sensors

Review Downhole Applications of Magnetic Sensors

Chinthaka P. Gooneratne *, Bodong Li and Timothy E. Moellendick

Drilling Technology Team, Exploration and Petroleum Engineering Center—Advanced Research Center (EXPEC-ARC), Dhahran 31311, Saudi Arabia; [email protected] (B.L.); [email protected] (T.E.M.) * Correspondence: [email protected]; Tel.: +966-(0)53-578-4190

Received: 12 August 2017; Accepted: 12 October 2017; Published: 19 October 2017

Abstract: In this paper we present a review of the application of two types of magnetic sensors—fluxgate magnetometers and nuclear magnetic resonance (NMR) sensors—in the oil/gas industry. These magnetic sensors play a critical role in drilling wells safely, accurately and efficiently into a target reservoir zone by providing directional data of the well and acquiring information about the surrounding geological formations. Research into magnetic sensors for oil/gas drilling has not been explored by researchers to the same extent as other applications, such as biomedical, magnetic storage and automotive/aerospace applications. Therefore, this paper aims to serve as an opportunity for researchers to truly understand how magnetic sensors can be used in a downhole environment and to provide fertile ground for research and development in this area. A look ahead, discussing other magnetic sensor technologies that can potentially be used in the oil/gas industry is presented, and what is still needed in order deploy them in the field is also addressed.

Keywords: fluxgate magnetometer; nuclear magnetic resonance; magnetic sensors; drilling technology; oil and gas; petroleum; downhole; harsh environment; high pressure high temperature (HPHT)

1. Introduction Magnetic sensors have been used in an extraordinary number of applications over the years, in the fields as diverse as automation, automotive, aerospace, biomedicine, computers, security, robotics, smart grids and textile technologies [1–19], and their utilization continues to increase at a rapid rate due to the advancements made in the area of nano-/microfabrication. In this paper, the application of magnetic sensors in the oil/gas industry, a relatively unexplored area of research compared with some of the aforementioned applications, is presented. Declining resources have forced oil/gas companies to drill deeper in different directions, and in more extreme and unknown environments. Therefore, it is important to monitor and analyze downhole environments in real-time when drilling a well in order to make timely decisions to optimize efficiency as well as prevent costly errors. One of the main ways of maximizing access to an oil/gas reservoir is to drill directional wells [20,21]. Directional drilling is the intentional deviation of a well from a vertical path at a predetermined trajectory, which allows access to reservoirs that cannot be reached efficiently with a vertical well drilled from the surface and maximizing reachability inside a reservoir. Therefore, directional drilling is used to optimize the production of hydrocarbons. Moreover, by drilling multiple directional wells from a drilling platform rather than drilling several vertical wells the drilling cost, impact on the environment and health and safety issues can be reduced. When planning directional wells, there are many considerations that have to be taken into account, such as target location, shape and size, well trajectory, geological formations, adjacent wells and rig surface facilities. The deviation of the well has to be accurately controlled in order to keep the trajectory of the well within the prescribed angle in order to reach the intended target. Failure to accurately drill a directional well can result in a ‘dry hole’, and significant financial losses for the company, as well as impacting their business strategy.

Sensors 2017, 17, 2384; doi:10.3390/s17102384 www.mdpi.com/journal/sensors Sensors 2017, 17, 2384 2 of 32

The oil/gas industry exploits the affordable, rugged, compact and reliable features of magnetic sensors, using them in harsh downhole environments. Fluxgate magnetometers (FGMs) and nuclear magnetic resonance (NMR) sensors play a significant role in optimizing well placement and completion resulting in maximum access to oil/gas reservoirs and higher production rates. In this paper we describe how FGMs and NMR sensors are utilized to obtain measurements inside wells during the drilling process so that wells can safely and efficiently reach oil/gas reservoirs located thousands of feet below the ground whilst also obtaining maximum access to these reservoirs. FGMs give the driller at the surface a means of navigating a well, whereas NMR sensors provide information about the geological characteristics of the formations being drilled through, in real-time.

2. Downhole Magnetometers

2.1. Principles of Fluxgate Magnetometers Since their inception in the 1930s, FGMs have been used to measure magnetic fields in a wide range of applications [22–24] and have recently progressed to solid-state sensors with the advancements made in micro/nanofabrication technology. Thorough reviews of FGMs can be found in [1,2,25–27]. Typical parameters of FGMs are shown in Table1. Referring to Table1, the magnetic field range, noise level and linearity allows FGMs to measure the Earth’s magnetic field, between 25 and 65 µT, and the sensitivity allows a measurable output with a 5 V power supply and simple signal processing. Moreover, the low temperature coefficient means that FGMs can be used when drilling wells with depths up to 20,000 feet, where temperatures can be as high as 230 ◦C. Several papers have demonstrated the stability of FGMs in a 180–250 ◦C temperature range [28,29]. Not only do FGMs have excellent noise characteristics compared with other magnetic sensors but they can be constructed easily according to well established design principles at low cost.

Table 1. Typical parameters of fluxgate magnetometers.

Field Range Sensitivity Linearity Temperature Coefficient Size Noise Frequency √ 10 pT–2 mT 20–50 mV/µT <10 ppm 0.25 nT/◦C mm 15 pT/ Hz 10 kHz

The working principle of an FGM in its simplest form can be explained with reference to Figure1. An FGM consists of two coils, an excitation and a pick-up coil, wound around a ferromagnetic rod as shown in Figure1(ai,bi). The ferromagnetic rod is driven to saturation when a large alternating current (AC) is applied to the excitation coil by a waveform generator and a magnetic flux density (B) is induced in the rod, as shown in Figure1(ai). As the rod is driven into saturation, as shown in Figure1(bi), it becomes progressively more difficult for magnetic field ( H) lines to pass through the rod and induce a B. This reluctance of the rod is sensed by the pick-up coil, which creates changes in the voltage of the pick-up coil. Since the rod is driven to saturation twice during each excitation cycle, the second harmonic of the output voltage of the pick-up coil is extracted by phase demodulation circuitry. When the FGM is in the presence of an external H (Hext), such as the Earth’s magnetic field, the induced B is distorted. This distortion is sensed by the pick-up coil causing a change in the output voltage; the magnitude corresponds to the strength of Hext and the phase to the orientation of the Hext. The magnetic hysteresis (B-H) curve in Figure1(aii) shows the operation of the FGM in the linear region during excitation, and the B-H curve in Figure1(bii) shows the operation of the FGM in saturation. The sensitivity of the FGM depends on the B-H curve, where a steeper magnetizing curve relates to a more sensitive FGM. The power consumption of an FGM depends on the coercivity and saturation fields as shown in Figure1(aii,bii). Lower saturation coercivity fields mean lower magnetic fields, and hence lower excitation currents and power, required to drive the rod to saturation and back to zero after being saturated. The frequency response of an FGM depends on the time lag between the application of the excitation field and the response of the ferromagnetic rod. Sensors 2017, 17, 2384 3 of 32 Sensors 2017, 17, 2384 3 of 32

(i) (i)

Magnetic field lines

Excitation coil AC excitation waveform

Ferromagnetic rod

Pick-up coil V Voltage output V

(ii) Not Saturated (ii) Saturated B B Working area Working area Coercive field H H

Working area

Saturation field

(a) (b)

FigureFigure 1. (a )1. Principle (a) Principle operation operation of of a a fluxgate fluxgate magnetometermagnetometer (FGM (FGM).). (i) ( Applicationi) Application of an of AC an current AC current and the induction of a magnetic flux density (B) in the rod and (ii) the corresponding B-H curve and the induction of a magnetic flux density (B) in the rod and (ii) the corresponding B-H curve showing the grey area the FGM operates in during this excitation phase; (b) (i) The FGM in saturation showing the grey area the FGM operates in during this excitation phase; (b)(i) The FGM in saturation mode where B has saturated and magnetic field (H) lines do not converge to the rod resulting in (ii) B H modethe where FGM operatinghas saturated in the saturated and magnetic area of the field B-H ( curve.) lines do not converge to the rod resulting in (ii) the FGM operating in the saturated area of the B-H curve. In reality, for a single ferromagnetic rod, the pick-up coil will sense both the excitation voltage Inas reality,well as the for output a single voltage. ferromagnetic This makes rod, it challenging the pick-up to coil filter will out sense the second both theharmonic, excitation obtain voltage its as well asph thease and output rectify voltage. it to obtain This makesvoltage itproportional challenging to to the filter magnitude out the of second the external harmonic, field. obtainIn order its to phase overcome this challenge two variants of the FGM, a Vacquier-type FGM, shown in Figure 2(ai), and and rectify it to obtain voltage proportional to the magnitude of the external field. In order to overcome a ring-core FGM, shown in Figure 2(aii), are commonly used [26,30–32]. Taking Figure 2a into this challenge two variants of the FGM, a Vacquier-type FGM, shown in Figure2(ai), and a ring-core account, the wires are wound on both rods in opposite directions to each other in a Vacquier-type FGM,FGM shown and, in similarly Figure2 for(aii), a ring are- commonlycore FGM, the used windings [ 26,30 are–32 such]. Taking that on Figure one half2a intoof the account, core they the are wires are woundin the opposite on both direction rods in oppositeto the other directions half. When to an each excitation other in current a Vacquier-type is applied, the FGM induced and, B similarly in one for a ring-corerod or half FGM, of the core windings will have are the such opposite that on polarity one half to ofB in the the core second they rod are or in the the other opposite half of direction the to thecore. other This half. results When in a annet excitationmagnetization current of zero is applied,and an output the inducedvoltage ofB zeroin one at the rod pick or-up half coil. of For the core will haveexample, the oppositeFigure 2( polaritybi,bii) show to B thatin the when second an exc roditation or the current other (orange half of the waveform) core. This is appliedresults, in B a net magnetizationincreases with ofzero the current and an and output reaches voltage saturation of zero at the at peak the pick-upof the excitation coil. For current. example, The B Figure produced2(bi,bii) showfro thatm both when rods an and excitation both sides current of the (orangecores are waveform) mirror images is applied,of each otherB increases along the with x-axis the (blue current and and green waveforms) resulting in a net B of zero [33]. The voltages from both rods and sides of the core reaches saturation at the peak of the excitation current. The B produced from both rods and both sides at the pick-up coil are also mirror images along the x-axis, are proportional to the rate of change of B, of the cores are mirror images of each other along the x-axis (blue and green waveforms) resulting in a net B of zero [33]. The voltages from both rods and sides of the core at the pick-up coil are also mirror images along the x-axis, are proportional to the rate of change of B, and increase and then reach SensorsSensors 20172017,, 1717,, 23842384 44 ofof 3232 and increase and then reach zero at saturation as the rate of change of B is zero at saturation. zeroHowever, at saturation when there as the is an rate Hext of, the change rod or of theB is half zero-core at saturation.that is generating However, an H when in the there same is direction an Hext, theas H rodext takes or the longer half-core to come that out is generating of saturation, an H thereforein the same the rod direction or the ashalfHext-coretakes generating longer to an come H in outthe ofopposite saturation, direction therefore comes the out rod of or saturation the half-core sooner. generating This can an beH seenin the in opposite Figure 2 direction(biii) from comes the short out ofand saturation long saturation sooner. times This canfor each be seen rod in or Figure half-core2(biii) every from half the cycle short of and the longwaveform. saturation This times creates for a eachnet change rod or half-corein B in the every pick half-up cyclecoil (black of the waveform), waveform. Thiswhich creates induces a net a voltage change in Bthein pick the pick-up-up coil coil(purple (black waveform), waveform), as whichshown inducesin Figure a voltage2(biv). A in clear the pick-up amplified coil waveform (purple waveform), (red waveform) as shown can be in Figureobtained2(biv). by tuning A clear the amplified pick-up waveform coil. (red waveform) can be obtained by tuning the pick-up coil.

Ferromagnetic ring (i) (ii) Excitation coil Ferromagnetic Excitation rod coil V

Pick-up V coil Pick-up coil

Rod 1 Rod 2 Side 1 Side 2 Vacquier type Ring-core type (a)

(i) Vexcitation Excitation Waveform

(ii) B No external magnetic field (Hext = 0) B generated by each Rod 1/Side 1 of Core rod or side of the core (No external field) Rod 2/Side 2 of Core

(iii) B External magnetic field B generated by each (Hext ≠ 0) rod or side of the core (External field) Net change in B at the pick-up coil

(iv) Shorter saturation times Vpick-up Induced voltage Voltage at pick-up coil Tuned voltage due to external field

Time

(b) FigureFigure 2.2. ((a)Variants)Variants ofof anan FGM.FGM. ((ii)) Vacquier-typeVacquier-type FGMFGM withwith wireswires woundwound onon bothboth rodsrods 11 andand 22 inin oppositeopposite directionsdirections to to each each other; other (; ii(ii)) Ring-core Ring-core type type FGM FGM where where the the windings windings on on side side 1 of1 of the the core core is inis oppositein opposite direction direction to side to side 2; (b 2;)( (ib)) Application (i) Application of an of excitation an excitation waveform waveform (orange (orange waveform) waveform) to (a)( toi) ( ora) ((ai)() orii); (a (ii) )(ii In); the(ii) absence In the absence of an external of an magneticexternal magnetic field (Hext ),fieldB induced (Hext), B in induced rod 1/side in 1rod (blue 1/side waveform) 1 (blue iswaveform) opposite in is polarityopposite to in B polarity induced to in B rod induced 2/side in 2 rod (green 2/side waveform), 2 (green waveform), so net magnetization so net magnetization and voltage (V)and induced voltage at (V the) inducedpick-up coil at theis zero; pick (iii-up) In coil the is presence zero; ( ofiii) an InH ext thethe presence rod/core of generating an Hext the a magnetic rod/core fieldgenerating in the a same magnetic direction field asin Htheext samehave direction a shorter as saturation Hext have timea shorter and saturation there is a nettime change and there in B is in a thenet pick-upchange in coil B in (black the pick waveform);-up coil (black (iv) This waveform) net change; (iv) in This B induces net change a voltage in B induces in the pick-upa voltage coil in (purplethe pick waveform).-up coil (purple A clear waveform). amplified A waveform clear amplified (red waveform) waveform can (red be obtainedwaveform) by can tuning be obtained the pick-up by coiltuning [33 ].the pick-up coil [33].

MoreMore recently, recently, miniature miniature FGMs FGMs have have been been fabricated fabricated using using complementarycomplementary metal-oxide-metal-oxide- semiconductorsemiconductor (CMOS),(CMOS), micro-fabricationmicro-fabrication andand printedprinted circuitcircuit boardboard PCBPCB methodsmethods [[3434––3737].]. Their size, compactness,compactness, low low power powe consumptionr consumption and theand possibility the possibility of integration of integration with electronics with electronics into integrated into circuitintegrated (IC) circuit chips ( makeIC) chips them make ideal them candidates ideal candidates for portable for portable devices. devices. However, However, one of theone majorof the major drawbacks of miniature FGMs is the limited number of turns possible in the excitation and

Sensors 2017, 17, 2384 5 of 32 drawbacks of miniature FGMs is the limited number of turns possible in the excitation and pick-up coilsSensors during 2017 the, 17, 2384 fabrication process. The limited number of turns in the excitation coil in a miniature5 of 32 FGM results in the rod or core not being properly saturated, and in a pick-up coil leads to lower pick-up coils during the fabrication process. The limited number of turns in the excitation coil in a sensitivities than traditional FGMs. Higher amplitudes and frequencies of the excitation current can miniature FGM results in the rod or core not being properly saturated, and in a pick-up coil leads to be usedlower to sensitivities compensate than for traditional this drawback FGMs. but Higher at the amplitudescost of higher and power frequencies consumption. of the excitation Moreover, comparedcurrent tocan traditional be used to simply-wound compensate for FGMs this drawback there is a but higher at the cost cost associated of higher with power microfabrication consumption. of miniatureMoreover, FGMs. compared to traditional simply-wound FGMs there is a higher cost associated with microfabrication of miniature FGMs. 2.2. Navigating a Well Using Magnetometers 2.2.In Navigating directional a drilling,Well Using the Magnetometers well is deviated from a vertical trajectory to a trajectory that is kept within prescribedIn directional limits drilling of azimuth, the well and is inclinationdeviated from to reach a vertical a final trajectory landing to point a trajectory as shown that in is Figure kept 3a. Directionalwithin prescribed drilling is limits performed of azimuth so that and theinclination final landing to reach point, a final typically landing apoint reservoir, as shown can in be Figure reached when3a. it Directional is below a populated drilling is performedarea or areas so inaccessible that the final due landing to obstructions point, typic suchally as a mountainsreservoir, can or rivers. be Directionalreached when drilling it is allowsbelow a multiple populated wells area or to areas be drilled inaccessible from adue single to obstructions vertical well such and as mountains significantly increasesor rivers. the accessDirectional and exposuredrilling allows to a reservoir multiple compared wells to be with drilled vertical from drilling. a single As vertical Figure well3b shows, and directionalsignificantly drilling increases is a three the dimensional access and exposure processwhere to a reservoir the azimuth compared is the deviation with vertical from drilling. the magnetic As Figure 3b shows, directional drilling is a three dimensional process where the azimuth is the north in the horizontal plane, and the inclination of the well is the angle the well deviates from deviation from the magnetic north in the horizontal plane, and the inclination of the well is the angle the vertical direction, represented as zero degrees. The azimuth is defined as the orientation of the well, the well deviates from the vertical direction, represented as zero degrees. The azimuth is defined as measured clockwise with respect to the magnetic north. The line along the vertical direction is always the orientation of the well, measured clockwise with respect to the magnetic north. The line along the parallelvertical to thedirection Earth’s is gravitationalalways parallel field. to the The Earth toolface,’s gravitational as shown field. in FigureThe toolface,3b, is theas shown angle thein Figure drill bit rotates3b, is on the the angle drilling the drill plane bit from rotates an on initial the drilling reference plane point. from an initial reference point.

Magnetic North Azimuth

(a) Projection of the well

Inclination angle

(b) Vertical direction

Azimuth

Magnetic North

Drill Toolface bit Inclination angle angle AA Top view A

Drilling Drill bit plane A rotation Drilling direction

FigureFigure 3. ( a3.) ( Azimutha) Azimuth and and inclination inclination when when drillingdrilling a directional directional well; well; (b (b) The) The azimuth azimuth of a of directional a directional well is the deviation from the magnetic north and the inclination is the deviation from the vertical well is the deviation from the magnetic north and the inclination is the deviation from the vertical direction of the well. The toolface is the angle the drill bit rotates on the drilling plane from an initial direction of the well. The toolface is the angle the drill bit rotates on the drilling plane from an initial reference point. reference point.

