PROCEEDINGS, Thrty-Frst Workshop on Geothermal Reservor Enneern Stanord Unversty, Stanord, Calorna, January 3-February 1, 26 SGP-TR-179 DOWNHOLE ENTHLPY MESUREMENT IN GEOTHERML WELLS Ell Julusson, Roland N. Horne Stanord Unversty, Department o Petroleum Enneern Green Earth Scences Buldn, 367 Panama Street Stanord, C, 4935-222, US e-mal: ellj@stanord.edu BSTRCT dvances have been made n the onon research to nd a way to measure enthalpy downhole n eothermal wells. The project has thus ar revolved around determnn applcable ways to determne the presence o ar vs. water, whch could ultmately lead to an estmate o the vod racton and enthalpy. The measurement prncples tested have been based on temperature, resstvty and optcal transmssvty. Successul results utlzn cross correlaton technques have lead to qute accurate estmates o bubble velocty usn both resstvty measurements and optcal measurements. However, so ar, temperature measurements have not proven to be successul. Prelmnary testn based on resstvty propertes o two phase low or determnaton o vod racton has beun. Future work ncludes dervn correlatons between vod racton and resstvty usn a new electrode desn whch looks outward rom an n-stu probe nto the well bore. Fnally, the possblty o cross correlatn the snal rom two such electrode setups (spaced a known dstance apart) s ben nvestated n the hope o obtann the vapor velocty. INTRODUCTION Downhole measurement o enthalpy n eothermal wells s o nterest to the ndustry or several reasons. For example, the enthalpy prole o a well could provde useul addtonal data or constrann reservor models by hstory matchn and reservor perormance montorn. ddtonally abrupt chanes n the prole would help reveal ractures and quanty the power output rom each racture drectly. The project s very challenn due to the problem o measurn o two phase low rates over a rane o low remes. It s urther complcated by the act that the measurement must be done n-stu and the sensor must be able to uncton at temperatures up to 35 C. t ths temperature, most electroncs wll al. Hence, ether a mechancal soluton must be ound or the electroncs must be specally desned to survve the downhole envronment. Successul applcatons have been desned or temperature, pressure and spnner measurements, where the electroncs are contaned n a vacuum lask and thereby solated rom the heat. However, the spnner measurements have not proven to ve a very accurate low descrpton. Recent developments o optcal ber technoloy have also brouht new ways to measure pressure and temperature downhole but a means to quanty the addtonal low parameters needed to drectly determne the enthalpy s not avalable. The enthalpy rate, as reerred to n ths paper, s dened as the amount o nternal enery (U) plus the compressve enery (PV) passn throuh a secton o the wellbore over a unt tme. Thus, a drect measurement o the enthalpy rate o a two phase low would requre knowlede o the temperature, vod racton and low rate o both phases. In practce t has proven dcult to develop sensors that can accurately predct the low rates o each phase n a two phase low over all low remes. Hence, the ocus o ths research project has been to look at ways to measure the vod racton and low rate o one o the phases, over a lmted rane o low remes. ter all, an estmate o these two parameters, n conjuncton wth pressure and temperature measurements and the al low rate at the well head would be sucent to dene a unque enthalpy prole. THEORY Enthalpy s a property o a system that can be dened (per unt mass) as: h u + Pv [kj/k] (1) Here u s the nternal enery o the system per unt mass, P s the pressure and v s the specc volume. Enthalpy s a thermodynamc property and can thereore be ound rom P-vs.-T relatons ven two o the parameters P, v and T. For lown luds t s
