THE WET-GAS TESTING OF TWO 8-INCH ORIFICE PLATES

Transcription

1 THE WET-GAS TESTING OF TWO 8-INCH ORIFICE PLATES A Report for National Measurement System Department for Innovation, Universities and Skills Kingsgate House Victoria Street London SWE 6SW Project No: FFRE45 April 2008 Report No: XXXX/XXX MONTH YEAR Project No: XXXXXX Page of XX

2 The work described in this report was carried out by TUV NEL Ltd under contract to the Department for Innovation, Universities & Skills ( the Department ) as part of the National Measurement System s Engineering & Flow Programme. The Department has a free licence to copy, circulate and use the contents of this report within any United Kingdom Government Department, and to issue or copy the contents of the report to a supplier or potential supplier to the United Kingdom Government for a contract for the services of the Crown. For all other use, the prior written consent of TUV NEL Ltd shall be obtained before reproducing all or any part of this report. Applications for permission to publish should be made to: Contracts Manager TUV NEL Ltd Scottish Enterprise Technology Park East Kilbride G75 0QF jduff@tuvnel.com Tel: +44 (0) TUV NEL Ltd 2007

3 TUV NEL Ltd EAST KILBRIDE GLASGOW G75 0QF UK Tel: +44 (0) Fax: +44 (0) THE WET-GAS TESTING OF TWO 8-INCH ORIFICE PLATES A Report for National Measurement System Department for Innovation, Universities and Skills Kingsgate House Victoria Street London SWE 6SW Prepared by: Date: 2 st April 2008 Dr D Hodges Approved by: Date: 2 st April 2008 Dr M J Reader-Harris for M Valente Managing Director Project No: FFRE45 Page of 39 April 2008

4 SUMMARY Two 8-inch orifice plates of diameter ratio 0.4 and 0.6 (with the diameter ratio 0.4 plate modified to a value of 0.42 after initial testing) have been tested in the TUV NEL wet-gas test facility. The aim of the tests was to investigate the over-reading performance of the plates and to determine if the presence of a drain hole influenced the plate performance, in both dry and wet-gas operating conditions. Operating pressures of 20 and 60 bar gauge were used for the test programme, with gas flow rates over the range 00 to 200 Am 3 /hr and a Lockhart-Martinelli parameter range of 0 to 0.3. Dry-gas baseline tests were completed prior to performing the wet-gas tests to determine the discharge-coefficient performance of the plates. The diameter ratio 0.6 plate gave a discharge coefficient within the uncertainty band defined by ISO 567-2:2003; however, the results for the diameter ratio 0.4 plate were found to be outside its corresponding uncertainty band. To improve the performance of this plate it was re-machined to produce a larger diameter ratio of 0.42 with a sharper leading edge. When the plate was retested the discharge coefficient was found to have shifted to the expected range of values, indicating that the re-machining had been successful. The performance of the orifice plates in wet gas was found to be somewhat inconsistent. The diameter ratio 0.6 plate produced wet-gas over-readings that were all very similar, irrespective of the gas flow rate. This is consistent with the fact that below a gas densiometric Froude number of.5, the two-phase flow pattern in the pipe tends to be of the stratified type, with only a small amount of liquid entrained in the gas phase. As the flow pattern is fairly constant it is expected that the over-reading will also not change much. However, the wet-gas over-readings for the diameter ratio 0.4 (and 0.42) plate showed a large spread as a function of the gas flow rate/froude number. This is inconsistent with the results for the diameter ratio 0.6 plate. The reason or reasons for the differences in the orifice-plate performance is currently unresolved. The drain hole used on the diameter ratio 0.6 orifice plate was found to shift the dry-gas discharge coefficient by 2.4% and.4% for the two pairs of flange tappings used, which is consistent with test work conducted on 4-inch orifice plates with drain holes []. As indicated by the differences in the shifts, the discharge coefficient is sensitive to the relative location of the tappings and the drain hole. The presence of the drain hole was found to have only a small effect on the over-reading performance of the plate. Project No: FFRE45 Page 2 of 39 April 2008

5 C O N T E N T S Page INTRODUCTION THE TUV NEL WET-GAS TEST FACILITY ORIFICE PLATE INSTALLATION AND TEST CONDITIONS RESULTS AND DISCUSSION DRY-GAS BASELINE RESULTS WET-GAS RESULTS DENSITY RATIO, DIAMETER-RATIO AND DRAIN HOLE EFFECTS THE EFFECT OF THE DRAIN HOLE CONCLUSIONS REFERENCES Project No: FFRE45 Page 3 of 39 April 2008

6 NOTATION A D Upstream Pipe Area m 2 A d Orifice Bore Area m 2 C Chisholm Model Constant - C gas Discharge - D Upstream Pipe Diameter m d Orifice Plate Bore m E Velocity of Approach Factor - Fr gas Gas Densiometric Froude number - g Acceleration due to Gravity m/s 2 Flow - m gas Gas Mass Flowrate kg/s m liquid Liquid Mass Flowrate kg/s Re Pipe Reynolds Number - X Lockhart-Martinelli Parameter - β Orifice Plate Diameter ratio (= d/d) - p gas Differential Pressure if only Dry Gas is/were flowing Pa p wet-gas Differential Pressure in Wet Gas Pa ε gas Gas Expansibility Factor - ρ gas Gas Density kg/m 3 ρ liquid Liquid Density kg/m 3 φ Orifice Plate Wet-Gas Over-Reading - Project No: FFRE45 Page 4 of 39 April 2008

