Abstract:
Various embodiments of methods and systems for wireless power and/or data communications transmissions to a sensor subassembly above a mud motor in a bottom hole assembly are disclosed. Power and/or data are supplied by rotary modulator and power generation system positioned above the mud motor. Wires may connect to an annular coil. Power and/or communications are transmitted through the annular coil to an inductively coupled second, mandrel coil that is attached to the rotor. By leveraging resonantly tuned circuits and impedance matching techniques for the coils, power and/or data can be transmitted efficiently from one coil to the other despite relative movement and misalignment of the two coils.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of and priority to U.S. Provisional Patent Application Ser. No. 61/704,630, entitled “Casing Drilling Bore Hole Assembly With A Wireless Power and Data Connection,” and filed on Sep. 24, 2012, U.S. Provisional Patent Application Ser. No. 61/704,805, entitled “System And Method For Wireless Power And Data Transmission In A Mud Motor,” and filed on Sep. 24, 2012, and U.S. Provisional Patent Application Ser. No. 61/704,758, entitled “Positive Displacement Motor Rotary Steerable System And Apparatus,” and filed on Sep. 24, 2012, the disclosures of which are hereby incorporated by reference in their entireties. 
    
    
     DESCRIPTION OF THE RELATED ART 
     During conventional measuring while drilling (MWD) or logging while drilling (LWD) operations, signals are passed between a surface unit and the BHA to transmit, for example commands and information. Typical telemetry systems involve mud-pulse telemetry that uses the drill pipe as an acoustic conduit for mud pulse telemetry. With mud pulse telemetry, mud is passed from a surface mud pit and through the pipes to the bit. The mud exits the bit and is used to contain formation pressure, cool the bit, and lift drill cuttings from the borehole. This same mud flow is selectively altered to create pressure pulses at a frequency detectable at the surface and downhole. Typically, the operating frequency is in the order 1-3 bits/sec, but can fall within the range of 0.5 to 6 bits/sec. 
     In conventional drilling, a well is drilled to a selected depth with drill pipe, and then the wellbore is typically lined with a larger-diameter pipe, usually called casing. Casing typically includes casing sections connected end-to-end, similar to the way drill pipe is connected. To accomplish this, the drill string and the drill bit are removed from the borehole in a process called “tripping.” Once the drill string and bit are removed, the casing is lowered into the well and cemented in place. The casing protects the well from collapse and isolates the subterranean formations from each other. After the casing is in place, drilling may continue or the well may be completed depending on the situation. 
     Conventional drilling typically includes a series of drilling, tripping, casing and cementing, and then drilling again to deepen the borehole. This process is very time consuming and costly. Additionally, other problems are often encountered when tripping the drill string. For example, the drill string may get caught up in the borehole while it is being removed. These problems require additional time and expense to correct. 
     The term “casing drilling” refers to the use of a casing string in place of a drill string which uses drill pipe. Like the drill string, a chain of casing sections are connected end-to-end to form a casing string. The BHA and the drill bit are connected to the lower end of a casing string, and the well is drilled using the casing string to transmit drilling fluid, as well as axial and rotational forces, to the drill bit. Upon completion of drilling, the casing string may then be cemented in place to form the casing for the wellbore. Casing drilling enables the well to be simultaneously drilled and cased. 
     Existing casing drilling systems that employ directional MWD and/or LWD assemblies have several drawbacks. A downhole drilling motor is typically used due to rotational limitations of the casing and provides power for rotation of the BHA, including the bit to drill the pilot hole and the under-reamer to enlarge the hole for the casing to pass. The downhole drilling motor typically includes a positive displacement mud motor (PDM) or turbodrill. In a directional/logging BHA for casing drilling, high speed mud pulse telemetry is seriously degraded and attenuated due to the operation of the drilling motor. Accordingly, there remains a need in the art for improved bottom hole assemblies (BHAs) for casing drilling systems. 
     SUMMARY OF THE DISCLOSURE 
     A casing drilling bottom hole assembly (BHA) may include a modulator and turbine power generation system, a wireless power and data connection, and a rotary steerable system (RSS). The modulator and turbine power generation system is coupled to a casing. The wireless power and data connection is coupled to a downhole end of the high speed modulator and turbine power generation system for providing power and data connectivity between the high speed modulator and turbine power generation system and a drilling motor. The RSS is coupled to the drilling motor for receiving power from and communicating with the high speed modulator and turbine power generation system via the wireless power and data connection and the drilling motor. 
     This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the Figures, like reference numerals refer to like parts throughout the various views unless otherwise indicated. For reference numerals with letter character designations such as “ 102 A” or “ 102 B”, the letter character designations may differentiate two like parts or elements present in the same figure. Letter character designations for reference numerals may be omitted when it is intended that a reference numeral to encompass parts having the same reference numeral in figures. 
         FIG. 1A  is a diagram of a system for wireless drilling and mining extenders in a drilling operation; 
         FIG. 1B  is a diagram of a wellsite drilling system that forms part of the system illustrated in  FIG. 1A ; 
         FIG. 1C  is a diagram of an embodiment of a casing drilling system that includes a BHA for enabling wireless power and data transfer between components in the BHA; 
         FIG. 2  is a schematic drawing depicting a primary or transmitting circuit and a secondary or receiving circuit; 
         FIG. 3  is a schematic drawing depicting a primary or transmitting circuit and a secondary or receiving circuit with transformers having turn ratios N S :1 and N L :1 that may used to match impedances; 
         FIG. 4  is a schematic drawing depicting an alternative circuit to that which is depicted in  FIG. 3  and having parallel capacitors that are used to resonate the coils&#39; self-inductances; 
         FIGS. 5A-5B  illustrate an embodiment of a receiving coil inside a transmitting coil; 
         FIGS. 6-7  are graphs illustrating the variation in k versus axial displacement of the receiving coil when x=0 is small and the transverse displacement when z=0 produces very small changes in k of given embodiments, respectively; 
         FIGS. 8-9  are graphs illustrating that power efficiency may also be calculated for displacements from the center in the z direction and in the x direction, respectively, of given embodiments; 
         FIG. 10  is a graph illustrating that the sensitivity of the power efficiency to frequency drifts may be relatively small in some embodiments; 
         FIG. 11  is a graph illustrating that drifts in the components values of some embodiments do not have a large effect on the power efficiency of the embodiment; 
         FIG. 12  depicts a particular embodiment configured to convert input DC power to a high frequency AC signal, f 0 , via a DC/AC convertor; 
         FIG. 13  depicts a particular embodiment configured to pass AC power through the coils; 
         FIG. 14  depicts a particular embodiment that includes additional secondary coils configured to transmit and receive data; 
         FIG. 15  is a diagram illustrating an embodiment of a casing drilling BHA that includes a wireless power and data connection for enabling wireless power and data transfer between components in the BHA; 
         FIG. 16  is a diagram illustrating a more detailed view of the wireless power and data connection in  FIG. 15 ; 
         FIG. 17  is a diagram illustrating another embodiment of casing drilling BHA; 
         FIG. 18  is a diagram illustrating an embodiment of the modulator and turbine power system of  FIG. 15  that includes a rotary pressure pulse generator or modulator; 
         FIG. 19  is an equation for comparatively modeling signal strengths in a casing versus drilling operation; 
         FIG. 20  shows an embodiment of a graphical output of the signal strength model of  FIG. 19 ; and 
         FIG. 21  shows another embodiment of a graphical output of the signal strength model of  FIG. 19 . 
     