n most cases easest to evaluate P and T, however at saturaton condtons the temperature and pressure become xed wth respect to each other. Hence the specc volume, v, must be determned to nd the enthalpy. t saturaton (boln) condtons the lud s partally evaporated so to ve an estmate o the specc volume the vod racton needs to be determned. In ths case, lttle varaton would be expected n the vertcal drecton so t can be dened as: V V α [-] (2) where V denotes volume and denotes horzontal cross sectonal area. From ths denton t can be shown the vapor mass racton can be related to the vod racton by: m m α v 1+ (1 α) v x [-] (3) lq Here m and m are the mass o the vapor and the al lud mxture respectvely. Gven ths racton and the saturaton pressure or temperature, the al specc volume can be ound, or more drectly, the enthalpy usn the steam tables. h h + xh @ Tsat [kj/k] (4) Here h s the enthalpy o the saturated vapor and h s the enthalpy o vaporzaton. Lookn at a lown lud t s oten useul to know the rate o enthalpy (e.. n eothermal enery utlzaton) lown throuh a xed volume or cross secton. To be able to determne ths, the low rate o the lud must be known. I the lud s lown n two phases the low rate o each phase must be known. In vertcal low the presence o buoyancy and rctonal orces reatly complcates the relaton between the veloctes o the two phases. Some emprcal relatons have been suested, e.. by Huhmark and Pressbur (1961) or a certan rane o dameters ( to 2.34 nches). Obvously ths sort o a relaton would be very useul because the only the low rate o ether phase would have to be measured. However, snce the relaton s emprcal and has not been valdated or all practcal cases, t should be used wth cauton. Presently, downhole enthalpy s usually estmated usn wellbore smulators. In that process a pror estmate o the number and poston o ractures s needed. Ths s normally obtaned rom radent chanes n temperature proles measured n the well just ater drlln s completed (.e. when the wellbore s stll relatvely cold). When the ractures have been dented, an estmate o the low and enthalpy o the lud comn out o each racture needs to be determned. Temperature and pressure proles or the well can then be calculated usn the wellbore smulator. The low and enthalpy rom each racture s determned nally by the values that ve the best match between the measured and calculated temperature and pressure proles. However, n many cases the soluton to ths problem s nonunque. Thereore, an estmate o a snle addtonal parameter (say vod racton or as low rate) could help to solve the problem unquely and mprove the estmate o the downhole enthalpy. In summary, to be able to measure enthalpy o a lown lud drectly at saturaton condtons one needs to measure ether temperature or pressure, vod racton and both the low rates o the vapor phase and the lqud phase. However, ndrect estmates o the downhole enthalpy prole rom wellbore smulatons mht be urther constraned ven measurements o only a ew o these parameters. Fure 1: P-v-T relatons or a substance. t saturaton (vapor-lqud) condtons P and T become xed wth respect to each other. (http://hyperphyscs.phy-astr.su.edu) Measurement alon a snle lne Usn resstvty, optcal transmssvty or some other means o obtann a snal aected by vapor-lqud chanes at a pont s a method that s lkely to work. n analyss o the problem ollows.
Fure 2: Cross secton o ppe wth vapor-lqud low. resstvty measurement (or equvalent) s ben taken at multple ponts across the measured lne. The oal s to nd the enthalpy rate.e. enery passn throuh the cross sectonal area [m 2 ] (5) + (here s the area occuped by lqud and s the area occuped by vapor bubble ) per tme unt. The enthalpy o the saturated vapor (h ) and lqud (h ) can be ound rom the steam tables and ven the low velocty (u) o each phase the low rate can be ound rom q q u u α [m 3 /s] (6) u [m 3 /s] (7) u ( 1 α) Then the al enthalpy rate or each phase can be ound as h H q & [J/s] (8) v h H q & [J/s] (eq.9) v Here the specc volumes v and v can be obtaned rom the steam tables, and the al enthalpy o the mxture s: H& H& + H& h αu v h ( 1 α) u + v [J/s] (1) So the averae racton o the cross secton occuped by steam needs to be determned,.e. the vod racton α [-] (11) Suppose a measurement s taken at multple ponts alon a lne across a cross secton o a ppe (Fure 2). ssumn the bubbles wll low randomly throuh the cross secton o the ppe, the racton o the lne that s occuped by vapor, averaed over tme, would ve the averae racton o steam on throuh the whole cross secton (Fure 3). Fure 3: The measured lne, averaed over tme, wll lkely orm a symmetrc dstrbuton o vapor concentraton. Lhter blue means more tme on averae occuped by vapor. I B(r) s dened as the tme the measurement lne s occuped by vapor at radus r dvded by the al tme the measurement s taken then as tme oes by B(r) wll orm a smooth symmetrc dstrbuton. Interatn the dstrbuton, B(r), over the cross