7 INTRODUCTION Despite recent advances in other flow metering technologies, the simplicity, reliability and capital cost of the orifice plate have ensured that it remains the instrument of choice for many applications. It is by far the most common flow meter in industrial service, accounting for over 40 per cent of the market, across a wide range of sectors including oil and gas, process, energy and chemical. However, where an orifice plate is used to meter a gas flow, the presence of small quantities of entrained liquid can present a problem as, if steps are not taken to allow the liquid to pass the plate, a pool will build up against the upstream face and undermine the metering accuracy. The most widely applied solution is to provide a liquid bypass in the form of a drain hole in the plate allowing liquids in a gas stream to pass through the plate. While drain-hole plates are a cost-effective way of measuring gas with a low liquid content, they are not as accurate as the standard design. As the extent of this inaccuracy is not well documented and as industry is sceptical of the existing formula, drain-hole plates are not as widely used as they might be: new data are therefore needed to give confidence in their use. Applications for the work include: gas off-take measurement where hydrocarbon liquids can be entrained, causing errors in inter-field allocation and impacting on company and tax revenues; gas-metering systems where water from compressor cleaning has to pass through the meter; and steam metering where condensate is present. Single-phase tests are described in []; wet-gas tests are described here. 2 THE TUV NEL WET-GAS TEST FACILITY The high-pressure wet-gas test facility at TUV NEL is based around a 6-inch (nominal bore) re-circulating loop and a 2 m 3 gas/liquid separator. A schematic diagram of the test facility arrangement is provided in Fig. (note, however, that only one test line is shown in this sketch). Although nominally 6-inch diameter, the two parallel test sections available can accommodate line sizes ranging from 4 inch to 8 inch. The natural gas/condensate simulant fluids used are oxygen-free nitrogen and a kerosene substitute (trade name Exxsol D80). At 20 o C the liquid phase has a density of kg/m 3 and a viscosity of cp. The facility operates at a nominal temperature of 8 C over a nominal pressure range of 5 to 63 bar gauge. This pressure range corresponds to a gas density range of 8.6 to 74.5 kg/m 3. Referring to the schematic diagram in Fig., gas is drawn from the top of the separator and is driven around the test loop by a 200 kw blower. The maximum achievable pressure-independent dry gas volumetric flow rate is 500 m 3 /hr when operating in wet gas mode (i.e. flowing through the separator), and at the minimum 6-inch test line resistance (i.e. no test meter installed). Liquid is injected using a 30 kw, -stage centrifugal pump through a specially designed spool over 60D upstream of the test section, up to a maximum flow rate of 80 m 3 /hr (minimum flow rate is 0.2 m 3 /hr). The gas and liquid phases mix at the injection point and pass through the test section in a form dictated by the gas velocity and pressure. The two-phase mixture then passes back into the separator for separation and recirculation. The gas and liquid stream temperatures are both maintained at a set level (to within ± 0. o C) using two chilled-water-controlled shell-and-tube heat exchangers. Project No: FFRE45 Page 5 of 39 April 2008

8 The gas flow rate is controlled by varying the speed of the blower, while the liquid injection flow rates are set manually at the injection point. The gas reference volumetric flow rate is measured using a 6-inch Daniel SeniorSonic ultrasonic meter, while the liquid reference flow rates are measured using traceable calibrated turbine meters. For the test work described in this report the expanded uncertainty on the gas reference volumetric flow rate is 0.5% and on the liquid reference volumetric flow rates measured is 0.2% (all at the 95% confidence level). All temperature, pressure and differential-pressure measurements are taken using traceable calibrated instrumentation. A modified sub-sea video camera can be used to monitor the two-phase flow in the test section. The camera allows the transition from stratified flow to annular-mist flow to be observed, although this is dependent upon the operating pressure and gas velocity. 3 ORIFICE PLATE INSTALLATION AND TEST CONDITIONS Figure A Schematic Representation Of The TUV NEL Wet-Gas Test Facility For this test programme two 8-inch orifice plates (note that one plate was tested on two occasions, one after modification, due to an insufficiently sharp edge causing a high discharge coefficient) were installed in a holder with two pairs of flange tapping holes, designated A2/A and B2/B. The designation 2 refers to the upstream pressure tap while the designation refers to the downstream pressure tap. The tapping holes were 6 mm in diameter. For the dry-gas and wet-gas tests conducted the tapping-hole pairs were used in the following spatial arrangements, with the locations being defined relative to the upstream face of the plate: Project No: FFRE45 Page 6 of 39 April 2008

