Patent Publication Number: US-9885234-B2

Title: System and method for measuring temperature using an opto-analytical device

Description:
RELATED APPLICATIONS 
     This application is a U.S. National Stage Application of International Application No. PCT/US2012/053466 filed Aug. 31, 2012, which designates the United States, and which is incorporated herein by reference in its entirety. 
     TECHNICAL FIELD 
     The present disclosure relates generally to downhole drilling tools and, more particularly, to a system and method for measuring temperature using an opto-analytical device. 
     BACKGROUND 
     Various types of downhole drilling tools including, but not limited to, rotary drill bits, reamers, core bits, and other downhole tools have been used to form wellbores in associated downhole formations. Examples of such rotary drill bits include, but are not limited to, fixed cutter drill bits, drag bits, polycrystalline diamond compact (PDC) drill bits, and matrix drill bits associated with forming oil and gas wells extending through one or more downhole formations. Fixed cutter drill bits such as a PDC bit may include multiple blades that each include multiple cutting elements. 
     In typical drilling applications, a PDC bit may be used to drill through various levels or types of geological formations with longer bit life than non-PDC bits. Typical formations may generally have a relatively low compressive strength in the upper portions (e.g., shallower drilling depths) of the formation and a relatively high compressive strength in the lower portions (e.g., deeper drilling depths) of the formation. 
     One or more drilling characteristics may affect the process of drilling in a formation. These drilling characteristics may include properties of the formation itself (e.g., porosity, plasticity, density, rock strength, rock type and composition (e.g. shale, sandstone, limestone, etc.)), changes in the formation being drilled, the presence of types of fluids in the formation, the presence of brines in the formation, the presence of hydrocarbons (e.g., oil, natural gas) in the formation, changes in concentration of gases as the formation is being drilled, temperatures of components of the drilling tool, vibration of the drilling tool and drill string, torsion, cutting element wear, depth of cut control, cutting sizes, etc. 
     SUMMARY 
     In one embodiment, a method includes drilling a wellbore in a formation with a drilling tool. The method further includes receiving electromagnetic radiation using an opto-analytical device coupled to the drilling tool. The method also includes detecting a temperature associated with drilling the wellbore based on the received electromagnetic radiation. 
     The method may also include emitting electromagnetic radiation from the drilling tool, wherein the received electromagnetic radiation is derived from the emitted electromagnetic radiation. In some embodiments, the received electromagnetic radiation is derived from heat of the drilling tool. In certain embodiments, the method also includes replacing the cutting element of the drilling tool based on the detected temperature. In particular embodiments, detecting a temperature associated with drilling the wellbore comprises detecting a temperature of a fluid between the drilling tool and the formation. 
     In some embodiments, detecting a temperature associated with drilling the wellbore comprises detecting a temperature of a cutting element of the drilling tool. In certain embodiments, detecting a temperature associated with drilling the wellbore comprises detecting a first temperature of a first cutting element of the drilling tool and detecting a second temperature of a second cutting element of the drilling tool. The method may additionally include comprising comparing the first temperature and second temperature, modifying a weight on the drilling tool based on the comparison, modifying an amount of fluid between the drilling tool and the formation based on the comparison. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present disclosure and its features and advantages, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  illustrates an example embodiment of a drilling system in accordance with some embodiments of the present disclosure; 
         FIG. 2A  illustrates an isometric view of a rotary drill bit oriented upwardly in a manner often used to model or design drill bits in accordance with some embodiments on the present disclosure, 
         FIG. 2B  illustrates an example graph of output torque of a motor as a function of rotational speed, fluid speed, and differential pressure; 
         FIG. 3  illustrates a block diagram of an opto-analytical device configured to determine one or more characteristics of a sample in accordance with some embodiments of the present disclosure; 
         FIG. 4  illustrates a cross-sectional view of an example configuration of drill bit  101  in accordance with some embodiments of the present disclosure; 
         FIG. 5  illustrates an example embodiment of a drill bit integrated with one or more opto-analytical devices in accordance with some embodiments of the present disclosure; 
         FIG. 6  illustrates an example method for analyzing cuttings associated with drilling a wellbore in accordance with some embodiments of the present disclosure; 
         FIG. 7A  illustrates an example embodiment of a temperature sensor including an opto-analytical device in accordance with some embodiments of the present disclosure; 
         FIG. 7B  illustrates example spectral signatures of a material at different temperatures in accordance with some embodiments of the present disclosure; 
         FIG. 7C  illustrates an example configuration of temperature sensors with cutting elements to determine one or more drilling characteristics based on the temperature of cutting elements in accordance with some embodiments of the present disclosure; 
         FIG. 7D  illustrates example plots and of the temperatures of cutting elements as a function of time, in accordance with some embodiments of the present disclosure; 
         FIG. 8  illustrates an example method for determining one or more drilling characteristics based on temperature in accordance with some embodiments of the present disclosure; 
         FIG. 9  illustrates and example configuration of a bottom hole assembly including opto-analytical devices configured to determine torsion of the drilling tool in accordance with some embodiments of the present disclosure; 
         FIG. 10  illustrates an example method for determining torsion of a drilling tool in accordance with some embodiments of the present disclosure; 
         FIG. 11  illustrates an example embodiment of a gap sensor in accordance with some embodiments of the present disclosure; 
         FIGS. 12A-12C  illustrate an example of bit whirl of a drill bit in a wellbore, in accordance with some embodiments of the present disclosure; 
         FIG. 12D  illustrates example plots of points that indicate the bit walk of two drill bits in accordance with some embodiments of the present disclosure; 
         FIG. 13A  illustrates a cross-sectional view of an example configuration of a drill bit including gap sensors in accordance with some embodiments of the present disclosure; 
         FIG. 13B  illustrates example plots of gaps between a drill bit and a wellbore over time in accordance with some embodiments of the present disclosure; 
         FIG. 14  illustrates an example configuration of a drill bit including a gap sensor configured to detect the depth of cut of a cutting element in accordance with some embodiments of the present disclosure; 
         FIG. 15  illustrates an example configuration of a drill bit including a gap sensor configured to detect the wear of a cutting element in accordance with some embodiments of the present disclosure; 
         FIG. 16  illustrates a flow chart of an example method for determining a gap between objects in accordance with some embodiments of the present disclosure; 
         FIG. 17A  illustrates an example embodiment of an accelerometer configured to determine acceleration of a drilling tool using an opto-analytical device in accordance with some embodiments of the present disclosure; 
         FIG. 17B  illustrates another embodiment of an accelerometer configured to determine acceleration of a drilling tool using an opto-analytical device in accordance with some embodiments of the present disclosure; 
         FIG. 18  illustrates an example configuration of an accelerometer integrated with a drill bit along the rotational axis of the drill bit such that accelerometer may detect axial vibration of the drill bit in accordance with some embodiments of the present disclosure; and 
         FIG. 19  illustrates an example configuration of accelerometers integrated with a drill bit to determine the rotational speed of the drill bit in accordance with some embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the present disclosure and its advantages may be understood by referring to  FIGS. 1 through 19 , where like numbers are used to indicate like and corresponding parts. 
       FIG. 1  illustrates an example embodiment of a drilling system  100  configured to drill a wellbore  114  into a geological formation in accordance with some embodiments of the present disclosure. While drilling through a geological formation, one or more drilling characteristics may affect the performance of drilling system  100 . Additionally, modifications may be made to the drilling of wellbore  114  based on the presence of certain drilling characteristics. Further, the design of one or more drilling tools (e.g., drill bit, reamer, stabilizer, hole enlarger, etc.) of drilling system  100  may be determined based on the drilling characteristics. These drilling characteristics may include properties of the formation itself (e.g., porosity, permeability, plasticity, density, rock strength, stress, etc.), changes in the formation being drilled (such as bedding planes, fractures, compositional elements, etc.), the presence of types of fluids in the formation, the presence of brines in the formation, the presence of hydrocarbons (e.g., oil, natural gas) in the formation, changes in concentration of gases in the formation, temperatures of components of the drilling tool, vibration of the drilling tool and drill string, weight on bit, torque on bit, bit rotational speed, rate of penetration, bit mechanicals, specific energy, torsion, bit whirl, bit walk, bit tilt, cutting element wear, depth of cut, cutting sizes, drilling fluid types and speed in the hole annuals, rock chemistry and/or composition, texture, water, salt, pH, impurities, temperature, pressure etc. 
     In many instances it may be advantageous to measure one or more drilling characteristics during the process of drilling wellbore  114 . Measuring one or more drilling characteristics during the process of drilling wellbore  114  may allow for a more accurate representation of the effects that drilling characteristics may have on the drilling process and drilling tools of drilling system  100 . For example, measuring drilling tool properties (e.g., the temperature, vibration, torsion, wear, etc. of drilling tools) during drilling may allow for a more accurate analysis of the physical conditions and strain that may affect the drilling tools of drilling system  100 . Additionally, measurements of formation properties (e.g., rock strength, stress, porosity, density, plasticity, rock type, and rock composition) during the process of drilling through the formation may also provide a more accurate analysis of the physical conditions that may affect the drilling tools and drilling system  100 . Further, measuring the presence of certain gases at or near the end of wellbore  114  may allow for preparations at well site  106 . For instance, the detection of certain gases at or near the end of wellbore  114  may require different preparations (e.g. safety) at well site  106 . 
     Accordingly, the drilling tools may be modified for improved performance through a more accurate representation of the physical conditions that may affect the drilling tools. For example, an analysis of the wear of a drilling tool during drilling and an analysis of the rock strength of the formation being drilled may allow for modifications of the design of the drilling tool (or other drilling tools to be used in the same location) to better cut through a formation having that particular rock strength. Additionally, an analysis of the measured temperature during drilling may allow for determining the particular temperature tolerances of the drilling tools of drilling system  100 . More examples of modifications that may be made with respect to certain drilling characteristics are discussed in detail below. 
     Measuring drilling characteristics during the process of drilling wellbore  114  may also allow for modifications to be made to the process of drilling wellbore  114  based on one or more drilling characteristics. For example, measuring an increased presence of a hydrocarbon (e.g., oil, natural gas) at or near the end of wellbore  114  may indicate that a drilling tool (e.g., drill bit) has reached a hydrocarbon reservoir. 
     As described in further detail below, in accordance with one or more embodiments of the present disclosure, one or more opto-analytical devices may be configured to measure one or more drilling characteristics. The one or more opto-analytical devices may be integrated with one or more drilling tools of drilling system  100  such that the one or more opto-analytical devices may measure the one or more drilling characteristics at or near the end of wellbore  114  during the process of drilling wellbore  114 . As discussed in further detail with respect to  FIG. 3 , an opto-analytical device may be configured to measure a drilling characteristic based on the interaction of electromagnetic radiation with the formation and/or drilling tool. Therefore, the one or more opto-analytical devices integrated with the one or more drilling tools may allow for measuring one or more drilling characteristics during the process of drilling wellbore  114 , which may allow for better design of drilling tools and desired modifications to the drilling of wellbore  114 . 
     Drilling system  100  may include a well surface or well site  106 . Various types of drilling equipment such as a rotary table, drilling fluid pumps and drilling fluid tanks (not expressly shown) may be located at a well surface or well site  106 . For example, well site  106  may include a drilling rig  102  that may have various characteristics and features associated with a “land drilling rig.” However, downhole drilling tools incorporating teachings of the present disclosure may be satisfactorily used with drilling equipment located on offshore platforms, drill ships, semi-submersibles and drilling barges (not expressly shown). 
     Drilling system  100  may include a drill string  103  associated with drill bit  101  that may be used to form a wide variety of wellbores or bore holes such as generally vertical wellbore  114   a  or generally horizontal wellbore  114   b  as shown in  FIG. 1 . Various directional drilling techniques and associated components of a bottom hole assembly (BHA)  120  of drill string  103  may be used to form horizontal wellbore  114   b . For example, lateral forces may be applied to BHA  120  proximate kickoff location  113  to form horizontal wellbore  114   b  extending from generally vertical wellbore  114   a.    
     BHA  120  may be formed from a wide variety of components configured to form a wellbore  114 . For example, components  122   a ,  122   b  and  122   c  of BHA  120  may include, but are not limited to, drill bits (e.g., drill bit  101 ), drill collars, rotary steering tools, directional drilling tools, downhole drilling motors, reamers, hole enlargers or stabilizers. The number of components such as drill collars and different types of components  122  included in BHA  120  may depend upon anticipated downhole drilling conditions and the type of wellbore that will be formed by drill string  103  and rotary drill bit  101 . As discussed in further detail below, one or more opto-analytical devices may be integrated with one or more components of BHA  120  such that one or more drilling characteristics may be measured in wellbore  114  during the process of drilling wellbore  114 . 
     Wellbore  114  may be defined in part by a casing string  110  that may extend from well surface  106  to a selected downhole location. Portions of a wellbore  114 , as shown in  FIG. 1 , that do not include casing string  110  may be described as “open hole.” Various types of drilling fluid may be pumped from well surface  106  through drill string  103  to attached drill bit  101 . Such drilling fluids may be directed to flow from drill string  103  to respective nozzles (depicted as nozzles  156  in  FIG. 2 ) passing through rotary drill bit  101 . The drilling fluid may be circulated back to well surface  106  through an annulus  108 . Annulus may refer to the space between the outside of the drill pipe or drill collars and the casing or wellbore, and may be defined in part by outside diameter  112  of drill string  103  and inside diameter  118  of wellbore  114   a . Inside diameter  118  may be referred to as the “sidewall” of wellbore  114   a . Annulus  108  may also be defined by outside diameter  112  of drill string  103  and inside diameter  111  of casing string  110 . 
     Drilling system  100  may also include a drill bit  101 . Drill bit  101  may be any of various types of drill bits including percussion bits, roller cone bits, coring bits and fixed cutter drill bits. Drill bit  101  may be designed and formed in accordance with teachings of the present disclosure and may have many different designs, configurations, and/or dimensions according to the particular application of drill bit  101 . As disclosed in further detail below with respect to  FIGS. 3-19 , one or more opto-analytical devices (not expressly shown) may be integrated with drill bit  101  such that the one or more opto-analytical devices may measure one or more drilling characteristics at or near the end of wellbore  114  during the process of drilling wellbore  114 . 
       FIG. 2  illustrates an isometric view of a rotary drill bit  101  oriented upwardly in a manner often used to model or design drill bits in accordance with some embodiments on the present disclosure. In the present embodiment, drill bit  101  may be any of various types of fixed cutter drill bits, including PDC bits, drag bits, matrix drill bits, and/or steel body drill bits operable to form wellbore  114  extending through one or more downhole formations. Drill bit  101  may be designed and formed in accordance with teachings of the present disclosure and may have many different designs, configurations, and/or dimensions according to the particular application of drill bit  101 . 
     Drill bit  101  may include one or more blades  126  (e.g., blades  126   a - 126   g ) that may be disposed outwardly from exterior portions of rotary bit body  124  of drill bit  101 . Rotary bit body  124  may have a generally cylindrical body and blades  126  may be any suitable type of projections extending outwardly from rotary bit body  124 . For example, a portion of blade  126  may be directly or indirectly coupled to an exterior portion of bit body  124 , while another portion of blade  126  may be projected away from the exterior portion of bit body  124 . Blades  126  formed in accordance with teachings of the present disclosure may have a wide variety of configurations including, but not limited to, substantially arched, helical, spiraling, tapered, converging, diverging, symmetrical, and/or asymmetrical. 
     In some cases, blades  126  may have substantially arched configurations, generally helical configurations, spiral shaped configurations, or any other configuration satisfactory for use with each downhole drilling tool. One or more blades  126  may have a substantially arched configuration extending from proximate rotational axis  104  of drill bit  101 . The arched configuration may be defined in part by a generally concave, recessed shaped portion extending from proximate bit rotational axis  104 . The arched configuration may also be defined in part by a generally convex, outwardly curved portion disposed between the concave, recessed portion and exterior portions of each blade which correspond generally with the outside diameter of the rotary drill bit. 
     Each of blades  126  may include a first end disposed proximate or toward bit rotational axis  104  and a second end disposed proximate or toward exterior portions of drill bit  101  (e.g., disposed generally away from bit rotational axis  104  and toward uphole portions of drill bit  101 ). The terms “uphole” and “downhole” may be used to describe the location of various components of drilling system  100  relative to the bottom or end of wellbore  114  shown in  FIG. 1 . For example, a first component described as uphole from a second component may be further away from the end of wellbore  114  than the second component. Similarly, a first component described as being downhole from a second component may be located closer to the end of wellbore  114  than the second component. 
