Abstract:
A method and system for measuring formation resisitivity is achieved by introducing one or more continuous phase modulated electrical signals into the formation, each signal introduced at a different location. The current of each introduced electrical signal is then sensed, producing an analog voltage signal as a measurement of the formation. Each introduced electrical signal is compared with its respective measured signal of the formation. Each comparison is made in a quadrature demodulation device, producing an in-phase demodulated signal. A quasi-direct-current signal is extracted from each in-phase demodulated signal, producing an analog measurement related to the resistivity of the formation. Each analog measurement is converted into a digital value for further processing. Successive measurements are digitally summed and averaged to increase the signal to noise ratio.

Description:
FIELD OF THE INVENTION 
     The present invention relates generally to hydrocarbon exploration and production, and more particularly relates to a logging method and system for determining earth formation resistivity. 
     BACKGROUND 
     Resistivity logging measures the electrical resistivity of formations surrounding an earth borehole. Resistivity logging is a commonly used technique of formation evaluation. For example, porous formations having high resistivity generally indicate the presence of hydrocarbons, while porous formations having low resistivity are generally water saturated. A logging device is lowered in the well bore on a wireline cable and measurements are taken with the device as the cable is withdrawn. One technique of resistivity logging uses electrodes. For example, button electrodes are used on a pad which is placed in close proximity to the borehole wall. A measured current flows in a circuit that connects a current source to one electrode, through the earth formation to a return electrode and back to the current source in the logging tool. 
       FIG. 1  illustrates one example of using electrical earth borehole logging for the determination of formation resistivity, R F . In this example, an earth formation  100  is penetrated by a wellbore  200 . Electrodes  10  and  12  are in wellbore  200 , in proximity of earth formation  100 . Electrode  10  is separated a distance from electrode  12 . A standoff zone  20  exists between electrodes  10  and  12  and earth formation  100 . Drilling fluids typically reside in wellbore  200 , including within standoff zone  20 . A current I, having a voltage V, is generated by a signal generator  1  and introduced into formation  100  through electrode  10 . Electrode  12  is a ground return. Current I penetrates through standoff zone  20  into formation  100 . Standoff zone  20  exhibits a standoff impedance Z C  between electrodes  10  and  12 , owing to the electrical characteristics of the drilling fluids. For example, Oil Based Mud (OBM) has a high resistance, causing a capacitive dielectric effect between electrodes  10  and  12 . A current sensor  2  detects the current at electrode  10 , producing voltage signal V I . A comparison is made of the voltage V from signal generator  1  and the detected current, as represented by voltage signal V I . A measure of the formation resistivity, R F  is determined from this comparison. 
       FIG. 2  illustrates an equivalent electrical schematic diagram of  FIG. 1 , of a formation undergoing stimulation and measurement. Signal generator  201  stimulates a formation exhibiting a formation resistivity R F . A standoff capacitive effect C S , due to Oil Based Mud and standoff zone  20  ( FIG. 1 ), is electrically in series between the formation resistivity R F  and signal generator  201 . Voltage V Z  is measured between signal generator  201  and standoff capacitive effect C S . Current I Z  is sensed between signal generator  201  and standoff capacitive effect C S  by use of current sensor  202 . 
     For Oil Based Mud (OBM), a high frequency driving source has to be used to excite the formation in order to measure the formation resistivity. The simplified impedance model of the Oil Based Mud (OBM) standoff and the formation is: 
                   Z   =         v   z       i   z       =         Z   R     +     jZ   C       ≈       R   F     +       jZ   C     ⁡     (       C   S     ,   ω     )                     (   1   )               
Where Z is the total impedance expressed as a complex number, v Z  is observed voltage V, i Z  is the observed current I, Z R  is the real component of the total impedance, j is the square root of minus one, Zc is the impedance from the standoff, R F  is formation resistance, C S  is the capacitance of the standoff, and ω is the frequency in radians.
 
