Russell James Department of Scientific and Industrial Research Taupo-ldairakei, New Zealand

Transcription

1 MEASUREMENT OF STEAM-TJATER FLOWS FOR THE TOTAL FLOW TURBIlJE Russell James Department of Scientific and Industrial Researc Taupo-ldairakei, New Zealand Hot water geotermal fields discarge steam-water mixtures, wic ave proved difficult to measure compared wit te dry steam from fields like Te Geysers and Larderello. Wit te development of te lip pressure metod, owever (James 1962), an accurate metod was derived wic could measure te flow wen a geotermal well discarges to te atmospere at sonic velocity. Fortunately most discarges from wells do in fact attain suc velocities, and as long as te entalpy of te mixture is known, te flow can be determined. Were te entalpy is unknown some oter measurement as also to be made in order to solve te two factors of flow and entalpy. By discarging te wole mixture into a silencer, te water portion can be estimated by means of a weir, and tis provides te second measurement (described in James 1966) required to solve bot unknowns. Te relationsip at te location of sonic flow as been empirically determined as follows: C were G 2 is te mass-velocity in lb/ft s o is entalpy in Btu/lb P is critical discarge pressure (lip pressure) in psia. C To convert units of G into units of W lb/ were d is te inside diameter of te discarge pipe in inces. Te Total Flow Turbine Tis approac entails te discarge of te wole unseparated steam-water mixture from te geotermal well troug nozzles onto te weel of a specially designed impulse turbine and tence into a separating condenser. A development program to solve te various problems involved is underway at te Lawrence Livermo: Laboratory, University of California. Wit te more conventional approac of separating te steam from te water and passing it into a steam turbine, flows can

2 be measured by means of orfice plate meters as described by te ASME (1959), altoug tere is some difficulty wit te ot water flow as tis is exactly at te boiling point and flas steam can appear in te line and falsify te flow estimate. Worse still, even a small quantity of carryover steam from te separator can wildly distort te readings and result in large errors (James 1975). Suc steam carryover is by no means uncommon; in fact, tere is some indication tat effective separation depends to an extent on small steam loss into te water pase due to vortexing witin te vessel. Te measurement problem can be overcome by external cooling of te water line or increasing te pressure ead by raising te level of te water witin te separator. How ten can we measure te flow of a steam-water mixture to a total flow turbine? Tis can be accomplised by means of te nozzle wic discar-ges onto te weel, so long as te mixture entalpy is known. As te LLL program is specifically directed to exploiting te large geotermal resources of te Salton Sea, te entalpies of te wells tere ap ear to be fairly stable and g draw on ot water wit temperatures of about 3 C (A.L. Austin and oters 1977). A canvergent-divergent nozzle is te means by wic te eat and pressure energy of te fluid is converted to kinetic energy for directing onto te turbine blades. Study of suc nozzles for te flow of supereated and saturated steam as been well documented in te literature and in textbooks on fluid flow and termodynamics (Streeter 1966). Sonic velocity is attained at te troat of suc nozzles and te rario between te troat pressure and te up-stream manifold pressure as been experimentally determined for steam. For supereated steam, te ratio is about.55 and for saturated (moist) steam is about.58 (Potter 1958). Unpublised tests by te autor on steam-water flows troug steam nozzles gave te same ratio of.59 as for saturated steam. Tis is confirmed by te tests undertaken by LLL in teir report on te program status (1977). Hence, it is clear tat so long as te mixture entalpy is known, togeter wit te nozzle troat pressure, ten te formula for te lip pressure given as equation (1) may be employed to determine te flow, wit P, taken as te troat pressure and d being te troat diameter. However, it would be unnecessary to attac a pressure tapping directly to te troat of te nozzle, as te manifold pressure just up-stream of te troat would be rater precisely controlled by a turbine governor valve and using te ratio of.58, te pressure at te troat were critical flow occurs (sonic velocity) can be estimated. Let suffix represent up-stream stagnation conditions witin te manifold and suffix t represent troat conditions were sonic flow occurs. From equation (l),

