Real-time compensation of a downhole signal

Abstract

A sensor circuit receives an analog signal from a sensor, which is filtered and then converted in an analog to digital ("A / D") converter into a digital signal. Combined with the sensor circuit is a calibration circuit having a calibration source and a reconstruction filter. The calibration source is configured to generate simulated sensor signals, which are filtered in the reconstruction filter and digitized in an A / D converter. Switches in the circuits are selectively opened and closed, which isolate designated portions of the circuits from one another and put the circuit into different configurations. Gain and bias in the calibration source, filters, and A / D converters are determined based on mathematical relationships governing the different configurations of the circuit and when subjected to different input voltages.

Description

Attorney Docket No.: 0005355.000246 (65DDR-510523-WO-2)PCT PATENT APPLICATION REAL-TIME COMPENSATION OF A DOWNHOLE SIGNALInventors: Thomas KUNKIELAmir SOUIIBACKGROUND OF THE INVENTION1. Field of Invention

[0001] The present disclosure relates to compensating a downhole signal received from a signal circuit in real-time.2. Description of Prior Art

[0002] Drilling systems having earth boring drill bits on an end of a drill string are typically used in the oil and gas industry for creating wells drilled into hydrocarbon bearing geologic formations. The drill bit is rotationally affixed to the drill string in some drilling systems. Drilling systems typically require a drilling rig on surface having either a top drive or rotary table to rotate the drill string and the drill bit to bore through the subterranean formation. In other varieties of drilling systems, the drill bit is part of a bottom hole assembly that mounts to a lower end of the drill string, and allows for the drill bit to rotate with respect to the drill string. The relative rotation is often generated by including a mud motor in the bottom hole assembly, which converts drilling mud flow into a rotational force for rotating the drill bit.

[0003] Bottom hole assemblies include often include steering systems for maintaining the drilling bit along a designated path within the formation. Steering is typically achieved by inducing a bend in the drill string or the drilling assembly that causes the drilling assembly to drill a curved section of the wellbore. The curvature of the wellbore causes high loads in the drilling assembly and the drill string when penetrating through the curved section. Sensors, such as accelerometers,-1- IM-#10828622.2magnetometers, and gyroscopes, are often included in the bottom hole assemblies for downhole orientation and navigation. Hardware for conditioning signals from these sensors is sensitive to temperature variations experienced within a wellbore, which can increase changes of gain and bias due to increased temperatures that often occur at greater depths in a well.-2- IM-#10828622.2SUMMARY OF THE INVENTION

[0004] Disclosed is an example method of wellbore operations that includes operating a drilling system having a drill string, a bottom hole assembly coupled with the drill string, a sensor in the bottom hole assembly, and a signal circuit that comprises a calibration circuit and a sensor circuit in communication with the sensor. The example method also includes selectively changing the signal circuit into different configurations, providing first and second input signals to the calibration circuit and to the sensor circuit, obtaining output signals from the sensor circuit and the calibration circuit while the signal circuit is in the different configurations, and obtaining a sensor signal that is based on the output signals and a numerical expression derived from mathematical relationships that each govern the different configurations and that is independent of a change of gain or bias. In one embodiment, forming isolated portions of the signal circuit involves operating switches in strategic locations in the signal circuit. The method further optionally includes generating simulated sensor signals by transmitting signals to the calibration circuit. In an example, one of the configurations isolates the sensor from the signal circuit. In an alternative, the calibration circuit includes an input in communication with a controller, a calibration source having a calibration source gain and a calibration source bias, a calibration filter having a calibration filter gain and a calibration filter bias, a calibration analog to digital (“A / D”) converter having a calibration A / D converter gain and a calibration A / D converter bias, and leads connecting the calibration source with the calibration filter and connecting the calibration filter with the calibration A / D converter. Further in this alternative the sensor circuit includes an input in communication with the sensor, a sensor filter having a sensor filter gain and a sensor filter bias, and a sensor A / D converter having a sensor A / D converter gain and a sensor A / D converter bias and leads connecting the sensor with the sensor filter and connecting the sensor filter with the sensor A / D converter. Options exist in which the calibration source driven by the controller, outputs from the sensor A / D converter and the calibration A / D converter are in communication with the controller, in one of the configurations the sensor A / D converter and the calibration A / D converter are isolated from other components of the signal circuit, or the calibration source and calibration filter are isolated from the calibration A / D converter and from the sensor circuit. Examples of the sensor include an accelerometer, magnetometer, and a gyroscope.