9 For the initial dry-gas baseline test of the β = 0.6 plate, where β is the diameter ratio, the A2/A tapping-hole pair was located in the o clock position and the B2/B tapping-hole pair was located in the 8 o clock position. For the β = 0.4 plate dry-gas baseline test, and the β = 0.4 and 0.6 plate wet-gas tests, the A2/A tapping-hole pair was located in the o clock position and the B2/B tapping-hole pair was located in the 0 o clock position. For the β = 0.42 and 0.6 (with drain hole) plates dry-gas baseline and wet-gas tests, the A2/A tapping-hole pair was located in the 2 o clock position and the B2/B tapping-hole pair was located in the 9 o clock position. Although the above shows that a number of different orientations were used for the orifice-plate holder during the baseline and wet-gas tests, it should be noted that the specific orientation used was of greatest importance during the drain-hole baseline and wet-gas test work. The drain hole was directly opposite the A2/A tapping-hole pair (and consequently at 90 o to the B2/B tapping-hole pair). Since the drain hole had to be located at the 6 o clock location to allow liquid to pass through it (i.e. at the bottom of the pipe) during wet-gas testing the A2/A tappings were then at the 2 o clock location and the B2/B tappings at the 9 o clock location. Each orifice plate was installed with 3D of matching pipe upstream (to the upstream face of the plate), and 8D of matching pipe downstream. A temperature probe was installed 6D downstream of the downstream face of the plate. Representative photographs of the installation are given in Figures 2 and 3 below. The upstream pipe diameter was mm, while the diameter of the two original orifice plates was 8.8 mm and 22.2 mm respectively (β = 0.4 and 0.6). The new diameter of the modified β = 0.4 plate was mm, giving a new diameter ratio of Both the dry and wet-gas tests were conducted at two static pressures, 20 and 60 bar gauge. This was done to obtain both a reasonable pipe Reynolds number range for the dry-gas tests, and to check for any effect of changing the gas-liquid density ratio on the orifice-plate over-reading performance. The dry-gas tests were conducted primarily as a baseline for the subsequent wet-gas test programme, but also to check the performance of the plates against the ISO 567 standard. The baselines are needed to allow the determination of the over-reading response of the orifice plates in the presence of a wet-gas flow. All calculations performed for the wet-gas data analysis are detailed in section 3. The orifice-plate dry-gas baseline tests were conducted over a number of slightly different ranges, dependent mainly on the orifice-plate diameter ratio (there are limits on pressure drop and maximum differential pressure), but also on the anticipated range of gas flow rates achievable on the test facility, given the required range of liquid injection rates at the two operating pressures in wet gas. It should also be noted that, in general, the gas flow rates used for the wet-gas tests are a subset of those used for the dry-gas baseline tests. The following summarises the gas flow rates used for each plate for both the dry and wet-gas tests: Diameter Ratio 0.4: 00, 200, 400, 600 and 800 Am 3 /hr. Diameter Ratio 0.42: 00, 200, 400, 600 and 800 Am 3 /hr, additionally 900 and 000 Am 3 /hr at 20 bar gauge only in dry-gas. Diameter Ratio 0.6: 200, 400, 600, 800, 000 and 200 Am 3 /hr, with and without the drain hole. Project No: FFRE45 Page 7 of 39 April 2008

10 The liquid flow rates used for the wet-gas tests were defined using the Lockhart-Martinelli parameter, a dimensionless number used for representing the liquid loading in a flow line. For this test programme the Lockhart-Martinelli parameter was set at the following values: 0, 0.0, 0.025, 0.05, 0.0, 0.5, 0.20, 0.25 and Figure 2 An Overview Of The Test Line Installation Figure 3 The 9 and 2 O clock Pressure Tapping Arrangement At The Orifice Plate Project No: FFRE45 Page 8 of 39 April 2008

11 4 RESULTS AND DISCUSSION The dry and wet-gas test measurements have been used to determine the orifice plate over-reading performance. The dry-gas discharge coefficients have been calculated using equation (), while a flow coefficient (a combination parameter which brings together the discharge coefficient, velocity of approach factor and expansibility) has been calculated using equation (2). Discharge, Cgas mgas = Eεgas Ad 2ρgas pgas () Flow, K gas = A m 2ρ gas p d gas gas (2) m gas is the reference gas mass flow rate, E is the velocity of approach factor 4 ( E = β ), β is the orifice plate diameter ratio, ε gas is the gas expansibility factor, A d is the throat area of the orifice plate, ρ gas is the gas density at the plate and p gas the measured dry-gas differential pressure. The dry-gas flow coefficient is a useful parameter when testing a differential-pressure meter in wet gas, in that it can be used to estimate what the differential pressure would be under wet-gas operating conditions if the gas flowed alone in the pipe (given knowledge of the reference gas mass flow rate), via the simple rearrangement of equation (2). This estimated dry-gas differential pressure can then be used to determine the over-reading of the differential pressure meter when combined with the measured wet-gas differential pressure ( p wet-gas ), as given in equation (3). Orifice Plate Over-Reading, φ = pwet gas pgas (3) The over-reading is simply a parameter which represents the extent to which the liquid presence in the flow line causes the measured differential pressure to increase relative to that which would be obtained if the line were completely dry. Differential-pressure meter over-readings are usually presented as a function of the Lockhart-Martinelli parameter (X), calculated here as defined in equation (4), and additionally as a function of the gas densiometric Froude number (Fr gas ) at the orifice plate location (equation (5)). Lockhart-Martinelli Parameter, mliquid X = mgas ρ ρ gas liquid (4) Gas Densiometric Froude Number, Fr gas = ρ gas m A gas D gd ρ ρ liquid gas ρ gas (5) where m liquid is the reference liquid mass flowrate, ρ liquid is the reference liquid density and D is the upstream pipe diameter, with A D being the corresponding upstream pipe area. Project No: FFRE45 Page 9 of 39 April 2008

12 The over-reading from the orifice plate can also be determined (for comparative purposes here) using a published model, such as that of Murdock [2] or Chisholm [3, 4]. The two models are given as equations (6) and (7, 8). Murdock Model Over-Reading, φ = +.26X (6) Chisholm Model Over-Reading, 2 φ = + CX + X (7) where ρgas ρliquid C = + when X ρ gas ρ liquid (8) 5 DRY-GAS BASELINE RESULTS The calculated dry-gas orifice-plate discharge and flow coefficients for each of the plates tested (both with and without drain holes), required for the subsequent wet-gas data analysis, are presented in Tables to 8. The flow coefficients presented in these tables have been used in the current analysis of the wet-gas data by obtaining a curve-fit to the values as a function of the pipe Reynolds number (also provided in the tables) calculated using the orifice plate upstream pipe diameter at the two test pressures used, i.e. 20 and 60 bar gauge. Other approaches can be used for estimating the flow coefficient (e.g. averaging the values), which would give slightly different over-reading results if used in the analysis. The Reynolds-number-based functions obtained from each orifice-plate dry-gas test are given in equations 9 to 24. These are presented in the same sequence as for the tables, with pairs of equations (e.g. 9 and 0) relating to the data taken at 20 and 60 bar gauge respectively for a given orifice plate and tapping-hole pair, A2/A first and B2/B second. Test Point No TABLE DIAMETER RATIO 0.4 ORIFICE-PLATE DRY-GAS DISCHARGE AND FLOW COEFFICIENTS FOR TAPPING-HOLE PAIR A2/A Pipe Reynolds 20 bar 20 bar, C gas 20 bar, Pipe Reynolds 60 bar 60 bar, C gas 60 bar,.883e E E E E E E E E E E E E E E E E E E E Project No: FFRE45 Page 0 of 39 April 2008

