 2” Pipe 0.080 Inch Capillary Expanding to ¼” Pipe
REYNOLDS* NUMBER MAIN FLOW (SCFH) SAMPLE FLOW (SCFH) SPLIT
14288 6321 42.64 148.2
12623 5506 37.67 146.2
11625 5083 34.69 146.5
9081 3934 27.10 145.2
8847 3847 26.40 145.7
7533 3920 22.48 146.3
7520 3280 22.44 146.2
4406 1942 13.15 147.7
*Reynolds number for flow in sample line channel.
REYNOLDS* NUMBER MAIN FLOW (SCFH) SAMPLE FLOW (SCFH) SPLIT Dynamic Range for flow=3.2
Mean Split=146.5
Figure 1. ENERGY FLOWMETER
REYNOLDS* NUMBER MAIN FLOW (SCFH) SAMPLE FLOW (SCFH) SPLIT Standard Deviation=0.7%
measured with a calibrated Roots meter and the sample flow with a wet test meter. A tee was used to separate the flow into a main stream and a sample stream. Both flow streams were vented to the atmosphere after passing through their respective flowmeters which were downstream of the flow constrictors. Pressure drops across the flowmeters were negligible compared to those across the flow constrictors. Thus the arrangement assured equal upstream and downstream pressures between the main line and sample line. In Table 1 the split appears as a function of gas flow Reynolds number in the channels. It is important to have a constant split because then energy flow in the main line is always in the same ratio to energy flow in the sample line. The latter energy flow is measured by the Flow-Titrator and then the main line energy flow can be calculated from the split.
The second main component of the energy flowmeter is the Flow-Titrator. This is a modified Therm- Titrator and its basic layout is shown in Figure 2. The fuel sample stream is mixed with air and burned. The air flow is adjusted so that the air-fuel mixture being burned is essentially at the stoichiometric point. This stoichiometric air flow is then measured and is proportional to the rate at which energy is being delivered in the main line. A continuous output from the energy flowmeter is displayed on a strip chart recorder as the percent of calibration reading for the instrument.
DISCUSSION OF PRECISION AND BIAS
The classic method of measuring energy delivered lacks some precision and has some sources of bias. There is some loss in precision when following by hand the circular chart traces of pressure and differential pressure.
This must be done when reading the circular charts to determine the integrated volumetric flow. This loss in precision is eliminated when using either a flow computer or the energy flowmeter, which both use microcomputers to handle the processing of the data. An instantaneous value of energy flow is integrated in the microcomputer and there is no human involvement in calculating the final result.
Adding to the loss in precision is the fact that normally average values of relative density are used in reading the circular charts. The relative density is used to calculate the meter factor for the orifice plate. The gas composition can vary significantly over the measurement period. When this happens a significant error can occur if there is a strong correlation between flow variations and composition changes. The correlation can be either positive or negative. This problem is amplified when one multiplies the integrated flow by the average calorific value in the classical method.
There are two approaches to eliminating these errors. The first approach is to use a flow computer supplied with a continuous measurement of calorific value and gravity. The errors are eliminated because all measurements are continuous and instantaneous. No averages are used and the energy flow itself is the only quantity integrated over the measurement period. In the second approach the energy flow is measured directly by the instrument so that the need of calculating it from other measured quantities is eliminated.
EXPERIMENTAL RESULTS
The first group of experimental results are shown in Table 2. These data compare the classic method with the energy flowmeter. The energy flowmeter is under development with support by the Gas Research Institute. Data obtained so far have been on a relative rather than an absolute basis. Equipment is still under
development for field calibration of the energy flowmeter and this is required for an absolute measurement.
Thus, in the tables the output of the energy flowmeter is given as the percent of calibration reading.
The error in any measuring instrument can be divided into three components: calibration bias, drift, and random errors. In our experiments the emphasis has been on assessing drift and random errors for the three measurement methods. Calibration error depends primarily on the quality of the standard that is being used.
Random errors occur in all measuring methods and drift may or may not occur. In our experiments these are estimated by comparing two methods.
Assume that M1 and M2 are simultaneous measurements of the energy delivered by methods 1 and 2. Let E be the true value of the energy delivered. In the methods that we have studied calibration involves a multiplicative calibration constant. In that case,
where C1 and C2 are calibration errors, d1 and d2 are drift, and e1 and e2 are random errors. in successive measurements with time C1 and C2 are constant, d1 and d2 would change monotonicaliy with time, and e1
and e2 would be random.