[0005] Also disclosed is another example of a method of wellbore operations that includes using a drill string having a drill bit to excavate the wellbore, monitoring information about excavating -3- IM-#10828622.2the wellbore with a signal circuit that includes, a sensor circuit in communication with a sensor included with the drill string, and a calibration circuit connected to the sensor circuit, transmitting a simulated signal having a designated potential to an input of the calibration circuit, receiving a sensed signal from the sensor at an input of the sensor circuit, creating different configurations of the signal circuit by isolating designated portions of the signal circuit from one another, monitoring output signals from the calibration circuit and the sensor circuit for each of the different configurations, and obtaining an output from the sensor that is free from gain or bias changes. In examples, components in the calibration circuit generate gain and bias changes. Optionally, the simulated signal is generated by a controller and the output signals are monitored by the controller. In an alternative, the different configurations are created by selectively activating switches located in the signal circuit, and in a further alternative, in a one of the different configurations, the sensor is isolated from the sensor circuit. In an embodiment, the sensor senses a direction of the drill bit and the method further includes comparing the sensed direction with a designated direction and changing operation of the drill bit when the sensed direction differs from the designated direction.

[0006] Also disclosed is an example of a system for use in wellbore operations, which includes a bottom hole assembly coupled with a drill string and configured for excavating a wellbore, a sensor in the bottom hole assembly, a signal circuit having a sensor circuit, a calibration circuit, and switches, the signal circuit in communication with an output from the sensor, the calibration circuit connected to the sensor circuit, and the switches that when selectively moved to an open position isolate portions of the signal circuit and put the signal circuit into different states. The example system also includes a controller in communication with the sensor circuit and calibration circuit, the controller configured to strategically open selected switches to put the signal circuit into the different states, transmit calibration signals to the calibration circuit, monitor outputs from the sensor circuit and calibration circuit, and identify a sensor signal that is independent from bias or gain changes, and that is based on the monitored outputs and an expression derived from mathematical equations that model operation of the different states of the signal circuit. The system optionally further includes a drill bit in the bottom hole assembly that is driven by a mud motor.-4- IM-#10828622.2BRIEF DESCRIPTION OF DRAWINGS

[0007] Some of the features and benefits of the present invention having been stated, others will become apparent as the description proceeds when taken in conjunction with the accompanying drawings, in which:

[0008] FIG. 1 is a side partial sectional view of an example drilling system excavating a well into a subterranean formation.

[0009] FIG. 2 is a schematical example of a signal circuit for transmitting information from a sensor in the drilling system, and which calibrates for bias and gain changes.

[0010] FIGS. 3-7 are schematic examples of the signal circuit of FIG. 2 identifying portions of the signal circuit being considered in sequential steps of analysis.

[0011] While subject matter is described in connection with embodiments disclosed herein, it will be understood that the scope of the present disclosure is not limited to any particular embodiment. On the contrary, it is intended to cover all alternatives, modifications, and equivalents thereof.-5- IM-#10828622.2DETAILED DESCRIPTION OF INVENTION

[0012] The method and system of the present disclosure will now be described more fully hereinafter with reference to the accompanying drawings in which embodiments are shown. The method and system of the present disclosure may be in many different forms and should not be construed as limited to the illustrated embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey its scope to those skilled in the art. Like numbers refer to like elements throughout. In an embodiment, usage of the term “about” includes + / - 5% of a cited magnitude. In an embodiment, the term “substantially” includes + / - 5% of a cited magnitude, comparison, or description. In an embodiment, usage of the term “generally” includes + / - 10% of a cited magnitude.