     Blades  126   a - 126   g  may include primary blades disposed about the bit rotational axis. For example, in  FIG. 2A , blades  126   a ,  126   c , and  126   e  may be primary blades or major blades because respective first ends  141  of each of blades  126   a ,  126   c , and  126   e  may be disposed closely adjacent to associated bit rotational axis  104 . In some embodiments, blades  126   a - 126   g  may also include at least one secondary blade disposed between the primary blades. Blades  126   b ,  126   d ,  126   f , and  126   g  shown in  FIG. 2  on drill bit  101  may be secondary blades or minor blades because respective first ends  141  may be disposed on downhole end  151  a distance from associated bit rotational axis  104 . The number and location of secondary blades and primary blades may vary such that drill bit  101  includes more or less secondary and primary blades. Blades  126  may be disposed symmetrically or asymmetrically with regard to each other and bit rotational axis  104  where the disposition may be based on the downhole drilling conditions of the drilling environment. In some cases, blades  126  and drill bit  101  may rotate about rotational axis  104  in a direction defined by directional arrow  105 . 
     Each blade may have a leading (or front) surface disposed on one side of the blade in the direction of rotation of drill bit  101  and a trailing (or back) surface disposed on an opposite side of the blade away from the direction of rotation of drill bit  101 . Blades  126  may be positioned along bit body  124  such that they have a spiral configuration relative to rotational axis  104 . In other embodiments, blades  126  may be positioned along bit body  124  in a generally parallel configuration with respect to each other and bit rotational axis  104 . 
     Blades  126  may include one or more cutting elements  128  disposed outwardly from exterior portions of each blade  126 . For example, a portion of cutting element  128  may be directly or indirectly coupled to an exterior portion of blade  126  while another portion of cutting element  128  may be projected away from the exterior portion of blade  126 . Cutting elements  128  may be any suitable device configured to cut into a formation, including but not limited to, primary cutting elements, backup cutting elements, secondary cutting elements or any combination thereof. By way of example and not limitation, cutting elements  128  may be various types of cutters, compacts, buttons, inserts, and gage cutters satisfactory for use with a wide variety of drill bits  101 . 
     Cutting elements  128  may include respective substrates with a layer of hard cutting material disposed on one end of each respective substrate. The hard layer of cutting elements  128  may provide a cutting surface that may engage adjacent portions of a downhole formation to form wellbore  114 . The contact of the cutting surface with the formation may form a cutting zone associated with each of cutting elements  128 . The edge of the cutting surface located within the cutting zone may be referred to as the cutting edge of a cutting element  128 . 
     Each substrate of cutting elements  128  may have various configurations and may be formed from tungsten carbide or other materials associated with forming cutting elements for rotary drill bits. Tungsten carbides may include, but are not limited to, monotungsten carbide (WC), ditungsten carbide (W 2 C), macrocrystalline tungsten carbide and cemented or sintered tungsten carbide. Substrates may also be formed using other hard materials, which may include various metal alloys and cements such as metal borides, metal carbides, metal oxides and metal nitrides. For some applications, the hard cutting layer may be formed from substantially the same materials as the substrate. In other applications, the hard cutting layer may be formed from different materials than the substrate. Examples of materials used to form hard cutting layers may include polycrystalline diamond materials, including synthetic polycrystalline diamonds. 
     In accordance with some embodiments of the present disclosure, as described below with respect to  FIGS. 5 and 6 , one or more opto-analytical devices may be integrated with drill bit  101  to determine one or more drilling characteristics associated with cutting elements  128  including temperatures of cutting elements  128  during drilling, the depth of cut of cutting elements  128 , wear of cutting elements  128 , the size of cuttings produced by cutting elements  128  etc. 
     In some embodiments, blades  126  may also include one or more depth of cut controllers (DOCCs)  129  configured to control the depth of cut of cutting elements  128 . A DOCC  129  may include an impact arrestor, a backup cutter and/or an MDR (Modified Diamond Reinforcement). Exterior portions of blades  126 , cutting elements  128  and DOCCs  129  may form portions of the bit face. 
     Blades  126  may further include one or more gage pads (not expressly shown) disposed on blades  126 . A gage pad may be a gage, gage segment, or gage portion disposed on exterior portion of blade  126 . Gage pads may often contact adjacent portions of wellbore  114  formed by drill bit  101 . Exterior portions of blades  126  and/or associated gage pads may be disposed at various angles, positive, negative, and/or parallel, relative to adjacent portions of generally vertical wellbore  114   a . A gage pad may include one or more layers of hardfacing material. 
     Uphole end  150  of drill bit  101  may include shank  152  with drill pipe threads  155  formed thereon. Threads  155  may be used to releasably engage drill bit  101  with BHA  120 , described in detail below, whereby drill bit  101  may be rotated relative to bit rotational axis  104 . Downhole end  151  of drill bit  101  may include a plurality of blades  126   a - 126   g  with respective junk slots or fluid flow paths  240  disposed therebetween. Additionally, drilling fluids may be communicated to one or more nozzles  156 . As mentioned above, in accordance with some embodiments of the present disclosure, one or more opto-analytical devices may be integrated with drill bit  101  to determine the temperature of one or more cutting elements  128  and the size of cuttings of the formation made by cutting elements  128 . Nozzles  156  may be designed based on the determined cutting sizes to more effectively deliver drilling fluids where needed. Additionally, nozzles  156  may be redesigned based on the measured temperatures of cutting elements  128  such that nozzles  156  may more effectively direct drilling fluid to cool cutting elements  128 . 
     The rate of penetration (ROP) of drill bit  101  is often a function of both weight on bit (WOB) and revolutions per minute (RPM). Referring back to  FIG. 1 , drill string  103  may apply weight on drill bit  101  and may also rotate drill bit  101  about bit rotational axis  104  to form wellbore  114  (e.g., wellbore  114   a  or wellbore  114   b ). The depth of cut per revolution (or “depth of cut”) may also be based on ROP and RPM of a particular bit and indicates how deeply drill bit cutting elements  128  are engaging the formation. 
     For some applications a downhole motor or “motor” (not expressly shown) may be provided as part of BHA  120  to also rotate drill bit  101  in order to provide directional and horizontal drilling to form wellbore  114   b  through kickoff location  113 . There are two drilling modes during directional and horizontal drilling using a motor. The first mode may be referred to as “sliding mode” drilling. In this mode, drill string  103  above the motor (not expressly shown) does not rotate in order for drill bit  101  to build/drop an angle and to drill into a curve. Sliding mode drilling may be used primarily to change drilling direction. The second mode may be referred to as “rotating mode” drilling. In this mode, both drill string  103  and the motor (not expressly shown) are rotating. Rotating mode drilling may be used to drill a lateral section or a straight hole as shown in generally horizontal wellbore  114   b.    
     When drilling through a curved section of a wellbore in sliding mode, it may be difficult to transfer axial force to drill bit  101  due to the axial friction between drill string  103  and kickoff downhole wall  118   b . As the angle of wellbore  114  changes from essentially vertical to essentially horizontal through kickoff location  113 , drill string  103  is held against the lower wall of the wellbore, e.g., kickoff downhole wall  118   b , by gravity. In this situation, drill string  103  from kickoff location  113  to generally horizontal wellbore  114   b  may not exert much force, or WOB, because most of the weight of drill string  103  is exerted on the lower wall of the wellbore. Force, or WOB, exerted on drill bit  101  must overcome the friction between drill string  103  and kickoff downhole wall  118   b  of wellbore  114 . This situation may lead to a small force, or WOB, in sliding mode in addition to a low ROP and depth of cut per revolution. 
     Additionally, in sliding mode drilling, torque on bit (TOB), which is the torque used to rotate drill bit  101 , may be limited because torque may only be provided by the motor (not expressly shown) and not by drilling rig  102 . The maximum output torque from the downhole motor (not expressly shown) may be a function of rotational speed expressed as revolutions per minute (RPM), fluid speed expressed as gallons per minute (GPM), and operational differential pressure across the motor expressed in pounds per square inch (psi). Accordingly,  FIG. 2B  illustrates graph  200  of output torque of a motor as a function of rotational speed, fluid speed, and differential pressure.  FIG. 2B  may be part of a technical specification that may be provided by a motor manufacturer. One example of a downhole motor is a SperryDrill® or GeoForce® motor (Sperry Drilling Services at Halliburton Company, TX). From  FIG. 2B , for a given RPM, GPM, and differential pressure, the maximum output torque may be determined. For example, as shown by point  210 , at approximately 130 RPM, approximately 450 GPM, and approximately 470 psi, the output torque may be approximately 4000 ft-lb for a motor having the characteristics illustrated in graph  200  of  FIG. 2B . If TOB is larger than approximately 4000 ft-lb, then the motor may stall such that the motor ceases to turn. Motor stall may occur if the instant depth of cut of drill bit  101  is large enough that the combination of TOB and RPM produced by the motor is not sufficient to rotate drill bit  101 . Additionally, as the TOB increases, the drill string may experience torsion (e.g., twist) causing the drill string to windup. As described in detail below with respect to  FIGS. 9-10 , in some embodiments one or more opto-analytical device integrated with one or more components of BHA  120  may be configured to measure drilling characteristics associated with torsion of the drill string. 
     Accordingly, as mentioned above and described in detail below, one or more opto-analytical devices may be integrated with one or more components of BHA  120  to determine one or more drilling characteristics at or near the end of wellbore  114  during the process of drilling wellbore  114 . The measurements obtained by the one or more opto-analytical devices may allow for improved designs of drilling tools. The measurements of the drilling characteristics may also allow for modifications to drilling operations during the drilling of wellbore  114  to improve the efficiency of drilling wellbore  114 . 
     Modifications, additions, or omissions may be made to  FIG. 2  without departing from the scope of the present disclosure. For example, a drill bit such as drill bit  101  may be designed such that the bit does not includes one or more blades  126 . In such embodiments, cutting elements  128  may be located directly on bit body  124 , and may still provide a cutting surface that may engage adjacent portions of a downhole formation to form wellbore  114 . 
       FIG. 3  illustrates a block diagram of an opto-analytical device  300  configured to determine one or more characteristics of a sample  304  in accordance with some embodiments of the present disclosure. As used herein, the term “characteristic” may refer to a chemical, mechanical or physical property of a substance or material. A characteristic of a substance may include a quantitative value or a concentration of one or more chemical components therein. Illustrative characteristics of a substance that can be monitored with the opto-analytical devices disclosed herein can include, for example, chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like. 
     Opto-analytical device  300  may include an integrated computational element (ICE)  302  configured to receive electromagnetic radiation  301  from a sample  304 . ICE  302  may be configured to detect a characteristic of sample  304  based on the received electromagnetic radiation  301 . 
     When electromagnetic radiation interacts with sample  304 , unique physical and/or chemical information about sample  304  may be encoded in electromagnetic radiation  301  that is reflected from, transmitted through or radiated from sample  304 . Information associated with each different characteristic may be encoded in electromagnetic radiation  301 . 
     As used herein, the term “electromagnetic radiation” refers to electromagnetic waves of any wavelength, including radio waves, microwave radiation, infrared and near-infrared radiation, visible light, ultraviolet light, X-Ray radiation and gamma ray radiation. Electromagnetic radiation  301  may come from any number of sources. For example, electromagnetic radiation  301  may originate from heat emanating from sample  304 . Electromagnetic radiation  301  may be radiation emanating from or fluorescing from sample  304 . In other embodiments, electromagnetic radiation  301  may be derived from an active electromagnetic source (e.g., infrared, UV, visible light) that illuminates sample  304 . The electromagnetic source may be located within a portion of the drill bit, such as within a cavity of the drill bit. In some embodiments, electromagnetic radiation may be derived from heat emanating from one or more portions of the drill bit. For example, a cutting element may be formed in a way that mimics a worn cutting element such that it generates heat and/or electromagnetic radiation when it is applied to the formation. In other embodiments, electromagnetic radiation may be naturally occurring either in the background or from the sample itself due to natural fluorescent or phosphorescent processes. In other embodiments, electromagnetic radiation may results from chemi-luminescent or tribo-luminescent processes. Finally, in other embodiments, electromagnetic radiation may be obtained from optical conveying devices such as electromagnetic radiation fibers, waveguides, light pipes, and the like readily appreciated by those familiar in the art. 
     Sample  304  may be any type of material or area that may have one or more characteristics that may be of interest. For example, in the context of drilling, sample  304  may be the formation itself, one or more components of drilling tools or a space within the wellbore that may include one or more liquids or gases, and/or the liquid or gas itself. Accordingly, electromagnetic radiation  301  received from sample  304  may include information associated with any number of characteristics associated with sample  304 . For example, if sample  304  is the formation, electromagnetic radiation  301  may include information indicating the chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like. As another example, if sample  304  is the space within a wellbore, electromagnetic radiation  301  may include spectral signatures associated with the presence and/or concentration of fluids (e.g., oil or natural gas) present in the wellbore. 
     ICE  302  may be configured to receive electromagnetic radiation  301  and detect a particular characteristic of sample  304  based on a correlation associated with the particular characteristic included in electromagnetic radiation  301 . The underlying theory behind using integrated computational elements for conducting analyses is described in more detail in the following commonly owned United States patents and patent application Publications, each of which is incorporated herein by reference in its entirety: U.S. Pat. Nos. 6,198,531; 6,529,276; 7,123,844; 7,834,999; 7,911,605; and 7,920,258; and U.S. Patent Publication Nos. 2009/0219538; 2009/0219539; and 2009/0073433. 
     There are a wide variety of implementations that may be employed to create ICE. In one embodiment, ICE  302  may include a plurality of alternating layers of optical elements (e.g., silicon, germanium, or other similar materials) with transmissive, reflective, and/or absorptive properties suitable for detecting a characteristic of interest. For example, the alternating layers may be niobium pentoxide (Nb 2 O 5 ), and Niobium and/or Silicon and quartz (SiO 2 ) deposited on a substrate (e.g., glass, diamond, quartz, sapphire, ZnSe, ZnS, Ge, Si, etc.). In general, the materials forming the alternate layers may consist of materials that have indices of refraction that differ from one another, e.g., one has a low index of refraction and the next has a high index of refraction. Other suitable materials for the layers may include, but are not limited to, metals and their oxides and semiconductor materials and their oxides, nitrides, and carbides such as germanium and Germania, MgF 2 , SiO, SiC, and other thin film capable materials familiar with those skilled in the art (more complete lists can be found at: http://www.plasmaterials.com/ThinFilmEvapMatSrcRef.pdf and http://www.cleanroom.byu.edu/TFE_materials.phtml). The number of layers and the thickness of the layers may be determined and constructed from the spectral attributes of the characteristic of interest as determined from a spectroscopic analysis of the characteristic using a conventional spectroscopic instrument. In general, the combination of layers correspond or are related to the spectral correlation of the characteristic of interest. 
     The multiple layers may have different refractive indices. By properly selecting the materials of the layers and their spacing, ICE  302  can be made to selectively transmit, absorb, and/or reflect predetermined fractions of electromagnetic radiation at different wavelengths. Each wavelength may be given a pre-determined weighting or loading factor. The thicknesses and spacing of the layers may be determined using a variety of approximation methods from the spectrograph of the characteristic of interest. These methods may include inverse Fourier transform (IFT) of the optical transmission spectrum and structuring the optical calculation device as the physical representation of the IFT. The approximations convert the IFT into a structure based on known materials with constant refractive indices. In addition to solids, ICE  302  may also contain liquids and/or gases in combination with solids to create the desired layers. ICE  302  may also include holographic optical elements, gratings, and/or acousto-optic elements, for example, that may create the transmission, reflection, and/or absorption properties of interest for the layers of ICE  302 . 
     The weightings that ICE  302  layers apply at each wavelength are set such that they relate or correlate to the regression weightings described with respect to a known equation, or data, or spectral correlation of the characteristic of interest. The intensity of transmitted, absorbed, or reflected electromagnetic radiation  303  is related to the amount (e.g., concentration) of the characteristic of interest associated with sample  304 . Accordingly, ICE  302  may be configured to detect a particular characteristic of sample  304  based on the correlation associated with the particular characteristic that is included in received electromagnetic radiation  301 . 
     Although the operation of ICE  302  is often illustrated in the optical transmission mode, it is readily understood that ICE can operate as well in other optical modes, such as reflection, absorption, transflectance, Raman, Brillion, and Raleigh scattering modes, emittance or fluorescent modes, as well as evanescent modes known to those skilled in the art. In addition, components of ICE  302  may also be realized with a variety of other techniques. These include, but are not limited to, holographic optical elements (HOE&#39;s), phase gratings, optical gratings, Digital Light Pipe (DLP) devices, liquid crystal devices, photo-acoustic devices, and even naturally occurring substances such as water (e.g. in a curvette or holder) and gases (e.g. water vapor, CO, CO2, methane, hydrocarbon gases, NO and NOx nitrogen gases, etc). 
     In addition, significant benefits may be realized by combining the outputs of two or more integrated computational elements with one another when analyzing a single characteristic of interest. Specifically, significantly increased detection accuracy may be realized. Analysis techniques utilizing combinations of two or more integrated computational elements are described in commonly owned U.S. patent application Ser. Nos. 13/456,255; 13/456,264; 13/456,283; 13/456,302; 13/456,327; 13/456,350; 13/456,379; 13/456,405; and 13/456,443; each filed on Apr. 26, 2012 and incorporated herein by reference in its entirety. 
     Opto-analytical device  300  may include a detector  306  configured to receive transmitted electromagnetic radiation  303  from ICE  302 . Detector  306  may include any suitable apparatus, system, or device configured to detect the intensity of transmitted electromagnetic radiation  303  and generate a signal related to the intensity of transmitted electromagnetic radiation  303  received from ICE  302 . For example, detector  306  may be configured to generate a voltage related to the intensity of transmitted electromagnetic radiation  303 . Detector  306  may communicate the signal (e.g., voltage signal) related to the intensity of transmitted electromagnetic radiation  303  to a processing unit  308 . Examples of detectors include split detectors, quad detectors, and array detectors. 