13 TABLE 2 β = 0.4 ORIFICE-PLATE DRY-GAS DISCHARGE AND FLOW COEFFICIENTS FOR TAPPING-HOLE PAIR B2/B Test Point No Pipe Reynolds 20 bar 20 bar, C gas 20 bar, Pipe Reynolds 60 bar 60 bar, C gas 60 bar,.883e E E E E E E E E E E E E E E E E E E E TABLE 3 β = 0.6 ORIFICE-PLATE DRY-GAS DISCHARGE AND FLOW COEFFICIENTS FOR TAPPING-HOLE PAIR A2/A Test Point No Pipe Reynolds 20 bar 20 bar, C gas 20 bar, Pipe Reynolds 60 bar 60 bar, C gas 60 bar, 4.872E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx.363e xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx.358e xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx.359e xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx.356e xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx.358e xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx.359e Project No: FFRE45 Page of 39 April 2008

14 TABLE 4 β = 0.6 ORIFICE-PLATE DRY-GAS DISCHARGE AND FLOW COEFFICIENTS FOR TAPPING-HOLE PAIR B2/B Test Point No Pipe Reynolds 20 bar 20 bar, C gas 20 bar, Pipe Reynolds 60 bar 60 bar, C gas 60 bar, 4.872E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx.363e xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx.358e xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx.359e xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx.356e xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx.358e xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx.359e TABLE 5 β = 0.42 ORIFICE-PLATE DRY-GAS DISCHARGE AND FLOW COEFFICIENTS FOR TAPPING-HOLE PAIR A2/A Test Point No Pipe Reynolds 20 bar 20 bar, C gas 20 bar, Pipe Reynolds 60 bar 60 bar, C gas 60 bar, 2.454E E E E E E E E E E E E E E E E E E E E E xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx E xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx E xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx E xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx Project No: FFRE45 Page 2 of 39 April 2008

15 TABLE 6 β = 0.42 ORIFICE-PLATE DRY-GAS DISCHARGE AND FLOW COEFFICIENTS FOR TAPPING-HOLE PAIR B2/B Test Point No Pipe Reynolds 20 bar 20 bar, C gas 20 bar, Pipe Reynolds 60 bar 60 bar, C gas 60 bar, 2.454E E E E E E E E E E E E E E E E E E E E E xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx E xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx E xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx E xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx Test Point No TABLE 7 β = 0.6 ORIFICE-PLATE (WITH DRAIN HOLE) DRY-GAS DISCHARGE AND FLOW COEFFICIENTS FOR TAPPING-HOLE PAIR A2/A Pipe Reynolds 20 bar 20 bar, C gas 20 bar, Pipe Reynolds 60 bar 60 bar, C gas 60 bar, 2.949E E E E E E E E E E E E E E E E E E E E E E E E E xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx Project No: FFRE45 Page 3 of 39 April 2008

16 Test Point No TABLE 8 β = 0.6 ORIFICE-PLATE (WITH DRAIN HOLE) DRY-GAS DISCHARGE AND FLOW COEFFICIENTS FOR TAPPING-HOLE PAIR B2/B Pipe Reynolds 20 bar 20 bar, C gas 20 bar, Pipe Reynolds 60 bar 60 bar, C gas 60 bar, 2.949E E E E E E E E E E E E E E E E E E E E E E E E E xxxxxxxxxx xxxxxxxxxx xxxxxxxxxx 3 2 = E 2.Re E 4.Re E 8.Re (9) 2 = E 6.Re E 0.Re (0) 3 2 = E 2.Re E 4.Re E 8.Re () 2 = E 6.Re E 0.Re (2) 2 = E 6.Re E 9.Re (3) 2 = E 7.Re E.Re (4) 2 = E 6.Re E 9.Re (5) 2 = E 7.Re E.Re (6) 3 2 = E 2.Re E 5.Re E 8.Re (7) 3 2 = E 23.Re E 6.Re E 9.Re (8) 3 2 = E 2.Re E 5.Re E 8.Re (9) 3 2 = E 23.Re E 6.Re E 9.Re (20) Project No: FFRE45 Page 4 of 39 April 2008

17 2 = 34505E 6.Re E 9.Re (2) 2 = E 7.Re E 0.Re (22) 2 = E 6.Re E 9.Re (23) 2 = E 7.Re E 2.Re (24) Figures 4 and 5 show the dry-gas discharge-coefficient results for the β = 0.4 orifice plate for the A2/A and B2/B tapping-hole pairs respectively. It is clear that both sets of coefficients lie outside the plotted ISO 567 uncertainty band. This indicated some problem with the manufacture of the orifice plate. Visual inspection of the plate showed that the orifice edge was insufficiently sharp; therefore this plate was modified to produce a slightly larger diameter ratio of 0.42, but with a much sharper edge. The results for the modified plate are presented in Figures 8 and 9. The discharge coefficient now lies on the ISO 567 calculated discharge coefficient, well within the acceptable uncertainty band. The discharge coefficient results for the β = 0.6 plate are given in Figures 6 and 7. The experimentally derived discharge coefficients lie between the lower ISO 567 uncertainty limit and the ISO calculated discharge coefficient value. Figures 0 and provide the dry-gas discharge coefficients for the β = 0.6 plate with the drain hole of diameter d h = 0.d. It is clear that the discharge coefficient has shifted in a positive direction relative to the non-drain-hole baseline tests, but by different extents for the A2/A and B2/B tapping-hole pairs. The shift is greater for the A2/A tapping-hole pair, with a mean shift relative to the baseline coefficient of 2.4%. For the B2/B tapping-hole pair this shift is of the order of.4% at the same pipe Reynolds number. The performance of the tapping-hole pairs is clearly sensitive to the relative location of the drain hole, with the largest effect seen when the tapping-hole pair is located at 80 o to the drain hole (i.e. the A2/A pair). At only 90 o to the drain hole position, the B2/B tapping-hole pair shows only 60% of the shift obtained from the A2/A tapping-hole pair. Project No: FFRE45 Page 5 of 39 April 2008

