An Exerimental Setu to Meaure the Conductivity of a Solid or Liquid Samle Utilizing Multi-Frequency LCR Meter Shahryar Darayan Deartment of Engineering Technologie Texa Southern Univerity Abtract A comuter-controlled automated data acquiition ytem i deigned to meaure the conductivity of the liquid (aline water) or the olid amle (rock aturated with aline water) in the frequency range 0 khz to 2 MHz. The et-u i baed on LCR (Inductor, Caacitor, and Reitor) multimeter and four-terminal amle holder ytem that wa develoed to reduce the contact reitance, to minimize any tray caacitance, and reidual inductance aociated with the tet lead or the tet fixture at high frequencie. However, the intrumentation calibration cheme cannot comletely eliminate the aforementioned error. In order to accomlih thi, a calibration model i deigned to comenate for the inherent error of the ytem. In thi tudy, the conductivity of ome amle wa meaured. The meaured data wa comared with conductivity rovided by Society of Core Analyi Guideline (SCA-GL). The agreement between available data and exerimental data i excellent. Introduction The increaed ability of thoe in the etroleum indutry to analyzed the formation characteritic from electrical reitivity data, it i imerative to have more recie method to meaure that arameter,2. Several tye of reitivity enor are available on MWD (Meaurement-While-Drilling) tool. The earlier one were hort normal enor oerating near DC (Direct Current) 3, 4, 5 and coil-tye enor oerating at 2 MHz 6, 7, 8. For intance, the coil-tye MWD reitivity tool meaure hae and attenuation. Then, ome converion algorithm are ued to tranform the meaured quantitie in term of aarent reitivitie. In thi converion, the formation dielectric contant i aumed to be either a contant value or a known function of the reitivity which i not a correct aumtion. Therefore, it i a common ractice to obtain ome amle from the core elected reervoir and then an actual electric ermittivity are meaured in the core meaurement facility. Proceeding of the 2005 American Society for Engineering Education Annual Conference & Exoition Coyright 2005, American Society for Engineering Education Page 0.74.
In order to be able to utilize the meaured dielectric ermittivity intead of the aumed value, an automated comuter controlled technique wa develoed for meauring the conductivity of the amle under the tet at the frequency range of 0 khz to 2 MHz. A multi-frequency LCR meter wa ued to meaure the imedance of a four-terminal amle holder containing the core or the liquid amle. The ytem error of the LCR meter and amle holder i comenated by a et of comenation arameter obtained exerimentally. After the ytem error i ubtracted from the meaured imedance, the conductivity of the amle i calculated. Intrumentation The chematic diagram of the low-frequency conductivity meaurement i hown in Figure, it conit of an HP 4275A multi-frequency LCR meter, one amle holder, one dek-to comuter, eriheral device, and four one-meter long coaxial cable with BNC (Bayonet Neill Concelman or Bayonet Nut Connector) connector. The comuter i ued for controlling the ytem and data collection uroe. The communication i achieved via HP-IB cable that connect the comuter to the multi-frequency LCR meter. The HP 4275A multi-frequency LCR meter i a fully automated tet intrument deigned to meaure the arameter of an imedance element in the 0 khz to 0 MHz range. The tet ignal level can be flexibly et at the deired amlitude within the range of mv to V. Figure. Block diagram of data acquiition ytem. Samle holder i comried of two Plexigla rectangular tank which are connected together by a circular Plexigla tube. Two air of latinum meh erve both otential electrode, and current electrode. The otential electrode are laced adjacent to the end urface of the rock amle. The current electrode are laced arallel to the otential electrode. Four iece of the latinum wire connect the latinum electrode to the BNC connector. Proceeding of the 2005 American Society for Engineering Education Annual Conference & Exoition Coyright 2005, American Society for Engineering Education Page 0.74.2
Meaurement Procedure The method of four-terminal meaurement i ued to reduce the contact reitance and to minimize any tray caacitance and reidual inductance aociated with the tet lead or the tet fixture at high frequencie (ee Figure 2). Figure 2. Four-terminal meaurement method. Proceeding of the 2005 American Society for Engineering Education Annual Conference & Exoition Coyright 2005, American Society for Engineering Education Page 0.74.3