     Processing unit  308  may be configured to receive the signal communicated from detector  306  and correlate the received signal with the characteristic of which ICE  302  is configured to detect. For example, ICE  302  may be configured to detect temperature of sample  304  and the intensity of transmitted electromagnetic radiation  303  transmitted from ICE  302  may accordingly be related to the temperature of sample  304 . Accordingly, detector  306  may generate a voltage signal based on the intensity of electromagnetic radiation  303  and may communicate the voltage signal to processing unit  308 . Processing unit  308  may then correlate the received voltage signal with a temperature such that processing unit  308  may determine a temperature of sample  304 . 
     Processing unit  308  may include a processor that is any system, device, or apparatus configured to interpret and/or execute program instructions and/or process data associated with opto-analytical device  300 . The processor may be, without limitation a microprocessor, microcontroller, digital signal processor (DSP), application specific integrated circuit (ASIC), or any other digital or analog circuitry configured to interpret and/or execute program instructions and/or process data. In some embodiments, the processor may interpret and/or execute program instructions and/or process data stored in one or more computer-readable media included in processing unit  308 . 
     The computer-readable media may be communicatively coupled to the processor and may include any system, device, or apparatus configured to retain program instructions and/or data for a period of time (e.g., computer-readable media). The computer-readable media may include random access memory (RAM), electrically erasable programmable read-only memory (EEPROM), a PCMCIA card, flash memory, magnetic storage, opto-magnetic storage, or any suitable selection and/or array of volatile or non-volatile memory that retains data after power to processing unit  308  is turned off. In accordance with some embodiments of the present disclosure, the computer-readable media may include instructions for determining one or more characteristics of sample  304  based on signals received from detector  306 . 
     ICE  302  may also be configured to reflect portions of electromagnetic radiation  301  not related to the characteristic of interest as reflected electromagnetic radiation  305 . In some embodiments, ICE  302  may reflect electromagnetic radiation  305  toward another detector (not expressly shown in  FIG. 3 ). The detector configured to receive reflected electromagnetic radiation  305  may be configured to generate a signal associated with reflected electromagnetic radiation  305  and communicate the signal to processing unit  308 . Processing unit  308  may use the signal associated with electromagnetic radiation  305  to normalize the signal associated with transmitted electromagnetic radiation  303 . In alternative embodiments, ICE  302  may be configured such that reflected electromagnetic radiation  305  may be related to the characteristic of interest and transmitted electromagnetic radiation  303  may be related to other characteristics of sample  304 . 
     Opto-analytical device  300  may be configured to detect and determine a characteristic of sample  304  based on electromagnetic radiation  301  received from sample  304 . Opto-analytical device  300  may include any number of ICEs  302  and associated detectors  306  configured to detect any number of characteristics of sample  304 . Processing unit  308  may accordingly be configured to determine one or more properties of sample  304  based on the different characteristics detected by different ICEs  302  and associated detectors  306 . Example characteristics that may be determined include chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like. In some embodiments, the characteristics described above directly correlate to the signal of the opto-analytical device and no further analysis is required to obtain the characteristic of interest. In other embodiments, processing unit  308  may determine other physical properties of the formation such as rock strength, porosity, density, or any other characteristic based upon the detected chemical compositions or characteristics of interest. Additionally, in some embodiments processing unit  308  may be configured to store collected data associated with a detected characteristic in any suitable storage medium. The collected data may then be retrieved at a later time and may be analyzed and processed to determine various properties of sample  304 . In embodiments where opto-analytical device  300  is integrated with a drilling tool, processing unit  308  may be configured to communicate information associated with a detected characteristic to a well site using any suitable measurement while drilling (MWD) communication system. 
     When monitoring more than one characteristic at a time, various configurations for multiple ICEs  302  may be used, where each ICE  302  has been configured to detect a particular characteristic of interest. In some embodiments, the characteristic may be analyzed sequentially using multiple ICEs  302  that are presented to a single beam of electromagnetic radiation being reflected from or transmitted through a sample. In some embodiments, multiple ICEs can be located on a rotating disc, where the individual ICEs are exposed to the beam of electromagnetic radiation for a short period of time. Advantages of this approach may include the ability to analyze multiple characteristics using a single optical computing device and the opportunity to assay additional characteristics simply by adding additional ICEs to the rotating disc. In various embodiments, the rotating disc can be turned at a frequency of about 1 RPM to about 30,000 RPM such that each characteristic in a sample is measured rapidly. In some embodiments, these values may be averaged over an appropriate time domain (e.g., about 1 millisecond to about 1 hour) to more accurately determine the sample characteristics. 
     In other embodiments, multiple ICEs  302  may be placed in parallel, where each ICE  302  is configured to detect a particular characteristic of interest. In such embodiments, a beam splitter may divert a portion of the electromagnetic radiation from the substance being analyzed to each ICE  302 . Each ICE  302 , in turn, may be communicatively coupled to detector  306  or array of detectors  306  configured to detect an output of electromagnetic radiation from the ICE  302 . Parallel configurations of ICEs  302  may be particularly beneficial for applications that require low power inputs and/or no moving parts. Parallel configurations of ICE&#39;s may also be particularly beneficial for applications where changes in characteristic values are rapid, such as high velocity flows. 
     In still additional embodiments, multiple ICEs  302  may be placed in series, such that characteristics are measured sequentially at different locations and times. For example, in some embodiments, a characteristic can be measured in a first location using a first ICE  302 , and the characteristic can be measured in a second location using a second ICE  302 . In other embodiments, a first characteristic may be measured in a first location using a first ICE  302 , and a second characteristic may be measured in a second location using a second ICE  302 . 
     Any of the foregoing configurations for the optical computing devices may be used in combination with a series configuration in any of the present embodiments. For example, two rotating discs having a plurality of ICEs may be placed in series for performing an analysis. Likewise, multiple detection stations, each containing ICEs  302  in parallel, may be placed in series for performing an analysis. 
     As mentioned above, an opto-analytical device  300  integrated with a drilling tool, such as drill bit  101  may be used to detect any number of characteristics associated with drilling a wellbore in a formation, such as chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, ionic strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, or the like. The detection of characteristics may also be used to determine an event associated with drilling a wellbore. In some embodiments, drilling of a wellbore may be modified based on the detected characteristic. 
     For example, opto-analytical device  300  may be configured to detect the concentration of certain gases in a wellbore (e.g., wellbore  114  as illustrated in  FIG. 1 ). Accordingly, when a change in gas concentration occurs, opto-analytical device  300  may detect change and drilling may be adjusted accordingly. As an example, opto-analytical device  300  may be configured to detect changes in the concentration of natural gas. A sharp increase in natural gas concentrations may indicate that the wellbore has reached a natural gas reservoir. Drilling may then be modified based on reaching the natural gas reservoir. For example, weight may be taken off the drill bit and a seal may be placed against the wall of the wellbore to seal the gas in the reservoir. In some embodiments, the sealing may be done at a BHA (e.g., BHA  120  as illustrated in  FIG. 1 ) by processing unit  308  communicating a control signal to expand a donut to seal the gas in the wellbore upon detecting the gas. For example, when the detected event is transmitted to the surface, drilling fluid flow rates may be increased and the drilling fluid density may be optimized to maintain a pressure at the surface higher than the formation pressure in order to maintain control of the well. The drilling fluid chemistry may also be changed to include materials designed to ameliorate the toxic effects the gas. Other events that may be detected using an opto-analytical device  300  may be a change in the chemistry, rock strength, porosity and/or density of the formation being drilled. The chemistry change may indicate that a different type of rock is being drilled into, which may have different physical properties (e.g., hardness, plasticity, permeability, porosity, etc.). Drilling may be modified accordingly (e.g., the RPM, WOB etc. may be increased or decreased depending on the change in the formation). For example, if the formation is hard and the rock strength is high, a new drill bit with high density of cutting elements and small size of cutting elements may be used. If the formation is very plastic, a new shape of cutting elements such as scribe cutters may be used. If there is a change from a hard dolomitic limestone to a shale, one or more changes in drilling (e.g., introduction of drilling fluid to prevent the shale from hydrating, a reduction in the WOB or an increase in the lubrication of the drilling fluid) may be made. In some high pressure and high temperature cases, a roller cone bit may be used instead of a PDC bit. As another example, the detection of a change from a hard dolomitic lime stone to a shale may call for multiple changes in the drilling operation, such as drilling fluid to prevent the shale form hydrating, a reduction in the weight on bit, or an increase in the drilling fluid system&#39;s lubricity. Normally, these changes that would be made by an observer present at the bit. However, these changes would only be observed after the drilling fluid has carried the cutting to surface, a lag time in which the drilling fluid bit interaction is less than optimum and potentially damaging to the well. According to embodiments of the present disclosure, however, these changes may be made at a faster rate based upon events detected by the opto-analytical device. 
     Another event that an opto-analytical device  300  may detect is a change in from one material state (e.g., solid, liquid, gas) to another. Such changes may indicate, for example, the entrance or exit of the drilling tool with respect to a hollow pocket in the formation. As another example, such changes may indicate that the drilling tool has encountered or exited oil or gas reservoirs. For instance, an opto-analytical device  300  embodied in a horizontal strata reservoir may analyze material state to detect a water/oil interface and ensure the wellbore is above the water/oil interface. In addition, the opto-analytical device  300  may detect whether the bit has exited a certain zone of interest based on changes in material states. In the event of a detected change of material state, one or more modifications may be made to the drilling, such as lowering or increasing an RPM or changing the direction of the drilling. Furthermore, because the fluid flow and pressure balance at the surface of the formation is a critical process in drilling, uncontrolled flow into the formation (sometimes referred to as “blow out”) can destroy the formation and may stop drilling until the fluid loss is controlled. Thus, in some embodiments, an opto-analytical device may detect the flow of reservoir fluids into the well bore, separate from the fluids that were in the rock freshly drilled by the bit. Certain modifications may then be made to the drilling procedure based on the detected flow. For example, fine pressure control may be achieved by increasing the drilling fluid flow rate, which may increase the local pressure at the surface through dynamic forces (e.g., viscosity of the drilling fluid). This may help disperse the incoming formation fluid while the drilling fluid system bulk density is changed at surface and circulated into the hole. Normally, this process has a lag time. However, certain embodiments of the present disclosure may correct this using downhole detection of fluids entering the well bore. For instance, the amount of water in the drilling fluid system may be modified in order to stabilize the formation based on washouts of materials such as clay or shale lenses can be detected. 
     An opto-analytical device  300  may also be configured to detect pH of a downhole fluid sample and thus changes in pH. The changes in pH may indicate whether the downhole fluid sample is from drilling fluids or another fluid present in the wellbore (e.g., oil, or water). A change in pH may also indicate, for example, where a fluid of interest (or its source) is located in the formation. As an example, two sources of water may be encountered: salt or fresh water. The pH would be different for each case, thereby enabling an operator of the drilling tool to determine the source of the fluid (and thereby enable the user to ameliorate or enhance its influence, depending upon the desirability.) Depending upon what fluid is encountered, a user may want to not only change a drilling speed, for example, but also a drilling direction. As another example, in the event of formation water entering the well bore (which is usually low pH due to the dissolution of acid gases in the water (predominantly carbon dioxide and hydrogen sulfide)), the drilling fluid system may be modified to maintain at least a neutral to high pH. 
     In the same or alternative embodiments, opto-analytical device  300  may be configured to determine a change in total dissolved solids within a drilling fluid. Examples may include dissolved rocks or rock salt dissolved in the fluid. This information may indicate what material is being encountered in the formation or the chemical or physical composition of the formation. Based on this information, a user may want to make drilling modifications. For instance, if a salt dome is encountered, the operator may want to change drilling parameters, such as RPM, WOB, or drilling direction. 
     Additionally, opto-analytical device  300  may be configured to determine residual stress of a formation. Residual stress may indicate the location of where the formation may fracture, and may be determined based on the gauge of the wellbore, as measured by the opto-analytical device, shortly after the drill bit has passed. Based on the determined residual stress, one or more modifications may be made to the drilling. For example, an operator may change the direction of drilling in order to avoid locations where the formation may fracture. As another example, the drilling may be stopped after determining a certain level of residual stress in order to avoid potential explosive, toxic, or corrosive gases and/or chemicals. Additionally, the stress state of the formation may inform the decision to case the well and to control the risk in the casing operation. For instance, long open hole sections under high stress conditions may collapse or may cause a casing to stick in the wellbore as the shape of the wellbore gradually oblates (i.e., changes from circular to elliptical). The casing installation may be delayed by such sticking and geometric locking, sometimes resulting in the abandonment of a section of the well or a sidetrack drilling operation, leading to great economic consequences. 
     The above is merely a list of examples of events associated with drilling a wellbore that may be detected by an opto-analytical device  300 . Additionally, the modifications to drilling listed are merely listed as examples. Any number of drilling modifications may be made based on events detected or measurements performed by one or more opto-analytical devices  300 . 
     One or more opto-analytical devices, such as opto-analytical device  300 , may be integrated with one or more drilling tools of a bottom hole assembly such as BHA  120  of  FIG. 1 .  FIG. 4  illustrates a cross-sectional view of an example configuration of drill bit  101  having opto-analytical device  300  integrated therein. Drill bit  101  of  FIG. 4  may include a cavity  408  formed in bit body  124  and configured to house opto-analytical device  300  described in detail above with respect to  FIG. 3 . Cavity  408  may also include power source  404  configured to provide power to one or more components of opto-analytical device  300 . For example, in some embodiments, power source  404  may be any suitable type of battery. Power source  404  may also be a piezoelectric device configured to generate electricity based on the movement and vibration of drill bit  101  during a drilling process. Although shown as having only one power source  404 , cavity  404  may include any number of power sources  404  used in any suitable combination. For example, in some embodiments cavity  408  may include a battery power source and a piezoelectric power source. In the same or alternative embodiments, the piezoelectric power source may be configured as a primary power source when drill bit  101  is moving and the battery power source may be configured as a backup power source when drill bit  101  is not moving. Additionally, in some embodiments, the piezoelectric power source may be configured to charge the battery power source. Other power sources may include generators, or micro-generators deriving their power from the movement (or differential movement) of the bit itself, or the movement of the fluids, chemical batteries, solar power sources (which would derive their power from the infrared/visible electromagnetic radiation generated by the drill bits themselves), or nuclear sources. 
     Cavity  408  may also be configured to house electromagnetic radiation source  406 . Electromagnetic radiation source  406  may include any suitable apparatus, system, or device configured to generate electromagnetic radiation in a desired spectrum. For example, an electromagnetic radiation source  406  may be configured to generate infrared light, visible light, UV light, X-rays etc. As explained further below, the electromagnetic radiation from electromagnetic radiation source  406  may be directed toward a sample (e.g., formation, wellbore, drilling tool component, etc) such that the electromagnetic radiation from electromagnetic radiation source  406  impinges the sample. The electromagnetic radiation may then be transmitted, reflected, refracted, absorbed, etc. by the sample and received by opto-analytical device  300  to determine one or more characteristics of the sample. Electromagnetic radiation source  406  may be configured to receive power from power source  404 . 
     Cavity  408  may also be coupled to one or more channels  402  configured to direct electromagnetic radiation to opto-analytical device  300  or from electromagnetic radiation source  406 . Channels  402  may be formed in any suitable location of drill bit  101  to direct electromagnetic radiation to or from any desired location on drill bit  101 . In the illustrated embodiment, channels  402  are formed in a blade  126  to direct electromagnetic radiation to or from different locations on blade  126 . For example, channel  402   a  is configured to direct electromagnetic radiation to or from the face of cutting element  128 , channel  402   b  is configured to direct electromagnetic radiation to or from DOCC  129 , channel  402   c  is configured to direct electromagnetic radiation to or from a gage portion of blade  126  and channel  402   d  is configured to direct electromagnetic radiation to or from a location on a side face of blade  126 . The actual locations of channels  402  may vary according to the desired location of illumination of an area with electromagnetic radiation or a desired area for receiving electromagnetic radiation for analysis by an opto-analytical device  300 . 
     Channels  402  may be configured to direct electromagnetic radiation using any suitable method, system, or device. For example, one or more channels  402  may be filled with an optically transmissive material such as diamond or sapphire that may direct electromagnetic radiation through channels  402 . As another example, one or more channels  402  may be coated with a reflective material such as aluminum that may direct electromagnetic radiation through channels  402 . Additionally, one or more channels  402  may include an optical fiber, waveguide, or light pipe configured to carry and direct electromagnetic radiation. In some embodiments, the end of channels  402  opposite of cavity  408  may include windows  401  configured to prevent materials from entering the channels  402 . Windows  401  may be any optically transmissive material suitable for withstanding drilling conditions, such as diamond, sapphire, zinc sulfide and zinc sulfide coated zinc selenide. 