Sensors 2017, 17, 2384 6 of 32

Sensors 2017, 17, 2384 6 of 32 The earliest directional drilling tools, such as lowering an acid bottle into a well to etch an acid ring on theThe bottle earliest and directional the Totco drilling mechanical tools, driftsuch recorder,as lowering only an measuredacid bottle the into inclination a well to etch of a an well acid [38 ]. Magneticring on single the bottle and multi-shotand the Totco surveys mechanical were drift the firstrecorder, instruments only measured to measure the inclination both inclination of a well and azimuth,[38]. Magnetic and consisted singleof and a magneticmulti-shot compass, surveys were inclinometer the first instruments and a camera to controlledmeasure both by inclination an electronic timerand [39 azimuth,]. These and single consisted and multi-shot of a magnetic devices compass, had to inclinometer be run on wireline and a camera down controlled a well or dropped by an downelectronic the drillstring timer [39]. assembly These single and retrieved and multi after-shot pulling devices the had drillstring to be run outon wireline of the well. down a well or dropped down the drillstring assembly and retrieved after pulling the drillstring out of the well. Early well deviating methods included setting whipstocks, jetting tools and build, drop and Early well deviating methods included setting whipstocks, jetting tools and build, drop and pendulum BHA assemblies [38,40–44]. However, the advent of the downhole mud motor and the rapid pendulum BHA assemblies [38,40–44]. However, the advent of the downhole mud motor and the development of compact, rugged sensors along with the mud pulse telemetry method of transmitting rapid development of compact, rugged sensors along with the mud pulse telemetry method of datatransmitting from downhole data from to the downhole surface allowedto the surface the azimuth allowed andthe azimuth inclination and toinclination be measured to be measured in real-time. Thein most real established-time. The mostmethod established of using methodthis measurement of using this while measurement drilling (MWD) while technique drilling (MWD) is using the configurationtechnique is using shown the in configuration Figure4a, which shown has in a Figure bent-housing 4a, which motor, has a several bent-hous stabilizersing motor, and several a MWD unit.stabilizers The bent-housing and a MWD motor unit. has The a hydraulic bent-hous motoring motor that ishas driven a hydraulic by the drillingmotor that fluid is flowingdriven by through the the drillingdrilling assembly.fluid flowing through the drilling assembly.

(a) Stabilizer (b)

Drillpipe Drill pipe

Triaxial FGMs Hz

MWD Hx √ Hx2+Hy2+Hz2 Drilling

assembly Hy Gz Triaxial Bent-housing accelerometers motor

Gx

√ Gx2+Gy2+Gz2

Gy

Drill bit

(i) Sliding Mode (ii) Rotating mode

Drill bit and drilling Drill bit rotation assembly rotation

(c)

FigureFigure 4. (4.a )(a Drilling) Drilling assembly assembly for directional directional drilling drilling with with an MWD an MWD unit unitconsisting consisting of FGMs of and FGMs andaccelerometers, accelerometers, as asshown shown in ( inb), (tob), obtain to obtain azimuth azimuth and inclination and inclination measurements measurements of the well, of a the bent well,- housing motor, as shown in (c) (i), that initiates the trajectory of the well being drilled, and stabilizers a bent-housing motor, as shown in (c)(i), that initiates the trajectory of the well being drilled, that allow side force to be generated at the bit. Once the desired trajectory is obtained the whole and stabilizers that allow side force to be generated at the bit. Once the desired trajectory is obtained drilling assembly and the bent-motor drills ahead as shown in (ii). the whole drilling assembly and the bent-motor drills ahead as shown in (ii).

Sensors 2017, 17, 2384 7 of 32

The MWD unit includes tri-axial FGMsand tri-axial accelerometers, as shown in Figure4b and the mud-pulse telemetry system (not shown), which is located above the fluxgate magnetometers and accelerometers. The stabilizers are used to control contact with the wellbore and form a fulcrum with the hydraulic motor behind it acting as a lever, thus allowing side force to be generated at the bit. The bend is adjusted according to the angle of the well being drilled and is normally set anywhere between 0◦ and 2◦ but sometimes as high as 3◦. Initially only the hydraulic motor powers the drill bit and there is no rotation of the drilling assembly above the drill string, as shown in Figure4(ci). The motor can be oriented in any desired manner to build angle, drop angle or turn. Once the desired trajectory of the well is attained the entire drilling assembly and the bit are rotated to drill straight ahead as shown in Figure4(cii). The Earth’s magnetic field has a different strength and orientation at every location on Earth and this field is measured using tri-axial FGMs while the inclination of a well is obtained by measuring the gravitational field by tri-axial accelerometers. FGMs are used to measure the toolface when the well is vertical (0◦ inclination) as the gravitational field will be constant, and accelerometers are used to measure the toolface when the well is horizontal (90◦ inclination). Any toolface measurement between an inclination of 0◦ and 90◦ is performed by both FGMs and accelerometers. Generally the directional MWD crosses over from magnetic tooolface to gravitational toolface at angles from 3◦ to 5◦. The position P of the drill bit in a well being drilled can be obtained at any time in terms of the magnetic field, inclination and toolface as shown below [45]:

! − Hx sin ϕ + Hy cos ϕ P = arctan
(1) Hz sin θ + cos θ Hx cos ϕ − Hy sin ϕ and: s  G 2 + G 2 = x y θ arctan  2  (2) Gz and:   Gy ϕ = arctan − (3) Gx where θ is the inclination, φ is the toolface angle and Gx, Gy and Gz are the orthogonal gravitational vectors measured by the accelerometer. While drilling, there are predetermined survey points along the well where information about the azimuth, inclination and toolface is obtained. Values at a given survey station are combined with previous values to obtain the well trajectory, where the computations are based on mathematical assumptions. This data is transmitted to the surface so that the driller on the surface knows the exact direction in which the well is being drilled. The sliding and rotating method, while established, is time consuming since the rate of penetration into the earth is significantly lower during the sliding mode compared to the rotating mode. The rotary steerable system (RSS) is a technology, introduced approximately 20 years ago, that allows the constant rotation of the entire drilling assembly while drilling a directional well, therefore increasing the average rate of penetration [46–48]. An increase in the rate of penetration means less time to drill a well and, hence, significant savings for the company. RSS is more expensive than sliding/rotating methods and therefore, how it can be optimized for a given well to increase the rate of penetration has to be carefully planned. Production potential of the well, earth formations, depth of a well, drill bit compatibility and expected hole problems are some of the factors that must be considered. There are two main RSS technologies, point-the-bit, as shown in Figure5a, and push-the-bit, as shown in Figure5b. In point-the-bit systems the bit shaft is bent relative to the rest of the drilling assembly. The amount of bend depends on the commands the driller on the surface sends downhole, where the commands are based on the directional measurements, azimuth, inclination and toolface, sent by the MWD from downhole to the driller at the surface. A servomotor controls the bend orientation and the servomotor Sensors 2017, 17, 2384 8 of 32

Sensors 2017, 17, 2384 8 of 32 downhole, where the commands are based on the directional measurements, azimuth, inclination and toolface, sent by the MWD from downhole to the driller at the surface. A servomotor controls rotatesthe bend at the orientation same speed and the as theservomotor drilling rotates assembly at the but same in thespeed opposite as the drilling direction, assembly thereby but allowing in the theopposite toolface direction, orientation the toreby stay allowing non-rotating the toolface while the orientation drilling assemblyto stay non rotates.-rotating The while reference the drilling stabilizer actsassembly as a reference rotates. toThe create reference the deflection stabilizer acts within as a the reference shaft and to create the trajectory the deflection of the within well changesthe shaft in theand direction the trajectory of the of bend. the well In push-the-bitchanges in the systems direction the of the pads, bend. shown In push in Figure-the-bit5 systemsb, are actuated the pads, by shown in Figure 5b, are actuated by the drilling fluid flow and pushed out against the wall of the the drilling fluid flow and pushed out against the wall of the well being drilled to direct the drillstring well being drilled to direct the drillstring assembly in a desired direction. A rotary valve opens and assembly in a desired direction. A rotary valve opens and closes the drilling fluid supply to the pads closes the drilling fluid supply to the pads and the timing and magnitude of pad actuation depends and the timing and magnitude of pad actuation depends on the commands the driller sends downhole on the commands the driller sends downhole from the surface based on the directional data sent to from the surface based on the directional data sent to the surface by the MWD. the surface by the MWD.

Rotary valve MWD information sent to surface Driller sends commands based on MWD data to change Reference direction of bit stabilizer Bit movement

Focal bearing Pads Range of Eccentric movement rings Housing

Bit shaft

Wall of the well

(a) (b)

FigureFigure 5. ( 5.a )( Point-the-bita) Point-the-bit system, system, where where the thebit shaft bit shaft is bent is relativebent relative to the to rest the of rest the drilling of the drilling assembly. Theassembly. bend orientation The bend orientation is controlled is controlled by a servomotor by a servomotor that rotates that atrotates the same at the speed same asspeed the as drilling the drilling assembly but in the opposite direction so that the toolface orientation is non-rotating; (b) assembly but in the opposite direction so that the toolface orientation is non-rotating; (b) Push-the-bit Push-the-bit system, where the pads are actuated by a flow and pushed out against the wall of the system, where the pads are actuated by a flow and pushed out against the wall of the well being drilled well being drilled to direct the drillstring assembly in a desired direction. to direct the drillstring assembly in a desired direction. One of the drawbacks of FGMs is that they have to be run within a nonmagnetic environment sinceOne the of the measured drawbacks azimuth of FGMs is with is that reference they have to to the be runmagnetic within north. a nonmagnetic Therefore, environment any magnetic since theinterference measured azimuth due to fields is with other reference than the to E thearth’s magnetic magnetic north. field Therefore, will cause any significant magnetic deterioration interference of due tomagnetic fields other azimuth than the accuracy. Earth’s To magnetic overcome field this will issue cause FGMs significant are enclosed deterioration in a nonmagnetic of magnetic drill azimuthcover accuracy.and run To inside overcome a well. this Depending issue FGMs on the are ‘proposed enclosed inazimuth’ a nonmagnetic and inclination, drill cover increasing and run amounts inside a of well. Dependingnon-magnetic on the drill ‘proposed collar are azimuth’ required and to effectively inclination, isolate increasing the FGMs. amounts Vertical of non-magnetic is the best case; drill 90° collar or arehorizontal required todue effectively east or west isolate is the the most FGMs. challenging. Vertical is the best case; 90◦ or horizontal due east or west is the most challenging. 2.3. Field Results 2.3. FieldFigure Results 6 shows real-time data transmission and visualization through a drilling assembly navigationFigure6 shows software real-time [49]. There data is transmission a real-time communication and visualization system, through ‘Rig a Chat drilling’, linking assembly the navigationnavigation software experts [in49 the]. There office, is rig a real-time personnel, communication and service companies, system, ‘Rigenabling Chat’, th linkingem to communicate the navigation expertswith each in the other office, to rigmonitor personnel, and guide and navigation service companies, operations enabling in an efficient them to manner. communicate As Figure with 6(a eachi) otherillustrates, to monitor there and is a guidereal-time navigation directional operations drilling display in an efficientavailable manner. to a drilling As Figureengineer6(ai) to show illustrates, the thereactual is atrajectory real-time of directionalthe well in 3D. drilling Figure display6(aii) shows available the the to real a- drillingtime azimut engineerh, inclination, to show measured the actual depth (MD) and total vertical depth (TVD) of the well along with the east-west and north-south trajectory of the well in 3D. Figure6(aii) shows the the real-time azimuth, inclination, measured depth coordinates (polar coordinates). MD is the total length of the well and TVD is the vertical distance (MD) and total vertical depth (TVD) of the well along with the east-west and north-south coordinates from the surface to the final depth of the directional well. The east-west and north-south polar (polar coordinates). MD is the total length of the well and TVD is the vertical distance from the surface coordinates shown in Figure 6(aiii) calculate distance (departure) from the surface and direction to the final depth of the directional well. The east-west and north-south polar coordinates shown in Figure 6(aiii) calculate distance (departure) from the surface and direction (azimuth). Figure6(aiv) shows the TVD vs. MD graph, where a change from a vertical to a directional trajectory can be seen after Sensors 2017, 17, 2384 9 of 32 Sensors 2017, 17, 2384 9 of 32

(azimuth). Figure 6(aiv) shows the TVD vs. MD graph, where a change from a vertical to a directional 6500 m. Figure6av shows real-time drilling parameters such as the well depth, current depth of the bit, trajectory can be seen after 6500 m. Figure 6av shows real-time drilling parameters such as the well the rate of penetration of the bit into the formation, gamma ray readings to indicate the formation depth, current depth of the bit, the rate of penetration of the bit into the formation, gamma ray there welladings is beingto indicate drilled the through formation and the the well inclination is being of drilled the well. through The navigationand the inclination data workflow of the well. shown inThe Figure navigation6b not only data involves workflow monitoring shown in Figure the well 6b not in real-time only involve buts alsomonitoring correlating the well and in interpreting real-time thebut data also obtained correlating by theand downhole interpreting sensors, the data which obtained measure by the drilling downhole dynamics sensors, such which as ROP, measure torque anddrilling downhole dynamics environmental such as data ROP, such torque as pressure, and downhole temperature environmental and density. data The such workflow as pressure, involves transferringtemperature data and from density. a rig The server workflow in a remote involves rig transferring to a real-time data datafrom servera rig server at the in analysis a remote center. rig Theto real-timea real-time data data server server then at the sends analysis this data center. to aThe real-time real-time visualization data server and then interpretation sends this data center to a so thatreal the-time drilling visualization engineers and on interpretation the remote rig center can be so guided that the remotely drilling toengineers accurately on reachthe remot thee final rig can target intobe a guided reservoir. remotely to accurately reach the final target into a reservoir.

(a) (i) (iii) (v)

Trajectory widget 1200

1000 )

m Hole Depth

( 800

8816.20 s

N 600

p s i 400 Bit Depth d 8910.30 Well being drilled 200

in real-time 0 -2400 -1800 -1200 -600 0 ROP 2ft/hr (ii) (iv) dispEw (m) Survey table 0 Near Bit Gamma MD Inclination Azimuth TVD DispE/W DispN/S 11.14 gAPI 1000 ft deg deg ft m m

8309 8309 8309 8309 8309 8309 2000 )

t Near Bit

8352 8352 8352 8352 8352 8352 f ( 8400 8400 8400 8400 8400 8400 3000 Inclination 90 deg

8453 8453 8453 8453 8453 8453 D 4000 V

8500 8500 8500 8500 8500 8500 T 8550 8550 8550 8550 8550 8550 5000 8599 8599 8599 8599 8599 8599 6000 8645 8645 8645 8645 8645 8645 8695 8695 8695 8695 8695 8695 7000 8736 8736 8736 8736 8736 8736 8000 6000 4000 2000 0 8816 8816 8816 8816 8816 8816 MD (ft)

(b)

Data transfer

Real-time data analysis Remote rig

Real-time Rig server data server Real-time Rig server visualization Real-time data Data loader transmission and viewer Interpretation database

FigureFigure 6. 6.( a()a) Real-time Real-time directional directional drilling drilling display display available to to a a drilling drilling engineer. engineer. (i) ( i Real) Real-time-time trajectory of a well in 3D where (ii) shows the real-time azimuth, inclination and measured depth trajectory of a well in 3D where (ii) shows the real-time azimuth, inclination and measured depth (MD) and total vertical depth (TVD) of the well as well as the east-west and north-south coordinates (MD) and total vertical depth (TVD) of the well as well as the east-west and north-south coordinates (polar coordinates); (iii) Graph showing the displacement of the well in polar coordinates, where they (polar coordinates); (iii) Graph showing the displacement of the well in polar coordinates, where they can be used to calculate distance (departure) from the surface and direction (azimuth); (iv) Graph can be used to calculate distance (departure) from the surface and direction (azimuth); (iv) Graph showing the measured depth, which is the total length of the well, and the true vertical depth, which showing the measured depth, which is the total length of the well, and the true vertical depth, which is is the vertical distance from the surface to the final depth of the directional well. A change from a the vertical distance from the surface to the final depth of the directional well. A change from a vertical vertical to a directional trajectory can be seen after an MD of 6500 m; (v) Real-time drilling parameters to a directional trajectory can be seen after an MD of 6500 m; (v) Real-time drilling parameters showing showing the well depth, current depth of the bit, the rate of penetration of the bit into the formation, thegamma well depth, ray readings current to depth indicate of the formation bit, the rate the of well penetration is being drilled of the through bit into and the formation,the inclination gamma of raythe readings well; (b to) Navigation indicate the workflow formation that the shows well is data being transfer drilled from through a remote and therig server inclination to a real of the-time well; (b)data Navigation server at workflow the analysis that center. shows Thedata real transfer-time from data a server remote then rig sends server th tois a data real-time to a datareal-time server at thevisualization analysis center.and interpretation The real-time center data so serverthat the then drilling sends engineers this data can to be a guided real-time during visualization drilling the and interpretationdirectional well center to accurately so that the reach drilling the engineersfinal target can into be a guidedreservoir during [49]. drilling the directional well to accurately reach the final target into a reservoir [49].

Sensors 2017, 17, 2384 10 of 32

Sensors 2017, 17, 2384 10 of 32 Figure7a shows a 3D visualization of real-time dip data, with drilling polarity indicated on the trajectoryFigure when 7a shows steering a 3D alongvisualization a thin reservoirof real-time interval dip data, with with high drilling permeability polarity indicated [50]. The on dipthe and inclinometertrajectory data when were steering not onlyalong used a thin to reservoir steer the interval well and with update high permeability the real-time [50]. trajectory The dip but and were also usedinclinometer to calculate data were the truenot only stratigraphic used to steer index the well of the and well update and the its real relative-time trajectory angle with but respectwere to the localalso structuralused to calculate dip to the accurately true stratigraphic profile loggingindex of the data. well The and trajectory its relative shows angle with several respect dips to throughthe whichlocal the structuralwell was steered,dip to accurately below the profile top surface logging of data. the Thereservoir. trajectory The shows drilling several polarity dips plots through indicate which the well was steered, below the top surface of the reservoir. The drilling polarity plots indicate if the well is being drilled stratigraphically up or down and are useful when steering wells in complex if the well is being drilled stratigraphically up or down and are useful when steering wells in complex reservoirsreservoirs or simple or simple but but very very thin thin interval interval reservoirs reservoirs such as as in in this this example. example.