     Given ω=2π·10 MHz as a nominal frequency value, the ratio of impedances for the Oil Based Mud (OBM) can range from 20 to 100 or higher, which is 
     
       
         
           
             
               
                 
                   20 
                   ≤ 
                   
                     
                       Z 
                       C 
                     
                     
                       R 
                       F 
                     
                   
                   ≤ 
                   100 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Direct measurements of the amplitude and phase of Z are obtained by comparing the voltage V from the signal generator and the detected current, as represented by voltage signal V I . These direct measurements are then used to calculate R F . For example, a fully integrated RF IC for measuring amplitude and the phase between two independent input signals can be used to compare voltage V and V I . In this example, the Z C  is dominant so that the observed phase is close to 90°. As a result, the resolutions for both amplitude and phase have to be very high to achieve accurate estimation of formation resistivity, R F  using this technique. A method for direct measurement is desired that does not have such a high resolution requirement in order to achieve accurate estimation of formation resistivity, R F . 
     In practice, it is desired to have in the borehole a plurality of electrodes, forming an array. Each electrode-ground pairing, a channel, provides an opportunity for taking a measurement. Due to a capacitive effect between adjacent electrodes in the array there is a risk of interference, or cross-talking, between adjacent channels. A method for direct measurement is desired that reduces cross-talk in order to take multiple measurements of formation resistivity, R F  using a plurality of electrodes. 
     SUMMARY OF THE INVENTION 
     In a first set of examples of the present invention, a method and system are disclosed for measuring formation resisitivity, the method includes the steps of: introducing a Maximum Length Sequence modulated electrical signal into a formation; sensing the current of the introduced electrical signal, whereby an analog formation measured signal is produced; comparing the introduced electrical signal with the formation measured signal in a quadrature demodulation device, whereby an in-phase demodulated signal is produced; and extracting a low frequency portion from the in-phase demodulated signal, whereby an analog measurement related to formation resistivity is produced. 
     In another example, the method includes the step of converting the analog measurement related to formation resistivity into a digital measurement. In a further example, the method includes the step of averaging successive digital measurements. 
     In a second set of examples of the present invention, a method and system are disclosed for measuring formation resisitivity, the method includes the steps of: introducing a Maximum Length Sequence modulated electrical signal into a first location of a formation; shifting the phase of the Maximum Length Sequence modulated electrical signal, whereby a phase-shifted Maximum Length Sequence modulated electrical signal is formed; introducing the phase-shifted Maximum Length Sequence modulated electrical signal into a second location of the formation; sensing the current of the introduced electrical signal, whereby a first analog formation measured signal is produced; sensing the current of the introduced phase-shifted electrical signal, whereby a second analog formation measured signal is produced; comparing the introduced electrical signal with the first formation measured signal in a first quadrature demodulation device, whereby a first in-phase demodulated signal is produced; comparing the introduced phase-shifted electrical signal with the second formation measured signal in a second quadrature demodulation device, whereby a second in-phase demodulated signal is produced; extracting a low frequency portion from the first in-phase demodulated signal, whereby a first analog measurement related to formation resistivity is produced; and extracting a low frequency portion from the second in-phase demodulated signal, whereby a second analog measurement related to formation resistivity is produced. 
     In another example, the method includes the step of converting at least one of the analog measurements related to formation resistivity into a digital measurement. In a further example, the method includes the step of averaging successive digital measurements. 
     In a third set of examples of the present invention, a system is disclosed for measuring formation resisitivity, the system including: a signal generator having an output for providing a current expressing a Maximum Length Sequence; a first electrode connected to the output of the signal generator; a current sensing device having an input connected to the first electrode and having an output; a ground electrode separated from the first electrode and connected to a ground of the signal generator and connected to a ground of the current sensing device; a quadrature demodulation device having a first input and a second input and an in-phase output, the first input connected to the output of the current sensor and the second input connected to the output of the signal generator; and a low pass filter having an input connected to the in-phase output of the quadrature demodulation device and having an output, whereby an analog measurement related to formation resistivity is produced. 