    
    
     DETAILED DESCRIPTION 
     The system described below mentions how power and/or communications may flow from an Measurement While Drilling (MWD) power system through a positive displacement motor to a rotary steerable system (“RSS”) and/or Logging While Drilling systems. One of ordinary skill in the art recognizes that communications may easily flow in the other direction—from the RSS and/or LWD equipment to the MWD system. 
     Referring initially to  FIG. 1A , this figure is a diagram of a system  102  for controlling and monitoring a drilling operation. The system  102  includes a control module  101  that is part of a controller  106 . The system  102  also includes a drilling system  104 , which has a logging and control module  95 , a bottom hole assembly (“BHA”)  100 , and wireless power and data connections  402 . The wireless power and data connections  402  may exist between several elements of the BHA  100  as will be explained below. 
     The controller  106  further includes a display  147  for conveying alerts  110 A and status information  115 A that are produced by an alerts module  110 B and a status module  115 B. The controller  106  in some instances may communicate directly with the drilling system  104  as indicated by dashed line  99  or the controller  106  may communicate indirectly with the drilling system  104  using the communications network  142   
     The controller  106  and the drilling system  104  may be coupled to the communications network  142  via communication links  103 . Many of the system elements illustrated in  FIG. 1A  are coupled via communications links  103  to the communications network  142 . 
       FIG. 1B  illustrates a wellsite drilling system  104  that forms part of the system  102  illustrated in  FIG. 1A . The wellsite can be onshore or offshore. In this system  104 , a borehole  11  is formed in subsurface formations by rotary drilling in a manner that is known to one of ordinary skill in the art. Embodiments of the system  104  can also use directional drilling, as will be described hereinafter. The drilling system  104  includes the logging and control module  95  as discussed above in connection with  FIG. 1A . 
     A drill string  12  is suspended within the borehole  11  and has a bottom hole assembly (“BHA”)  100  which includes a drill bit  105  at its lower end. The surface system includes platform and derrick assembly  10  positioned over the borehole  11 , the assembly  10  including a rotary table  16 , kelly  17 , hook  18  and rotary swivel  19 . The drill string  12  is rotated by the rotary table  16 , energized by means not shown, which engages the kelly  17  at the upper end of the drill string. The drill string  12  is suspended from a hook  18 , attached to a traveling block (also not shown), through the kelly  17  and a rotary swivel  19  which permits rotation of the drill string  12  relative to the hook  18 . As is known to one of ordinary skill in the art, a top drive system could alternatively be used instead of the kelly  17  and rotary table  16  to rotate the drill string  12  from the surface. The drill string  12  may be assembled from a plurality of segments  125  of pipe and/or collars threadedly joined end to end. 
     In the embodiment of  FIG. 1B , the surface system further includes drilling fluid or mud  26  stored in a pit  27  formed at the well site. A pump  29  delivers the drilling fluid  26  to the interior of the drill string  12  via a port in the swivel  19 , causing the drilling fluid to flow downwardly through the drill string  12  as indicated by the directional arrow  8 . The drilling fluid exits the drill string  12  via ports in the drill bit  105 , and then circulates upwardly through the annulus region between the outside of the drill string  12  and the wall of the borehole  11 , as indicated by the directional arrows  9 . In this system as understood by one of ordinary skill in the art, the drilling fluid  26  lubricates the drill bit  105  and carries formation cuttings up to the surface as it is returned to the pit  27  for cleaning and recirculation. 
     The BHA  100  of the illustrated embodiment may include a logging-while-drilling (“LWD”) module  120 , a measuring-while-drilling (“MWD”) module  130 , a roto-steerable system (“RSS”) and motor  150  (also illustrated as  280  in  FIG. 15  described below), and drill bit  105 . 
     The LWD module  120  is housed in a special type of drill collar, as is known to one of ordinary skill in the art, and can contain one or a plurality of known types of logging tools. It will also be understood that more than one LWD  120  and/or MWD module  130  can be employed, e.g. as represented at  120 A. (References, throughout, to a module at the position of  120 A can alternatively mean a module at the position of  120 B as well.) The LWD module  120  includes capabilities for measuring, processing, and storing information, as well as for communicating with the surface equipment. In the present embodiment, the LWD module  120  includes a directional resistivity measuring device. 
     The MWD module  130  is also housed in a special type of drill collar, as is known to one of ordinary skill in the art, and can contain one or more devices for measuring characteristics of the drill string  12  and drill bit  105 . The MWD module  130  may further include an apparatus (not shown) for generating electrical power to the BHA  100 . 
     This apparatus may include a mud turbine generator powered by the flow of the drilling fluid  26 , it being understood by one of ordinary skill in the art that other power and/or battery systems may be employed. In the embodiment, the MWD module  130  includes one or more of the following types of measuring devices: a weight-on-bit measuring device, a torque measuring device, a vibration measuring device, a shock measuring device, a stick slip measuring device, a direction measuring device, and an inclination measuring device. 
     The foregoing examples of wireline and drill string conveyance of a well logging instrument are not to be construed as a limitation on the types of conveyance that may be used for the well logging instrument. Any other conveyance known to one of ordinary skill in the art may be used, including without limitation, slickline (solid wire cable), coiled tubing, well tractor and production tubing. 
       FIG. 1C  illustrates an embodiment of the drilling system  104  that includes a casing drilling system  200 . The casing drilling system  200  may have several parts which are similar to those illustrated in the standard drillpipe drilling system  104  as illustrated in  FIG. 1B . Therefore, only the differences between the two systems  104 ,  200  will be described below. 
     The casing drilling system  200  may include casing  404  that couples with a BHA  100  via a drilling latch assembly (“DLA”)  406 . The DLA  406  may coupled with an under-reamer  412  that is also attached to a drill bit  105 . The under-reamer  412  may form the reamed hole  418  which has a diameter which is greater than the diameter of the pilot hole  416  for by the drill bit  105 . 
     The casing drilling system  200  may further include conductor pipe  491  which may surround and protect the casing  404  near the Earth&#39;s surface. The casing drilling system  200  may further include casing slips  444 , a casing drive head/assembly  441 , draw works  442 , and a guide rail and top drive/block dolly  443  as understood by one of ordinary skill the art. Further details of a modified BHA  100  having wireless power and data connections  402  for the casing drilling system  200  will be described below in connection with  FIGS. 15-18 . 
       FIG. 2  is a schematic drawing depicting a primary or transmitting circuit  210  and a secondary or receiving circuit  220 . In this description, the time dependence is assumed to be exp(jωt) where ω=2πf and f is the frequency in Hertz. Returning to the  FIG. 2  illustration, the transmitting coil is represented as an inductance L 1  and the receiving coil as L 2 . In the primary circuit  210 , a voltage generator with constant output voltage V S  and source resistance R S  drives a current I 1  through a tuning capacitor C 1  and primary coil having self-inductance L 1  and series resistance R 1 . The secondary circuit  220  has self-inductance L 2  and series resistance R 2 . The resistances, R 1  and R 2 , may be due to the coils&#39; wires, to losses in the coils magnetic cores (if present), and to conductive materials or mediums surrounding the coils. The Emf (electromotive force) generated in the receiving coil is V 2 , which drives current I 2  through the load resistance R L  and tuning capacitor C 2 . The mutual inductance between the two coils is M, and the coupling coefficient k is defined as:
 