     In some embodiments, channels  402  may be configured to house one or more components of opto-analytical device  300 . For example, ICE  302  (described in  FIG. 3 ) may be included in one or more channels  402  behind windows  401  such that the ICE  302  may receive electromagnetic radiation at or near windows  401 . Additionally, detector  306  (described in  FIG. 3 ) may be placed behind ICE  302  in channels  402 . In the same or alternative embodiments, a plurality of ICEs  302  may be placed in series with each other in one or more channels  402 . 
     Accordingly, in accordance with the present disclosure, through the use of windows  401 , channels  402  and cavity  408 , drill bit  101  may be configured to have one or more opto-analytical devices  300 , power sources  404  and electromagnetic radiation sources  406  integrated therein. Therefore, drill bit  101  may be configured to direct electromagnetic radiation to and from desired locations such that the one or more opto-analytical devices  300  may analyze and detect one or more drilling characteristics. 
     Modifications, additions, or omissions may be made to  FIG. 4  without departing from the scope of the present disclosure. For example, the same principles described with respect to integrating opto-analytical device  300  with drill bit  101  may be used to integrate opto-analytical device  300  with any other drilling tool (e.g., a reamer, a stabilizer, etc.). Additionally, the locations and configurations of windows  401 , channels  402 , cavity  408 , power source  404 , electromagnetic radiation source  406  and opto-analytical device  300  are merely shown as a conceptual embodiment and the actual configuration may vary depending on the particular application. It will be understood by those of ordinary skill in the art that the illustrative examples and embodiments described herein for transmission modes (i.e. directing electromagnetic radiation toward a sample) would equally apply to absorptive or reflective implementations, and vice-versa. 
     One or more opto-analytical devices  300  may be configured to determine any number of performance indicators of a drilling tool. For example, one or more opto-analytical devices  300  may be configured to determine the size and quantity of cuttings created by cutting elements  128  cutting into a formation. In some embodiments, certain characteristics of the cuttings (e.g., size and/or number) may indicate the cutting efficiency of a drill bit. As such, it may be advantageous to monitor the cuttings in flow channels of the drill bit to determine if the drill bit is efficiently cutting into the formation.  FIG. 5  illustrates an example embodiment of drill bit  101  including one or more opto-analytical devices (not shown) configured to determine the size of cuttings  502  created by cutting elements  128 , in accordance with some embodiments of the present disclosure. The one or more opto-analytical devices may be located in any suitable location of drill bit  101  to determine the size of cuttings  502 . For example, the opto-analytical device may be located in channels of drill bit  101 , in windows  401  of drill bit, on one or more cutting elements  128  of drill bit  101 , on one or more DOCCs  129  of drill bit  101 , on one or more blades  126  of drill bit  101 , in one or more nozzles  156  of drill bit  101 , in fluid flow paths  240  of drill bit  101 , on shank  152  of drill bit  101 , or any other similar location for determining the size of cuttings  502 . In some embodiments, a processing unit  308  of opto-analytical device  300  may be configured to determine and store the size or other characteristic(s) of cuttings  502  as a function of time in a computer-readable medium to allow for retrieval of the data at a later time. In the same or alternative embodiments, the processing unit  308  may be configured to transmit the size determinations during drilling operations via any suitable MWD system. 
     In the illustrated embodiment, the leading face of blade  126   g  may include an electromagnetic radiation source (not expressly shown) and channel (not expressly shown) configured to direct electromagnetic radiation through window  401   a  of drill bit  101 . In some embodiments, the electromagnetic radiation source may be configured to generate visible light and may include an incandescent light source (e.g. tungsten), a light emitting diode (LED), a laser, a fluorescent and/or phosphorescent light source, a tribo-luminescent source, or any other suitable electromagnetic radiation source. 
     The electromagnetic radiation transmitted from window  401   a  may illuminate cuttings  502  that move through a flow channel of drill bit  101  and past window  401   a . Cuttings  502  may be pieces of a rock formation that are cut away by cutting elements  128 . In some embodiments, cuttings  502  may be directed past through the flow channel and window  401   a  by drilling fluid flowing out of a nozzle  156 . When the electromagnetic radiation impinges cuttings  502 , cuttings  502  may reflect the electromagnetic radiation. Window  401   b  of blade  126   g  may be configured to receive the electromagnetic radiation reflected by cuttings  502 . Window  401   b  may also be configured to direct the reflected electromagnetic radiation toward opto-analytical device  300  in channel  402  (described in  FIGS. 3 and 4 , and not expressly shown in  FIG. 5 ). Although not expressly shown, in some embodiments of drill bit  101  each blade  12  may include window  401   a  configured to direct electromagnetic radiation from an electromagnetic radiation source onto cuttings  502 . Additionally, although not expressly shown each blade  126  may include window  401   b  configured to receive electromagnetic radiation reflected by cuttings  502 . 
     Opto-analytical device  300  may be configured to detect the size of cuttings  502  based on the intensity of the electromagnetic radiation received by opto-analytical device  300  because electromagnetic radiation transmitted, reflected, or absorbed by the cuttings is correlated and/or related to the size and distribution of the cuttings. In some embodiments, opto-analytical device  300  may be configured to detect and determine an approximation of the maximum and/or minimum size of cuttings  502 . The sizes of the cuttings  502  may indicate the efficacy of cutting elements  128 . For example, if the sizes of cuttings  502  decrease, this may indicate that one or more cutting elements  128  are being worn and/or that cutting elements  128  have transitioned into cutting into a harder rock. Conversely, if the sizes of cuttings  502  increase, this may indicate that cutting elements  128  have transitioned into cutting into a softer rock. 
     In addition to determining the size of cuttings  502 , opto-analytical device  300  may be configured to determine other characteristics of cuttings  502  such as their chemical composition, hardness, etc. The chemical composition, hardness, etc. of the cuttings  502  may be compared with the sizes of the cuttings  502  to help better correlate the efficacy of cutting elements  128  with respect to different rock types. Accordingly, opto-analytical device  300  may measure and collect data that may be helpful in designing cutting elements for different formations having different properties (e.g., rock strength, stress, porosity, density, plasticity, rock type, rock composition, etc.). 
     Additionally, the efficacy and wear of cutting elements  128  (and thus the associated sizes of cuttings  502 ) may be based on the amount of drilling fluid moving past cutting elements  128 . For example, the drilling fluid may cool cutting elements  128  to prolong the life of cutting elements  128 . Additionally, the drilling fluid may help move cuttings  502  away from cutting elements  128  to allow cutting elements  128  to more effectively cut into the formation. The sizes of cuttings  502  may therefore indicate how much drilling fluid is reaching cutting elements  128 . For example, the size of cuttings  502  measured by one opto-analytical device  300  on drill bit  101  may be substantially smaller than the size of cuttings  502  measured by another opto-analytical device  300  on drill bit  101 , indicating that the cutting elements  128  associated with the smaller cuttings  502  may not be receiving a sufficient amount of drilling fluid. Therefore, the design of drill bit  101 , including the number, size, and/or orientation of nozzles  156 , may be modified to better deliver drilling fluid to those cutting elements  128 . 
     One or more opto-analytical devices  300  may also be configured to determine the concentration of cuttings  502  in the drilling fluid moving past window  401   b  based on the size and distribution of the cuttings. The concentration of cuttings  502  may indicate the efficacy of cutting elements  128  where a higher concentration of cuttings  502  may indicate a higher cutting efficiency and a lower concentration of cuttings may indicate a lower efficiency of cutting elements  128 . Additionally, a higher concentration of cuttings  502  may indicate a higher rate of penetration than a lower concentration of cuttings  502 . Furthermore, a concentration of cuttings  502  as measured by one of opto-analytical devices  300  that is lower than the concentration of cuttings  502  measured by another opto-analytical device  300  on drill bit  101  may indicate that cutting elements  128  on different areas of drill bit  101  are cutting into the formation at different depths. Also, the concentration of cuttings  502  in drilling fluid may indicate the efficacy of nozzles  156  in delivering drilling fluid to cutting elements  128  to carry cuttings  502  away from cutting elements  128 . One or more cutting elements  128  and/or nozzles  156  may accordingly be designed based on the cuttings concentration measurements to improve the flow of fluid past cutting elements  128  and/or the efficacy of cutting elements  128 . 
     One of skill in the art will appreciate that one or more characteristics of cuttings  502  may be determined at any location in the wellbore. For instance, one or more characteristics of cuttings  502  may be determined further uphole than drill bit  101 . For example, by measuring the size of cuttings  502  both at drill bit  101  and further uphole, it may be determined that the size of cuttings  502  is changing as they are removed from wellbore  114 . An increase in the size cuttings  502 , for example, may indicate that cuttings  502  have expanded in the drilling fluid. Accordingly, the amount or composition of the drilling fluid may be altered to avoid cuttings  502  from increasing or decreasing in size as they are removed from wellbore  114 . 
     Therefore, one or more opto-analytical devices  300  may be configured to determine one or more characteristics of cuttings  502  such as the size, porosity, composition, and/or the amount or concentration of cuttings  502 . The characteristics of cuttings  502  may indicate the efficacy of one or more components of a drilling tool, such as cutting elements  128  and nozzles  156 , as well as the performance of the drilling tool itself (e.g., the rate of penetration of the drilling tool). The size of cuttings may be directly related to the depth of cut per revolution of cutting elements (which is a function of bit rotational speed and ROP or WOB). Therefore, for a given drill bit, the size of cuttings may indicate whether an applied WOB and/or bit rotational speed leads to efficient drilling. Accordingly, any suitable change, including the modification of the WOB, RPM, or direction or orientation of the drill bit, may be made as necessary or dictated by the determined characteristics. In addition, control and modulation of the fluid through individual jets may be accomplished based on the determined cuttings sizes, which is very desirable. The drilling fluid through each nozzle  156  may modulated to optimize rate of penetration by keeping individual cutters cool, transporting cuttings, and hydraulically jet-drilling softer formations. Taken to an extreme, the modulated flow can cause cavitation at the rock surface, causing the rock to fail and allowing spoil to be transported uphole. 
     Modifications, additions, or omissions may be made to  FIG. 5  without departing from the scope of the present disclosure. For example, a roller cone drill bit, a reamer or any other drilling tool may be similarly configured to detect one or more characteristics of cuttings  502 . Additionally, the locations of windows  401  and the particular electromagnetic radiation source may vary depending on the application. 
       FIG. 6  illustrates an example method  600  for analyzing cuttings associated with drilling a wellbore, in accordance with some embodiments of the present disclosure. Method  600  may be performed by any suitable system, apparatus, or device. In the present example, method  600  may be performed using a drill bit  101  configured as described with respect to  FIG. 5 . However, method  600  may be performed using any suitable drilling tool configured to analyze cuttings created by the drilling tool. 
     Method  600  may start and at step  602  drill bit  101  may be used to drill a wellbore by cutting into a geological formation. At step  604 , an electromagnetic radiation source, located in a first channel formed in drill bit  101  may direct electromagnetic radiation through a first window and toward cuttings created by drill bit  101  cutting into a formation. The window and channel may be located at any suitable location on drill bit  101 . At step  606 , opto-analytical device  300  of drill bit  101  may detect electromagnetic radiation from the electromagnetic radiation source that reflects off of the cuttings. The electromagnetic radiation may be directed to opto-analytical device  300  via the first window and first channel, where opto-analytical device  300  is located. Alternatively, as described with respect to  FIG. 5 , the electromagnetic radiation may be directed to opto-analytical device  300  via a second window and a second channel, where opto-analytical device  300  is located. In one embodiment, the second window may be located on a second blade opposite of the first window, as shown in  FIG. 5 . In another embodiment, the second window may be located on the same blade as the first window where opto-analytical device  300  is located. 
     At step  608 , opto-analytical device  300  may detect and determine one or more characteristics of cuttings  502  based on the electromagnetic radiation received from the cuttings. As described above with respect to  FIG. 5 , example characteristics of cuttings  502  that may be detected and determined are the size, porosity, composition, and/or the amount or concentration of cuttings  502 , or any combination thereof. These characteristics may be used to determine the amount of desirable and/or undesirable materials inside the formation. 
     At step  610 , the characteristics associated with the cuttings may be analyzed. For example, the sizes, shapes, and/or concentrations of cuttings as measured by different opto-analytical devices  300  located at different areas of drill bit  101  may be analyzed to compare the cutting efficiency of cutting elements  128  at different locations of drill bit  101 . Additionally, the sizes and/or concentrations of the cuttings may be compared with the chemical composition of the cuttings to determine cutting efficiency for different formation types. Further, the sizes, shapes, and/or concentrations of the cuttings may be analyzed to determine the efficacy of nozzles  156  in delivering drilling fluid to cutting elements  128 . The sizes, shapes, and/or concentrations of the cuttings may also be used to determine the effectiveness of the drilling fluid such as drilling fluid density and drilling fluid capacity. In addition, the cutting characteristics may also indicate a certain drilling direction or bit orientation. 
     At step  612 , one or more parameters of drill bit  101  may be modified based on the analysis of the cuttings. For example, the sizes and/or concentrations of cuttings at different locations of drill bit  101  may indicate uneven cutting by cutting elements  128  and/or fluid distribution by nozzles  156 . Accordingly, the placement, size, and/or configuration of one or more nozzles  156  and/or cutting elements  128  may be modified to achieve more even cutting and/or fluid distribution. Further, the sizes and/or concentrations of the cuttings with respect to the composition of the cuttings may indicate the efficacy of cutting elements  128  with respect to formations having that particular composition. Accordingly, determinations may be made regarding whether or not the design of cutting elements  128  may be modified to improve cutting into formations having similar compositions. For example, if the equivalent circulating density (ECD) of the drilling fluid becomes too high, the formation could be damaged. Accordingly, decreasing the ROP by reducing the WOB or RPM may result in a lower rate of cuttings entering the fluid flow and may reduce the equivalent density of the drilling fluid. For example, the size of cuttings for a given formation may be directly related to the density of cutting elements on the bit face. The small size of the cuttings may indicate that the cutting elements grind the formation with low cutting efficiency. In this case, the number of blades and the number of cutting elements on the drill bit may be reduced. As another example, the drilling direction or bit orientation may be altered based on the determined cuttings characteristics. 
     Another performance indicator of a drilling tool that may be measured by opto-analytical device  300  may be the temperature of one or more cutting elements  128 . In some embodiments, an increase in temperature of a cutting element may indicate an increased force on the drill bit and/or significant wear of the cutting element. As such, it may be advantageous to monitor the temperature of one or more cutting elements on the drill bit to determine if there is increased force on the drill bit or excessive wear of the cutting elements in order to modify the drilling conditions.  FIG. 7A  illustrates an example embodiment of temperature sensor  700  including opto-analytical device  300  configured to measure the temperature of cutting element  128  of drill bit  101 . Temperature sensor  700  may include channel  702  (similar to channels  402  described with respect to  FIG. 4 ) formed in cutting element  128  and blade  126 . In the illustrated embodiment, channel  702  may be behind face  704  of cutting element  128 . Channel  702  may be configured to direct infrared electromagnetic radiation to opto-analytical device  300  including ICE  302  (as illustrated in  FIG. 3 , and not expressly shown in  FIG. 7A ) configured to detect temperature based on a spectral signature associated with temperature.  FIG. 7B  illustrates example spectral signatures  706  and  708  of a material for temperatures of approximately 900 degrees and 700 degrees, respectively. The y-axis shown is the spectral radiant density with units of W/(nm*m^2) and the x-axis shown is the wavelength with unit of nm. In some embodiments, a processing unit of an opto-analytical device (e.g., opto-analytical device illustrated in  FIG. 3 ) of temperature sensor  700  may be configured to determine and store the temperature as a function of time in a computer-readable medium to allow for retrieval of the data at a later time. In the same or alternative embodiments, the processing unit  308  may be configured to transmit the temperature measurements during drilling operations via any suitable MWD system. 
     The amount of wear of cutting elements  128  may be based on a variety of factors including cutting force, cutting speed and cutting element temperature. Additionally, as cutting element  128  wears, it may be less effective at cutting into a formation such that the temperature of the cutting element  128  may increase. Further, as drilling conditions change (e.g., the formation changes), the efficacy of cutting element  128  may also change such that the temperature of the cutting element  128  changes. Accordingly, temperature sensor  700  may be used to determine any number of drilling characteristics based on the temperature of one or more cutting elements  128 . Additionally, processing the signal of temperature sensor  700  may yield an acoustic signature of a formation, which may be used in determining a formation type and/or wear conditions of cutting elements  128 . 
       FIG. 7C  illustrates an example configuration of temperature sensors  700  integrated with cutting elements  128  and configured to indicate one or more drilling characteristics based on the temperature of cutting elements  128 . In the illustrated embodiment cutting element  128   b , which is on a cone portion of blade  126  of drill bit  101 , may include a temperature sensor  700   a  integrated therein, such as shown with respect to  FIG. 7A . Cutting element  128   d , which is located within a nose portion of blade  126 , may include temperature sensor  700   b  integrated therein. Temperature sensors  700   a  and  700   b  may be configured to measure the temperatures of cutting elements  128   b  and  128   d , respectively. In some embodiments, temperature sensors  700   a  and  700   b  may be configured to store the temperatures as a function of time in a computer-readable medium, such that the measurements may be retrieved at a later time. In other embodiments, the measurements may be communicated to the well site using any suitable MWD system. 
