Patent Publication Number: US-2015083493-A1

Title: Drilling System and Associated System and Method for Monitoring, Controlling, and Predicting Vibration in an Underground Drilling Operation

Description:
TECHNICAL FIELD 
     The present disclosure relates to a drilling system for underground drilling, and more particularly to a method for monitoring, controlling and predicting vibration for a drilling operation. 
     BACKGROUND 
     Underground drilling, such as gas, oil, or geothermal drilling, generally involves drilling a bore through a formation deep in the earth. Such bores are formed by connecting a drill bit to long sections of pipe, referred to as a “drill pipe,” so as to form an assembly commonly referred to as a “drill string.” The drill string extends from the surface to the bottom of the bore. The drill bit is rotated so that the drill bit advances into the earth, thereby forming the bore. In rotary drilling, the drill bit is rotated by rotating the drill string at the surface. Pumps at the surface pump high-pressure drilling mud through an internal passage in the drill string and out through the drill bit. The drilling mud lubricates the drill bit, and flushes cuttings from the path of the drill bit. In some cases, the flowing mud also powers a drilling motor, commonly referred to as a “mud motor,” which turns the bit. In any event, the drilling mud flows back to the surface through an annular passage formed between the drill string and the surface of the bore. In general, optimal drilling is obtained when the rate of penetration of the drill bit into the formation is as high as possible while a vibration of drilling system is as low as possible. The rate of penetration (“ROP”) is a function of a number of variables, including the rotational speed of the drill bit and the weight-on-bit (“WOB”). The drilling environment, and especially hard rock drilling, can induce substantial vibration and shock into the drill string, which has an adverse impact of drilling performance. 
     Vibration is introduced by rotation of the drill bit, the motors used to rotate the drill bit, the pumping of drilling mud, imbalance in the drill string, etc. Vibration can cause premature failure of the various components of the drill string, premature dulling of the drill bit, or may cause the catastrophic failures of drilling system components. Drill string vibration includes axial vibration, lateral vibration and torsional vibration. “Axial vibration” refers to vibration in the direction along the drill string axis. “Lateral vibration” refers to vibration perpendicular to the drill string axis. Lateral vibration often arises because the drill string rotates in a bent condition. Two other sources of lateral vibration are “forward” and “backward”, or “reverse”, whirl. “Whirl” refers to a situation in which the bit orbits around the borehole in addition to rotating about its own axis. In backward whirl, the bit orbits in a direction opposite to the direction of rotation of the drill bit. “Torsional vibration,” also of concern in underground drilling, is usually the result of what is referred to as “stick-slip.” Stick-slip occurs when the drill bit or lower section of the drill string momentarily stops rotating (i.e., “sticks”) while the drill string above continues to rotate, thereby causing the drill string to “wind up,” after which the stuck element “slips” and rotates again. Often, the bit will over-speed as it unwinds. 
     Various system can be used to obtain and process information concerning a drilling operation, which can help improve drilling efficiency. Systems have been developed that can receive and process information from sensors near the drill bit and then transmit that information to surface equipment. Other systems can determine vibration of the bottomhole assembly, either downhole during a drill run, or at the surface. Many of such systems use finite element and/or finite difference techniques to assist in in analysis of drilling data, including vibration information. 
     SUMMARY 
     An embodiment of the present disclosure includes a method, computer program product embodied on a non-transitory computer readable medium, and a system for predicting vibration information for a drilling system having a drill string. The drill string includes a drill bit that is configured to form a borehole in an earthen formation during a drilling operation. The method, whether executed via a computer program product or implemented via system includes the step of accessing, via a computer processor, drilling system component information, the drilling system component information including one or more characteristics of the drill string, and accessing, via the computer processor, expected operating information for the drilling operation, the expected operating information including at least a weight-on-bit (WOB), a rotational speed of the drill bit, a borehole diameter, and a vibration damping coefficient. Additional steps include predicting vibration information for the drill string via the computer processor, the predicted vibration information including at least on an amplitude for each of an axial vibration, a lateral vibration, and a torsional vibration of the drill string. The prediction of the vibration information being based on the drilling system component information and an energy balance of the drill string operating according to the expected operation information for the drilling operation. 
     Another embodiment of the present disclosure is a drilling system configured to form a borehole in an earthen formation during a drilling operation. The drilling system can include a drill string supporting a drill bit, the drill bit configured to defined the borehole. The drilling system can including at least one computing device including a memory portion having stored thereon drilling system component information, the drilling system component information including one or more characteristics of the drill string. The memory portion further including expected operating information for the drilling operation, the expected operating information including at least a weight-on-bit (WOB), a rotational speed of the drill bit, a borehole diameter, and a vibration damping coefficient. The drilling system further including a computer processor in communication with the at least one computing device, the computer processor configured to predict vibration information for the drill string, the predicted vibration information including at least an amplitude for each of an axial vibration, a lateral vibration, and a torsional vibration of the drill string. The prediction of the vibration information can be based on the drilling system component information and an energy balance of the drill string operating according to the expected operation information for the drilling operation. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing summary, as well as the following detailed description of illustrative embodiments of the present application, will be better understood when read in conjunction with the appended drawings. For the purposes of illustrating the present application, there is shown in the drawings illustrative embodiments. It should be understood, however, that the application is not limited to the precise arrangements and instrumentalities shown. In the drawings: 
         FIG. 1  is a schematic of an underground drilling system according to an embodiment of the present disclosure; 
         FIG. 2A  is a block diagram of a computing device used in the drilling system shown in  FIG. 1 ; 
         FIG. 2B  is a block diagram illustrating a network of one or more computing devices and a drilling data database of the drilling system shown in  FIG. 1 ; 
         FIG. 3A  is a block diagram illustrating a method of operating a drilling system shown in  FIG. 1 , according to an embodiment of the present disclosure; 
         FIG. 3B  is a block diagram illustrating a method of creating a drilling system model, according to an embodiment of the present disclosure; 
         FIG. 4  is a block diagram illustrating a method for revising the drill system model based on the difference between the predicting vibration information and the measured vibration information; 
         FIG. 5  is a block diagram illustrating a method for revising the drilling system model to reduce deviations between predicted and measured vibration according to an embodiment of the present disclosure; and 
         FIG. 6  is a block diagram illustrating a method for operating a drilling system shown in  FIG. 1  in order to attain a desired rate of penetration and avoid excessive vibration; 
         FIG. 7  is an exemplary computer generated display of an energy balance of a drilling system illustrating amplitude as a function of input load, according to the present disclosure; 
         FIG. 8  is a computer generated display for an exemplary vibratory mode shape curve generated according to the present disclosure; 
         FIG. 9  is a computer generated display for an exemplary critical speed map generated according to the present disclosure; 
     
    
    
     DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
     Referring to  FIG. 1 , a drilling system or drilling rig  1  is configured to drill a borehole  2  in an earthen formation  3  during a drilling operation. The drilling system  1  includes a drill string  4  for forming the borehole  2  in the earthen formation  3 , a drilling data system  12 , and at least one computing device  200 . The computing device  200  can host one or more drilling operation applications, for instance software applications, that are configured to perform various methods for monitoring the drilling operation, controlling the drilling operation, predicting vibration information concerning the drilling operation, and/or predicting vibration information concerning the drill string  4  for use in a drilling operation. The computing device  200  cooperates with the drilling data system  12  and the one or more software application to execute the various methods described herein. While the borehole  2  is illustrated as a vertical borehole, the systems and methods described herein can be used for a directional drilling operation, i.e, horizontal drilling. For instance, the drill string  4  can be configured to form a borehole  2  in the earthen formation  3  that is orientated along a direction that is transverse to an axis that is perpendicular to the surface  11  of the earthen formation  3 . 
     Continuing with  FIG. 1 , the drilling system or rig  1  includes a derrick  9  supported by the earth surface  11 . The derrick  9  supports a drill string  4 . The drill string  4  has a top end  4   a , a bottom end  4   b , a top sub  45  disposed at the top end  4   a  of the drill string  4 , and a bottomhole assembly  6  disposed at the bottom end  4   b  of the drill string  4 . The bottomhole assembly  6  includes top end  6   a  and a bottom end  6   b . A drill bit  8  is coupled to the bottom end  6   b  of a bottomhole assembly  6 . The drilling system  1  has a prime mover (not shown), such as a top drive or rotary table, configured to rotate the drill string  4  so as to control the rotational speed (RPM) of, and torque on, the drill bit  8 . Rotation of the drill string  4  and drill bit  8  thus defines the borehole  2 . As is conventional, a pump  10  is configured to pump a fluid  14 , for instance drilling mud, downward through an internal passage in the drill string  4 . After exiting at the drill bit  8 , the returning drilling mud  16  flows upward to the surface  11  through an annular passage formed between the drill string  4  and the borehole  2  in the earthen formation  3 . A mud motor  40 , such as a helicoidal positive displacement pump or a “Moineau-type” pump, may be incorporated into the bottomhole assembly  6 . The mud motor is driven by the flow of drilling mud  14  through the pump and around the drill string  4  in the annular passage described above. 
     A drilling operation as used herein refers to one more drill runs that define the borehole  2 . For instance a drilling operation can include a first drill run for defining a vertical section of the borehole  2 , a second drill run for defining the bent section of the borehole  2 , and a third drill run for defining a horizontal section of the borehole  2 . More than three drill runs are possible. For difficult drilling operations, as much as 10 to 15 drill runs may be completed to define the borehole  2  for hydrocarbon extraction purposes. It should be appreciated that one or more bottomhole assemblies can be used for each respective drill run. The systems, methods, software applications as described herein can be used to execute methods that monitor, control, and predict vibration information the drilling operation, as well as monitor, control, and prediction vibration information for specific drilling runs in the drilling operation. 
     In the illustrated embodiment, the computing device  200  can host the software application that is configured to predict vibration information for the drill string  4  using a drilling system model, as will be further detailed below. The vibration information can include the axial, lateral and torsional vibration information of the drill string  4 , and specifically, the mode shape and frequency for each of an axial, lateral, and torsional vibration of the drill string  4 . It should be appreciated that vibration mode shape is indicative of the relative displacements along the drill string. As an advancement on prior systems, the software application as described herein can predict vibration information noted above based on the drill string geometry, the applied drilling loads based on the expected drilling operation (e.g. expected weight-on-bit, rotary speed and flow rate). In predicting vibration information, the software application takes into account the energy balance to determine the vibration severity based on a frequency domain type of finite element technique, as further detailed below. A software application based on the energy balance of the drilling system  1 , as opposed to a software application that uses various finite element techniques based on time domain, result in significant processing time improvements. The software applications ability to revise predicted vibration information based on real-time data from a drilling operation, as discussed below, results in more precise and accurate drilling operation information that the rig operator or drill string designer can reply upon. During a drilling operation, the software application described herein can be used predict anticipated drilling dysfunctions, such a component wear and potential lost time incidents due to component replacement, and can further determine modified drilling set points to avoid the drilling dysfunction. Further, the software application can predict vibration information for the drill string  4 , access data indicative of the measured vibration of the drill string  4 , and revise the predicted vibration information in the event there is a difference between the predicted vibration information and the measured vibration, as will be further detailed below. 
     Referring to  FIG. 1 , the drilling system  1  can include a plurality of sensors configured to measure drilling data during a drilling operation, for use in methods described herein. Drilling data can include expected operating parameters, for instance the expected operating parameter for WOB, rotary speed (RPM) and the drill bit rotational speed (RPM). In the illustrated embodiment, the drill string top sub  45  includes one or more sensors for measuring drilling data. For instance, the one or more sensors can be strain gauges  48  that measure the axial load (or hook load), bending load, and torsional load on the top sub  45 . The tob sub  45  sensors also include a triaxial accelerometer  49  that senses vibration at the top end  4   a  of the drill string  4 . 
     Continuing with  FIG. 1 , the bottomhole assembly  6  can also include one or more sensors that are configured to measure drilling parameters in the borehole  2 . In addition, the bottomhole assembly  6  includes a vibration analysis system  46  configured to determine various vibration parameters based on the information regarding the drilling operation obtained from the sensors in the borehole. The vibration analysis module will be further detailed below. The bottomhole assembly sensors can be in the form of strain gauges, accelerometers, pressure gauges and magnetometers. For instance, the bottomhole assembly  6  can include downhole strain gauges  7  that measure the WOB. A system for measuring WOB using downhole strain gauges is described in U.S. Pat. No. 6,547,016, entitled “Apparatus For Measuring Weight And Torque An A Drill Bit Operating In A Well,” hereby incorporated by reference herein in its entirety. In addition, the strain gauges  7  can be configured to measure torque on bit (“TOB”) and bending on bit (“BOB”) as well as WOB. In alternative embodiments, the drill string can include a sub (not numbered) incorporating sensors for measuring WOB, TOB and BOB. Such a sub can be referred to as a “WTB sub.” 
     Further, the bottomhole assembly sensors can also include at least one magnetometer  42 . The magnetometer is configured to measure the instantaneous rotational speed of the drill bit  8 , using, for example, the techniques in U.S. Pat. No. 7,681,663, entitled “Methods And Systems For Determining Angular Orientation Of A Drill String,” hereby incorporated by reference herein in its entirety. The bottomhole assembly sensors can also include accelerometers  44 , oriented along the x, y, and z axes (not shown) (typically with ±250 g range) that are configured to measure axial and lateral vibration. While accelerometer  44  is shown disposed on the bottomhole assembly  6 , it should be appreciated that multiple accelerometers  44  can be installed at various locations along the drill string  4 , such that axial and lateral vibration information at various location along the drill string can be measured. 
     As noted above, the bottomhole assembly  6  includes a vibration analysis system  46 . The vibration analysis system  46  is configured to receive data from the accelerometers  44  concerning axial and lateral vibration of the drill string  4 . Based on the data receive from the accelerometers, the vibration analysis system  46  can determine the measured amplitude and mode shape of axial vibration, and of lateral vibration due to forward and backward whirl, at the location of the accelerometers on the drill string  4 . The measured amplitude and frequency of axial vibration and of lateral vibration can be referred to as measured vibration information. The measured vibration information can also transmitted to the surface  11  and processed by drilling data system  12  and/or the computing device  200 . The vibration analysis system  46  can also receive data from the magnetometer  42  concerning the instantaneous rotational speed of the drill string at the magnetometer  42  location. The vibration analysis system  46  then determines the amplitude and frequency of torsional vibration due to stick-slip. The measured frequency and amplitude of the actual torsional vibration is determined by calculating the difference between and maximum and minimum instantaneous rotational speed of the drill string over a given period of time. Thus, the measured vibration information can also refer to the measured torsional vibration. 
     According to the present disclosure, to reduce data transmissions for vibration information, drilling data may be grouped into ranges and simple values used to represent data in these ranges. For example, vibration amplitude can be reported as 0, 1, 2 or 3 to indicate normal, high, severe, or critical vibration, respectively. One method that may be employed to report frequency is to assign numbers 1 through 10, for example, to values of the vibration frequency so that a value of 1 indicates a frequency in the 0 to 100 hz range, a value of 2 indicates frequency in the 101 to 200 hz range, etc. The mode of vibration may be reported by assigning a number 1 through 3 so that, for example, a value of 1 indicates axial vibration, 2 indicates lateral vibration, and 3 indicates torsional vibration. If only such abbreviated vibration data is transmitted to the surface, at least some of the data analysis, such as a Fourier analysis used in connection with the use of backward whirl frequency to determine borehole diameter, could be performed in a processor installed in the bottomhole assembly  6 . {Note: Currently we don&#39;t do this, but have thought about implementing it in the future} 
     The bottom hole assembly sensors can also include at least first and second pressure sensors  51  and  52  that measure the pressure of the drilling mud flowing through drilling system components in the borehole  2 . For instance, the first and second sensors  51  and  52  measure pressure of the drilling mud flowing through the drill string  4  (in a downhole direction), and the pressure of the drilling mud flowing through the annular gap between the borehole wall and the drill string  4  in an up-hole direction, respectively. Differential pressure is referred to as the difference in pressure between the drilling mud following in downhole direction and the drilling mud flowing in the up-hole direction. Sometimes differential pressure can be referred to as the difference in off-bottom and on-bottom pressure, as is known in the art. Pressure information can be transmitted to the drilling data acquisition system  12  and/or computing device  200 . In the illustrated embodiment, the first and second pressure sensors  51  and  52  can be incorporated in the vibration analysis system  46 . 