Figure 7. (a) Real time 3D visualization of directional drilling in a very thin but high quality reservoir, Figure 7. (a) Real time 3D visualization of directional drilling in a very thin but high quality reservoir, where the ‘dip’ refers to the orientation of the reservoir bedding. The drilling polarity plots indicate where the ‘dip’ refers to the orientation of the reservoir bedding. The drilling polarity plots indicate whether the well was being drilled stratigraphically up or down; (b) (i) Formation resistivity image whetherlog showing the well the was well being being drilled steered stratigraphically inside the reservoir. up (1) or Well down; being (b )(drilledi) Formation at an inclination resistivity of 89° image; ◦ log showing(2) Inclination the well increased being to steered 91° based inside on resistivity the reservoir. and mobility (1) Well logs being; (3) drilled Inclination at an kept inclination at 90.5° as of 89 ; ◦ ◦ (2) Inclinationformation increasedapparent dip to was 91 basedestimated on from resistivity the real and-time mobility resistivity logs; log (3)to be Inclination 0.4° dipping kept towards at 90.5 as ◦ formationthe surface apparent; (4) Resistivity dip was image estimated and other from logs the indicated real-time that resistivity the high mobility log to be was 0.4 belowdipping the bit towards so the surface;an inclination (4) Resistivity of 90° was imageheld to gradually and other drill logs downward indicated into that the the target; high (5) mobilityInclination was was below dropped the bit so anto inclination 89.5° based ofon 90resistivity◦ was held logs; to(6) graduallyInclination drillwas built downward and held intoat 90° the and target; the formation (5) Inclination dip was was droppedalso toestimated 89.5◦ based to be almost on resistivity flat; (7) logs;Dip was (6) estimated Inclination to be was dipping built andaway held from at the 90 ◦surfaceand the at about formation dip was+0.5° also so i estimatednclination was to be dropped almost to flat; 89.5° (7); ( Dip8) Since was the estimated reservoirto dip be was dipping estimated away to frombe flat the thesurface well at was drilled with an inclination of 90° until final target was reached; (ii) Plot corresponding to (i) about +0.5◦ so inclination was dropped to 89.5◦; (8) Since the reservoir dip was estimated to be flat showing the formations drilled through, where formation 1 is the top, and the actual well drilled with the well was drilled with an inclination of 90◦ until final target was reached; (ii) Plot corresponding to the aid of logging vs the planned well trajectory before drilling [50]. (i) showing the formations drilled through, where formation 1 is the top, and the actual well drilled with theFigure aid 7 of(b loggingi) shows vs the the well planned being wellsteered trajectory inside the before thin drilling reservoir [50 with]. the aid of resistivity logs obtained while drilling. In (1) the trajectory of the well has an inclination of 89° and in (2) it was Figure 7(bi) shows the well being steered inside the thin reservoir with the aid of resistivity logs obtained while drilling. In (1) the trajectory of the well has an inclination of 89◦ and in (2) it was Sensors 2017, 17, 2384 11 of 32 increased to 91◦ based on the resisitivity logs and mobility information. In (3) resistivity logs indicated ◦ that theSensors reservoir 2017, 17, 2384 formation apparent dip was 0.4 , dipping towards the surface, so the inclination11 of 32 was kept to 90.5◦. Increased mobility below the bit was indicated by resistivity and other logs so an inclinationincreased to of 91° 90◦ basedwas on held the to resisitivity gradually logs drill and downward mobility information. into the target. In (3) resistivity The drilling logs assemblyindicated was that the reservoir formation apparent dip was 0.4°, dipping towards the surface, so the inclination then pulled out of the well due to problems in the well and run in the well again. In (5) inclination was was kept to ◦90.5°. Increased mobility below the bit was indicated by resistivity and other logs so an droppedinclination to 89.5 of and90° was then held once to thegradually resistivity drill downward logs confirmed into the that target. the bitThe was drilling in the assembly target reservoirwas ◦ againthen the pulled inclination out of was the builtwell due and to held prob atlems 90 insince the well the formationand run in dipthe well was again. estimated In (5) to inclination be almost flat as shownwas dropped in (6). After to 89.5° drilling and then ahead once the the dip resistivity was estimated logs confirmed to be dipping that the away bit was from in the the target surface at ◦ ◦ aboutreservoir +0.5 so again the inclinationthe inclination was was dropped built and to held 89.5 at .90° Further since the drilling formation showed dip was that estimated the reservoir to be dip was flatalmost so theflat restas shown of the in well (6). After was drilleddrilling atahead an inclination the dip was ofestimated 90◦ until to thebe dipping target depth away from was reached.the Figuresurface7(bii) at shows about the +0.5° different so the inclination reservoir formationwas dropped layers to 89.5°. drilled Further through, drilling where showed formation that the 1 is the top,reservoir and the dip actual was flat well so drilledthe rest withof the the well aid was of dr loggingilled at vs an the inclination planned of well 90° until trajectory the target before depth drilling. Therewas is significant reached. Figure deviation 7(bii) from shows the the originally different planned reservoir well formation but real-time layers drilled logging through, data correlated where to formation 1 is the top, and the actual well drilled with the aid of logging vs the planned well trajectory the position of the well aided navigation of the well through the reservoir, maximizing the reach into before drilling. There is significant deviation from the originally planned well but real-time logging the reservoir.data correlated to the position of the well aided navigation of the well through the reservoir, Figuremaximizing8a shows the reach the into complex the reservoir. setting of directional wells in a field [ 51]. When drilling new directionalFigure wells 8ato sho reachws the reservoirs, complex setting avoiding of directional collision wells with in wells a field already [51]. When drilled drilling in the new field is imperative.directional Figure wells8 b to shows reach reservoirs,the cross-section avoiding of collision an active with drilling wells alreadywell and drilled an offset in the well field located is nearby,imperative. and Figure Figure8c shows 8b shows a 3D the visualization cross-section ofof Figurean active8b. drilling The position well and of thean offset active well well located given by the directionalnearby, and sensors Figure aids8c shows the driller a 3D visualization to clearly plan of Figure the trajectory 8b. The position of the wellof the taking active intowell accountgiven by other wellsthe in thedirectional vicinity. sensors These aids previously the driller drilled to clearly wells, plan called the trajectory offset wells, of the can well be taking vertical into or account directional and theirother locations wells in arethe built vicinity. into These the navigation previously model. drilled By wells, knowing called their offset location wells, can the be driller vertical can or adjust directional and their locations are built into the navigation model. By knowing their location the the trajectory of the well so that the active well is drilled at a safe distance from the offset wells to driller can adjust the trajectory of the well so that the active well is drilled at a safe distance from the avoidoffset collisions wells to so avoid as not collisions to affect so theiras not production to affect thei potential.r production Furthermore, potential. Furthermore, while the while active the well is drilledactive at a well safe is distance drilled at to a safe offset distance wells to it isoffset also wells important it is also to important ensure that to ensure the active that the well active is navigated well towardsis navigated the reservoir towards in the a trajectory reservoir thatin a trajectory can optimize that can access optimize to the access reservoir. to the reservoir.

Vertical well Directional well Offset Active well Offset Active well well well

Formations (a) (b) (c) FigureFigure 8. (a 8.)3D (a) visualization3D visualization of of drilled drilled wells wells inin a field.field. Drilling Drilling in insuch such a complex a complex field field with with many many vertical and directional wells requires careful planning to avoid well collisions; (b) Cross-sectional vertical and directional wells requires careful planning to avoid well collisions; (b) Cross-sectional view of an active well being drilled in the vicinity of an offset well; (c) 3D view of the same well in (b) view of an active well being drilled in the vicinity of an offset well; (c) 3D view of the same well in (b) showing the active well approaching the offset well [51]. showing the active well approaching the offset well [51]. The errors due to combined/collective sensor error/accuracy can be determined by ellipses of Theuncertainty. errors due An to ellipsoid combined/collective of uncertainty (EOU) sensor er error/accuracyror model, applicable can be to determined a basic MWD, by ellipses was of uncertainty.developed An by ellipsoid the industry of uncertainty steering committee (EOU) error on wellbore model, applicablesurvey (ISCWSA) to a basic and MWD, is the recognized was developed by theand industry current steeringindustry committeestandard for on calculating wellbore well survey position (ISCWSA) uncertainty and [52]. is the The recognized EOU error and model current takes into account tools from different service companies and makes use of directional drilling industry standard for calculating well position uncertainty [52]. The EOU error model takes into software developed to integrate with subsurface applications to visualize well position uncertainty. account tools from different service companies and makes use of directional drilling software The errors are calculated at well survey stations, placed a maximum of 100 ft apart, and are developedmodeled to integrateas vectors with based subsurface on three elements; applications the azimuth, to visualize inclination well position and the uncertainty. depth of the well. TheToolface errors angle are is calculated also taken into at well account survey when stations, modeling placed of the apropagation maximum of of errors. 100 ft Errors apart, from and are modeleddifferent as vectorssources are based statistically on three independent, elements; theare cumulative azimuth, inclinationand propagate and in theproportion depth to of how the well. Toolface angle is also taken into account when modeling of the propagation of errors. Errors from

Sensors 2017, 17, 2384 12 of 32

far you are from the origin. Therefore, the final position of the well can be anywhere within the final position uncertainty shown in Figure 9a. An error source is a physical phenomenon that influences Sensors 2017the measurement, 17, 2384 obtained by a survey tool such as an MWD and is described by an error term [53].12 of 32 An error model is therefore a set of error terms chosen to account for all the different error sources that affects a survey tool. The error terms in the EOU model are sensor errors, errors due to steel in differentthe sourcesdrilling assembly are statistically near the MWD, independent, directional are sensor cumulative assembly and misalignments propagate and in proportion magnetic dip to how far youand are field from strength the origin. uncertainties. Therefore, the final position of the well can be anywhere within the final position uncertaintyAs shown in shown Figure 9 in(bi Figure), the lateral9a. An dimension error source of an ellipse is a physical of uncertainty phenomenon is proportional that influencesto the the measurementazimuth error obtained and the high by aside survey dimension tool suchis proportional as an MWD to the and inclination is described error. byA thinner an error ellipse term [53]. represents the case where the azimuth is more accurate than the inclination and a more spread-out An error model is therefore a set of error terms chosen to account for all the different error sources ellipse represents the opposite case where the inclination is more accurate than the azimuth, where that affectsthe latter a survey example tool. is more The typical error termsin the field. in the Figure EOU 9 model(bii) shows are the sensor third errors, component errors of duethe error, to steel in the drillingthe measured assembly depth near of the well, MWD, resulting directional in an almond sensor-like assembly shape, elliptical misalignments in all three and orthogonal magnetic dip and fieldplanes. strength uncertainties.

Drillstring Well 1

A Azimuth error Well 2 Ellipse of B C uncertainty Inclination error D Final position (i) uncertainty of well Depth error Separation factor = AD/(AB+CD)

(ii) (b) (c) (a) FigureFigure 9. (a) 9. The (a) ellipsesThe ellipses of uncertaintyof uncertainty gets gets larger larger as the the depth depth from from the the surface surface increases increases since sinceerrors errors from differentfrom different sources sources are statistically are statistically independent, independent, are cumulative are cumulative and errors and errors propagate propagate in proportion in proportion to how far you are from the origin; (b) The lateral dimension of the ellipse of uncertainty to how far you are from the origin; (b) The lateral dimension of the ellipse of uncertainty is proportional is proportional to the azimuth error and the high side dimension is proportional to the inclination to the azimutherror; (c) Calculation error and theof separation high side factor dimension between is two proportional wells to avoid to the well inclination collision [5 error;2]. (c) Calculation of separation factor between two wells to avoid well collision [52]. EOUs are used to estimate the accuracy of hitting the target reservoir, especially when the Asreservoir shown isin thin, Figure and also9(bi), more the importantly lateral dimension to avoid collision of an ellipse of wells. of Figure uncertainty 1c shows is the proportional simplest to the azimuthmethod error of evaluating and the the high collision side dimension risk, a separation is proportional factor that tois calculated the inclination in a plane error. at right A thinner angles ellipse to the well that has already been drilled. A separation factor of 1 indicates that the wells are just represents the case where the azimuth is more accurate than the inclination and a more spread-out ellipse touching but doesn’t necessarily mean there would be a collision as a probability with 2 or 3 standard representsdeviations the opposite are used casewhen where determining the inclination the size of the is more ellipses. accurate However, than the the risk azimuth, of collision where increases the latter exampleas the is more overlapping typical region in the increases. field. Figure Other9(bii) methods shows of thecalculating third component the separation of thefactor error, can be the found measured depthin of [52]. the well, resulting in an almond-like shape, elliptical in all three orthogonal planes. EOUs are used to estimate the accuracy of hitting the target reservoir, especially when the reservoir is thin,3. and Nuclear also Magnetic more importantly Resonance to (NMR) avoid collision of wells. Figure1c shows the simplest method of evaluating the collision risk, a separation factor that is calculated in a plane at right angles to the well that 3.1. Principles of NMR has already been drilled. A separation factor of 1 indicates that the wells are just touching but doesn’t necessarilyA meann atom there nucleus would can be be a thought collision of as a probabilitysmall bar magnet with 2with or 3 a standard magnetic deviationsmoment and are a used magnetic field since it has a positive charge and behaves as though it is spinning along a spin rotation when determining the size of the ellipses. However, the risk of collision increases as the overlapping axis, as shown in Figure 10a. In the absence of a strong external magnetic field the nucleus will be regionoriented increases. in a Otherrandom methods direction, of even calculating though it thewill separationbe weakly aligned factor with can bethe foundEarth’s in magnetic [52]. field.

3. Nuclear Magnetic Resonance (NMR)

3.1. Principles of NMR An atom nucleus can be thought of as a small bar magnet with a magnetic moment and a magnetic field since it has a positive charge and behaves as though it is spinning along a spin rotation axis, as shown in Figure 10a. In the absence of a strong external magnetic field the nucleus will be oriented in a random direction, even though it will be weakly aligned with the Earth’s magnetic field. When the nucleus is exposed to a large external static magnetic field the orientation of the nucleus will no Sensors 2017, 17, 2384 13 of 32

Sensors 2017, 17, 2384 13 of 32 longer be randomWhen the nucleus and will is exposed be aligned to a large with external the direction static magnetic of the field external the orientation magnetic of the field, nucleu ass shown in Figure 10(bi).will no The longer orientation be random will and now will onlybe aligned flip infrequentlywith the direction between of the external the low magnetic and high field, energy as states comparedshown to when in Figure there 1 was0(bi). noThe static orientation magnetic will now field. only flip infrequently between the low and high energy states compared to when there was no static magnetic field.

Spin axis (a) Spin Magnetic field N Nucleus S

(b) (i) z (ii) Magnetic (iii) Magnetic y torque moment x

N N

N N S S S S Turn off Applied static Alternating alternating magnetic field magnetic field magnetic field Precession motion (vi) (v) (iv)

N N N

S S S

Relaxation Signal during relaxation Tuned coil

Figure 10. (a) A spinning nucleus emanating a magnetic field; (b) (i) Application of a static external Figure 10.magnetic(a) A spinning field results nucleus in the orientation emanating of the a nucleus magnetic to be field;in the same (b)( directioni) Application as the external of a staticfield. external magnetic field(ii) Application results in of the an RF orientation magnetic field of theperpendicular nucleus toto the be instatic the field same tips directionthe nucleus as away the from external field. (ii) Applicationthe static of field. an RF(iii) magneticWhen the nucleus field perpendicularis tipped away from to the the static static magnetic field field tips the the orientation nucleus of away from the static field.its rotational (iii) When axis changes the nucleus leads to precession. is tipped ( awayiv–vi) During from the precession static magnetic motion the field nucleus the emits orientation of RF waves that can be detected by a tuned coil and when the RF field is turned off the nucleus relaxes iv vi its rotationalback axis to thermal changes equilibrium leads to and precession. aligns itself (with– the) Duringstatic magnetic the precession field. motion the nucleus emits RF waves that can be detected by a tuned coil and when the RF field is turned off the nucleus relaxes back to thermalBy applying equilibrium a radio frequency and aligns (RF) itself magn witheticthe field static perpendicular magnetic to field. the static magnetic field the nucleus can be tipped away from the static magnetic field direction as shown in Figure 10(bii). The RF magnetic field can be applied as a series of short, pulses, usually in the range of microseconds. By applyingThe irradiation a radio energy frequency in the RF magnetic (RF) magnetic field is equal field to the perpendicular difference in energies to theof the static two nuclear magnetic field the nucleusspins can with be differenttipped away orientations from (low the and static high magnetic energy) and field the absorptiondirection of as this shown energy in by Figure the 10(bii). The RF magneticnuclear spins field causes can be it to applied flip from as higher a series to low ofer short, energy pulses, and lower usually to higher in theenergy range in a ofprocess microseconds. The irradiation energy in the RF magnetic field is equal to the difference in energies of the two nuclear spins with different orientations (low and high energy) and the absorption of this energy by the nuclear spins causes it to flip from higher to lower energy and lower to higher energy in a process known as resonance. The energy required for resonance depends on the strength of the static magnetic field B0, and can be obtained by the following equation [54]:

γhB ∆E = 0 (4) 2π Sensors 2017, 17, 2384 14 of 32 known as resonance. The energy required for resonance depends on the strength of the static magnetic field B0, and can be obtained by the following equation [54]: Sensors 2017, 17, 2384 14 of 32 hB E  0 (4) 2 −27 where hh isis Planck’sPlanck’s constant constant (6.63 (6.63× × 1010−27 ergerg sec). sec). The The Bohr Bohr condition condition ( ∆E =hvhv)) enables enables the the frequency frequency v0 ofof the nuclear transition to be written as: γBB vv = 00 (5(5)) 0 0 2π

Equation (5) (5) is is known known as the as Larmor the Larmor equation, equation, where ω where0 = 2 πv0 is2 thev0 angular is the Larmor angular resonance Larmor frequency,resonance andfrequency,γ is the and gyromagnetic γ is the gyromagnetic ratio, which ratio, is a constant which is for a constant a given nucleus for a given and isnucleus proportional and is toproportional the magnetic to the strength magnetic of the strength nucleus. of the nucleus. When the nucleus is tipped away from the static magnetic fieldfield the orientation of its rotational axis changes leading leading to to precession, precession, as as shown shown in in Figure Figure 10 10(b(biii).iii). The The speed speed of precession of precession depends depends on onthe the strength strength of of the the static static magnetic magnetic field field and and the the properties properties of of the the nucleus. nucleus. During During the precession motion the nucleus emits RF waves that can be detected by a tuned coil, since the RF waves will induce aa voltagevoltage inin the the coils, coils, as as shown shown in in Figure Figure 10 10(biv–bvi).(biv–bvi When). When the the RF RF magnetic magnetic field field is turned is turned off, theoff, nucleusthe nucleus will will continue continue to spin to spin for a for while a while until until it eventually it eventually reaches reaches thermal thermal equilibrium equilibrium and aligns and itselfaligns again itself withagain the with direction the direction of the staticof the magnetic static magnet field,ic as field, shown as shown in Figure in Figure10(bvi). 10(bvi). During the relaxation process after a static magnetic field field is applied, there is a non non-radiative-radiative transfer ofof energyenergy wherewhere the the spin spin distribution distribution approaches approaches an an equilibrium equilibrium state, state, as shownas shown in Figure in Figure 11a. The11a. timeThe time taken taken to reach to reach equilibrium equilibrium is called is called the polarizing the polarizing time (PT)time and(PT)T andI is theTI is relaxation the relaxation time, alsotime, known also known as the as longitudinal the longitudinal or spin-lattice or spin-lattice relaxation, relaxation, where whereTI is T theI is the time time required required for for nuclei nuclei to reachto reach 63% 63% of of the the final final thermal thermal equilibrium equilibrium magnetization magnetization in in the thez z-direction.-direction. WhenWhen an RF pulse is is applied t thehe nuclei are tipped away from the static magnetic field, field, leading to precession motion as as shown in Figure 1111b.b. The rate of relaxation is dictated by the time constant TTIIII.. When When the the RF RF pulse pulse is is turned off the net magnetization in the the x--y planeplane will will decrease decrease exponentially exponentially as as shown shown in in Figure Figure 12b,12b, and this signal, known as free free-induction-decay-induction-decay (FID), is measured by a tuned coil. This FID signal is is known as thethe TTIIII relaxation, transverse,transverse, oror thethe spin-spinspin-spin relaxation relaxation time. time. Note Note that that the the magnetization magnetization is inis in the thez, orz, axialor axial direction, direction, during during PT, andPT, and in the inx the-y plane x-y plane during during the pulse the pulse sequence, sequence, since thesince nuclei the arenuclei tipped are tipped away from away the from static the magnetic static magnetic field by field the RFby pulses.the RF pulses.

