文丘里湿气测量(英文论文).pdf

flow measurement and instrumentation 12 (2002) 361372 /locate/fl owmeasinst wet gas metering with a horizontally mounted venturi meter r.n. steven a,b, aflow centre, nel, east kilbride, glasgow, g75 0qu, uk bdepartment of mechanical engineering, university of strathclyde, glasgow, uk received 15 may 2001; received in revised form 9 january 2002; accepted 9 january 2002 abstract wet gas metering is becoming an increasingly important problem to the oil and gas industry. the venturi meter is a favoured device for the metering of the unprocessed wet natural gas production fl ows. wet gas is defi ned here as a two-phase fl ow with up to 50% of the mass fl owing being in the liquid phase. metering the gas fl owrate in a wet gas fl ow with use of a venturi meter requires a correction of the meter reading to account for the liquids effect. currently, most correlations in existence were created for orifi ce plate meters and are for general two-phase fl ow. however, due to no venturi meter correlation being published before 1997 industry was traditionally forced to use these orifi ce plate meter correlations when faced with a venturi metering wet gas fl ows. this paper lists seven correlations, two recent wet gas venturi correlations and fi ve older orifi ce plate general two-phase fl ow correlations and compares their performance with new independent data from the nel wet gas loop with an isa controls ltd. standard specifi cation six inch venturi meter of 0.55 beta ratio installed. finally, a new correlation is offered. 2002 elsevier science ltd. all rights reserved. keywords: wet gas metering; two-phase fl ow metering; venturi meter; flow measurement 1. introduction wet natural gas metering is becoming an increasingly important technology to the operators of natural gas pro- ducing fi elds. with many gas fi elds coming to the latter stages of their production lives their previously dry gas fl ows are becoming “wet” when the heavier hydrocarbon components condense due to the reducing pressure in the production lines and changing conditions in the well itself can also cause water to be present in the fl ow. also, when some wells produced wet gas fl ows from the pro- duction outset the separator on the off-shore platform was sized accordingly, so with an increasing amount of liquid present in the wells later life these separators are undersized and the result is a wet gas leaving the separ- ators “dry” gas outlet to the dry gas meters. these oper- ators are also encountering wet gas fl ows when, due to their desire to utilize the existing off-shore infrastruc- tures to the maximum, they open “marginal” fi elds. present address: mccrometer inc., 3255 weat stetson avenue, hemet, ca 92545-7799, usa. tel.: +1-909-765-5344; fax: +1-909- 652-3078. e-mail address: richards (r.n. steven). 0955-5986/02/$ - see front matter 2002 elsevier science ltd. all rights reserved. pii: s0955-5986(02)00003-1 these are relatively small fi elds that produce wet gas fl ows in the vicinity of these older larger wells and the two wells fl ows are combined upstream of the now communal off-shore platform. that is, small fi elds that produce wet gas fl ows from the outset and would not be profi table if they required their own infrastructures (i.e. off-shore platforms with a separator) are being tapped by running this wet gas fl ow to the neighbouring main wells production pipeline upstream of the separator. there is therefore a necessity to meter this wet gas fl ow prior to the mixing point as traditionally the platforms are designed to have gas fl ow metered after the separ- ator. “wet gas” is a term commonly used in the industry but as yet no one defi nition has been agreed upon. as a result every operator, meter manufacturer and academic tends to have his own defi nition. these can vary con- siderably but there is general agreement that the term denotes a relatively small amount of liquid in a fl ow that is predominantly of gas. this research decided to adopt the shell expro defi nition of the wet gas range, which is a fl ow with a gas volume fraction greater than 95%. that is, the gas phase occupies in excess of 95% of the pipe volume. at the fl ow conditions typical in the north 362r.n. steven / flow measurement and instrumentation 12 (2002) 361372 nomenclature dthe pipe diameter atthe area of the venturi throat kg,l the gas and liquid fl ow coeffi cients (i.e. for each phase, the respective product of the