     Further, the drilling system  1  can also include one or more sensors disposed on the derrick  9 . For instance, the drilling system can include a hook load sensor  30  for determining WOB and an additional sensor  32  for sensing drill string rotational speed of the drill string  4 . The hook load sensor  30  measures the hanging weight of the drill string, for example, by measuring the tension in a draw works cable (not numbered) using a strain gauge. The cable is run through three supports and the supports put a known lateral displacement on the cable. The strain gauge measures the amount of lateral strain due to the tension in the cable, which is then used to calculate the axial load, and WOB. In another embodiment, drill data can be obtained using an electronic data recorder (EDR). The EDR can measure operating loads at the surface. For instance, the EDR can use sensors to measure the hook load (tensile load to of the drill string at the surface), torque, pressure, differential pressure, rotary speed, flow rate. The weight-in-bit (WOB) can be calculated from the hook load, drill string weight, and off-bottom to on-bottom variations of load. Torque can measured from the motor current draw. Flow rate can be based on the counts the pump strokes and the volume pumped per stroke. The differential pressure is the difference between on-bottom and off-bottom pressure. 
     The drilling data system  12 , as will be further detailed below, can be a computing device in electronic communication with the computing device  200 . The drilling data system  12  is configured to receive, process, and store various drilling operation information obtained from the downhole sensors described above. Accordingly, the drilling data system  12  can include various systems and methods for transmitting data between drill string components and the drilling data system  12 . For instance, in a wired pipe implementation, the data from the bottomhole assembly sensors is transmitted to the top sub  45 . The data from the top sub  45  sensors, as well as data from the bottomhole assembly sensors in a wired pipe system, can be transmitted to the drilling data system  12  or computing device  200  using wireless telemetry. One such method for wireless telemetry is disclosed in U.S. application Ser. No. 12/389,950, filed Feb. 20, 2009, entitled “Synchronized Telemetry From A Rotating Element,” hereby incorporated by reference in its entirety. In addition, the drilling system  1  can include a mud pulse telemetry system. For instance, a mud pulser  5  can be incorporated into the bottomhole assembly  6 . The mud pulse telemetry system encodes data from downhole equipment, such as vibration information from the vibration analysis system  46  and, using the pulser  5 , transmits the coded pulses to the surface  11 . Further, drilling data can be transmitted to the surface using other means such as acoustic or electromagnetic transmission. 
     Referring to  FIG. 2A , any suitable computing device  200  may be configured to host a software application for monitoring, controlling and prediction vibration information as described herein. It will be understood that the computing device  200  can include any appropriate device, examples of which include a desktop computing device, a server computing device, or a portable computing device, such as a laptop, tablet or smart phone. In an exemplary configuration illustrated in  FIG. 2A , the computing device  200  includes a processing portion  202 , a memory portion  204 , an input/output portion  206 , and a user interface (UI) portion  208 . It is emphasized that the block diagram depiction of computing device  200  is exemplary and not intended to imply a specific implementation and/or configuration. The processing portion  202 , memory portion  204 , input/output portion  206  and user interface portion  208  can be coupled together to allow communications therebetween. As should be appreciated, any of the above components may be distributed across one or more separate devices and/or locations. For instance, any one of the processing portion  202 , memory portion  204 , input/output portion  206  and user interface portion  208  can be in electronic communication with the drilling data system  12 , which as noted above can be a computing device similar to computing device  200  as described herein. Further, any one of the processing portion  202 , memory portion  204 , input/output portion  206  and user interface portion  208  can be capable of receiving drill data from one or more the sensors and/or the vibration analysis system  46  disposed on the drill string  4 . 
     In various embodiments, the input/output portion  106  includes a receiver of the computing device  200 , a transmitter of the computing device  200 , or an electronic connector for wired connection, or a combination thereof. The input/output portion  206  is capable of receiving and/or providing information pertaining to communication with a network such as, for example, the Internet. As should be appreciated, transmit and receive functionality may also be provided by one or more devices external to the computing device  200 . For instance, the input/output portion  206  can be in electronic communication with the data acquisition system  12  and/or one or more sensors disposed on the bottomhole assembly  6  downhole. 
     Depending upon the exact configuration and type of processor, the memory portion  204  can be volatile (such as some types of RAM), non-volatile (such as ROM, flash memory, etc.), or a combination thereof. The computing device  200  can include additional storage (e.g., removable storage and/or non-removable storage) including, but not limited to, tape, flash memory, smart cards, CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, universal serial bus (USB) compatible memory, or any other medium which can be used to store information and which can be accessed by the computing device  200 . 
     The computing device  200  can contain the user interface portion  208 , which can include an input device  209  and/or display  213  (input device  210  and display  212  not shown), that allows a user to communicate with the computing device  200 . The user interface  208  can include inputs that provide the ability to control the computing device  200 , via, for example, buttons, soft keys, a mouse, voice actuated controls, a touch screen, movement of the computing device  200 , visual cues (e.g., moving a hand in front of a camera on the computing device  200 ), or the like. The user interface  208  can provide outputs, including visual information, such as the visual indication of the plurality of operating ranges for one or more drilling parameters via the display  213 . Other outputs can include audio information (e.g., via speaker), mechanically (e.g., via a vibrating mechanism), or a combination thereof. In various configurations, the user interface  208  can include a display, a touch screen, a keyboard, a mouse, an accelerometer, a motion detector, a speaker, a microphone, a camera, or any combination thereof. The user interface  208  can further include any suitable device for inputting biometric information, such as, for example, fingerprint information, retinal information, voice information, and/or facial characteristic information, for instance, so to require specific biometric information for access the computing device  200 . 
     Referring to  FIG. 2B , an exemplary and suitable communication architecture is shown that can facilitate monitoring a drilling operation of the drilling system  1 . Such an exemplary architecture can include one or more computing devices  200 ,  210  and  220  each of which can be in electronic communication with a database  230  and a drilling data acquisition system  12  via common communications network  240 . The database  230 , though schematically represented separate from the computing device  200  could also be a component of the memory portion  104  of the computing device  200 . It should be appreciated that numerous suitable alternative communication architectures are envisioned. Once the drilling control and monitoring application has been installed onto the computing device  200 , such as described above, it can transfer information between other computing devices on the common network  240 , such as, for example, the Internet. For instance configuration, a user  24  may transmit, or cause the transmission of information via the network  240  regarding one or more drilling parameters to the computing device  210  of a supplier of the bottomhole assembly  6 , or alternatively to computing device  220  of another third party (e.g., a drilling system owner  1 ) via the network  240 . The third party can view, via a display, the plurality of operating ranges for the one or more drilling parameters as described herein. 
     The computing device  200  and the database  230  depicted in  FIG. 2B  may be operated in whole or in part by, for example, a rig operator at the drill site, a drill site owner, drilling company, and/or any manufacturer or supplier of drilling system components, or other service provider, such as a third party providing drill string design services. As should be appreciated, each of the parties set forth above and/or other relevant parties may operate any number of respective computers and may communicate internally and externally using any number of networks including, for example, wide area networks (WAN&#39;s) such as the Internet or local area networks (LAN&#39;s). Database  230  may be used, for example, to store data regarding one or more drilling parameters, the plurality of operating ranges from a previous drill run, a current drill run, and data concerning the models for the drill string components. Further it should be appreciated that “access” or “accessing” as used herein can include retrieving information stored in the memory portion of the local computing device, or sending instructions via the network to a remote computing device so as to cause information to be transmitted to the memory portion of the local computing device for access locally. In addition or alternatively, accessing can including accessing information stored in the memory portion of the remote computing device. 
     Turning to  FIG. 3A , according to an illustrated embodiment, a method  50  for monitoring, controlling of drilling data, and the prediction vibration information for a drilling operation is initiated in step  100 . In step  100 , a user can input drilling component data. For instance, the user may specify a drill string component, for instance a bottomhole assembly or Measurement While Drilling (“MWD”) tool, and the vibration limits applicable to each such component. The drill string and/or bottomhole assembly data can be input by the operator or stored in database  230  or in memory of the computing device  100 . Bottomhole assembly data can be accessed as noted above by the software application. Data input in step  100  may include:
         (i) the outside and inside diameters of the drill pipe sections that make up the drill string,   (ii) the locations of stabilizers,   (iii) the length of the drill string,   (iv) the inclination of the drill string,   (v) the bend angle if a bent sub is used,   (vi) the material properties, specifically the modulus of elasticity, material density, torsional modulus of elasticity, and Poisson&#39;s ratio,   (vii) the mud properties for vibration damping, specifically, the mud weight and viscosity,   (viii) the borehole diameters along the length of the well,   (ix) the azimuth, build rate and turn rate,   (x) the diameter of the drill bit and stabilizers, and   (xi) information concerning the characteristics of the formation, such as the strike and dip.       

