A New Logging-While-Drilling Method for Resistivity Measurement

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Article A New Logging-While-Drilling Method for † Resistivity Measurement in Oil-Based Mud

Yongkang Wu 1, Baoping Lu 2, Wei Zhang 2,3, Yandan Jiang 1, Baoliang Wang 1,* and Zhiyao Huang 1 1 State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China; [email protected] (Y.W.); [email protected] (Y.J.); [email protected] (Z.H.) 2 Sinopec Research Institute of Petroleum Engineering, Beijing 100101, China; [email protected] (B.L.); [email protected] (W.Z.) 3 State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Eﬀective Development, Beijing 100101, China * Correspondence: [email protected] This paper is an extended version of an earlier conference paper: “Wu, Y.K.; Ni, W.N.; Li, X.; Zhang, W.; † Wang, B.L.; Jiang, Y.D. and Huang, Z.Y. Research on characteristics of a new oil-based logging-while-drilling instrument. In Proceedings of the 11th International Symposium on Measurement Techniques for Multiphase Flow, Zhenjiang, China, 3–7 November 2019.”

Received: 21 December 2019; Accepted: 11 February 2020; Published: 16 February 2020

Abstract: Resistivity logging is an important technique for identifying and estimating reservoirs. Oil-based mud (OBM) can improve drilling efficiency and decrease operation risks, and has been widely used in the well logging field. However, the non-conductive OBM makes the traditional logging-while-drilling (LWD) method with low frequency ineffective. In this work, a new oil-based LWD method is proposed by combining the capacitively coupled contactless conductivity detection (C4D) technique and the inductive coupling principle. The C4D technique is to overcome the electrical insulation problem of the OBM and construct an effective alternating current (AC) measurement path. Based on the inductive coupling principle, an induced voltage can be formed to be the indirect excitation voltage of the AC measurement path. Based on the proposed method, a corresponding logging instrument is developed. Numerical simulation was carried out and results show that the logging instrument has good measurement accuracy, deep detection depth and high vertical resolution. Practical experiments were also carried out, including the resistance box experiment and the well logging experiment. The results of the resistance box experiment show that the logging instrument has good resistance measurement accuracy. Lastly, the results of the well logging experiment indicate that the logging instrument can accurately reflect the positions of different patterns on the wellbore of the experimental well. Both numerical simulation and practical experiments verify the feasibility and effectiveness of the new method.

Keywords: resistivity logging; oil-based mud (OBM); logging-while-drilling (LWD); capacitively coupled contactless conductivity detection (C4D) technique; inductive coupling principle

1. Introduction Reservoir evaluation plays an important role in the exploration and development of oil and gas. With the increase of unconventional wells in the drilling operations such as high angle wells and horizontal wells, logging-while-drilling (LWD) technology has become an important research aspect in the well logging ﬁeld. LWD technology enables practitioners to measure the formation parameters for geological analysis while drilling.

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Reservoir drilling is generally carried out in water-based mud (WBM) due to its convenience, low cost and little pollution to the environment [1]. However, with the development of LWD, WBM is no longer a good choice [1,2]. On the one hand, to achieve the fine reservoir evaluation in WBM environment, the expensive and quite time-consuming full-hole coring has to be adopted [1]. On the other hand, with the increase of deepwater wells and unconventional wells, WBM is no longer applicable because of the high temperature and high pressure resulted from these kinds of wells [2]. Due to the advantages of high temperature resistance, good lubricity and low reservoir damage, oil-based mud (OBM) is more suitable for most of deepwater wells and unconventional wells than WBM [3]. It can improve drilling efficiency and decrease operation risks. Thus, it has been widely used in the well logging field [4]. However, because the continuous phase of the OBM is oil, the resistivity of the OBM is usually million times the resistivity of the WBM resistivity [5]. It means the traditional measurement method with low frequency is no longer feasible in the OBM environment. In view of the non-conductive OBM, new methods for solving the electrical insulation problem of the OBM have been proposed [2,4,6–19]. There are four main categories. The first method is to research and develop a conductive OBM system that possesses not only good lubricity and stability as the conventional OBM has, but also low resistivity comparable to that of WBM [7]. To increase the conductivity of the OBM significantly, additives such as conductive solid particles [8], polar base oil [9], oil soluble ionic salts [10], specified ionic liquids [11], nanomaterials [12–15] are required to be added into the OBM. With the conductive OBM, the traditional LWD method becomes still effective. However, this method is limited by the high cost of early research-development and the environmental consideration on the toxic additives. The second method is to make a knife-like electrode which is sharp enough to cut through the mud cake, so that a conductive path will be established between the electrode and the formation, and the conventional low-frequency measurement method becomes still applicable [16,17]. However, this method becomes infeasible in the complex wellbore conditions including the thick mud attachment, irregular wall, spiral and deviated well. The third method is called the four-terminal measurement, which is to utilize the potential difference between the two vertical offset voltage electrodes for calibrating the formation resistivity in an alternating current field [18]. This method has the advantages of large measurement range and good adaptability of the mud cake thickness. However, there are several disadvantages accompanying this method, such as low resolution and limited pad structure. The fourth method is based on the capacitive coupling principle [2,4,6,19]. In this method, a current-carrying electrode is used to emit a high-frequency current to the formation and then the resistivity information of the formation can be obtained by measuring the voltage of the voltage-sensing electrode. However, the structure and the control process of the electrodes are complex, and the electrodes wear easily while drilling. Besides, this method is still in the stage of simulation research. Thus, more research work on resistivity measurement in OBM should be undertaken. Capacitively coupled contactless conductivity detection (C4D) technique is proposed as a contactless method for conductivity detection [20–22], which provides an effective approach for solving the blocking problem of non-conductive mediums. It has the advantages of low cost, simple construction, and good real-time performance [23–28]. Currently, C4D technique is mainly applied in the research field of analytical chemistry [20–22]. The inductive coupling principle is an indirect excitation method, which is generating an induced voltage in the secondary coil by applying an AC excitation signal to the primary coil [29–31]. By referring to the idea of the C4D technique and the inductive coupling principle, a new oil-based LWD method is proposed in this work [32]. On the one hand, the C4D technique is introduced to the well logging field to solve the electrical insulation problem of the OBM. In detail, the C4D technique is used to construct an effective alternating current (AC) measurement path for the measurement signal to go through the non-conductive OBM, so the influence of the electrical insulation problem of the OBM on formation resistivity measurement is overcome. On the other hand, the inductive coupling principle is used to form an induced voltage signal and implement indirect excitation of the AC measurement path. Based on the proposed method, a corresponding logging instrument will SensorsSensorsSensors 2019 20192020, ,,19 1920, ,,x x 1075FOR FOR PEER PEER REVIEW REVIEW 33 3of of of 16 16 16 logginglogging instrumentinstrument willwill bebe developed,developed, andand numericalnumerical simulationsimulation andand practicalpractical experimentsexperiments willwill bebe be developed, and numerical simulation and practical experiments will be carried out to verify the carriedcarried outout toto verifyverify thethe feasibilityfeasibility anandd effectivenesseffectiveness ofof thethe proposedproposed method.method. feasibility and effectiveness of the proposed method. 2.2. MethodsMethods 2. Methods

2.1.2.1. ApplicationApplication ofof CC44DD TechniqueTechnique inin LWDLWD 2.1. Application of C4D Technique in LWD TheThe basicbasic structurestructure ofof thethe CC44DD sensorsensor [33][33] isis shownshown inin FigureFigure 1.1. TheThe CC44DD sensorsensor includesincludes anan ACAC The basic structure of the C4D sensor [33] is shown in Figure1. The C 4D sensor includes an AC source,source, twotwo metalmetal electrodeselectrodes (the(the excitationexcitation elecelectrodetrode andand thethe pick-uppick-up elecelectrode),trode), anan insulatinginsulating source, two metal electrodes (the excitation electrode and the pick-up electrode), an insulating channel channelchannel andand aa currentcurrent detectiondetection unit.unit. and a current detection unit.

ExcitationExcitation The measured Pick-up InsulatingInsulating channel channel The measured Pick-up electrodeelectrode fluidfluid electrodeelectrode

IIoutout uuii ACAC source source

CurrentCurrent detection detection unit unit

4 FigureFigureFigure 1. 1. 1. Basic BasicBasic structure structure structure of of of the the the C C C44DDD sensor. sensor. sensor.