     The temperature measurements of cutting elements  128   b  and  128   d  over time may indicate one or more drilling characteristics.  FIG. 7D  illustrates example plots  710  and  712  of the temperatures of cutting elements  128   b  and  128   d  as a function of time, according to some embodiments of the present disclosure. Both plots  710  and  712  show a relatively rapid increase in temperature at time t 1 . In many drilling cases, cutting elements located on the cone portion of a blade (e.g., cutting element  128   b ) may experience little wear. Therefore, a relatively rapid increase in temperature of cutting element  128   b  at time t 1  may indicate that a drilling condition has changed (e.g., the formation hardness has increased). Additionally, the increase in temperature at time t 1  of both cutting elements  128   b  and  128   d  may indicate that the increase in temperature may be caused by a change in drilling conditions. 
     However, plot  712  shows an increase in temperature of cutting element  128   d  at time t 2  while plot  710  does not show an increase in temperature of cutting element  128   b  at time t 2 . Therefore, the temperature increase at time t 2  in plot  712  may indicate wear of cutting element  128   d  (and perhaps cutting elements  128  located near cutting element  128   d ). Similarly, the lack of a substantial temperature increase of cutting element  128   b  at time t 2  in plot  710  may indicate little to no wear of cutting element  128   b  (and perhaps cutting elements  128  near cutting element  128   b ). Therefore, one or more temperature sensors  700  that include opto-analytical device  300  may be integrated with a drill bit to detect one or more drilling characteristics such as cutting element wear, drilling condition changes, etc. 
     Based on a comparison of the temperatures of cutting elements  128   b  and  128   d , one or more drilling factors may be modified. In some embodiments, WOB may be modified based on the comparison. For example, if the temperature of a particular cutting element increases significantly, this cutting element may be subjected too much force. Thus, WOB may be lowered in such a condition. As another example, if the temperature of one or more cutting elements in a nose zone of the drill bit increases, but the temperature of the cutting elements in the cone zone of the drill bit remains the same or does not increase significantly, cutting elements in the nose zone may be subjected to too much wear. Accordingly, the amount of drilling fluid may be modified based on the comparison. For example, a high temperature at both cutting elements may indicate the need for additional drilling fluid for lubricant. Accordingly, more drilling fluid may be added. As another example, drilling may be slowed or stopped if high bit temperatures are sensed in order to avoid certain types of gases escaping to the surface of the drilling site. As yet another example, drilling may be stopped in order to service or otherwise perform maintenance on the drill bit. 
     Modifications, additions, or omissions may be made to  FIGS. 7A-7D  without departing from the scope of the present disclosure. For example, the particular placement and configuration of temperature sensors  700  depicted in  FIGS. 7A-7D  is for illustrative purposes only. The placement, number, and configuration of temperature sensors  700  may vary depending on the application. Additionally, temperature sensor  700  may be used to determine the temperature of any number of objects associated with drilling (e.g., the formation, the drilling fluid, other components of a drill bit, drilling tool or the drill string) and is not limited to determining the temperature of a cutting element  128 . Furthermore, opto-analytical device  300  of temperature sensor  700  may be configured to detect any number of other drilling characteristics (e.g., chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like) while also determining temperature measurements. 
       FIG. 8  illustrates an example method  800  for determining one or more drilling characteristics based on temperature, in accordance with some embodiments of the present disclosure. Method  800  may be performed by any suitable system, apparatus, or device. In the illustrated embodiment, method  800  may be performed using a drill bit  101  configured with a temperature sensor  700  as described with respect to  FIGS. 7A-7D . However, method  800  may be performed using any suitable drilling tool configured to analyze cuttings created by the drilling tool. 
     Method  800  may start and at step  802  drill bit  101  may form a wellbore by drilling into a geological formation. At step  804 , electromagnetic radiation associated with heat of a cutting element  128  may be received by channel  702  associated with a temperature sensor  700 , as described above with respect to  FIG. 7A . At step  806 , temperature sensor  700  may detect and determine the temperature of the cutting element  128  using an opto-analytical device  300  included in temperature sensor  700 , as described above with respect to  FIGS. 7A-7D . In some embodiments, temperature sensor  700  may be configured to store the temperature of the cutting element  128  as a function of time in a computer readable medium, or may be configured to transmit the temperature of the cutting element  128  as a function of time uphole via a MWD system. 
     At step  808 , temperature sensor  700  determines whether there has been a change in temperature. If a temperature change has been detected at step  808 , the method moves to step  810 , where one or more drilling parameters may be modified based on the detected change in temperature. For instance, if a temperature increase is detected, it may indicate that the input mechanical energy to the bit is too high and either RPM or WOB may be reduced. A higher temperature associated with cutting elements may also indicate that the cuttings created on bottom may not be properly cleared and drilling fluid density and/or speed at which drilling fluid is introduced may be adjusted. If drilling in a high pressure and high temperature formation, measurement of temperature becomes even more important. As another example, a change in temperature may indicate a transition from one formation type to another, which may require one or more parameters (e.g. amount/composition/flow rate of drilling fluid, power applied to drill bit  101 , RPM, WOB, etc.) to be modified for optimum drilling of the new formation type. Further, as explained above with respect to  FIGS. 7C and 7D , an increase in temperature may indicate wear of one or more cutting elements  128 . Accordingly, the drill bit  101  may be replaced or modified in response. For instance, the design or configuration of cutting elements  128  may be modified based on the temperature measurements of one or more cutting elements  128  during drilling to improve the efficacy of the cutting elements. In addition, the temperature of one or more cutting elements  128  during drilling may also be used to validate or invalidate the arrangement of nozzles  156  on a bit body. For example, if the temperature of a cutting element in the cone zone is higher than that of a cutting element in the nose or gage zones, then the orientation of one or more nozzles in the cone zone may be adjusted or the number of nozzles may be increased to provide an improved flow pattern for the drilling fluid over the cutting elements in the cone zone. If no temperature change is detected at step  808 , however, the method moves to step  812  where drilling continues without any modification to drilling parameters. 
     Modifications, additions, or omissions may be made to method  800  without departing from the scope of the present disclosure. For example, any number of other drilling characteristics (e.g., chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like) may be determined while also determining temperature measurements of cutting elements  128 . In addition, temperature measurements may be taken from any portion of the drilling tool and/or formation, in addition to or in lieu of cutting elements  128 . Further, other opto-analytical devices  300  may analyze properties of cutting element  128  other than temperature, while the temperature of the cutting element is being monitored. 
     An opto-analytical device  300  may also be configured to determine torsion (also known as windup) of a drill string.  FIG. 9  illustrates an example configuration of BHA  120  including opto-analytical devices  300   a  and  300   b  configured to determine torsion of the drill string associated with BHA  120 . In some embodiments, a processing unit of opto-analytical device  300  may be configured to determine and store the amount of torsion as a function of time in a computer-readable medium to allow for retrieval of the data at a later time. In the same or alternative embodiments, processing unit  308  may be configured to transmit the torsion determinations during drilling operations via any suitable MWD system. 
     The torsion or windup of the drilling tool may be measured by recognizing changes in rotational velocity of the drill bit, and by matching up reamer data to determine the amount of torque present in the drill strip. The combination of tool phase and a real time composition/porosity map can be used to locate the position of the drilling tool in the formation. Opto-analytical device  300  may sense an identifiable feature in the formation as the tool rotates thereby providing an extremely accurate measurement of rotational velocity of the bit. In some embodiments, the identifiable feature in the formation may be a line or gouge running vertically on the wellbore, and may be naturally occurring or may be placed in the wellbore by a drilling operator. In other embodiments, the identifiable feature in the formation may be some compositional change in the formation such as fracture plane or bedding plane. By measuring the amount of time between detections of the identifiable feature, an operator can see the bit speed up or slow down, such as for instance, in response to various formation conditions encountered. Assuming constant power to the tool, a slow down in rotational velocity may indicate a harder rock, and thus increased torque on the bit and torsion of the drilling tool. 
     In certain embodiments, two or more opto-analytical devices  300  may be separated by a distance along the vertical length of the drilling tool, allowing the detection of a radial offset between the two sensors. This offset may be determined based on the detections of the identifiable feature in the formation described above. Alternatively, the offset may be determined based on the position of the two sensors with respect to one or more points on the drilling tool. Based on the determined offset, the distance between the sensors, the material properties of the tool, cross sectional dimensions of the wellbore, or other factors, the amount of torsion in the drilling tool may be determined. Since there are dynamic and physical limits to the amount of torsion that can be tolerated in a drilling system, drilling may then be slowed or stopped when high amounts of torsion are detected, thereby avoiding any negative consequences such as torsional locking of the bit (i.e., sticking in the formation), sudden releases of the torsional energy in the drill, unwinding of the pipe joint, tearing of the drill pipe, etc. 
     Modifications, additions, or omissions may be made to  FIG. 9  without departing from the scope of the present disclosure. For example, the illustrated embodiment depicts drill bit  101  and reamer  902  integrated with opto-analytical devices  300   a  and  300   b , respectively, to determine torsion of the drilling tool. However, any combination of drill bit  101 , reamer  902 , hole enlarger  904  and/or stabilizer  906  (or any other suitable drilling tool) may include one or more opto-analytical devices  300  to determine torsion. Furthermore, opto-analytical device  300  may be configured to detect any number of other drilling characteristics (e.g., chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like) while also determining torsion. 
       FIG. 10  illustrates an example method  1000  for determining torsion of a drilling tool in accordance with some embodiments of the present disclosure. Method  1000  may be performed by any suitable, system, apparatus, or device. In the illustrated embodiment, method  1000  may be performed using opto-analytical device  300  described with respect to  FIG. 9 . 
     Method  1000  may start and at step  1002 , drill bit  101  may form a wellbore by drilling into a geological formation. The method proceeds to step  1004 , where opto-analytical device  300  directs electromagnetic radiation toward an object (e.g., the wall of a wellbore  114 ). At step  1006 , opto-analytical device  300  mounted on a drilling tool (e.g. a drill bit, a reamer, a stabilizer, a hole enlarger, etc.) receives electromagnetic radiation reflected from a wellbore. Then, at step  1008 , opto-analytical device  300  detects an identifiable feature in the object. For instance, the identifiable feature in the object may be a line or gouge running vertically on the wellbore, and may be naturally occurring or placed in the wellbore by a drilling operator. In other embodiments, the identifiable feature in the formation may be some compositional change in the formation such as fracture plane or bedding plane. In particular embodiments, the identifiable feature may be detected based on the detection of a deviation in the electromagnetic radiation received at a point in time, and may include peaks/spikes or valleys/dips in the amount of radiation being received at a particular point in time. 
     At step  1010 , opto-analytical device  300  determines a torsion in the drilling tool. This may be accomplished, for example, by determining a velocity of the drill bit over time based on the period of the deviations detected in the received electromagnetic radiation. This will provide an observed velocity over time. Based on changes in the velocity over time, the opto-analytical device may determine an amount of torsion in the drill bit at step  1010 . As another example, two or more opto-analytical devices  300  may be separated by a distance along the vertical length of the drilling tool, allowing the detection of a radial offset between the two sensors, as described above. Based on the determined offset, the distance between the sensors, the material properties of the tool, the cross sectional dimensions of the wellbore, and/or other factors, the amount of torsion in the drilling tool may be determined. This may assist the operator in determining, for example, whether the drill bit is twisting or turning in the wellbore, and may allow the operator to make one or more modifications at step  1012 . For instance, the operator may increase or reduce the amount of power to the drill tool, add or remove WOB, add or remove drilling fluid, change the chemistry of the drilling fluid, or stop the drilling entirely based on the determined amount of torsion. 
     Modifications, additions, or omissions may be made to  FIG. 10  without departing from the scope of the present disclosure. For example, any number of other drilling characteristics (e.g., chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like) may be determined while also determining torsion. 
     Another performance indicator of a drilling tool that may be measured by opto-analytical device  300  may be the distance or gap between, for example, an object on the drilling tool (e.g., a cutting element, an impact arrestor, a nozzle, a blade, the bit body, etc) and another object in the wellbore (e.g., the side wall of the wellbore). In some embodiments, the gap between an object on the drill bit and an object in the wellbore may indicate bit whirl, bit walk, worn cutting elements, vibration of a bit, and/or tilt of a bit. As such, it may be advantageous to monitor the gap between the object on the drill bit and the object in the wellbore to determine if bit whirl (i.e., movements of the bit away from its rotational axis), bit walk (i.e., the lateral movement of the bit as drilling progresses over time), worn cutting elements, vibration of a bit, and/or tilt of a bit is present.  FIG. 11  illustrates an example embodiment of a gap sensor  1100  configured to determine the gap between objects using an opto-analytical device  300 , according to some embodiments of the present disclosure. 
     Gap sensor  1100  may include electromagnetic radiation source  406  configured to direct electromagnetic radiation toward object  1102  (e.g., a wall of a wellbore, drilling fluid cake, etc.) such that the electromagnetic radiation reflects off of object  1102  toward opto-analytical device  300 . Gap sensor  1100  may be located in one or more channels of drill bit  101 , in one or more windows  401  of drill bit, on one or more cutting elements  128  of drill bit  101 , on one or more DOCCs  129  of drill bit  101 , on one or more blades  126  of drill bit  101 , in one or more nozzles  156  of drill bit  101 , in fluid flow paths  240  of drill bit  101 , on shank  152  of drill bit  101 , a reamer, a stabilizer, or any other similar location for determining the gap between drill bit  101  and object  1102 . Processing unit  308  of opto-analytical device  300  of  FIG. 11  may be configured to determine the distance between the object and gap sensor  1100  based on reflected electromagnetic radiation from object  1102 . Because the intensity of the reflected electromagnetic radiation received is based in large part by the inverse square law of light, the distance may be determined based on the ratio of the respective intensities of the electromagnetic radiation directed toward object  1102  and the electromagnetic radiation reflected back from object  1102 . Alternatively, in other embodiments, the gap may be determined when detector  306  of opto-analytical device  300  includes a split detector, quad detector, array detector, or imaging device. In such embodiments, the gap may be encoded in the electromagnetic radiation detected by the various detector sub-elements, and may be determined through certain signal processing techniques. For example, in some embodiments, the optical train can be configured so that the gap is related to difference between sub-elements while the characteristic signal is obtained from the sum of the sub elements. In other embodiments, the gap signal may be derived from a more complex relationship between the subelements (e.g., in a quad detector, subelement  1  plus subelement  2  minus subelement  3  minus subelement  4 ) in parallel with detection of the characteristic signal which in general is obtained by the sum of the sub-element signals. 
     Processing unit  308  of opto-analytical device  300  of gap sensor  1100  may be configured to store the gap measurements as a function of time in a computer-readable storage medium such that the gap measurements may be retrieved at a later time after drill bit  101  has been removed from a wellbore (e.g., wellbore  114  as illustrated in  FIG. 1 ). In the same or alternative embodiments, processing unit  308  may be configured to transmit the gap measurements to the well site while drill bit  101  is in the wellbore via any suitable MWD system. 
     The gap as measured by gap sensor  1100  may be used to determine any number of drilling characteristics. For example, one or more gap sensors  1100  may be used to determine bit motion, including, but not limited to, bit whirl, bit walk and bit tilt. Additionally, one or more gap sensors  1100  may be used to determine the depth of cut of cutting elements and/or wear of cutting elements. For example, three or more gap sensors may be mounted circumferentially on a drill bit to estimate the diameter of the hole drilled by the drill bit. An oversized hole may be due to bit wear, downhole vibration, and/or unexpected tilt angle of downhole motor. Likewise, a change in the symmetry of the hole may raise issues for future drilling activities such as laying casing in the hole or for changing drilling direction. In addition, the determined gap may be used to calculate the volume of the hole, which is a vital calculation for drilling operation design. Such calculations are used, for example, in determining drilling fluid circulation volume and cementing operation parameters. 
     Modifications, additions, or omissions may be made to gap sensor  1100  without departing from the scope of the present disclosure. For example, opto-analytical device  300  of gap sensor  1100  may be configured to detect any number of other drilling characteristics (e.g., chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like) while also determining gap measurements. 
     Gap sensors  1100  may be configured to determine the bit whirl and bit walk of a drill bit in a wellbore.  FIGS. 12A-12C  illustrate an example of bit whirl of drill bit  101  in wellbore  114 , according to some embodiments of the present disclosure. In  FIG. 12A , drill bit  101  may rotate around its center (Ob) at an angular radian frequency (ω). Additionally, in some instances, bit center Ob may whirl around the center of wellbore  114  (Oh) at a whirl radian frequency (Ω). The radius of the bit whirl (ΔR) may be expressed as the distance between the drill bit center (Ob) and the wellbore center (Oh). Points A, B and C, of drill bit  101  may be points on the bit body of drill bit  101  (e.g., on the gage pad of drill bit  101 ) and points A 1 , B 1 , and C 1  may points on the wall of wellbore  114  at a time t that correspond with points A, B, and C, respectively. In the present embodiment, drill bit  101  may include gap sensor  1100  at each of points A, B, and C to determine the gap between points A and A 1  (AA 1 ), points B and B 1  (BB 1 ) and points C and C 1  (CC 1 ) respectively. 
     The coordinates of points A 1 , B 1 , and C 1  in a Cartesian coordinate system with an x-axis (Xb) and a y-axis (Yb) intersecting at the center of drill bit  101  (Ob) may be expressed by the following equations:
 