sectonal area ves the area occuped by steam on averae,,av and dvdn by the al area ves the ormula or the averae vod racton α, av D / 2 8 D 2 2πrB( r) dr πd D / 2 2 / 4 rb( r) dr [-] (12) Ths shows that t would suce to measure the presence o as vs. water at a ew ponts alon a snle lne across the ppe dameter to determne the averae vod racton. EXPERIMENTS Experments testn the applcablty o usn temperature, resstvty and optcal sensors were carred out n a smple setup o semented ar-water low. Temperature was measured wth a ast response (~2 ms) thermocouple (type: Omea 5TC-TT-T-4-36). resstvty sensor was made by xn two electrodes (open ended wres) a small dstance apart (~2 mm). When the sensor was placed n the low path the voltae drop across the electrodes would depend on the resstance o the surroundn medum. The optcal sensor conssted o a phoransstor on one sde o the tube and a lht source on the opposte sde. When a bubble passed, less lht passed throuh and the resstance o the phoransstor ncreased. schematc daram o the crcut or the resstvty and optcal sensors s shown n Fure 4. schematc daram o the experment s shown n Fure 5. The ure shows how a mxed ar-water low (lown vertcally upwards) passes three types o sensors, at three derent spots. t spots 1 and 2 we have an optcal, temperature and resstvty measurement. t spot 3 we only have a temperature measurement. ter the lud mxture passed the sensors t was separated and the quantty o each phase was measured over a specc tme nterval to nd the ndvdual low rates. Ths basc conuaton was used wth low tubes o two derent szes. Frst a 1/8 n. dameter brass tube was used, n whch semented ar-water low could be assumed. 1 n. tube n whch a snle ully ormed bubble would low throuh the cross secton was later used. In ths case the lenth o the tube compared to the sensor spacn was too short such that the bubble pattern had chaned sncantly on the way rom one sensor to the other. Thereore the results n the 1 n. tube were used more qualtatvely to asses the applcablty o usn one sensor type vs. the other. The data acquston proram was developed n LabVew. The proram loed all seven sensors smultaneously at 1 khz and wrote the results to a scaled bnary output le. The output le was then decoded n Matlab or urther data processn. Each test run was loed or approxmately 1 seconds. There were some problems wth 6 Hz electrcal nose n the measurements. Groundn the power source made a partcularly lare mprovement n that respect but nevertheless the nose n the temperature snal was never reduced to less than ±.5 C. Moreover, there were some ssues reardn cross talk between the two resstvty sensors.e. a luctuaton n the snal rom sensor 1 was sometmes seen at the same tme n sensor 2. Ths phenomena s dscussed urther n the next secton. Fure 4: crcut daram or the phoransstor and resstvty sensors. s the daram shows, a snle 12V DC source drves the whole crcut. When an ar bubble passes one o the sensors, the resstance o the electrode/phoransstor chanes, hence a derent voltae drop s measured across the reerence resstor connected to the termnal block.
Fure 5: schematc o the experment setup. vertcal ar-water low s nvestated by three types o sensors. smple low meter then measures the low rate o each phase separately. DT NLYSIS Bubble velocty In order to drectly calculate the enthalpy rate o a two-phase low, the steam and lqud averae veloctes need to be determned. part o that would be to nd the velocty o the steam bubble as t traveled up the borehole. Usn the snals obtaned rom two sensors, spaced a known dstance apart, ths bubble velocty could be nerred. Gven the dstance between the sensors, L, the mean bubble velocty would be L v. [m/s] (13) t t In the case o our experment, the tme, t t, t took the bubble to travel rom one sensor to the other,.e. the tme sht between the patterns measured by each sensor s what needed to be ound. For slow and dspersed bubble low (Fure 6) ths could easly be seen rom a quck look at the snals but when the bubble low became more rapd (Fures 7 and 8) the pattern n the snal became harder to dscern. 1 1.3 1.2 1.1.6.5 9.6 9.4 9.2 Resstvty1 1.1 1.2 1.3 1.4 1.6 1.7 1.8 1.9 2 Phorans1 1.1 1.2 1.3 1.4 1.6 1.7 1.8 1.9 2 1 Resstvty2.32.3.28.26.24.22 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Phorans2 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Tme [s] Fure 6: Snals obtaned rom the resstvty and optcal sensors at two derent locatons The bubble low was relatvely slow and dspersed. Hence a bubble pattern s clearly detectable and the tme sht can be estmated vsually. Ths wll be reerred to as Plot test 2.