Four, one-meter long, coaxial cable are ued a lead from the BNC connector on the LCR meter to the amle holder. Thee coaxial cable are connected, at one end, to the high current, the high otential, the low otential, and the low current ort of the LCR meter. The other end of thee cable (the inner conductor) are connected to four terminal on the amle holder. The four outer conductor of thee cable are hort-circuited at the end near the amle holder, they erve a the return ath for the meaurement current. The ame current flow through both the center conductor and the outer hield conductor (in ooition direction) o that no external magnetic field are generated around the conductor. Thu, the tet lead do not contribute any additional meaurement error due to the elf or the mutual inductance between the individual lead. Since the meaurement circuit ha inherent tray caacitance, reidual inductance, and reitance, the meaured value may be unaccetably influenced deending on the meaurement range and the magnitude of the reidual arameter. The ZERO offet adjutment function of the HP 4275A LCR meter automatically comenate for uch reidual, and minimize the incremental error 9. Setu Calibration To check on the accuracy of the ytem everal two-terminal element, uch a bra and ome reciion reitor, were oldered to the otential electrode one at the time and the current electrode wa horted to the otential electrode in each ide uing latinum wire. The imedance of thee element were meaured, and ome of thee reult are hown in Table and 2. The error aear to be very mall at low reitance value. Table. A comarion between meaured imedance and corrected imedance of the bra wire i hown. Frequency (khz) Meaured Imedance Corrected Imedance Real Part (Ω) Img Part (Ω) Real Part (Ω) Img Part 0 0.0 0.0 0.00 0.00 20 0.0 0.02 0.00 0.00 40 0.0 0.03 0.00 0.00 00 0.0 0.08 0.00 0.00 200 0.0 0.7 0.00 0.00 400 0.0 0.34 0.00 0.00 000 0.0 0.87 0.00 0.00 2000 0.06.76 0.00 0.00 Proceeding of the 2005 American Society for Engineering Education Annual Conference & Exoition Coyright 2005, American Society for Engineering Education Page 0.74.4
Table 2. A comarion between meaured imedance and corrected imedance of a tandard reitor (5000Ω ±0.% tolerance) i hown. Frequency (khz) Meaured Imedance Real Part (Ω) Img Part (Ω) Corrected Imedance Real Part(Ω) Img Part(Ω) 0 4953.7 +38.65 4999.99-0.0 20 4952.9 +35.77 4999.99-0.02 40 495.72-64.85 4999.99-0.03 00 4944.46-230.09 4999.99-0.08 200 4927.30-484.04 4999.99-0.7 400 4863.9-960.65 4999.99-0.34 000 4589.32-2347.35 4999.99-0.87 2000 3756.40-4429.99 4999.99 -.76 In order to reduce the error of the ytem, the model hown in Figure 3 wa ued to correct the meaured imedance. Figure 3.Thi model i ued to eliminate the conductance, tray caacitance, reidual inductance, and reitance due to the cable and amle holder Proceeding of the 2005 American Society for Engineering Education Annual Conference & Exoition Coyright 2005, American Society for Engineering Education Page 0.74.5
The reidual inductance, tray caacitance, and reitance of thi model were comuted by uing two-terminal element, namely, a iece of bra (hort circuit) and reciion reitor (5 k-ohm). The total admittance of thi model, in general cae, can be exreed by = + C G jω + ( R + jωl + Z ) amle () Z = R + jω L (2) = G + jω C (3) where Z Samle = imedance of the unknown amle, Z = Serie imedance, = Parallel admittance, R = Serie reitance, G = Parallel Conductance, L = Reidual inductance, and C = Stray caacitance. To comenate for the error, a hort (bra wire) i ued which reduce the Equation () to: o = G + C jω + ( R + jω ) L (4) When a very high-value reciion reitor (5 k-ohm) i ued, the following equation i obtained where = G + C jω + ( R + jωl + R ) (5) 0 = admittance of the circuit with a hort-circuited bra amle, = admittance of a circuit with a 5 kω reitor, and R = a 5-k-Ohm reciion reitor. Proceeding of the 2005 American Society for Engineering Education Annual Conference & Exoition Coyright 2005, American Society for Engineering Education Page 0.74.6
Subtracting (5) from (4) yield 0 - = ( )( [ R + j ω L R + j ω L + R ) ] R (6) for imlification, it i aumed that R i much greater than (R + jωl ), o ( 0 - ) can be reduced to 0 - = ( R + jω ) L (7) Therefore, the erie imedance and arallel admittance can be obtained a follow and Z = ( ) o (8) = - R (9) At thi tage, all error term can be calculated, and then the raw data of the unknown amle can be corrected. The following exreion can be ued to eliminate thee error from the meaured data Z = Samle ( ) m - Z (0) where m = admittance of the meaured amle. The conductivity of the amle can be calculated uing the following exreion: Proceeding of the 2005 American Society for Engineering Education Annual Conference & Exoition Coyright 2005, American Society for Engineering Education Page 0.74.7