     In alternative embodiments, during step  100 , the information concerning the drill string components can also be updated by the operator each time a new section of drill string is added or when a new drill run is initiated. 
     In step  101 , expected operating information for the drilling operation can be input in the software application and stored as need in drilling data system or computing device  100 . Expected operating information can developed at drill site or can be determined according to a drilling plan. Expected operating information includes (i) the WOB, (ii) the drill string rotational speed, (iii) the mud motor rotation speed, (iv) the diameter of the borehole, and (v) any damping coefficients. 
     In step  102 , the software application predicts the vibration information for the drill string. The predicted vibration information includes at least an amplitude for each of an axial vibration, a lateral vibration, and a torsional vibration of the drill string  4 . As will be further detailed below and illustrated in  FIG. 3B , the prediction of the vibration information is based on the drilling system component information and an energy balance method of the drill string operating according to the expected operation information for the drilling operation. In addition, the prediction vibration information can include frequency and mode shape information. During step  102 , the software application can also initiate one or more analyses for use in the prediction model discussed below. In particular, the software application can conduct a static bending analysis to determine the bending information of the bottomhole assembly  6 . The bending information includes calculated bottomhole assembly deflections, the side forces along the length of the bottomhole assembly, the bending moments, and the nominal bending stress. The software application also performs a so-called “predict analysis” in which it uses the bending analysis information to predict the direction in which the drill string will drill. 
     In step  104 , the software application calculates vibration warning limits for specific drill string components based on the vibration information measured by the sensors in the vibration analysis system  46 . For example, as discussed below, based on the predicted mode shapes, the software application can determine what level of measured vibration at the accelerometer locations would result in excessive vibration at the drill string location of a critical drilling string component. 
     In step  106 , the drilling operation continues or is initiated. For instance, one or more the previous steps, for instance steps  100  through  104 , could be initiated prior to a drilling operation to help develop a drilling plan or and aid in designing a bottomhole assembly. 
     In step  108 , the software application can receive drilling data from the rig surface sensors. In step  109 , the software application can receive drilling data from the downhole sensors. It should be appreciated that the rig surface drilling data and the downhole drilling data may be stored in computer memory in the drilling data system  12  and/or computing device  200 . The communication system can transmit the drilling data from the rig surface sensors and the downhole sensors to the drilling data system  12 . Drilling data from the surface sensors are preferably transmitted to the system  12  continuously. Drilling data from the downhole sensors is transmitted to the drilling data system  12  whenever downhole drilling data is sent to the surface, preferably at least every few minutes. The software application can then access the rig surface drilling data and the downhole drilling data. Regardless of whether the software application accesses or receives drilling data, the drilling data can be used by the software application on an on-going basis during the drilling operation. 
     In step  110 , drilling data and drilling status can be transmitted to a remote computing device, for instance a remote computing device  210  ( FIG. 2B ). Users not located at the rig site can download and review the data, for example by logging into the computing device  210 , and accessing the drilling data via the communications network  240 , such as the internet. In step  112 , the software application determines whether any of the drilling parameters input into software application have changed. If the drilling parameters have changed, the software application updates the drilling data accordingly. Further, if the drilling parameters have not changed, in block  114 , an optional lost performance analysis can be run, for instance similar to the lost performance analysis disclosed in U.S. Pat. No. 8,453,764, herein incorporated by reference. Process control can be transferred and the method  701  shown in  FIG. 5  can be initiated, as will be further detailed below. 
     Turning to  FIG. 3B , which illustrates a method  70  for predicting vibration information for a drilling system. It should be appreciated that aspect of the method  70  can be performed prior to or along with steps  100  through  102  discussed above.  FIG. 3B  illustrates how a drilling system model can be developed and used in a drilling operation. Accordingly, each and every step of method  70  need not be performed at the rig site or during a drilling operation, but could occur before a drilling operation. 
     Continuing with  FIG. 3B , the method  70  initiates in step  260 , by defining a drilling system model using finite element techniques, as further detailed below. In step  260 , the method can included accessing drilling system component data. The drilling system component data includes one or more characteristics of the drill string typically used in finite element models. The one or more characteristics of the drill string include drill string geometry data. Drill string geometry data includes the outside and inside diameters of the drill pipe sections that make up the drill string, the locations of stabilizers, the length of the drill string, the inclination of the drill string, the bend angle if a bent sub is used, the diameter of the drill bit and stabilizers. Drill string geometry data also includes the material properties of drill string components, specifically the modulus of elasticity, material density, torsional modulus of elasticity, and Poisson&#39;s ratio, as well as a vibration damping coefficient, based on the properties of the drilling mud properties, specifically, the mud weight and viscosity. In step  262 , the software application can access borehole information. Borehole information can include borehole diameters along the length of the borehole, the azimuth, build rate, turn rate, information concerning the characteristics of the formation, such as the strike and dip. 
     Continuing with  FIG. 3B , in steps  266  to  272 , the components of the drill system model is further processed using finite element system, for instance ANSYS and/or LISA. In steps  274  to  280 , the static bending analysis and the so-called predict analysis are performed. In step  282 , based on the bending information determined in steps  274 - 280 , the software application determines if the forces are balanced at the drill bit. In step  282 , the software application can determine whether the side forces on the bit are equal to zero. For instance, if the forces are not balanced on the bit, then the model is indicating contact with the borehole wall (in the model). If the forces are not balanced, then process control is transferred to step  284  and the curvature of the borehole is modified, and steps  272  to  282  are re-run until a balance is obtained in step  282 . 
     In steps  286  to  294 , the software application predicts vibration information for the drill string. In step  286 , the software application initiates a vibration analysis operation. For instance, the software application initiates the vibration modal analysis. The predicted vibration information includes an amplitude for the axial vibration, the lateral vibration, and the torsional vibration of the drill string. Further, frequency and the mode shape for axial, lateral and torsional vibration are developed. The prediction of the vibration information is based on the drilling system component information and an energy balance of the drill string operating according to the expected operation information, as will be further detailed below. 
     In step  288 , the software application can first determine the drilling excitation forces of the model drilling string components. In step  289 , the software application applies the determined drilling excitation forces to the model. For instance, the software application can apply known excitation loads to the drill string based on the expected operating loads and frequency of the drill string. 
     In step  290 , the software application applies an energy balance methodology to determine vibration information along the drill string, in particular determines the amplitude of axial, lateral and torsional vibration along the drill string. Using the energy balance methodology, the predicted vibration information is based on analysis of energy supplied to the drilling operation, considering the energy dissipated during the drilling operation due to vibration of the drilling system components, as function of one or more forces applied to the drill string. The energy supplied ES (J) to a drilling system can be calculated from the equation: 
         E   S   =q ·π·Cos β·∫ y ( x )· dx,   (1)
 