1 9.6 Resstvty1.1.2.3.5.6.7.8.9 1 Phorans1.6.8.5.1.2.3.5.6.7.9 1 Resstvty2 9.6.9 1 9.4 9.2.1.2.3.5.6.7.8.3 Phorans2.1.2.25.3.5.6.7.8.9 1.2 Tme [s] Fure 7: Snals rom the resstvty and optcal sensors. s seen by comparson to the snals n Fure 6, the bubble low s ettn more rapd and the pattern s now harder to dscern. Ths wll be reerred to as Plot test 1. 1.2 1 9.6.5.3 1.2 1 9.6 9.4.25.2 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 Phorans1 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 Resstvty1 Resstvty2 Phorans2 stochastc n nature. Ths s most oten the case n turbulent two-phase lows. The method was tested on each o the snals and the results or Plot test 2 and 3 are shown n Fures 9 and 1. Sample cross-correlaton.7.6.5.3.2.1 -.1 -.2 Tme sht.279 [s] Tme sht.283 [s] -.3 -.5.5 Tme ncrements-τ [s] Fure 9: Ths raph o R xy (τ) or each sensor type (test correspondn to Fure 6) shows a clear maxmum at τ.28 s. Phoransstor data are n reen and resstance data are n maenta. Ths s to very that the cross-correlaton method works..15 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 Tme [s] Fure 8: Here we see the response rom the same sensors as n used prevously but now the bubble low s much more rapd. The bubble pattern s very hard to dscern. Ths wll be reerred to as Plot test 3. Cross correlatons relatvely smple but robust method to nd the tme sht n the snals was to calculate the crosscorrelaton uncton (XCF) between the two snals. The cross-correlaton uncton s a uncton o the correlaton coecent between the two snals, where one o the snals has been shted n tme. The tme at whch the XCF has ts maxmum value then corresponds to the tme sht between the two snals. The XCF s dened as ollows: R xy 1 t ( ) ( x( t τ ) x)( y( t) y) dt t τ (14) Here x and y are the two snals, x and y are the snal averaes over the entre measurement nterval, t, and τ s the tme sht. Ths method s commonly used n low metern technoloy and has worked well to measure concentraton snals that are Fure 1: Ths raph o R xy (τ) or each sensor type (test correspondn to Fure 8) shows a clear mnmum at τ.11 s. The erroneous value o -.1 s s predcted by the resstvty sensor because o crosstalk between the electrodes. It was shown that the tme sht could be ound surprsnly clearly and accurately by ths method. The only case n whch the method broke down, was when measurn the rapd bubble low usn the resstvty sensors. In that case the maxmum correlaton was ound or tme sht τ. Ths erroneous result was ntroduced because o crosstalk between the two electrode sensors. Ways to resolve the problem are dscussed n a later secton.
Scaled snal derences second method to determne the tme sht was also devsed, and s presented here to ve comparson to the results obtaned rom the cross-correlaton uncton. The basc dea was to nd the tme sht that ves the mnmum derence when one snal was subtracted rom the other. Snce the snals were not necessarly at the same scale they had to be scaled by the rato o the averaes o the two snals, beore takn the derence. The tme sht between the snals was the value that mnmzed ths quantty. More compactly, the oal was to nd τ subject to: x mn ( τ ) x( t) y( t + τ ) y xy (15) Snce the data sets at hand were usually not very lare t was easy to calculate the derence xy as a uncton o τ on some reasonable nterval and nd the tme sht correspondn to the mnmum value n that dataset. Fures 11 and 12 show xy(τ), calculated rom the snals n Plot tests 1 and 3. The results o ths method were very consstent wth those rom the cross-correlaton technque. In these two cases t seems that ths method s more consstent, snce the varablty between the tme shts predcted by each sensor s smaller. Mean derence between snals.12.11.1.9.8.7.6.5 Tme sht.18 [s].4 Tme sht.179 [s].3.2.6.8 1 1.2 1.4 1.6 1.8 2 Tme ncrements [s] Fure 11: Ths raph o xy(τ) or each sensor type (test correspondn to Fure 7) shows a clear mnmum at τ.18 s. Phoransstor data are n reen and ressvty data are n blue. Mean derence between snals.18.16.14.12.1.8.6 Tme sht.19 [s] Correct tme sht value Tme sht.1 [s] Erroneous tme sht value Tme sht.18 [s].4.2.6.8 1 1.2 1.4 1.6 1.8 2 Tme ncrements [s] Fure 12: Ths raph o xy(τ) or each sensor type (test correspondn to Fure 8) shows a clear mnmum at τ.11 s. The erroneous value o.1 s s aan predcted by the resstvty sensor because o crosstalk between the electrodes. Vod racton and bubble eometry One o the more mportant quanttes that one would lke to measure n downhole wellbore low s the vod racton. To that end, estmatn the bubble requences and ben able to count the bubbles becomes mportant. Ths proved nontrval usn the electrcal resstvty measurements, due to a low snal-to-nose rato and crosstalk eects. Ths secton ntroduces some o the problems nvolved and the methods that were used or the analyss. Snce the experment dealt wth semented low the bubble eometry could be modeled as a cylnder o dameter equal to the tubn dameter and lenth L b, whch could be calculated as L b vtb,, [m] (16) where v s the bubble velocty (as obtaned earler) and the t b, s the tme t took bubble number to pass the sensor. nother property arsn rom the act that the low was semented was that the water and ar low veloctes were the same, and thereore the vod racton could be calculated as α L L b, L t L t b, / v b. / v [-] (17) where L s the al lenth o lud (ar and water) that passed throuh the measured secton and all other quanttes are as dened earler.