 k=M /√{square root over ( L   1   L   2 )}  (1)
 
     While a conventional inductive coupler has k≈1, weakly coupled coils may have a value for k less than 1 such as, for example, less than or equal to about 0.9. To compensate for weak coupling, the primary and secondary coils in the various embodiments are resonated at the same frequency. The resonance frequency is calculated as: 
     
       
         
           
             
               
                 
                   
                     ω 
                     0 
                   
                   = 
                   
                     
                       1 
                       
                         
                           
                             L 
                             1 
                           
                           ⁢ 
                           
                             C 
                             1 
                           
                         
                       
                     
                     = 
                     
                       1 
                       
                         
                           
                             L 
                             2 
                           
                           ⁢ 
                           
                             C 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     At resonance, the reactance due to L 1  is cancelled by the reactance due to C 1 . Similarly, the reactance due to L 2  is cancelled by the reactance due to C 2 . Efficient power transfer may occur at the resonance frequency, f 0 =ω 0 /2π. In addition, both coils may be associated with high quality factors, defined as: 
     
       
         
           
             
               
                 
                   
                     Q 
                     1 
                   
                   = 
                   
                     
                       
                         
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             L 
                             1 
                           
                         
                         
                           R 
                           1 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       and 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         Q 
                         2 
                       
                     
                     = 
                     
                       
                         
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             L 
                             2 
                           
                         
                         
                           R 
                           2 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     The quality factors, Q, may be greater than or equal to about 10 and in some embodiments greater than or equal to about 100. As is understood by one of ordinary skill in the art, the quality factor of a coil is a dimensionless parameter that characterizes the coil&#39;s bandwidth relative to its center frequency and, as such, a higher Q value may thus indicate a lower rate of energy loss as compared to coils with lower Q values. 
     If the coils are loosely coupled such that k&lt;1, then efficient power transfer may be achieved provided the figure of merit, U, is larger than one such as, for example, greater than or equal to about 3:
 
 U=k √{square root over ( Q   1   Q   2 )}&gt;&gt;1.  (4)
 
     The primary and secondary circuits are coupled together via:
 
 V   1   =jωL   1   I   1   +jωMI   2  and  V   2   =jωL   2   I   2   +jωMI   1 ,  (5)
 
where V 1  is the voltage across the transmitting coil. Note that the current is defined as clockwise in the primary circuit and counterclockwise in the secondary circuit. The power delivered to the load resistance is:
 
                       P   L     =       1   2     ⁢     R   L     ⁢            I   2          2         ,           (   6   )               
while the maximum theoretical power output from the fixed voltage source V S  into a load is:
 
     
       
         
           
             
               
                 
                   
                     P 
                     MAX 
                   
                   = 
                   
                     
                       
                         
                            
                           
                             V 
                             S 
                           
                            
                         
                         2 
                       
                       
                         8 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           R 
                           S 
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     The power efficiency is defined as the power delivered to the load divided by the maximum possible power output from the source, 
     
       
         
           
             
               
                 
                   η 
                   ≡ 
                   
                     
                       
                         P 
                         L 
                       
                       
                         P 
                         MAX 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     In order to optimize the power efficiency, η, the source resistance may be matched to the impedance of the rest of the circuitry. Referring to  FIG. 2 , Z 1  is the impedance looking from the source toward the load and is given by: 
     
       
         
           
             
               
                 
                   
                     Z 
                     1 
                   
                   = 
                   
                     
                       R 
                       1 
                     
                     - 
                     
                       j 
                       / 
                       
                         ( 
                         
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             C 
                             1 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       jω 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         L 
                         1 
                       
                     
                     + 
                     
                       
                         
                           ω 
                           2 
                         
                         ⁢ 
                         
                           M 
                           2 
                         
                       
                       
                         
                           R 
                           2 
                         
                         + 
                         
                           R 
                           L 
                         
                         + 
                         
                           jω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             L 
                             2 
                           
                         
                         - 
                         
                           j 
                           / 
                           
                             ( 
                             
                               ω 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 C 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     When ω=ω 0 , Z 1  is purely resistive and may equal R S  for maximum efficiency. 
     