where σ = A d Re( Z Samle d = the thickne of the amle, A = cro-ection area of the amle, σ = conductivity of the amle, and Re = indicate the real art. ) () Reult and Dicuion Several meaurement were erformed on the aline water at variou alinitie, ranging from 0. km to 9 km. The meaured data were corrected for the uncertaintie of the ytem which are in term of comlex erie imedance and a comlex arallel admittance. The meaured conductivity and the corrected conductivity curve were lotted veru frequency. Thee reult were comared to the Society of Core Analyi Guideline (SCA GL) data 0. The corrected data i in good agreement with the available data (the error i le than 3%). The correction eem to be ignificant when the alinity i le than 0.9 Mho/m. Some of thee reult are reented in Figure 4 through 7. Figure 4. It how the conductivity meaurement veru frequency for the water with the alinity of 0. km and meaurement temerature of 23.9 o C. Proceeding of the 2005 American Society for Engineering Education Annual Conference & Exoition Coyright 2005, American Society for Engineering Education Page 0.74.8
Figure 5. It how the conductivity meaurement veru frequency for the water with the alinity of 2.00 km and meaurement temerature of 23.7 o C. Figure 6. It how the conductivity meaurement veru frequency for the water with the alinity of 3.00 km and meaurement temerature of 24.0 o C. Proceeding of the 2005 American Society for Engineering Education Annual Conference & Exoition Coyright 2005, American Society for Engineering Education Page 0.74.9
Figure 7. It how the conductivity meaurement veru frequency for the water with the alinity of 9.00 km and meaurement temerature of 23.5 o C. Concluion A fully automatic data acquiition ytem wa deigned to meaure the conductivity of either a liquid or a olid amle, uing multi-frequency LCR meter. A correction model wa introduced to comenate the uncertaintie of the ytem. Thi model i comried of one comlex erie imedance and one comlex arallel admittance. Samle of variou alinitie were meaured and reult were comared to the Society of Core Analyi Guideline data. From the foregoing analyi and exeriment, the correction eem to be ignificant at the low alinitie (le than 0.9 Mho/m). Furthermore, ince the down-hole MWD tool i oerated at 2 MHz, a et of corrected data i eential for the tool calibration and the raw data correction. Therefore, the correction at the higher frequencie, uch a 2 MHz, which i eential for MWD logging, ha been develoed. Bibliograhy. Zhou, Q., Udated urvey of MWD reitivity tool, Chevron Texaco reort, July 2004. 2. Owen, J.E., and Greer, W.J., The guard electrode logging ytem, AIME, 95. 3. Jan,.M., and Cambell, R.L., Jr., Borehole correction of MWD gamma ray and reitivity log, aer PP, in 25 th Annual Logging Symoium Tranaction: Society of Profeional Well Log Analyt, 984. Proceeding of the 2005 American Society for Engineering Education Annual Conference & Exoition Coyright 2005, American Society for Engineering Education Page 0.74.0
4. Corbern, M.E., and Nuckol, E.B., Alication of MWD reitivity log for evaluation of formation invaion, aeroo, in 26 th Annual Logging Symoium Tranaction: Society of Profeional well Log Analyt,.. OO-6, 985. 5. Pake, W.C., Mack, S.G., Rao, M.V., Sro, L., and Twit, J.R., Meaurement of the hole ize While Drilling, SPWLA Thirty-Firt Annual Logging Symoium, aer G, June 24-27. 990. 6. Cooe, D., Shen, L.C., and Huang, F.S.C., Theory of 2 MHz reitivity tool and it alication to meaurement-while-drilling, the Log Analyt, V. 25, no. 3,. 35-46, May-June 984. 7. Hutchinon, M., Dubinky, V., Henneue, H., and Aquitaine, E., An MWD down-hole aitant driller, SPE 30523, Society of Petroleum Engineer, 995. 8. Patrick, M., Advance in MWD and formation evaluation for 2000, World oil, March 2000. 9. Hewlett Packard, 4275A, Multi-frequency LCR meter Service Manual, 994. 0. Worthington, R.F., Evan, R.J., Klein, J.D., and White, G., SCA Guideline for amle rearation and oroity meaurement of electrical reitivity amle, art iii-the mechanic of electrical reitivity meaurement on rock amle, The Log Analyt, vol. 3,. 64-67, 990. Biograhy: Shahryar Darayan received a Ph.D. degree in Electrical Engineering from Univerity of Houton in 993. At the reent, he i a rofeor and rogram coordinator of Electronic Engineering Technology rogram at Texa Southern Univerity. Hi reearch area are alied electromagnetic and intrumentation, comuter hardware and oftware deign, and numerical method. Proceeding of the 2005 American Society for Engineering Education Annual Conference & Exoition Coyright 2005, American Society for Engineering Education Page 0.74.