     where, 
     q is the distributed force (N) along the drill string, 
     β is the phase angle (rad), and 
     y(x) is the displacement (mm) along the length of the drill string. 
     The energy dissipated ED (J) from the drilling system, due to damping, etc., can be calculated from the equation: 
         ED=π·k·b·Y   2 , where,  (2)
 
     K is the spring rate, 
     b is damping coefficient (N s/m), and 
     Y is displacement (mm) 
     The energy supplied ES and energy dissipated ED graphically represented as a displacement, or amplitude, as a function of input load is illustrated in  FIG. 7 . Assuming the energy supplied is equal to the energy dissipated, the software application can predict the amplitude (or displacement in the equations) of vibration at a given input load. Based on assumption that the energy is balanced, the software application uses the follow equation to predict amplitude of axial vibration: 
         Ym =( F   o   ·π·S   z )/(δ· w   2 )· H   na , where  (3)
 
     Ym is the maximum amplitude, or displacement (mm), for axial vibration, 
     Fo is total force (N), 
     Sz is an amplification factor defined is an indication of the proximity of an expected frequency to the natural frequency for a structure, such as drill string component, 
     δ is displacement (mm), 
     W is the angular velocity (rads/s), and 
     Hna is the relative mode shape efficiency factor for axial vibration. 
     As can be seen from the above equations, the software application predicts vibration information based upon information indicating the relative mode shape efficiency (Hn) for axial, lateral and torsional vibration along the drill string. The mode shape efficiency is a measure of how much energy from the applied load goes into vibration. For example, the mode efficiency is highest for the first mode of a cantilevered beam with the load applied at the free end of the beam because the vibration is a maximum. Applying the load to the fixed end of the beam results in a mode efficiency factor of 0 since there is not any displacement at this location. 
     In step  290 , the software application can also predict the amplitude of vibration taking into account bit whirling. Using the energy balance methodology discussed above, the software application uses the follow equation to predict amplitude for lateral vibration: 
         Yo =( Y   b   ·π·S   z )/(δ· w   2 )· H   nl , where  (4)
 
     Y o  is the maximum amplitude, or displacement (mm), for lateral vibration, 
     Y b  is displacement (mm), 
     S z  is the amplification factor as noted above, δ is displacement (mm), 
     W is the angular velocity (rad/s), and 
     H nl  is the relative mode shape efficiency factor for lateral vibration, as noted above. 
     In step  290 , the software application can also predict the amplitude of vibration taking into account bit moment. Using the energy balance methodology discussed above, the software application uses the follow equation to predict amplitude for torsional vibration: 
       θ m =( M   b   ·π·S   z )/(δ· w   2 )· Hnt , where  (5)
 