The simplified equivalent circuit of the measurement path of the C4D sensor is shown in Figure2. TheThe simplified simplified equivalent equivalent circuit circuit of of the the measurementmeasurement path path of of the the CC44DD sensor sensor is is shown shown in in Figure Figure 2.2. C1 is the coupling capacitance formed by the excitation electrode, the insulating channel, and the CC11 is is thethe couplingcoupling capacitancecapacitance formedformed byby thethe excitatiexcitationon electrode,electrode, thethe insulainsulatingting channel,channel, andand thethe measured conductive fluid. C2 is the coupling capacitance formed by the pick-up electrode, the measuredmeasured conductiveconductive fluid.fluid. CC22 isis thethe couplingcoupling capacitancecapacitance formedformed byby thethe pick-uppick-up electrode,electrode, thethe insulating channel, and the measured conductive fluid. R is the equivalent resistance of the measured insulatinginsulating channel, channel, and and the the measured measured conductive conductive fluid. fluid. R R is is the the equivalent equivalent resi resistancestance of of the the measured measured fluid between the two electrodes. When an AC voltage ui is applied to the excitation electrode, an fluidfluid betweenbetween thethe twotwo electrodes.electrodes. WhenWhen anan ACAC voltagevoltage uui i isis appliedapplied toto thethe excitationexcitation electrode,electrode, anan output current Iout will be obtained on the pick-up electrode by the current detection unit. With the outputoutput currentcurrent IIoutout willwill bebe obtainedobtained onon thethe pick-uppick-up electrodeelectrode byby thethe currentcurrent detectiondetection unit.unit. WithWith thethe obtained output current, the conductivity of the measured fluid can be obtained. obtainedobtained outputoutput current,current, thethe conductivityconductivity ofof thethe measuredmeasured fluidfluid cancan bebe obtained.obtained.

CC11 RR CC22 IIout uuii out CurrentCurrent detectiondetection unit unit MeasurementMeasurement path path FigureFigureFigure 2. 2. 2. Simplified SimplifiedSimpliﬁed equivalent equivalent equivalent circuit circuit circuit of of of the the the measurement measurement measurement path path path of of of the the the C C C44D4DD sensor. sensor. sensor.

TheTheThe characteristic characteristic characteristic of of of the the the C C C44D4DD technique technique technique is is is to to to measure measure measure the the the conductivity conductivity conductivity of of of the the the measured measured measured object object object when when when ananan insulatinginsulating insulating mediummedium medium existsexists exists betweenbetween between thethe the electrodelectrod electrodeee andand and thethe the object.object. object. TheThe The measurementmeasurement measurement approachapproach approach ofof of thethe the CCC44D4DD technique technique technique has has has provided provided provided an an an alternative alternative alternative solution solution solution to to to solve solve solve the the the problem problem problem of of of blocking blocking blocking the the the low-frequency low-frequency low-frequency measurementmeasurementmeasurement path path path betweenbetween between electrodes electrodes electrodes and and and the the the fo fo formationrmationrmation caused caused caused by by by thethe the non-conductivenon-conductive non-conductive OBM.OBM. OBM. 4 The diagram of the application of the C D technique in LWD is shown in Figure3. Cd1 is the coupling capacitance formed by the drill collar, the non-conductive OBM and the formation. Cd2 is the coupling capacitance formed by the pick-up electrode, the non-conductive OBM and the formation. Rf is the equivalent resistance of the formation. The application of the C4D technique can overcome the electrical insulation problem of the OBM and construct an eﬀective AC measurement path.

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Drill collar Wellbore

Cd1

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Sensors 2019, 19, x FOR PEER REVIEWFormation Rf 4 of 16 Io Io The AC C measurement d2 Drill collar pathWellbore Pick-up Cd1 electrode Oil-based mud

Formation Rf Io Drill bit Io The AC C measurement d2 4 Figure 3. Diagrampath of the application of the C D techniquePick-up in LWD. electrode The diagram of the applicationOil-based of mud the C4D technique in LWD is shown in Figure 3. Cd1 is the coupling capacitance formed by the drill collar, the non-conductive OBM and the formation. Cd2 is the coupling capacitance formed by the pick-up electrode, the non-conductiveDrill bit OBM and the formation. Rf is the equivalent resistance of the formation. The application of the C4D technique can overcome the electrical insulation problem of the OBM and construct an effective4 AC measurement path. FigureFigure 3. 3.Diagram Diagram of of the the application application of of the the C C4DD techniquetechnique inin LWD.LWD. 2.2. Application of Inductive Coupling Principle in LWD 2.2. ApplicationThe diagram of Inductive of the application Coupling Principle of the inC4D LWD technique in LWD is shown in Figure 3. Cd1 is the couplingOriginally, capacitance aa low-frequency low-frequency formed by excitation theexcitation drill voltagecollar, voltage the is directlyisnon-conductive directly applied applied to OBM the to electrode theand electrodethe formation. system system in LWD. Cd 2in is However,LWD.the coupling However, the capacitance manufacturing the manufacturing formed process by the ofpr electrodesocesspick-up of electrode,electrodes is diﬃcult the is and non-conductivedifficult the electrodes and the OBM areelectrodes easy and tothe wearare formation. easy while to 4 drilling,wearRf is thewhile limitingequivalent drilling, the resistancelimiting application the of applicationofthe the formation. direct of excitation the The direct application method. excitation of In the method. 1967, C D researcher technique In 1967, ARPS,researcher can overcome J.J. applied ARPS, the theJ.J.electrical inductiveapplied insulation the coupling inductive problem principle coupling of the to LWD OBM principle [ 29and]. Theconstruct to basicLWD principlean [29]. effective The of theACbasic inductivemeasurement principle coupling of path. the principle inductive is showncoupling in Figureprinciple4. Takeis shown the transformer in Figure 4. as Take an example. the transformer As can be as seen an example. from Figure As4 ,can the be transformer seen from 2.2. Application of Inductive Coupling Principle in LWD isFigure composed 4, the oftransformer a primary coil,is composed a secondary of a coilprimary and acoil, core. a Thesecondary number coil of and turns a ofcore. the The primary number coil of is turns of the primary coil is N1 and the number of turns of the secondary coil is N2. N1 andOriginally, the number a low-frequency of turns of the secondaryexcitation coilvoltage is N 2is. directly applied to the electrode system in LWD. However, the manufacturing process of electrodes is difficult and the electrodes are easy to wear while drilling, limiting the application of theCore direct excitation method. In 1967, researcher ARPS, J.J. applied the inductive coupling principle to LWD [29]. The basic principle of the inductive coupling principle is shown in Figure 4. Take the transformer as an example. As can be seen from U1 N1 N2 U2 Figure 4, the transformer is composed of a primary coil, a secondary coil and a core. The number of turns of the primary coil is N1 and the number of turns of the secondary coil is N2.

Primary coil Secondary coil Core Figure 4. Basic principle of the in inductiveductive coupling principle.

By applying an AC voltage UU11to the primaryN1 coil, an inducedN2 U voltage2 U2 will be generated in the By applying an AC voltage U1 to the primary coil, an induced voltage U2 will be generated in secondary coil. The induced voltage U2 is determined by the following equation: the secondary coil. The induced voltage U2 is determined by the following equation: U N PrimaryUU coil== 1 22 Secondary coil (1) 22 (1) N1 Figure 4. Basic principle of the inductive coupling principle. Based on the inductive coupling principle, a stablestable induced voltage can be generated in the secondary coilcoil of of the the transformer, transformer, which which can becan used be asused the excitationas the excitation voltage of voltage the logging of the instrument. logging By applying an AC voltage U1 to the primary coil, an induced voltage U2 will be generated in Theinstrument. diagram The of thediagram application of the application of the inductive of the couplinginductive principle coupling inprinciple LWD is in shown LWD is in shown Figure 5in. the secondary coil. The induced voltage U2 is determined by the following equation: AnFigure excitation 5. An excitation coil is introduced coil is introduced as the primary as the coil. primary The measurement coil. The measurement path consisted path of consisted the drill of collar, the drill collar, the pick-up electrodes, the OBM and =theU 1formationN2 is regarded as the secondary coil. By the pick-up electrodes, the OBM and the formationU2 is regarded as the secondary coil. By applying(1) an ACapplying voltage an to AC the voltage excitation to coil,the excitation an induced coil, voltage an induceduNis1 generated voltage at u theis generated upper and at lower the upper drill collar and to provideBased an on indirect the inductive excitation coupling voltage principle, for the logging a stable instrument. induced voltageZ is the can impedance be generated of the OBMin the andsecondary the formation. coil of the transformer, which can be used as the excitation voltage of the logging instrument. The diagram of the application of the inductive coupling principle in LWD is shown in Figure 5. An excitation coil is introduced as the primary coil. The measurement path consisted of the drill collar, the pick-up electrodes, the OBM and the formation is regarded as the secondary coil. By applying an AC voltage to the excitation coil, an induced voltage u is generated at the upper and

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Sensorslower2020 drill, 20 ,collar 1075 to provide an indirect excitation voltage for the logging instrument. Z 5is of the 16 impedance of the OBM and the formation.