       
         
           
             
               
                 
                   
                     Z 
                     1 
                   
                   = 
                   
                     
                       
                         R 
                         1 
                       
                       + 
                       
                         
                           
                             ω 
                             2 
                           
                           ⁢ 
                           
                             M 
                             2 
                           
                         
                         
                           
                             R 
                             2 
                           
                           + 
                           
                             R 
                             L 
                           
                         
                       
                     
                     ≡ 
                     
                       
                         R 
                         S 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     Similarly, the impedance seen by the load looking back toward the source is 
     
       
         
           
             
               
                 
                   
                     Z 
                     2 
                   
                   = 
                   
                     
                       R 
                       2 
                     
                     - 
                     
                       j 
                       / 
                       
                         ( 
                         
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             C 
                             2 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       jω 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         L 
                         2 
                       
                     
                     + 
                     
                       
                         
                           ω 
                           2 
                         
                         ⁢ 
                         
                           M 
                           2 
                         
                       
                       
                         
                           R 
                           1 
                         
                         + 
                         
                           R 
                           S 
                         
                         + 
                         
                           jω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             L 
                             1 
                           
                         
                         - 
                         
                           j 
                           / 
                           
                             ( 
                             
                               ω 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 C 
                                 1 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     When ω=ω 0 , Z 2  is purely resistive and R L  should equal Z 2  for maximum efficiency 
     
       
         
           
             
               
                 
                   
                     Z 
                     2 
                   
                   = 
                   
                     
                       
                         R 
                         2 
                       
                       + 
                       
                         
                           
                             ω 
                             2 
                           
                           ⁢ 
                           
                             M 
                             2 
                           
                         
                         
                           
                             R 
                             1 
                           
                           + 
                           
                             R 
                             S 
                           
                         
                       
                     
                     ≡ 
                     
                       
                         R 
                         L 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     The power delivered to the load is then: 
                       P   L     =       1   2     ⁢         R   L     ⁢     ω   0   2     ⁢     M   2     ⁢            V   S          2           [         (       R   S     +     R   1       )     ⁢     (       R   2     +     R   L       )       +       ω   0   2     ⁢     M   2         ]     2           ,           (   13   )               
and the power efficiency is the power delivered to the load divided by the maximum possible power output,
 
     
       
         
           
             
               
                 
                   
                     η 
                     ≡ 
                     
                       
                         P 
                         L 
                       
                       
                         P 
                         MAX 
                       
                     
                   
                   = 
                   
                     
                       
                         4 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           R 
                           S 
                         
                         ⁢ 
                         
                           R 
                           L 
                         
                         ⁢ 
                         
                           ω 
                           0 
                           2 
                         
                         ⁢ 
                         
                           M 
                           2 
                         
                       
                       
                         
                           [ 
                           
                             
                               
                                 ( 
                                 
                                   
                                     R 
                                     S 
                                   
                                   + 
                                   
                                     R 
                                     1 
                                   
                                 
                                 ) 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     R 
                                     2 
                                   
                                   + 
                                   
                                     R 
                                     L 
                                   
                                 
                                 ) 
                               
                             
                             + 
                             
                               
                                 ω 
                                 0 
                                 2 
                               
                               ⁢ 
                               
                                 M 
                                 2 
                               
                             
                           
                           ] 
                         
                         2 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     The optimum values for R L  and R L  may be obtained by simultaneously solving 
                       R   S     =         R   1     +           ω   2     ⁢     M   2           R   2     +     R   L         ⁢           ⁢   and   ⁢           ⁢     R   L         =       R   2     +         ω   2     ⁢     M   2           R   1     +     R   S               ,           (   15   )               
with the result that:
 
 R   S   =R   1 √{square root over (1+ k   2   Q   1   Q   2 )} and  R   L   =R   2 √{square root over (1+ k   2   Q   1   Q   2 )}.  (16)
 