18 bar 60 bar ISO 567 Cd ISO 567 Uncertainty Discharge E+00.0E E E E E E+06 Pipe Reynolds Number Figure 4 β = 0.4 Orifice Plate Discharge Tapping-Hole Pair A2/A bar 60 bar ISO 567 Cd ISO 567 Uncertainty Discharge E+00.0E E E E E E+06 Pipe Reynolds Number Figure 5 β = 0.4 Orifice Plate Discharge Tapping-Hole Pair B2/B Project No: FFRE45 Page 6 of 39 April 2008

19 bar 60 bar 60 bar repeats ISO 567 Cd ISO 567 Uncertainty Discharge E+00.0E E E E E E E E E+06 Pipe Reynolds Number Figure 6 β = 0.6 Orifice Plate Discharge Tapping-Hole Pair A2/A bar 60 bar 60 bar repeats ISO 567 Cd ISO 567 Uncertainty Discharge E+00.0E E E E E E E E E+06 Pipe Reynolds Number Figure 7 β = 0.6 Orifice Plate Discharge Tapping-Hole Pair B2/B Project No: FFRE45 Page 7 of 39 April 2008

20 bar 60 bar ISO 567 Cd ISO 567 Uncertainty Discharge E+00.0E E E E E E+06 Pipe Reynolds No Figure 8 β = 0.42 Orifice Plate Discharge Tapping-Hole Pair A2/A bar 60 bar ISO 567 Cd ISO 567 Uncertainty Discharge E+00.0E E E E E E+06 Pipe Reynolds No Figure 9 β = 0.42 Orifice Plate Discharge Tapping-Hole Pair B2/B Project No: FFRE45 Page 8 of 39 April 2008

21 bar 60 bar ISO 567 Cd ISO 567 Uncertainty Discharge E+00.0E E E E E E E E E+06 Pipe Reynolds Number Figure 0 β = 0.6 Orifice Plate with Drain Hole Discharge Tapping-Hole Pair A2/A bar 60 bar ISO 567 Cd ISO 567 Uncertainty Discharge E+00.0E E E E E E E E E+06 Pipe Reynolds Number Figure β = 0.6 Orifice Plate with Drain Hole Discharge Tapping-Hole Pair B2/B Project No: FFRE45 Page 9 of 39 April 2008

22 6 WET-GAS RESULTS The calculated wet-gas over-readings for the tests conducted on the various orifice plates used here are presented in Figures 2 to 27 for both tapping-hole pairs, A2/A and B2/B. The figures provide the over-readings obtained as functions of the Lockhart-Martinelli parameter and the gas densiometric Froude number. It should be noted, however, that the gas test flow conditions were specified in terms of the actual volumetric flow rate. The figures also include the predictions of the Murdock [2] and Chisholm [3] models, as described in section 3, and these curves can be seen highlighted in red and blue respectively. The gas Froude number range presented on the graphs was from 0. to 5 for the β = 0.4 and 0.42 plates over the operating pressure range of the tests. For the β = 0.6 plate the gas Froude number range was 0.45 to.94. Previous data has suggested that below an upstream gas Froude number of.5, the over-reading will not change very much because the gas-liquid flow pattern is relatively unchanging, being either stratified or stratified-wavy with only minimal entrainment of the liquid in the gas flow. In the case of this test programme, most of the upstream gas Froude numbers used were below the.5 limiting value, with only two flow rates giving gas Froude numbers above.5 for the β = 0.6 orifice plate tests. It is, therefore, somewhat surprising that for both the β = 0.4 and 0.42 orifice plate results (Figures 2-5 and 20-23) there is such a strong gas Froude number effect, with over-readings at the limiting Lockhart-Martinelli parameter value of 0.3 in the approximate range.32 to.4 over a gas Froude number range of 0. to 0.65 at 20 bar gauge, and approximately.3 to.35 over a gas Froude number range of 0.9 to 5 at 60 bar gauge. The reason for the spread in the over-reading with gas Froude number is unknown. Small gas Froude numbers (and small steps in the gas Froude number) are producing significant spreads in the over-reading value at a given Lockhart-Martinelli parameter, where none would be expected. It may be that because of the damming effect of the orifice plate the over-reading continues to change as the gas Froude number reduces from.5. For the β = 0.6 plate tests (both with and without the drain hole: Figures 6-9 and 24-27) there is almost no observable gas Froude number effect. This behaviour is more consistent with expectations based on previously published data and the upstream gas Froude number range used. The difference between the data obtained using the β = 0.4 and 0.42 plates and those obtained using the β = 0.6 plate obviously requires some explanation. Tests at different diameter ratios may well need to be performed to determine the interpretation of the current data sets. Visualisation tests could prove useful in determining what is happening. On all of the figures the Chisholm model predictions tend to track the higher gas Froude number over-reading curves, while also accounting for the change in the gas-liquid density ratio. Murdock is a fixed over-reading function (only dependent on the Lockhart-Martinelli parameter), and so while the over-reading data set encompasses the Murdock model prediction at 20 bar gauge, it does not do so at 60 bar gauge. Based on this data set, using the Murdock model at high pressure (i.e. high gas-liquid density ratio) would therefore produce a significant overcorrection of the gas flow rate over the range of gas Froude numbers tested. Project No: FFRE45 Page 20 of 39 April 2008