Drill collar ui AC source Z u Excitaion coil

FigureFigure 5.5. DiagramDiagram ofof thethe applicationapplication ofof thethe inductiveinductive couplingcoupling principleprinciple inin LWD.LWD.

TheThe measurementmeasurement path including the the drill drill collar, collar, the the OBM OBM and and the the formation formation can can be be regarded regarded as asthe the secondary secondary side side of of a atransformer transformer with with one one turn. turn. The The induced induced voltage voltage u is determineddetermined byby thethe followingfollowing equation:equation: ui u = ui (2) u =Nt (2) Nt where ui is the voltage of the AC source, Nt is the number of turns of the excitation coil. where ui is the voltage of the AC source, Nt is the number of turns of the excitation coil. 2.3. The New Oil-Based LWD Method 2.3. The New Oil-based LWD Method In order to describe the new oil-based LWD method clearly, the proposed method is applied to the developmentIn order to describe of a logging the new instrument. oil-based TheLWD basic method structure clearly, of the the proposed logging instrument method is applied is shown to inthe Figure development6. The logging of a logging instrument instrument. consists The of anbasic AC structure source, anof excitationthe logging coil, instrument a current is detection shown in unit,Figure a pick-up6. The logging electrode, instrument a drill consists collar and of an a drillAC source, bit. The an applicationexcitation coil, of thea current C4D techniquedetection unit, can overcomea pick-up theelectrode, electrical a drill insulation collar and problem a drill of bit. the The OBM application and construct of the an C4 eDﬀ ectivetechnique AC measurementcan overcome path.the electrical The AC insulation measurement problem path of includes the OBM the and drill construct collar, the an OBM, effective the AC formation measurement and the path. pick-up The electrode.AC measurement According path to includes the measurement the drill collar, principle the of OBM, the C the4D technique,formation and the pick-upthe pick-up electrode, electrode. the non-conductiveAccording to the OBM measurement and the conductive principle formation of the canC4D form technique, a coupling the capacitance, pick-up electrode, which constitutes the non- anconductive AC circuit OBM path and for the the conductive measurement formation signal tocan go form through a coupling the OBM. capacitance, In this way, which the constitutes electrical insulationan AC circuit problem path offor the the OBM measurement is overcome. signal The to inductivego through coupling the OBM. principle In this is way, used the to generateelectrical aninsulation indirect problem excitation of source the OBM for is the overcome. AC measurement The inductive path. coupling For the wholeprinciple resistivity is used measurementto generate an process,indirect ﬁrstly,excitation according source to for the the inductive AC measurem couplingent principle, path. For when the whole an AC resistivity source is appliedmeasurement to the excitationprocess, firstly, coil, an according induced to voltage the inductive can be formedcoupling above principle, and below when thean AC excitation source coil,is applied which to is the to beexcitation the excitation coil, an voltage induced of voltage the AC can measurement be formed ab path.ove and Secondly, below thethe signalexcitation goes coil, through which theis to AC be measurementthe excitation path, voltage and thenof the a currentAC measurement which carries pa theth. resistivity Secondly, information the signal ofgoes the formationthrough the can AC be measuredmeasurement on the path, pick-up and then electrode a current by the which current carries detection the resistivity unit. Lastly, information the formation of the resistivityformation cancan beSensorsbe obtainedmeasured 2019, 19 with, xon FOR the PEER pick-up measured REVIEW electrode current. by the current detection unit. Lastly, the formation resistivity6 of 16 can be obtained with the measured current. The equivalent circuit of the measurement path of the logging instrument is shown in Figure 7. Cd1 is the coupling capacitance formed by the drill collar, the OBM and the formation. Cd2 is the coupling capacitance formed by the pick-up electrode, the OBM and the formation. Rf is the equivalent resistance of the formation, which is the measurement target. The simplified equivalent circuit of the measurement path of the logging instrument is shown in Figure 8. Cd is the combined capacitance of Cd1 and Cd2.

FigureFigure 6.6. BasicBasic structurestructure ofof thethe logginglogging instrument.instrument.

Cd1 Rf Cd2 uIo Current detection unit Figure 7. Equivalent circuit of the measurement path of the logging instrument.

Cd Rf I u o Current detection unit Figure 8. Simplified equivalent circuit of the measurement path of the logging instrument.

The equivalent resistance of the formation Rf, also termed the apparent resistance of the formation, can be determined by the following equation: = u ()ψ Rf cos (3) Io

where u is the induced voltage, Io is the measured current, ψ is the impedance angle of the impedance of the formation and the OBM. The apparent resistivity of the formation Ra is the measured resistivity of the logging instrument, which can be determined by the following equation: = u ()ψ Rkafcos = kR (4) Io where k is the instrument constant. It is determined by the following equation: RI RI k = ao= to uucos()ψψ cos() (5)

where Rt is the real resistivity of the formation. The instrument constant k is a key parameter of the logging instrument and is affected by the size of the pick-up electrode. Generally, k is used to convert the measured apparent resistance of the formation to the apparent resistivity of the formation. It can be obtained by assuming that the apparent resistivity Ra is equal to the real resistivity Rt when the parameters such as the wellbore diameter, the OBM resistivity and the formation resistivity are known.

3. Results

3.1. Numerical Simulation In order to verify the feasibility of the proposed method, numerical simulation of the developed logging instrument was carried out. In this part, various instrument parameters such as the

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The equivalent circuit of the measurement path of the logging instrument is shown in Figure7. Cd1 is the coupling capacitance formed by the drill collar, the OBM and the formation. Cd2 is the coupling capacitance formed by the pick-up electrode, the OBM and the formation. Rf is the equivalent resistance of the formation, which is the measurement target. The simpliﬁed equivalent circuit of the measurement path of the logging instrument is shown in Figure8. Cd is the combined capacitance of Figure 6. Basic structure of the logging instrument. Cd1 and Cd2.

Cd1 Rf Cd2 Cd1 Rf Cd2 uIo uIo Current detection unit detection unit Figure 7. Equivalent circuit of the measurement path of the logging instrument. FigureFigure 7. 7. EquivalentEquivalent circuit circuit of of the the measurement measurement path path of of the the logging logging instrument. instrument.

Cd Rf Cd Rf u Io u o Current detection unit detection unit FigureFigure 8. 8. SimplifiedSimpliﬁed equivalent equivalent circuit circuit of of the the meas measurementurement path path of of the the logging logging instrument. instrument.