     If the source and load resistances do not satisfy equations (16), then it is envisioned that standard methods may be used to transform the impedances. For example, as shown in the  FIG. 3  illustration, transformers with turn ratios N S :1 and N L :1 may be used to match impedances as per equations (16). Alternatively, the circuit illustrated in  FIG. 4  may be used. In such an embodiment in  FIG. 4 , parallel capacitors are used to resonate the coils&#39; self-inductances according to equation (2). As before, Z 1  is defined as the impedance seen by the source looking toward the load, while Z 2  is defined as the impedance seen by the load looking toward the source. In addition, there are two matching impedances, Z S  and Z T  which may be used to cancel any reactance that would otherwise be seen by the source or load. Hence Z 1  and Z 2  are purely resistive with the proper choices of Z S  and Z T . Notably, the source resistance R S  may equal Z 1 , and the load resistance R L  may equal Z 2 . The procedures for optimizing efficiency with series capacitance or with parallel capacitance may be the same, and both approaches may provide high efficiencies. 
     Turning now to  FIGS. 5A and 5B , a cross sectional view of two coils  232 ,  234  is illustrated in  FIG. 5A  and a side view of the two coils  232 ,  234  is illustrated in  FIG. 5B . In these two figures, a receiving coil  232  inside a transmitting coil  234  of a particular embodiment  230  is depicted. The receiving coil  232  includes a ferrite rod core  235  that, in some embodiments, may be about 12.5 mm (about 0.49 inch) in diameter and about 96 mm (about 3.78 inches) long with about thirty-two turns of wire  237 . Notably, although specific dimensions and/or quantities of various components may be offered in this description, it will be understood by one of ordinary skill in the art that the embodiments are not limited to the specific dimensions and/or quantities described herein. 
     Returning to  FIG. 5 , the transmitting coil  234  may include an insulating housing  236 , about twenty-five turns of wire  239 , and an outer shell of ferrite  238 . The wall thickness of the ferrite shell  238  in the  FIG. 5  embodiment may be about 1.3 mm (about 0.05 inch). In certain embodiments, the overall size of the transmitting coil  234  may be about 90 mm (about 3.54 inch) in diameter by about 150 mm (about 5.90 inches) long. The receiving coil  232  may reside inside the transmitting coil  234 , which is annular. 
     The receiving coil  232  may be free to move in the axial (z) direction or in the transverse direction (x) with respect to the transmitting coil  234 . In addition, the receiving coil  232  may be able to rotate on axis with respect to the transmitting coil  234 . The region between the two coils  232 ,  234  may be filled with air, fresh water, salt water, oil, natural gas, drilling fluid (known as “mud”), or any other liquid or gas. The transmitting coil  234  may also be mounted inside a metal tube, with minimal affect on the power efficiency because the magnetic flux may be captured by, and returned through, the ferrite shell  238  of the transmitting coil  234 . 
     The operating frequency for these coils  232 ,  234  may vary according to the particular embodiment, but, for the  FIG. 5  example  230 , a resonant frequency f=100 kHz may be assumed. At this frequency, the transmitting coil  234  properties are: L 1 =6.76·10 −5  Henries and R 1 =0.053 ohms, and the receiving coil  232  properties are L 2 =7.55·10 −5  Henries and R 2 =0.040 ohms. The tuning capacitors are C 1 =3.75·10 −8  Farads and C 2 =3.36·10 −8  Farads. Notably, the coupling coefficient k value depends on the position of the receiving coil  232  inside the transmitting coil  234 . The receiving coil  232  is centered when x=0 and z=0 and there is k=0.64. 
     The variation in k versus axial displacement of the receiving coil  232  when x=0 may be relatively small, as illustrated by the graph  250  in  FIG. 6 . The transverse displacement when z=0 may produce very small changes in k, as illustrated by the graph  252  in  FIG. 7 . The receiving coil  232  may rotate about the z-axis without affecting k because the coils are azimuthally symmetric. According to equations (16), an optimum value for the source resistance may be R S =32 ohms, and for the load resistance may be R L =24 ohms when the receiving coil  232  is centered at x=0 and z=0. The power efficiency may thus be η=99.5%. 
     The power efficiency may also be calculated for displacements from the center in the z direction in mm (as illustrated by the graph  254  in  FIG. 8 ) and in the x direction in mm (as illustrated by the graph  256  in  FIG. 9 ). It is envisioned that the efficiency may be greater than about 99% for axial displacements up to about 20.0 mm (about 0.79 inch) in certain embodiments, and greater than about 95% for axial displacements up to about 35.0 mm (about 1.38 inches). It is further envisioned that the efficiency may be greater than 98% for transverse displacements up to 20.0 mm (about 0.79 inch) in some embodiments. Hence, the position of the receiving coil  232  inside the transmitting coil  234  may vary in some embodiments without reducing the ability of the two coils  232 ,  234  to efficiently transfer power. 
     Referring now to  FIG. 10 , it can be seen in the illustrative graph  258  where the Y-axis denotes efficiency in percentage and the X-axis denotes frequency in Hz that the sensitivity of the power efficiency to frequency drifts may be relatively small. A ±10% variation in frequency may produce minor effects, while the coil parameters may be held fixed. The power efficiency at 90,000 Hz is better than about 95%, and the power efficiency at 110,000 Hz is still greater than about 99%. Similarly, drifts in the component values may not have a large effect on the power efficiency. For example, both tuning capacitors C 1  and C 2  are allowed to increase by about 10% and by about 20% as illustrated in the graph  260  of  FIG. 11 . Notably, the other parameters are held fixed, except for the coupling coefficient k. The impact of the power efficiency is negligible. As such, the system described herein would be understood by one of ordinary skill in the art to be robust. 
     It is also envisioned that power may be transmitted from the inner coil to the outer coil of particular embodiments, interchanging the roles of transmitter and receiver. It is envisioned that the same power efficiency would be realized in both cases. 
     Referring to  FIG. 12 , an electronic configuration  262  is illustrated for converting input DC power to a high frequency AC signal, f 0 , via a DC/AC convertor. The transmitter circuit in the configuration  262  excites the transmitting coil at resonant frequency f 0 . The receiving circuit drives an AC/DC convertor, which provides DC power output for subsequent electronics. This system  262  is appropriate for efficient passing DC power across the coils. 
     Turning to  FIG. 13 , AC power can be passed through the coils. Input AC power at frequency f 1  is converted to resonant frequency f 0  by a frequency convertor. Normally this would be a step up convertor with f 0 &gt;&gt;f 1 . The receiver circuit outputs power at frequency f 0 , which is converted back to AC power at frequency f 1 . Alternatively, as one of ordinary skill in the art recognizes, the  FIG. 13  embodiment  264  could be modified to accept DC power in and produce AC power out, and vice versa. 