     In another example, the system includes an analog-to-digital converter having an analog input connected to the output of the low pass filter and having a digital output, whereby a digital measurement related to formation resistivity is produced. In a further example, the system further includes an integrator connected to the digital output of the analog-to-digital converter. 
     In another example, the system further includes: a phase shifter having an input connected to the output of the signal generator and having an output; a second electrode, separated from said first electrode, and connected to the output of the phase shifter; a second current sensing device having an input connected to the second electrode and having an output; a second quadrature demodulation device having a first input and a second input and an in-phase output, the first input of the second quadrature demodulation device connected to the output of the second current sensor and the second input of the second quadrature demodulation device connected to the output of the phase shifter; and a second low pass filter having an input connected to the in-phase output of the second quadrature demodulation device and having an output, whereby a second analog measurement related to formation resistivity is produced. 
     In another example, the system further includes an analog-to-digital converter having an analog input connected to the output of one of the low pass filters and having a digital output, whereby a digital measurement related to formation resistivity is produced. In a further example, the system further includes an integrator connected to the digital output of the analog-to-digital converter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention is best understood with reference to the attached drawings in which like numerals refer to like elements, and in which: 
         FIG. 1  illustrates a conceptual diagram of a method and system for determination of formation resistivity using direct measurements of amplitude and phase; 
         FIG. 2  illustrates an equivalent electrical schematic diagram of a formation undergoing stimulation and measurement; 
         FIG. 3  illustrates a conceptual diagram of a method and system for determination of formation resistivity using coherent analog in-phase demodulation; 
         FIG. 4A  illustrates a graph of a sinusoidal signal for generation by a signal generator and the corresponding graph of the spectral response of the sinusoidal signal; 
         FIG. 4B  illustrates a graph of a non-sinusoidal impulse signal for generation by a signal generator and the corresponding graph of the spectral response of the non-sinusoidal impulse signal; 
         FIG. 4C  illustrates a graph of a non-sinusoidal sinc signal for generation by a signal generator and the corresponding graph of the spectral response of the non-sinusoidal sinc signal; 
         FIG. 4D  illustrates a graph of a non-sinusoidal square wave signal for generation by a signal generator and the corresponding graph of the spectral response of the non-sinusoidal square wave signal; 
         FIG. 4E  illustrates a graph of a non-sinusoidal spread-spectrum signal for generation by a signal generator and the corresponding graph of the spectral response of the non-sinusoidal spread-spectrum signal; 
         FIG. 5  illustrates a graph of a Maximum Length Sequence spread-spectrum signal for generation by a signal generator and the corresponding graph of the autocorrelation coefficient of the Maximum Length Sequence spread-spectrum signal; 
         FIG. 6  illustrates an equivalent electrical schematic diagram of a method and system for determination of formation resistivity using a plurality of electrodes and a Maximum Length Sequence modulated signal; and 
         FIG. 7  illustrates a conceptual diagram of a method and system for determination of formation resistivity using coherent analog in-phase demodulation with integration in the digital domain. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 3  illustrates a conceptual diagram of a method and system for determination of formation resistivity using coherent analog in-phase demodulation. Instead of using direct impedance measurement, a coherent analog in-phase demodulation is used to detect the R F . In this example, a current I is generated by signal generator  1  and introduced into the formation through electrode  10 . Electrode  12  is a ground return. Current I penetrates through standoff zone  20  into formation  100 . Standoff zone  20  exhibits a standoff impedance Z C , owing to the electrical characteristics of the drilling fluids. Current sensor  2  detects the current at electrode  10 , producing voltage signal V I . Integrated Circuit  3  receives the detected current, as represented by voltage signal V I . Integrated circuit  3 , for example, is a dual-phase shifter and in-phase/quadrature (I/Q) demodulator that enables coherent summing and phase alignment of multiple analog data channels. An AD8333 (manufactured by Analog Devices, Inc.) is an example of such an integrated circuit. Integrated circuit  3  also receives voltage V from signal generator  1 , which is also referred to as a