TheThe equivalentequivalent resistanceresistance of of the the formation formationR , alsoRf, termedalso termed the apparent the apparent resistance resistance of the formation, of the The equivalent resistance of the formationf Rf, also termed the apparent resistance of the formation,can be determined can be determined by the following by the equation:following equation: = uu ()ψ Rf = cos()ψ (3) RRff = coscos(ψ) (3)(3) Io IIoo where u is the induced voltage, Io is the measured current, ψ is the impedance angle of the impedance wherewhere uu isis the the induced induced voltage, voltage, IIoo isis the the measured measured current, current, ψψ isis the the impedance impedance angle angle of of the the impedance impedance ofof the the formation formation and and the the OBM. OBM. The apparent resistivity of the formation Ra is the measured resistivity of the logging instrument, TheThe apparent apparent resistivity resistivity of of the the formation formation RRaa isis the the measured measured resistivity resistivity of of the the logging logging instrument, instrument, whichwhich can can be be determined determined by by the the following following equation: equation: = u ()ψ Rkaf= u cos()ψ = kR (4) RkafI cos = kR (4) Ra = k Iocos(ψ) = kR f (4) Ioo where k is the instrument constant. It is determined by the following equation: where k is the instrument constant. It is determined by the following equation: RIao RI to k = RIao= RI to k = ()ψψ= () (5) uucosRaI()oψψ cosR()tIo (5) k = uucos= cos (5) u cos(ψ) u cos(ψ) where Rt is the real resistivity of the formation. The instrument constant k is a key parameter of the where Rt is the real resistivity of the formation. The instrument constant k is a key parameter of the logging instrument and is affected by the size of the pick-up electrode. Generally, k is used to convert loggingwhere R instrumentt is the real and resistivity is affected of the by formation.the size of the The pick-up instrument electrode. constant Generally,k is a key k is parameter used to convert of the thelogging measured instrument apparent and resistance is affected ofby the the formation size of the to the pick-up apparent electrode. resistivity Generally, of the formation.k is used to It convert can be obtained by assuming that the apparent resistivity Ra is equal to the real resistivity Rt when the obtainedthe measured by assuming apparent that resistance the apparent of the formation resistivity to R thea isapparent equal to resistivitythe real resistivity of the formation. Rt when It the can parameters such as the wellbore diameter, the OBM resistivity and the formation resistivity are known. parametersbe obtained such by assumingas the wellbore that thediameter, apparent the resistivityOBM resistivityRa is equaland the to formatio the realn resistivity resistivityR aret when known. the parameters such as the wellbore diameter, the OBM resistivity and the formation resistivity are known. 3. Results 3. Results 3.1. Numerical Simulation 3.1. Numerical Simulation In order to verify the feasibility of the proposed method, numerical simulation of the developed loggingIn orderinstrument to verify was the carried feasibility out. of theIn proposedthis part, method,various numericalinstrument simulation parameters of thesuch developed as the logging instrument was carried out. In this part, various instrument parameters such as the measurement accuracy of formation resistivity, the detection depth and invasion radius, the influence of surrounding rock and the vertical resolution were examined to test the performance of the logging instrument. SensorsSensors 2019 2019, 19, ,19 x ,FOR x FOR PEER PEER REVIEW REVIEW 7 of7 16of 16 measurementmeasurement accuracy accuracy of offormation formation resistivity, resistivity, the the detection detection depth depth and and invasion invasion radius, radius, the the influence influence of ofsurrounding surrounding rock rock and and the the vertical vertical resolution resolution were were examined examined to totest test the the performance performance of ofthe the logging logging instrument.instrument. Sensors 2020, 20, 1075 7 of 16 3.1.1.3.1.1. Numerical Numerical Simulation Simulation Setup Setup 3.1.1.In Numerical Inthe the well well logging Simulation logging field, field, Setup logging logging response response is isgenerally generally analyzed analyzed by by numerical numerical methods methods rather rather thanthan Inanalytical theanalytical well logging methods, methods, field, because loggingbecause responsethe the loggin loggin is generallyg genvironment environment analyzed is by isextremely numerical extremely methodscomplex, complex, rather and and than all all environmentalanalyticalenvironmental methods, factors factors because such such as the aswellbore, loggingwellbore, environmentinvasion invasion zone, zone, is surrounding extremely surrounding complex, rock, rock, mud andmud cake, all cake, environmental temperature temperature andfactorsand pressure suchpressure as wellbore,will will all all affect invasion affect the the zone, logging logging surrounding result results rock,s[34,35]. [34,35]. mud In cake, Inthis this temperaturework work, the, the software and software pressure COMSOL COMSOL will all MultiphysicsaffMultiphysicsect the logging (COMSOL, (COMSOL, results [Inc.,34 Inc.,,35 Stockholm,]. Stockholm, In this work, Sweden) Sweden) the software is isused used COMSOLto toanalyze analyze Multiphysics the the logging logging (COMSOL,response response of Inc.,ofthe the instrument,Stockholm,instrument, Sweden)which which is is isa used commerciala commercial to analyze finite finite the element logging element responsemodeling modeling of software thesoftware instrument, in inthe the well which well logging logging is a commercial field. field. The The loggingfinitelogging element instrument instrument modeling is isdeveloped softwaredeveloped in in theCOMSOL COMSOL well logging software software field. and and The the loggingthe AC/DC AC/DC instrument module module of is ofthe developed the COMSOL COMSOL in softwareCOMSOLsoftware is software isused used to and tocarry carry the out AC out /theDC the numerical module numerical of thesimulation. simulation. COMSOL The softwareThe diagram diagram is used of ofthe to the carrylogging logging out instrument the instrument numerical is is shownsimulation.shown in inFigure TheFigure diagram 9. 9.As As is ofisshown theshown logging in inFigure Figure instrument 9, 9,the the logging islogging shown instrument instrument in Figure 9consists. consists As is shown of ofthe the indrill drill Figure collar, collar,9, the the the excitationloggingexcitation instrument coil coil and and the consists the detection detection of the electrode drillelectrode collar, array. array. the excitation coil and the detection electrode array.

FigureFigure 9. Diagram9. Diagram of ofthe the logging logging instrument. instrument. The simulation setup is shown in Figure 10. There are mainly two parts, one is the wellbore and TheThe simulation simulation setup setup is isshown shown in inFigure Figure 10. 10. Ther There aree are mainly mainly two two parts, parts, one one is isthe the wellbore wellbore and and the logging instrument, and the other is the measured formation. The logging instrument is situated thethe logging logging instrument, instrument, and and the the other other is isthe the measured measured formation. formation. The The logging logging instrument instrument is issituated situated inside the wellbore and there is oil-based mud between the logging instrument and the wellbore. insideinside the the wellbore wellbore and and there there is isoil-based oil-based mud mud between between the the logging logging instrument instrument and and the the wellbore. wellbore. Figure 10b shows the meshing diagram of the whole area. FigureFigure 10b 10b shows shows the the meshing meshing diagram diagram of ofthe the whole whole area. area.

(a)(a) (b)(b)

FigureFigure 10. 10. Simulation Simulation setup setup of ofthe the logging logging instrument: instrument: ( a ))( asetup; ) setup; ( b )( bmeshing ) meshing diagram. diagram.

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In COMSOL software, the finite element method (FEM) is used to analyze the logging response. TheSensors logging 2019, 19 model, x FORneeds PEER REVIEW to satisfy quasi-static electromagnetic field conditions, i.e. 8 of 16 In COMSOL software, the finite element method (FEM) is used to analyze the logging response.  ((σ(x, y, z) + jωε(x, y, z)) ν(x, y, z)) = 0 (x, y, z) Π  ∇ · ∇ ⊆ The logging model needsν (x, yto, zsatisfy) = U quasi-static electromagnetic field(x, conditions,y, z) Γ i.e.,  1 1  ∇⋅(((,σωενxyz ,) + j (, xyz ,)) ∇ (, xyz ,))0 = (, xyz ,) ⊆Π⊆ (6)  ν2(x, y, z) = 0 (x, y, z) Γ2  ν =⊆Γ⊆  ∂ν(x,y,z) 1(xyz , , ) U ( xyz , ,) 1   = 0 (x, y, z) Γ0 →n ν =⊆Γ ∂  2 (,xyz,) 0 (,,) xyz 2⊆ (6)  ∂ν (x,,)yz where σ(x, y, z) is the space conductivity, =⊆Γ0 ε ( x , y , z )is the dielectric (xyz constant, , , ) v(x, y, z) is the potential  ∂n 0 distribution, ω is the angle frequency of the AC voltage, Π is the sensing field, Γ1 is the space location where σ(x, y, z) is the space conductivity, ε(x, y, z)is the dielectric constant, v(x, y, z) is the potential of upper drill collar, Γ2 is the space location of lower drill collar, Γ0 is the surrounding formation boundarydistribution, and ω→n isis the the angle unit normalfrequency vector of the of theAC surroundingvoltage, Π is formationthe sensing boundary. field, Γ1 is the space location of upper drill collar, Γ2 is the space location of lower drill collar, Γ0 is the surrounding formation  3.1.2.boundary Numerical and n Simulation is the unit Results normal vector of the surrounding formation boundary. 1. Measurement Accuracy of Formation Resistivity 3.1.2. Numerical Simulation Results According to the relevant published literatures, the range of oil-based logging instrument is 1. Measurement Accuracy of Formation Resistivity generally between 0.2 Ω m and 10,000 Ω m [6,17,18]. In the numerical simulation, the formation According to the relevant· published literatures,· the range of oil-based logging instrument is resistivity is set between 0.2 Ω m and 10,000 Ω m. The relative dielectric constant of OBM is set generally between 0.2 Ω·m and· 10,000 Ω·m [6,17,18].· In the numerical simulation, the formation to 3 and the resistivity of OBM is set to 1e11 Ω m. resistivity is set between 0.2 Ω·m and 10,000 Ω· ·m. The relative dielectric constant of OBM is set Into this 3 and work, the theresistivity relative of error OBM is is introduced set to 1e11 to Ω evaluate·m. the measurement accuracy of the logging instrument.In this work, The the relativerelative errorerror σisR introducedcan be determined to evaluate by the measurement following equation: accuracy of the logging instrument. The relative error σR can be determined by the following equation: RRRa− Rt σσR =×= at− 100% (7) R Rt × 100% (7) Rt