23 .45.4 Orifice Plate Over-Reading Fr(gas)=0. Fr(gas)=0.2 Fr(gas)=0.43 Fr(gas)=0.54 Fr(gas)=0.65 Murdock Chisholm Lockhart-Martinelli Parameter Figure 2 β = 0.4 Orifice Plate, Tapping-Hole Pair A2/A Over-Reading Curves at 20 Bar Gauge.45.4 Orifice Plate Over-Reading Fr(gas)=0. Fr(gas)=0.2 Fr(gas)=0.43 Fr(gas)=0.54 Fr(gas)=0.65 Murdock Chisholm Lockhart-Martinelli Parameter Figure 3 β = 0.4 Orifice Plate, Tapping-Hole Pair B2/B, Over-Reading Curves at 20 Bar Gauge Project No: FFRE45 Page 2 of 39 April 2008

24 .45.4 Orifice Plate Over-Reading Fr(gas)=0.9 Fr(gas)=0.38 Fr(gas)=0.76 Fr(gas)=5 Murdock Chisholm Lockhart-Martinelli Parameter Figure 4 β = 0.4 Orifice Plate, Tapping-Hole Pair A2/A, Over-Reading Curves at 60 Bar Gauge.45.4 Orifice Plate Over-Reading Fr(gas)=0.9 Fr(gas)=0.38 Fr(gas)=0.76 Fr(gas)=5 Murdock Chisholm Lockhart-Martinelli Parameter Figure 5 β = 0.4 Orifice Plate, Tapping-Hole Pair B2/B, Over-Reading Curves at 60 Bar Gauge Project No: FFRE45 Page 22 of 39 April 2008

25 .45.4 Orifice Plate Over-Reading Fr(gas)=0.45 Fr(gas)=0.67 Fr(gas)=0.89 Fr(gas)=2 Murdock Chisholm Lockhart-Martinelli Parameter Figure 6 β = 0.6 Orifice Plate, Tapping-Hole Pair A2/A, Over-Reading Curves at 20 Bar Gauge.45.4 Orifice Plate Over-Reading Fr(gas)=0.45 Fr(gas)=0.67 Fr(gas)=0.89 Fr(gas)=2 Murdock Chisholm Lockhart-Martinelli Parameter Figure 7 β = 0.6 Orifice Plate, Tapping-Hole Pair B2/B, Over-Reading Curves at 20 Bar Gauge Project No: FFRE45 Page 23 of 39 April 2008

26 .45.4 Orifice Plate Over-Reading Fr(gas)=0.77 Fr(gas)=6 Fr(gas)=.55 Fr(gas)=.94 Murdock Chisholm Lockhart-Martinelli Parameter Figure 8 β = 0.6 Orifice Plate, Tapping-Hole Pair A2/A, Over-Reading Curves at 60 Bar Gauge.45.4 Orifice Plate Over-Reading Fr(gas)=0.77 Fr(gas)=6 Fr(gas)=.55 Fr(gas)=.95 Murdock Chisholm Lockhart-Martinelli Parameter Figure 9 β = 0.6 Orifice Plate, Tapping-Hole Pair B2/B, Over-Reading Curves at 60 Bar Gauge Project No: FFRE45 Page 24 of 39 April 2008

27 .45.4 Orifice Plate Over-Reading Fr(gas)=0. Fr(gas)=0.22 Fr(gas)=0.44 Fr(gas)=0.66 Murdock Chisholm Lockhart-Martinelli Parameter Figure 20 β = 0.42 Orifice Plate, Tapping-Hole Pair A2/A, Over-Reading Curves at 20 Bar Gauge.45.4 Orifice Plate Over-Reading Fr(gas)=0. Fr(gas)=0.22 Fr(gas)=0.44 Fr(gas)=0.66 Murdock Chisholm Lockhart-Martinelli Parameter Figure 2 β = 0.42 Orifice Plate, Tapping-Hole Pair B2/B, Over-Reading Curves at 20 Bar Gauge Project No: FFRE45 Page 25 of 39 April 2008

28 .45.4 Orifice Plate Over-Reading Fr(gas)=0.9 Fr(gas)=0.38 Fr(gas)=0.77 Fr(gas)=7 Murdock Chisholm Lockhart-Martinelli Parameter Figure 22 β = 0.42 Orifice Plate, Tapping-Hole Pair A2/A, Over-Reading Curves at 60 Bar Gauge.45.4 Orifice Plate Over-Reading Fr(gas)=0.9 Fr(gas)=0.38 Fr(gas)=0.77 Fr(gas)=7 Murdock Chisholm Lockhart-Martinelli Parameter Figure 23 β = 0.42 Orifice Plate, Tapping-Hole Pair B2/B, Over-Reading Curves at 60 Bar Gauge Project No: FFRE45 Page 26 of 39 April 2008

29 .45.4 Orifice Plate Over-Reading Fr(gas)=0.43 Fr(gas)=0.65 Fr(gas)=0.87 Fr(gas)=.09 Murdock Chisholm Lockhart-Martinelli Parameter Figure 24 β = 0.6 Orifice Plate with Drain Hole, Tapping-Hole Pair A2/A, Over-Reading Curves at 20 Bar Gauge.45.4 Orifice Plate Over-Reading Fr(gas)=0.43 Fr(gas)=0.65 Fr(gas)=0.87 Fr(gas)=.09 Murdock Chisholm Lockhart-Martinelli Parameter Figure 25 β = 0.6 Orifice Plate with Drain Hole, Tapping-Hole Pair B2/B, Over-Reading Curves at 20 Bar Gauge Project No: FFRE45 Page 27 of 39 April 2008