 X   A1 =( Rb+AA 1)cos(α a ), Y   A1 =( Rb+AA 1)sin(α a );
 
 X   B1 =( Rb+BB 1)cos(α b ), Y   B1 =( Rb+BB 1)sin(α b );
 
 X   C1 =( Rb+CC 1)cos(α c ), Y   C1 =( Rb+CC 1)sin(α c );
 
     Where Rb is the radius of drill bit  101  and αa, αb and αc are the angles of points A, B, and C with respect to axis Xb (αa and αb are expressly shown in  FIG. 12 ). 
     If it is assumed that wellbore  114  is substantially circular, then the coordinates of points of A 1 (X A1 , Y A1 ), B 1 (X B1 , Y B1 ) and C 1 (X C1 , Y C1 ) obtained above may be located on the circle. The center coordinates (Xo, Yo) and the radius Rh of the circle may be determined by solving the following equations: 
                            2   ⁢   XA   ⁢           ⁢   1           2   ⁢   YA   ⁢           ⁢   1           -   1               2   ⁢   XB   ⁢           ⁢   1           2   ⁢   YB   ⁢           ⁢   1           -   1               2   ⁢   XC   ⁢           ⁢   1           2   ⁢   YC   ⁢           ⁢   1           -   1                ⁢     {         Xo           Yo           q         }       =     {             XA   ⁢           ⁢     1   2       +     YA   ⁢           ⁢     1   2                     XB   ⁢           ⁢     1   2       +     YB   ⁢           ⁢     1   2                     XC   ⁢           ⁢     1   2       +     YC   ⁢           ⁢     1   2               }           
Where the hole radius Rh may be expressed as:
 
             Rh   =         Xo   2     +     Yo   2     -   q             
and the whirl radius may be expressed as:
 
Δ R =√{square root over ( Xo   2   +Yo   2 )}
 
     Additionally, the whirl frequency of drill bit  101  may be obtained by plotting the trajectory of the center of drill bit  101  in the XY plane of a coordinate system with an x-axis (Xh) and y-axis (Yh) intersecting at the center of wellbore  114  (Oh) at time t where: the x-coordinate of Ob with respect to Xh equals Xo(t) and the y-coordinate of Ob with respect to Yh equals Yo(t). The value of Xo(t) and Yo(t) may be obtained by solving the above equation at time instant t. 
       FIG. 12B  illustrates an example plot of Xo of the center of drill bit  101  (Ob) with respect to time. The whirl frequency (Ω) may be determined based on the period (Δt) of the wave of the plot of  FIG. 12B  as expressed by the equations below. 
     