wherewhereR Raais is thethe measuredmeasured apparent apparent resistivity resistivity of of the the logging logging instrument, instrument,R Rt tis is the the real real resistivity resistivity ofof the the measured measured formation. formation. The resistivity measurement result of the logging instrument is shown in Figure 11. The resistivity measurement result of the logging instrument is shown in Figure 11.

FigureFigure 11. 11.Resistivity Resistivity measurement measurement result result of of the the logging logging instrument. instrument.

As is shown in Figure 11, the measured apparent formation resistivity is very close to the real As is shown in Figure 11, the measured apparent formation resistivity is very close to the real formation resistivity. For the range of 0.2 Ω·m to 2000 Ω·m, the maximum relative error σR is ± formation resistivity. For the range of 0.2 Ω m to 2000 Ω m, the maximum relative error σR is 0.56% and for the range of 2000 Ω·m to 10,000· Ω·m, the ·maximum relative error σR is ± 6.37%. 0.56% and for the range of 2000 Ω m to 10,000 Ω m, the maximum relative error σR is 6.37%. ±The simulation result shows that the· logging instrument· has good measurement accuracy± in the The simulation result shows that the logging instrument has good measurement accuracy in the common range of 0.2 Ω·m to 10,000 Ω·m. common range of 0.2 Ω m to 10,000 Ω m. 2. Detection Depth and Invasion· Radius· 2. Detection Depth and Invasion Radius In the well logging field, detection depth refers to the horizontal range of the detectable formation that affects the measurement results, while invasion radius means the invasion degree of the OBM into the formation while drilling [36,37]. The detection depth of the logging instrument is generally determined by the pseudo geometric factor, i.e. the detection depth

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In the well logging field, detection depth refers to the horizontal range of the detectable formation that affects the measurement results, while invasion radius means the invasion degree of the OBM into the formation while drilling [36,37]. The detection depth of the logging instrument Sensorsis 2019 generally, 19, x FOR determined PEER REVIEW by the pseudo geometric factor, i.e. the detection depth equals to9 theof 16 Sensorsinvasion 2019, 19, x radius FOR PEER where REVIEW the pseudo geometric factor is 0.5 [36,37]. The pseudo geometric factor9 of G16 isequals determined to the byinvasion the following radius equation:where the pseudo geometric factor is 0.5 [36,37]. The pseudo equalsgeometric to the factor invasion G is determined radius where by the the following pseudo geometricequation: factor is 0.5 [36,37]. The pseudo − geometric factor G is determined by the followingRRRata equation:Rt GG== − (8) RRRRR−−x Rt G = atx t − − (8) where Ra is the apparent resistivity of the formation,RRx t Rt is the real resistivity of the formation, Rx where Ra is the apparent resistivity of the formation, Rt is the real resistivity of the formation, Rx whereisis the the apparent Rapparenta is the apparent resistivity resistivity resistivity of of the the formation formatio of the formation,n when when the the invasionR invasiont is the real radius radius resistivity is is infinite. infinite. of the formation, Rx isAs the is apparent shown in resistivity Figure 12, of thethe formatiopseudo ngeometric when the factorinvasion G increasesradius is infinite.with the increase of the Asinvasion isis shownshown radius. in in Figure Figure When 12 , 12, the the pseudoinvasion pseudo geometric radius geometric is factor large factorG enough,increases G increases the with pseudo the with increase geometric the increase of the factor invasion of theG is invasionradius.almost unchanged. Whenradius. the When invasion At Gthe = 0.5, invasion radius the invasion is radius large radius is enough, large is 0.35enough, the m, pseudo so the the pseudo geometricdetection geometric depth factor ofG factortheis almostlogging G is almostunchanged.instrument unchanged. is At 0.35G =m.At0.5, G = the0.5, invasionthe invasion radius radius is 0.35 is 0.35 m, m, so so the the detection detection depth depth of ofthe the logginglogging instrumentinstrument is is 0.35 m.

FigureFigure 12. 12.Detection Detection depth depth and and invasion invasion radius. radius. Figure 12. Detection depth and invasion radius. 3.3. Influence Influence of of Surrounding Surrounding Rock Rock and and Vertical Vertical Resolution Resolution 3. InfluenceInfluenceInfluence of ofof Surrounding surroundingsurrounding Rock rockrock and refersrefers Vertical toto thethe Resolution influenceinfluence ofof upperupperand and lower lower surrounding surroundingrock rock Influenceresistivity of (R surroundings) on the target rock formation refers resistivityto the influence (Rt). The of three-layer upper and formation lower surrounding model is shown rock in resistivity (Rs) on the target formation resistivity (Rt). The three-layer formation model is shown resistivity (Rs) on the target formation resistivity (Rt). The three-layer formation model is shown in inFigure Figure 13. 13 . Figure 13.

Figure 13. Three-layer formation model. Figure 13.13. Three-layer formation model.

Sensors 2020, 20, 1075 10 of 16 Sensors 2019, 19, x FOR PEER REVIEW 10 of 16

Correction coefficient Rt/Ra is generally used to describe the influence of surrounding rock [36,37]. The closer Rt/Ra is to 1, the smaller the influence of surrounding rock is. As is shown in Figure 14, correction coefficient Rt/Ra is negatively correlated with the thickness of the target formation and Sensors 2019, 19, x FOR PEER REVIEW 10 of 16 positively correlated with Rt/Rs, which is consistent with the theory of well logging [36,37].

Figure 14. Influence of surrounding rock.

Correction coefficient Rt/Ra is generally used to describe the influence of surrounding rock [36,37]. The closer Rt/Ra is to 1, the smaller the influence of surrounding rock is. As is shown in Figure 14, correction coefficient Rt/Ra is negatively correlated with the thickness of the target formation and positively correlatedFigureFigure 14. 14.Influence Influencewith Rt of/ Rofs surrounding, surrounding which is rock.consistent rock. with the theory of well logging [36,37]. Correction coefficient Rt/Ra is generally used to describe the influence of surrounding rock OklahomaOklahoma formation formation model model is a is classic a classic isotropic isotropic model model used to used test electric to test logging electric methods logging [36,37]. The closer Rt/Ra is to 1, the smaller the influence of surrounding rock is. As is shown in [36,38,39].methods [ It36 has,38, 39a large]. It has change a large in changeresistivity in resistivityand thickness, and thickness,and the thinnest and the formation thinnest formationthickness Figure 14, correction coefficient Rt/Ra is negatively correlated with the thickness of the target isthickness only 0.2 m, is only which 0.2 can m, fully which reflect can fullythe complex reflect the situation complex of the situation real formation of the real and formation evaluate andthe formation and positively correlated with Rt/Rs, which is consistent with the theory of well performanceevaluate the performanceof the logging of theinstrument. logging instrument. As is shown As in is shownFigure in15, Figure the vertical 15, the verticaldepth of depth the logging [36,37]. Oklahomaof the Oklahoma formation formation is 80 m is 80and m andthe diameter the diameter of the of theOklahoma Oklahoma formation formation is is30 30 m. m. In In the Oklahoma formation model is a classic isotropic model used to test electric logging methods OklahomaOklahoma formationformation model,model, the the grid grid density density reflects reflects the thickness the thickness of the formation.of the formation. The thickness The [36,38,39]. It has a large change in resistivity and thickness, and the thinnest formation thickness thicknessof formation of formation changes greatly, changes which greatly, can testwhich the ca verticaln test resolutionthe vertical of resolution the logging of instrument. the logging instrument.is only 0.2 m, which can fully reflect the complex situation of the real formation and evaluate the performance of the logging instrument. As is shown in Figure 15, the vertical depth of the Oklahoma formation is 80 m and the diameter of the Oklahoma formation is 30 m. In the Oklahoma formation model, the grid density reflects the thickness of the formation. The thickness of formation changes greatly, which can test the vertical resolution of the logging instrument.