[0013] It is to be further understood that the scope of the present disclosure is not limited to the exact details of construction, operation, exact materials, or embodiments shown and described, as modifications and equivalents will be apparent to one skilled in the art. In the drawings and specification, there have been disclosed illustrative embodiments and, although specific terms are employed, they are used in a generic and descriptive sense only and not for the purpose of limitation.

[0014] Shown in a side partial elevational view in FIG. 1 is an example of a drilling system 10 forming a wellbore 12 through a formation 14. A drill string 16 is included with the drilling system 10, and is shown having a bottom hole assembly (“BHA”) 18 on a lowermost end of the drill string 16. Drill string 16 is made up of a number of joints (not shown) of pipe that are threaded together on surface. Included with BHA 18 is a drill bit 20 for crushing rock to excavate through the formation 14. In the example of FIG. 1 a controller 22 and sensor 24 are shown included with BHA 18. Examples of sensor 24 include an accelerometer, a gyroscope, or any other sensor for providing downhole information during formation of a wellbore. More specifically, examples of sensor 24 include devices for indicating a direction and or position of the BHA 18 within formation 14. A communication means 26 is schematically illustrated for providing communication between controller 22 and or sensor 24, and back to surface 28, shown outside a wellbore 12. Examples of communication means 26 include conductive material, such as wiring, radio waves, mud pulses, and other forms of currently known or later developed telemetry. A wellhead assembly 30 is shown mounted over an opening of wellbore 12 and for providing pressure control over wellbore 12 and-6- IM-#10828622.2a way to access wellbore 12. A blowout preventer is included in the wellhead assembly 30. Erected over wellhead assembly 30 is a derrick 32 for supporting systems and machinery used in the excavating process, such as platforms for personnel and devices for inserting the joints of pipe into the wellbore 12. Also on surface 28 is a mud tank 34 for storing drilling mud or other fluids used in the drilling process, a line 36 connects tank 34 to a kelly 38 attached to an uppermost end of the drill string 16 shown extending out from above the wellhead assembly 30. A mud pump 40 is shown for providing a motive force of the mud through line 36 and into the drill string 16. A controller, 42 is schematically shown outside wellbore 12 and a communication means 44 is schematically illustrated to represent communication between controller 42 and within wellbore 12. In alternatives, controllers 22, 42 are combined into a single unit, and in alternatives, communication means 26, 44 are also combined into a single unit. As explained in more detail below, controller(s) 22, 42 provide(s) instruction and or direction for operation of the drilling system 10.

[0015] An example of a signal circuit 46 is shown in FIG. 2, which schematically illustrates signal pathways and processing for signals generated by sensor 24 and includes a sensor circuit 48 and a calibration circuit 50. The signals generated by sensor 24 includes information sensed by sensor 24 while in wellbore 12, examples of the information sensed by sensor 24 in wellbore 12 include single axis Cartesian acceleration (e.g„ acceleration in a single direction), vector Earth acceleration, and environmental vibration. In an example of sensing vector Earth acceleration and environmental vibration, the sensor is an accelerometer that measures the acceleration force in unit (m / s)2and obtains measurements in one, two, or three planes. If no external acceleration is applied to the accelerometer, the device will measure only the standard acceleration of free fall, i.e. the force of gravity, if external acceleration is applied, then the sensor will measure the vibration. In the circuit 46 is a lead 52 extending from an output of sensor 24 to an input to a sensor signal filter 54, which alternatively referred to herein as a main filter. Within sensor signal filter 54 is an amplifier 55 for providing an amount of gain G2 and bias B2 to the signal transmitted from sensor 24.. A lead 56 extends between an output of the sensor signal filter 54 and an input to a sensor signal analog to digital converter 58 (“A / D converter”). An amplifier stage 59 is shown within the A / D converter 58, and having a gain represented as G3 and a bias represented as B3. An output of the A / D converter 58 is shown as U_MAIN. For the purposes of discussion herein, the filter 54, A / D converter 58, and leads 52, 56 are referred to as the sensor circuit 48. Included within the-7- IM-#10828622.2calibration circuit 50 is a calibration input signal D / A converter 60 having an amplifier 61 with a gain represented as G5 and a bias represented as B5. An output of the D / A converter 60, also referred to herein alternatively as a calibration source, is represented by the value of Ul. A lead 62 is shown connected between an output of D / A converter 60 and a calibration filter 64, which is alternatively referred to herein as a reconstruction or low pass filter. An amplifier 65 is shown included within filter 64 and having a gain represented as G1 and a bias represented as Bl. An output of the filter 64 is referred to as U2. A lead 66 connects to the output of filter 64 on its inlet end. and an outlet end of lead 66 connects to a calibration output signal A / D converter 68. An input to the A / D converter 68 is designated as U4. An amplifier 69 is included within the calibration output signal A / D converter and shown having a gain represented by G4, a bias represented by B4, and an output signal shown as U_CAL.