velocity of approach, the discharge coeffi cient and the expansibility factor) m . g,l,tp the gas, liquid and two-phase fl owrates respectively ?pg,l the superfi cial gas and liquid differential pressures between the upstream and throat tappings respectively ?ptpthe actual two-phase differential pressures between the upstream and throat tappings rg,lthe gas and liquid densities respectively x the “quality” of a two-phase fl ow, i.e. the ratio of the gas to total mass fl owrate x the modifi ed lockhartmaretinelli parameter, defi ned as the square root of the ratio of ?p1& ?pg frgthe gas densiometric froude number usg the superfi cial gas velocity gthe gravitational constant (9.812 m/s2) sea natural gas production this loosely translates to the maximum liquid content for wet gas being when the liquid phase has equal mass to the gas phase. beyond this limit is considered to be general two-phase/multi- phase fl ow. currently, wet gas metering is a technology in its infancy. no meter design has yet to prove itself to be capable of metering wet gas fl ows to the accuracy desired by industry. however, one of the favoured met- ers for wet natural gas production fl ow metering is the venturi meter. like all differential pressure (dp) meters the venturi meter readings of the wet gas fl ow are adversely affected by the liquid presence. that is, the liquid presence directly affects the pressure differential read by the venturi between the upstream and throat pressure tappings. therefore, in order to derive the cor- rect gas fl owrate a correlation needs to be applied. there are only two wet gas venturi correlations known to the general industry and these have only been available for the last few years. as venturis have been used long before this for metering wet gas fl ows traditionally industry used general two-phase fl ow orifi ce plate meter correlations due to a lack of any alternatives. the current problem facing operators is that nobody knows which of the existing correlations is the most accurate when applied to wet gas venturi meters. there is a distinct lack of independent data to check the performance of each correlation. all existing data has been used in the creation of the existing correlations. this paper uses independent data obtained from the nel wet gas loop with an installed standard north sea specifi cation venturi supplied by isa controls ltd to check the performance of these two existing wet gas venturi meter correlations. (it should be noted that the venturi had two non-standard specifi cations which were that the pressure tappings were positioned at the top of the meter only to stop fl ooding and there were two extra tappings downstream of the diffuser.) selected orifi ce plate meter correlations known to have been used or available for use by operators prior to these wet gas ven- turi meter correlations existence were also included in this comparison. after this comparison trends in the data are discussed and a new correlation is offered that more accurately fi ts the isa controls venturi meter geometry. unfortunately, due to the lack of both new independent data and the unavailability of the small quantity of exist- ing data used to create the two existing wet gas venturi correlations it has not been possible to compare this new correlation with other data sets. 2. differential pressure meter correlations before the existence of the two wet gas venturi corre- lations industry was forced to choose between existing general two-phase fl ow orifi ce plate meter correlations. of the many that exist (a good summary is given by lin 1) this research judged fi ve to be suitable for use with actual production wet natural gas fl ows. the others were disregarded as the data used to create them was judged unsuitable, e.g. the liquid to gas fl ow ratio, the fl uid type combination,thepipediameter,thepressure,the fl owrates, etc. not being within reasonable agreement with actual gas production fl ows. it should be noted that the following fi ve orifi ce plate meter correlations did not have perfect matches of test to actual conditions either but were judged to be closer than the others. (the choice was therefore subjective.) these correlations all work on the same principle of using the dp meter single phase equation (eq. 1) and then applying a correction factor based on the liquid quantity to correct for the fact that in wet gas fl ows a two-phase differential pressure ? 