Figure 15. OklahomaOklahoma formation formation model.

Figure 16 shows the logging response of the logging instrument to the Oklahoma formation. As is shown in Figure 16, the measured apparent resistivity of the logging instrument is close to the real

formation resistivity. Further, the variation trend of the apparent resistivity is basically consistent with that of the real formationFigure resistivity, 15. Oklahoma indicating formation that themodel. logging instrument can accurately reﬂect the resistivity change of the Oklahoma formation. Besides, the logging instrument can reﬂect the thickness change of the Oklahoma formation and even detect the formation with the thickness of 0.2 m at the vertical depth range of 68 m to 68.2 m, showing that the logging instrument has a high vertical resolution of thin formation layers.

SensorsSensors2020 2019, 20, 19, 1075, x FOR PEER REVIEW 1111 of of 16 16

FigureFigure 16. 16.Logging Logging response response of of the the logging logging instrument instrument to to the the Oklahoma Oklahoma formation. formation. Figure 16 shows the logging response of the logging instrument to the Oklahoma formation. As 3.2. Practical Experiments is shown in Figure 16, the measured apparent resistivity of the logging instrument is close to the Inreal order formation to further resistivity. test the Furthe performancer, the variation of the logging trend of instrument, the apparent resistance resistivity box is and basically well loggingconsistent experiments with that were of carried the real out. formation The resistance resistivity, box indicating experiment that isthe a logging principle instrument veriﬁcation can experiment.accurately The wellreflect logging the resistivity experiment change is carried of outthe toOklahoma evaluate the formation. performance Besides, of the the developed logging logginginstrument instrument. can reflect the thickness change of the Oklahoma formation and even detect the formation with the thickness of 0.2 m at the vertical depth range of 68 m to 68.2 m, showing that 3.2.1. Resistancethe logging Box instrument Experiment has a high vertical resolution of thin formation layers. As the resistance box experiment is a principle veriﬁcation experiment, the parameters of the logging3.2. Practical instrument Experiments such as the excitation frequency, electrode shape and size are not optimized. In this part,In order a resistance to further box test is the chosen performance to simulate of the the logging formation instrument, and diesel resistance oil is used box toand simulate well logging the OBM.experiments In order were to obtaincarried a out. larger The current, resistance a circularbox expe pick-upriment is electrode a principle is usedverification without experiment. considering The thewell azimuth logging recognitionexperiment is ability. carried The out experimentalto evaluate the setup performance of resistance of the developed box experiment logging is instrument. shown in Figure 17. The experimental setup includes the developed logging instrument, a resistance box and a computer.3.2.1. Resistance The equivalent Box Experiment circuit of the measurement path of the logging instrument is the same as that of Figure7. Sensors 2019As the, 19, xresistance FOR PEER REVIEWbox experiment is a principle verification experiment, the parameters12 of of 16the logging instrument such as the excitation frequency, electrode shape and size are not optimized. In this part, a resistance box is chosen to simulate the formation and diesel oil is used to simulate the OBM. In order to obtain a larger current, a circular pick-up electrode is used without considering the azimuth recognition ability. The experimental setup of resistance box experiment is shown in Figure 17. The experimental setup includes the developed logging instrument, a resistance box and a computer. The equivalent circuit of the measurement path of the logging instrument is the same as that of Figure 7.

(a) (b)

Figure 17. Experimental setup of resistance box experiment: ( a)) schematic; ( b) photo.

The excitation frequency is set to 20 kHz. The resistance of the resistance box ranges from 2 kΩ to 30 kΩ. Again, the relative error of resistance measurement is used to present the results. The relative error σr can be determined by the following equation: rr− σ =×at r 100% (9) rt where ra is the measured apparent resistance by the logging instrument, rt is the value of the resistance box.

(a) (b)

Figure 18. Results of resistance box experiment: (a) measured resistance; (b) relative errors.

Figure 18 shows the results of the resistance box experiment. As is shown in Figure 18, the relative errors σr of the resistance measurement by the developed instrument are less than ± 1.67%. This result indicates that the logging instrument has good resistance measurement accuracy.

3.2.2. Well Logging Experiment Considering the real logging conditions, an experimental well is built to simulate the real formation. The experimental well is composed of sandstone, which is one of the common rocks in the real formation. The sandstones are provided by the Huiyu stone company, Hangzhou, China and the origin of the sandstones is Chengdu, China. The resistivity of the sandstones is about 4000 Ω·m. There

Sensors 2019, 19, x FOR PEER REVIEW 12 of 16

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The excitation frequency(a) is set to 20 kHz. The resistance of the resistance(b) box ranges from 2 kΩ to 30 kΩ. Again, the relative error of resistance measurement is used to present the results. The relative Figure 17. Experimental setup of resistance box experiment: (a) schematic; (b) photo. error σr can be determined by the following equation:

The excitation frequency is set to 20 kHz.ra Thert resistance of the resistance box ranges from 2 kΩ σr = − 100% (9) to 30 kΩ. Again, the relative error of resistancert meas× urement is used to present the results. The relative error σr can be determined by the following equation: where r is the measured apparent resistance by the logging instrument, r is the value of the a rr− t σ =×at resistance box. r 100% (9) r Figure 18 shows the results of the resistance boxt experiment. As is shown in Figure 18, the relative errorswhereσ raof is the measured resistance measurementapparent resistance by the by developed the logging instrument instrument, are lessrt is the than value1.67%. of the This resistance result ± indicatesbox. that the logging instrument has good resistance measurement accuracy.

(a) (b)

FigureFigure 18. 18.Results Results ofof resistanceresistance box box experiment: experiment: (a(a)) measured measured resistance; resistance; ( b(b)) relative relative errors. errors. 3.2.2. Well Logging Experiment Figure 18 shows the results of the resistance box experiment. As is shown in Figure 18, the relativeConsidering errors σr the of realthe resistance logging conditions, measurement an experimental by the developed well is built instrument to simulate are theless real than formation. ± 1.67%. TheThis experimental result indicates well that is composed the logging of sandstone, instrument which has good is one resistance of the common measurement rocks in the accuracy. real formation. The sandstones are provided by the Huiyu stone company, Hangzhou, China and the origin of the Sensors 2019, 19, x FOR PEER REVIEW 13 of 16 sandstones3.2.2. Well isLogging Chengdu, Experiment China. The resistivity of the sandstones is about 4000 Ω m. There are several · areartiﬁcial severalConsidering patterns artificial on the patterns the real wellbore loggingon the of wellbore theconditions, experimental of the an experimental experimental well. In addition, well. well In silicone isaddition, built oil to issilicone simulate used to oil simulate theis used real totheformation. simulate OBM instead theThe OBM experimental of diesel instead oil, of becausewell diesel is composed oil, it is because more of environmentally itsandstone, is more environmentally which friendly is one than of thefriendly diesel common oil. than Though rocks diesel in oil. the the Thoughexcitationreal formation. the frequency excitation The sandstones should frequency be asare should high provided as be possible asby highthe in Huiyu orderas possible stone to reduce company, in order the capacitive toHangzhou, reduce reactance the China capacitive and of the the reactanceOBM,origin the of theof excitation the sandstones OBM, frequency the is excitation Chengdu, is set frequency to China. 50 kHz The dueis resistivity set to to the 50 limitationkHz of the due sandstones to of the the limitation excitation is about of coil.4000 the In Ωexcitation·m. order There to coil.test theIn azimuthorder to recognitiontest the azimuth ability ofrecognition the logging ability instrument, of the alogging button pick-upinstrument, electrode a button is used pick-up in the electrodeexperiment is used instead in the of theexperiment circular electrode.instead of Thethe circular developed electrode. experimental The developed well is shown experimental in Figure well 19 isand shown the experimental in Figure 19 setupand the is experimental shown in Figure setup 20. is shown in Figure 20.