resstvty measurements (Fure 15). Thus, ths method was abandoned or the tme ben, keepn n mnd that t mht become easble the response tme and accuracy o the sensors could be mproved. 3 25 Values correspondn to presence o water 2 Frequency 15 1 Values correspondn to presence o ar 5 Threshold value?.25.3.35 5.5.55.6.65.7 Sensor measurement value [V] Fure 14: hstoram o measurements made wth phoransstor 1 at an ntermedate low rate. It s not clear where the threshold value or transton between ar and water measurements les. 2 Fure 13: smpled model o vertcal semented low. By assumn that the water and ar veloctes are the same, the vod racton can be calculated as the rato between the al tme the sensor measures the presence o ar and the al measurement tme. Gven these assumptons, the al tme that bubbles were present was all that was needed to calculate the vod racton. However, ths quantty was not easly determned rom the measurements because o the relatvely slow response tme o the sensors. Moreover, n the case o the resstvty measurements, the low snal-to-nose rato and the crosstalk complcated the analyss stll urther. Two basc methods were nvestated to ner consstent estmates o the vod racton between all our sensors. Threshold rom hstoram In the rst method a hstoram o the measurement ponts was made and some ntermedate value that could correspond to a transton value between ar and water measurements was to be determned. Ths ntermedate value had to be somewhere between the two peaks correspondn to measurement values or ar and water as shown n Fure 14 (data taken rom Plot test 1). The threshold value or transton between ar and water measurements was not dened clearly rom the hstoram or the phoransstor measurements and the stuaton dd not mprove by lookn at the Freqency 18 16 14 12 1 8 6 4 2 Values correspondn to presence o ar? Values correspondn to presence o water Threshold value? 9 9.2 9.4 9.6 1 1.2 Sensor measurement value [V] Fure 15: hstoram o measurements made wth resstvty sensor 1 at an ntermedate low rate. It s hard to determne whch snals correspond to presence o ar and where to put the threshold value or the transton between the luds. Movn averae threshold The second method nvestated was to draw a threshold lne that vared n tme based on local varatons n the snal. One advantae o usn a method lke ths was that t mht be useul n stuatons the propertes o the lud were chann n tme (e.. the measurement tool s ben lowered downhole, the resstvty o the lud would vary wth depth and tme). The threshold lne was drawn as a one second movn averae (note that the actual snal had also been ltered to remove the 6 Hz electrcal nose). Fure 16 llustrates data rom the phoransstor and Fure 17 has data rom the resstvty sensor (data taken rom Plot test 1).