N Longitudinal z-component z N of magnetization Alternating y S magnetic field Precession S x Applied static magnetic field

M0(1-e-t/TI)

)

t

)

(

t

(

y

-

z x

M 0 -t/TII M M e )

Time (t) Time (t) (a) (b) Figure 11. (a) Application of a static magnetic fieldfield in the z-direction-direction results in the spin distributions approach an equilibrium state and the net magnetization of of the nucleus being being in in the the z--direction.direction.

Relaxation time TTI Iisis known known as as the the longitudinal longitudinal or or spin spin-lattice-lattice relaxation relaxation time; time; (b) ( bApplication) Application of an of analternating alternating magnetic magnetic field field perpendicular perpendicular to the to thestatic static field field tips tipsthe thenet netmagnetization magnetization away away from from the

thestatic static field field onto onto the thex-y xplane-y plane leading leading to precession to precession motion. motion. Relaxation Relaxation time time TII isT II knownis known as the as thetransverse transverse or the or thespin spin-spin-spin relaxation relaxation time time of the of thenucleus. nucleus.

Sensors 2017, 17, 2384 15 of 32 Sensors 2017, 17, 2384 15 of 32

Radio Radio Drill pipe frequency frequency transmitter transmitter Radio /receiver frequency receiver Magnet Sweep coils Formation Formation Control S N S system and Oscilloscope N /Recorder Magnet

Sample tube Sweep generator (a) (b) FigureFigure 12.12. ((aa)) LaboratoryLaboratory NMR NMR experimental experimental setup setup where where the the sample sample to be to analyzed be analyzed is placed is placed inside inside a pair ofa pair magnets of magnets and transmitter and transmitter and receiver and receiver coils; ( bcoils) NMR; (b) logging NMR logging setup, referredsetup, referred to as ‘inside to as ‘ outinside NMR’, out whereNMR’, the where sample, the the sample, formation, the to be formation, analyzed is to outside be analyzed the magnets is and outside the transmitter/receiver the magnets and coils. the transmitter/receiver coils. 3.2. NMR for Obtaining Geological Parameters 3.2. NMR for Obtaining Geological Parameters Evaluating downhole parameters is an important part of the drilling process and nuclear magnetic resonanceEvaluating (NMR) downholeplays a key roleparameters in identifying is an downhole important fluid part types, of the formations drilling and process oil/gas and production nuclear potential.magnetic Oneresonance of the main(NMR) advantages plays a key NMR role offers in identifying for drillers isdownhole a non-radioactive fluid types, option formations for obtaining and theoil/gas porosity production and permeability potential. One of of rock the main formations; advantages crucial NMR information offers for drillers to quantify is a non the-radioactive volume of hydrocarbonsoption for obtaining present the in aporosity formation. and Ideally permeability the formations of rock wouldformations; have oil/gascrucial andinformation large interconnected to quantify poresthe volume that allow of hydrocarbons the oil/gas to present flow freely in a out formation. of the formation Ideally the and formations up on to the would surface. have oil/gas and largeThe interconnected earliest studies pores on NMRthat allow properties the oil/gas of fluids to flow in porous freely mediaout of startedthe formation in the 1950s and up at aon number to the ofsurface. oil company research laboratories, and the first patents on NMR well logging was published by RusselThe Varian earliest and studies Harold on SchwedeNMR properties [55,56]. of The fluids first in nuclear porous magnetic media started logging in the tool 1950s was at introduced a number inof 1960oil company and these research early tools laboratories, measured and the the FID first in thepatents Earth’s on NMR magnetic well field logging [57– was59]. Evenpublished though by theseRussel tools Varian were and not Harold commercially Schwede successful, [55,56]. The the first research nuclear behind magnetic these logging tools laid tool a firmwas foundationintroduced forin 1960 later and work. these There early was tools a lull measure in progressd the of FID NMR in loggingthe Earth’s tools magnetic until Jackson field et[57 al.–59 started]. Even working though onthese remote tools were ‘inside not out’ commercially NMR in the successful, late 1970s the and research early behind 1980s, these focused tools on laid methods a firm offoundation creating regionsfor later ofwork. homogenous There was magnetic a lull in progress fields in of geological NMR logging formations tools until external Jackson to theet al NMR. started device working and investigatingon remote ‘inside the sensitivityout’ NMR in of the NMR late detection 1970s and [60 early–62]. 1980s, These focused works triggeredon methods further of creating research regions and developmentof homogenous into the magnetic ‘inside out’fields NMR in concept, geological where, formations instead of external placing tothe thesample NMR inside device the NMR and apparatus,investigating the the apparatus sensitivity was of placed NMR inside detection the sample, [60–62]. which These in works this case triggered was the further Earth. Thisresearch required and thedevelopment projection into of large the ‘inside static magnetic out’ NMR fields concept, and highwhere, frequency instead of RF placing fields outside the sample the NMRinside apparatus the NMR andapparatus, into the the surrounding apparatus geological was placed formations. inside the The sample, first field which test in with this a case new wasdesign the consisting Earth. This of arequired permanent the magnetprojection and of a large pulsed static RF NMRmagnetic technique fields wasand performedhigh frequency in 1989, RF andfields the outside first commercial the NMR toolsapparatus were available and into for the use surrounding the following geological year [59 formations.]. The first field test with a new design consistingResearch of a in permanent the late 1980s magnet and and the 1990sa pulsed showed RF NMR that technique complex networks was performed of pore in spaces 1989, resultedand the infirst multi-exponential commercial tools relaxation,were available and for the use distribution the following of relaxation year [59]. times were strongly related to the diffusionResearch regimesin the late of 1980s the pore and spaces the 1990s [63 –showed71]. Algorithms that complex were networks developed of pore in the spaces late 1990sresulted to implementin multi-exponential variable smoothingrelaxation, and of distributions the distribution so that of relaxation the smoothing times were was roughlystrongly uniformrelated to over the thediffusion sharp and regimes broad of features the pore of quasi-continuous spaces [63–71]. distributions Algorithms were of relaxation developed times in [72 the]. These late 1990s research to worksimplement in multi-exponential variable smoothing relaxation of distributions formed the so foundation that the smoothing for studies was on roughly pore size uniform distributions over the of differentsharp and types broad of porousfeatures media of quasi and-continu were laterous adopted distributions to develop of relaxation algorithms times for 2D[72]. NMR These of diffusionresearch andworks relaxation in multi- toexponential obtain diffusion-diffusion relaxation formed and the diffusion-relaxation foundation for studies correlation on pore functions size distributions [73–76]. of differentThe research types of efforts porous in media the 1990s and and were early later 2000s adopted also toled develop to pioneering algorithms research for 2Don compact, NMR of mobilediffusion devices and relaxation that could to measure obtain diffusion NMR signals-diffusion from and objects diffusion outside-relaxation the magnet correlation in a non-invasive functions [73–76].

Sensors 2017, 17, 2384 16 of 32 manner [77–83]. These single-sided NMR devices shed light on how to obtain increased field homogeneity, field strength, and even controlled static field gradients. While there were many advantages with these portable single-sided tools there were also problems with significant reduction in field strength and homogeneity, limiting the analysis capability of these tools to only TI and TII relaxometry. Work was carried out to improve the S/N ratio and optimize the pulse trains by investigating spin dynamics in inhomogenous fields and its effects on diffusion and relaxation [74,84,85]. Based on the results obtained from these works, 2D experiments were performed with a leading diffusion experiment followed by a TII sensitive Carr-Purcell-Meiboom-Gill (CPMG) pulse train, where the 2D dataset was processed to obtain 2D maps that correlated diffusion coefficients and transverse relaxation times [73,74,86–88]. These works investigating diffusion and relaxation in porous media and determination of pore size and distribution resulted in the ability to unlock the fluid properties from the NMR data and determine the different types of fluid present. In order to run wireline NMR tools, first commercially available in the 1990s, drilling had to cease and the drilling assembly had to be pulled out of the well before the wireline NMR could be lowered into it. However, NMR logging while drilling (NMR-LWD) tools, which started appearing in the oil/gas industry in the early 2000s [89–94], could determine and identify different fluid phases and their dynamics in geological formations in real-time, while drilling, thus saving time and reducing the cost in a drilling operation. NMR-LWD is rapidly becoming an important logging tool in the oil/gas industry [95] and more recent works on NMR [96–103] continue to drive advancements in NMR-LWD tools to provide more accurate and better characterization of geological formations [104–109]. NMR was first used in the petroleum industry as a tool in laboratory core analysis. In such a setup, a formation core extracted from a well is placed inside a sample chamber, as shown in Figure 12a. The sample chamber has two magnets that produce a static magnetic field and a transmitter coil that transmits RF radiation energy via pulses to the sample. The receiver coil surrounding the sample receives the emission of the absorbed RF energy and sends it to an oscilloscope/recorder for analysis. The sweep coils are used to vary the magnetic field over a small range while observing the emitted RF signal from the sample to obtain an NMR spectrum. However, unlike laboratory testing, downhole NMR tools, either run by wireline or LWD, have to measure NMR signals outside the tool, from external geological formations, as show in Figure 12b. In a laboratory setting, the sample is placed inside the magnet and the RF transmitter/receiver coils so that the static magnetic field and RF pulse are projected into the sample. In NMR-LWD, the sample, the formation, is outside the magnet and RF transmitter/receiver coils, so the static magnetic field and the transmitted RF pulse has to be projected out to the sample. NMR well logging is referred to as ‘inside out’ NMR due to the geometry of the magnets and transmitter/receiver coils being inverse to the geometry of a laboratory setting. ‘Inside out’ NMR introduces several complexities such as the need for radially symmetric, high strength static magnetic fields and high frequency RF magnetic fields to ensure sufficient penetration through the well hole and into geological formations, hole size and resultant limits on tool real estate, tool eccentricity inside the hole, drilling fluids, downhole environmental parameters such as, temperature, pressure, pH etc., as along with drilling conditions such as shock and vibration. LWD tools are required to make measurements while rotating, in real or near-real time. Commercially available wireline and LWD tools address these issues and measure NMR signals using different techniques [89–93,95,110–117], but the common objective in all of these tools is to magnetically manipulate and measure NMR signals from the hydrogen nuclei in formation fluids. One important point to note is that the polarization and decay are time-sensitive components and therefore, lateral motion/vibration of the drillstring might result in the magnet and antennas not remaining in one position for long enough to fully polarize a region in the formation and measure the full decay. Such lateral motion/vibration-induced decay primarily affects long TII values that may reduce the accuracy of NMR measurements, particularly in light hydrocarbon and carbonate formations. However, magnetometers and accelerometers can be used for quality control of NMR measurements by using the magnetometers and accelerometers to measure lateral motion/vibration-induced parameters such as, frequency, amplitude, trajectory Sensors 2017, 17, 2384 17 of 32 Sensors 2017, 17, 2384 17 of 32 measurements by using the magnetometers and accelerometers to measure lateral motion/vibration- induced parameters such as, frequency, amplitude, trajectory and timing of the vibration, and then and timing of the vibration, and then utilizing this data to calculate a theoretical maximum T value utilizing this data to calculate a theoretical maximum TII value resolvable during motion and anII NMR resolvablequality indicator during that motion can be and sent an NMRwith the quality NMR indicator data [90]. that can be sent with the NMR data [90]. In these tools, the T relaxation time is be measured by either of two methods: either inversion In these tools, the TII relaxation time is be measured by either of two methods: either inversion ◦ recovery or saturation recovery [[54,112,113].54,112,113]. In the inversion recovery method an initialinitial 180180° pulsepulse inverts the the spins. spins. These These spins spins then gradually relax towards towards thermal thermal equilibrium. equilibrium. After After a given ◦ recovery time another 9090° pulse is applied to obtain the FID signal. In the saturation saturation recovery method ◦ ◦ an initial 9090° pulse is followed by another 9090° pulse after a given recovery time to obtain the FID signal. The T relaxation time can be obtained by the spin echo technique as shown in Figure 13a inset. signal. The TIIII relaxation time can be obtained by the spin echo technique as shown in Figure 13a ◦ Ininset. the In spin-echo the spin technique,-echo technique, a 90 RF a pulse90° RF tips pulse the nucleustips the awaynucleus from away the staticfrom fieldthe static onto thefield transverse onto the ◦ xtransvers-y planee and x-y toplane precession and to motion.precession A 180motion.pulse A 180° flips pulse the direction flips the of direction net spin, of which net spin, eventually which causeseventually the spinscauses with the spins different with angular different momentums angular momentums to refocus to at refocus a certain at time,a certain which time, is thewhich echo is ◦ ◦ timethe echo (the time delay (the between delay between the 90 theand 90° 180 andpulses). 180° pulses). Therefore, Therefo there, dephasing the dephasing caused caused by spin-spin by spin- interactionsspin interactions and non-homogeneity and non-homogeneity of the staticof the magnetic static magnetic field can field be removed can be removed and the phase and the difference phase betweendifference the between spins canthe bespins maintained, can be maintained, resulting in resulting a strong in echo a strong signal. echo Echo signal. signals Echo are signals produced are ◦ betweenproduced the between train of 180the trainpulses of at 180° the same pulses frequency at the same as the frequency RF pulses asand the decay RF exponentially pulses and decay with a relaxation time T during the measurement cycle as shown in Figure 13a. exponentially withII a relaxation time TII during the measurement cycle as shown in Figure 13a.

90° 180°

(a) Echo

Echo spacing

I

e T buildup

d u

t RF pulse

i

l

p m

A TII decay Echo

90° 180° 180° 180° 180° Time (t) Polarizing time (c) Pore size (b) Long Void (pore) Interconnected space void

(i) (ii) e d

Fluid u

t i flow l

p Relaxation time

m A

Porosity Permeability Short

(d) TII cutoffs TII (ms)

More viscous and higher aggregation

e

d

u

t

i

l

p

m A

CBW BVI Free fluid TII (ms) Dry Clay bound Cappilary clay water bound water Movable fluid Bound fluids Micro Meso Macro Pore size Figure 13. (a) Polarization and decay of a nucleus resulting in echo signals (inset shows the spin-echo Figure 13. (a) Polarization and decay of a nucleus resulting in echo signals (inset shows the spin-echo technique); (b) (i) Porosity refers to the percentage of void space in a rock formation and (ii) technique); (b)(i) Porosity refers to the percentage of void space in a rock formation and (ii) permeability permeability refers to the degree of interconnection between these void spaces that allows fluids to refers to the degree of interconnection between these void spaces that allows fluids to flow through flow through the voids; (c) In fully water saturated pores larger pore sizes indicate long relaxation the voids; (c) In fully water saturated pores larger pore sizes indicate long relaxation times and smaller times and smaller pores short relaxation times; (d) Fluids in formations can be characterized as bound pores short relaxation times; (d) Fluids in formations can be characterized as bound or movable fluids or movable fluids based on TII cut-off values. Bound fluids have micro and meso pores and are highly based on TII cut-off values. Bound fluids have micro and meso pores and are highly aggregated andaggregated more viscous and more than viscous free fluids, than whichfree fluids, have which larger have macro larger pores. macro Heavy pores. oils Heavy such as oils tar such fall within as tar thefall boundwithin fluidthe bound region fluid whereas region intermediate whereas intermediate and light oils and and light gases oils fall an withind gases the fall free within fluid the region. free fluid region.