     θm is the maximum angular displacement (rad/s) for torsional vibration 
     M b  is the bending moment (N-m), 
     S z  is an amplification factor as noted above, 
     δ is displacement (mm) 
     W is the angular velocity (rad/s), 
     Hn is the relative mode shape efficiency factor for lateral vibration as noted above, 
     When, in step  290 , the energy balance method has predicted the amplitude of vibration of axial, lateral and torsional vibration, in step  292 , the software application can output the amplitude of vibration for a range of drill bit rotational speeds. Process control can be transferred to step  294 . In step  294 , the software application can determine the critical speeds of the drill string. The step of determining the critical speeds includes determining the critical speeds as a function of the loads applied on the drill string. It should be appreciated that the software application can associate the predicted vibration information with a range of critical speeds, a range of WOB, rotary speeds, flow rates and torque values for the drilling operation. 
     According to another embodiment of the present disclosure, the software application is configured to update the drilling system model as needed. The software application develops a drilling system model by first defining the drill string and the borehole parameters that are not subject to change during drilling operation. The drill string and borehole parameter are stored in a computer memory of the computing device  200 . As the drilling operation continues and certain drilling conditions change, the drill string and borehole parameters are modified and the analysis is re-run. For instance, the drilling parameters that change during drilling include drill bit rotational speed, WOB, inclination, depth, azimuth, mud weight, and borehole diameter. The software application, accesses and/or receive updating operation information based on real-time values of the drilling operating parameters based on the measurements of the surface and downhole sensors. For instance, the software application can access updated operating information stored in the memory portion of the computing device, and/or data acquisition system. Updated operating information can may be automatically measured and stored in memory, or alternatively, updated operating information may be obtain via separate systems and the data manually input in the computing device via the user interface, said data stored for access. Based on the updated operating parameters, the software application calculates the critical speeds for a range of operating conditions. The software application can also create a mode shape for the measured and predicted vibration information for each of an axial, lateral and torsional vibration. As shown in  FIG. 4 , the software application can cause the user interface to display the mode shapes at any given combination of RPM and WOB. In addition, the software application can cause the user interface to display the critical spends on a critical speed map. As shown in  FIG. 5 , the software application causes the display of drill bit rotational speed (RPM) on the x-axis and WOB on the y-axis. 
     Turning to  FIG. 4 , in accordance with another embodiment of the present disclosure, as indicated in connection with step  102  (method  70 ), the software application performs a vibration analysis in which it predicts (i) the natural frequencies of the drill string in axial, lateral and torsional modes and (ii) the critical speeds of the drill string, mud motor (if any), and critical speeds of the drill bit that excite these frequencies, as previously discussed. The software application can adjust the drilling system model if the actual critical speeds are have shifted from the predicted critical speeds such that drilling system model can correctly predict the critical speeds experienced by the drill string. As can be seen in  FIG. 4 , the software application can perform a method  300  that can adjust the drilling system model if the predicted critical speed at a drill bit rotational speed (RPM) during actual operation reveals the predicted critical speed does not result in resonant vibration. If a critical speed is encountered at drill bit rotation speed at which the drilling system model does not predict resonant vibration, then the drilling system model can be adjusted as well. It should be appreciated that the adjustment of critical speeds based an analysis of predicted vs. actual critical speeds can be completed after a successful elimination of high vibration that caused a loss of drilling performance, as discussed in above in connection with step  114 . 
     Continuing with  FIG. 4 , the software application first determines in step  330  whether a predicted critical speed differs from a measured critical speed by more than a predetermined amount. If it does, in step  332 , the software application determines whether the vibratory mode associated with the critical speed was related to the axial, lateral or torsional vibratory mode. If the critical speed was associated with the torsional or axial modes, then in step  334  the software application determines if the RPM at which the mud motor is thought to be operating, without encountering the predicted resonant vibration, is on the lower end of the predicted critical speed band. If it is, then in step  336  the motor RPM used by the model is decreased until the critical speed is no longer predicted. This accounts the motor having a different revolutions per gallon (RPG) than stated on the specification documentation for motor. Motor specification normally list the RPG at room temperature no load conditions. If it determines that the motor RPM is on the upper end of the predicted critical speed band, then in step  338  the motor RPM is increased until the critical speed is no longer predicted. If the mud motor is not being used, then in step  340  the software application determines whether the predicted critical speed is higher or lower than the speed at which the drill bit is operating. If it is higher, then in step  342  the drill string stiffness is decreased until the critical speed is no longer predicted. If it is lower, then in step  344 , the drill string stiffness is increased until the critical speed is no longer predicted. 
     If the critical speed was associated with the lateral vibratory mode, then in step  346  the software application determines if the lateral vibration is due to drill bit, mud motor, or drill string lateral vibration. If the lateral vibratory mode is associated with the drill string, then in step  348  the software application determines whether the RPM at which the drill string is thought to be operating, without encountering resonance, is on the lower or higher end of the predicted critical speed band. If it is on the high end, then in step  350  the drill string speed used in the model is reduced or, if that is unsuccessful, a stabilizer OD is increased. If it is on the low end, then in step  352  borehole size used in the model is increased or, if that is unsuccessful, the OD of a stabilizer is decreased. 
     If the lateral vibratory mode is associated with the mud motor, then in step  354  the software application determines whether the RPM at which the mud motor is thought to be operating, without encountering resonant vibration, is on the lower or higher end of the predicted critical speed band. If it is on the high end, then in step  356  the mud motor speed used in the model is increased until the critical speed is no longer predicted. If it is on the low end, then in step  358  the mud motor speed used in the model is decreased until the critical speed is no longer predicted. If the lateral vibratory mode is associated with the drill bit, then in step  360  the software application determines whether the RPM at which the drill is thought to be operating is on the lower or higher end of the critical speed band. If it is on the high end, then in step  362  the drill bit speed is decreased until the critical speed is no longer predicted. If it is on the low end, then in step  364  the drill bit speed is increased until the critical speed is no longer predicted. 
     As noted above, the software application can predict vibration for a future drilling run, based on real-time information obtained during a current drill run. For instance, the software application can predict vibration information based on the current measured operating or real-time parameters. The software application can predict vibration, using the methodology discussed above, at each element along the drill string based on the real time values of: (i) WOB, (ii) drill bit RPM, (iii) mud motor RPM, (iv) diameter of borehole, (v) inclination, (vi) azimuth, (vii) build rate, and (viii) turn rate. For purposes of predicting vibration, WOB is preferably determined from surface measurements using the top drive sub  45 , as previously discussed, although downhole strain gauges could also be used as previously discussed. Drill bit RPM is preferably determined by summing the drill string RPM and the mud motor RPM. The drill string RPM is preferably based on a surface measurement using the RPM sensor  32 . The mud motor RPM is preferably based on the mud flow rate using a curve of mud motor flow rate versus motor RPM or an RPM/flow rate factor, as previously discussed. The diameter of the borehole is preferably determined from the backward whirl frequency using method described in U.S. Pat. No. 8,453,764 discussed above, although an assumed value could also be used, as also previously discussed. Inclination and azimuth are preferably determined from accelerometers  44  and magnetometers  42  in the bottomhole assembly  6 , as previously discussed. Build rate is preferably determined based on the change in inclination. Turn rate is determined from the change in azimuth. Preferably, the information on WOB, drill string RPM and mud motor RPM is automatically sent to the processor  202 . Information on inclination and azimuth, as well as data from the lateral vibration accelerometers (the backward whirl frequency if the Fourier analysis is performed downhole), are transmitted to the processor  202  by the mud pulse telemetry system or a wired pipe or other transmission system at regular intervals or when requested by the applications or when triggered by an event. Based on the foregoing, the software application calculates the frequency of the vibration at each point along the drill string (the amplitude having been determined previously), during the drilling operation. The software application, as noted above, can cause the user interface to display an image of the mode shape, as shown in  FIG. 5 , for the current operating condition, the vibratory mode shape of the drill string, which is essentially the relative amplitude of vibration along the drill string. 
     According to the present disclosure, three oscillating excitation forces are used to predict vibration levels: (i) an oscillating excitation force the value of which is the measured WOB and the frequency of which is equal to the speed of the drill bit multiplied by the number of blades/cones on the bit (this force is applied at the centerline of the bit and excites axial vibration), (ii) an oscillating force the value of which is the measured WOB and frequency of which is equal to the number of vanes (or blades) on drill bit times the drill bit speed (this force is applied at the outer diameter of the bit and creates a bending moment that excites lateral vibration), and (iii) an oscillating force the value of which is the calculated imbalance force based on the characteristics of the mud motor, as previously discussed, and the frequency of which is the frequency of which is equal to N (n+1), where N is the rotary speed of the rotor and n is the number of lobes on the rotor. 
     Vibration amplitude, or displacement in the above reference equations, is measured at the locations of vibration sensors, such as accelerometers. However, of importance to the operator is the vibration at the location of critical drill string components, such as an MWD tool. In step  104 , the software application determines the ratio between the amplitude of vibration at a nearby sensor location and the amplitude of vibration at the critical component for each mode of vibration. The analysis in step  104  is based on predicted vibration mode shape and the known location of such critical drill string components as inputted in the model. Based on the inputted vibration limit for the component, the software application determines the vibration at the sensor that will result in the vibration at the component reaching its limit. The software application can cause the computing device to initiate a high vibration alarm if the vibration at the sensor reaches the correlated limit. For example, if the maximum vibration to which an MWD tool should be subjected is 5 g and the mode shape analysis indicates that, for lateral vibration, the ratio between the vibration amplitude at sensor #1 and the MWD tool is 1.5—that is, the amplitude of the vibration at the MWD tool is 1.5 times the amplitude at sensor #1, the software would advise the operator of the existence of high vibration at the MWD tool if the measured lateral vibration at sensor #1 exceeded 1.33 g. This extrapolation could be performed at a number of locations representing a number of critical drill string components, each with its own vibration limit. In addition to predicting vibration along the length of the drill at current operating conditions in order to extrapolate measured vibration amplitudes to other locations along the drill string, the software application can also predict vibration along the length of the drill string based on projected operating conditions. The software application can then determine whether a change in operating parameters, such as RPM or WOB, will affect vibration. 