Snal Water() or r(1) Fure 16: movn averae threshold used to determne whether the snal rom a phoransstor corresponds to ar or water. Snal Water() or r(1).7.6.5.3 1.8.6.2 1.1 1 9.9 9.7 1.8.6.2 Movn averae threshold or phoransstor 1 n semented bubble low 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 Tme [s] r-water dstrbuton ctual snal (ltered) 1 second movn averae 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 Tme [s] Movn averae threshold or restvty sensor 1 n semented bubble low ctual snal (ltered) 1 second movn averae 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 Tme [s] r-water dstrbuton 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 Tme [s] Fure 17: movn averae threshold used to determne whether the snal rom resstvty sensor corresponds to ar or water. s ndcated by Fures 16 and 17, a arly accurate bulk estmate o the presence o bubbles was obtaned. The bubble snals rom the two sensors showed a relatvely ood correlaton and the calculated vod racton was 29.3% as calculated rom the phoransstor 1 measurement but 31.1% usn the resstvty sensor 1. Note also that because o the electrcal nose n the resstvty measurement, t tended to estmate more requent and smaller bubbles than dd the phoransstor. The movn averae threshold method works arly well as lon as the vod racton s n the ntermedate ranes (say 2-8%), but as the lmt o pure water or pure ar s approached the method wll cease to work because the movn averae threshold wll move too close to the snal o the domnant lud. Hence, an underestmate o the domnant lud s obtaned. Tables 1 to 3 summarze estmates o bubble velocty, averae bubble lenth, vod racton and the number o bubbles counted over the measurement perod or each o the three Plot tests. Table 4 shows the measured low rates and low rate ratos measured usn the smple low meter. Gven the aorementoned assumptons or semented low, the rato Q ar /Q should equal the vod racton and hence the two values could be compared to et an estmate o the accuracy o these calculatons. Some cauton should be taken n the comparson snce the uncertanty n the measurements rom the low meter was rather lare. Table 1: Summarzed results or calculated bubble low propertes rom Plot test 1. Plot test 1 Sensor: Resstvty1 Resstvty2 Phorans1 Phorans2 STD Bbl Velocty [m/s]:.287.287.281.281.38 v Bbl Lenth [mm]: 6.5 5.4 9 8.6 1.7 Vod Fracton: 31.1% 27.6% 29.3% 3.8% 2% Number o Bbls: 279 296 184 23 55 Table 2: Summarzed results or calculated bubble low propertes rom Plot test 2. Plot test 2 Sensor: Resstvty1 Resstvty2 Phorans1 Phorans2 STD Bbl Velocty [m/s]:.181.181.179.179.8 v Bbl Lenth [mm]: 6.4 4.8 9.3 8.2 2. Vod Fracton: 27.4% 24.8% 2.1% 2.1% 4% Number o Bbls: 143 173 71 82 49 Table 3: Summarzed results or calculated bubble low propertes rom Plot test 3. Plot test 3 Sensor: Resstvty1 Resstvty2 Phorans1 Phorans2 STD Bbl Velocty [m/s]: 67 67 67 67. v Bbl Lenth [mm]: 8.2 9.2 12.8 1.3 2. Vod Fracton: 35.9% 49.6% 58.2% 54.9% 1% Number o Bbls: 378 464 392 459 45
Table 4: Measurement results rom the smple low meter. The rato Q ar /Q can be compared to the vod ractons reported n Tables 1 to 3. Note the relatvely lare uncertanty n the measurements made by the low meter. s expected the movn averae threshold method seemed to work arly well when the vod racton was at an ntermedate value. Ths was seen n Plot test 2. In Plot test 1 the vod racton had become too low or a proper estmate to be made by ths method and an underestmate o the water (the domnant lud) was seen. In the case o Plot test 3, an underestmate o ar was seen, whch was not predcted by ths smple model o the semented low, but ths could perhaps be explaned by turbulence and vbratonal eects that the low had on the electrode. Electrcal nose and crosstalk may also have played a role here. Crosstalk In the case o the resstvty measurements a crosstalk eect was seen between the two sensor readns. Ths means or example, that sometmes when a bubble passed the resstvty sensor at spot 1, a snal chane was seen n the resstvty measurement at spot 2 also. Ths was very clear e.. n the snal seen around tme 7.7s n Fure 6. In an attempt to explan ths behavor one could propose that the anode o electrode 1 and the