If there is drift in either instrument then either d1 or d2 or both will be significant and will either continuously increase or decrease with time. Since the two instruments are independent, the drifts in each will not be the same and the measurement ratio, (M2/M1) will also drift. In our experiments no evidence has been found for a drift in the ratio (M2/M1) when comparing the energy flowmeter with either the flow computer method or the classical method. Thus, it is concluded that none of the three methods being studied have significant drift over the periods of measurement, which have been one to two weeks in duration.
Figure 2. FLOW SAMPLING DEVICE
Table 2. COMPARISON OF ENERGY FLOWMETER WITH CLASSICAL METHOD DATE LONE STAR GAS
VOLUME MMCF
LONE STAR CALORIFIC VALUE BTU/SCF
MMBTU/ DAY ENERGY FLOWMETER % OF CALIBRATION
RATIO OF CLASSICAL METHOD TO ENERGY FLOWMETER
5–5 18.155 1017 18464 90.85 203.2
5–6 19.549 1024 20018 104.42 191.7
5–7 18.727 1016 19027 90.47 210.3
5–8 16.761 1016 17029 82.37 206.7
5–10 16.992 998 16958 87.65 193.5
5–11 15.792 1012 16994 80.14 212.1
5–12 16.049 1017 16322 79.19 206.1
5–13 17.341 1018 17653 87.56 201.6
5–15 17.819 1017 18122 92.52 195.9
5–16 17.660 1016 17942 90.49 198.3
Mean=202.0 STD. DEV=3.5%
The next step was estimating the magnitude of the random errors for the three methods from the measured ratios (M2/M1) and (M3/M1) . In this notation the subscripts 1, 2, and 3 refer to the energy flowmeter, the classic method, and the flow computer method respectively. Let s1, s2, and s3 equal the variances of the measured values, M1 , M2, and M3. For example if there are N measurements or M1 then an estimate of s1 is given by:
For a large number of data points the square root of the variance would be equal to the standard deviation for the method.
The variance for the ratio (M2/M1) is given by (s1+ s2) when the variances are small. Thus (s1+s2) can be estimated from the standard deviation for the data in Table 2, which is 3.5%. Likewise (s1+s3) can be estimated from the standard deviation for the data in Table 3, which is 0.3%.
Table 3. ENERGY FLOWMETER—FLOW COMPUTER COMPARISON
RATIO OF FLOW COMPUTER TO ENERGY FLOWMETER
ENERGY FLOV7METER READING %
FLOW COMP. MMBTU/
DAY
12 HR. AVERAGE 24 HR. AVERAGE
FIRST MEASUREMENT PERIOD
8/14 120.61 11525 95.6
119.57 11487 96.1 95.8
8/15 122.09 11580 94.8
126.91 12143 95.7 95.3
RATIO OF FLOW COMPUTER TO ENERGY FLOWMETER
ENERGY FLOV7METER READING %
FLOW COMP. MMBTU/
DAY
12 HR. AVERAGE 24 HR. AVERAGE
FIRST MEASUREMENT PERIOD
8/16 118.41 11226 94.8
85.31 8205 96.2 95.4
8/17 88.29 8475 96.0
SECOND MEASUREMENT PERIOD
8/18 84.26 8216 97.5
90.52 8803 97.2 97.4
8/19 92.22 8999 97.6
90.02 8846 98.3 97.9
8/20 85.54 8246 96.4
90.80 8887 97.9 97.2
8/21 84.63 8106 95.8
From this analysis it is possible to conclude from the Table 3 data that the precision of either the energy flowmeter method or the flow computer method must be better than 0.3%. On the other hand it can be concluded from the Table 2 data that the standard deviation for the classical method would be greater than 3.
4%.
CONCLUSIONS
Experimental work is continuing on these methods of energy measurement. From the initial data, however, we can conclude that there are two alternatives to the classical method that can provide a significant increase in precision. One method would use an orifice meter, flow computer, and continuous measurements of calorific value and realtive density. The other is a new instrument under development which measures energy flow directly. In addition to having a high precision these methods integrate an instantaneous value of energy flow thereby avoiding errors caused by using an average calorific value.
This work was partially supported by the Gas Research Institute.