     In lieu of, or in addition to, passing power, data signals may be transferred from one coil to the other in certain embodiments by a variety of means. In the above example, power is transferred using an about 100.0 kHz oscillating magnetic field. It is envisioned that this oscillating signal may also be used as a carrier frequency with amplitude modulation, phase modulation, or frequency modulation used to transfer data from the transmitting coil to the receiving coil. Such would provide a one-way data transfer. 
     An alternative embodiment includes additional secondary coils to transmit and receive data in parallel with any power transmissions occurring between the other coils described above, as illustrated in  FIG. 14 . Such an arrangement may provide two-way data communication in some embodiments. The secondary data coils  266 ,  268  may be associated with relatively low power efficiencies of less than about 10%. It is envisioned that in some embodiments the data transfer may be accomplished with a good signal to noise ratio, for example, about 6.0 dB or better. The secondary data coils  266 ,  268  may have fewer turns than the power transmitting  234  and receiving coils  232 . 
     The secondary data coils  266 ,  268  may be orthogonal to the power coils  232 ,  234 , as illustrated in  FIG. 14 . For example, the magnetic flux from the power transmitting coils  232 ,  234  may be orthogonal to a first data coil  266 , so that it does not induce a signal in the first data coil  266 . A second data coil  268  may be wrapped as shown in  FIG. 14  such that magnetic flux from the power transmitters does not pass through it, but magnetic flux from first data coil  266  does. Notably, the configuration depicted in  FIG. 14  is offered for illustrative purposes only and is not meant to suggest that it is the only configuration that may reduce or eliminate the possibility that a signal will be induced in one or more of the data coils by the magnetic flux of the power transmitting coils. Other data coil configurations that may minimize the magnetic flux from the power transmitter exciting the data coils will occur to those with ordinary skill in the art. 
     Moreover, it is envisioned that the data coils  266 ,  268  may be wound on a non-magnetic dielectric material in some embodiments. Using a magnetic core for the data coils  266 ,  268  might result in the data coils&#39; cores being saturated by the strong magnetic fields used for power transmission. Also, the data coils  266 ,  268  may be configured to operate at a substantially different frequency than the power transmission frequency. For example, if the power is transmitted at about 100.0 kHz in a certain embodiment, then the data may be transmitted at a frequency of about 1.0 MHz or higher. In such an embodiment, high pass filters on the data coils  266 ,  268  may prevent the about 100.0 kHz signal from corrupting the data signal. In still other embodiments, the data coils  266 ,  268  may simply be located away from the power coils  232 ,  234  to minimize any interference from the power transmission. It is further envisioned that some embodiments may use any combination of these methods to mitigate or eliminate adverse effects on the data coils  266 ,  268  from the power transmission of the power coils  232 ,  234 . 
       FIG. 15  illustrates an embodiment of a casing drilling BHA  100  for providing wireless power and data connectivity/communications  402  between components. It should be appreciated that various BHA components may be used and various configurations may be implemented for arranging the BHA components. These and other configurations may provide wireless power and data transfer to components above and/or below a downhole drilling motor  410  and, thereby, advantageously enable real-time measurement and control of various drilling conditions for optimizing drilling performance and/or reducing drilling costs. 
     The BHA  100  includes drilling latch assembly (“DLA”)  406  for coupling the BHA  100  to a casing  404 . The BHA  100  further includes a casing drilling modulator and turbine power system  408 , a wireless power and data connection  402 , a drilling motor  410 , an under-reamer  412 , an RSS/MWD/LWD assembly  414  (see also LWD  120  and MWD  130  of  FIG. 1B ), and a drill bit  105 . The under-reamer  412  enlarges the borehole to form the reamed hole  418  relative to the pilot hole  416  formed by the drill assembly  105 . Specifically, the under-reamer  412  enlarges the borehole to form the reamed hole  418  such that it has a second diameter which is larger than the pilot hole  416  having a first diameter formed by the drill bit  105 . 
     The casing drilling modulator and turbine power system  408  is located below the drilling latch assembly (“DLA”)  406  with a downhole end connected to the drilling motor  410 . As understood by one of ordinary skill the art, the DLA  406  allows the turbine power system  408  and remaining equipment downward through the drill bit  105  to be retrieved and withdrawn through the casing  404  when the appropriate depth has been reached. Specifically, the diameter of the drill bit  105  is smaller than the inner diameter of the casing  404 . In this way, the casing  404  generally remains in place after drilling operations have ceased such that equipment from the turbine power system  408  may be retrieved upward and through the casing  404 . The DLA  406  also forms a fluid tight seal between the turbine power system  408  and the casing  404  so that fluid, such as mud, does not leak between the casing  404  in the turbine power system  408 . 
     Power and data pass through the wireless power and data connection  402  between the modulator and turbine power system  408  and the drilling motor  410 . The under-reamer  412 , the RSS/MWD/LWD assembly  414 , and the drill assembly  105  may be located below the drilling motor  410 . As understood by one of ordinary skill in the art, positioning units requiring power and/or communications below a drilling motor  410  has not been possible previously because of the need for power generation with these units, such as the MWD module  130  and LWD module  120 . 
     The under-reamer  412  may include a wired, collapsible under-reamer. The RSS/MWD/LWD assembly  414  generally includes a rotary steerable system (RSS)  150 , the MWD module  130 , and the LWD module  120 . The wireless power and data connection  402  may include a wireless, tuned-inductive coupler mechanism for passing both power and data communications to downhole components of the BHA  100 . It should be appreciated that separate coils may be used for power and communication transmissions. The wireless power and data connection  402  may allow the RSS module  414  to receive power from the turbine power system  408 . Meanwhile, in conventional BHA assemblies, RSS modules  414  may have their own internal power source. The RSS modules  414  of the BHA  100  of this disclosure may have their own power source but also have the option of being powered by the turbine power system  408  through the wireless power and data connection  402 . 
     The wireless power and data connection  402  allows relative motion between the modulator and turbine power system  408  (which is coupled to an external housing of the drilling motor  410 ) and a rotor of the drilling motor  410  (which is wired and coupled to the under-reamer  412 , the RSS/MWD/LWD assembly  414 , and the drill bit assembly  105 ), allowing power and data transfer throughout the entire BHA  100 . 
       FIG. 16  illustrates in more detail the modulator and turbine power system  408  and the drilling motor  410  with the wireless power and data connection  402  in between. The drilling motor  410  is also known as a mud motor or a positive displacement motor as understood by one of ordinary skill in the art. 