Sensors 2017, 17, 2384 18 of 32

The amplitude of the echo signals are directly proportional to the net magnetization in the transverse plane, and gives an indication of the quantity of hydrogen nuclei present in a formation. This information is used for porosity measurements, where the porosity, as shown in Figure 13(bi), refers to the percentage of void space found in a rock formation, which could be water, oil or gas, whereas the permeability, as shown in Figure 13(bii), is the degree of interconnection of these void spaces and how easily fluid can flow between the spaces,. The first point of FID or extrapolation of the first echo with accurate exponential fitting is the formation porosity. Assuming a fully water saturated pore, the relaxation time TII provides an indication of the pore size, and as Figure 13c shows, large pores have a long TII and small pores have a short TII. Multiple fully water saturated pores have multiple TII values for the different pore sizes resulting in a multi-exponential decay curve. While there are many means for nuclei to lose energy and return to equilibrium, one of the main ways they can return to equilibrium, when in a fluid molecule such as a formation fluid for example, is by colliding into the molecule walls. In larger pores these collisions are less frequent than in smaller pores, therefore, nuclei in larger pores have longer relaxation times. Information about the pore size can also be used to estimate the permeability of a formation, since the permeability is proportional to the square of the diameter of the pore. Therefore, the rate of decay of the NMR signal amplitude is used to obtain information about the permeability of the formation. Determination of pore size distribution is another important measurement obtained by NMR since the pore size distribution in a formation can vary significantly leading to a broad distribution. By analyzing this distribution a geological interpretation of the formation can be obtained. The relaxation times TI and TII are influenced by the type of fluid and paramagnetic materials in the formation and diffusion effects of the fluid. For example, when the fluid type is brine, shorter relaxation times indicate smaller pores and longer relaxation times indicate larger pores. The three main mechanisms influencing TII relaxation times are grain surface relaxation, relaxation by bulk fluid processes and relaxation from molecular diffusion [113]. Grain surface relaxation is related to pore-size distribution, while bulk fluid and molecular diffusion relaxations are influenced by the type of fluid in the pores. For example, heavy oils and tar have short relaxation times while light oils and gas have longer relaxation times. TII relaxation times can be used to provide estimates of, (i) clay bound water (CBW) and bulk volume irreducible water (BVI), which are called bound fluids, and (ii) moveable or free fluids, in formations, as shown in Figure 13d. The bound fluid region indicates micro and meso pores where the fluid cannot move freely while the movable fluid region indicates larger macro pores. The TII cut off times vary with formation lithology. A very heavy oil like tar falls within the CBW spectrum. Heavy oils fall within the CBW and BVI spectrums and intermediate/light oils and gases fall within the free fluid spectrum. Intermediate oils are at the beginning of the free fluid spectrum and gases are towards the end of the free fluid spectrum. Interpretation of NMR signals using only TII relaxation times has its limitations. TII relaxation data analyzed by differential spectrum and enhanced diffusion techniques result in 1D analysis of data with the ability to only characterize fluids not quantify them. One of the major drawbacks is the difficulty in distinguishing between water and oil, and, therefore, the inability to quantify the amount of hydrocarbons present. Molecular diffusion opens up the possibility of calculating the water saturation and viscosity of fluids. The diffusion rates of water and gas can be calculated for specific downhole conditions, while the diffusion rate of oil depends on its molecular structure. The resulting 2D cross-plots have data in a 2D space with diffusion and relaxation dimensions [54,113,118–120]. This means that heavy oil, conventional oil, light oil, water and gas can be identified and quantified in an oil/gas reservoir. Moreover, the oil/gas water contact measurements using 2D NMR cross-plots are used for field reserve estimates and reservoir field development. It must be noted that TI relaxation measurements also provide 1D data sets; additionally 2D TI–TII data sets can be obtained by acquiring a full TII echo decay signal during each TI acquisition [113]. Moreover, 3D NMR measurements, correlation of fluid properties for TI, TII and D, and 4D NMR measurements, inclusion of the radial distance from the formation wall, are also possible [113]. The accurate profiling of fluids in an oil/gas Sensors 2017, 17, 2384 19 of 32 reservoir has a significant bearing not only on the economic valuation of a reservoir field but also on the surface and production facilities required to optimize the production of a well. Sensors 2017, 17, 2384 19 of 32 3.3. Field Results 3.3. Field Results FigureFigure 14 14a showsa shows porosity porosity estimations estimations fromfrom anan NMRNMR tool and and a a neutron neutron-density-density tool, tool, which which is is anotheranother LWD LWD tool tool that that measures measures porosity porosity and and used used for for comparison comparison purposes purposes with with the the NMR NMR tool tool [121 ]. Neutron[121]. logging Neutron tools logging use a tools chemical use asource chemical or an source electronic or an neutron electronic generator neutron to emit generator neutrons, to emit which collideneutrons, with hydrogenwhich collide atoms with in hydrogen a formation atoms and in reach a formation thermal and equilibrium. reach thermal The equilibrium. rate at which The thermal rate equilibriumat which thermalis reached equilibrium is proportional is reached to the is hydrogen proportional concentration, to the hydrogen and this concentration, information and is used this to obtaininformation neutron is porosity. used to obtain neutron porosity.

(a) (b)

Track 1 2 3 4 5 1 2 3 4 5 6 )

Resistivity t Porosity Distribution Resistivity Lith Fluid volume NMR-1 NMR-2

Lith )

f t

Ohm.m ( % ms % % %

V/V Ohm.m V/V f

(

Deep h TP-ND

t TP-ND h BFV BFV

0.2 2000 II t

p BFV T p e Deep Water Shallow TP-NMR e

D TP-NMR TP-NMR Anhydrite 0.2 2000 0 1 50 0 0.5 4096 0.2 2000 Shallow D Hydrocarbons TP-ND TP-ND Dolomite X000 Calcite 0.2 2000 0 1 50 0 50 0 50 0 Shale X050 TP-ND

X100 BFV Neutron density (TP-ND) X200 TP-NMR Bound X100 Hydrocarbons fluids volume (BFV) X300 TP-ND and TP-NMR similar

X150 X400 Water

Difference X500 between TP-ND Total and TP-NMR porosity NMR (TP- X200 NMR) X600

X700

FigureFigure 14. 14.(a )(a Comparison) Comparison between between an an NMR NMR andand aa neutron density tool. tool. Track Track 1 1shows shows the the resistivity resistivity of theof the formation, formation, Track Track 2 shows2 shows the the lithology lithology ofof thethe formations,formations, such as as anhydrite, anhydrite, dolomite, dolomite, calcite calcite andand shale shale formations formations and and Track Track 3 3 shows shows the the depthdepth atat which measurements measurements were were made. made. Track Track 4 shows 4 shows thethe porosity porosity measurements, measurements, wherewhere the red red curve curve shows shows the the total total porosity porosity measurements measurements obtained obtained by the neutron porosity tool (TP-ND) and the yellow and gray shaded areas show the total porosity and by the neutron porosity tool (TP-ND) and the yellow and gray shaded areas show the total porosity bound fluid volume, respectively, obtained by the LWD NMR tool (TP-NMR and bound fluid volume and bound fluid volume, respectively, obtained by the LWD NMR tool (TP-NMR and bound fluid (BFV)). Track 5 shows the TII distributions of the NMR measurements. The images in Track 4 show volume (BFV)). Track 5 shows the TII distributions of the NMR measurements. The images in Track 4 that there is excellent agreement between the NMR and neutron-density results when computing total show that there is excellent agreement between the NMR and neutron-density results when computing porosity results since the porosity percentages of the red curves and the yellow shaded areas are total porosity results since the porosity percentages of the red curves and the yellow shaded areas similar throughout the depths at which the logs were taken; (b) An NMR tool was run twice in the are similar throughout the depths at which the logs were taken; (b) An NMR tool was run twice in hole since measurements obtained during the first run, NMR-1 in Track 5, did not compare well with the hole since measurements obtained during the first run, NMR-1 in Track 5, did not compare well measurements obtained by the neutron density tool in Track 4. In Track 4 the blue-shaded area withcorresponds measurements to volume obtained of water by theand neutronthe red-shaded density area tool to in hydrocarbons. Track 4. In Track The red 4 the curve blue-shaded seen in Track area corresponds5 corresponds to volume to the ofoutline water of and the the total red-shaded porosity obtained area to hydrocarbons. by the neutron The density red curve tool (TP seen-ND) in Track in 5 correspondsTrack 4 (water+hydrocarbons). to the outline of the The total differences porosity obtainedbetween the by TP the-ND neutron and TP density-NMR tool are shown (TP-ND) in inTrack Track 4 (water+hydrocarbons).5 and were found out to The be due differences to the effect between of high the salinity TP-ND drilling and TP-NMR fluid used are inside shown the in well. Track After 5 and wereadj foundusting out for to high be due salinity to the the effect NMR of hightool was salinity run drilling inside the fluid well used again inside resulting the well. in After a significant adjusting forimprovement high salinity thein the NMR results tool as was shown run in inside Track the 6 [121]. well again resulting in a significant improvement in the results as shown in Track 6 [121]. Track 1 in Figure 14a shows the resistivity of the formation. Resistivity measures the degree to whichTrack a 1formation in Figure 14cana showsoppose the the resistivity flow of electric of the formation. current. Resistivity Resistivity is measures therefore thethe degree reciprocal to which of a formationconductivity, can opposewhich measures the flow ofhow electric easily current. a current Resistivity can flow isin therefore a formation. the reciprocalWhile fresh of water conductivity, does not conduct electricity, most of the water found in formations have salt ions and therefore conduct electric current and so have low resistivity. Hydrocarbons on the other hand are non-conductive, so the resistivity values increase as the pores in a formation become more saturated with hydrocarbons.

Sensors 2017, 17, 2384 20 of 32 which measures how easily a current can flow in a formation. While fresh water does not conduct electricity, most of the water found in formations have salt ions and therefore conduct electric current and so have low resistivity. Hydrocarbons on the other hand are non-conductive, so the resistivity values increase as the pores in a formation become more saturated with hydrocarbons. The deep and shallow resistivity logs refer to the depths of investigation (DOI), where the shallow logs refer to measurements obtained at the wall of the wellbore, closest to the resistivity logging tool, and the deep logs refer to measurements obtained deep within the formation, furthest away from the logging tool and uncontaminated by the resistivity logging tool. The separation between the shallow and deep logs gives an indication of the diameter of invasion by the drilling fluid and the permeability of the different zones in a formation. It must be noted, however, that resistivity in itself does not always provide an accurate interpretation of a formation and is therefore only used with other logging measurements to aid in the interpretation of formations. Track 2 illustrates the lithology (lith) of the formations, such as anhydrite, dolomite, calcite and shale formations, as a fraction of the rock volume. Track 3 shows the depth at which measurements were made. Track 4 shows the porosity measurements, where the red curve shows the total porosity measurements obtained by the neutron porosity tool (TP-ND), and the yellow and gray shaded areas show the total porosity and bound fluid volume, respectively, obtained by the LWD-NMR tool (TP-NMR and BFV). Track 5 shows the TII distributions of the NMR measurements. The images in Track 4 show that there is excellent agreement between the NMR and the neutron-density when computing total porosity results since the porosity percentages of the red curves and the yellow shaded areas are similar throughout the depths at which the logs were taken. Figure 14b shows another comparison between a neutron-density tool and an NMR tool, where Track 1 is the resistivity, 2 the lithology and 3 the depth, as in Figure 14a. Track 4 shows the measurements obtained by the neutron density tool, where the blue-shaded area corresponds to volume of water and the red-shaded area to hydrocarbons. The NMR tool was run twice in the well and Track 5 (NMR-1) shows the measurements obtained during its initial run. The yellow shaded area is the total porosity (TP-NMR) and the grey shaded area is the bound fluid volume (BFV). The red curve seen in this Track corresponds to the outline of the total porosity obtained by the neutron density tool (TP-ND) in Track 4, and is added as a reference to Track 5 for comparison with TP-NMR. However, a clear difference can be seen between TP-ND and TP-NMR, and this difference was found to be due to the effect of high salinity drilling fluid used inside the well. The NMR tool was then pulled out of the well and the tool was adjusted to compensate for high salinity and run inside the well again. Track 6 (NMR-2) shows the measurements obtained during this second run, and it can be seen that the measurements from TP-ND and TP-NMR are in good agreement. Figure 15 shows the estimation of viscosity and how this information is used to identify a heavy oil transition zone in the reservoir. In the heavy oil transition zone shown between the two brown lines the total porosity measurements obtained by both NMR (TP-NMR) and neutron density (TP-ND) in Track 5 decrease due to pores being saturated with heavy oil, viscosity in Track 7 increases, the mobility in Track 8, which is the ratio of effective permeability to phase viscosity, decreases and the TII distribution times become shorter due to restricted molecular motion. A less obvious indicator is resistance in Track 1, which increases slightly in the heavy oil transition zone. Figure 16 shows basic and advanced 2D NMR analyses on data obtained by an NMR tool [118]. Track 1 shows gamma ray and caliper measurements. Gamma ray measurements provide information about the formation lithology (Track 5) in gamma-ray, American Petroleum Industry (GAPI) units while caliper measurements provide information on the width of the well in inches. Tracks 4, 5 and 6 provide depth, lithology and fluid volume information. TI and TII spectrum data (Tracks 8 and 10) and 1D partial porosity data (Tracks 9 and 11) obtained by inversion techniques is referred to as basic data, where each element of this spectrum is a volume of fluids with a given TI or TII relaxation time. CBW, BVI and free fluids are calculated by the summation of partial porosities within different ranges of the CBW, and BVI cut off values in the spectrum (Tracks 8–11). Track 7 shows the permeability, estimated by NMR porosity analysis. 2D NMR data was obtained by the inversion of multi-echo train data sets, and, as illustrated by the 2D images in Tracks 12 and 13, this well contains gas and high gas/oil ratio oil. Sensors 2017, 17, 2384 21 of 32 Sensors 2017, 17, 2384 21 of 32 Sensors 2017, 17, 2384 21 of 32

Track 1 2 3 4 5 6 7 8 Resistivity Lith Saturation Porosity Distribution Viscosity Mobility Track 1 2 3 ) 4 5 6 7 8

Ohm.m V/V t V/V % ms cP MD/CP f

Resistivity Lith ( Mobility

Saturation Porosity Distribution Viscosity )

t TP-ND Ohm.m V/V h V/V % ms cP MD/CP

Deep f t

( BFV

0.2 2000 p TP-ND TII e Deep h Shallow t SWT TP-NMR

D BFV

0.2 2000 p II 0.2 2000 1 0 50 0 0.5 T 4096 1 4096 0.01 10000 Shallow 0 1 e SWT TP-NMR 2000 D 1 0 50 0 0.5 4096 1 4096 0.01 10000 0.2 0 1 TP-NMR X000 TP-NMR X000 Viscosity Vinisccroeasisteys increases TP-ND Heavy oil X500 TP-ND traHnseiatvioyn o zilo ne Resistivity X500 transition zone Rienscirsetiavsietys increases Total pToorotasli ty Mobility dpeocrroesaitsye s TII times Y000 dMeocbreilaistye s decreases TdIeI ctirmeaesse Y000 decreases decrease

Y500 Y500

FigureFigure 15. 15.Calculation Calculation of of viscosity viscosity and and determination determination ofof aa heavyheavy oiloil transitiontransition zone. In the heavy heavy oil oil Figuretransition 15. Calculationzone shown of between viscosity the and two determination brown lines, ofthe a heavytotal porosity oil transition measurements zone. In the obtained heavy oilby transitiontransition zone zone shown shown betweenbetween thethe twotwo brownbrown lines,lines, thethe totaltotal porosity measurements obtained obtained by by bothboth NMR NMR (TP-NMR) (TP-NMR) and and neutron neutron density density (TP-ND)(TP-ND) inin TrackTrack 55 decreasedecrease duedue to pores being saturated bothwith NMRheavy (TP oil-,NMR) viscosity and in neutron Track 7density increases, (TP -theND) mobility in Track in 5 Trackdecrease 8, which due to is pores the ratio being of saturated effective withwith heavy heavy oil, oil, viscosity viscosity inin TrackTrack 77 increases,increases, thethe mobilitymobility in Track 8, which is the ratio ratio of of effective effective permeability to phase viscosity, decreases and the TII distribution times become shorter due to permeability to phase viscosity, decreases and the TII distribution times become shorter due to restricted permeabilityrestricted molecular to phase motion. viscosity, A less decreases obvious indicator and the isT IIresistance distribution in Track times 1, becomewhich increases shorter slightly due to molecular motion. A less obvious indicator is resistance in Track 1, which increases slightly in the heavy restrictedin the heavy molecular oil transition motion. zone A less [121]. obvious indicator is resistance in Track 1, which increases slightly oilintransition the heavyzone oil transition [121]. zone [121].