30 .45.4 Orifice Plate Over-Reading Fr(gas)=0.76 Fr(gas)=5 Fr(gas)=.54 Fr(gas)=.93 Murdock Chisholm Lockhart-Martinelli Parameter Figure 26 β = 0.6 Orifice Plate with Drain Hole, Tapping-Hole Pair A2/A, Over-Reading Curves at 60 Bar Gauge.45.4 Orifice Plate Over-Reading Fr(gas)=0.76 Fr(gas)=5 Fr(gas)=.54 Fr(gas)=.93 Murdock Chisholm Lockhart-Martinelli Parameter Figure 27 β = 0.6 Orifice Plate with Drain Hole, Tapping-Hole Pair B2/B, Over-Reading Curves at 60 Bar Gauge Project No: FFRE45 Page 28 of 39 April 2008

31 7 DENSITY RATIO, DIAMETER-RATIO AND DRAIN HOLE EFFECTS As has been seen with other differential pressure meters, there is a small but clear effect of the gas-liquid density ratio on the over-reading obtained from an orifice plate. Figures show the orifice plate over-reading data rearranged to compare any effect of the gas-liquid density ratio that may be present. For both the β = 0.4 and 0.42 orifice plate tests (Figures 28, 29, 32 and 33) the spread in the over-reading data obscures the effect of the density ratio to some extent, but there is definitely a small effect present, showing itself as a reduction in the over-reading as the density ratio increases. For the β = 0.6 plate results (both with and without the drain hole; Figures 30, 3, 34 and 35), there is a clearer effect of the density ratio on the over-reading performance of the orifice plate, primarily due to the lack of an observed gas Froude number effect on the over-reading. There is also a noticeable effect of the tapping-hole pair location for the β = 0.6 plate. The A2/A tapping-hole pair has larger over-readings (particularly at 20 bar gauge) than the B2/B tapping pair at the same Lockhart-Martinelli parameter value. Figures 36 to 39 were created to help to determine if there is a clear effect of the orifice-plate diameter ratio on the observed over-readings. The data for all four wet-gas test runs have been included on the figures, and the individual data sets have had quadratic functions fitted through them to allow comparisons of the means of the data sets. However, comparison is still not that straightforward as for the nominally two diameter ratios used the gas Froude number ranges are different. A cursory examination of the figures shows that there is a diameter-ratio effect in evidence, but it is small and not particularly consistent. Looking at the data in more detail, in Figure 36 there is a noticeable separation at 20 bar gauge between the fitted curves for the β = 0.6 orifice plate, with and without the drain hole for the A2/A tapping-hole pair. There is also a separation between the β = 0.6 and 0.4/0.42 fitted curves, with the β = 0.6 plate curves having larger over-readings than the 0.4/0.42 plate curves. It should be noted, however, that this conclusion might be different if it were possible to test the 0.4/0.42 and 0.6 orifice plates over the same gas Froude number range. It is also noticeable that the β = 0.4/0.42 fits are almost identical. For the equivalent results for the B2/B tapping-hole pair (Figure 37), there does not appear to be much of an effect observable; however, this seems to be partly due to the fact that the results with the drain hole are much closer to those without a drain hole for the B2/B tapping-hole pair than for the A2/A tapping-hole pair. Differences between the fitted over-reading curves (and by inference the diameter ratio effect) are seen to reduce further at 60 bar gauge (Figures 38 and 39), mainly highlighting how the gas-liquid density ratio effect is causing the over-reading data both to both reduce in value and to converge, indicating a diminishing influence of diameter ratio as the gas-liquid density ratio increases. Although the effect is reducing, it is clear that an effect of diameter ratio appears to be present, particularly for the A2/A tapping-hole pair data sets. Again, the convergence of the data is partly due to the fact that the results with the drain hole are much closer to those without a drain hole for the B2/B tapping-hole pair than for the A2/A tapping hole. Project No: FFRE45 Page 29 of 39 April 2008

32 .45.4 Orifice Plate Over-Reading bar gauge 60 bar gauge Lockhart-Martinelli Parameter Figure 28 Effect of Gas-Liquid Density Ratio for the β = 0.4 Orifice Plate and the A2/A Tapping-Hole Pair.45.4 Orifice Plate Over-Reading bar gauge 60 bar gauge Lockhart-Martinelli Parameter Figure 29 Effect of Gas-Liquid Density Ratio for the β = 0.4 Orifice Plate and the B2/B Tapping-Hole Pair Project No: FFRE45 Page 30 of 39 April 2008

33 .45.4 Orifice Plate Over-Reading bar gauge 60 bar gauge Lockhart-Martinelli Parameter Figure 30 Effect of Gas-Liquid Density Ratio for the β = 0.6 Orifice Plate and the A2/A Tapping-Hole Pair.45.4 Orifice Plate Over-Reading bar gauge 60 bar gauge Lockhart-Martinelli Parameter Figure 3 Effect of Gas-Liquid Density Ratio for the β = 0.6 Orifice Plate and the B2/B Tapping-Hole Pair Project No: FFRE45 Page 3 of 39 April 2008

34 .45.4 Orifice Plate Over-Reading bar gauge 60 bar gauge Lockhart-Martinelli Parameter Figure 32 Effect of Gas-Liquid Density Ratio for the β = 0.42 Orifice Plate and the A2/A Tapping-Hole Pair.45.4 Orifice Plate Over-Reading bar gauge 60 bar gauge Lockhart-Martinelli Parameter Figure 33 Effect of Gas-Liquid Density Ratio for the β = 0.42 Orifice Plate and the B2/B Tapping-Hole Pair Project No: FFRE45 Page 32 of 39 April 2008