[0016] Controller unit 22, 42 of FIG. 2 is shown in communication with the A / D converters 58, 68 via a lead 70. A reference voltage 72 is shown, which as described in more detail below provides a reference voltage VREF. A lead 74 provides communication between A / D converter 68 and reference voltage 72, and A / D converter 58 is also in communication with reference voltage 72 via a lead 75 shown connecting A / D converter 58 with lead 74. A lead 76 provides communication between reference voltage 72 and calibration input signal D / A converter 60. As shown, controller unit 22, 42 is in communication with an input to the calibration input signal D / A converter 60 via a lead 78. In the example of FIG. 2, the calibration circuit 50 includes the calibration input signal D / A converter 60. the filter 64, and the calibration output signal A / D converter 68. Reference voltage 72 connects to lead 66 via lead 80 and lead 82, in which lead 82 branches from lead 80. A resistor R1 is in lead 80 between reference voltage VREF and where lead 82 branches away. A resistor R2 is also in lead 82, shown disposed between where lead 82 branches from lead 80. and an end of lead 80 that terminates to ground G.

[0017] Still referring to FIG. 2, sensor circuit 48 and calibration circuit 50 are shown in selective communication via lead 86, which branches from lead 66 downstream of filter 64 and connects to lead 52 upstream of filter 54. A series of switches S 1-S9 are shown in strategic locations in various leads 52, 56, 66, 86, 82, 84, 92. Switches S1-S9 are, as explained below in more detail, selectively reconfigured between open and closed positions so that different portions of circuit 46 are strategically in communication with one another. Switch S1 is shown in lead 52 and between sensor 24 and filter 54. Switch S2 is shown in lead 66 between an output of filter 64 and the branch -8- IM-#10828622.2connection between lead 66 and lead 86. Switch S3 is shown in lead 86 and switches S4 and S5 are shown in lead 82 where switch S4 is between the connection between lead 66 and lead 82, and switch S5 is between lead 66 and ground G. Additional leads 88, 90. 92 are shown within the sensor circuit 48, where lead 88, which includes resistor R3, branches from lead 52 upstream of switch SI. Lead 90 branches from lead 52 downstream of switch SI and includes resistor R4. An end of lead 88 opposite from lead 54 connects to lead 90. the point where lead 88 connects to lead 90 is between resistor R4 and where an end of lead 90 connects to ground G. Lead 92 extends between lead 52 and lead 88 downstream of resistor R3. Switch S8 is in lead 92. Switch S6 is in a portion of lead 84 and between lead 80 and lead 56, switch S7 is also in lead 84 and between lead 56 and ground G. Switch S9 is in lead 56 downstream of filter 54.

[0018] In an example of operation of the signal circuit 46 of FIG. 2, a digital code is transmitted from controller 22, 42 to the calibration signal D / A converter 60. Which is alternatively referred to as “DAC DATA” and represented by U_DA at an input to the calibration signal D / A converter 60. “DAC DATA can be described for a 3-bit D / A converter as follows:

[0019] DAC DATA = 101 represents a 3-bit digital code transmitted by the controller unit.

[0020] The resulting analogue voltage U_DA within the D / A converter can be described for the 3- bit code as follows:

[0021] U_DA= 1 * 22+ 0 * 21+ 1 * 0 * 21) = 11^,,.