Track Track Gamma TI/TII-TII D-TII NMR TII NMR TII NMR TI NMR TI ray spectrum porosity spectrum porosity II Gamma ) TI/TII-TII D-T t NMR TII NMR TII NMR TI NMR TI Caliper f Shallow (

ray spectrum porosity spectrum porosity

) h

t CBW Cutoff CBW Cutoff t Caliper Medium f

CAL (

Shallow p

6 In 18 e h CBVWI Cuttooffff CBVWI Cuttooffff t NMR TI

CAL MDedeeiupm D p

6 In 18 e BVTII IC GuMtoff BVTI IC GuMtoff 2000 NNMMRR TTIII GR 0.D2 eep D 0 GAPI 200 Ohm.m 0.2TII GmsM 2896 0.2 TI GmsM 2896 GR 0.2 2000 NMR TII 0 GAPI 200 Ohm.m XX00 0.2 ms 2896 0.2 ms 2896 Gas XX00 XX10 Gas Oil XX10 XX20 TI BFV Oil TII BFV XX20 TI BFV XX30 Difference in TII BFV XX30 permeability XX40 Difference in values obtained permeability XX40 by TI and TII XX50 values obtained by TI and TII XXXX5600 XX60

Figure 16. Basic and 2D NMR analyses of a well. TI and TII spectrum data (Tracks 8 and 10) and 1D Figure 16. Basic and 2D NMR analyses of a well. TI and TII spectrum data (Tracks 8 and 10) and 1D Figurepartial 16. porosityBasic anddata 2D(Tracks NMR 9 analysesand 11) obtained of a well. by TinversionI and TII techniquesspectrum datais referred (Tracks to 8as and basic 10) data, and partial porosity data (Tracks 9 and 11) obtained by inversion techniques is referred to as basic data, 1Dwhere partial each porosity element data of this (Tracks spectrum 9 and is 11) a volume obtained of byfluids inversion with a given techniques TI or T isII referredrelaxation to time. as basic 2D where each element of this spectrum is a volume of fluids with a given TI or TII relaxation time. 2D data,NMR where data was each obtained element by of the this inversion spectrum of multi is a volume-echo train of data fluids sets, with and a as given shownTI byor theTII 2relaxationD images NMR data was obtained by the inversion of multi-echo train data sets, and as shown by the 2D images time.in Tracks 2D NMR 12 and data 13, wasthis obtainedwell contains by thegas inversion and high ofgas/oil multi-echo ratio oil. train As shown data sets, in the and boxes as shown outlined by in Tracks 12 and 13, this well contains gas and high gas/oil ratio oil. As shown in the boxes outlined thein 2Dred imagesin Tracks in 7, Tracks 9 and 1211, andat depths 13, this XX00 well–XX10, contains between gas andthe two high brown gas/oil lines, ratio there oil. is As a noticeable shown in in red in Tracks 7, 9 and 11, at depths XX00–XX10, between the two brown lines, there is a noticeable thedifference boxes outlined between in red the inTI Tracksand T 7,II 9bound and 11, fluid at depths volumes XX00–XX10, and their between corresponding the two permeability brown lines, difference between the TI and TII bound fluid volumes and their corresponding permeability thereestimates. is a noticeable While this difference is due to betweenthe gas signal the T Ibeingand TpushedII bound below fluid the volumes BVI cutoff and line their due corresponding to the effect estimates. While this is due to the gas signal being pushed below the BVI cutoff line due to the effect permeabilityof diffusion, estimates.TI on the other While hand this is not is due affected to the by gas diffusion signal and being therefore, pushed provides below the the BVI correct cutoff bou linend of diffusion, TI on the other hand is not affected by diffusion and therefore, provides the correct bound duefluid to estimation. the effect of The diffusion, 2D NMRTI plotson the estimate other hand the volume is not affected of gas present by diffusion by summing and therefore, the NMR provides signals fluid estimation. The 2D NMR plots estimate the volume of gas present by summing the NMR signals thewithin correct a ’ boundbox’ centered fluid estimation. on the theoretical The 2D NMRposition plots as estimateshown in the Tracks volume 12 ofand gas 13. present The gas by volume summing at within a ’box’ centered on the theoretical position as shown in Tracks 12 and 13. The gas volume at theXX10 NMR was signals predicted within to be a a ’box’ gas-oil centered contact on and the this theoretical was later positionconfirmed as by shown further in tests Tracks [118]. 12 and 13. XX10 was predicted to be a gas-oil contact and this was later confirmed by further tests [118]. The gas volume at XX10 was predicted to be a gas-oil contact and this was later confirmed by further testsAs [shown118]. in the boxes outlined in red in Tracks 7, 9 and 11, at depths XX00–XX10, between the As shown in the boxes outlined in red in Tracks 7, 9 and 11, at depths XX00–XX10, between the two brown lines, there is a noticeable difference between the TI and TII bound fluid volumes and their two brown lines, there is a noticeable difference between the TI and TII bound fluid volumes and their

Sensors 2017, 17, 2384 22 of 32

As shown in the boxes outlined in red in Tracks 7, 9 and 11, at depths XX00–XX10, between the two brown lines, there is a noticeable difference between the TI and TII bound fluid volumes and their corresponding permeability estimates. While this is due to the gas signal being pushed below the BVI cutoff line due to the effect of diffusion, TI on the other hand is not affected by diffusion and therefore, provides the correct bound fluid estimation.The 2D NMR plots estimate the volume of gas present by summing the NMR signals within a ‘box’ centered on the theoretical position, as shown in Tracks 12 and 13. The gas volume at XX10 was predicted to be a gas-oil contact, a fact later confirmed by further tests. Figure 17 shows an example of how 4D NMR processing results in more accurate estimation of fluid volumes and properties [113,122]. While 3D NMR measurements obtain echo data at multiple polarization times (for TI) and multiple echo spacings (for diffusion) to construct 3D maps, 4D measurements incorporate a fourth dimension, the radial distance d from the tool to the formation, which results in the acquisition of data at multiple depths of investigation, as shown in Figure 17a. The shells refer to the depth of investigation (DOI) inside the formation, where shell 1 is closest to the tool, at a distance of d1, followed by shell 4, at a distance of d2, and shell 8, which is the furthest away at a distance of d3. Data from the closest shell to the formation was used to correct data from the shells deeper inside the formation, thereby compensating for the decreasing magnetic fields and echo signals resulting in poorer signal-to-noise ratios in deeper shells. A major assumption made in 4D NMR processing is that the bound fluid volume does not change with the DOI since the invasion of filtrate from drilling fluids does not generally change clay and capillary-bound fluids. Constraining the bound fluids in the deeper shells to be equal to the bound fluid in the more accurate shallower shells, and reassigning the total porosity across the fluid spectrum, leads to more accurate NMR analysis. Figure 17b shows the bound and free fluid porosity measurements from Tracks 2 to 5, where Track 1 includes caliper measurements and the depth, 2 and 4 are the standard bound and free fluids, respectively, and Tracks 3 and 5 are the 4D bound and free fluids, respectively. It is difficult to distinguish between the bound fluid volumes measured by the 3 shells (shells 1, 4 and 8) in Track 2 as well as the free fluid volumes measured by the three shells in Track 4. However, constraining the bound volumes and reassigning the porosity contributions results in a much clearer picture where there is less deviation between the results obtained by the 3 shells, as shown in Tracks 3 and 5. Tracks 6–11 in Figure 17b shows the fluid volumetric analysis results and shows an example where fluid properties were affected by hole conditions from X120 to X135 ft (between the two brown lines). In this case a hole washout results in a larger diameter of the well, as shown by the caliper readings in Track 1, and the increased porosity measurements from shallower shells (Tracks 6, 7, 9 and 10). Shell 8 measurements in Tracks 8 and 11 are from beyond the washout and provide more accurate data. Figure17c illustrates how the diffusion and TI maps used for saturation computation for each shell demonstrate the effectiveness of 4D processing. Standard 2D NMR processing in Figure 17(ci) shows shells 1 and 4 having similar bound fluid volumes but shell 8 having a lower bound fluid volume than 1 and 4, even though the bound fluid volumes are expected to be the same across all shells. 4D NMR processing in Figure 17(cii) provides a more accurate measurement for shell 8 by constraining the fluid volume to be the same below a TI cutoff value and reapportioning the porosity to account for the bound fluid volume. Sensors 2017, 17, 2384 23 of 32 Sensors 2017, 17, 2384 23 of 32

Standard 2D NMR Processing (a) (c) (i) Shell 1 Shell 4 Shell 8

Formation n

o

i

s

u

f

f

i

D

1

8

4

l

l

l

l

l

l

e

e

e

e

d

h

h

h

S

u

S

S

l

t

i

l

o

p

o

T

m

A R

M TI (ms) N Standard 4D NMR Processing

d1 (ii) Shell 1 Shell 4 Shell 8

n o

d2 i

s

u f

3 f

d i D

Depths of investigation

e

d

u

t

i

l

p

m A

TI (ms) (b) 6 7 8 9 10 11 Track Standard 2D NMR Processing 4D NMR Processing Heavy oil Heavy oil Heavy oil Heavy oil Heavy oil Heavy oil 1 2 3 4 5 Standard 4D Bound Standard Free Oil Oil Oil Oil Oil Oil 4D Free Fluid Bound Fluid Fluid Fluid Free water Free water Free water Caliper Shell 1 Shell 1 Shell 1 Shell 1 Free water Free water Free water 6 in 16 Shell 4 Shell 4 Shell 4 Shell 4 Bound Bound Bound Bound Bound Bound Washout Shell 8 Shell 8 Shell 8 Shell 8 water water water water water water Depth Porosity % Porosity % Porosity % Porosity % Porosity % Porosity % ft 50 % 0 50 % 0 25 % 0 25 % 0 Shell 1 Shell 4 Shell 8 Shell 1 Shell 4 Shell 8 50 0 50 0 50 0 50 0 50 0 50 0

More Less Less Actual Actual coherent More coherent coherent porosity from porosity from X100 coherent Increased beyond the beyond the washout Increased washout X110 Increase in porosities n region porosities region

o width of well

i g

e X120

r

t

u X130

o

h s

a X140 W X150

Figure 17. 17. 4D NMR processing. ( (aa)) 4D 4D measurements incorporate a fourth dimension, the radial distance d, from the tool to the formation formation leading to acquisition of data at multiple depths of investigation (d1, d2 and d3); (b) Bond and free fluid porosity measurements are shown from Tracks 2– investigation (d1, d2 and d3); (b) Bond and free fluid porosity measurements are shown from Tracks 2–5. It5. isIt is difficult difficult to to distinguish distinguish between between the the standard standard bound bound fluid fluid volumesvolumes measuredmeasured byby thethe 3 shells (shells 1, 4 and 8) in Track 2 and as well as for free free fluid fluid volumes volumes measured measured by the three three shells in in Track Track 4. However, constraining the bound volumes and reassigning the porosity contributions resulted in a much clearer picture with less deviation between the results obtained by the 3 shells, as shown in Tracks 33 andand 5.5. Fluid volumetric analysis results are shown from Tracks 6–11.6–11. Fluid properties were affectedaffected by hole a a washout washout from from X120 X120 to to X135 X135 ft ft (between (between the the two two brown brown lines), lines), which which resulted resulted inin a alarger larger diameter diameter of ofthe the well, well, shown shown by the by thecaliper caliper readings readings in Track in Track 1 and 1 the and increased the increased porosities porosities from fromshallower shallower shells shells (Tracks (Tracks 6, 7, 9 6, and 7, 9 10). and Shell 10). Shell8 in Trac 8 inks Tracks 8 and 8 11 and were 11 were from from beyond beyond the washout the washout and

andprovided provided more more accurate accurate measurements; measurements; (c) D- (Tc)I maps;D-TI maps; (i) Standard (i) Standard 2D NMR 2D NMRprocessing processing shows shows shells shells1 and 14 andhaving 4 having similar similar bound bound fluid fluidvolumes volumes but shell but shell 8 having 8 having a lower a lower bound bound fluid fluid volume volume than than 1 1and and 4, 4,even even though though the the bound bound fluid fluid volumes volumes are expected are expected to be to the be same the same across across all shells all shells;; (ii) 4D ( iiNMR) 4D NMRprocessing processing provides provides a more a moreaccurate accurate measurement measurement for shell for shell 8 by 8constraining by constraining the thefluid fluid volume volume to be to

bethethe same same below below a T aI TcutoffI cutoff value value and and reapportioning reapportioning the the porosity porosity to to accoun accountt for for the the bound fluidfluid volume [[113113,,122].].

Sensors 2017, 17, 2384 24 of 32

4. Discussion: Research Opportunities for Other Types of Magnetic Sensors The harsh and hostile downhole environment is characterized by high temperature, high pressure, acidic and corrosive environments, as well as high torque, shock and vibration effects resulting from the drill bit grinding through formations. Based on the typical parameters encountered by drilling tools downhole shown in Table2, it is safe to state that not many applications expose sensors and instrumentation to such severe conditions. The failure of sensors could result in drilling companies incurring a significant loss since, in such a situation the drilling has to be stopped, the whole drilling assembly has to be pulled out of the well for repairs and maintenance and then has to be run inside the well again. FGMs and NMR sensors are designed, fabricated and packaged to survive these conditions. However, FGMs are bulky, since they involve ferromagnetic cores and many windings, which take up a significant amount of space in a drillstring, where space is at a premium [2,123]. The ferromagnetic core design, such as the geometry, materials, and the intrinsic losses in the core, along with the errors pertaining to the windings of the coils, also influence the performance, and FGMs are not easy to calibrate [2,124,125]. Another key limitation is the high power consumption of FGMs; up to 1 W. Power usage in a downhole environment has to be managed carefully due to the inaccessibility from the surface. The power to downhole sensors and instrumentation is generally provided by a turbine generator and/or battery pack. The turbine is used to generate electricity by the flow of drilling fluids in the drillstring assembly, and batteries provide continuous, finite power that is rechargeable by the turbine. However, power usage of sensors and instrumentation such as FGMs dictate the turbine/battery pack design to be expensive and occupy a significant amount of space in a drillstring. The advent of microelectromechanical systems (MEMS) technology has allowed the scaling down of mm size devices into the micro-nano range. This provides the opportunity to package and fit these sensors into smaller areas in a drillstring as well as reduce the effects of shock and vibration. The smaller sizes allow sensor arrays thus, increasing the resolution of measurements, and also seamless integration with other electronic components leading to ‘system on chip devices’ that can be mass produced. MEMS devices have low power requirements and the small size of the sensors makes it more tolerant to mechanical shocks and vibrations. Recent research has also shown that MEMS sensors can match much larger and higher power FGMs when it comes to noise performance [126]. FGMs can be scaled down using microfabrication techniques but several challenges remain as explained in Section 2.1. This gives rise to the question; what other types of magnetic sensors have the potential to be used in downhole environments?

Table 2. Typical downhole parameters.

Temperature Pressure pH Vibration Shock 125–230 ◦C 15,000–30,000 psi 2–5 30 g peak at 50–1000 Hz 1000 g, 0.5 ms, Half sine

Several magnetic sensors have the potential to be used in downhole environments and magnetoresistive (MR) sensors [127–131] can be considered the frontrunners in this regard due to their high sensitivity, high temperature tolerance, temperature stability, low power consumption and well established method of fabrication on silicon substrates. Magnetoresistance refers to the change in electrical resistance of a material or system of materials in response to an applied magnetic flux density. MR sensors can measure the Earth’s magnetic field but can also accurately measure magnetic fields from permanent magnets and soft ferromagnetic structures and magnetic fields generated by electric currents. This gives rise to the use of these sensors not only as directional sensors but as potential sensors for measurement of rotation speed, angle and positioning of the drilling assembly and drill bit. For example, by utilizing a ring of permanent magnets as a reference and a MR sensor/sensor array it may be possible to measure the drill bit/drilling assembly speed, torque, angle and position. These parameters can be optimized to increase the rate of penetration of the drillbit into the formations. Moreover, these measurements can be used generating drilling road maps for different formations Sensors 2017, 17, 2384 25 of 32 in different oil/gas fields therefore, optimizing drilling efficiency. MR sensors have been used in commercial applications operating at temperatures up to 225 ◦C, pressures up to 20,000 psi and mechanical shocks up to 1500 g [132]. Recent research has also shown that MR sensors can be used to calculate the length of directional wells, where the length can be used in fitting the drilling profile, computing the deviation, designing the drilling profile, and developing an algorithm for automated directional drilling [133], to measure NMR signals at room temperature [134] and operate at temperatures up to 175 ◦C for 5000 h with low energy consumption [128]. Apart from meeting the criteria for use in harsh environments low power consumption is a key advantage in these sensors since power is at a premium in downhole environments. This feature can be exploited to design and fabricate autonomous, wireless sensors, which are important in poorly accessible areas like the downhole environment, since the sensors and electronics are energy efficient and most of the power will then only be used for wireless transmission. Hall effect sensors create a Hall voltage across a p-type semiconductor when the continuous electrons running through it will move to one side of the sensor when it is exposed to an external magnetic field [1,2,135,136]. Hall effect sensors can also be prospective downhole magnetic field sensors but they are less sensitive than magnetoresistive sensors, are affected by the piezo effect leading to a lower offset stability than the magnetoresistive sensors and are less mechanically robust than MR sensors. Also, the performance of Hall sensors decrease rapidly at temperatures above 150 ◦C and currently there are no commercially available Hall sensors that can operate above 200 ◦C. However, Hall sensors have a higher linear range compared with magnetoresistive sensors, can be integrated onto a single chip with electronics and unlike MR sensors, which can measure a maximum of 180◦ around a circle due to its periodic behaviour, Hall sensors can measure a full 360◦ around a circle. Recent research works show the progress made in developing Hall effect sensors for extreme environments [137–140] but Hall effect sensors need further research to build up on these preliminary investigations with the aim of commercialization and to increase its stability under severe mechanical effects. Giant magnetoimpedance (GMI) sensors are another type of magnetic sensor that can be exploited for use in downhole environments. GMI refers to the change in the complex impedance of a ferromagnetic conductor with a high frequency current flowing through it when exposed to an external magnetic field. GMI structures are generally in the form of a microwire, thin film or thin ribbon [1,141,142]. Compared with MR and Hall sensors GMI is the least established magnetic sensor and there are only a few commercial GMI sensors currently available in the market and these sensors only operate at temperatures below 100 ◦C. One of the major drawbacks of GMI sensors is the high frequency they work at, especially the drive current that is generally in the GHz range making it difficult to integrate it with signal processing electronics into a single chip. Moreover, they have higher temperature offset drifts compared to MR and Hall sensors. However, GMI sensors are robust devices that have high sensitivity and can be made into flexible and passive wireless sensors [143–145] making them an attractive area of research for downhole environments. Even though the sensitivity of GMI sensors decrease with temperatures they still remain high enough at downhole temperatures [146,147] and if the temperature offset can be sufficiently compensated they can be potentially be used in downhole applications. Current commercial applications include electronic compasses in smart phones and in biomedical applications [148].

5. Conclusions The principles and applications of two types of magnetic sensors, fluxgate magnetometers (FGMs) and nuclear magnetic resonance (NMR) sensors, used in the oil/gas industry have been described in this paper. The method of utilizing FGMs in a drilling assembly to accurately obtain well trajectory information while drilling, to navigate a well to a desired zone has also been described. Additionally, the technique of using NMR sensors to obtain information regarding downhole geological properties while drilling, which enables the characterization and quantification of downhole fluids in reservoirs, Sensors 2017, 17, 2384 26 of 32 has been presented. Finally, a discussion on magnetic sensors that present research opportunities for utilization in downhole environments has been provided.