35 .45.4 Orifice Plate Over-Reading bar gauge 60 bar gauge Lockhart-Martinelli Parameter Figure 34 Effect of Gas-Liquid Density Ratio for the β = 0.6 Orifice Plate with a Drain Hole and the A2/A Tapping-Hole Pair.45.4 Orifice Plate Over-Reading bar gauge 60 bar gauge Lockhart-Martinelli Parameter Figure 35 Effect of Gas-Liquid Density Ratio for the β = 0.6 Orifice Plate with a Drain Hole and the B2/B Tapping-Hole Pair Project No: FFRE45 Page 33 of 39 April 2008

36 .45.4 Orifice Plate Over-Reading Beta 0.4 Beta 0.6 Beta 0.42 Beta 0.6 Drain Hole Lockhart-Martinelli Parameter Figure 36 Effect of Diameter Ratio for the Four Plates Tested for Tapping-Hole Pair A2/A at 20 Bar Gauge.45.4 Orifice Plate Over-Reading Beta 0.4 Beta 0.6 Beta 0.42 Beta 0.6 Drain Hole Lockhart-Martinelli Parameter Figure 37 Effect of Diameter Ratio for the Four Plates Tested for Tapping-Hole Pair B2/B at 20 Bar Gauge Project No: FFRE45 Page 34 of 39 April 2008

37 .45.4 Orifice Plate Over-Reading Beta 0.4 Beta 0.6 Beta 0.42 Beta 0.6 Drain Hole Lockhart-Martinelli Parameter Figure 38 Effect of Diameter Ratio for the Four Plates Tested for Tapping-Hole Pair A2/A at 60 Bar Gauge.45.4 Orifice Plate Over-Reading Beta 0.4 Beta 0.6 Beta 0.42 Beta 0.6 Drain Hole Lockhart-Martinelli Parameter Figure 39 Effect of Diameter Ratio for the Four Plates Tested for Tapping-Hole Pair B2/B at 60 Bar Gauge Project No: FFRE45 Page 35 of 39 April 2008

38 8 THE EFFECT OF THE DRAIN HOLE The effect of the presence of the drain hole is shown in Figures 40 to 43, which present the over-reading data for the β = 0.6 plate. On the whole, for a given tapping-hole pair the effect can be seen to be quite small, with the A2/A tapping-hole pair showing the larger differences in over-reading. Reviewing the figures, it is debatable whether or not a maximum average relative error of.2% can be considered to constitute a significant and real shift in the performance of the plate due to the drain hole, since the over-readings with pairs of tappings in only slightly different orientations without a drain hole can differ by a similar magnitude. Project No: FFRE45 Page 36 of 39 April 2008

39 .45.4 Orifice Plate Over-Reading Baseline Drain Hole Lockhart-Martinelli Parameter Figure 40 Comparison of the Baseline and Drain Hole Over-Readings for Tapping-Hole Pair A2/A at 20 Bar Gauge.45.4 Orifice Plate Over-Reading Baseline Drain Hole Lockhart-Martinelli Parameter Figure 4 Comparison of the Baseline and Drain Hole Over-Readings for Tapping-Hole Pair B2/B at 20 Bar Gauge Project No: FFRE45 Page 37 of 39 April 2008

40 .45.4 Orifice Plate Over-Reading Baseline Drain Hole Lockhart-Martinelli Parameter Figure 42 Comparison of the Baseline and Drain Hole Over-Readings for Tapping-Hole Pair A2/A at 60 Bar Gauge.45.4 Orifice Plate Over-Reading Baseline Drain Hole Lockhart-Martinelli Parameter Figure 43 Comparison of the Baseline and Drain Hole Over-Readings for Tapping-Hole Pair B2/B at 60 Bar Gauge Project No: FFRE45 Page 38 of 39 April 2008

41 9 CONCLUSIONS In dry gas, the presence of a drain hole shifted the orifice plate discharge coefficient in a positive direction by 2.4% for the A2/A tapping-hole pair and.4% for the B2/B tapping-hole pair. This is consistent with the shifts determined from tests both in water (on 8-inch orifice plates) and on a series of 4-inch orifice plates also tested in water and in dry gas []. In wet gas, the orifice plate over-readings corresponded more closely with the Chisholm model than the Murdock model, with the Chisholm model tracking the gas-liquid density ratio effect on the over-reading, particularly at the high end of the gas Froude number ranges tested. For the β = 0.6 plate no effect of the gas Froude number on the over-reading was found, which is consistent with the concept that below a gas Froude number of.5, the upstream gas-liquid flow pattern is of the stratified type, which should not vary significantly as the Froude number decreases below.5. However, this behaviour was not obtained from the β = 0.42 (and 0.4) plates, where larger spreads in over-reading were measured, particularly at the lower gas-liquid density ratio tested, over an upstream gas Froude number range smaller than that for the β = 0.6 plate. The reason for the behaviour of the smaller diameter-ratio plate is unknown. Further work is required. Differences in the β = 0.6 orifice-plate over-reading were also found between the A2/A and B2/B tapping-hole pairs, of the order of 2.4% at 20 bar gauge and within % at 60 bar gauge. No differences were obtained from the β = 0.4 (and 0.42) plate. It has also been found that the presence of a drain hole causes a small increase in over-reading relative to a plate with no drain hole. REFERENCES READER-HARRIS, M. J., and BARTON, N. The effect of drain holes in orifice plates on the discharge coefficient. TUV NEL Report No on Project No FFRE45. East Kilbride, Glasgow: NEL, MURDOCK, J. W. Two-Phase Flow Measurement with Orifices. Journal of Basic Engineering, pp , CHISHOLM, D. Flow of Incompressible Two-Phase Mixtures through Sharp- Edged Orifices. Journal of Mechanical Engineering Science, 9, No., CHISHOLM, D. Research Note: Two-Phase Flow through Sharp-Edged Orifices. Journal of Mechanical Engineering Science, 9, No. 3, 977. Project No: FFRE45 Page 39 of 39 April 2008