     The software application can cause the user interface to display in a computer display a critical speed map as shown in  FIG. 5  and further discussed below. As noted above, the critical speed may displays information indicating the combinations of WOB and drill string rotation speed should be avoided to avoid high axial or lateral vibration or stick slip. The software application can cause the user interface to display a critical speed map including information that indicates the combinations of WOB and mud motor rotation speed that should be avoided. The critical speed maps can be used as a guide for setting drilling parameters. 
     Turning to  FIG. 5 , in accordance with another embodiment of the present disclosure, the software application can determine that the difference between the predicted and measured vibration for any of the axial, lateral or torsional vibrations at sensor locations exceeds a predetermined threshold. In response, the software application revises the drilling system model by varying the operating parameter inputs used in the drilling system model, according to a predetermined hierarchy, until the difference is reduced below the predetermined threshold. Such an exemplary hierarchy is illustrated in the method  701  shown in  FIG. 5 . When the software application receives drilling data from the downhole sensors, the software application compares the measured level of vibration at the sensor locations to the predicted level of vibration at the same locations. Based on the analysis performed by the software application noted above, the drilling data system  12 , computing device  200 , and/or the database  230  can include store therein: (i) the measured axial, lateral and torsional vibration at the locations of the sensors downhole, (ii) the resonant frequencies for the axial, lateral and torsional vibration predicted by the software application, (iii) the mode shapes for the axial, lateral and torsional vibration based on real-time operating parameters predicted by the software application, and (iv) the levels of axial, lateral and torsional vibration at each point along the entire length of the drill string predicted by the software application. This information is used to determine how predicted and measured vibration information agrees. 
     Continuing with  FIG. 5 , a method  701  is used in which the hierarchy in parameters for which changes are attempted is preferably mud motor rotational speed, followed by WOB, followed by borehole size. In step  700 , a determination is made whether the deviation between the measured and predicted vibration exceeds the predetermined threshold amount. If so, in steps  702  through  712 , incremental increases and decreases in the mud motor rotational speed used in the drilling system model, within a prescribed permissible range of variation, are attempted until the deviation drops below the threshold amount. If no value of the mud motor rotational speed within the permissible range of variation results in the deviation in the vibration at issue dropping below the threshold amount, the software application revises the mud motor rotational speed used in the drilling system model to the value that reduced the deviation the most, but that did not cause the deviation between the predicted and measured values for another vibration to exceed the threshold amount. 
     If variation in mud motor rotational speed does not reduce the deviation below the threshold amount, in steps  714 - 724 , the WOB used in the drilling system model is then decreased and increased, within a prescribed permissible range of variation, until the deviation drops below the threshold amount. If no value of WOB within the permissible range of variation results in the deviation between the measured and predicted vibration dropping below the threshold amount, the software application revises the WOB used in the model to the value that reduced the deviation the most, but that did not cause the deviation between the predicted and measured values for another vibration to exceed the threshold amount. 
     If variation in WOB does not reduce the deviation below the threshold amount, in steps  726 - 736 , the assumed borehole size used in the model is then decreased and increased within a prescribed permissible range of variation—which range may take into account whether severe washout conditions were expected, in which case the diameter could be double the predicted size—until deviation drops below the threshold amount. If a value of borehole size results in the deviation dropping below the threshold amount, without causing the deviation in another vibration to exceed the threshold amount, then the model is revised to reflect the new borehole size value. If no value of borehole size within the permissible range of variation results in the deviation between the measured and predicted vibration dropping below the threshold amount, the software revises the borehole size used in the model to the value that reduced the deviation the most, but that did not cause the deviation in another vibration level to exceed the threshold amount. Alternatively, rather than using the sequential single variable approach discussed above, the software application could be programmed to perform multi-variable minimization using, for example, a Taguichi method. Further, if none of the variations in mud motor RPM, WOB and borehole diameter, separately or in combination, reduces the deviation below the threshold, further investigation would be required to determine whether one or more of the inputs were invalid, or whether there was a problem down hole, such as a worn bit, junk (such as bit inserts) in the hole, or a chunked out motor (rubber breaking down). 
     It should be appreciated that other hierarchies can be used to revise the drilling system model. For instance, if the step of comparing the predicted versus measured vibration is performed by the software application following a successful mitigation of high vibration (for instance step  114  in  FIG. 3A ) as described in U.S. Pat. No. 8,453,764, which is incorporated by reference herein, the results of the mitigation are used to guide the revision of the drilling system model used to predict the vibration. As will be appreciated by one skill in the art, the method of mitigating lost performance due to high vibration cannot be employed if the attempted mitigation was unsuccessful or if mitigation was unnecessary. 
     Referring now to  FIG. 6 , according to yet another embodiment of the present disclosure, the software application automatically determines if the optimum drilling performance is being achieved and makes recommendations if optimum drilling performance is not being achieved. In general, the higher the drill bit RPM and the greater the WOB, the higher the rate of penetration by the drill bit into the formation, resulting in more rapid drilling. However, increasing drill bit RPM and WOB can increase vibration, which can reduce the useful life of the bottomhole assembly components. A method  901  for optimizing drilling efficiency includes the initial step  900  of performing one or more drilling tests are performed so as to obtain a database of ROP versus WOB and drill string and drill bit RPM. In addition, in step  900 , the drilling test can be begin with a pre-run analysis of the drilling operation using the software application. The pre-run analysis can be used to design a bottomhole assembly that will drill the planned well, have sufficient strength for the planned well and to predict critical speeds to avoid during the drilling operation. During the pre-analysis process components of the drill string can be moved or altered to achieve the desired performance. Modifications may include adding, subtracting or moving stabilizers, selecting bits based on vibration excitation and performance and specifying mud motors power sections, bend position and bend angle. Based on the analysis the initial drilling component information and drilling operation parameters are set. 
     In step  902 , the software application can determine a set of drilling parameters that can optimize ROP without producing excessive vibration, based in part on the drilling performance results and predicted vibration levels conducted during the drilling tests. Alternatively, the software application can generate graphical display illustrating predicted axial vibration versus WOB and the measured rate of penetration versus WOB. Using these graphical displays, the operator can select the WOB that will result in the maximum rate of penetration without incurring excessive axial vibration. Similar graphs would be generated for other modes of vibration. In addition, during step  902 , the software application determines the critical speeds of the drill string and then determines whether operation at the WOB and drill string/drill bit rotation speeds that yielded the highest ROP based on the drilling test data will result in operation at a critical speed. Alternatively, the software application can predict the level of vibration at the critical components in the drill string at the WOB and drill string/drill bit RPMs that yielded the highest ROP to determine whether operation at such conditions will result in excessive vibration of the critical components. In any event, if the software application predicts vibration problems at the operating conditions that resulted in the highest ROP, it will then check for high vibration at the other operating conditions for which data was obtained in the drilling tests until it determines the operating conditions that will result in the highest ROP without encountering high vibration. The software application will then recommend to the operator that the drill string be operated at the WOB and drill string/drill bit rotation speeds that are expected to yield the highest ROP without encountering excessive vibration. The drilling operation will continue at the determined set of drilling parameters that optimized ROP. 
     In step  904 , the drilling operation will continue at the set operating at the parameters recommended by the software application. The drilling operation would continue until there was a change to the drilling conditions. Changes may include bit wear, different formation type, changes in inclination, azimuth, depth, vibration increase, etc. In step  906 , the software application will periodically access drilling data from the downhole and surface sensors, as discussed above. 
     In step  908 , the software application will determine whether the measured and predicted vibration information agree. If the software application determines in step  908  that the measured and predicted vibration information do not agree, or match, process control is transferred to step  910  and the drilling system model will be revised. If software application determine in step  908  that the measured and predicted vibration information agree, process control is transferred to step  912 . Thus, the optimization of drilling parameters will be performed using an updated drilling system model that predicts vibration based on real-time data from the sensors downhole. 
     In step  912 , the software application determines whether, based on drilling data from the sensors downhole, the vibration in the drill string is high, for example, by determining whether the drill string operation is approaching a new critical speed or whether the vibration at a critical component exceeds the maximum for such component. If the software application determine that vibration is high, then process control is transferred to step  902 , and the steps  902  to  910  are repeated and the software application determines another set of operating parameters that will result in the highest expected ROP without encountering excessive vibration. If, in step  912 , the software application determines that vibration data is low, process control is transferred to block  914 . 
     Based on data from the ROP sensor  34 , in step  914 , the software application determines whether the ROP has deviated from that expected based on the drilling test. If it has, the software application may recommend that further drilling tests be performed to create a new data base of ROP versus WOB and drill string/drill bit RPM. 
     For purposes of illustration the optimization method  901  discussed above, assume a drilling test produced the following ROP data (for simplicity, assume no mud motor so that the drill bit RPM is the same as the drill string RPM): 
     