Acknowledgments: We would like to thank the Society of Petroleum Engineers (SPE), the Society of Petrophysicists and Well Log Analysts (SPWLA) and Oilfield Review for giving us permission to reproduce and publish some figures that originally appear in papers published by them. We would also like to thank Hyung T. Kwak and Mustafa Hakimuddin for their help with the NMR section of the paper, Mahmoud Abughaban for the discussion on ellipses of uncertainty and Erica T. Jolly for proof-reading the article. Author Contributions: C.P.G. conceived the outline of the review paper, performed a literature survey and wrote the paper. B.L. and T.E.M. contributed to the writing of the paper and revised the paper. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Lenz, J.; Edelstein, A.S. Magnetic Sensors and Their Applications. IEEE Sens. J. 2006, 6, 631–649. [CrossRef] 2. Ripka, P.; Janosek, M. Advances in Magnetic Field Sensors. IEEE Sens. J. 2010, 10, 1108–1116. [CrossRef] 3. Blachowicz, T.; Ehrmann, A. Simulation of magnetic coatings in textile fibers. J. Phys. Conf. Ser. 2016, 738, 012057. [CrossRef] 4. Huang, Q.; Song, Y.; Sun, X.; Jiang, L.; Pong, P.W.T. Magnetics in Smart Grid. IEEE Trans. Magn. 2014, 50, 0900107. [CrossRef] 5. Yassine, O.; Gooneratne, C.P.; Smara, D.A.; Li, F.; Mohammed, H.; Merzaban, J.; Kosel, J. Isolation of cells for selective treatment and analysis using a magnetic microfluidic chip. Biomicrofluidics 2014, 8, 034114. [CrossRef][PubMed] 6. Gooneratne, C.P.; Yassine, O.; Giouroudi, I.; Kosel, J. Selective Manipulation of Superparamagnetic Beads by a Magnetic Microchip. IEEE Trans. Magn. 2013, 49, 3418–3421. [CrossRef] 7. McFadyen, I.R.; Fullerton, E.E.; Carey, M.J. State-of-the-Art Magnetic Hard Disk Drives. MRS Bull. 2006, 31, 379–383. [CrossRef] 8. Ripka, P. Security applications of magnetic sensors. J. Phys. Conf. Ser. 2013, 450, 012001. [CrossRef] 9. Díaz-Michelena, M. Small Magnetic Sensors for Space Applications. Sensors 2009, 9, 2271–2288. [CrossRef] [PubMed] 10. Gooneratne, C.P.; Kurnicki, A.; Yamada, S.; Mukhopadhyay, S.C.; Kosel, J. Analysis of the Distribution of Magnetic Fluid inside Tumors by a Giant Magnetoresistance Probe. PLoS ONE 2013, 8, e81227. [CrossRef] [PubMed] 11. Teichmann, D.; Kuhn, A.; Leonhardt, S.; Walter, M. The MAIN Shirt: A Textile-Integrated Magnetic Induction Sensor Array. Sensors 2014, 14, 1039–1056. [CrossRef][PubMed] 12. Lai, Y.C.; Jan, S.S.; Hsiao, F.B. Development of a Low-Cost Attitude and Heading Reference System Using a Three-Axis Rotating Platform. Sensors 2010, 10, 2472–2491. [CrossRef][PubMed] 13. Lin, G.; Makarov, D.; Schmidt, O.G. Magnetic sensing platform technologies for biomedical applications. Lab Chip 2017, 17, 1884–1912. [CrossRef][PubMed] 14. Hermanis, A.; Cacurs, R.; Greitans, M. Shape sensing based on acceleration and magnetic sensor system. In Proceedings of the 2015 IEEE International Symposium on Inertial Sensors and Systems (ISISS), Hapuna Beach, HI, USA, 23–26 March 2015. [CrossRef] 15. Ribeiro, M. Robot-Aided Magnetic Sensors Readout Suit. In Proceedings of the 2015 9th International Conference on Sensing Technology (ICST), Auckland, New Zealand, 8–10 December 2015. [CrossRef] 16. Altun, K.; Barshan, B.; Tuncel, O. Comparative study on classifying human activities with miniature inertial and magnetic sensors. Pattern Recognit. 2010, 43, 3605–3620. [CrossRef] 17. Childress, J.R.; Fontana, R.E., Jr. Magnetic recording head sensor technology. C. R. Phys. 2005, 6, 997–1012. [CrossRef] 18. Ouyang, Y.; He, J.; Hu, J.; Zhao, G.; Wang, Z.; Wang, S.X. Contactless Current Sensors Based on Magnetic Tunnel Junction for Smart Grid Applications. IEEE Trans. Magn. 2015, 51, 4004904. [CrossRef] 19. Treutler, C.P.O. Magnetic sensor for automotive applications. Sens. Actuators A Phys. 2001, 91, 2–6. [CrossRef] 20. Hussain, M.E.; AL-Majed, A.A. Horizontal and Directional Drilling, in Fundamentals of Sustainable Drilling Engineering; John Wiley and Sons Inc.: Hoboken, NJ, USA, 2015. Sensors 2017, 17, 2384 27 of 32

21. Bourgoyne, A.T.; Millheim, K.K.; Chenevert, M.E.; Young, F.S., Jr. Applied Drilling Engineering; Society of Petroleum Engineers: Houston, TX, USA, 1991; pp. 351–443. 22. Kaluza, F.; Gruger, A.; Gruger, H. New and future applications of fluxgate sensors. Sens. Actuators A Phys. 2003, 106, 48–51. [CrossRef] 23. Djamal, M.; Sanjaya, E.; Yulkifli; Ramli. Development of fluxgate sensors and its applications. In Proceedings of the 2011 2nd International Conference on Instrumentation, Communications, Information Technology, and Biomedical Engineering, Bandung, Indonesia, 8–9 November 2011; pp. 421–426. [CrossRef] 24. Vcelak, J.; Petrucha, V.; Kaspar, P. Compact Digital Compass with PCB Fluxgate Sensors. IEEE Sens. 2006, 859–861. [CrossRef] 25. Primdahl, F. The fluxgate magnetometer. J. Phys. E Sci. Instrum. 1979, 12, 241–253. [CrossRef] 26. Ripka, P. Advances in fluxgate sensors. Sens. Actuators A Phys. 2003, 106, 8–14. [CrossRef] 27. Ripka, P. Review of fluxgate sensors. Sens. Actuators A Phys. 1992, 33, 129–141. [CrossRef] 28. Sebbes, P.; Ludwig, F.; Schilling, M. Fluxgate magnetometer for temperatures up to 180 ◦C. J. Electr. Eng. 2010, 61, 21–23. 29. Ruhmer, D.; Bogeholz, S.; Ludwig, F.; Schilling, M. Vector fluxgate magnetometer for high operation temperatures up to 250 ◦C. Sens. Actuators A Phys. 2015, 228, 118–124. [CrossRef] 30. Primdahl, F.; Brauer, P.; Merayo, J.M.G.; Nielsen, O.V. The fluxgate ring-core internal field. Meas. Sci. Technol. 2002, 13, 1248. [CrossRef] 31. Janosek, M. Parallel Fluxgate Magnetometers. In High Sensitivity Magnetometers in Smart Sensors Measurement and Instrumentation; Springer: Cham, Switzerland, 2017; Volume 19. [CrossRef] 32. Primdahl, F. The fluxgate mechanism, part I: The gating curves of parallel and orthogonal fluxgates. IEEE Trans. Magn. 1970, 6, 376–383. [CrossRef] 33. Fluxgate Magnetometers. Available online: http://www.imperial.ac.uk/space-and-atmospheric-physics/ research/areas/space-magnetometer-laboratory/space-instrumentation-research/magnetometers/ fluxgate-magnetometers/ (accessed on 12 August 2017). 34. Baschirotto, A.; Dallago, E.; Malcovati, P.; Marchesi, M.; Venchi, G. A Fluxgate Magnetic Sensor: From PCB to Micro-Integrated Technology. IEEE Trans. Instrum. Meas. 2007, 56, 25–31. [CrossRef] 35. Ciudad, D.; Díaz-Michelena, M.; Perez, L.; Aroca, C. Small Fluxgate Magnetometers: Development and Future Trends in Spain. Sensors 2010, 10, 1859–1870. [CrossRef][PubMed] 36. Lu, C.C.; Huang, J.; Chiu, P.K.; Chiu, S.L.; Jeng, J.T. High-Sensitivity Low-Noise Miniature Fluxgate Magnetometers Using a Flip Chip Conceptual Design. Sensors 2014, 14, 13815–13829. [CrossRef][PubMed] 37. Lu, C.C.; Huang, J. A 3-Axis Miniature Magnetic Sensor Based on a Planar Fluxgate Magnetometer with an Orthogonal Fluxguide. Sensors 2015, 15, 14727–14744. [CrossRef][PubMed] 38. Buchanan, A.; Finn, C.A.; Love, J.J.; Worthington, E.W.; Lawson, F.; Maus, S.; Okewunmi, S.; Poedjono, B. Geomagnetic Referencing—The Real-Time Compass for Directional Drillers. Oilfield Rev. 2013, 25, 32–47. 39. Thorgood, J.L.; Knott, D.R. Surveying Techniques with a Solid State Magnetic Multishot Device. SPE Drill. Eng. 1990, 5, 209–214. [CrossRef] 40. Ma, T.; Chen, P.; Zhao, J. Overview on vertical and directional drilling technologies for the exploration and exploitation of deep petroleum resources. Geomech. Geophys. Geo-Energy Geo-Resour. 2016, 2, 365–395. [CrossRef] 41. Mantle, K. The Art of Controlling Wellbore Trajectory. Oilfield Rev. 2013, 25, 54–55. 42. Felczak, E.; Torre, A.; Godwin, N.D.; Mantle, K.; Naganathan, S.; Hawkins, R.; Li, K.; Jones, S.; Slayden, F. The Best of Both Worlds—A Hybrid Rotary Steerable System. Oilfield Rev. 2011, 23, 36–44. 43. De Almeida, I.N., Jr.; Antunes, P.D.; Gonzalez, F.O.C.; Yamachita, R.A.; Nascimento, A.; Goncalves, J.L. A Review of Telemetry Data Transmission in Unconventional Petroleum Environments Focused on Information Density and Reliability. J. Softw. Eng. Appl. 2015, 8, 455–462. 44. Makohl, F.; Jurgens, R. Evolution and Differences of High-Performance Downhole Motors. In Proceedings of the SPE/IADC Drilling Conference, Dallas, TX, USA, 9–12 February 1986. [CrossRef] 45. Russel, M.K.; Russel, A.W. Surveying of Boreholes. U.S. Patent 4,163,324, 7 August 1979. 46. Downton, G.; Klausen, T.S.; Hendricks, A.; Pafities, D. New directions in rotary steerable drilling. Oilfield Rev. 2000, 26, 18–29. Sensors 2017, 17, 2384 28 of 32

47. Schaaf, S.; Pafitis, D.; Guichemerre, E. Application of a Point the Bit Rotary Steerable System in Directional Drilling Prototype Well-bore Profiles. In Proceedings of the SPE/AAPG Western Regional Meeting, Long Beach, CA, USA, 19–22 June 2000. [CrossRef] 48. Al Yami, H.; Kubaisi, A.; Nawaz, K.; Awan, A.H.; Verma, J.K.; Ganda, S. Powered Rotary Steerable Systems Offer a Step Change in Drilling Performance. In Proceedings of the SPE Asia Pacific Oil and Gas Conference and Exhibition, Perth, Australia, 20–22 October 2008. [CrossRef] 49. Khudiri, M.; Al-Sanle, F.; Miyajan, R.; Wuhalmed, A.; Hawi, M.; Abbas, M.; Kashif, M.; Meraj, H.; Ahmed, F. Utilization of Single Real Time Data Visualization and Transmission Solution in Oil and Gas Field Development. In Proceedings of the Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, UAE, 9–12 November 2015. [CrossRef] 50. Al-Suwaidi, S.; Lyngra, S.; Roberts, I.; Al-Hussain, J.; Pasaribu, I.; Laota, A.S.; Hutabarat, S. Successful Application of a Novel Mobility Geosteering Technique in a Stratified Low-Permeability Carbonate Reservoir. In Proceedings of the SPE Saudi Arabia Section Technical Symposium and Exhibition, Al-Khobar, Saudi Arabia, 19–22 May 2013. [CrossRef] 51. Al-Maskeen, A.M.A.; Sung, R.R.; Ali, S.S. Horizontal Well Correlation Using Real Time Data and Log Prediction in Geosteering Complex Reservoirs of Saudi Arabia. In Proceedings of the SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain, 10–13 March 2013. [CrossRef] 52. Jamieson, A. Introduction to Wellbore Surveying. Available online: http://www.uhi.ac.uk/en/research- enterprise/energy/wellbore-positioning-download (accessed on 12 August 2017). 53. Williamson, H.S. Accuracy Prediction for Directional Measurement While Drilling. SPE Drill. Complet. 2000, 15, 221–233. [CrossRef] 54. James, T.L. Fundamentals of NMR; Department of Pharmaceutical Chemistry, University of California: San Francisco, CA, USA, 1998; pp. 1–31. 55. Varian, R.H. Method and Means for Correlating Nuclear Properties of Atoms and Magnetic Fields. U.S. Patent 2,561,490, 21 October 1948. 56. Schwede, H.F. Nuclear Resonance Well Logging Method and Apparatus. U.S. Patent 3,528,000, 5 March 1954. 57. Brown, R.J.S.; Gamson, B.W. Nuclear Magnetism Logging; SPE-1305-G; Society of Petroleum Engineers: Houston, TX, USA, 1960; pp. 201–209. 58. Brown, R.J.S. The Earth’s-field NML development at Chevron. Concepts Magn. Reson. 2001, 13, 344–366. [CrossRef] 59. Kleinberg, R.L.; Jackson, J.A. An introduction to the history of NMR well logging. Concepts Magn. Reson. 2001, 13, 340–342. [CrossRef] 60. Cooper, R.K.; Jackson, J.A. Remote (Inside-Out) NMR. I. Remote Production of a Region of Homogeneous Magnetic Field. J. Magn. Reson. 1980, 41, 400–405. [CrossRef] 61. Burnett, L.J.; Jackson, J.A. Remote (Inside-Out) NMR. II. Sensitivity of NMR Detection for External Samples. J. Magn. Reson. 1980, 41, 406–410. 62. Jackson, J.A.; Burnett, L.J.; Harmon, F. Remote (Inside-Out) NMR. III. Detection of Nuclear Magnetic Resonance in a Remotely Produced Region of Homogeneous Magnetic Field. J. Magn. Reson. 1980, 41, 411–421. [CrossRef] 63. Lipsicas, M.; Banavar, J.R.; Willemsen, J. Surface relaxation and pore sizes in rocks-a nuclear magnetic resonance analysis. Appl. Phys. Lett. 1986, 48, 1554. [CrossRef] 64. Borgia, G.C.; Fantazzini, P.; Mesini, E. Water 1H spin-lattice relaxation as a fingerprint of porous media. Magn. Reson. Imaging 1990, 8, 435–447. [CrossRef] 65. Kleinberg, R.; Kenyon, W.; Mitra, P. Mechanism of NMR relaxation of fluids in rock. J. Magn. Reson. Ser. A 1994, 108, 206–214. [CrossRef] 66. Mitra, P.P.; Sen, P.N.; Schwartz, L.M.; Le Doussal, P. Diffusion propagator as a probe of the structure of porous media. Phys. Rev. Lett. 1992, 68, 3555–3558. [CrossRef][PubMed] 67. Mair, R.W.; Wong, G.; Hoffmann, D.; Hürlimann, M.D.; Patz, S.; Schwartz, L.M.; Walsworth, R.L. Probing porous media with gas diffusion NMR. Phys. Rev. Lett. 1999, 83, 3324. [CrossRef][PubMed] 68. Hurlimann, M.; Helmer, K.G.; Latour, L.; Sotak, C.H. Restricted diffusion in sedimentary rocks. Determination of surface-area-to-volume ratio and surface relaxivity. J. Magn. Reson Ser. A 1994, 111, 169–178. [CrossRef] Sensors 2017, 17, 2384 29 of 32

69. Mitra, P.P.; Sen, P.N.; Schwartz, L.M. Short-time behavior of the diffusion coefficient as a geometrical probe of porous media. Phys. Rev. B 1993, 47, 8565. [CrossRef] 70. Prammer, M.; Drack, E.D.; Bouton, J.C.; Gardner, J.S.; Coates, G.R.; Chandler, R.N.; Miller, M.N. Measurements of Clay-Bound Water and Total Porosity by Magnetic Resonance Logging; SPE-36522-MS; Society of Petrophysicists and Well-Log Analysts: Houston, TX, USA, 1996. [CrossRef] 71. Hürlimann, M.; Flaum, M.; Venkataramanan, L.; Flaum, C.; Freedman, R.; Hirasaki, G. Diffusion-relaxation distribution functions of sedimentary rocks in different saturation states. Magn. Reson. Imaging 2003, 21, 305–310. [CrossRef] 72. Borgia, G.C.; Brown, R.J.S.; Fantazzini, P. Uniform-penalty inversion of multiexponential decay data. J. Magn. Reson. 1998, 132, 65–77. [CrossRef][PubMed] 73. Venkataramanan, L.; Song, Y.Q.; Hurlimann, M.D. Solving Fredholm integrals of the first kind with tensor product structure in 2 and 2.5 dimensions. IEEE Trans. Signal Process. 2002, 50, 1017–1026. [CrossRef] 74. Hürlimann, M.D.; Venkataramanan, L. Quantitative measurement of two-dimensional distribution functions of diffusion and relaxation in grossly inhomogeneous fields. J. Magn. Reson. 2002, 157, 31–42. [CrossRef] [PubMed] 75. Song, Y.-Q.; Venkataramanan, L.; Hürlimann, M.D.; Flaum, M.; Frulla, P.; Straley, C. T(1)-T(2) correlation spectra obtained using a fast two-dimensional Laplace inversion. J. Magn. Reson. 2002, 154, 261–268. [CrossRef][PubMed] 76. Song, Y.-Q.; Venkataramanan, L.; Kausik, R.; Heaton, N. Diffusion NMR of Confined Systems: Fluid Transport in Porous Solids and Heterogeneous Materials; Valiullin, R., Ed.; RSC: London, UK, 2016; Chapter 4; pp. 111–155. 77. Blümich, B.; Blümler, P.; Eidmann, G.; Guthausen, A.; Haken, R.; Schmitz, U.; Saito, K.; Zimmer, G. The NMR-mouse: Construction, excitation, and applications. Magn. Reson. Imaging 1998, 16, 479–484. [CrossRef] 78. Balibanu, F.; Hailu, K.; Eymael, R.; Demco, D.; Blumich, B. Nuclear magnetic resonance in inhomogeneous magnetic fields. J. Magn. Reson. 2000, 145, 246–258. [CrossRef][PubMed] 79. Blümich, B.; Anferov, V.; Anferova, S.; Klein, M.; Fechete, R.; Adams, M.; Casanova, F. Simple NMR-mouse with a bar magnet. Concepts Magn. Reson. 2002, 15, 255–261. [CrossRef] 80. Blümich, B.; Anferov, V.; Anferova, S.; Klein, M.; Fechete, R. An NMR-MOUSE-for analysis of thin objects, Macromol. Mater. Eng. 2003, 288, 312–317. 81. Casanova, F. Two-dimensional imaging with a single-sided NMR probe. J. Magn. Reson. 2003, 163, 38–45. [CrossRef] 82. Blümich, B.; Casanova, F.; Perlo, J.; Anferova, S.; Anferov, V.; Kremer, K.; Goga, N.; Kupferschläger, K.; Adams, M. Advances of unilateral mobile NMR in nondestructive materials testing. Magn. Reson. Imaging 2005, 23, 197–201. [CrossRef][PubMed] 83. Todica, M.; Fechete, R.; Blümich, B. Selective NMR excitation in strongly inhomogeneous magnetic fields. J. Magn. Reson. 2003, 164, 220–227. [CrossRef] 84. Hürlimann, M.D.; Griffin, D.D. Spin dynamics of Carr-Purcell-Meiboom-Gilllike sequences in grossly inhomogeneous B(0) and B(1) fields and application to NMR well logging. J. Magn. Reson. 2000, 143, 120–135. [CrossRef][PubMed] 85. Hürlimann, M.D. Diffusion and relaxation effects in general stray field NMR experiments. J. Magn. Reson. 2001, 148, 367–378. [CrossRef][PubMed] 86. Hürlimann, M.; Venkataramanan, L.; Flaum, C. Diffusion-editing: New NMR measurement of saturation and pore geometry. In Proceedings of the 43rd Annual SPWLA Meeting, Oiso, Japan, 2–5 June 2002. 87. Leu, G.; Fordham, E.J.; Hürlimann, M.D.; Frulla, P. Fixed and pulsed gradient diffusion methods in low-field core analysis. Magn. Reson. Imaging 2005, 23, 305–309. [CrossRef][PubMed] 88. Song, Y.Q. Categories of coherence pathways for the CPMG sequence. J. Magn. Reson. 2002, 157, 82–91. [CrossRef][PubMed] 89. Prammer, M.G.; Drack, E.; Goodman, G.; Masak, P.; Menger, S.; Morys, M.; Zannoni, S.; Suddarth, B.; Dudley, J. The Magnetic-Resonance While Drilling Tool: Theory and Operation. SPE Reserv. Eval. Eng. 2001, 4, 270–275. [CrossRef] 90. Alvarado, R.J.; Damgaard, A.; Hansen, P.; Raven, M.; Heidler, R.; Hoshun, R.; Kovats, J.; Morriss, C.; Rose, D.; Wendt, W. Nuclear Magnetic Resonance Logging While Drilling. Oilfield Rev. 2003, 15, 40–51. Sensors 2017, 17, 2384 30 of 32