       
         
           
             
               ΩΔ 
               ⁢ 
               
                   
               
               ⁢ 
               t 
             
             = 
             
               
                 2 
                 ⁢ 
                 π 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 or 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 Ω 
               
               = 
               
                 
                   2 
                   ⁢ 
                   π 
                 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   t 
                 
               
             
           
         
       
     
     The whirl frequency (Ω) of drill bit  101  may also be determined by performing a Fast Fourier Transform (FFT) on either Xo(t) or Yo(t). 
     The bit angular rotational frequency (w) may be obtained by plotting the distance of AA 1  (or BB 1  or CC 1 ) as a function of time.  FIG. 12C  illustrates an example plot of AA 1  as a function of time. In  FIG. 12C , the bit angular rotational frequency (ω) may be determined based on the period (Δt) of the wave of the plot of  FIG. 12C  as expressed by the equations below. 
     
       
         
           
             
               ωΔ 
               ⁢ 
               
                   
               
               ⁢ 
               t 
             
             = 
             
               
                 2 
                 ⁢ 
                 π 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 or 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 ω 
               
               = 
               
                 
                   2 
                   ⁢ 
                   π 
                 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   t 
                 
               
             
           
         
       
     
     Performing an FFT on either AA 1 ( t ) or BB 1 ( t ) or CC 1 ( t ) may also result in obtaining the bit rotational frequency (ω) of drill bit  101 . 
     Accordingly, a plurality of gap sensors  1100  including opto-analytical devices  300  may be configured to determine and record the whirl of drill bit  101  in accordance with some embodiments of the present disclosure. The whirl of drill bit  101  as measured and determined using gap sensors  1100  may be used to improve the design of drill bit  101  to decrease whirl. For example, several anti-whirl technologies, including low-friction pads (as described in U.S. Pat. No. 4,932,484 and hereby incorporated by reference in its entirety), and track-loc cutter arrangement (as described in U.S. Pat. No. 5,265,685 and hereby incorporated by reference in its entirety) may be used to avoid bit whirl. If whirl is detected during drilling, an operator may decrease bit rotational speed and/or increase weight on bit in order to avoid whirl. Additionally, as mentioned above, opto-analytical devices  300  of gap sensors  1100  may be configured to detect, determine and record any number of other drilling characteristics such as properties of the formation being drilled (e.g., chemical composition, rock strength, plasticity, porosity, etc.) Therefore, in some embodiments, formation characteristics may be correlated with the detected amount of bit whirl to determine which formations may cause the most or least whirl of drill bit  101 . 
     Additionally, the trajectory of the center of drill bit  101  (Ob) in the XhYh plane may be determined by plotting the x and y coordinates of Ob at different times t in the XhYh plane (Xo(t) and Yo(t), respectively). The locations of the points ((Xo(ti), Yo(ti)) in the XhYh plane may accordingly indicate bit walk of drill bit  101 .  FIG. 12D  illustrates example plots  1202  and  1204  of points ((Xo(ti), Yo(ti)) that indicate the bit walk of two drill bits  101 . Plot  1202  indicates a trajectory of the center of the associated drill bit  101  that is up and to the left, thus, indicating that the associated drill bit  101  may walk up and to the left with respect to the XhYh plane. In contrast, plot  1204  indicates a trajectory of the center of the associated drill bit that is up and to the right, thus, indicating that the associated drill bit  101  may walk up and to the right, with respect to the XhYh plane. Plots  1202  and  1204  are merely examples of bit walk and a drill bit  101  may walk in any number of directions. 
     Accordingly, a plurality of gap sensors  1100  including opto-analytical devices  300  may be configured to determine and record the bit walk of a drill bit  101  in accordance with some embodiments of the present disclosure. The bit walk of the drill bit  101  as measured and determined using gap sensors  1100  may be used to improve the design of drill bit  101  to decrease the walk of drill bit  101 . For example, if gap sensors  1100  determine that the bit walks left, a deep cone profile may be needed to reduce the walk left tendency. Additionally, a small gauge pad may help to reduce bit walk left. Conversely, if gap sensors  1100  determine that the bit walks right, a shallower cone profile and/or a larger gage pad may be needed to reduce the walk right tendency. Furthermore, the bit walk of the drill bit  101  as measured and determined using gap sensors  1100  may be used to guide the rotary steerable system to change drilling azimuth direction to follow the desired drilling path. Additionally, as mentioned above, the opto-analytical devices  300  of gap sensors  1100  may be configured to detect, determine and record any number of other drilling characteristics such as properties of the formation being drilled (e.g., chemical composition, rock strength, plasticity, porosity, etc.) Therefore, in some embodiments, formation properties may be correlated with bit tilt to determine which formations may cause the most or least bit walk of drill bit  101 . 
     Modifications, additions, or omissions may be made to  FIGS. 12A-12D  without departing from the scope of the present disclosure. For example, the coordinate systems used and their respective orientations are for illustrative purposes only, any suitable coordinate system may be used. Additionally, the equations used to determine bit whirl and bit walk using the gap between a drill bit and wall of a wellbore are for illustrative purposes and any other suitable equation or expression may be used to determine bit whirl and bit walk. Additionally, as mentioned above, the opto-analytical devices of gap sensors may be configured to detect any number of other drilling characteristics (e.g., chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like) while also being used to determine bit walk and/or bit whirl. Accordingly, bit walk and/or bit whirl may be correlated with other properties of the formation being drilled into. 
     Gap sensors  1100  may also be configured to determine the tilt and tilting motion of drill bit  101  in wellbore  114 .  FIG. 13A  illustrates a cross-sectional view of an example configuration of drill bit  101  including gap sensors  1100   a  and  1100   b  configured such that tilt and tilting motion of drill bit  101  may be determined, according to some embodiments of the present disclosure. In the illustrated embodiment, gap sensors  1100   a  and  1100   b  may be placed at different elevations (with respect to the rotational axis of drill bit  101 ) on a gage pad of blade  126  of drill bit  101 . 
     Gap sensors  1100   a  and  1100   b  may be configured to determine the distance between the gage pad at their respective locations and wall  1302  of wellbore  114 . The distance between gap sensors  1100   a  and  1100   b  and wall  1302  are indicated as ΔA and ΔB, respectively, in  FIG. 13A . The difference between the values of ΔA and ΔB represent the amount of tilt of drill bit  101  with respect to wall  1302  of wellbore  114 . For example, the tilt angle of drill bit  101  at a given time t may be determined based on the difference between ΔA and ΔB at that time t and the distance between gap sensors  1100   a  and  1100   b  with respect to the rotational axis of drill bit  101  (L), as indicated by the expression below:
 
β= a  tan((Δ A−ΔB )/ L )
 
     Plots of ΔA and ΔB with respect to time may also indicate the tilting motion of drill bit  101 .  FIG. 13B  illustrates example plots  1304  and  1306  of ΔA and ΔB, respectively, with respect to time. 
     Accordingly, a plurality of gap sensors  1100  including opto-analytical devices  300  may be configured to determine and record the bit tilt of drill bit  101  in accordance with some embodiments of the present disclosure. The bit tilt of drill bit  101  as measured and determined using gap sensors  1100  may be used to improve the design of drill bit  101  to decrease the interaction between gage pad and the wall of wellbore  114  to improve drilling efficiency. In other embodiments, such as directional drilling, where the tilt may indicate a desired change in direction of drill bit  101 , the bit tilt may indicate the degree in which drill bit  101  is changing direction. Therefore, modifications may be made to drill bit  101  and/or the associated steering mechanism based on the tilt data to improve the steerability of drill bit  101  during directional drilling. Additionally, as mentioned above, opto-analytical devices  300  of gap sensors  1100  may be configured to detect, determine and record any number of other drilling characteristics such as properties of the formation being drilled (e.g., chemical composition, rock strength, plasticity, porosity, etc.) Therefore, in some embodiments, formation properties may be correlated with bit tilt to determine which formations may cause the most or least tilt of drill bit  101 . 
     Modifications, additions, or omissions may be made to  FIGS. 13A and 13B  without departing from the scope of the present disclosure. For example the actual location and configuration of gap sensors  1100   a  and  1100   b  on a drill bit  101  may vary. In addition, the number of gap sensors  1100  of a drill bit  101  configured to determine the tilt of drill bit  101  may vary. Furthermore, although the above description is given with respect to a drill bit  101 , gap sensors  1100  may be configured to determine the tilt of any other drilling tool, as applicable. Additionally, opto-analytical device  300  of gap sensor  1100  may be configured to detect any number of other drilling characteristics (e.g., chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like) while also determining tilt of a drill bit. 
     Another performance indicator of a drilling tool that may be measured by opto-analytical device  300  may be the depth of cut of a cutting element in a formation. In some embodiments, a decreased gap between a portion of a blade  126  and the formation may indicate wear or decreased rate of penetration (ROP) into the formation. As such, it may be advantageous to monitor the gap between a blade  126  and the formation to determine if cutting elements are worn or if ROP has changed, and possibly modify the drilling parameters (e.g., power to the tool, WOB, RPM, etc.) to achieve optimal ROP. A gap sensor  1100  may also be configured to determine the depth of cut of a cutting element in a formation.  FIG. 14  illustrates an example configuration of drill bit  101  including gap sensor  1100  configured to detect the depth of cut of a cutting element  128 , according to some embodiments of the present disclosure. In the illustrated embodiment, gap sensor  1100  may be placed at the base of blade  126  that includes cutting element  128 . Gap sensor  1100  may be placed in front of cutting element  128  in the direction of rotation of drill bit  101  and may be configured to measure the distance (parallel to the rotational axis of drill bit  101 ) between the base of blade  126  and formation  1402  (illustrated as distance D). The distance (parallel to the rotational axis of drill bit  101 ) between gap sensor  1100  and the tip of cutting element  128  (illustrated as distance D 0  in  FIG. 14 ) may be a known parameter of drill bit  101 . 
     The depth of cut of the cutting element  128  (Δc) may be determined by taking the difference between D and D 0  as expressed by the following equation:
 
Δ c=D   0   −D  
 
In some embodiments, a processing unit of an opto-analytical device (e.g., opto-analytical device illustrated in  FIG. 3 ) of gap sensor  1100  may be configured to determine the depth of cut and store the depth of cut as a function of time in a computer-readable medium to allow for retrieval of the data at a later time. In the same or alternative embodiments, the processing unit  308  may be configured to transmit the depth of cut determinations during drilling operations via any suitable MWD system. Additionally, in some embodiments, the processing unit may be configured to determine, store and/or transmit the distance D and the depth of cut may be determined using any other suitable, system, apparatus or device based on the measured D and known D 0 .
 
     The depth of cut may be used to determine other drilling characteristics. For example, the ROP of drill bit  101  may be related to the depth of cut of cutting elements  128  and the revolutions per minute (RPM) of the drill bit  101  as expressed by the equation below:
 
ROP=5*RPM*Δ c  
 
Accordingly, one or more gap sensors  1100  including opto-analytical devices  300  may be configured to determine and record the depth of cut of one or more cutting elements  128  of drill bit  101  in accordance with some embodiments of the present disclosure. The depth of cut of cutting elements  128  as measured and determined using gap sensors  1100  may also be used to improve the design of drill bit  101  and cutting elements  128 . For example, the actual depth of cut of cutting elements  128  during drilling may be used to verify the effectiveness of the DOCCs and to update the design of drill bit  101 . Additionally, as mentioned above, opto-analytical device  300  of gap sensor  1100  may be configured to detect, determine and record any number of other drilling characteristics such as properties of the formation being drilled (e.g., chemical composition, rock strength, plasticity, porosity, etc.) Therefore, in some embodiments, formation properties may be correlated with depth of cut to determine how different formation properties may affect the depth of cut.
 