363r.n. steven / flow measurement and instrumentation 12 (2002) 361372 (?ptp) is read instead of the single phase pressure differ- ential (?pg). m . g? kgat?2rg?pg (1) these fi ve orifi ce plate meter correlations and the two venturi meter correlations all assume that the fl ows are incompressible, that there are no appreciable thermodyn- amic effects and the liquid fl owrate is initially known. also, the authors of these correlations assume that the difference between the actual gas mass fl ow and the indi- cated gas mass fl ow is due to the effect of the liquid presence alone. that is, any dry gas metering errors were ignored. the fi ve orifi ce plate correlations here are. 2.1. the homogeneous fl ow model the homogeneous fl ow model treats the two-phase fl ow as if it were a single-phase fl ow by using a homo- geneous density expression (eq. 2) which averages the phase densities so that the single-phase orifi ce plate meter equation can be used (i.e. eq. 1). 1 rh ? x rg ? 1?x rl (2) where x is the mass quality, rhis the homogeneous den- sity and subscripts l and g are for liquid and gas respectively. therefore substituting this homogeneous value for density into eq. (1) and replacing ?pgwith ?ptpand rearranging gives eq. (3). m . g? x.? kgat?2rg?ptp ? rg rl ? x?1?rg rl? (3) (note: in dry gas (i.e. x ? 1) eq. (3) reduces to eq. (1) as ?ptp? ?pg). note that unlike the other correlations discussed in this paper the homogeneous model is not actually a cor- relation as no data was used in its creation. also unlike the other correlations it takes no account of the fl ow pat- tern. many researchers now considered it important to take account of the fl ow pattern when correcting the error in a dp meter caused by the presence of liquid. this is because although the physical mechanisms involved in the phase interaction during two-phase fl ow through a venturi are not well understood it is clear that the fl ow pattern affects the pressure loss in the fl ow and therefore directly effects the pressures read by the meter. the most recent fl ow pattern map (see the shell expro flow pattern map 2) and the semi-empirical fl ow pat- tern prediction method (see the taitel and duckler 3) predict that typical wet natural gas production fl ows will have annular dispersed (or “mist”) fl ows. that is, the liquid is likely to be entrained in droplet form in the gas fl ow. (it should be noted here that horizontal and vertical fl ows of otherwise similar conditions have different fl ow patterns and hence wet gas dp meter correlations are restricted to the orientation of the meter used to collect the data sets used in their creation. this paper discusses horizontal fl ow only.) 2.2. the murdock correlation the murdock correlation 4 is based on orifi ce plate meters and it was formed with a large data set encompassing general two-phase fl ow and it is therefore not restricted to wet gas fl ows. murdocks method was to consider the two-phase fl ow to be separated (or “stratifi ed”) fl ow. this was the fi rst indirect indication in a published paper that the fl ow pattern is important when predicting a dp meters liquid induced error. how- ever, it should be noted that the modeled fl ow pattern is not the fl ow pattern that typically exists in wet natural gas production. the murdock correlation is given as eq. (4). m . g? kgat?2rg?ptp 1 ? 1.26m . l m . g? kg kl? rg rl ? kgat?2rg?ptp 1 ? mx (4) note that x is a modifi ed version of the lockhartmarti- nelli parameter as it is the ratio of the superfi cial fl ows momentum pressure drops and not the friction pressure drops as in the original defi nition by lockhart and marti- nelli. murdocks defi nition is: x ?pl ?pg ?m . l m . g? kg kl? rg rl (5) the value 1.26 represents the gradient of a best fi t line through all murdocks data plotted on the graph ?ptp/?pgvs. x. hence murdocks correlation factor is a function of x alone. 2.3. the chisholm correlation chisholm published a general two-phase orifi ce plate meter correlation 5 and then later improved it for the case of higher quality two-phase fl ows (i.e.x?1) 6. chisholms model assumes stratifi ed fl ow and the shear force at the boundary is directly considered. this resulted in the correlation allowing for the effect of pressure independently of the modifi ed lockhartmarti- nelli parameter (x). the chisholm correlation offered in 6 is given as eq. (6). ? 