91. Allen, D.; Flaum, C.; Ramakrishnan, T.S.; Bedford, J.; Castelijns, K.; Fairhurst, D.; Gubelin, G.; Heaton, N.; Minh, C.C.; Norville, M.A.; et al. Trends in NMR Logging. Oilfeild Rev. 2000, 12, 2–19. 92. Prammer, M.G.; Goodman, G.D.; Menger, S.K.; Morys, M.; Zannoni, S.; Dudley, J.H. Field Test of an Experimental NMR LWD Device. In Proceedings of the SPWLA 41st Annual Logging Symposium, Dallas, TX, USA, 4–7 June 2000. 93. Heidler, R.; Morriss, C.; Hoshun, R. Design and Implementation of a New Magnetic Resonance Tool for the While Drilling Environment. In Proceedings of the SPWLA 44th Annual Logging Symposium, Galveston, TX, USA, 22–25 June 2003. 94. Borghi, M.; Porrera, F.; Lyne, A.; Kruspe, T.; Krueger, V. Magnetic Resonance Logging While Drilling Streamlines Reservoir Evaluation. In Proceedings of the SPWLA 46th Annual Logging Symposium, New Orleans, LA, USA, 26–29 June 2005. 95. Blanz, M.; Kruspe, T.; Thern, H.F.; Kurz, G.A. Nuclear Magnetic Resonance Logging While Drilling (NMR-LWD): From an Experiment to a Day-to-Day Service for the Oil Industry. Available online: www.diffusion-fundamentals.org (accessed on 12 August 2017). 96. Evseev, N.; Dinariev, O.; Hurlimann, M.; Safanov, S. Coupling Multiphase Hydrodynamic and NMR Pore-Scale Modeling for Advanced Characterization of Saturated Rocks. Petrophysics 2015, 56, 32–44. 97. Kurup, A.; Valori, A.; Bachman, H.N.; Korb, J.-P.; Hürlimann, M.; Zielinski, L. Frequency Dependent Magnetic Resonance Response of Heavy Crude Oils: Methods and Applications. In Proceedings of the SPE Saudi Arabia Section Technical Symposium and Exhibition, Al-Khobar, Saudi Arabia, 19–22 May 2013. [CrossRef] 98. Hürlimann, M.D.; Freed, D.E.; Zielinski, L.J.; Song, Y.Q.; Leu, G.; Straley, C.; Boyd, A.; Minh, C.C. Hydrocarbon Composition From NMR Diffusion And Relaxation Data. Petrophysics 2009, 50, 116–129. 99. Carneiro, G.; Souza, A.; Boyd, A.; Schwartz, L.; Song, Y.Q.; Azeredo, R.; Willian, T.; Santos, B.; Rios, E.; Machado, V. Evaluating Pore Space Connectivity by NMR Diffusive Coupling. In Proceedings of the SPWLA 55th Annual Logging Symposium, Abu Dhabi, UAE, 18–22 May 2014. 100. Veselinovic, D.; Green, D.; Dick, M. Determination of Natural Fracture Porosity Using NMR. In Proceedings of the Unconventional Resources Technology Conference, San Antonio, TX, USA, 1–3 August 2016. [CrossRef] 101. Veselinovic, D.; Green, D.; Dick, M. NMR at Different Temperatures to Evaluate Shales. In Proceedings of the Unconventional Resources Technology Conference, Austin, TX, USA, 24–26 July 2017. 102. Mandal., S.; Borneman, T.W.; Koroleva, V.D.M.; Hürlimann, M.D. Direct optimization of signal-to-noise ratio of CPMG-like sequences in inhomogeneous fields. J. Magn. Reson. 2014, 247, 54–66. [CrossRef][PubMed] 103. Kausik, R.; Hürlimann, M.D. Sensitivity and resolution of two-dimensional NMR diffusion-relaxation measurements. J. Magn. Reson. 2016, 270, 12–23. [CrossRef][PubMed] 104. Mutalib, K.H.; Han, M.; Khoo, C.Y.; Lee, S.S.; Lwin, M.M.; Wong, F.K. LWD NMR for Hydrocarbon Typing and Formation Evaluation in a Challenging Offshore Trajectory. In Proceedings of the SPE/IATMI Asia Pacific Oil & Gas Conference and Exhibition, Nusa Dua, Bali, Indonesia, 20–22 October 2015. [CrossRef] 105. Bachman, N.; Jain, V.; Gunawan, Y.; Bonningue, P.; Hazboun, N.; Kuptsov, K.; Teran, N.; Bastidas, M.; Morales, O.; Sanchez, F.M.; et al. A New Large Hole Nuclear Magnetic Resonance Logging While Drilling Tool for Early Stage Formation Evaluation. In Proceedings of the SPWLA 57th Annual Logging Symposium, Reykjavik, Iceland, 25–29 June 2016. 106. Abouzaid, A.; Thern, H.; Said, M.; ElSaqqa, M.; Elbastawesy, M.; Ghozlan, S. Nuclear Magnetic Resonance Logging While Drilling in Complex Lithology—Solution for a Glauconitic Sandstone Reservoir. In Proceedings of the SPE/AAPG Africa Energy and Technology Conference, Nairobi City, Kenya, 5–7 December 2016. 107. Kuptsov, K.; Griffiths, R.; Maggs, D. Magnetic Resonance-While-Drilling System Improves Understanding of Complex Reservoirs. J. Pet. Technol. 2015, 67, 26–29. [CrossRef] 108. Heaton, N.J.; Jain, V.; Boling, B.; Oliver, D.; Degrange, J.M.; Ferraris, P.; Hupp, D.; Prabawa, H.; Torres, M.T.; Vervest, E.; et al. New Generation Magnetic Resonance While Drilling. In Proceedings of the SPE Annual Technical Conference and Exhibition, San Antonio, TX, USA, 8–10 October 2012. [CrossRef] 109. Coman, R.; Tietjen, H.; Thern, H.; Blanz, M. New Large-Hole Magnetic Resonance Logging-While-Drilling Tool with Short Inter-Echo Time and Improved Vertical Resolution. In Proceedings of the SPWLA 55th Annual Logging Symposium, Abu Dhabi, UAE, 18–22 May 2014. Sensors 2017, 17, 2384 31 of 32

110. Akkurt, R.; Kersey, D.; Zainalabedin, K. Towards Everyday-NMR: An Operator’s Perspective. Petrophysics 2009, 50, 498–510. 111. Seifert, D.J.; Akkurt, R.; Al-Dossary, S.; Shokeir, R.; Ersoz, H. Nuclear Magnetic Resonance Logging: While Drilling, Wireline and Fluid Sampling. In Proceedings of the SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain, 11–14 March 2007. [CrossRef] 112. Freedman, R. Advances in NMR Logging. J. Pet. Technol. 2006, 58, 60–66. [CrossRef] 113. Akkurt, R.; Bachman, H.N.; Minh, C.C.; Flaum, C.; LaVigne, J.; Leveridge, R.; Carmona, R.; Crary, S.; Decoster, E.; Heaton, N.; et al. Nuclear Magnetic Resonance Comes Out of Its Shell. Oilfield Rev. 2009, 20, 4–23. 114. Kanfar, M. Real-Time Integrated Petrophysics: Geosteering in Challenging Geology and Fluid Systems. In Proceedings of the SPE Saudi Arabia section Young Professionals Technical Symposium, Dhahran, Saudi Arabia, 19–21 March 2012. [CrossRef] 115. Kharraa, H.S.; Al-Amri, M.A.; Mahmoud, M.A.; Okasha, T.M. Assessment of Uncertainty in Porosity Measurements Using NMR and Conventional Logging Tools in Carbonate Reservoir. In Proceedings of the SPE Saudi Arabia Section Technical Symposium and Exhibition, Al-Khobar, Saudi Arabia, 19–22 May 2013. [CrossRef] 116. Menger, S.; Sands, P. NMR in Motion. Petrophysics 2003, 44, 190–195. 117. Kruspe, T.; Thern, H.F.; Kurz, G.; Blanz, M.; Akkurt, R.; Ruwaili, S.; Seifert, D.; Marsala, A. Slimhole Application of Magnetic Resonance while Drilling. In Proceedings of the SPWLA 50th Annual Logging Symposium, The Woodlands, TX, USA, 21–24 June 2009. 118. Hursan, G.; Silva, A.; Zeglache, M.L. Evaluation and Development of Complex Clastic Reservoirs using NMR. In Proceedings of the SPE Annual Technical Conference and Exhibition, Dubai, UAE, 26–28 September 2016. [CrossRef] 119. Hursan, G.; Deering, J.S.; Kelly, F.N. NMR Logs Help Formation Testing and Evaluation. In Proceedings of the SPE Saudi Arabia Section Annual Technical Symposium and Exhibition, Al-Khobar, Saudi Arabia, 21–23 April 2015. [CrossRef] 120. Meridji, Y.; Hursan, G.; Mahmoud, E.; Balliet, R. Fluid Identification in Complex Clastic Reservoirs Using 2D NMR Maps: A Case Study From Saudi Arabia. In Proceedings of the SPE Saudi Arabia Section Technical Symposium and Exhibition, Al-Khobar, Saudi Arabia, 19–22 May 2013. [CrossRef] 121. Akkurt, R.; Marsala, A.F.; Seifert, D.; Al-Harbi, A.; Buenrostro, C.; Kruspe, T.; Thern, H.F.; Kurz, G.; Blanz, M.; Kroken, A. Collaborative Development of a Slim LWD NMR Tool: From Concept to Field Testing. In Proceedings of the SPE Saudi Arabia Section Technical Symposium, Al-Khobar, Saudi Arabia, 9–11 May 2009. [CrossRef] 122. Decoster, E.; Carmona, R. Application of Recent Nmr Developments To The Characterization Of Orinoco Belt Heavy Oil Reservoirs. In Proceedings of the 49th Annual Logging Symposium, Austin, TX, USA, 25–28 May 2008. 123. Ramos, H.G.; Ribeiro, A.L. Present and Future Impact of Magnetic Sensors in NDE. Procedia Eng. 2014, 86, 406–419. [CrossRef] 124. Koch, R.H.; Deak, J.G.; Grinstein, G. Fundamental limits to magnetic field sensitivity of fluxgate magnetic sensors. Appl. Phys. Lett. 1999, 75, 3862. [CrossRef] 125. Korepanov, V.; Marusenkov, A. Flux-Gate Magnetometers Design Peculiarities. Surv. Geophys. 2012, 33, 1059–1079. [CrossRef] 126. Deak, J.G.; Zhou, Z.; Shen, W. Tunneling magnetoresistance sensor with pT level 1/f magnetic noise. AIP Adv. 2017, 7, 056676. [CrossRef] 127. Reig, C.; Cardoso, S.; Mukhopadhyay, S.C. Giant Magnetoresistance Sensors—From basis to state-of-the-art applications. In Smart Sensors Measurement and Instrumentation; Springer: New York, NY, USA, 2013. [CrossRef] 128. Jogschies, L.; Klaas, D.; Kruppe, R.; Rittinger, J.; Taptimthong, P.; Wienecke, A.; Rissing, L.; Wurz, M.C. Recent Developments of Magnetoresistive Sensors for Industrial Applications. Sensors 2015, 15, 28665–28689. [CrossRef][PubMed] 129. Gooneratne, C.P.; Kodzius, R.; Li, F.; Foulds, I.G.; Kosel, J. On-Chip Magnetic Bead Manipulation and Detection Using a Magnetoresistive Sensor-Based Micro-Chip: Design Considerations and Experimental Characterization. Sensors 2016, 16, 1369. [CrossRef][PubMed] Sensors 2017, 17, 2384 32 of 32

130. Cubells-Beltrán, M.D.; Reig, C.; Madrenas, J.; De Marcellis, A.; Santos, J.; Cardoso, S.; Freitas, P.P. Integration of GMR Sensors with Different Technologies. Sensors 2016, 16, 939. [CrossRef][PubMed] 131. Gooneratne, C.P.; Liang, C.; Giouroudi, I.; Kosel, J. An integrated micro-chip for rapid detection of magnetic particles. J. Appl. Phys. 2012, 111, 07B327. [CrossRef] 132. Slatter, R. Magnetoresistive (MR) Sensors for Angle-, Path- and Current Measurement in Harsh Environments. In Proceedings of the 17th International Conference on Sensors and Measurement Technology, Nürnberg, Germany, 19–21 May 2015. [CrossRef] 133. Wang, Y.; Wen, G.; Chen, H. Horizontal Directional Drilling-Length Detection Technology While Drilling Based on Bi-Electro-Magnetic Sensing. Sensors 2017, 17, 967. [CrossRef][PubMed] 134. Verpillat, F.; Ledbetter, M.P.; Xu, S.; Michalak, D.J.; Hilty, C.; Bouchard, L.-S.; Antonijevic, S.; Budker, D. Remote detection of nuclear magnetic resonance with an anisotropic magnetoresistive sensor. Proc. Natl. Acad. Sci. USA 2008, 105, 2271–2273. [CrossRef][PubMed] 135. Ramsden, E. Hall Effect Sensors—Theory and Applications, 2nd ed.; Elsevier: Amsterdam, The Netherlands, 2006. 136. Paun, M.-A.; Sallese, J.-M.; Kayal, M. Hall Effect Sensors Design, Integration and Behavior Analysis. J. Sens. Actuator Netw. 2013, 2, 85–97. [CrossRef] 137. Koide, S.; Takahashi, H.; Abderrahmane, A.; Shibasaki, I.; Sandhu, A. High Temperature Hall sensors using AlGaN/GaN HEMT Structures. J. Phys. Conf. Ser. 2012, 352, 012009. [CrossRef] 138. Jankowski, J.; El-Ahmar, S.; Oszwaldowski, M. Hall Sensors for Extreme Temperatures. Sensors 2011, 11, 876–885. [CrossRef][PubMed] 139. Abderrahmane, A.; Koide, S.; Sato, S.I.; Ohshima, T.; Sandhu, A.; Okada, H. Robust Hall Effect Magnetic Field Sensors for Operation at High Temperatures and in Harsh Radiation Environments. IEEE Trans. Magn. 2012, 48, 4421–4423. [CrossRef] 140. Lu, H.; Sandvik, P.; Vertiatchikh, A.; Tucker, J.; Elasser, A. High temperature Hall effect sensors based on AlGaN/GaN heterojunctions. J. Appl. Phys. 2006, 99, 114510. [CrossRef] 141. Mahdi, A.E.; Panina, L.; Mapps, D. Some new horizons in magnetic sensing: High-Tc SQUIDs, GMR and GMI materials. Sens. Actuators A Phys. 2003, 105, 271–285. [CrossRef] 142. Nishibe, Y.; Ohta, N. Thin Film Magnetic Sensor Utilizing Magneto Impedance Effect. Sens. Actuators A Phys. 2000, 82, 155–160. [CrossRef] 143. Li, B.; Kavaldzhiev, M.N.; Kosel, J. Flexible magnetoimpedance sensor. J. Magn. Magn. Mater. 2015, 378, 499–505. [CrossRef] 144. Li, B.; Yassine, O.; Kosel, J. A surface acoustic wave passive and wireless sensor for magnetic fields, temperature, and humidity. IEEE Sens. J. 2015, 15, 453–462. [CrossRef] 145. Li, B.; Kosel, J. A thin film passive magnetic field sensor operated at 425 MHz. In Proceedings of the Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS & EUROSENSORS XXVII), Barcelona, Spain, 16–20 June 2013. [CrossRef] 146. Mohri, K.; Uchiyama, T.; Panina, L.V.; Yamamoto, M.; Bushida, K. Recent Advances of Amorphous Wire CMOS IC Magneto-Impedance Sensors: Innovative High-Performance Micromagnetic Sensor Chip. J. Sens. 2015, 2015, 718069. [CrossRef] 147. Kurniawan, M.; Roy, R.K.; Panda, A.K.; Greve, D.W.; Ohodnicki, P.R., Jr.; McHenry, M.E. Interplay of stress, temperature, and giant magnetoimpedance in amorphous soft magnets. Appl. Phys. Lett. 2014, 105, 222407. [CrossRef] 148. AICHI STEEL. Available online: https://www.aichi-steel.co.jp (accessed on 12 August 2017).

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).