base signal or a coherent reference, enabling comparison of voltage signal V I  with voltage V from signal generator  1 . Voltage V from signal generator  1  therefore acts as a coherent reference to voltage signal V I . Both Voltage V and voltage signal V I  are analog signals. Integrated circuit  3  acts as a quadrature demodulation device and is used for in-phase demodulation which rejects the quadrature component. The quadrature component, or common mode signal, is mainly caused by the standoff capacitance, Cs. Integrated circuit  3  outputs the in-phase component of the comparison to low pass filter  6 . Low pass filter  6  receives the in-phase component from integrated circuit  3  and passes the low frequency portion of the in-phase component as a quasi-DC signal for output to analog-to-digital converter  4 . Analog-to-digital converter  4  receives the quasi-DC signal from low pass filter  6  and converts the quasi-DC in-phase signal into a digital value, producing a direct measure of formation resistivity, R F . In one example, the formation resistivity, R F  is digitized in 8 to 10 bits, which provides enough Signal-to-Noise Ratio (SNR) for image quality. 
       FIG. 4A  illustrates a graph of a sinusoidal signal for generation by a signal generator and the corresponding graph of the spectral response of the sinusoidal signal. Sinusoidal signal  401  is shown varying in amplitude along the y-axis with time T referenced along the x-axis. Spectral response  411  of sinusoidal signal  401  is shown on the corresponding spectral response graph, with the y-axis representing spectral power Sp and the x-axis representing frequency f. A frequency cutoff f CUT-OFF  is shown by a vertical dashed line. Spectral response  411  represents a concentration of spectral energy at a single frequency for sinusoidal signal  401  and appears as a spike on the spectral response graph. Noise floor N represents residual spectral power at various frequencies, relative to spectral response  411 . The sinusoidal signal exhibits a baseline signal-to-noise ratio, a baseline complexity to generate and receive, but exhibits relatively poor power efficiency. 
       FIG. 4B  illustrates a graph of a non-sinusoidal impulse signal for generation by a signal generator and the corresponding graph of the spectral response of the non-sinusoidal impulse signal. Non-sinusoidal impulse signal  402  is shown varying in amplitude along the y-axis with time T referenced along the x-axis. Spectral response  412  of non-sinusoidal impulse signal  402  is shown on the corresponding spectral response graph, with the y-axis representing spectral power Sp and the x-axis representing frequency f. A frequency cutoff f CUT-OFF  is shown by a vertical dashed line. Spectral response  412  represents a wide band of spectral energy across the frequencies for non-sinusoidal impulse signal  402  and appears as a flat horizontal line across the spectral response graph. Noise floor N represents residual spectral power at various frequencies, at a magnitude comparably relative to spectral response  412 . The impulse signal exhibits a relatively poor signal-to-noise ratio, a relatively low complexity to generate and receive, and relatively good power efficiency. 
       FIG. 4C  illustrates a graph of a non-sinusoidal sinc signal for generation by a signal generator and the corresponding graph of the spectral response of the non-sinusoidal sinc signal. Non-sinusoidal sinc signal  403  is shown varying in amplitude along the y-axis with time T referenced along the x-axis. Spectral response  413  of non-sinusoidal sinc signal  403  is shown on the corresponding spectral response graph, with the y-axis representing spectral power Sp and the x-axis representing frequency f. A frequency cutoff f CUT-OFF  is shown by a vertical dashed line. Spectral response  413  represents a band of spectral energy across a limited range of frequencies for non-sinusoidal sinc signal  403  and appears as a flat boxcar on the spectral response graph. Noise floor N represents residual spectral power at various frequencies, relative to spectral response  413 . The sinc signal exhibits a relatively good signal-to-noise ratio, a relatively high complexity to generate and receive, but has a relatively poor power efficiency. 
       FIG. 4D  illustrates a graph of a non-sinusoidal square wave signal for generation by a signal generator and the corresponding graph of the spectral response of the non-sinusoidal square wave signal. Non-sinusoidal square wave signal  404  is shown varying in amplitude along the y-axis with time T referenced along the x-axis. Spectral response  414  of non-sinusoidal square wave signal  404  is shown on the corresponding spectral response graph, with the y-axis representing spectral power Sp and the x-axis representing frequency f. A frequency cutoff f CUT-OFF  is shown by a vertical dashed line. Spectral response  414  represents a plurality of spikes at various frequencies for non-sinusoidal square wave signal  404  and appears as a flat boxcar on the spectral response graph. Noise floor N represents residual spectral power at various frequencies, relative to spectral response  414 . The square wave signal exhibits a relatively better signal-to-noise ratio, a relatively low complexity to generate and receive, and has a relatively good power efficiency. 