[0022] The output voltage from the calibration signal D / A converter 60 is illustrated as Ui, and described by Equation 1:

[0023] MIW = (-^-(DAC^DATAyjG 5 4" 465 ^5 Equation IThe analogue output voltage Ui resulting from the digital code DAC DATA provided by the controller unit depends on the resolution “n” of the digital to (D / A-converter) and the reference voltage VREF and is modified by its gain error G5 and a bias B5.

[0024] As noted above, signals received by controller 22, 42 from sensor signal A / D converter 58 via lead 70 and representing measurements sensed by sensor 24 (i.e.. values of USens) are often distorted by one or more of gain G2, gain, G3, bias B2, and bias B3 from the sensor signal filter 54 and sensor signal A / D converter 58. In alternatives, the distortions include or are from changes-9- IM-#10828622.2in one or more of gain G2, gain G3, bias B2, and bias B3. Schematically illustrated in FIG. 3 is a first sequence of a non-limiting example of compensating for these gains and biases as well as any changes in the gains and biases. As shown, switches S2, S3, and S9 are in a closed position (set conductive), and the remaining switches (SI and S4-S8) are in an open position (set non-conductive). Placing switches S2, S3, and S9 in the closed position and placing switches SI and S4-S8 in the open position arranges the signal circuit 46 into what is referred to herein as a first configuration. Putting signal circuit 46 into the first configuration isolates sensor 48 from the remaining components of the signal circuit 46. In this example and while in the first configuration, two different signals are successively emitted from the calibration signal D / A converter 60, which is initiated by transmitting a digital code from controller 22, 42 to calibration signal D / A converter 60. Further in this example, the two sequential signals are digitized in the sensor signal A / D converter 58 and in the calibration signal A / D converter 68 at substantially the same time, which captures a total of 4 signals and results in two signals measured in each ADC-channel as shown in Table 1 below.Session 1 Mathematical Description[U_DA=0]U_CALUCAL I(PDA= °) = (B5GAG1+ B1GA+U_MAIN UMain I(UDA= 0) = (B5G1G2G3+ S1G2G3+ B2G3+ B3)"VREFSession 2 Mathematical Description[U_DA=l / 2VREF]U_CAL UCALJ (UDA= 1) = (^G5G1G4+ B5G4G1+ B. G, + B4)^U_MAIN UMaln_ 2 (UDA= 1) = (^f£G5G1G2G3+ B5G1G2G3+ B1G2G3+ B2G3+ B3)^Table 1

[0025] Where UMainj and UCAL-I represent digitized outputs respectively from the sensor signal and calibration A / D converters 58, 68 in response to a 0 voltage input to the calibration input signal-10- IM-#10828622.2D / A converter 60 when the signal circuit 46 is in the first configuration, and where UMain_2 and UCAL-2 represent digitized outputs respectively from the sensor signal and calibration A / D converters 58, 68 in response to a voltage input of VREF / 2 to the calibration input signal D / A converter 60 when the signal circuit 46 is in the first configuration. The subtraction of the signals in the individual ADC-channel lead to expressions provided in Table 2:SubtractionUcAL_DIFF_l ~ UCAL_2 (UDA~2^REF^~ ^CAL_1(,^DA~ 0) -2G5G1G4in theCAL-ADCSubtractionin theUMO™ DIFF 1 — uMain2 (UDA—2vREF^- uMainI(UDA— 0) -2G5G1G2G3MAIN- ADCTable 2

[0026] The differences of the received signals in the individual channels remove the additive terms and lead to expressions that are dependent on the individual signal gain contributions Gl, G2, G3, and G5, the quotient of the subtracted values within the sensor signal A / D converter 58 (MAIN-ADC) and calibration output signal A / D converter 60 (CAL-ADC) is calculated to lead to Equation 2.VREFr r r r (271-!)GMainDIFF ±

[0027] Q =2_VREF — pG3VRE Equation 2uCAL_DIFF_1 Fr r r2G-—G^C4VREF4

[0028] The value of Q is stored in memory (such as in controller 22, 42) and applied as described below in subsequent steps. Described in Equation 2 is a gain of the sensor signal (main signal) path independently from further bias and VREF contributions.