Figure 19. Experimental well.

Figure 20. Experimental setup of well logging experiment.

In this work, part of the experimental well with the length of 26 cm is tested and three patterns on the wellbore are to be measured within this range. This experiment is to investigate the logging response of the instrument concerning the measured patterns, which is shown in the dotted box in Figure 19. The three patterns are rectangular with the same length and different widths, and are placed at different positions along the axial direction of the drill collar. The diagram of the measured patterns is shown in Figure 21. Different patterns introduce air gaps of different sizes at different positions. Due to the air gap, the resistivity of the pattern areas is higher than other areas in the experimental well. During experiment, the pick-up electrode is moved by moving the drill collar. The experimental result is shown in Figure 21. As is shown in Figure 21, the measured resistance increases when the pick-up electrode moves toward the patterns, and decreases when the electrode moves away from the patterns. It is found that there are three peaks at the movement distances of 6 cm, 12 cm and 24 cm, which are consistent with the center positions of the three patterns. Besides, as the three patterns have different widths, the widths of the three peaks are also different. The experimental result shows that the logging instrument can accurately reflect the positions of the three patterns, further indicating the feasibility of the proposed logging method.

Sensors 2019, 19, x FOR PEER REVIEW 13 of 16 are several artificial patterns on the wellbore of the experimental well. In addition, silicone oil is used to simulate the OBM instead of diesel oil, because it is more environmentally friendly than diesel oil. Though the excitation frequency should be as high as possible in order to reduce the capacitive reactance of the OBM, the excitation frequency is set to 50 kHz due to the limitation of the excitation coil. In order to test the azimuth recognition ability of the logging instrument, a button pick-up electrode is used in the experiment instead of the circular electrode. The developed experimental well is shown in Figure 19 and the experimental setup is shown in Figure 20.

Sensors 2020, 20, 1075 13 of 16 Figure 19. Experimental well.

Figure 20. Experimental setup of well logging experiment.

In this work, part of the experimental well with the length of 26 cm is tested and three patterns on the wellbore are to bebe measuredmeasured withinwithin thisthis range.range. This experiment is to investigate the logging response of the instrument concerning the measur measureded patterns, which is shown in the dotted box in Figure 1919.. TheThe threethree patterns patterns are are rectangular rectangular with with the the same same length length and diandfferent different widths, widths, and are and placed are placedat different at different positions positions along the along axial the direction axial direction of the drill of the collar. drill The collar. diagram The diagram of the measured of the measured patterns patternsis shown is in shown Figure in 21 Figure. Different 21. Different patterns introducepatterns in airtroduce gaps ofair di gapsfferent of sizesdifferent at di sizesfferent at positions.different positions.Due to the Due air gap,to the the air resistivity gap, the of resistivity the pattern of areasthe pattern is higher areas than is otherhigher areas than in other the experimental areas in the well.experimental During experiment,well. During the experime pick-upnt, electrode the pick-up is moved electrode by moving is moved the by drill moving collar. the The drill experimental collar. The experimentalSensorsresult 2019 is shown, 19, xresult FOR in Figure PEER is shown REVIEW 21. in Figure 21. 14 of 16 As is shown in Figure 21, the measured resistance increases when the pick-up electrode moves toward the patterns, and decreases when the electrode moves away from the patterns. It is found that there are three peaks at the movement distances of 6 cm, 12 cm and 24 cm, which are consistent with the center positions of the three patterns. Besides, as the three patterns have different widths, the widths of the three peaks are also different. The experimental result shows that the logging instrument can accurately reflect the positions of the three patterns, further indicating the feasibility of the proposed logging method.

Figure 21. Logging response of the instrument in well logging experiment.

4. ConclusionsAs is shown in Figure 21, the measured resistance increases when the pick-up electrode moves toward the patterns, and decreases when the electrode moves away from the patterns. It is found that Our study focuses on the measurement of the formation resistivity in the oil-based mud environment. A new oil-based LWD method is proposed by referring to the idea of the C4D technique and combining with the inductive coupling principle, which can solve the electrical insulation problem of the OBM and make the measurement of the formation resistivity feasible. Based on the proposed method, a corresponding logging instrument is developed and its performance is investigated by both numerical simulation and practical experiments. Numerical simulation results show that the logging instrument has good measurement accuracy in a wide measurement range of the formation resistivity. The maximum relative error of resistivity measurement in the common range of 0.2 Ω·m to 2000 Ω·m is ± 0.56%. Moreover, the logging instrument has deep detection depth and high vertical resolution, and can accurately reflect the resistivity change of the Oklahoma formation. The results of resistance box experiment show that the logging instrument has good resistance measurement accuracy and the maximum relative error is ± 1.67%. The results of well logging experiment show that the logging instrument can accurately reflect the positions of the patterns on the wellbore of the experimental well. Both numerical simulation and practical experiments verify the feasibility and effectiveness of the new method. Compared with the conventional methods, such as making OBM conductive, using a knife-like electrode to cut through the mud cake and four-terminal measurement, the proposed method has the advantages of low cost, simple construction, and good real-time performance. Useful knowledge and experience concerning the oil-based LWD have been obtained in this work. The research results can provide useful reference and guidance for further lateral resistivity measurement of oil-based LWD and design of logging instruments. However, the proposed method also has some limitations at the current stage. According to the measurement principle of C4D, the existence of the two coupling capacitances makes the measurement possible, but only the resistance

Sensors 2020, 20, 1075 14 of 16 there are three peaks at the movement distances of 6 cm, 12 cm and 24 cm, which are consistent with the center positions of the three patterns. Besides, as the three patterns have different widths, the widths of the three peaks are also different. The experimental result shows that the logging instrument can accurately reflect the positions of the three patterns, further indicating the feasibility of the proposed logging method.

4. Conclusions Our study focuses on the measurement of the formation resistivity in the oil-based mud environment. A new oil-based LWD method is proposed by referring to the idea of the C4D technique and combining with the inductive coupling principle, which can solve the electrical insulation problem of the OBM and make the measurement of the formation resistivity feasible. Based on the proposed method, a corresponding logging instrument is developed and its performance is investigated by both numerical simulation and practical experiments. Numerical simulation results show that the logging instrument has good measurement accuracy in a wide measurement range of the formation resistivity. The maximum relative error of resistivity measurement in the common range of 0.2 Ω m to 2000 Ω m · · is 0.56%. Moreover, the logging instrument has deep detection depth and high vertical resolution, ± and can accurately reflect the resistivity change of the Oklahoma formation. The results of resistance box experiment show that the logging instrument has good resistance measurement accuracy and the maximum relative error is 1.67%. The results of well logging experiment show that the logging ± instrument can accurately reflect the positions of the patterns on the wellbore of the experimental well. Both numerical simulation and practical experiments verify the feasibility and effectiveness of the new method. Compared with the conventional methods, such as making OBM conductive, using a knife-like electrode to cut through the mud cake and four-terminal measurement, the proposed method has the advantages of low cost, simple construction, and good real-time performance. Useful knowledge and experience concerning the oil-based LWD have been obtained in this work. The research results can provide useful reference and guidance for further lateral resistivity measurement of oil-based LWD and design of logging instruments. However, the proposed method also has some limitations at the current stage. According to the measurement principle of C4D, the existence of the two coupling capacitances makes the measurement possible, but only the resistance of the formation is the useful information and the coupling capacitances are the background signal. In further research, the influence of the coupling capacitances needs to be either reduced by increasing the excitation frequency or canceled by introducing effective methods like the impedance elimination method and the series resonance method. In addition, the resistivity measurement is easily affected by the experimental temperature. Thus, temperature compensation should be considered in the future to overcome the influence of environmental temperature on the resistivity measurement.