3 so Gt = 11 4 Pt Oog6 = = 6758 P o.96 1.lo As it is more usual to give flow troug nozzles in lb/s w lb/s = 36.8 dt2 P.96 O 1.12 (3) Illustrative Example Taking te LLL report (1977) on a nozzle test from teir Table 3-2, we ave Po = 367 psia, o Btu/lb Nozzle troat diameter calculated from te troat area of 6.87 (lor4 ft2 given on teir Figure dt =.35 inces diameter. From equation (3) above: = 36.8 (.35) (367).96 - = 1.31 lb/s 5261 * 12 Tis equals te flow-rate given for teir test conditions, so agreement looks very good. Saturated Water Flow Troug Nozzles - In observing steam-water flow troug nozzles we assume tat tere is steam present witin te up-stream manifold wit a volume exceeding tat of te associated water. In te example above, for instance, te LLL test gave a -2-

4 manifold dryness fraction of 14% quality and suc steam is necessary to give a ratio of.58 for Pt and for sonic conditions to prevail at te troat. - I Were an all-water state occurs in te manifold, even if it is exactly at te boiling point for te liquid pressure, te troat pressure as been found from tests at Wairakei to be greater tan.9 P. It appears tat te time duration is so sort wen te fluid passes from?e manifold to te troat tat none is available for bubble formation. Hence, only an all-water condition exists at te troat. Tis invalidates te conditions for sonic flow and tus te relationsip of equation (3) does not old. It is also difficult to sustain stable flow as te flas front witin te nozzle constantly "unts" from te troat to some distance downstream witin te convergent part, leading to pulsations of pressure and presumably cyclic flow variation. Tis migt create problems wen applied to a turbine as resonance effects migt follow. Terefore it may be necessary to execute some degree of trottling upstream of te nozzle manifold in order to permit some steam to exist witin tis camber and tereby stabilize te flow; peraps tis will allow sonic flow at te nozzle troat. If tis proves correct, measurement of te discarge may again be possible as for genuine steam-water flow described above. Field Test Conditions Tis example was based on values taken from a laboratory test using clean water and negligible non-condensible gas. Future tests in te Salton Sea geotermal field will involve steam-water mixtures were te water contains up to 3% wt of dissolved solids, wile te steam pase may contain substantial quantities of gas, mainly carbon dioxide (peraps up to 1% wt). Correction factors will ave to be estimated to allow for tese significant departures from te steam-.water employed in laboratory experiments. Grens (1975) as calculated te effect of intense brines on dryness fraction and entalpies of suc mixtures. Also te quantity of gas can be used to compute te partial gas pressure at te nozzle troat wic, togeter wit te vapor pressure of te steam, combines to give te total troat pressure. Obviously some field tests will be required to ascertain te effectiveness of tese ''corrections'' on true f low-rates. CONCLUSIONS Wit te oped-for commercial success of te total energy turbine in te near future, it will be necessary to ave a means of measuring te steam-water flow into te macine. As long as te entalpy of te flowing fluid is known, tere sould be no intrinsic difficulty in obtaining tis, as te nozzles temselves act as metering devices due to te penomena of sonic velocity at te troat. Hig gas concentrations in te steam pase, togeter wit ig cemical content in te water pase, require te use of t'correctionstt wic will ave to be determined from field tests to confirm teory. Clean steam-water mixtures appear to present no difficulties

5 REFERENCES ASME, 1959 Austin, A.L James. R James, R James. R Potter, P.J Fluid meters - teir teory and application. American SOC. Mec. Engrs., New York, U.S.A. Te LLL Geotermal energy program status report, Jan Jan Lawrence Livermore Laboratory, University of California. Steam-water critical flow troug pipes. Proc. Inst. Mec. Engrs., 176 (26):741. Measurement of steam-water mixtures discarging at te speed of sound to te atmospere. New Zealand Engineering, 21 (1):437. Possible serious effects of te presence of steam on ot-water flow measurements utilizing an orfice meter. Sec. U.N. Symp. on te Develp. and Use of Geotermal Resources, San Francisco, University of California. Power plant teory and design. Te Ronald Press, New York, U.S.A. Streeter, V.L Fluid mecanics. McGraw-Hill Book Co., New York, U.S, -22-