[0029] Solving for G2 yields Equation 3:

[0030] G2= Q — Equation 3G3-11- IM-#10828622.2

[0031] In an alternative, the gain G2is estimated, which is optionally performed in a subsequent Qstep, based on the value Q with knowledge of gain contribution — of the amplifier stage 59 in “3sensor signal A / D converter 58 (MAIN- ADC) and the amplifier 69 in calibration output signal A / D converter 60 (CAL-ADC), i.e., individual ADC channels.

[0032] In a second sequence of the example of compensation, and as schematically shown in FIG.4, switches S2, S3, are S9 are placed in an open position (set non-conductive) and switches S4 and S6 are placed in a closed position (set conductive), which isolates the A / D converter 58 and calibration output signal A / D converter 60 from the other components in the signal circuit 46. In the second sequence, the sensor signal A / D converter 58 and calibration output signal A / D converter 68 are fed by simultaneously. Switches that are not mentioned are stated asnonconductive. The second sequence, together with a third sequence, optionally provides derivation of mathematical descriptions in Table 3 below. These descriptions include gains G3 and G4 that are optionally used to solve the derived equation from the first sequence, which leads to representations of digital signal outputs from the calibration output signal and sensor signal A / D converters 58, 68.Session 1 [U_4 & U_5=VREF / 2] Mathematical DescriptionU_CAL VREF(2n- 1)UCAL 2 = (4^G4+ S4)L VREFU_MAIN VREF(2n- 1) UMain2 = (-y1G3+ F3)\ -Z VREFTable 3

[0033] Solving for G4 leads to Equation 4:uTjVREFCA L_2 o

[0034] G^= -V^EF- Equation 42

[0035] Solving for G3 leads to Equation 5:r,.VREFuMain_2fon_1\~tni3

[0036] G3= - y---^ - Equation 5-12- IM-#l 0828622.2

[0037] In Equations 1-5 above, the unknown parts are the bias contributions B3and B4of the ADC channels and VREP. which are optionally determined in a third sequence of the example method of compensation. In the third sequence, schematically shown in FIG. 5. switches S4 and S6 are placed in an open position (set non-conductive) and switches S5 and S7 are placed in a closed position (set-conductive). In the third sequence, the A / D converter 58 and calibration output signal D / A converter 60 are isolated from the other components in the signal circuit 46, and also isolated from VREF, SO that the individual ADC channels are fed by 0 V simultaneously. Digital signal outputs from the ADC channels for the third sequence are provided in Table 4 below.Session 1 [U_4 & U_5=0] Mathematical DescriptionU_CAL (2n- 1)UcAL 3 = - -VREFU_MA1N (2n- 1)~ B3VREFTable 4

[0038] Substituting the values from Table 4 into Equations 4 and 5 above to solve for B3 and B4 leads to Equations 6 and 7:

[0039] B3=UM^a EFEquation 6

[0040] S4=Uc^n3\REFEquation 7

[0041] Including B4 and B3 from third sequence in the expression for G3 and G4 from the second sequence leads to Equations 8 and 9:UCAL_2VREFUCAL_2VREFUCAL_3VREF

[0042] GA= ^EF=V~EF=(UCAL 2- UCAL 3) Equation 82 2uMain_2vREFuMam_2vREFuMain_3vREF

[0043] G3= ~3= = (UMain2- UMainJ-^- Equation 9

[0044] Setting G4 / G3 ratio leads to Equation 10:-13- IM-#10828622.2UCAL_2VREFUCAL_3VREF- VREF-UCAL_2VREFUCAL_3VREF100451 — = _ _ = _(2n-ri_t2n-]> _ =UCAL_2~UCAL_3Eauationin LVIWDJ UMain 2VREFUMain 3VREFU Main 2VREF U MainVREFUf,.,ntlLldL1Un(2"-l) _ (2"-l) (2^ (JnTTjM ain-2 M am-3VREF2