     Power and data wiring exits the downhole end of the modulator and turbine power system  408  and is coupled to a stationary coil  502  of the wireless power and data connection  402  located in the drilling motor  410  external housing. Power and data is transmitted between the stationary coil  502  and a rotating coil  504  via tuned-inductive methods, as described above and illustrated in  FIGS. 2-14 . Wiring is coupled to the rotating coil  504  and passes through an interior sealed channel in the center of a wired rotor  506  of the drilling motor  410 . The modulator and turbine power system  408  are coupled to the casing  404  illustrated in  FIG. 15 . And the stationary coil  502  is coupled to the modulator and turbine power system  408 . 
     The power system  408  and stationary coil  502  track whatever movement may exist with the casing  404 . In some instances, the casing  404  may have some slight rotation at low revolutions per minute (“RPM”) relative to the borehole and therefore, the stationary coil  502  may follow this rotational movement of the casing  404 . Meanwhile, the rotating coil  404  rotates with the drilling motor  410 , and specifically the wired rotor  506 , which rotates at significantly higher RPMs in order to rotate the drill assembly  105  as understood by one of ordinary skill in the art. 
     At the bottom of the rotor  506 , the wire is terminated at a connection  508  to the rotating BHA. The connection may include a threaded rotary shouldered joint and a sealed electrical connector mechanically and electrically coupling the rotating mechanism of the drilling motor  410  to the downhole components of the rotating BHA  100  (e.g., under-reamer  412 , RSS  150 , LWD module  120 , MWD module  130 , drill bit  105 ). 
       FIG. 17  illustrates another embodiment of the BHA  100  in which the MWD module is integrated with the modulator and turbine power system  408 . In this embodiment, the MWD module may include a direction &amp; inclination (D&amp;I) sensor package  477 . One of ordinary skill in the art will appreciate that this configuration may provide several desirable benefits. For example, when a D&amp;I sensor package  477  is located below the drilling motor  410  (rather than above, as illustrated in  FIG. 17 ), the pumps  29  must be disabled to prevent rotation of the D&amp;I sensor package  477 . 
     Furthermore, turbine power is not available when pumps are off, so a battery would be used to power the D&amp;I sensor package  477  along with logic using other parts of the system to detect when pumps are turned off. The embodiment illustrated in  FIG. 17  may eliminate the need for battery power in an MWD module  130  (since the D&amp;I sensor package may be powered by the modulator and turbine power system  408 ) and it also may reduce the need for stationary surveys of the borehole with pumps  29  turned off. 
     The power system  408  may also include a battery  488  that utilizes the wireless power and data connection  402 . The battery  488  may be used in conjunction with a modulator and turbine power system. Alternatively, the battery  488  may include the sole or primary power source for the power system  408 . 
     In an embodiment, as illustrated in  FIG. 18 , the modulator and turbine power system  408  may include a high-speed rotary “siren” pressure-pulse generator. It should be appreciated that the rotary modulator and turbine power system  408  may be capable of high speed operation, which can generate high frequencies and data rates. Unlike conventional “poppet” type or reciprocating pulsers, the use of the rotary modulator  408  is not inherently limited in speed of operation due to limits of acceleration/deceleration and motion reversal with associated problems of wear, flow-erosion, fatigue, power limitations, etc. 
     The power and telemetry system  408  may include a stator  483 , a rotor  487 , and a turbine  485 . Stator  483  and rotor  487  are the modulator for producing the telemetry. Stator  483  is static (non-moving) while rotor  487  rotates to create modulation for the telemetry using mudflow. 
     Mudflow through the power system  408  rotates these elements in order to produce power and the telemetry signals. As noted previously, the power system  408  may include a battery  488  which could be used as a substitute for the turbine  485 . Alternate combinations of power generation (i.e. mechanical or electrical/chemical, etc.) for the power system  408  are included within the scope of this disclosure as understood by one of ordinary skill the art. This power and telemetry system  408  may generate negative mud pulse signals as well as positive mud pulse signals. EM telemetry pulse signals from coils (using the data coils  266 ,  268  of  FIG. 14  if the main power coils  237  and  234  cannot pass data) may be produced for internal communications within the BHA as understood by one of ordinary skill the art. As noted above, the D&amp;I sensor package  477  may be powered by the turbine  485  of the modulator and power system  408 . 
     Referring now to  FIGS. 19-21 , it should be further appreciated that the speed/bandwidth advantages of the rotary modulator and power system  408  and the low rate of attenuation due to the large diameter of the acoustic conduit of casing  404  may result in, for example, approximately a one order of magnitude increase in data rate, when using mud pulse signaling telemetry, as compared to conventional drill pipe conveyed operations when the rotary modulator and power system  408  is located above the drilling motor  410  so high speed telemetry is not degraded. The rotary modulator and power system  408  located above the downhole drilling motor  410  provides for the transmission of large amounts of data for casing drilling. 
     The equation illustrated in table  1900  of  FIG. 19  shows the general effect of various parameters of the mud pulse signal strength and the rate of attenuation in the BHA  100  for casing drilling. In casing drilling applications, the effect of the larger inside diameter (d) within the casing  404  relative to conventional drill pipe BHAs  100  makes higher carrier frequencies (and hence data rate) possible since the rate of attenuation is much less for casing drilling as compared to a conventional drill pipe. 
     This lower rate of attenuation with the intrinsically high data rate of a rotary mud pulse telemetry system, enable greater bandwidth of real-time data than has been possible with existing directional practice and drill-pipe conveyed MWD systems. The viscosity and bulk modulus of the mud are strongly dependent on type of mud, temperature and pressure and will therefore be functions of total depth, vertical depth, water depth, geographical area, etc. 
     The equation in graph  1900  of  FIG. 19  also demonstrates that more accurate MWD measurements may be made when the D&amp;I sensor package  477  is incorporated in the modulator and turbine power system  408  above the motor  410  as illustrated in  FIG. 17 . As noted previously, mudflow and mud pulse signaling may be continued even while the D&amp;I sensor package  477  is operating since the sensor package  477  is above the drilling motor  410  and is therefore not rotating with the drill assembly  105 . The D&amp;I sensor package  477  may be powered by the turbine  485  of the modulator and power system  408  as described above, so a battery or another external powering system outside of the turbine power system  408  to power the D&amp;I sensor package  477  is not required. 