     Modifications, additions, or omissions may be made to  FIG. 14  without departing from the scope of the present disclosure. For example the actual location and configuration of gap sensor  1100  and cutting element  128  of  FIG. 14  may vary. In addition, the number of gap sensors  1100  of a drill bit  101  each configured to determine the depth of cut of an associated cutting element  128  may vary. Furthermore, although the above description is given with respect to a drill bit  101 , a gap sensor  1100  may be configured to determine the depth of cut of cutting elements of any other drilling tool. Additionally, opto-analytical device  300  of gap sensor  1100  may be configured to detect any number of other drilling characteristics (e.g., chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like) while also determining depth of cut measurements. 
     Another performance indicator of a drilling tool that may be measured by opto-analytical device  300  may be the wear of cutting elements  128 . In some embodiments, an increase in the measured gap may indicate wear of one or more cutting elements  128 . As such, it may be advantageous to monitor the gap between one or more cutting elements  128  on drill bit  101  and an object in the wellbore (e.g., the side wall of the wellbore) to determine if there is increasing wear on cutting elements  128 .  FIG. 15  illustrates an example configuration of a drill bit  101  including gap sensor  1100  configured to detect the wear of a cutting element  128 , according to some embodiments of the present disclosure. In the illustrated embodiment, gap sensor  1100  may be disposed on the surface of blade  126  that includes cutting element  128 . Gap sensor  1100  may be placed behind the cutting element  128  in the direction of rotation of drill bit  101  and may be configured to measure the distance (parallel to the rotational axis of drill bit  101 ) between the surface of blade  126  and formation  1502  after being cut into by the cutting element  128  (illustrated as distance D). As the cutting element  128  wears, the distance D illustrated in  FIG. 15  will get smaller. 
     In some embodiments, a processing unit (e.g., processing unit  308  of  FIG. 3 ) of the opto-analytical device (e.g., opto-analytical device  300  of  FIG. 3 ) of gap sensor  1100  may be configured to determine the distance D and store the distance D as a function of time in a computer-readable medium to allow for retrieval of the data at a later time. In the same or alternative embodiments, the processing unit may be configured to transmit the distance D to the well site during drilling operations via any suitable MWD system. Therefore, an analysis of distance D may indicate wear of the cutting element  128 . 
     Accordingly, one or more gap sensors  1100  including opto-analytical devices may be configured to detect and record data associated with the wear of one or more cutting elements  128 . The wear of cutting elements  128  as determined based on the data detected and recorded by gap sensors  1100  may be used to improve the design of one or more cutting elements  128 . For example, the wear of the cutting elements may be used to design and locate backup cutting elements and non-cutting elements (e.g., DOCCs, blades, etc.). The amount of wear of the cutting elements during drilling may also be an indicator of when the drill bit will need replacing. For example, based on the amount of wear over time, an operator may be able to estimate the amount of time remaining for the current drill bit, or the amount of time a future drill bit will last. Additionally, as mentioned above, an opto-analytical device of gap sensor  1100  may be configured to detect, determine and record any number of other drilling characteristics such as properties of the formation being drilled (e.g., chemical composition, rock strength, plasticity, porosity, etc.) Therefore, in some embodiments, formation properties may be correlated with cutting element wear to determine how different formation properties may affect the wear of cutting elements. 
     Modifications, additions, or omissions may be made to  FIG. 15  without departing from the scope of the present disclosure. For example the actual location and configuration of gap sensor  1100  and cutting element  128  of  FIG. 15  may vary. Further, the number of gap sensors  1100  of a drill bit  101  each configured to determine the wear of an associated cutting element  128  may vary. Further, although the above description is given with respect to drill bit  101 , gap sensor  1100  may be configured to determine the wear of cutting elements of any other drilling tool. 
       FIG. 16  illustrates a flow chart of an example method  1600  for determining a gap between objects, according to some embodiments of the present disclosure. Method  1600  may be performed by any suitable, system, apparatus, or device. In the illustrated embodiment, method  1600  may be performed using gap sensor  1100  described with respect to  FIG. 11 . 
     Method  1600  may start, and at step  1602  gap sensor  1100  mounted on a drilling tool (e.g. a drill bit  101 , a reamer, a stabilizer, a hole enlarger, etc.) may direct electromagnetic radiation toward an object (e.g., the wall of a wellbore  114 ). At step  1604 , gap sensor  1100  may detect the electromagnetic radiation that has been reflected off of an object such as the wellbore, the formation, the drill bit, or another portion of the drilling tool. At step  1606 , the gap sensor  1100  may determine a distance between the object and the gap sensor  1100  based on the reflected electromagnetic radiation. 
     At step  1608 , one or more drilling characteristics may be determined based on the distance determined at step  1606 . For example, bit motion such as bit whirl, bit walk and bit tilt may be determined as described above with respect to  FIGS. 12A-13B . Additionally, the depth of cut and wear of cutting elements may be determined based on the gap measurements, as described with respect to  FIGS. 14 and 15 , respectively. Furthermore, if at least three gap sensors are mounted circumferentially on a drill bit, the diameter of the hole drilled by the bit may be estimated. The actual hole size is usually larger than that of a drill bit, especially in directional drilling using a downhole motor. An oversized hole may be due to bit wear, downhole vibration, and/or unexpected tilt angle of a downhole motor. 
     At step  1610 , one or more drilling parameters may be modified based on the determined drilling characteristics. For example, if bit whirl is detected during drilling, an operator may decrease bit rotational speed and/or increase weight on bit in order to avoid whirl. As another example, if the bit walks, a deeper or shallower cone profile or a larger or smaller gage pad may be needed to reduce the walk tendency. Furthermore, the drilling azimuth direction may be modified by increasing or decreasing power to the tool, WOB, RPM, etc. in order to follow the desired drilling path. Additionally, based on a detected change in the depth of cut or the diameter of the hole, a drill bit may be replaced with a new bit as the change may indicate wear of the cutting elements. Accordingly, method  1600  may use a gap sensor  1100  that includes an opto-analytical device  300  to determine one or more drilling characteristics. 
     Modifications, additions, or omissions may be made to method  1600  without departing from the scope of the present disclosure. For example, as mentioned above, an opto-analytical device  300  of a gap sensor  1100  may be configured to detect, determine and record any number of other drilling characteristics (e.g., chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like) while also determining gap measurements. Therefore, in some embodiments, formation properties may be correlated with drilling characteristics associated with gap measurements to determine the effect of the formation properties on the drilling characteristics associated with the gap measurements. 
     In addition to the above applications, an opto-analytical device  300  may also be used as an accelerometer to determine one or more drilling characteristics.  FIG. 17A  illustrates an example embodiment of an accelerometer  1700  configured to determine acceleration of a drilling tool using an opto-analytical device  300 , according to some embodiments of the present disclosure. Accelerometer  1700  may be integrated with any suitable drilling tool and in the illustrated embodiment may be integrated in a cavity  402  of a drill bit  101 . In some embodiments, a processing unit of opto-analytical device  300  may be configured to determine and store the acceleration of the drilling tool as a function of time in a computer-readable medium to allow for retrieval of the data at a later time. In the same or alternative embodiments, processing unit  308  may be configured to transmit the acceleration determinations during drilling operations via any suitable MWD system. 
     Accelerometer  1700  may include an electromagnetic radiation source  406  configured to direct electromagnetic radiation  1701  toward an opto-analytical device  300 . Accelerometer  1700  may also include a mass  1702  coupled to a spring  1704  having a spring constant K and a damper  1706  having a damping coefficient C. When drill bit  101  moves (e.g., vibrates) mass  1702  may also move and block at least part of electromagnetic radiation  1701  received by an opto-analytical device  300  of  FIG. 17A  that includes an ICE  302 , detector  306  and processing unit  308 . Therefore, the intensity of electromagnetic radiation  1701  received by ICE  302  of opto-analytical device  300  may vary according to the movement of mass  1702  such that the acceleration of drill bit  101  may be determined based on the varied intensity of electromagnetic radiation  1701  received by opto-analytical device  300  of accelerometer  1700 . 
     As will be appreciated and recognized by one of ordinary skill in the art, the motion of mass  1702  having a mass M may be described as follows:
 
 M{umlaut over (x)}+C{dot over (x)}+Kx=−M{umlaut over (x)}   S  
 
     If the natural frequency of accelerometer  1700  ( p ) as expressed by 
             p   =       K   M             
is higher than the measured frequency of drill bit  101  (e.g., the vibration frequency of drill bit  101 ), then the measured x may be proportional to the acceleration of drill bit  101 .  FIG. 17B  illustrates an alternative embodiment of accelerometer  1700  that uses the same principles as described with respect to  FIG. 17A , according to some embodiments of the present disclosure.
 
     Modifications, additions, or omissions may be made to  FIGS. 17A and 17B  without departing from the scope of the present disclosure. For example, although described with respect to a drill bit  101 , accelerometer  1700  may be integrated with any suitable drilling tool. Additionally, opto-analytical device  300  of accelerometer  1700  may be configured to receive electromagnetic radiation from channels (not expressly shown) configured to direct the electromagnetic radiation from the formation being drilled into to opto-analytical device  300  of accelerometer  1700 . Accordingly, opto-analytical device  300  may be configured to detect, determine and record any number of other drilling characteristics (e.g., chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like) while also determining acceleration. Therefore, in some embodiments, formation properties may be correlated with the movement and acceleration (e.g., vibration) of drill bit  101  as measured by accelerometer  1700 . 
     Accelerometer  1700  may be used to determine any number of drilling characteristics. For example,  FIG. 18  illustrates an example configuration of an accelerometer  1700  integrated with a drill bit  101  along the rotational axis of the drill bit  101  such that accelerometer  1700  may detect axial vibration of drill bit  101 , according to some embodiments of the present disclosure. Accelerometer  1700  may also be used to detect drill bit shocks when the magnitude of acceleration is above a pre-defined level, for example, 50 g. 
     Modifications, additions, or omissions may be made to  FIG. 18  without departing from the scope of the present disclosure. For example, although described with respect to determining axial vibration of a drill bit  101 , accelerometer  1700  may be integrated with any suitable drilling tool to determine vibrations associated with that drilling tool. Further, accelerometer  1700  may be integrated at any number of locations of a drilling tool other than at or near the rotational axis to determine vibration of the drilling tool at the any number of locations. Additionally, opto-analytical device  300  of accelerometer  1700  may be configured to receive electromagnetic radiation from channels (not expressly shown) configured to direct the electromagnetic radiation from the formation being drilled into to opto-analytical device  300  of accelerometer  1700 . Accordingly, opto-analytical device  300  may be configured to detect, determine and record any number of other drilling characteristics (e.g., chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like) while also determining acceleration. Therefore, in some embodiments, formation properties may be correlated with the vibration of drill bit  101  (or any other drilling tool) as measured by accelerometer  1700 . 
     Accelerometer  1700  may also be configured to determine the rotational speed of a drilling tool.  FIG. 19  illustrates an example configuration of accelerometers  1700   a  and  1700   b  integrated with a drill bit  101  to determine the rotational speed of the drill bit  101 , according to some embodiments of the present disclosure. Accelerometers  1700   a  and  1700   b  may be integrated at two opposite ends of the drill bit  101  as depicted in  FIG. 19 . The measured acceleration at accelerometer  1700   a  (Ax 1 ) and accelerometer  1700   b  (Ax 2 ) may be expressed below using the bit coordinate system (XbYb plane) of  FIG. 12A :
 
 Ax 1=−Δ RΩ   2  cos(ω−Ω) t−R   1 ω 2  and  Ax 2=−Δ RΩ   2  cos(ω−Ω) t−R   1 ω 2  
 
     and 
             ω   =             Ax   ⁢           ⁢   2     -     Ax   ⁢           ⁢   1         2   ⁢     R   1           .           
Where ω is the rotational speed of drill bit  101 , Ω is the whirl speed of drill bit  101 , ΔR is the whirl radius, and R 1  is the radial distance of the lateral accelerometer. The bit center acceleration of drill bit  101  in the X direction (Ax) (as indicated by the X-axis of  FIG. 19 ) may be obtained as expressed below:
 
     
       
         
           
             Ax 
             = 
             
               
                 
                   
                     Ax 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   + 
                   
                     Ax 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 2 
               
               = 
               
                 
                   - 
                   Δ 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 R 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   Ω 
                   2 
                 
                 ⁢ 
                 
                   cos 
                   ⁡ 
                   
                     ( 
                     
                       ω 
                       - 
                       Ω 
                     
                     ) 
                   
                 
                 ⁢ 
                 t 
               
             
           
         
       
     
     Additionally, if two other accelerometers  1700  are placed on drill bit  101  opposite from each other along the Y-axis of  FIG. 19  (e.g., accelerometers  1700   c  and  1700   d ) the bit center acceleration of drill bit  101  in the Y direction (Ay) (as indicated by the Y-axis of  FIG. 19 ) may be obtained based on the acceleration as measured by accelerometer  1700   c  (Ay 1 ) and the acceleration as measured by accelerometer  1700   d  (Ay 2 ) as expressed below: 
     
       
         
           
             Ay 
             = 
             
               
                 
                   
                     Ay 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   + 
                   
                     Ay 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 2 
               
               = 
               
                 
                   - 
                   Δ 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 R 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   Ω 
                   2 
                 
                 ⁢ 
                 
                   sin 
                   ⁡ 
                   
                     ( 
                     
                       ω 
                       - 
                       Ω 
                     
                     ) 
                   
                 
                 ⁢ 
                 t 
               
             
           
         
       
     
     Based on the bit center accelerations Ax and Ay, an unwrapped phase angle may be obtained for drill bit  101  as expressed below: 
     
       
         
           
             
               ϕ 
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               
                 
                   arctan 
                   ⁡ 
                   
                     ( 
                     
                       Ay 
                       Ax 
                     
                     ) 
                   
                 
                 + 
                 
                   ϕ 
                   0 
                 
               
               = 
               
                 
                   
                     ( 
                     
                       ω 
                       - 
                       Ω 
                     
                     ) 
                   
                   ⁢ 
                   t 
                 
                 + 
                 
                   ϕ 
                   0 
                 
               
             
           
         
       
       
         
           
             
               
                 d 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 ϕ 
               
               
                 d 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 t 
               
             
             = 
             
               ω 
               - 
               Ω 
             
           
         
       
     
     At any time, t, unwrapped phase angle φ(t) is calculated from bit center accelerations Ax and Ay. Therefore, (ω−Ω) may be deduced by performing a linear least square fitting on φ(t), such that when bit rotational speed co is known, the bit whirl speed Ω may be obtained. 
     Accordingly, a plurality of accelerometers  1700  may be integrated with a drilling tool (e.g., a drill bit  101 , a reamer, a stabilizer, a hole enlarger, etc. to determine drilling characteristics such as the whirl speed of the drilling tool). Three accelerometers  1700  may be mounted in a mutually orthogonal arrangement along the center line of a drilling tool such as drill bit, downhole motor and MWD tool. The axial and lateral accelerations may be used to measure axial and lateral shocks. 
     Modifications, additions, or omissions may be made to  FIG. 19  without departing from the scope of the present disclosure. For example, although described with respect to determining whirl speed of a drill bit  101 , accelerometer  1700  may be integrated with any suitable drilling tool to determine vibrations associated with that drilling tool. Further, accelerometer  1700  may be integrated at any number of locations of a drilling tool other than at or near the rotational axis to determine vibration of the drilling tool at the any number of locations. Additionally, opto-analytical device  300  of accelerometer  1700  may be configured to receive electromagnetic radiation from channels (not expressly shown) configured to direct the electromagnetic radiation from the formation being drilled into to opto-analytical device  300  of accelerometer  1700 . Accordingly, opto-analytical device  300  may be configured to detect, determine and record any number of other drilling characteristics (e.g., chemical composition of the formation (e.g. identity and concentration in total or of individual components), formation fluid content (e.g., oil, gas, and/or brines), lithology of the formation (e.g. the concentration ratio of shale, sandstone, limestone and dolomite, the amount of sand, grain size in the formation, etc.), impurity content, pH, viscosity, density, strength, total dissolved solids, salt content, porosity, opacity, bacteria content, combinations thereof, and the like). Therefore, in some embodiments, formation properties may be correlated with the whirl speed of drill bit  101  (or any other drilling tool such as a reamer or stabilizer) as measured by accelerometers  1700 . 
     Although the present disclosure has been described with several embodiments, various changes and modifications may be suggested to one skilled in the art. For example, although the present disclosure describes the configurations of DOCCs with respect to drill bits having specific blade configurations, the same principles may be used to reduce the imbalance forces of any suitable drilling tool according to the present disclosure. It is intended that the present disclosure encompasses such changes and modifications as fall within the scope of the appended claims.