[0046] The gain G4 / G3 quotient from Equation 10 becomes independent from the digitalization process and optionally stored in memory, such as but not limited to one or both of controller 22, 42. Based on the determined Q value from Equation 2 in the first sequence and the determined gain G4 / G3 quotient from Equations 4 and 5 in the second and third sequences, leads to calculation of gain G2 of the sensor signal filter 54 (i.e., main stage filter) as provided in Equation 11:

[0047] G2= Q^- = (UMain^FF_i\ * / uCAL_2-uCAL_3 A Equation 11

[0048] A fourth sequence of the example method of compensation is schematically shown in FIG.6. In the fourth sequence, switches SI and S9 are placed into a closed position (set conductive) with switches S2-S8 placed in an open position (set to non-conductive), which isolates D / A converter 60 and filter 64 from the remaining components in the signal circuit 46 and activates the main path so that after being filtered by filter 54, output signal USENS is transmittable to A / D converter 58. A mathematical expression modeling the configuration of the signal circuit 46 in the fourth sequence and as shown in FIG. 6 leads to Equation 12 below. In Equation 12, the bias terms are excluded and where the equation from sequences 1-3 described above are included to solve for the sensor value.

[0049] t / Main_4(L / Sens) = [G3G2Usensor + #2^3 + ^3]Vre^ Equation 12

[0050] An example of a fifth sequence of the example method of compensation is illustrated schematically in FIG. 7. As shown, switch SI is placed in an open position and switch S8 is placed in a closed position. Based on an analysis of the fourth and fifth sequences, a mathematical description is derived for Usens as measured in the main ADC channel, which leads to Equation 13 below.

[0051] UMain_5(USens= 0) = [B2G3+ B3] Equation 13

[0052] Equation 14 below is obtained by taking the difference of: UMai - UMains-14- IM-#10828622.2(2n— ll

[0053] ^Mam^uSens) ~ UMain$(jjSens) ~ [^3^2 ^Sensor + ^2^3 + ^3] U?2^3 + f2n— it f2”-ll 53] = G3G2USensor^ Equation 14

[0054] Including the terms for G2 and G3 leads to Equation 15 below, which provides a solution for the sensor value USENS that is determinable based on the sensor signal and the VREF, and that provides corrected values of USENS over an anticipated range of temperatures expected in a wellbore. Equation 15 is free of and / or independent of values of gain or bias, and instead is determinable based on following terms.

[0055] USensor= aSe)~s(u^„s0,))(2n— 1)I ^LD,FF1

[0056] In examples, switches S 1-S9 are changed between open and closed positions by mechanical or electrical actuators and in response to commands, which optionally are generated and / or transmitted by controller 22, 42 or another processor. In an example, controller 22, 42 includes a computer having one or more of a master node processor and memory coupled to the processor to store within operating instructions (such as for conducting operation of the example compensation method described herein), sensed data, control information, database records, and values calculated by processor. Examples of the controller 22, 42 include a multicore processor with nodes such as those from Intel Corporation or Advanced Micro Devices (AMD), or an HPC Linux cluster computer. In alternatives, all or a part of controller 22, 42 is a computer of any conventional type of suitable processing capacity, such as a personal computer, laptop computer, or any other suitable processing apparatus. It should thus be understood that a number of commercially available data processing systems and types of computers may be used for this purpose. Controller 22, 42 optionally includes a processor for performing calculations of Equations 1-15 above.

[0057] The present invention described herein, therefore, is well adapted to carry out the objects and attain the ends and advantages mentioned, as well as others inherent therein. While one or more embodiments have been given for purposes of disclosure, numerous changes exist in the details of procedures for accomplishing the desired results. These are intended to be encompassed within the spirit of the present invention disclosed herein and the scope of the appended claims.-15- IM-#10828622.2

Claims

CLAIMSWhat is claimed is:

1. A method of wellbore operations comprising:operating a drilling system that comprises a drill string, a bottom hole assembly coupled with the drill string, a sensor in the bottom hole assembly, and a signal circuit that comprises a calibration circuit and a sensor circuit in communication with the sensor;selectively changing the signal circuit into different configurations;providing first and second input signals to the calibration circuit and to the sensor circuit; obtaining output signals from the sensor circuit and the calibration circuit while the signal circuit is in the different configurations; andobtaining a sensor signal that is based on the output signals and a numerical expression derived from mathematical relationships that each govern the different configurations and that is independent of a change of a gain or a bias.