     The positive impact of the larger diameter (such as 7.0 inch or 17.8 cm diameter) in casing drilling compared to standard drill pipe drilling (such as 5.0 inch or 12.7 cm diameter) is very apparent in the graph  2005  illustrated in  FIG. 20 . Graph  2005  is derived from signal strength modeling and prediction software, which takes all of mud pulse signaling parameters into account for a typical deepwater application using synthetic oil based mud. 
     Graph  2005  shows that with a larger internal diameter of casing (see line with point  2015 ), telemetry rates in the range of about 12 bit/sec may be possible to depths of approximately 20,000.0 feet or 6.01 km (point  2015 ) as compared to a smaller drill pipe diameter of about 5.0 inches or 12.7 cm (see line with point  2010 ) where about a 12 bit/sec data rate is limited to approximately 13,000 feet or 3.96 km. Line  2020  defines a minimum threshold of about 1.0 psi for detecting a signal using mud pulse signaling/modulation. 
     Further benefits and advantages of the BHA  100  are shown with reference to graph  2105  of  FIG. 21 . This modeling comparison shows that telemetry with mud pulse signaling using drill pipe having a diameter of about 5.0 inches or 12.7 cm may be limited to approximately 1 bit/sec data rates (see line with point  2110 ). Hence, there may be a one order of magnitude higher data rate possible under these conditions with casing drilling having a diameter of about 7.0 inches or 17.8 cm (see line with point  2115 ) compared to the drill pipe scenario (see point  2110 ). 
     There may also be an approximately four-fold increase in signal amplitude with casing drilling as compared to standard drill-pipe drilling for about a 1 Hz telemetry in mud pulse signaling. Based on the data in graph  2105 , the maximum depth at which a signal may still be detected using casing drilling with 1 Hz telemetry may fall within the range of between about 40,000 to about 50,000 feet (about 12.19 km to about 15.24 km). 
     It should be appreciated that the above-described configurations for the casing drilling BHA  100  may be integrated with accompanying computer programs for configuring, operating, or otherwise interacting with the real-time measurement and control functionalities enabled by the corresponding BHA configurations. The computer programs may be implemented in control module(s)  101  and/or alert module(s)  110 , which include logic for instructing CPU(s) in the controller  106  to execute corresponding methods. 
     With the system described above, power and/or communications may be efficiently passed from a tool located above the mud motor to the rotor via two coils. One coil may be annular and located in the ID of the drill collar. The other coil is attached to the rotor and is located within the first coil. The coils are high Q and resonated at the same frequency. The impedance of the power source is matched to the impedance looking toward the transmitting coil. The impedance of the load is matched to the impedance looking back toward the source. 
     Advantages of the inventive method and system include, but are not limited to, the second coil of the two coils being able to rotate and to move in the axial and radial directions without loss of efficiency. According to the inventive method and system, room exists for mud to flow through the two coils. Further, power may be transmitted from the tool above the motor to the bit by passing the wires through the rotor. 
     Various sensors of the inventive system and method may be located at the bit, powered by the tool located above the mud motor. Measurements at the bit may include, but are not limited to, resistivity, gamma-ray, borehole pressure, bit RPM, temperature, shock, vibration, weight on bit, or torque on bit. 
     Another advantage of the inventive method and system is that two way communications may be made through the mud motor by adding a second set of coils. Additionally, resistivity measurements at the bit may be made by using two coils as receivers, as powered by this inventive system and method. 
     The inventive method and system may provide for efficient power transfer. According to one aspect, power may be transmitted between two coils where the two coils do not have to be in close proximity (see equation 1 discussed above) in which k may be less than (&lt;1) or equal to one. Another potential distinguishing aspect of the inventive method and system includes resonating the power transmitting coil with a high quality factor (see equation 3 discussed above) in which Q may be greater than (&gt;) or equal to about 10. Another distinguishing aspect of the system and method may include resonating the power transmitting coil with series capacitance (see equation 2 listed above). 
     Other unique aspects of the inventive method and system may include resonating the power transmitting coil with parallel capacitance and resonating the power receiving coil with a high quality factor Q (see equation 3) in which Q is greater than (&gt;) or equal to 10. Other unique features of the inventive method and system may include resonating the power receiving coil with series capacitance (see equation 2 discussed above) as well as resonating the power receiving coil with parallel capacitance. 
     Another unique feature of the inventive method and system may include resonating the transmitting coil and the receiving coil at similar frequencies (see equation 2 described above) as well as matching the impedance of the power supply to the impedance looking toward the transmitting coil (see equation 10 described above). Another distinguishing feature of the inventive method and system may include matching the impedance of the load to the impedance looking back toward the receiving coil (see equation 12 described above). 
     An additional distinguishing aspect of the inventive method and system may include using magnetic material to increase the coupling efficiency between the transmitting and the receiving coils. Further, the inventive method and system may include a power receiving coil that includes wire wrapped around a ferrite core (for example, see  FIG. 14 ). Meanwhile, the power transmitting coil may include a wire located inside a ferrite core (see  FIG. 14 ). According to another aspect, the power receiving coil may be located inside the power transmitting coil (see  FIG. 14 ). 
     Although a few embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the embodiments without materially departing from this disclosure. Accordingly, such modifications are intended to be included within the scope of this disclosure as defined in the following claims. In the above discussion of the casing drilling BHA  100 , both LWD and RSS equipment are located below the downhole drilling motor  410 . However, the RSS could run without the LWD equipment, or the LWD equipment could be run without the RSS. In the claims, means-plus-function clauses are intended to cover the structures described herein as performing the recited function and not only structural equivalents, but also equivalent structures. Thus, although a nail and a screw may not be structural equivalents in that a nail employs a cylindrical surface to secure wooden parts together, whereas a screw employs a helical surface, in the environment of fastening wooden parts, a nail and a screw may be equivalent structures. It is the express intention of the applicant not to invoke 35 U.S.C. §112, sixth paragraph for any limitations of any of the claims herein, except for those in which the claim expressly uses the words ‘means for’ together with an associated function.