364r.n. steven / flow measurement and instrumentation 12 (2002) 361372 m . g? kgat?2rg?ptp ?1 ? rl rg? 1/4 ?rg rl? 1/4? x ? x2 (6) note that the chisholm correlation factor is a function of x and pressure (through the gas density term). 2.4. the lin equation the lin correlation 7 is for general stratifi ed two- phase fl ows through orifi ce plate meters. like chish- olm, lin includes the effect of shear between the phases and the correlation allows for the independent effects of pressure and liquid mass content. the lin correlation is given as eq. (7) with one of the terms (i.e. the “shear function”) expanded in eq. (8). m . g? klat?2rl?ptp ?m . l m . g? q ?rl rg (7) where: q ? 1.48625?9.26541(rg/rl) ? 44.6954(rg/rl)2 ?60.615(rg/rl)3?5.12966(rg/rl)4(8) ? 26.5743(rg/rl)5 note that lin chose to use the liquid single phase equ- ation in the numerator as he was dealing with general two-phase fl ow. 2.5. the smith & leang correlation the smith & leang correlation 8 is formed for ori- fi ce plate and venturi meters using the concept of a “blockage factor”. that is, eq. (1) can be altered to take account of the liquid presence by introducing a para- meter that accounts for the partial blockage of the pipe area by the liquid. the letters bf denote this parameter. eq. (9) gives the bf factor and eq. (10) gives the smith and leang correlation. bf ? 0.637 ? 0.4211x?0.00183 x2 (9) and m . g? kgat(bf)?2rg?pg (10) hence, the smith and leang correlation corrects for the liquid induced error by a correction factor that is a func- tion of the fl ow quality (x) alone. the two more recent wet gas venturi meter corre- lations are. 2.6. the modifi ed murdock correlation in 1998 phillips petroleum informed this author that they had logged wet gas venturi data from an actual production well and had then used the data to update the murdock correlation (i.e. change the gradient m from 1.26 to 1.5.) the resulting correlation was used in-house and never published. the pressure was 45 bar but no other parameters are known. the correlation is given as eq. (11). m . g? kgat?2rg?ptp 1 ? 1.5m . l m . g? kg kl? rg rl ? kgat?2rg?ptp 1 ? mx (11) 2.7. the de leeuw correlation the de leeuw correlation is the only venturi wet gas correlation yet published. de leeuw claims the liquid induced error in the gas fl ow prediction is not only dependent on the pressure and the lockhartmartinelli parameter but also the gas densiometric froude number (frg). eq. (12) shows the gas densiometric froude num- ber calculation. frg? usg ?gd? rg rl?rg (12) de leeuws correlation is given in the form of chisholms correlation with the constant of 1/4 replaced by a para- meter denoted as n. de leeuw claims that n is solely a function of the gas densiometric froude number (frg) as shown in eqs. (13a) and (13b): n ? 0.41 for 0.5?frg?1.5(13a) n ? 0.606(1?e?0.746frg) for frg?1.5(13b) the fact that there are two values of nis of interest. according to the shell expro two-phase fl ow pattern map 2 the gas densiometric froude number value of 1.5 which divides eqs. (13a) and (13b) is on the bound- ary of two different fl ow patterns. hence, de leeuw is claiming the fl ow pattern plays an important part in the magnitude of the error induced by the gas being wet. the de leeuw correlation is given as eq. (14). m . g? kgat?2rg?ptp ?1 ? rl rg? n ?rg rl? n? x ? x2 (14) it should be noted that de leeuw used a simplifi ed defi - nition of the modifi ed lockhartmartinelli parameter by assuming the superfi cial fl ows fl ow coeffi cients to be equal and hence they cancel in eq. (5). therefore, pro- ? 365r.n. steven / flow measurement and instrumentation 12 (2002) 361372 vided the meter geometry, the fl uid properties, the liquid fl owrate, the pressure, the single phase discharge coef- fi cientsandthedifferentialpressurebetweenthe upstream and throat tappings are known an iteration pro- cedure can predict the gas mass fl owrate for each of the above correlations. 3. the nel wet gas loop tests the comparison of these existing correlations and the development of the new correlation presented in this paper were achieved by the use of independent data obtained from the new wet gas loop at nel. an isa controls standard north sea specifi cation 6” venturi meter with a 0.55 diameter (or “beta”) ratio of 6 mm pressure tappings was the meter installed. the upstream pressure tapping and the throat pressure tapping lengths were approximately 1809 and 210 mm respectively. this system uses nitrogen and a kerosene substitute as the fl uids simulating wet natural gas