       
         
           
               
               
               
             
               
                 TABLE I 
               
               
                   
               
               
                 WOB, lbs 
                 200 RPM 
                 300 RPM 
               
               
                   
               
             
            
               
                 10k 
                 10 fpm 
                 20 fpm 
               
               
                 20k 
                 15 fpm 
                 25 fpm 
               
               
                 30k 
                 20 fpm 
                 30 fpm 
               
               
                 40k 
                 25 fpm 
                 33 fpm 
               
               
                   
               
            
           
         
       
     
     The software application can predict if operating the drill string at 40 k WOB and 300 RPM (the highest ROP point in the test data) will result in the drilling system operating at a critical speed or in excessive vibration at a critical component. If the process determines that operating the drill string at 40 k WOB and 300 RPM (the highest ROP point in the test data) does not result in a critical speed or excessive vibration, the software application can cause the computer system to display to the user a recommendation to operate at 40 k WOB and 300 RPM. Thereafter, each time a new set drilling data is obtained (or a new section of drill pipe added), the software application will (i) revise the drilling system model if the predicted vibration at the respective location of the sensors does not agree with the measured vibration, and (ii) determine whether the vibration is excessive. The software application can determine if the vibration is excessive using the revised drilling system model to determine the vibration at the critical components by extrapolating the measured vibration. 
     If, at some point, the process determines that vibration of the drill string has become excessive, the process predicts that the vibration at 30 k WOB and 300 RPM (the second highest ROP point from the drilling test data) and recommends that the operator go to those operating conditions unless it predicted excessive vibration at those conditions. Thereafter, each time another set of drilling data was obtained (and the model potentially revised), the software application will predict whether it was safe to again return to the initial operating conditions associated with the highest ROP (40 k WOB/300 RPM) without encountering excessive vibration. If the software never predicts that it is safe to go back to the initial operating conditions but, at some point, it determines that the vibration has again become excessive, it will predict vibration at the two sets of parameters that resulted in the third highest ROP—20 k WOB/300 RPM and 40 k WOB/200 RPM—and recommend whichever one resulted in the lower predicted vibration. 
     In some embodiments, instead of merely recommending changes that the operator makes to the operating parameters, the method automatically adjusts the operating parameters so as to automatically operate at the conditions that resulted in maximum drilling performance. 
     According to another embodiment of the present disclosure, rather than using ROP as the basis for optimization, the software can use the Mechanical Specific Energy (“MSE”) to predict the effectiveness of the drilling, rather than the ROP. The MSE can be calculated, for example, as described in F. Dupriest &amp; W. Koederitz, “Maximizing Drill Rates With Real-Time Surveillance of Mechanical Specific Energy,” SPE/IADC Drilling Conference, SPE/IADC 92194 (2005) and W. Koederitz &amp; J. Weis, “A Real-Time Implementation Of MSE,” American Association of Drilling Engineers, AADE-05-NTCE-66 (2005), each of which is hereby incorporated by reference in its entirety. For purposes of calculating MSE, the software obtains the value of ROP from one or more drilling tests, as described above, as well as the torque measured during each drilling test. Based on these calculations, the process can generate a recommendation to the user/operator that the drill bit rotation speed and WOB to revise values that yielded the highest MSE value. 
     Although the invention has been described with reference to specific methodologies for monitoring vibration in a drill string, the invention is applicable to the monitoring of vibration using other methodologies based on the teachings herein. For example, although the invention has been illustrated using mud motor rotary drilling it can also be applied to pure rotary drilling, steerable systems, rotary steerable systems, high pressure jet drilling, and self propelled drilling systems, as well as drills driven by electric motors and air motors. Accordingly, the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof and, accordingly, reference should be made to the appended claims, rather than to the foregoing specification, as indicating the scope of the invention.