Author Contributions: Conceptualization, B.W.; methodology, B.W. and Z.H.; software, Y.W.; validation, Y.W., W.Z. and Y.J.; formal analysis, Y.W. and Y.J.; investigation, Y.W. and Y.J.; resources, B.L., B.W. and Z.H.; data curation, Y.W.; writing—original draft preparation, Y.W.; writing—review and editing, B.L., Y.J., B.W. and Z.H.; visualization, Y.W.; supervision, W.Z. and B.W.; project administration, W.Z. and B.W.; funding acquisition, B.L. and B.W. All authors have read and agreed to the published version of the manuscript. Funding: This work is supported by the National Science and Technology Major Program of China (2016ZX05021-002). Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Ekstrom, M.P.; Dahan, C.A.; Chen, M.Y. Formation imaging with microelectrical scanning arrays. In Proceedings of the SPWLA 27th Annual Logging Symposium, Houston, TX, USA, 9–13 June 1986. 2. Gao, J.S.; Liu, X.; Zhao, J.P. A new electrical imaging logging method in oil-based mud for low-resistivity formation based on concave electrode couples. J. Petrol. Sci. Eng. 2020, 185, 106675. [CrossRef] Sensors 2020, 20, 1075 15 of 16

3. Færgestad, I.M.; Strachan, C.R. Developing a high-performance oil-base fluid for exploration drilling. Oilfield Review. 2014, 26, 26–33. 4. Gao, J.S.; Sun, J.M.; Jiang, Y.J. A novel quantitative imaging method for oil-based mud: the full-range formation resistivity. J. Petrol. Sci. Eng. 2018, 162, 844–851. [CrossRef] 5. Habashy, T.; Hayman, A.; Chen, Y.H. System and method for imaging properties of subterranean formations. US patent No. US8754651B2, 7 June 2012. 6. Gao, J.S.; Jiang, L.M.; Liu, Y.P. Review and Analysis on the Development and Applications of Electrical Imaging Logging in Oil-Based Mud. J. Appl. Geophy. 2019, 171, 1–11. [CrossRef] 7. Yang, J.; Garcia, A.R.; Arensdorf, J.J.; Clapper, D.K.; Darugar, Q.A. Electrically Conductive Oil-Based Fluids. US patent No. US10280356B2, 7 May 2019. 8. Halliday, W.S.; Schwertner, D.W.; Strickland, S.D. Drilling Fluids Comprising Sized Graphite Particles. US patent No. 7087555B2, 8 August 2006. 9. Thaemlitz, C.J. Electrically Conductive Oil-Based Mud. US patent No. 7112557B2, 26 September 2006. 10. Jones, T.G.J.; Tustin, G.J. Electrically Conductive Non-Aqueous Wellbore Fluid. US patent No. 7399731B2, 15 July 2008. 11. Palmer, B.J.; Fu, D.; Card, R. Wellbore Fluids and Their Application. US patent 6608005B2, 19 August 2003. 12. Monteiro, O.; Quintero, L. Graphene-Containing Fluids for Oil and Gas Exploration and Production. US patent 20120245058A1, 27 September 2012. 13. Hoelscher, B.K.P.; Bovet, C.; Friedheim, J. Electrically Conductive Wellbore Fluids and Methods of Use. US patent No. 20150284619A1, 8 October 2015. 14. Quintero, L.; Cardenas, A.E.; Clark, D.E. Nanofluids and Methods of Use for Drilling and Completion Fluids. US patent No. 8822386B2, 2 September 2014. 15. Zanten, R.V. Electrically Conductive Oil-Based Drilling Fluids. US patent No. 8763695B2, 1 July 2014. 16. Clark, B.O.; Kleinberg, R.L.; Seleznev, N.V. Electrical Heating of Oil Shale and Heavy Oil Formations. US patent No. 9410408B2, 9 August 2016. 17. Williams, P.; McQuown, S.; Palacio, M.D.B. A new small diameter, memory based, microresistivity imaging tool engineered for oil-based mud: Design and applications. In Proceedings of the SPWLA 57th Annual Logging Symposium, Reykjavik, Iceland, 25–29 June 2016. 18. Liu, Y.; Yu, Y.; Wu, D. Development and application of oil base mud resistivity imaging logging instrument OBIT. In Proceedings of the 18th Annual Logging Symposium, Urumchi, China, 7 October 2013. 19. Sun, J.M.; Gao, J.S.; Jiang, Y.J. Resistivity and relative permittivity imaging for oil-based mud: A method and numerical simulation. J. Petrol. Sci. Eng. 2016, 147, 24–33. [CrossRef] 20. Gas, B.; Demjanenko, M.; Vacik, J. High-frequency contactless conductivity detection in isotachophoresis. J. Chromatogr. 1980, 192, 253–257. [CrossRef] 21. Zemann, A.J.; Schnell, E.; Volgger, D. Contactless conductivity detection for capillary electrophoresis. Anal. Chem. 1998, 70, 563–567. [CrossRef] 22. Da Silva, J.A.K.; Do Lago, C.L. An oscillometric detector for capillary electrophoresis. Anal. Chem. 1998, 70, 4339–4343. [CrossRef] 23. Rosthal, R.A. Formation evaluation and geological interpretation from the Resistivity-at-the-Bit Tool. Eukaryot. Cell 1995, 7, 268–278. 24. Gas, B.; Zuska, J.; Coufal, P. Optimization of the high-frequency contactless conductivity detector for capillary electrophoresis. Electrophoresis. 2002, 23, 3520–3527. [CrossRef] 25. Pumera, M. Contactless conductivity detection for microfluidics: designs and applications. Talanta. 2007, 74, 358–364. [CrossRef][PubMed] 26. Kuban, P.; Hauser, P.C. A review of the recent achievements in capacitively coupled contactless conductivity detection. Anal. Chem. 2008, 607, 15–29. 27. Kuban, P.; Hauser, P.C. Ten years of axial capacitively coupled contactless conductivity detection for CZE-a review. Electrophoresis. 2009, 30, 176–188. [CrossRef][PubMed] 28. Kuban, P.; Hauser, P.C. Capacitively Coupled Contactless Conductivity Detection for Microseparation Techniques–Recent Developments. Electrophoresis. 2011, 32, 30–42. [CrossRef][PubMed] 29. Arps, J.J. Inductive resistivity guard logging apparatus including toroidal coils mounted on a conductive stem. US patent No. 3305771A, 21 February 1967. Sensors 2020, 20, 1075 16 of 16

30. Bonner, S.; Burgess, T.; Clark, B. Measurements at the bit: a new generation of MWD tools. Oilfield Review. 1993, 5, 44–54. 31. Bonner, S.; Fredette, M.; Lovell, J. Resistivity while drilling-images from the string. Oilfield Review. 1996, 8, 4–19. 32. Wu, Y.K.; Ni, W.N.; Li, X. Research on characteristics of a new oil-based logging-while-drilling instrument. In Proceedings of the 11th International Symposium on Measurement Techniques for Multiphase Flow, Zhenjiang, China, 3–7 November 2019. 33. Ji, H.F.; Lyu, Y.C.; Wang, B.L. An improved capacitively coupled contactless conductivity detection sensor for industrial applications. Sens. Actuator A Phys. 2015, 235, 273–280. [CrossRef] 34. Scott, R.J.; Leichti, R.J.; Miller, T.H. Finite-element modeling of log wall lateral force resistance. Forest Prod. J. 2005, 55, 48–54. 35. Xing, G.L.; Wang, H.J.; Ding, Z. New Combined Measurement Method of the Electromagnetic Propagation Resistivity Logging. IEEE Trans. Geosci. Remote Sens. 2008, 5, 430–432. [CrossRef] 36. Kang, Z.M.; Ke, S.Z.; Jiang, M. Environmental corrections of a dual-induction logging while drilling tool in vertical wells. J. Appl. Geophy. 2018, 151, 309–317. [CrossRef] 37. Xu, W.; Ke, S.Z.; Li, A.Z. Response simulation and theoretical calibration of a dual-induction resistivity LWD tool. J. Appl. Geophy. 2014, 11, 31–40. [CrossRef] 38. Li, K.S.; Gao, J.; Ju, X.D. Study on ultra-deep azimuthal electromagnetic resistivity LWD tool by influence quantification on azimuthal depth of investigation and real signal. Pure Appl. Geophys. 2018, 175, 4465–4482. [CrossRef] 39. Davydycheva, S. 3D modeling of new-generation (1999-2010) resistivity logging tools. Lead. Edge 2010, 29, 780–789. [CrossRef]

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