       FIG. 4E  illustrates a graph of a non-sinusoidal spread-spectrum signal for generation by a signal generator and the corresponding graph of the spectral response of the non-sinusoidal spread-spectrum signal. A spread-spectrum signal is also referenced as continuous phase modulation. Non-sinusoidal spread-spectrum signal  405  is shown varying in amplitude along the y-axis with time T referenced along the x-axis. Spectral response  415  of non-sinusoidal spread-spectrum signal  405  is shown on the corresponding spectral response graph, with the y-axis representing spectral power Sp and the x-axis representing frequency f. A frequency cutoff f CUT-OFF  is shown by a vertical dashed line. Spectral response  415  represents a wide band of spectral energy across the frequencies for non-sinusoidal spread-spectrum signal  405  and appears as a flat horizontal line across the spectral response graph. Noise floor N represents residual spectral power at various frequencies, at a magnitude comparably lower than spectral response  415 . The spread-spectrum signal exhibits a relatively high signal-to-noise ratio, a moderate complexity to generate and receive, and has a relatively good power efficiency. 
     From the comparison of various signal modulation techniques, spread spectrum (continuous phase) modulation provides relatively better data communication characteristics over several other forms of modulation. 
       FIG. 5  illustrates a graph of a Maximum Length Sequence spread-spectrum signal for generation by a signal generator and the corresponding graph of the autocorrelation coefficient of the Maximum Length Sequence spread-spectrum signal. A Maximum Length Sequence is a train of boxcar pulses where the information is carried in the duration of the each boxcar. In the example as illustrated in  FIG. 5 , train  501  is a Maximum Length Sequence of one hundred and twenty-eight (128) pulse time slots. The sequence begins at the zero time slot value and finishes at the one-hundred-twenty-seven (127) time slot value. The amplitude of train  501  is shown along the y-axis with time slot values referenced along the x-axis. An autocorrelation  502  of train  501  produces a very strong spike at zero shift and very little correlation at any other shift. Since the autocorrelation is extremely strong for Maximum Length Sequence signals, a slight phase shift in a Maximum Length Sequence signal will result in a dramatic drop in correlation. In one example, a phase shift in a Maximum Length Sequence signal is accomplished by rotating the pulse time slots, for instance, by starting the sequence at other than the zero time slot value, advancing through the time slot values to the one-hundred-twenty-seven (127) time slot value, continuing with the zero time slot value, and finishing with the time slot value just preceding the starting time slot value. 
     In measurement of formation resistivity using Maximum Length Sequence modulation, the impedance detection sensitivity requirements determine the smallest practical pulse interval. In one example, for Oil Based Mud (OBM) the base pulse frequency is selected between 2 MHz and 50 MHz (0.5 microseconds and 20 nanoseconds). An approximate 16 dB improvement in signal-to-noise ratio is theoretically achievable due to the lack of correlation between a Maximum Length Sequence signal and random noise. In another example, multiple broadcasts of the Maximum Length Sequence signal are received and averaged in the digital domain, further improving the signal-to-noise ratio. 
       FIG. 6  illustrates an equivalent electrical schematic diagram of a method and system for determination of formation resistivity using a plurality of electrodes and a Maximum Length Sequence modulated signal. Instead of using direct impedance measurement, a coherent analog in-phase demodulation is used to detect values for R F . In this example, a current is generated by signal generator  601  and introduced into the formation through an electrode at node  610 . The current generated by signal generator  601  is phase-shifted by shifter  641 . The output signal from shifter  641  is introduced into the formation through an electrode at node  611 . As illustrated in this example, additional phase shifting is performed by shifters  642  and  643  with the outputs introduced into the formation through electrodes  612  and  613 , respectfully. The Maximum Length Sequence modulated signal is thereby introduced into the formation at various locations, with a particular phase-shift of the signal introduced at each location. 
     The measurement of formation resistivity R f , m at node  611  further illustrates the various electrical contributions occurring during overall stimulation and measurement. The phase-shifted Maximum Length Sequence modulated signal from shifter  641 , and introduced at node  611 , represents a signal voltage and current I(m). Current sensor  621  detects the current at node  611 , producing a voltage that represents the detected current I(m). Demodulation device  631  receives from current sensor  621  the voltage that represents the detected current. Demodulation device  631  also receives the signal voltage from shifter  641 , enabling comparison of the signal voltage with the voltage that represents the detected current. An AD8343 (a high-performance broadband active mixer manufactured by Analog Devices, Inc.) is an example of such an integrated circuit. Various factors contribute to current I(m):
 