2. The method of Claim 1, wherein forming isolated portions of the signal circuit comprises operating switches in strategic locations in the signal circuit.

3. The method of Claim 1, further comprising generating simulated sensor signals by transmitting signals to the calibration circuit.

4. The method of Claim 1, wherein one of the configurations isolates the sensor from the signal circuit.

5. The method of Claim 1, whereinthe calibration circuit comprises,an input in communication with a controller,a calibration source having a calibration source gain and a calibration source bias, a calibration filter having a calibration filter gain and a calibration filter bias,a calibration analog to digital (“A / D”) converter having a calibration A / D converter gain and a calibration A / D converter bias, and-16- IM-#10828622.2leads connecting the calibration source with the calibration filter and connecting the calibration filter with the calibration A / D converter,the sensor circuit comprises,an input in communication with the sensor,a sensor filter having a sensor filter gain and a sensor filter bias, and a sensor A / D converter having a sensor A / D converter gain and a sensor A / D converter bias andleads connecting the sensor with the sensor filter and connecting the sensor filter with the sensor A / D converter.

6. The method of Claim 5, wherein the calibration source is driven by the controller, wherein in each of the configurations, outputs from the sensor A / D converter and the calibration A / D converter are in communication with the controller, and wherein in one of the configurations the sensor A / D converter and the calibration A / D converter are isolated from other components of the signal circuit.

7. The method of Claim 5, wherein in one of the configurations the calibration source and calibration filter are isolated from the calibration A / D converter and from the sensor circuit.

8. The method of Claim 1, wherein the sensor comprises a device selected from the group consisting of an accelerometer and a gyroscope.

9. A method of wellbore operations comprising:using a drill string having a drill bit to excavate the wellbore;monitoring information about excavating the wellbore with a signal circuit that comprises, a sensor circuit in communication with a sensor included with the drill string, and a calibration circuit connected to the sensor circuit;transmitting a simulated signal having a designated potential to an input of the calibration circuit;receiving a sensed signal from the sensor at an input of the sensor circuit;-17- IM-#10828622.2creating different configurations of the signal circuit by isolating designated portions of the signal circuit from one another;monitoring output signals from the calibration circuit and the sensor circuit for each of the different configurations; andobtaining an output from the sensor that is free from a change of a gain or bias by obtaining a sensor signal that is based on,the output signals, anda numerical expression derived from mathematical relationships that govern each of the different configurations.

10. The method of Claim 9, wherein components in the calibration circuit and the sensor circuit generate gain and bias.

11. The method of Claim 9, wherein the simulated signal is generated by a controller and wherein the output signals are monitored by the controller.

12. The method of Claim 9, wherein the different configurations are created by selectively activating switches located in the signal circuit, and wherein in a one of the different configurations, the sensor is isolated from the sensor circuit.

13. The method of Claim 9, wherein the sensor senses a direction of the drill bit, the method further comprising comparing the sensed direction with a designated direction and changing operation of the drill bit when the sensed direction differs from the designated direction.

14. A system for use in wellbore operations comprising:a bottom hole assembly coupled with a drill string and configured for excavating a wellbore;a sensor in the bottom hole assembly;a signal circuit comprising,a sensor circuit in communication with an output from the sensor, a calibration circuit connected to the sensor circuit, and-18- IM-#10828622.2switches that when selectively moved to an open position isolate portions of the signal circuit and put the signal circuit into different states; anda controller in communication with the sensor circuit and calibration circuit, the controller configured to strategically open selected switches to put the signal circuit into the different states, transmit calibration signals to the calibration circuit, monitor outputs from the sensor circuit and calibration circuit, and identify a sensor signal that is independent from a change of a bias or gain, and that is based on the monitored outputs and an expression derived from mathematical equations that model operation of the different states of the signal circuit.

15. The system of Claim 14, further comprising a drill bit in the bottom hole assembly that is driven by a mud motor.-19- IM-#10828622.2

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