cathode o electrode 2 were connected throuh the water and ormed another electrode. Let the resstance across ths electrode be denoted by R e12. Then the measured voltae drop n crcut 2 could be calculated as V I 1 R2 ( ) Re2 Re 12 1 V [V] (17) + where R e2 s the voltae drop across electrode 2 and V 12V s the al voltae suppled to the crcut. When a bubble passes electrode 1 the connecton between electrodes 1 and 2 weakens and R e12 oes up. ccordn to equaton 13 ths leads to a lower value o V R2. The chane n the snal because o ths dsturbance would be much smaller than the chane n the snal the bubble were passn at spot 2 because R e12 >> R e2 smlar relaton should exst the other way around, between electrodes 2 and 1, but t was not seen as stronly, perhaps because the current could not travel as easly upstream,.e. R e12 was not equal to R e21. 1 Ths could be because o a second bubble, traveln n between the sensors, that mpeded the current. Ths explanaton s perhaps not completely satsactory and usn separate power supples or each sensor has been suested by specalsts that have developed a smlar technoloy at the Schlumberer Expermental Facltes n Cambrde, UK. lternatve ways to deal wth the crosstalk,.e. snal processn methods, were also nvestated. The way that ave the best results was to subtract the lan snal (y) rom the leadn snal (x) and then cross correlate z x - y to y. Ths way, the erroneous part o the snal (resultn rom crosstalk) could be subtracted out o the leadn snal and the peak n R xy (τ) at τ was elmnated (Fure 18). Sample cross-correlaton.3.2.1 -.1 -.2 -.3 Tme sht.17 [s] Tme sht.17 [s] - -.5.5 Tme ncrements-τ [s] Fure 18: The cross-correlaton between the lan snal (y) and the derence between the leadn and the lan snal (zx-y) provdes an approprate estmate o the tme sht. FUTURE WORK Full-sze applcaton desn Some prelmnary measurements have been made n a ull-szed artcal well. The artcal well conssts o a 6 n. dameter plexlass tube whch has adjustable ar and water low. low mxer s at the bottom o the tube so the low wll be homoeneous. Prelmnary measurements wth an electrode desn
whch s sketched rouhly n Fure 19 have yelded results that show enerally ncreased resstance as the amount o ar s ncreased but a low meter or the ar s yet to be obtaned. Boles, M.. and Çenel, Y..: Thermodynamcs, n Enneern pproach, McGraw-Hll Companes, Inc., 22. Chen, C.Y., Horne, R.N., L, K., and Vllaluz,.L.: Quarterly Report or Contract DE-FG36-2ID14418, Stanord Geothermal Proram, prl-june 24, Stanord Unversty, 24, pae 4. Chen, C.Y., Dastan,., Julusson, E., Horne, R.N., L, K., Stacey, R.W. and Vllaluz,.L.: Quarterly Report or Contract DE-FG36-2ID14418, Stanord Geothermal Proram, January-March 25, Stanord Unversty, 25. Cheremsno, P.N., Cheremsno, N.P.: Flow Measurement or Enneers and Scentsts, Marcel Dekker, nc, 1988. p. 11-13 Fure 19: Shown s a cross secton o a wellbore wth an n-stu probe that conssts o an electrode made o two brass plates (brown). The resstance across the electrode depends on the vod racton o the welbore low. s soon as the ar low rate can be measured, the reerence vod racton can be calculated and correlatons or the relaton between resstance and vod racton can be made. To obtan an addtonal reerence or the vod racton, a manometer wll be attached to the sde o the artcal well and the vod racton then calculated rom the weht o the arwater column. REFERENCES zz, K. and Gover, G.W.: The Flow o Complex Mxtures n Ppes, Van Nostrand Renold Company, 1972, paes 338-339. Crow, C.T., Sommereld, M., Tsujnaka, Y., Multphase Flows Wth Droplets and Partcles, CRC Press, 1997. p. 39 Huhmark, G.., and Pressbur, B.S.:"Holdup and pressure drop wth as-lqud low n a vertcal ppe,".i.ch.e. Journal, Vol. 7; pae 677 (1961). Partn, J.K., Davdson, J.R., Sponsler, E.N. and Mnes, G.L.: Deployment o an Optcal Steam Qualty Montor n a Steam Turbne Inlet Lne, presented at the Geothermal Resource Councl 24 annual meetn, uust 29- September 1, 24, Indan Wells, Calorna, US; GRC Trans. 28 (23). Spelman, P.: "Contnuous Enthalpy Measurement o Two-Phase Flow orm a Geothermal Well," presented at the Geothermal Resource Councl 23 annual meetn, October 12-15, 23, Morela, Mexco; GRC Trans. 27 (23).