 I ( m )= I   f ( m )+ I   c ( m,m− 1)+ I   c ( m,m +1)− I   c ( m− 1, m )− I   c ( m+ 1, m )  (3)
 
where I(m) is the detected current for node  611 , I f (m) is the formation current for node  611 , I c (m,m−1) is the leakage (or “cross-talking”) current between nodes  610  and  611 , I c (m,m+1) is the leakage current between nodes  611  and  612 , I c (m−1,m) is the diffusion current between nodes  610  and  611 , and I c (m+1,m) is the diffusion current between nodes  611  and  612 . Both the diffusion currents and the cross-talking currents are caused by voltage differences corresponding to the different voltage driving signals when no equal-potential adjustment occurs. However, the in-phase demodulator rejects cross-talking current interferences owing to the dramatic lack of correlation between phase-shifted Maximum Length Sequence signals.
 
       FIG. 7  illustrates a conceptual diagram of a method and system for determination of formation resistivity using coherent analog in-phase demodulation with integration in the digital domain. In this example, the introduced voltage Vz and measured current Iz are collected from a signal generator that is connected to a node (not illustrated). Voltage Vz passes through a gain amplifier  701  to produce a voltage V V . Current Iz is sensed by a current-to-voltage circuit  702  to produce voltage signal V I . Demodulation device  703  receives the detected current, as represented by voltage signal V I . Demodulation device  703  also receives voltage V V , which is also referred to as a base signal or a coherent reference, enabling comparison of voltage signal V I  with voltage V V . Both Voltage V V  and voltage signal V I  are analog signals. Demodulation device  703  acts as a quadrature demodulation device and is used for in-phase demodulation which rejects the quadrature component. Demodulation device  703  outputs the in-phase component of the comparison to low pass filter  706 . Low pass filter  706  receives the in-phase component from demodulation device  703  and passes the low frequency portion of the in-phase component as a quasi-DC signal for output to analog-to-digital converter  704 . Analog-to-digital converter  704  receives the quasi-DC signal from low pass filter  706  and converts the quasi-DC in-phase signal into a digital value. Multiple broadcasts from the signal generator result in production of a succession of digital values by analog-to-digital converter  704 . A digital integrator  707  sums the succession of digital values to produce an averaged value for formation resistivity in the digital domain, further improving the signal-to-noise ratio. 
     It is to be understood that the selection of particular computer system hardware and software is not believed to be of particular relevance to the understanding and practice of the invention, so long as it meets the general criteria just stated. Those of ordinary skill in the art will undoubtedly be aware of numerous computer systems, hardware, associated application software, and/or combinations thereof suitable for the purposes of practicing the invention as disclosed herein. 
     In at least one example, the processing of the data is accomplished by a downhole processor. In at least one example, the processing of the data is accomplished by a surface processor. Implicit in the control and processing of the data is the use of a computer program implemented on a suitable machine-readable medium that enables the processor to perform the control and processing. The machine-readable medium may include ROMs, EPROMs, EAROMs, flash memories and/or optical disks. 
     The foregoing disclosure is presented for purposes of illustration and description, and is not intended to limit the invention to the forms disclosed herein. Consequently, variations and modifications commensurate with the above disclosures and the disclosure of the relevant art are within the spirit of the invention. Such variations will readily suggest themselves to those skilled in the relevant art. Further, the examples described are also intended to explain the best mode for carrying out the invention, and to enable others skilled in the art to utilize the invention and such or other embodiments and with various modifications required by the particular applications or uses of the invention. It is intended that the appended claims be construed to include alternative embodiments to the extent that is permitted by prior art.